It’s about how one of the most abstract theories in economics is secretly the exact same thing as the most boring asset on Wall Street.

Same idea, entirely different worlds.

The Atomic Bet

Think about what a financial security actually is. At its core, whether it’s a stock or a bond, it’s just a claim on future cash flows. You own a “promise” that under certain circumstances, you get money.

But the future is uncertain. The world could go into a recession, it could boom, or it could just stay flat. In economics, we call these scenarios “states of the world.” Let’s represent a specific state with a simple letter:

Now, here is the key question: What if you could buy a weird, hyper-specific security that pays you exactly $1 if and only if the world ends up in a specific state s (like the “down” state) and pays nothing otherwise?

Why would you even want that?

Well, if you own a normal portfolio of stocks, the “down” state is the one that hurts you. If you hold this weird $1 security, you get cash exactly when you need it most. It’s perfect customized insurance.

Back in 1954, two economists: Kenneth Arrow and Gérard Debreu, theorized this exact thing. They called it a State Price Security (now known as an Arrow-Debreu security). One security, one state. It pays $1 in that specific reality, and $0 everywhere else.

Because you have to buy this security today, it has a price. Let’s call the price of an Arrow-Debreu security for state s :

Here is the core insight that won them Nobel prizes: If you had an Arrow-Debreu security for every possible state of the world, you could build literally any financial product in existence.

Think about it. A stock is just an asset that pays out different amounts of cash depending on what state the world is in. Let’s call the cash payout of a stock in state s:

If you know the price of the state (q) and you know the payout of the stock in that state (s​), pricing any complex asset is just basic multiplication and addition. You just multiply the state prices by the payouts and add them all up.

In math terms, the price of any financial asset (P) is simply:

It’s that simple. Any complex stock is just a bundle of these atomic pieces.

Does this remind you of anything? Leave it in the comments!

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Now, How much should q actually cost? Your first instinct is probably just probability. If there is a 10% chance of a crash, the security should cost 10 cents, right?

Not quite.

Think about the “down” state versus the “up” state. Even if they have the exact same probability of happening, people desperately need money more during a crash. Money in bad times is fundamentally worth more than money in good times.

So q is not just probability. It’s actually a cocktail of three distinct things: the raw probability of the state happening, the basic time value of money (because you have to wait for the payout), and risk aversion—how much people value a dollar in that specific scenario.

And that brings us to a really fun realization1. What happens if you try to buy a $1 payout for every single possible state?

The Boring Reality

Let’s say you actually do it. You walk up to our Arrow-Debreu vending machine and press every single button. You buy one state price security for literally every parallel universe that could possibly exist2.

Mathematically, you are just summing up the prices of all states. Let's call the price of this specific "buy-every-universe" portfolio

Think about what you’ve just built.

• If the market booms... you get $1.

• If the market stays flat... you get $1.

• If the market crashes... you get $1.

Because you own a ticket for every possible reality, it doesn’t matter what the future holds. Uncertainty has been completely eliminated. You are 100% guaranteed to receive exactly $1.

Now, let’s leave the theoretical chalkboard and walk onto a Wall Street trading floor.

If you ask a trader (or any quant out there) for the safest, most basic, unsexy financial instrument in existence, an asset that guarantees you exactly $1 in the future with zero risk, what do they hand you?

A Zero Coupon Bond (like a US Treasury Bill)!

There are no dividends. There are no complicated payouts based on market conditions. You just buy the bond for a slight discount today, and on a specific date in the future, the government hands you exactly $1.

Because it’s risk-free, its price today is just $1 discounted by the risk-free interest rate. Let’s call that rate r. The price of this bond3 is:

The Crossroad

This is where the two worlds touch each other.

If buying every single Arrow-Debreu state guarantees you $1, and a Zero Coupon Bond guarantees you $1, then financially speaking, they are equivalent. They must command the exact same price today.

We can write this as one, unified equation:

where we have used (as above) that the payoff (c) of a ZC is always $1.

Just look at the irony in that equality.

On the left side, you have two Nobel laureates wrestling with the fundamental nature of risk, trying to conquer the infinite unknown by carving reality into atomic states.

On the right side, you have the most boring asset ever.

One is a profound attempt to map every possible timeline. The other is what you buy when you don’t want to think about the future at all.

But at the crossroad, they are the exact same trade. It turns out that perfectly pricing the multiverse is just another way of playing it completely safe.

There is a catch: the channel is entirely in Spanish. But if you can speak the language, or are willing to rely on auto-generated subtitles, the content is absolutely outstanding.

What makes it special is the rare combination of disciplines Isaac brings to the screen. He is an engineer by training, but he also possesses a vast, almost encyclopedic knowledge of history. While most history content tells you what happened and engineering content tells you how things work, Isaac gives you both at once: the conquest alongside the construction technique, the politics alongside the gradients. The result is genuinely delightful to follow.

Most of his videos focus on Roman infrastructure, specifically the calzadas (roads) that stitched the empire together. He explains how they were surveyed, how they were built, and why they’ve outlasted nearly everything around them. But he also covers Roman cities, aqueducts, bridges, and monuments scattered across Spain and the wider Roman world. He doesn’t just tell you a bridge is impressive; he explains, as an engineer, exactly why it is still standing two thousand years later.

He is also a formidable myth-buster. Across Spain, old bridges and roads are routinely labeled “Roman” out of habit or local pride. Armed with engineering logic and historical evidence, Isaac demystifies these structures, showing which ones are genuinely Roman and which are medieval or modern reconstructions that have simply been wearing the Roman label for centuries. Watching him dismantle a beloved local myth, stone by stone, is half the fun.

I’ve learned an immense amount from his videos. As a small token of gratitude for his work, I built a little hobby project: an interactive map.

👉 Explore the Isaac Moreno Gallo Video Map

The map geolocates his videos, placing every road, city, aqueduct, and historical site where it actually belongs. Each thumbnail sits on the exact spot the video covers; clicking it takes you straight to the original on YouTube.

Under the hood, it’s a simple project: I pulled the channel’s videos, used a small AI model to identify the location of each topic, and plotted them on an open-source map. The best part is how it changes how you consume his work: instead of scrolling through an endless list of titles, you can wander through his catalog geographically. You can zoom into a corner of Hispania and watch the Roman world light up.

A few quick, honest notes:

• This is an unofficial, non-commercial fan project.

• All rights to the videos belong entirely to Isaac; the map simply links back to YouTube and hosts no content itself.

• Because locations were assigned automatically from the video titles, a few might be slightly off (corrections are very welcome!).

If you’ve never seen his channel, you can start directly on his YouTube page: @IsaacMorenoGallo. And if you’d like to explore his work geographically, the map is ready for you.

Gracias, Isaac.

The objective of this post is to guide you through this process. We will use Qwen2-VL as our reference. At the end of this post, you will be able to look at the following image and actually understand what is going on. At least until the QwenLM Decoder part.

Let’s start…

An image is worth 100 patches

To understand modern AI vision, we have to start with a breakthrough 2020 paper by Dosovitskiy et al., which introduced the concept of the Vision Transformer (ViT).

Before this, models looked at images pixel by pixel or through complex convolutional filters. ViT introduced a much simpler, highly effective standard: split the image into tiny, fixed-size patches, and treat every small patch as its own “token.” Just like a language model reads a sentence word by word, a Vision Transformer reads an image patch by patch.

Great, so now we have our image chopped up into tiny patches ready to be transformed into tokens. But, some practical questions arise. Do we standardize all images to the same size, or adapt to their original proportions? Once we decide that, how many patches do we actually need? Furthermore, how do we ensure the model knows which patches are next to each other? Then, how do we translate these raw visual patches into a feature space that captures their actual meaning? And finally, what is the connection with text tokens, if any?

Let’s attack them one by one.

Do we standardize all images to the same size, or adapt to their original proportions?

To answer this, let’s look at what the authors of say:

Unlike Qwen-VL, Qwen2-VL can now process images of any resolution, dynamically converting them into a variable number of visual tokens.

But what does that actually mean?

In the past, vision models forced every image into a rigid, standard square (like 224x224 pixels). If you uploaded a wide landscape or a long, vertical infographic, the model would squish or crop it, losing valuable details in the process.

To fix this, Qwen2-VL uses an approach inspired by the Patch n’ Pack paper. Instead of forcing the image to fit a predetermined box, the model adapts to the image. It takes the original width and height, maintains the aspect ratio, and just rescales it slightly so that the new dimensions are perfectly divisible by the chosen patch size in both rows and columns.

Check the code below from Qwen2’s github, it’s telling you how to resize the image for further processing.

def smart_resize(
    height: int, width: int, factor: int = 28, min_pixels: int = 56 * 56, max_pixels: int = 14 * 14 * 4 * 1280
):
    """Rescales the image so that the following conditions are met:

    1. Both dimensions (height and width) are divisible by 'factor'.

    2. The total number of pixels is within the range ['min_pixels', 'max_pixels'].

    3. The aspect ratio of the image is maintained as closely as possible.

    """
    if max(height, width) / min(height, width) > 200:
        raise ValueError(
            f"absolute aspect ratio must be smaller than 200, got {max(height, width) / min(height, width)}"
        ) Now, 
    h_bar = round(height / factor) * factor
    w_bar = round(width / factor) * factor
    if h_bar * w_bar > max_pixels:
        beta = math.sqrt((height * width) / max_pixels)
        h_bar = max(factor, math.floor(height / beta / factor) * factor)
        w_bar = max(factor, math.floor(width / beta / factor) * factor)
    elif h_bar * w_bar < min_pixels:
        beta = math.sqrt(min_pixels / (height * width))
        h_bar = math.ceil(height * beta / factor) * factor
        w_bar = math.ceil(width * beta / factor) * factor
    return h_bar, w_bar

How many patches do we actually need?

Once we have read the previous answer, this one becomes easy!

We have done a slight rescaling (see the code) so that:

but the new h and w are perfectly divisible by a “factor” 28. Now, let’s assume our model uses a standard patch size, for example, 14 (this means that each patch will be 14x14 pixels).

To find out how many patches make up your image, you just do a little division:

• Patches per Row: Image Width ÷ Patch Size

• Patches per Column: Image Height ÷ Patch Size

Then, to get the total number of patches, you just multiply them together: (Patches per Row) × (Patches per Column).

Let’s run an example. Imagine i give you an image of h=244 and w=244 . Could you tell me in advance how many patches would this image be split into?

You can read the asnwer in the paper itself!

Do you want to understand it visually? I have created the following interactive page to test it. Feel free to check it out with your own images.

How do we translate these visual patches into a feature space?

Recall1 that our goal following ViT paper was to split the image into patches and then feed it to the “Transformer Encoder” in the paper’s notation (I’ll prefer to call it just Visual Encoder).

If the Visual Encoder is well-trained, its job is to look at the raw pixels of a single patch and return a dense mathematical vector. This vector should capture actual meaning of the patch, the colors, the edges, the textures, and the visual information contained inside that specific little square.

But before this, just a small step to add for the sake of detail. Once we have the patches, we need to be able to trasnform them into some kind of vector that the Visual Encoder can process. What Qwen2-VL does it to run them through a convolution (specifically a 3D convolution, which cleverly allows it to process video frames as well).

Check the code below:

class PatchEmbed(nn.Module):
    def __init__(
        self,
        patch_size: int | list[int] | tuple[int, int] = 14,
        temporal_patch_size: int | list[int] | tuple[int, int] = 2,
        in_channels: int = 3,
        embed_dim: int = 1152,
    ) -> None:
        super().__init__()
        self.patch_size = patch_size
        self.temporal_patch_size = temporal_patch_size
        self.in_channels = in_channels
        self.embed_dim = embed_dim

        kernel_size = [temporal_patch_size, patch_size, patch_size]
        self.proj = nn.Conv3d(in_channels, embed_dim, kernel_size=kernel_size, stride=kernel_size, bias=False)

    def forward(self, hidden_states: torch.Tensor) -> torch.Tensor:
        target_dtype = self.proj.weight.dtype
        hidden_states = hidden_states.view(
            -1, self.in_channels, self.temporal_patch_size, self.patch_size, self.patch_size
        )
        hidden_states = self.proj(hidden_states.to(dtype=target_dtype)).view(-1, self.embed_dim)
        return hidden_states

The result? Every single patch is mathematically crunched into a single, dense vector (a list of 1280 numbers).

Now the next question becomes even more excruciating…

How do we ensure the model knows which patches are next to each other?

Transformers process data in parallel. If we just dump this long sequence of vectors into the model at once, it loses all sense of the image’s layout. Hence, we need to give the model some sense of position in the image.

Given we are working with a 2D image, the simplest way is to assign a pair of coordinates to each patch—like a (row, col) label.

In reality, the mechanism is more complex, but the core intuition is exactly that. Instead of just appending simple absolute coordinates, Qwen2-VL uses a mechanism called 2D-RoPE (Rotary Position Embeddings).2

Without getting lost in the heavy math, 2D-RoPE effectively bakes those (row, col) coordinates directly into the mathematical rotation of the vectors. This is crucial because it makes the positioning relational rather than absolute. The model doesn’t just know a patch is at position (2,4); it understands the distance and relationship between that patch and the one at (2,5).

Armed with this spatial awareness, the patches pass through standard ViT blocks where they can finally "talk" to each other.

As you know the output will be a vector, but not any vector. It will be a fully “contextualized” vector, one that understands both its neighbours and its position in the image.

What is the connection with text tokens, if any?

This is the bridge between the Vision Encoder and the Text LLM.

After the ViT step, a standard 448x448 image will give you 1,024 highly contextualized patches. The better the quality or bigger the size,this number could rise drastically.

Why is this a problem? Because in this final step, we are passing these contextual patches to the Text LLM. Transformer computations scale quadratically, meaning if the LLM has to process thousands of extra visual tokens, the compute cost skyrockets. It eats up the chatbot’s context window and slows everything down to a crawl.

To solve this, Qwen2-VL uses a Patch Merger to aggressively compress the data before handing it to the language model.

It takes a 2x2 block of adjacent patches (4 patches total) and collapses them into 1 single token. It does this by concatenating the four vectors together and passing them through a linear projection layer. This linear layer translates the combined vector into the exact same dimension size that the text LLM uses for normal text tokens.

You can see exactly how this happens in the actual source code:

class PatchMerger(nn.Module):
    def __init__(self, dim: int, context_dim: int, spatial_merge_size: int = 2) -> None:
        super().__init__()
        self.hidden_size = context_dim * (spatial_merge_size**2)
        self.ln_q = LayerNorm(context_dim, eps=1e-6)
        self.mlp = nn.Sequential(
            nn.Linear(self.hidden_size, self.hidden_size),
            nn.GELU(),
            nn.Linear(self.hidden_size, dim),
        )

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        x = self.mlp(self.ln_q(x).view(-1, self.hidden_size))
        return x

The merger is essentially asking the Vision Encoder: “Instead of 4 small, highly detailed patch summaries, give me 1 big summary of this region.”

If you have been reading carefully, you can now understand a subtle mathematical detail from the beginning of this process. When dynamically resizing our image, we actually ensure its dimensions are perfectly divisible by 28, not just 14.

Why? Because our patch size is 14, and our spatial merger squishes them into 2x2 blocks (14 × 2 = 28). By ensuring the image is divisible by 28 from the very beginning, we guarantee that when it’s time to merge them, everything fits together perfectly without any awkward, leftover edge pieces.

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The Picture is Complete

Let’s bring it all back to where we started.

Scroll back up and take one more look at that Qwen2-VL diagram from the introduction. What initially looked like an intimidating jumble of boxes and arrows is now a clear, logical pipeline (at least the visual encoding part)

You now know exactly how a chatbot “sees.” It dynamically resizes your image, chops it into patches, maps their spatial relationships using 2D-RoPE, and mathematically compresses them through a Patch Merger until they speak the exact same language as text.

The next time you drag and drop a photo into an AI prompt, you’ll know exactly what is happening under the hood.

Thanks for reading, see you next time!

This post is going to be a visual recap of those themes, along with a fascinating new addition. To do this, we are traveling back to Constantinople, specifically, to a place tucked right up against the ancient Theodosian walls: the Chora Church.

Why return to this topic? Because concepts read on a screen are generally easy to forget. My hope is that by providing a little “spaced repetition,” combined with some history, these patterns will be intuitively drilled into your memory.

But before we walk inside... if you haven’t read it yet, you can check out the previous post below to get caught up. (It’s a year and a half old... yikes!)

A tiny bit of context: The Church of the Holy Saviour in Chora gets its name from the Greek word for "countryside" or "outside the city," because the original monastery was built just outside the old walls of Constantinople. While it is much smaller and more intimate than Hagia Sophia, it is famous worldwide for holding some of the best-preserved Byzantine mosaics and frescoes in existence. It is the perfect, quiet classroom for our visual review.

Looking at the map, you can see how the church was eventually swallowed up by the expanding city walls. While the very first version of this building dates all the way back to the 4th century, the stunning art we are about to look at is much “newer.”

Between 1315 and 1321, a powerful Byzantine statesman, scholar, and poet named Theodore Metochites decided to give the church a massive reconstruction. He poured his wealth into commissioning the breathtaking mosaics and frescoes that cover the interior. Art historians consider this specific decoration the finest surviving example of the “Palaeologan Renaissance”, a late period of Byzantine art known for being more vibrant, emotional, and dynamic.

A quick historical spoiler: After a change in political power, Theodore lost his wealth and was exiled. But two years later, he was allowed to return to the city, living out the final years of his life peacefully as a monk... right inside the very church he had so beautifully decorated.

Now, let’s step inside his masterpiece and test our memories1.

Quiz #1

Actually, since I already broke the rules and showed you an image from inside, let’s use it for our first test. Look (above) at the figure of Christ sitting on the throne receiving the church from Theodore. Do you recognize the patterns from the previous article?

1. The Letters: Look closely at the gold background near Christ’s head. There they are: IC and XC, the Greek abbreviations for Jesus Christ, complete with the little undulating lines above them telling us it’s an abbreviation.

2. The Gesture: Look at his right hand. He is holding it up in that exact same gesture of blessing and teaching.

3. The Book: In his left hand, he holds the Gospels.

4. The Colors: He is wrapped in the familiar deep blue (representing the celestial realm and truth) over a golden tunic (representing divine light).

While this specific scene is Christ Enthroned rather than the classic waist-up Pantocrator we saw in the domes of Cappadocia, the “visual vocabulary” is exactly the same. The artist is using the same letters, colors, and gestures to say: This is the Ruler of All.

Quiz #2

As you walk through the doors, this is the figure looking down at you from above the main entrance. Do you recognize the patterns?

But here is something completely new (a hidden Easter egg!). Look at the extra words written beneath the IC and XC. On the left, it says “Η ΧΩΡΑ” (He Chora). On the right, “TΩN ZΩNTΩN” (ton zonton).2

Remember how I mentioned “Chora” means “countryside” or “outside the walls”? Well, Byzantines here repurposed the name of the church to give it a new dimension: “Jesus Christ, the Land (Chora) of the Living.”

Quiz #3

Moving further inside, we encounter this towering mosaic. Before reading ahead, look closely at the image below. Based on our lessons from the previous article, can you identify her official title, find the Greek letters that prove it, and recognize the specific emotion on her face?

Let’s see how you did!

• The Letters: Tucked into the remaining gold background on the top left, you can clearly see MP. (The other side is damaged, but it would have said ΘY). This stands for Μήτηρ Θεοῦ—Mother of God.

• The Title: Because she bears the Christ child, she is the Theotokos (the God-Bearer).

• The Expression: Look at her eyes. Just like the mosaic we saw in Hagia Sophia, she isn’t smiling. She has that classic, solemn, almost sorrowful gaze reflecting her foreknowledge of her son’s ultimate sacrifice.

Bonus points for the observers out there:
Did you notice the word below "MP"? It's : "H XΩPA" (He Chora). While Christ was called the "Land of the Living," Mary has a different poetic title here. She is referred to as "The Land (Chora) of the Uncontainable", a beautiful theological concept meaning that her human womb managed to contain the infinite God, whom the entire universe cannot contain.

From Majestic Portraits to Action Movies

So far, the art we’ve reviewed (the Pantocrator and the Theotokos) shares a specific mood. They are static, eternal, and monumental. They are looking directly at us, demanding reverence.

But during the Palaeologan Renaissance under Theodore Metochites, Byzantine art went through a massive shift. It became less about static portraits and more about dynamic storytelling and deep emotion. If this artistic awakening sounds familiar, it should: right around this exact same time, the early Italian Renaissance was starting to blossom across the sea, bringing a very similar focus on human emotion and movement.

To see the ultimate example of this, we need to step off to the side of the main church and enter the Parekklesion a side chapel built specifically to be a funerary chapel (a place for tombs, including Theodore's own).

Because this room was dedicated to death and the hope of resurrection, it holds one of the most breathtaking, action-packed pieces of Christian art ever created: The Anastasis (The Harrowing of Hell).

Before moving on, note that, unlike the glittering glass mosaics we just looked at, this is a fresco (painted directly onto wet plaster).3

Right at the top, you can read the Greek letters Η ΑΝΑCΤΑCΙC (He Anastasis), naming the scene. Notice they use that curved, lunate sigma (C) we learned about last time!

The word Anastasis is Greek for “resurrection.” This is the traditional Orthodox Easter image, but it doesn’t show an empty tomb. Instead, it depicts the exact moment Christ descends into Hades to break down the gates of hell and release the Old Testament figures who believed in him prior to his incarnation.

This magisterial fresco is an absolute force of nature. Look at Christ, clad magnificently in white, his robes flying behind him to show the sheer force of his arrival. He has completely trampled the crossed doors of the underworld. If you look closely into the dark abyss beneath those crushed doors, locks, and keys, you can see Satan lying there, bound and gagged.

Then move your gaze from the center image slighly outwards notice how Christ is raising Adam (left) and Eve (right) from their sarcophagi. He isn’t holding their hands. He is gripping them firmly by the wrists. This is a deliberate theological statement: humanity cannot save itself [1]. They are limp; Christ is forcefully dragging them from death into life. (The figures to the left watching in awe include Kings David and Solomon).

But the brilliance of this artwork isn’t just in the action; it is deeply integrated into the chapel’s actual architecture through a concept called “visual mimesis” (imitating the physical world). Notice the diagonal angles of Adam and Eve’s sarcophagi. They aren’t random. They are designed to lead the viewer’s eye directly toward the actual arched tombs (arcosolia) built along the chapel’s lateral walls. The painting bridges the painted space with the physical burial space of the room.

Ufff... quite a ride, right?

And to think, the Anastasis is just the end of the funerary chapel. To get to this dramatic climax, the artists spent the entire building leading up to the story. For example, in the dome just before this one, there is a sprawling, awe-inspiring depiction of the Last Judgment.

However, I’ll let you see that for yourself someday...

Before we officially exit the Chora Church, it’s time for your final exam. Let’s see how well our “spaced repetition” worked. I’m going to leave you with three final images.

Take a close look and tell me in the comments: What patterns, letters, colors, or themes can you identify?

Leave your answers in the comments below! Let’s see who gets an A+ in Byzantine Iconography.

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Quiz #4

Quiz #5

Quiz #6

Recently I have read an article here on Substack. I wish have it saved but I cannot find it now.

Anyways, its main thesis is the cycle of currencies and the so-called “Curse of Empires”. In other words how being an empire both leads to a strong currency but makes your enemies to be stronger (currency-wise). This has lead to some debates with some colleagues at work.

One of them revolved around China, and it was the genesis of this post. The question is how do they keep such a weak currency despite being the biggest exporter in the world?1

This post is an introduction to the chinese FX Swap trade.2

WARNING: I may oversimplify the topics, focusing only on currencies. It’s definetely intended, just enough to help intuition to kick in.

The Problem

Imagine you own a factory in Shenzhen. You make widgets and sell them to Americans. You get paid in US Dollars. But you can’t pay your workers or your electric bill in dollars; you need Renminbi (Yuan).

So, you go to the market to sell your dollars and buy yuan.

If millions of factory owners do this at once, the demand for yuan skyrockets. The price of the yuan goes up. If the yuan gets too expensive, your widgets become too expensive for Americans, and your factory closes.

This is the nightmare scenario for Beijing. To prevent this, the People’s Bank of China (PBOC) steps in. They will buy the dollars from you to keep the yuan cheap.

But this, also poses a problem: if the PBOC prints fresh yuan to buy those dollars, they flood the domestic economy with cash, which would lead to inflation.

Thus, you cannot print your way out of the problem, what to do then?

The Solution

Instead of buying the dollars outright, the PBOC uses a Swap. They say to the banks: “Give me your dollars, and I will lend you yuan. But, we sign a contract today stating that in three months, we will reverse this transaction.”

Because the yuan injection is temporary—a loan rather than a purchase—it doesn’t permanently expand the money supply. It solves the currency problem without immediately triggering the inflation problem.

For the bank is a win/win situation, the swap it's just a tool to manage its currency position, not necessarily where profit comes from3.

And then everyone is happy, no? Well…

Quo Vadis?

There is never a free lunch; it is always a system of trade-offs. In our case the exporters profit because the get their yuan, the PBOC also profits becasue it tames the inflation and keeps economic activity going.

Then, who is losing?

Let’s see… the FX swap policy ensures the yuan remains weaker than it naturally would be. What is a weak currency bad to?

Mainly imports.

So a weak yuan is acting as a shield, keeping their goods cheap on the global market, keeping also factories humming and employment high BUT at the expense of keeping foreign made products and service overexpensive.

In other words, a weak currency acts as a hidden tariff on imports. It forces a trade-off: domestic labor is sold at a discount, while foreign goods are purchased at a premium.

Since China is not an autarky—it needs to import massive amounts of oil, soy, and chips—someone has to pay that premium. That “someone” is the Chinese household. It is a silent wealth transfer: consumers accept lower purchasing power just to keep the factories competitive.

Potential Energy

Now let me make a jump—the sort of jump that defines this newsletter.

Let’s go back to high-school physics and the concept of the compressed spring.

Hooke’s Law teaches us that if you stretch a spring, it pulls back. If you compress it, it pushes out. To keep a spring compressed away from its natural length, you have to apply constant force.

Here is the connection:

The “natural length” of the spring is the fair market value of the Yuan (which should be higher). The “force” holding it down is the PBOC’s intervention via these Swaps.

China has engaged in this intervention for decades. It has built an entire socio-economic structure—infrastructure, supply chains, urban migration patterns—based on the premise of a cheap currency.

This is Path Dependency 101. The further you walk down this road, the harder it is to turn back.

If China were to stop the intervention (release the spring) today:

• The yuan would appreciate violently.

• Exports would collapse.

• Unemployment would spike.

• Social stability would fracture.

So, the SHOW MUST GO ON.

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The Trap

But as with any system held far from its natural equilibrium, the energy doesn’t disappear; it accumulates. Every swap, every intervention, adds tension to the spring.

The system is now trapped. It cannot stop intervening because the economy is structurally addicted to the intervention.

To paraphrase Nassim Taleb, this is the definition of a fragile system: one that requires constant, increasing maintenance just to stay in the same place.

We often mistake “stability” for equilibrium. We see a flat line on a chart—like a stable exchange rate—and assume the system is at rest. But often, that stability is actually a compressed spring, waiting for the hand that holds it to slip.

When Does the Spring Break?

What causes the hand to slip?

In this case, the risk is Capital Flight.

If Chinese citizens and investors believe the Yuan is permanently suppressed—or if the economy slows down—they stop wanting Yuan entirely. They try to get their money out of China and into Dollars, Gold, or Bitcoin.

If enough people try to sell Yuan for Dollars at the same time, the PBOC’s swap machine gets overwhelmed. They run out of Dollars to swap.

Why? In capital flight, the swap reverses:

• PBOC gives dollars, receives yuan

• But PBOC’s dollars are finite (~$3 trillion)

If people see the PBOC's reserves declining rapidly as they defend the yuan, they would demand even more yuan. And so on, and so forth.

Result, the physics takes over. The dam breaks, and the currency adjusts. Violently.

End of the party.

Except Capital Controls are applied of course. But that would be another story…

They introduced the Model Context Protocol (MCP).

At the time, the headlines were dominated by “agentic AI” and reasoning capabilities, but MCP was tackling a much duller, yet more critical infrastructure problem: how to connect AI models to data without building a new bridge every single time.

Anthropic described it as a “USB-C port for AI applications.” It’s an open standard that allows developers to build a connector to their data once, and have it work across multiple AI clients immediately.

The Problem: The Glass Wall

But to understand why this matters, we need to leave the abstract definitions behind and look at a real-world annoyance.

Imagine I want to book a train. I want my AI assistant (be it Claude, ChatGPT, or another) to check the prices for high-speed trains between Madrid and Barcelona for next week, compare the options, and tell me which day is cheapest.

This sounds simple, but historically, it has been impossible. Your AI lives behind a glass wall, trapped in the “chat” window:

1. It doesn’t know today’s prices: Its training data is months old.

2. It can’t click buttons: Unless you give it specific browser access, it can’t navigate the Renfe (Spanish rail) website.

3. Searching doesn’t always work: Train companies often obfuscate trip search results from search engines to prevent scraping. If an LLM tries to “Search the Web,” it hits a wall of JavaScript or CAPTCHAs, making it blind to the direct results.

4. The “Integration Hell”: To fix this, a developer would historically have to write a specific plugin for OpenAI. Then, if they wanted to use Claude, they’d have to write a totally different plugin for Anthropic.

My Experiment: renfe_mcp_server

I decided to test if MCP actually solves this by building a tool called renfe_mcp_server.

The goal was straightforward: I wanted to ask Claude Desktop, “Find me the cheapest train to Barcelona,” and have it actually fetch live data using the Renfe API, bypassing the clumsy website entirely.

However, the fundamental problem with connecting AI to the real world is the language barrier.

Rail companies like Renfe don’t speak English; they speak complex JSON. They don’t know what “Madrid” is; they only know Station IDs (e.g., MADRID-PUERTA DE ATOCHA is 60000). They don’t allow you to just “browse” their database; they have specific API endpoints that require precise date formats (YYYY-MM-DD) and strict headers.

If you just ask a standard LLM to “check prices,” it fails because it cannot guess these internal IDs or handle the strict API parameters.

This is where the architecture splits into three distinct roles:

1. The Server : This is the code I wrote. It sits locally on my machine. It doesn’t know how to be a chatbot; it simply exposes specific Tools—like get_stations or get_trips—and handles the “dirty work” of authenticating with Renfe and parsing their ugly JSON.

2. The Client: This is the AI interface (like Claude Desktop). It handles the conversation and the reasoning.

3. The Protocol (MCP): The standardized pipe connecting them.

When people talk about MCP, they are generally talking about these three roles. Anthropic has standardized the Protocol, and they built one of the clients (Claude Desktop), but the servers can be created by anyone, anywhere.

In other words, by creating functions (Tools) that the Client can trigger and interact with, we are giving it power that it didn’t have before. For example, if you ask a chatbot to multiply large numbers, the answer might be right or wrong, but you are never sure which. If instead, you code a simple numpy function that the AI can “call” to do the multiplication, you are making an uncertain action become certain.

This is the goal: drive directly without doubts.

Great. Now let’s drill it down. Let me show you exactly what happens when I type: “Find trains from Madrid to Barcelona for tomorrow.”

Step 1: The Intent & The Missing Info
Claude analyzes the prompt. It sees “Madrid” and “Barcelona.” But it looks at the tool definition for get_trips provided by my server and realizes it needs Station IDs, not city names. It knows it cannot guess them. It checks its other tools and sees get_stations.

Step 2: The First Tool Call (Station Lookup)
Claude sends a structured request to the MCP Host:

“Call tool get_stations with query ‘Madrid’.”

The MCP Server runs the Python function, hits the Renfe API, and returns a JSON list:

[
  {"name": "MADRID-PUERTA DE ATOCHA", "id": "60000"},
  {"name": "MADRID-CHAMARTIN", "id": "17000"}
]

It repeats this logic for Barcelona.

Step 3: The Reasoning
Claude reads this JSON. It doesn’t show this to the user. It “thinks” silently: Okay, the user likely wants Atocha to Sants. I have the IDs now. I can finally call the pricing tool.

Step 4: The Second Tool Call
Claude constructs the main request:

“Call tool get_trips with origin=’60000’, destination=’71801’, date=’2025-02-12’.”

Step 5: The Raw Output
The MCP server hits the Renfe endpoint and returns the raw, ugly truth:

[
  {"train": "AVE", "dep": "07:30", "arr": "10:00", "price": 45.50, "currency": "EUR"},
  {"train": "AVLO", "dep": "08:15", "arr": "11:15", "price": 19.00, "currency": "EUR"}
]

Step 6: The Final Synthesis
Only now does Claude speak to me. It takes that raw JSON and translates it into natural language:

“I found several options for tomorrow. The cheapest is the AVLO at 08:15 for €19.00. If you prefer the faster AVE, there is one at 07:30 for €45.50.”

Stanrdization Wins

If this Renfe experiment were just about checking train prices, it would be a neat party trick. But the implications are much bigger.

Before MCP, if I wanted to give this same “train checking” superpower to ChatGPT, I would have to rewrite my code to fit OpenAI’s specific plugin architecture. If I wanted to give it to Google Gemini, I’d have to rewrite it again.

This is the “Integration Hell” I mentioned earlier. It forces developers to pick sides in a platform war.

MCP changes the game because it creates a universal standard.
Because renfe_mcp_server is written in MCP, it doesn’t care who the client is. Today, I am using it with Claude Desktop. Tomorrow, if an IDE like VS Code or a terminal like Warp adopts MCP (which they are doing), I can check train prices directly from my code editor without changing a single line of my Python script.

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We are moving from a world of “Walled Gardens” to a world of modular building blocks.

This brings us back to the most important shift: Certainty.

As I mentioned with the math example, LLMs are probabilistic—they are dreamers. They guess the next word. But the real world operates on certainty. You don’t want an AI to guess the price of a train ticket; you want it to read the price. And do it faster than you can scroll.

By wrapping code in MCP tools, we are effectively giving the dreamer a calculator, a web browser, and a database client. We are grounding their hallucinations in reality.

At Crossroads, we often look for the moment technology becomes invisible. MCP is exactly that. It is the plumbing that nobody sees, but that finally allows the water to flow. The tracks are laid. The standard is set. Now, it’s up to us to decide what to load onto the train.

Thank you for reading, until next time!

You can find the code for the Renfe experiment here.

You don’t understand the word “sentence” in isolation. Your brain isn’t rebooting every time your eyes jump to a new word. Instead, you are holding the context of the previous words—”As,” “you,” “read,” “this”—in a fluid, working memory. You are weaving a narrative. Creating an story.

For a long time, Artificial Intelligence did not have this. Traditional neural networks (the kind that recognize cats in photos) are amnesiacs. They process data in static snapshots. If you show a standard neural network a movie, it won’t know that the person in Frame 2 is the same as the person in Frame 1. To the network, every moment is the Big Bang; history is reset every millisecond.

But the world doesn’t happen in snapshots. It happens in sequences. Language, music, video, and stock markets are all streams of data where the present makes no sense without the past.

To solve this, researchers needed a new architecture. They needed a machine with a memory loop. They needed Recurrent Neural Networks (RNNs).

Breaking the Fixed Mold

In his famous essay The Unreasonable Effectiveness of Recurrent Neural Networks [1], Andrej Karpathy highlights a fundamental limitation of “vanilla” neural networks: they are constrained by fixed sizing.

Imagine a standard algorithm as a function box. You must feed it a fixed-size input (like a 64x64 pixel image) and it spits out a fixed-size output (like a label: “Apple”).

But what if you want to translate a sentence from English to French?

• Input: “I like apples.” (3 words)

• Output: “J’aime les pommes.” (3 words)

Easy enough. But what about:

• Input: “He fell.” (2 words)

• Output: “Il est tombé.” (3 words)

Standard networks choke here. They don’t know how to handle inputs and outputs that stretch and shrink. RNNs changed the game because they operate on sequences of vectors. They allow us to process variable-length inputs (like a sentence) or produce variable-length outputs (like a caption).

The Intuition: The Unrolled Loop

So, how do we give a machine a memory?

The diagram for a standard neural network looks like traffic flowing down a one-way street:

Input -> Hidden Layer -> Output

An RNN adds a detour. It takes the output of the hidden layer and loops it back into itself.

At first glance, this loop looks confusing. But if you borrow Christopher Olah’s [2] visualization technique and “unroll” the loop, the intuition clicks.

Imagine the RNN not as one static circle, but as multiple copies of the same network lined up in a row—one for each step in time.

1. Step 1: The network reads the first word (”The”). It produces an output, but it also creates a “Hidden State”—a bundle of numbers representing what it has learned so far.

2. Step 2: It passes that Hidden State to the next copy of itself.

3. Step 3: The network reads the second word (”cat”). But it also reads the Hidden State from Step 1. It combines “The” (memory) + “cat” (current input) to update its understanding.

It’s like a game of “Telephone” (or Chinese Whispers), but with a twist. Each person in the line listens to the new secret whispered by the person before them, adds their own piece of information, and whispers the combined story to the next person.

This “Hidden State” is the machine’s working memory. It is the vector that carries the context of “The” all the way to the end of the sentence.

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But what are we learning? What changes?

This is the secret sauce. If we look inside that loop, what is actually physically changing?

We need to distinguish between the Memory and the Rules.

1. The Memory (The Hidden State): This is the vector of numbers that changes at every single step of the sequence. When the RNN reads “The,” the numbers shift to represent a singular article. When it reads “cat,” the numbers shift again to represent a specific animal. This is dynamic and fleeting—it is the “thought” currently in the machine’s head.

2. The Rules (The Weights): This is the matrix of numbers that dictates how the memory shifts. And here lies the genius of the RNN: The weights are shared.

In a traditional neural network, Layer 1 has a different set of weights than Layer 2. But in an RNN, we apply the exact same weight matrix (let’s call it ) at every single step of the sequence.

Think of the weights as a pair of tinted glasses.

• The network looks at the first word through these glasses.

• It updates its memory.

• Then it looks at the second word through the exact same pair of glasses.

This is huge. It means the network learns a universal set of rules for language that applies regardless of position. It learns that the word “not” flips the meaning of a sentence, whether “not” appears at the beginning, middle, or end.

So, when we say the network is “learning,” we mean it is tuning that single pair of glasses (the Weight Matrix) so that it knows how to correctly update the memory (the Hidden State) no matter what sequence of data flows through it.

The Magic of Context

This simple loop allows for profound complexity. As Karpathy noted, we aren’t explicitly teaching the machine grammar rules. We are just asking it to predict the next character in a sequence.

By trying to minimize its error, the RNN learns the structure of data itself.

• It learns that an open parenthesis ( usually implies a closing parenthesis ) later on.

• It learns that the word “King” relates to “Queen” in the same mathematical direction that “Man” relates to “Woman.”

It moves AI from classification (What is this image?) to storytelling (What happens next?).

When the Whisper Fades

However, the standard RNN has a fatal flaw.

Recall our game of Telephone. If the line of people is short, the message survives. But what if the line is 100 people long? By the time the message reaches the end, the original whisper is distorted or lost entirely.

In an RNN, this is known as the problem of Long-Term Dependencies (often caused by the “Vanishing Gradient”).

Consider this sentence:
“I grew up in France... [200 words of context] ... and so naturally, I speak fluent ____.”

To predict “French,” the network needs to remember the word “France” from the very beginning. But in a standard RNN, that information has been overwritten and diluted by the 200 words in between. The memory is too short. The signal dies before it reaches the end.

The RNN gave AI a memory, but it was a fleeting one. To truly understand language and complex sequences, we needed a way to control that memory—a way to decide exactly what to keep and what to forget.

That architecture is called the LSTM (Long Short-Term Memory). And that is where we will go next week.

1. The Unreasonable Effectiveness of Recurrent Neural Networks - Andrej Karpathy blog

2. Understanding LSTM Networks - colah’s blog

I am curently reading a book called Reader, Come Home, by neuroscientist Maryanne Wolf. There, she writes chapters as letters to the reader in a fascinating type of essay format.

But today I would like to share the second letter, “Building a Reading Brain,” where she uncovers what actually happens in your brain when you read.

Your Brain Wasn’t Born to Read

Unlike spoken language, which we are biologically hardwired to learn, reading is an invention. There is no “reading” gene or single reading center in the brain.

So, how do we do it? Wolf explains it as an act of “neuronal recycling”. The brain, like a clever electrician rewiring an old house, repurposes existing structures—those originally built for vision, language, and cognition—to create a brand-new, intricate circuit for reading.

This ability to adapt is a testament to our brain’s incredible “plasticity within limits.” It forms a new piece of machinery from parts that were already there.

Welcome to the Brain’s Three-Ring Circus

To help us visualize this, Wolf invites us into the “big top” of the reading brain. Imagine three massive, overlapping rings, each bustling with performers:

1. The Ring of Vision: This is where the light from the letters first enters. It’s responsible for identifying the lines, curves, and shapes that form our alphabet.

2. The Ring of Language: These performers connect those shapes to sounds (phonemes) and meanings (morphemes—like the “un-” prefix or the “-ed” suffix).

3. The Ring of Cognition and Affect: This is where the magic deepens. Here, the brain brings your own memories, thoughts, feelings, and experiences to the word, giving it context and emotional weight.

A Single Word on the Center Stage: “Tracks”

To see the circus in action, Wolf follows a single word—”tracks”—on its journey through the brain. This all happens in about 400 milliseconds, but we’re watching in slow motion.

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Act 1: The Spotlights of Attention (First 50 milliseconds)
Before anything else, your brain’s attentional “spotlights” have to turn on and focus. They help you disengage from whatever you were just doing and focus on the word in front of you.

Act 2: The Ring of Vision
Next, performers from the Ring of Vision get to work. Information from your eyes races to the visual cortex. Tiny “orbs” recognize the letters (t-r-a-c-k-s) while others identify the features that make up those letters (the lines, the circles, the diagonals).

Act 3: The Ring of Language
The visual information is passed to the Ring of Language. Here, acrobats begin matching the visual word with its sound and possible meanings. “Does ‘tracks’ rhyme with ‘snacks’?” “Is it an animal track, a sport track, or a railway track?” The brain considers all these possibilities at once.

Act 4: The Rings of Cognition and Affect (The Grand Finale)
Finally, the word leaps into the vast Rings of Cognition and Affect. This is where the performance becomes personal.

• A tiny train might chug into view, reminding you of Thomas the Tank Engine from your childhood.

• A more somber image might surface: Anna Karenina from literature, standing by the train tracks.

• Your own memories—of hiking, of a song, of a specific conversation—are activated.

Within a fraction of a second, your brain has done more than just decode a word. It has connected it to a universe of stored knowledge, memories, and emotions. As Wolf puts it, “we are left with an ever-so-slight frisson of vestigial sadness... We begin to appreciate the multilayered beauty in the brain’s design for storing and retrieving words.”

What feels instantaneous to us is, in reality, a “zigzagging, feed-forward, and feed-backward” symphony of thousands of neuronal groups firing in perfect concert.

Reading a single word activates a galaxy within us. Imagine what happens when you read a full sentence, a poem, or an entire book.

I hope this gives you a new sense of awe for what your brain is doing right now. It’s a miracle we perform every day, one we should never take for granted.

Today, I wanted to share with you that not all cultures saw it that way. Some of them built cities that were… round.

Yes, you read that well. Round cities. So where and why did this pattern emerge? Let’s dive in.

City of Peace

We are in 762 AD on the banks of the Tigris River. There, imagine a ruler so confident in his vision that he traces the plan for his new capital in the dirt with his own hands. Then, to make the vision real, he orders cotton balls soaked in oil to be placed along the lines and set ablaze, creating a fiery outline against the Mesopotamian night.

The ruler was the Abbasid Caliph al-Mansur, and the fiery circle was the foundation of his new capital: Madinat al-Salam, the “City of Peace,” known to history as Baghdad.

For centuries, Baghdad would be the world’s center of learning, culture, and science. But its most striking feature was its design. It was not a city that grew organically; it was a perfect circle, a masterpiece of urban planning with the Caliph’s palace and the grand mosque at its absolute center.

But, why a perfect circle?

On a practical level, the design was a work of defensive genius. A round city has no corners—no weak points for an invading army to exploit. The city was protected by a deep moat and a formidable double wall, with four gates positioned at the cardinal directions. Guards could see any approaching threat from a distance, and the layout allowed for the rapid movement of troops from the center to any point on the circumference. The city was, in essence, a fortress.

The design was also a powerful piece of political messaging. In the geometric hierarchy of the city, everything revolved around the center. The Caliph’s palace, the “Golden Gate,” and the grand mosque sat in the central enclosure. Radiating outwards were the quarters for his guards, his children, and his closest officials. Further out were the homes of merchants and the city’s markets, connected by four main thoroughfares that ran from the outer gates to the center.

The message was unmistakable: all power, all commerce, and all life in the city flowed from and pointed toward one man—the Caliph. The city was a diagram of his absolute authority.

An Echo of Ancient Empire

These two reasons alone—impenetrable defense and absolute power—are enough to make the design of Baghdad a work of genius. They explain the logic of the circle.

But they don’t explain its origin.

To understand that, we have to look at the seismic political shift that brought Caliph al-Mansur to power. The Abbasid Caliphate was born from a revolution that overthrew the previous dynasty, the Umayyads. This wasn’t just a change of leadership; it was a fundamental reorientation of the entire Islamic world.

Under the Umayyads, the empire was distinctly Arab-centric, ruled from Damascus in Syria. Power and influence were largely reserved for the Arab aristocracy. The Abbasid revolution, however, drew its strength from the empire’s eastern provinces, particularly the region of Khorasan in Persia.

When the Abbasids took control, the center of gravity tilted eastward. The old Arab elite were replaced. Suddenly, Persian culture, which had been developing for over a thousand years, began to permeate the court of the Caliph. Persian scribes, administrators, scientists, and engineers became indispensable to the new regime. They brought with them sophisticated systems of statecraft and a deep history of imperial grandeur.

This was a new era, and it needed a new capital that reflected this new, cosmopolitan identity.

And if you are going to build a new world, you look to the blueprints of the old masters. For the Abbasids, that meant looking to the architectural legacy of the Sasanians, the great Persian dynasty that had ruled these lands for centuries.

And the Sasanians were masters of the round city.

Long before Baghdad, the founder of the Sasanian Empire, Ardashīr I, had built his capital, Gūr, as a perfect circle, so precise it was said to have been “drawn by a pair of compasses.” This wasn’t an anomaly; other Sasanian cities like Dārābgerd followed the same circular plan.

But this was far more than a stylistic choice. These cities were cosmic diagrams.

As the research paper “Solar Considerations in Planning of Three Circular Cities in Ancient Persia” shows, the gates of these Sasanian cities were often aligned with celestial events. The eastern gates of Gūr, Dārābgerd, and the ancient city of Balkh were all precisely oriented to face the sunrise on the winter solstice. This was no accident. The solstice was a pivotal day in the Persian calendar, symbolizing the rebirth of the sun. By aligning their capitals with the cosmos, Sasanian kings sent a clear message: their rule was in harmony with the divine and natural order of the universe.

This is the architectural language of power that Caliph al-Mansur chose to speak.

The final piece of evidence is the most compelling. When it came time to lay the foundations for Baghdad, al-Mansur didn’t just copy a shape; he hired the experts. Historical sources confirm he entrusted the project to a renowned Persian astronomer, Naubakht, to help design the layout and choose the most astrologically auspicious moment to begin construction.

This was a political masterstroke. By adopting the circular, cosmically-aligned design of the Sasanians, Al-Mansur was wrapping his new dynasty in the mantle of Persian imperial grandeur. He was signaling to his subjects—many of whom were Persian—that his rule was not a foreign conquest, but the rightful continuation of a timeless legacy.

The city’s very shape declared its imperial destiny.

Al-Mansur’s Round City was a spectacular success. For centuries, it was the vibrant heart of the Islamic world. The original city no longer stands, lost to the floods of the Tigris and the devastating Mongol siege of 1258 that razed it to the ground. All that remains are the descriptions in historical texts and the enduring legacy of Baghdad as a center of a golden age.

But the disappearance of the Round City also marks a historical turning point, which raises a final, fascinating question: if this design was so brilliant, why have so few round cities been built since?

Why did the square win?

The answer, it seems, lies in a clash of two powerful, competing traditions.

The circular city, as we’ve seen, was the architectural expression of a specific Persian worldview: cosmic, hierarchical, and looking inward towards a single center of power.

But the dominant tradition in Europe was inherited from the Greeks and, especially, the Romans. Because the Romans were such prolific city-builders, their pragmatic grid plan became the foundational blueprint for countless settlements, from London to Cologne. When newer cities were founded, planners often tried to replicate what they had seen before—and what they had seen was the successful, expandable Roman grid.

Of course, history is never so simple. After the fall of Rome, grand urban planning largely ceased in Europe for centuries. During the Middle Ages, growth became mostly organic. Towns huddled and grew around a central authority—a castle or a church that could guarantee protection. This often resulted in a maze of winding streets that could look roughly circular from a distance, but it was the unplanned result of people seeking safety, not a deliberate, cosmic design.

It wasn’t until the Renaissance that planners returned to designing “ideal cities” from scratch. Some experimented with the circle, creating spectacular fortress towns like Palmanova for the Venetian Republic. But these were often rigid, defensive projects that struggled to grow. As commercial centers, many were considered failures, reinforcing the ultimate triumph of the more adaptable grid.

As the world modernized, cities became less the statement of a single ruler and more the chaotic, sprawling engines of trade. In that new world, the practical Roman grid was simply a better fit. The square, a symbol of rational, repeatable order, overtook the circle, a symbol of divine, singular unity.

So the next time you walk the streets of a city, look at its shape. Is it a grid of endless possibility, or does it wind organically around an ancient core? The cities we build are never just a collection of streets… they are Crossroads of people, places and ideas.

I read something a couple of days ago that finally gave me a name for this phenomenon. It’s a powerful, invisible principle at work, one that explains why advantages tend to accumulate for those who already have them.

It’s not just luck, and it’s more than just talent.

This phenomenon is called the Matthew Effect, and once you learn to see it, you’ll start noticing it everywhere.

What is the Matthew Effect?

The term was first coined in 1968 by sociologist Robert K. Merton. He named it after a surprisingly stark verse from the Gospel of Matthew in the New Testament:

“For to everyone who has, more will be given, and he will have an abundance. But from the one who has not, even what he has will be taken away.”

Put simply, the Matthew Effect describes the phenomenon of accumulated advantage. It’s the idea that a small initial edge can snowball into a much larger one over time. In countless systems, success doesn’t just breed success—it multiplies it. Merton first used it to describe how eminent scientists are more likely to receive credit for their work than lesser-known researchers, even if their work is collaborative or similar.

But this concept isn’t confined to the sociology of science. It’s a fundamental pattern that appears across remarkably different disciplines. It is, factually, a crossroad of crossroads!

Crossroad 1: Sociology

The starting point. Merton observed that eminent scientists received disproportionate credit for their work compared to lesser-known colleagues, even when their contributions were collaborative. This initial recognition granted them better funding, more talented students, and prestigious opportunities—a virtuous cycle that solidified their place at the top.

This is also where we see the “Matilda Effect,” a term coined by Margaret Rossiter, which describes the specific bias where female scientists’ contributions are wrongfully attributed to their male colleagues.

Crossroad 2: Sports

In his book Outliers, Malcolm Gladwell famously illustrated the Matthew Effect using Canadian youth hockey leagues. He noticed that a huge number of professional players were born in January, February, and March. Why? Because the eligibility cutoff for age-class hockey is January 1st.

A boy who turns 10 on January 2nd is competing against boys who don’t turn 10 until later in the year. At that age, a few months of extra physical development provides a significant advantage in size and coordination. These slightly older, bigger kids are then selected for elite teams, where they receive superior coaching and far more practice time. What began as a tiny, arbitrary advantage compounds into a massive skill gap over time.

Crossroad 3: Education

Psychologist Keith Stanovich applied the concept to explain how children learn to read. His research showed that children who enter school with a slight edge in reading are given more advanced books and positive reinforcement. Because they find it rewarding, they read more often, which rapidly accelerates their vocabulary.

Meanwhile, children who struggle early on may come to see reading as a frustrating chore. They avoid it, fall further behind, and the gap between the two groups widens exponentially. Stanovich famously summarized it as “the rich get richer and the poor get poorer” in the context of literacy.

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Crossroad 4: Technology and Algorithms

The digital world runs on the Matthew Effect. Think of a YouTube video or an Instagram post. Algorithms are designed to promote content that is already performing well. A video that gets a surge of views and likes in its first few hours is shown to a wider audience. This increased exposure leads to more views, which signals to the algorithm to promote it even more aggressively. This feedback loop is why content often either languishes in obscurity or goes viral—there is very little middle ground.

This is also a form of “preferential attachment,” a cornerstone of network theory where the most connected nodes (or popular creators) are the most likely to gain new connections (or followers).

Crossroad 5: Psychology

The Matthew Effect even operates inside our own minds. Neuroscientist Ian Robertson describes a phenomenon known as the “winner effect.” When we achieve a success—even a small one—it can re-wire our brain’s chemistry, increasing our confidence and appetite for risk. This psychological boost makes us more likely to succeed in our next endeavor, creating an upward spiral of achievement and self-assurance. The reverse is also true; a string of failures can diminish our confidence, leading to a downward spiral. It’s the internal monologue of accumulated advantage.

Crossroad 6: The Fable

So, is the Matthew Effect an inescapable law? Does the person who starts ahead always win? A 2,500-year-old fable, The Tortoise and the Hare, suggests the answer is no. In fact, the story serves as a perfect lesson on the Matthew Effect’s greatest vulnerability.

• The Hare is “Advantage without Effort.” It perfectly represents the starting power of the Matthew Effect. His natural speed gives him an immediate, massive lead. But his advantage breeds complacency. He takes his lead for granted and stops putting in the work. He breaks the cycle of accumulated advantage.

• The Tortoise is “Effort without Advantage.” It is the ultimate underdog, with no initial edge. His victory comes from a different, more powerful force: the compounding of consistent effort. His slow but steady progress eventually overtakes the talented but lazy competitor.

The fable teaches us that while the Matthew Effect describes a powerful tendency in the world, it is not destiny. Advantage is useless without continued effort. And for those of us starting without an advantage, consistency is the great equalizer. It is the one strategy that can create our own momentum, step by plodding step.

The Matthew Effect is not just an academic theory; it’s a lens for understanding the world. It reveals that success and failure are not always simple reflections of merit, but are often the result of initial advantages or disadvantages compounded over time.

It shows us why an arbitrary birth date can shape a sports career, why early childhood interventions are so critical, and why a single breakout success can define a career.

Most importantly, it challenges us to look for the starting points. How can we create our own small wins to kickstart a “winner effect”? Could you “attract” success by identifying the effect in your own domain?

Despite the answer, the first step would be to learn to see the pattern.

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Thank you for reading. I went down this rabbit hole because the idea felt so true. For me, it was a new name for the power of compound interest, a reminder that any step you take in a direction ultimately gives you an edge as time goes by.

“Ceci tuera cela”, he says. “This will kill that”.

On the surface, it’s a simple prophecy: the book will kill the cathedral. But it's not about physical destruction. It’s a profound observation about how the technology we invent doesn’t just change how we communicate, but fundamentally alters the very architecture of our minds. It’s an idea from 1831 that feels more urgent today than ever before.

The Book Against the Building

To truly understand Hugo’s anxiety, we have to start with his character, the archdeacon Frollo, watching his world slip away. When he gestures to the first printed book on his desk and declares, “This will kill that,” he isn’t just being a reactionary. He is witnessing the very foundation of his reality being dismantled, page by page.

Hugo, writing in 1831 with the French Revolution a recent memory and the industrial revolution stirring, saw this as a profound metaphor. Before the printing press, he argued, architecture was humanity’s great book. Cathedrals were not just buildings; they were encyclopedias in stone. For a largely illiterate population, every carved figure, every stained-glass window, and every architectural choice told the shared stories of a culture, preserving knowledge for generations.

But no technology is ever just a neutral tool. It is an active force that reshapes our relationship with the world, and its most profound consequences are the subtle, second-order effects that quietly rewire our habits of mind. The printing press didn’t just offer a faster way to make a Bible; it fundamentally altered the very experience of faith, community, and knowledge itself.

The book was a revolution. It took knowledge that had been monumental, public, and permanent and made it portable, private, and personal. A thought that was once locked in stone, accessible only to those who stood in its physical presence, could now be slipped into a saddlebag and carried across a continent. The singular, authoritative voice of the cathedral was suddenly challenged by a thousand different voices whispering from cheap pamphlets and leather-bound volumes.

This was a profound act of democratization, liberating knowledge from the clergy and the stonecutters. But it was also an act of fragmentation. The grand, communal experience of reading the cathedral together was replaced by the solitary, silent act of reading a book alone.

The shared universe of meaning began to fracture into a million individual worlds.

Hugo understood this trade-off better than anyone. As a novelist, he was a master of the very technology that was replacing the world he was nostalgic for. He saw the immense promise, but he also saw the loss, and it led him to the essential question: what happens when a society no longer shares one great story, but millions of small ones? It was a shift from one central truth to a thousand perspectives, a fragmentation he could see clearly.

He just couldn't have imagined the one that was to follow.

The Stream Against the Mind

Hugo's shift from the cathedral to the book was a fragmentation of knowledge. Our shift, from the book to the infinite scroll, is a fragmentation of attention itself. The new “this” isn't a tangible object like a book, but a relentless, formless stream of information. And the “that” it threatens to kill is not a building, but the very cognitive architecture of deep thought.

We feel this every day. It's the phantom itch to check our phones, the dozen open tabs on our browser, the sense of being everywhere and nowhere at once. Researchers have given it a name: “continuous partial attention”. It is the default state of the modern mind—a low-grade, perpetual scan that prevents the sustained focus required to read a cathedral, a novel, or even a complex argument.

Where the book democratized access to narratives, the algorithm now curates them. Our journey of discovery is no longer a quiet wander through the library stacks, but a high-speed, algorithmically-paved highway designed to hold our gaze for another 2.3 seconds. Serendipity—the unexpected connection, the challenging idea that stops you in your tracks—is engineered out of existence in favor of frictionless engagement.

The parallel is as striking as it is chilling. Hugo worried that print would kill architectural thinking. Our fear is that the stream is killing deep thinking altogether.

What Cathedral Are We Building?

The stakes feel higher now because the trade-off is no longer clear. Hugo’s generation gained a world of knowledge, but they did not forget how to look up. They learned to navigate two architectures of meaning; they could read both the cathedral and the book.

Can we say the same? Can we, with equal facility, read a dense novel and a torrent of notifications? Can we build a sustained, original thought amidst the digital cacophony designed to tear it apart?

The loss of the cathedral was the loss of a shared public commons for meaning. The potential loss of deep thinking is the loss of our private, interior space for creating it.

Frollo was right: the book did, in its way, kill the cathedral. It replaced a shared physical monument with millions of individual worlds. His question now becomes ours: what is the cathedral we are dismantling within ourselves, and what, if anything, are we building in its place?

Joining these two ideas was a leap I've wanted to make for some time. It all started with my reaction to the book: even considering Frollo is the antagonist (no spoilers here), I felt a strange pity for him. It was hard to explain at first, but I think I understand it now. Frollo represents something deeply human: the terror of watching the world you understand disappear.

What do YOU think? See you next week!

What does a newsletter actually look like? Not a single post, but the whole collection. After publishing 29 articles here, I’ve started to feel that a chronological archive is like a library where all the books are lined up by the date they were acquired, not by the stories they tell.

The connections between finance and history, or data science and writing, get lost in the list. So I started an experiment with a simple question: What if, instead of scrolling through a list, you could fly through a galaxy of your own ideas?

That's what this post is about. I'm turning my entire body of work into a 3D, searchable object, and I'm going to show you exactly how.

The Stack: The Tools for the Job

This project was built entirely in a Python notebook. Here are the core libraries I used:

• Embeddings (The AI Brains): sentence-transformers (for text), transformers & CLIP (for images)

• Dimensionality Reduction & Clustering: umap-learn, scikit-learn

• Visualization: plotly

Step 1: Extracting the Raw Material

First, I needed the content. I used Substack’s export feature to get an archive of all my posts as HTML files. Then, I wrote a simple script using BeautifulSoup to parse each file, pulling out the raw text content and any image URLs.

import os
from bs4 import BeautifulSoup
import pandas as pd

posts_data = []
# as I did it in Google Colab this is the generic path
colab_files_dir = '/content/' # The directory with my HTML files 

for filename in os.listdir(colab_files_dir):
    if filename.endswith('.html'):
        filepath = os.path.join(colab_files_dir, filename)

        with open(filepath, 'r', encoding='utf-8') as f:
            soup = BeautifulSoup(f.read(), 'html.parser')

            # Extract all text content
            text_content = soup.get_text(separator=' ', strip=True)

            # Extract all image URLs
            img_urls = [img['src'] for img in soup.find_all('img', src=True)]

            posts_data.append({
                'title': soup.find('title').get_text() if soup.find('title') else filename,
                'content': text_content,
                'image_urls': img_urls,
                'source_file': filename
            })

df = pd.DataFrame(posts_data)
print(f"Extracted data from {len(df)} posts.")
# Output: Extracted data from 28 posts.

This gave me a clean DataFrame with the text and images for every article, ready for the machine learning pipeline.

Step 2: Creating a "Semantic Fingerprint" from Text

To compare articles, I first needed to convert their meaning into a numerical format—a process called creating “embeddings”. I used the sentence-transformers library with the all-MiniLM-L6-v2 model, which is lightweight but powerful. It reads the content of each post and outputs a 384-dimensional vector—a “fingerprint”—that numerically represents the article's topics and concepts.1

from sentence_transformers import SentenceTransformer

# Load a pre-trained model
text_model = SentenceTransformer('all-MiniLM-L6-v2')

print("Generating Text Embeddings...")
texts = df['content'].tolist()

# This one line converts all 28 articles into vectors
text_vectors = text_model.encode(texts, show_progress_bar=True)

print(f"Text vectors generated. Shape: {text_vectors.shape}")
# Output: Text vectors generated. Shape: (28, 384)

Step 3: Understanding the Visual Language with CLIP

My posts aren't just text; images provide critical context. To capture this, I used OpenAI's CLIP model. CLIP is amazing because it understands both images and text and can map them into the same “meaning space”. I wrote a function to process each image and then applied it to every post.

from transformers import CLIPProcessor, CLIPModel
from PIL import Image
import requests
import torch
import numpy as np

# Load CLIP model and processor
clip_model = CLIPModel.from_pretrained("openai/clip-vit-base-patch32")
clip_processor = CLIPProcessor.from_pretrained("openai/clip-vit-base-patch32")

def get_image_vector(url):
    """Fetches an image from a URL and returns its CLIP vector."""
    try:
        response = requests.get(url, timeout=5)
        img = Image.open(BytesIO(response.content)).convert("RGB")
        inputs = clip_processor(images=img, return_tensors="pt")
        with torch.no_grad():
            image_features = clip_model.get_image_features(**inputs)
        return image_features.squeeze().cpu().numpy()
    except Exception:
        return None # Return None if image fails

# ... (loop through dataframe rows to apply this function) ...
# Finally, stack all average image vectors into a single array
image_vectors = np.stack(image_vectors_list)
print(f"Image vectors generated. Shape: {image_vectors.shape}")
# Output: Image vectors generated. Shape: (28, 512)

Step 4: From 896 Dimensions Down to 3 with UMAP

Now I had two vectors for each post: one for text (384 dimensions) and one for images (512 dimensions). I combined them into a single 896-dimensional vector.

The problem is that this is impossible for a human to visualize.

This is where the magic happens. I used a powerful algorithm called UMAP (Uniform Manifold Approximation and Projection) to reduce those 896 dimensions down to just three (X, Y, Z). UMAP is brilliant because it preserves the local and global structure of the data. In simple terms, if two posts were similar in the original 896 dimensions, UMAP ensures they remain close neighbors in the final 3D plot.

from sklearn.preprocessing import normalize
import umap.umap_ as umap

# Normalize vectors so text/images have equal weight
norm_text_vectors = normalize(text_vectors)
norm_image_vectors = normalize(image_vectors)

# Fuse them into one vector per post
fused_vectors = np.hstack((norm_text_vectors, norm_image_vectors))

# Configure and run UMAP
mapper_3d = umap.UMAP(
    n_components=3,      # We want X, Y, and Z
    n_neighbors=15,      # Balances local vs. global structure, to game with...
    min_dist=0.1,        # How tightly to pack points
    metric='cosine',     # Best for comparing semantic vectors
    random_state=42
)
points_3d = mapper_3d.fit_transform(fused_vectors)

# Add the new 3D coordinates back to our DataFrame
df['x'] = points_3d[:, 0]
df['y'] = points_3d[:, 1]
df['z'] = points_3d[:, 2]

Step 5: Finding Clusters in the Chaos

This was the moment of truth. I now had a 3D coordinate (an X, Y, and Z value) for every single one of my 28 posts. My first instinct was to just throw them onto a 3D scatter plot and see what happened. I didn't apply any coloring or labels yet. I just wanted to see the raw structure.

And when I did, something incredible happened.

Distinct clusters were immediately visible to the naked eye.

Without any prompting or supervision, the points had self-organized into what looked like four different continents in my tiny data galaxy. This was the visual proof that the embeddings had worked. The clusters that emerged visually seemed to perfectly match the four main themes I cover in this newsletter: Finance/Economics, History/Geography, Math/Data Science, and my more personal, varied posts.

The question was, could an algorithm see what my eyes could see?

To confirm my observation, I turned to K-Means, a classic clustering algorithm. I asked it to find four clusters in the 3D data, giving it no other information—just the raw coordinates.

from sklearn.cluster import KMeans

print("Running K-Means clustering on 3D coordinates...")
n_clusters = 4
kmeans = KMeans(n_clusters=n_clusters, random_state=42, n_init=10)

# The key is fitting on the low-dimensional points
kmeans.fit(points_3d)

# Assign the machine-generated labels back to the DataFrame
df['cluster'] = [f'Visual Cluster {label + 1}' for label in kmeans.labels_]

print(f"Assigned posts to {n_clusters} visual clusters.")
print(df['cluster'].value_counts())

The result was stunning. The algorithm almost did a perfect job, algorithmically separating my posts into the very same thematic groups I had identified by eye. This was the confirmation: it's possible to perfectly map and cluster my topics in 3D, in a completely unsupervised way.

What’s most remarkable to me is that this was all achieved with “off-the-shelf” models and a rather simple procedure. all-MiniLM-L6-v2 and the base CLIP model are fantastic, but they are far from the absolute bleeding edge of AI research.

The process of embedding text (and images) into vectors and then reduce their dimensionality to be able to visualise it is far from new!

The fact that these readily available, free-to-use tools can produce such clear, meaningful results is a testament to how far the field has come. It proves you don't need a massive research budget to start building fascinating things.

The Result: Our Thematic Galaxy

By coloring the points according to the clusters found by K-Means, the structure becomes undeniable.

The clusters are coherent. It's a map of my newsletter's soul, discovered by the machine, not dictated by me.

Next Steps: Making It Interactive

This is just the beginning. The final step in my notebook was to export these coordinates and metadata to a JSON file, which now powers a live, interactive web page.

You can rotate the galaxy, click on any point to read the article, and see the clusters for yourself.

Feel free to play around with the final result!

Explore the 3D Post Galaxy

What do you think of this approach? Are there other features you'd find useful in a tool like this? Does it work for you?

Let me know in the comments!

Every month, headlines announce that the European Central Bank (ECB) has 'raised' or 'lowered' interest rates. This decision can ripple through the economy, affecting everything from your mortgage payments to the interest on your savings.

But what is the ECB actually changing? It all comes down to three main rates that act as the control panel for Europe's financial system. Let's break them down, one by one.

But the control panel of our financial system doesn't need to be a mystery. In fact, it can be understood with a simple fable.

Once upon a time, the entire life of a valley depended on a single, powerful river. The valley was known as the Economy, and the river was called Liquidity. As long as the river flowed with a gentle, steady current, the valley flourished...

When the river flows just right, the valley thrives. Crops grow, merchants trade, and the people are prosperous.

But if the river floods, it swamps the fields and rots the harvest. This is inflation. If the river dries to a trickle, the crops wither and the people go thirsty. This is recession.

Guarding the source of this river, high in the mountains, lives a solitary, powerful figure: the River Keeper (our European Central Bank). The Keeper's only job is to ensure the valley gets the perfect amount of water. To do this, they don't use magic; they use three ancient, masterfully engineered taps.

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Tap #1: The Surplus Pool (The Deposit Rate – 2%)

The main merchants in the valley (the commercial banks) sometimes have more water than they need for the day's business. They can let it sit idly, or they can carry it all the way back up the mountain to the River Keeper.

To encourage them, the Keeper has a special reservoir, the Surplus Pool. For every bucket of water a merchant deposits there overnight, the Keeper adds a little extra water as a reward.

This is the deposit rate.

When the Keeper sees signs of a flood coming (inflation), they make the reward for using the Surplus Pool much more attractive. The merchants, seeing they can earn a good, risk-free return, bring their excess water up the mountain instead of selling it in the valley. This reduces the flow of the river, calms the flood, and brings things back into balance.

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Tap #2: The Main Sluice Gate (The Refi Rate – 2.15%)

Every week, the merchants come to the River Keeper to get their main supply of water for the week ahead. The Keeper opens the Main Sluice Gate to fill their barrels, but not for free. The price they charge for each barrel is set here.

This is the refi rate.

It's the primary, most common way water enters the valley's economy. The price set at this gate influences the price of every single cup of water sold down in the valley, from the farmer's irrigation to the baker's dough. It is the baseline cost of water for everyone.

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Tap #3: The Emergency Valve (The MLF Rate – 2.4%)

Sometimes, a merchant miscalculates and runs desperately short of water right before nightfall. Their customers are thirsty, and their reputation is on the line.

For these emergencies, the River Keeper has a special, high-pressure Emergency Valve. A merchant can get water instantly, anytime, no questions asked. But this water is expensive—the highest price in the land.

This is the marginal lending facility rate.

It's a safety net. It ensures no merchant ever truly goes dry, which prevents panic in the valley. But because it's so expensive, they only use it as a last resort. This high price also sets a clear ceiling on how much merchants will charge each other for last-minute loans down in the valley.

This story isn't just about a mythical valley. The River Keeper is the ECB. The merchants are your banks. And the river's flow is the supply of money that dictates the cost of your mortgage, the interest on your savings, and the health of the entire economy.

When you read that the ECB has "hiked rates," it means the River Keeper is making all three taps more expensive to use. They are trying to gently reduce the river's flow to prevent a flood of inflation.

When you understand this story of the three taps, you understand the heart of European monetary policy.

This is all for today. Now, you can go tell this story to your children and make them understand how their money is part of a great, flowing river, and why sometimes that river needs a gentle hand to guide it for the good of everyone in the valley.

For regular readers, you'll know my posts are typically structured along three axes:

• History

• Data Science - Machine learning

• Finance/Economics

But this very year 2025 a new axis that emerged by itself:

• My own essays

I don’t know how to describe them but they are more personal views and reflections about our society. As I say they are the result of my views formed after talking with people, they are far from an objective truth. But, dear reader, it should make you think.

My Process: From Idea to (Unfnished) Drafts

In the previous paragraph I wrote:

Note I use the word emerged. Like if it came from deep down my brain until arriving to the screen. Without plan, just crawling all the way up until reaching the surface.

So I wanted to spend some time here thinking about why it happened.

Remember my goal with this newsletter is not to make money or get views, but to document cool things I see through my day-to-day life. Yes, like a diary. So, basically I do my normal life and when I consider something it’s worth to write about I start a draft about it. Given how different we all are and how different contexts we are in, you will be surprised if you start just jotting down for fun interesting things about your day. You will see how life is far from being dull. There are plenty of rabbit holes all around us; you just need to pay attention. And as it happens writing helps a lot. I already have an article about this and other to follow:

OK, going back to my modus operandi. Initially every draft was equal a post and I didn’t have too much backlog to review. If I have notes I would develop them far because there weren’t so many.

Right now, the number of unfinished drafts is roughly equal to the number of published posts. I don't see as a failure but as evidence of an acquired skill: the ability to read, process and identify an idea worth pursuing. The challenge comes later.

Which it’s not a trivial thing. However, when you start taking notes, you will see that there are too many interesting things in this universe and moreover, you are one of them. Last sentemce illustrates the consequence of my current state. As I explained the number of drafts I’ll have will explode as time advances.

It is a simple physical reality that I don’t have enough time to finish them faster than new ideas appear (right now). But … is this really true? How many times have you heard or said the previous sentence?

In my case, I deeply think it’s wrong. My issue is laziness. I’ll explain you why.

You might think the solution is to force a schedule. I tried that at the beginning, but it felt hollow. My solution has been a flexible deadline: publish within two weeks, but honor the creative sprees when they come. This tells me the issue isn't a lack of discipline, but something else...

It’s a daring thing to say given that I am writing for pleasure. No? Well… before I explained how I come with the ideas and what i do with them. Now the key is what happens after. An idea can be a title, a picture, some paragraph read online or some quote.

And then you need to develop it. You may be tempted to think that laziness becomes the strongest here. But you will be wrong (at least in my case).

Honestly, for me, writing feels like the tides. I might write this entire article in two hours one morning, and then for a whole week not find the inner peace to string two sentences together. I know I'm not alone in this feeling.

For me, the problem is the final touch. The last reads. Maybe the last big 20 modifications. There is a world between unconnected ideas, and an article.

Is it too long? Is it boring? Are there blatant coherence problems? is it readable?

Interesting to see that the issue is finishing. Not so much starting to write or developing ideas, but terminating them. Maybe this have a projection into life also.

The human connection discovery

One thing that genuinely surprised me this year was realizing there are more people reaching out to talk about my pieces than I have subscribers.

At first, I thought this was odd. Shouldn't the most engaged readers be the ones who subscribe? But then I understood something deeper: behind every visualization stat, there is a human.

These conversations happen in unexpected places - someone mentions an article at a birthday, another sends a message on WhatsApp, a colleague references something I wrote months ago. The newsletter format captures subscribers, but the ideas travel much further than any dashboard can track.

And the cool part is that they are totally unexpected!

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Future Improvments

One idea I had since the beggining was to give the trasncription to some TTS model to generate an audio/podcast of the article.

I think it’s a really cool idea not only for those that prefer to listen over read but also for those who may have vision impairment.

Expect this to be implemented soon…

This wraps up the article, where I have shared with you my journey and what I have learnt in this first year. It is a rather short article (around 5 mins to read) so its perfect for summer time. As always, thank you for reading!

See you next time.

In the world of data science, we have a standard toolkit. For categorical features, we often reach for One-Hot Encoding (OHE). For dimensionality reduction, we almost always start with Principal Component Analysis (PCA).

It seems natural to combine them. You one-hot encode your “city” or “product_category” feature, and then you run PCA on the resulting sparse matrix to reduce its dimensions. But what is PCA actually finding when you do this? The answer is both elegant and counter-intuitive, and understanding it is key to avoiding common interpretation pitfalls.

The Simple Case of Two Categories

Let's start with the simplest possible scenario: a single feature with only two categories, A and B. One-Hot Encoding transforms this into two columns. If the category is 'A', the vector is [1, 0]. If it's B, the vector is [0, 1].

Right away, we see a crucial fact: these two columns are perfectly redundant. Because the categories are mutually exclusive, the value of the B column is always 1 minus the value of the A column. This means that while we have two dimensions, there is only one degree of freedom.

This is the core idea of OHE, which we covered in detail last week. Feel free to check it out for a refresher:

What happens when we run PCA?

The plots above tell the whole story:

1. Explained Variance (Top-Left): The first principal component (PC1) captures 100% of the variance. The second (PC2) captures zero. PCA immediately identifies the redundancy.

2. Data Points & PC1 Direction (Top-Right): In the OHE space, our data can only exist at two points: (1, 0) and (0, 1). PCA finds the single straight line that connects these two points and explains all the variance. This line is the first principal component.

3. PC1 Loadings (Bottom-Middle): The loadings for PC1 are [0.707, -0.707]. This shows that PC1 represents a perfect opposition between feature A and feature B. Moving along this component means decreasing the A value and increasing the B value.

The takeaway is clear: in the simplest case, PCA doesn't discover a hidden pattern; it simply rediscovers the fundamental constraint of the encoding itself. No surprises here.

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Beyond Two Categories: Probabilities vs. Eigenvalues

This is cool, but what happens with three categories? Or ten? As we increase the number of categories, k, a fascinating relationship emerges between the eigenvalues of the PCA and the underlying probabilities of the categories.

In short: the eigenvalues are not random. They are deeply connected to how frequently each category appears.

The plots above show this beautifully. For a 3-category feature:

• Uniform Probabilities: When each category has an equal probability (0.333), the two non-zero eigenvalues are also equal.

• Non-Uniform Probabilities: As soon as we make the probabilities unequal, the eigenvalues also become unequal, but they don't match the probabilities directly.

This relationship is governed by the covariance matrix of the OHE data. There are key properties that always hold:

1. Sum of eigenvalues = trace(Cov) = Σ pᵢ(1-pᵢ)

2. One eigenvalue is always zero due to the rank deficiency.

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The Special Symmetry of the Uniform Distribution

The case of a uniform distribution (where all categories are equally likely) is particularly elegant. This is the state of maximum entropy—maximum uncertainty. In this state, the covariance matrix becomes perfectly symmetric.

This symmetry leads to a clean, predictable result: for k categories, you get k-1 non-zero eigenvalues that are all exactly equal to 1/k.

A Quick Look at the Geometry

Geometrically, the one-hot encoded vectors form the vertices of a shape called a simplex. For three categories, our data lives at the corners of a triangle in 3D space: (1,0,0), (0,1,0), and (0,0,1).

All the data lies on the 2D plane that connects these three points. PCA simply finds the axes that best describe the spread of data on this plane, and the eigenvalues represent the amount of variance along those axes.

What Happens When We Combine Features?

We've established how PCA behaves on a single OHE feature. But the real world is messy. What happens when we run PCA on a dataset with multiple OHE features?

The key thing to remember is that PCA is a global method. It doesn't know that some columns relate to one feature and others to another. It simply sees a point cloud and searches for the directions of maximum variance. This leads to a crucial question: which feature's structure will PCA prioritize?

This leads us to a powerful generalization, but with a critical nuance:

PCA prioritizes the directions of maximum variance one by one. The feature with the highest Total Variance Contribution will have a larger footprint on the PCA, but not necessarily the single largest eigenvalue.

The battle for dominance is fought component by component. A feature with its variance concentrated in one dimension can easily produce the single largest eigenvalue, even if its total variance is lower than another feature's. This is perfectly illustrated in the chart below.

This effect isn't just limited to a battle between two and three categories. In fact, the dominance of the balanced, low-cardinality feature is a general rule. A balanced binary feature's single eigenvalue will always be 0.5. A balanced 4-category feature will produce three eigenvalues of 0.25 each. A balanced 10-category feature produces nine eigenvalues of 0.1 each. None of these individual components can ever overpower the one from the simple binary feature. This creates a predictable hierarchy where the most balanced features with the fewest categories will almost always produce the largest individual eigenvalues.

This leads us to the most critical takeaway of this entire analysis. Running PCA on a dataset of one-hot encoded features creates a predictable artifact. It systematically elevates features to the top of the importance list based on their statistical properties—balance and low cardinality—rather than their actual predictive power. Imagine you have a highly predictive but heavily skewed feature like zip_code (with thousands of categories) and a less predictive but perfectly balanced binary feature like gender. PCA will invariably flag the component representing gender as more important because it explains more variance. If you blindly select the top principal components for a downstream model, you risk building a model on features that are simply "loud" in the variance space, while ignoring the ones that are quiet but carry the real signal.

So, Is PCA on OHE a Good Idea?

After this journey, we can give a clear verdict. The answer is nuanced but direct:

PCA on OHE is a powerful exploratory tool but a dangerous automated step.

In fact, it really depends how do you use it. For Exploratory Data Analysis (EDA). Running PCA may quickly reveal some properties of your data.
However, as a pre-processing step for modeling, to reduce dimensionality, will be risky because PCA is selecting for variance, not predictive power. You are more likely to select for simple, balanced features than for complex, predictive ones.

This analysis shows that PCA on OHE is a technique with a surprising amount of hidden depth and potential pitfalls if used without care.

I'd love to hear your thoughts. Have you run into this artifact in your own work? What are your go-to methods for handling high-cardinality categorical features?

Thanks for following this deep dive, and I'll see you next week. See you next week!

A (very) simple start

Let’s start with a simple, relatable challenge. Imagine you're building a model to predict which movie your family should watch next on Netflix. You decide to use a key feature: the movie's genre.1

Your family's preferences are diverse:

• Dad likes Action.

• Mom likes Thrillers.

• You like Sci-fi movies.

How do you feed this information to a model? This is a classic data science problem. Your data—the genre—is categorical, not numerical. Unfortunately, most machine learning models are built on mathematics; they understand numbers, not words. They can't multiply “Action” by a coefficient or find the average of “Thriller” and “Sci-fi”.

We have to convert these categories into numbers. While many options exist, one of the most common and robust methods is one-hot encoding. Let’s not worry about the alternatives for now; I want to cement understanding in this technique for now.

One-hot encoding takes a single column with “N” different categories and creates “N” new columns—one for each unique category. For any given movie, you place a 1 in the column corresponding to its genre and 0s in all the others.

It looks like this:

So, an “Action” movie is no longer represented by a word, but by the vector [1, 0, 0,]. A “Sci-fi” movie becomes [0, 0, 1]. Each genre now has its own unique numerical identity.

So, let's visualize this. The one-hot encoded vectors are:

• Action: [1, 0, 0]

• Thriller: [0, 1, 0]

• Sci-Fi: [0, 0, 1]

Think of these as coordinates (x, y, z) in a 3D space. The first dimension is our “Is_Action” axis, the second is our “Is_Thriller” axis, and the third is our “Is_SciFi” axis.

What happens when we plot these points?

Each genre sits perfectly on one of the axes, exactly one unit away from the origin (the point [0, 0, 0]). They are at right angles (90°) to each other. In geometric terms, these vectors are orthogonal. And, put simply, they form a triangle in 3D.

It's the mathematical guarantee that the model sees “Action” and “Thriller” as completely independent things. Moving along the “Action” axis doesn't change your position on the “Thriller” axis at all. This solves the problem we saw with simple integer encoding, where categories had false relationships.

Before we fully embrace that 3D triangle, let's make it even simpler. What if we only had two categories? Let's say, Action and Sci-Fi.

Our vectors would be:

• Action: [1, 0]

• Sci-Fi: [0, 1]

This is a simple 2D plot. The “Is_Action” feature becomes our x-axis, and “Is_SciFi” becomes our y-axis. When we plot these points, we see the same fundamental pattern: each category sits perfectly on an axis, one unit away from the origin [0, 0].

Here’s a plot of that 2D space.

The Simplex: A Hidden Shape

Now, let's step back and look at what we've created.

• In the 2-category case, we made a 2D space, but our points [1, 0] and [0, 1] simply form the endpoints of a 1D line segment.

• In the 3-category case, we made a 3D space, but our points [1, 0, 0], [0, 1, 0], and [0, 0, 1] form the corners of a flat, 2D equilateral triangle.

This shape has a name: a simplex.

A simplex is the most basic geometric shape that can exist in any given dimension.

• A point is a 0-simplex.

• A line segment (connecting 2 points) is a 1-simplex.

• A triangle (connecting 3 points) is a 2-simplex.

• A tetrahedron (connecting 4 points) is a 3-simplex.

The one-hot encoding of k categories places our data perfectly at the vertices of a (k-1)-simplex.

This is a critical insight because it tells us that our high-dimensional space is mostly empty. Our data is confined not only to this very specific surface, but also to its corners.

Think about the first sentence of this post again. Imagine you live in this space. Now you will be at the same distance of every other point.

Further characterization of this space

Beyond the elegant geometry, this one-hot encoded space has fascinating statistical properties. Let's dig in.

Recall that each encoded vector ([1, 0, 0], [0, 1, 0], etc.) represents a single observation. If we consider the feature across our entire dataset, each column becomes a random variable.

For our movie example, the "Is_Action" column is a random variable X_action that takes the value 1 with some probability p_action (the frequency of action movies in the dataset) and 0 otherwise. This is a classic Bernoulli random variable.

• Expectation: The expected value (or mean) of this variable is simply its probability:

• Variance: As you correctly pointed out, its variance is

  . This measures the "spread" of that single category.

Now, what happens when we consider two categories together, like X_action and X_thriller? We look at their covariance.

The key is the first term in the right. The product X_action * X_thriller is 1 only if a movie is both an action movie and a thriller. By the definition of one-hot encoding, this is impossible. The product is always 0. Therefore, E[X_action * X_thriller] = 0.

This gives us the simple and powerful result for the covariance between any two categories i and j:

This negative covariance is the statistical proof of what we know intuitively: the categories are mutually exclusive. If one is present, the others cannot be.

The Check: Sum of Variances vs. Variance of the Sum

Now, let's do a cool check. I want to compute the toltal variance of this feature. When people talk about "total variance," they can mean two different things. Let's compute both and see why the negative correlation we just found is so important.

1. The Sum of the Variances:

This is the standard definition of total variance in feature analysis and is what, for example, PCA seeks to maximize. It's the sum of the variances of each column, one by one.

As we discovered, this simplifies beautifully:

This is the Gini Impurity of our categorical feature. It measures the total spread of our data points across the corners of the simplex.

2. The Variance of the Sum:

Now, let's compute the variance of the sum of the columns.

Intuitively, we know that for any movie, exactly one of these columns is 1 and the rest are 0. This means their sum is always 1. The variance of a constant value is, by definition, zero.

Why the Difference? We've proven that

The reason is the negative covariance.

Adding the mixtures

In the uniform world we've explored so far, we assumed our family had one member for each movie genre. But reality is rarely so balanced.

What happens when we create a bigger family of 100 members, where the preferences are skewed? Let's say it's predominantly composed of dads who love Action movies. Our new composition is:

• Action (Dad): 98% (p_action = 0.98)

• Thriller (Mom): 1% (p_thriller = 0.01)

• Sci-Fi (Me): 1% (p_scifi = 0.01)

How does this change things? Let's revisit our two perspectives: the geometry and the statistics.

The Geometry: Stable as a Rock

The fundamental geometry of the space remains intact. The vertices of our triangle are still fixed at [1, 0, 0], [0, 1, 0], and [0, 0, 1]. The space itself doesn't care about the distribution of our data.

What has changed is the “center of mass” of our data. Before, our data was scattered equally. Now, 98% of our data points are piled up on the “Action” vertex. Imagine the points on the plot are now “weighted”. The point representing Action is now incredibly “heavy”, while the others are very light.

The Statistical Characterization: A Drop in Uncertainty

This is where something cool happens. Our new mixture is much less uncertain! If you were to randomly pick a family member, you'd be overwhelmingly confident that they prefer Action movies.

This powerful intuition should be perfectly reflected in our total variance formula (the Gini Impurity). Let's check the math.

Case 1: The Balanced Mixture (1/3, 1/3, 1/3)

Total Variance = 1 - [ (1/3)² + (1/3)² + (1/3)² ]

= 1 - [ 1/9 + 1/9 + 1/9 ]

= 1 - 3/9 = 1 - 1/3 = 0.667

Case 2: The Imbalanced Mixture (0.98, 0.01, 0.01)

Total Variance = 1 - [ 0.98² + 0.01² + 0.01² ]

= 1 - [ 0.9604 + 0.0001 + 0.0001 ]

= 1 - 0.9606 = 0.0394

The result is stunning. The total variance has plummeted from 0.667 to just 0.0394. Our math has validated our intuition: a more predictable, less uncertain system has far less variance. The "spread" of our data is now tiny because it's all clustered around one point.

Visualizing Variance and Uncertainty

We can generalize this with a plot. Let's imagine a simple 2-category case (say, “Action” and “Not Action”). We can plot the Total Variance as the probability of “Action” goes from 0% to 100%.

As you can see, the variance is at its absolute maximum when there is maximum uncertainty (p=0.5), where either outcome is equally likely. As our mixture becomes more skewed and predictable in either direction, the total variance collapses towards zero.

This check brilliantly illustrates the structure of our data. We have individual components that have variance (the Gini Impurity), but they are locked together in a rigid system.

This post arrives to the end here. But it’s the perfect setup for our next post, where we'll use PCA to find the most meaningful directions of variance within this rigid system. And maybe realise that’s not the right thing to do…

How did the monks of Mount Athos, sworn to a life of peace and prayer, survive the ravages of pirates, the fall of Constantinople, and even the shadow of Nazism?

The answer may lie in a remarkable modus vivendi—a unique blend of unshakable faith and shrewd political pragmatism.

A Place Beyond the Map

In the northeastern corner of Greece, a rugged finger of land juts into the Aegean Sea. It is part of the European Union, yet it lies outside the Schengen Area's border-free travel. You cannot simply arrive. This is Mount Athos, known to Greeks as Agios Oros (the Holy Mountain), a self-governing monastic republic where entry is granted not by a passport stamp, but by a special permit1, and where the rules of the outside world begin to fade the moment you step ashore.

But its uniqueness is written not just in modern treaties, but in ancient stone and legend. Long before the first monk arrived, mythology claimed this land was forged in a battle of titans. The story goes that during the Gigantomachy, the epic war between the gods and giants, a titan named Athos hurled a massive mountain at the sea god Poseidon. The rock landed in the Aegean, creating the peninsula that still bears his name. 2

A Masterclass in Survival

The story of Christian Athos begins not with a charter, but with a miracle. Tradition holds that the Virgin Mary, blown off course on a journey to Cyprus, landed on its shores and, struck by its beauty, claimed it as her 'garden.' This divine consecration established Athos as the preeminent holy land of Orthodoxy. But spiritual authority alone was not enough. In 963 AD, the monk Athanasius the Athonite established the first great monastery, securing an imperial charter from the Byzantine Emperor in Constantinople. This was the blueprint for Athonite survival: trade spiritual legitimacy and unwavering prayer for imperial protection and political autonomy. It was a deal they would master.

This 'deal' was first brutally tested in the early 14th century. The Byzantine Empire, fatally weakened by the Fourth Crusade, could no longer guarantee its protection. Into this power vacuum marched the Catalan Company, a ruthless band of mercenaries seeking revenge on the Empire. For two years, they turned the 'Garden of the Mother of God' into their personal fiefdom. They sacked monasteries, burned priceless manuscripts, and slaughtered monks who refused to submit. The Catalan Vengeance was more than an attack; it was a lesson carved in blood and stone. It proved that faith needed high walls, and it solidified the Athonite identity of monasteries as spiritual fortresses, forever wary of the outside world.

When Constantinople finally fell to the Ottoman Turks in 1453, the monks did not flee. They pivoted. Displaying stunning political acumen, they immediately sent envoys to Sultan Mehmed II. Recognizing their spiritual importance (and their value as a source of tax revenue), the Sultan re-affirmed their autonomy, becoming their new protector. They had swapped a Christian Emperor for a Muslim Sultan without missing a beat.

Perhaps the most surreal chapter of this story unfolded during World War II. As Nazi forces occupied Greece, the Athonite modus vivendi faced its ultimate test. Hitler, reportedly fascinated by the pure monastic state and its ancient heritage, declared Mount Athos under his personal protection. In a chillingly pragmatic gesture of diplomacy, the Holy Council of monks bestowed upon the Führer the ancient Byzantine title of High Protector of the Holy Mountain, placing him in the same lineage as the emperors who had once shielded them. It was a move that ensured their gates remained closed and their way of life intact, even as the world burned around them.

But, Why So Special?

All of this history—the charters, the raids, the chilling diplomacy—has served to protect one thing: a way of life completely alien to the modern world. So what is the modus vivendi that these monks guard so fiercely?

First, time itself is different here. Most monasteries still follow Byzantine time, where the day begins anew at sunset, untethered from the globalized 24-hour clock. Life is not organized around productivity, but around prayer. The rhythm is set not by a smartphone alarm, but by the sound of the semantron—a monk striking a wooden plank with a mallet—calling the brethren to services that begin in the dead of night.

Between these services, monks perform their diakonima, or “obedience”. One might tend the monastery’s vast vegetable gardens, another might paint icons in a centuries-old style, while another bakes bread or hosts pilgrims. This is not work as we know it; it is a form of active prayer, a duty performed for the community.

Central to this protected world is its most famous and unyielding rule: the avaton. This is a strict ban on the entry of women, established by imperial charter over a thousand years ago in dedication to the Virgin Mary, the sole female presence permitted. The rule is interpreted so absolutely that it extends even to female domestic animals. For centuries, no cows, goats, or hens were allowed. The only exceptions today are cats, valued for their pest control, and chickens, whose egg yolks are an essential ingredient for the tempera used in icon painting. For the monks, this isn't misogyny but a spiritual tool—a way to preserve their celibacy and focus the mind entirely on the soul's path to God.

This entire society, a federation of 20 ruling monasteries, governs itself from a small capital, Karyes. It is a world defined by a profound quiet, where every action is aimed at a single, ultimate goal: theosis, the mystical union of the soul with God.

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Well, what do you think about Mont Athos? Agios Oros is a fascinating crossroad of time and culture. One of the few places where time flows at a different speed than the rest of the world. The key is that it has not been secluded from history in a remote island or in the middle of the jungle. No, it has been in the middle of the Aegean Sea, some kilometers away from the important city of Thesaloniki.

And despite this, they have managed during 1000 years to mantain their identity and ways of life.

The phrase hit me hard because it explains the breakdown of a story many of us were told. Remember the blueprint? You start your career full of ambition. You work hard to prove yourself and, most importantly, to learn. By mid-career, you face a trade-off: play politics to climb higher or find contentment where you are, likely with a family and responsibilities beyond your own. The final act was supposed to be a slow, gentle coast toward retirement.

That entire map feels like a historical artifact now. For my generation, the promise that hard work pays off feels like a lie. With the future more uncertain than ever, the return on investment for sheer effort has plummeted. Why sacrifice when the rewards are so abstract?

This isn't just a feeling; I see it playing out everywhere—from our workplaces and our media, all the way to our politicians. Who cares about lying if the news cycle will erase it by tomorrow?

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Think about the typical office job. Beyond your direct manager, who really cares about the quality of your work? In many large companies, the system is so bloated that a high-performing team can easily mask an individual who does next to nothing. The corporate effort required to identify and fire these people is often greater than the damage they cause by staying.

It leads to a toxic question: who is more damaging to a company?

1. A non-performing employee who everyone knows is non-performing?

2. A non-performing employee who no one notices at all?

The second one, of course. They are a ghost in the machine, a symptom of a system so large and impersonal that individual contribution becomes meaningless. This is the "Who Cares?" era in practice: a place where you can underperform without consequence, breeding a quiet culture of apathy. We end up with a group of people who simply don't care, because the system doesn't give them a reason to.

But this isn't just about lazy colleagues. It’s a symptom of a much deeper cultural rot.

“Every augmentation is also an amputation.”

I read that somewhere, and it perfectly captures our technological paradox. Progress often means making things easier, but ease can lead to atrophy.

• Spelling a word correctly is harder than letting autocorrect do it.

• Cooking a meal takes more effort than microwaving a pre-made one.

• Playing outside requires more energy than winning a video game.

With AI now generating images, text, and video in an instant, what is the value of human creation itself? We are constantly outsourcing our skills, and in doing so, we risk amputating the very parts of us that learn, strive, and grow.

This shift is reflected in who we celebrate. Now, people mostly consume content with reality TV stars and social media influencers as their primary guides—figures famous for being famous. When the culture celebrates manufactured hype over genuine skill, is it any wonder that diligence and sacrifice are diminishing when our culture monetizes pure exhibitionism?

It’s emblematic of a mindset where feelings are the primary driver for truth. "Excellence" gets redefined as anything that makes you feel good in the moment. In such a world, of course apathy thrives. It’s easy. It’s comfortable. It asks nothing of you.

Some might blame it on strong European welfare states, postmodernism, or what one writer called "hyperscale bureaucracy"—systems so vast they strip people of agency, authority, and creativity.

Whatever the cause, the diagnosis is clear. We are losing our will to try.

The other day I went to a boulangerie in Paris. A child 8 or 10 years old was talking with her dad and the owner of the shop about what will she want to do in the future. She said: “office job”. It makes me wonder what that child has observed about the world. Maybe she's seen that the creative, entrepreneurial paths are unstable, risky, unrewarding. Maybe she's absorbed the message that security trumps everything else

So, what's the solution? Is there one? The author of the initial article believes the antidote is a personal rebellion that starts with two words: Start caring.

He argues we must care about the email we’re writing, the meal we’re cooking, the conversation we’re having. To reclaim our own standards from the world's indifference.

I don't disagree, but I believe it's missing a key component. Caring isn't just a feeling; it's an action.

For me, the true antidote is agency.

It’s the decision to create something, no matter what. To try to build something for yourself, from scratch. It’s channeling that care into something you control. The possibilities are infinite. It’s how you become who you truly want to be.

If this post resonated with you, the best way you can support my work is by sharing it with someone who might need to read it. Thank you!

But two of Napoleon's most audacious marshals, Jean Lannes and Joachim Murat, had a rather different plan. This is the story of one of history's most brilliant and brazen bluffs.

Context

Just months earlier, in the autumn of 1805, Emperor Napoleon was poised to fulfill his most fervent desire: the invasion of England. He had amassed a formidable army near Calais, the "Armée des côtes de l'Océan," anxiously awaiting the naval transports that would carry them across the Channel.

Spoiler: those transports never came. Admiral Nelson's decisive victory at the Battle of Trafalgar obliterated the combined Franco-Spanish fleet, shattering Napoleon's English dream into a million pieces.

Ever the opportunist, Napoleon didn't let his magnificent army go to waste. While he was preoccupied with England, Russia and Austria, sensing an opening, had formed the Third Coalition and launched an attack on France's allies in Bavaria. With his invasion plans scuttled, Napoleon, never one to reject a good battle, swiftly pivoted. He marched his army east to confront this new threat, thus beginning the Ulm Campaign and the wider War of the Third Coalition.

The Race to Tabor Bridge

After a brilliant series of maneuvers, Napoleon had encircled and forced the surrender of a large Austrian army at Ulm. The remaining Austrians, and their Russian allies under General Kutuzov, could only retreat, hoping to regroup further east. To slow the French pursuit, they systematically destroyed every bridge spanning the Danube as they fell back. Every single one.

Well, almost every one.

They left the Tabor Bridge standing, but it was a deadly trap. It was heavily mined, bristling with artillery, and defended by a significant force of infantry and cavalry under the command of Prince Auersperg von Mautern. His orders were explicit: blow the bridge the instant the French appeared.

The stakes could not have been higher. For Napoleon to continue his pursuit and bring the allies to a decisive battle, he had to cross the Danube quickly. The Tabor Bridge was the key.

Enter the Performers

On the misty morning of November 13th, 1805, two of Napoleon's most daring and flamboyant commanders, Marshal Jean Lannes and Marshal Joachim Murat (Napoleon's own brother-in-law, famous for his cavalry charges and extravagant uniforms), decided on a plan so audacious it bordered on madness.

Instead of launching a bloody assault, these two theatrical performers simply strolled towards the Austrian-held Tabor Bridge, accompanied by only a few staff officers, as if they owned the world. No formations, no drawn swords, just an air of confident nonchalance.

As bewildered Austrian sentries leveled their muskets, demanding they halt, Lannes and Murat laughed, waved dismissively, and loudly proclaimed their delight at the "just concluded" armistice and the wonderful peace treaty that had apparently been signed between France and Austria. They expressed mock surprise that the guards hadn't heard the good news.

Still chattering amiably about the end of hostilities, they walked onto the bridge itself. Reaching the far side, still seemingly without a care in the world, they politely asked to speak with the commander, Prince Auersperg, wondering aloud if he had perhaps already departed for the peace signing ceremony.

While a messenger was dispatched to fetch the Prince, the two marshals engaged the Austrian officers and guards in casual, friendly conversation. They complimented their discipline, inquired about their families, and all the while, hidden from Auersperg's main force by the bridge's structure and the morning mist, French grenadiers under General Oudinot began to quietly, almost casually, stroll onto the bridge behind them, a few at a time.

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The Moment of Truth (and a Pipe)

The tension was palpable. One Austrian artillery sergeant, his instincts screaming that this "armistice" was far too convenient, decided he wasn't buying it. He grabbed a lit match and moved to ignite the fuses that would blow the bridge sky-high.

This was the critical moment. But Marshal Lannes, a man renowned for his fiery courage in battle, showed a different kind of nerve. He calmly walked over to the sergeant, snatched the match from his hand, and extinguished it. He then proceeded to sternly berate the austrian officer for his "hasty" action and for attempting to destroy "public property" during a time of supposed peace!

The Masterclass in Manipulation

When Prince Auersperg finally arrived, flustered and unsure what to make of the situation, he was completely taken in. Here were two of Napoleon's most celebrated marshals, treating him with utmost courtesy and respect, discussing the supposed details of this wonderful peace agreement that had brought an end to all the unpleasantness.

The suspicious Austrian sergeant, still fuming, tried to protest and warn his commander. This was Murat's cue. He flew into a theatrical rage, loudly berating Auersperg for the "shocking indiscipline" of his soldiers, accusing the sergeant of attempting to sabotage the peace and jeopardize the armistice with his "unauthorized actions." How could an underling be allowed to mouth off and potentially restart a war that had just ended?

The psychology was masterful. Instead of defending his alert and correct sergeant, Prince Auersperg, embarrassed by the apparent lack of discipline in front of these distinguished French marshals and terrified of being responsible for breaking a supposed peace, was browbeaten into submission. He ordered the sergeant arrested and, incredibly, turned control of the bridge over to the French "to ensure no further incidents" until the peace was formally announced.

The very man who might have saved the bridge, and potentially altered the course of the campaign, was silenced by his own commander's gullibility and the French marshals' manipulative genius.

A Bridge Won, A Campaign Advanced

With the Austrians confused and neutralized, Oudinot's French grenadiers swarmed across the Tabor Bridge, quickly disarming the remaining explosives and securing the vital crossing. The bluff had worked beyond Lannes's and Murat's wildest dreams.

The capture of the Tabor Bridge intact was a strategic coup of immense importance. It allowed Napoleon's army to pour across the Danube unimpeded, continue their relentless pursuit of Kutuzov's Russians and the remaining Austrians, and ultimately corner them for the decisive engagement Napoleon craved. Just a few weeks later, on December 2nd, 1805, Napoleon would achieve his most legendary victory at the Battle of Austerlitz, a triumph made possible, in no small part, by this audacious bluff.

As for Prince Auersperg? He was subsequently court-martialed and disgraced for his catastrophic blunder. Napoleon himself, upon hearing of the exploit, was reportedly amused and impressed, though likely also slightly exasperated by the near-insane risks his marshals were willing to take.

What do you think? Was it Lannes's cool-headed intervention or Murat's dramatic performance that truly sealed the deal? Share your thoughts in the comments below!

The recent blackouts in Spain and Portugal were a stark reminder of just how much we rely on electricity. And with the European Parliament already warning citizens to prepare a survival kit ... well, I used to think that was a bit extreme, maybe even a joke.

Not anymore.

Here at Crossroads, we often look at historic events or concepts that are pivotal accross disciplines. Survival may be the definitive 'crossroad' mixing all of your life knowledge in a (hopefully) short period.

This post is about what would consist a basic survival kit and why so.

Let’s warm up with a quick poll.

The event

Of course, not all crisis situations are the same. While the preparedness needed for war or a major flood differs greatly, a widespread electricity blackout presents a surprisingly vulnerable point for our modern, dependent lives.

Focusing on the blackout scenario allows us to identify essential items that can help in this specific, and perhaps increasingly likely, disruption.

The First Hours

So suddenly, electricity disappears. That means no water for many (if your pump is electric), communications networks struggle or fail, and accessing money becomes impossible as payment systems crash1.

The first hours after a widespread outage can be the most critical and chaotic. This is a time when the noise-to-signal ratio is at its highest. Rumors fly, official information is scarce, and it's hard to know what's truly happening or what to do.

We saw a preview of this kind of reaction during the early days of the pandemic, remember? In Spain, like elsewhere, people instinctively rushed the supermarkets, leading to those photos of empty shelves where water, food, and yes, even toilet paper, used to be. That panic surge happens precisely because people aren't prepared and don't know what else to do.

That instinctual rush highlights a critical point: to truly optimize your response during an emergency like a blackout, you need to bypass that initial panic and have essential supplies already on hand. Having your own store of non-perishable food is key, but as I mentioned earlier, the single biggest issue in a widespread power cut will likely be water – without electricity, many people can't access their usual supply.

Beyond basic supplies, the second instinct kicks in: "What do we do? What's happening?" Since major blackouts aren't a regular occurrence for most of us, we're simply not mentally prepared for the disruption, and our natural inclination is to turn to reliable information sources. But when the internet is down, cell towers are overloaded or without power, and even landlines might be affected, how do you cut through that intense chaos and actually get the good info?

This is where the first truly essential item in your survival kit comes into play, something easily overlooked in our hyper-connected world: an analog radio.

Why a simple radio? Because it operates on broadcast signals that are independent of the grid and cellular networks. A sturdy, battery-powered or hand-crank radio (ideally one that can tune into emergency broadcast frequencies if available in your area) is your lifeline to the outside world when everything else goes silent. It's your way of understanding the scope of the situation, getting official directives, and knowing what areas might be affected or where help is available.

And of course, a radio is useless without power. Which brings us to the next non-negotiable item: a substantial supply of extra batteries specifically sized for your radio.

But having those batteries brings a new dimension of capability to your kit. Access to this portable energy source means you can power other essential tools you'll desperately need in the dark. The most obvious, and arguably the next critical item after your radio and its power source, is a reliable flashlight or, even better, a headlamp.

When the grid goes down at night (or plunges buildings into darkness during the day), you need immediate, portable light to navigate safely, find supplies, or signal for help. A headlamp is particularly useful as it leaves your hands free for carrying things or attending to tasks. And just like the radio, it's only useful if you have those spare batteries ready to go when the first set dies.

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Hard Mode

OK. So far, we've focused on the essential tools for getting information and seeing in the dark – critical needs for navigating the immediate chaos of a power outage, especially if it's a shorter one that's resolved relatively quickly. But what if the situation isn't a "simple case" of the lights flicking back on after a few hours? What if the outage lasts longer, or is part of a larger, more disruptive event?

Welcome to Hard Mode.

In this "hard mode" scenario, the challenges escalate significantly. Your initial reserves dwindle. Basic needs like sustained access to clean water, reliable food, sanitation, and maintaining health become paramount. The focus shifts from simply enduring the first hours to surviving and maintaining well-being over days, maybe even longer.

At this point, trying to predict the exact sequence of events becomes incredibly difficult, verging on impossible. So please don't see this section as a prediction, but rather as a cautionary tale – exploring the potential consequences of prolonged system failure and what you might need to face them.

One unsettling reality in such a scenario is that cities, ironically, could become the worst places to be. Their high density of people combined with a total reliance on external supply chains for food, water, and energy creates a dangerous combination when those systems fail. Natural resources within the city are scarce or non-existent.

As the threshold passes from hours to days, societal codes can begin to fray under the pressure of scarcity and uncertainty. The instinct for survival becomes dominant. While hopefully order would be maintained, prolonged disruption significantly increases the potential for social instability, especially in heavily populated areas. Authorities may need to take extraordinary measures to maintain control.

This shift in dynamic means your survival kit needs to address more than just immediate information and light. It needs to provide sustained self-sufficiency when external help is unavailable or overwhelmed, and when navigating your environment becomes more complex and potentially riskier.

So, what essential items prepare you for this kind of prolonged "Hard Mode" scenario? The focus now turns to the fundamental pillars of survival: reliable sources of water and food, robust first aid and sanitation, and potentially basic shelter and security.

Water: The Ultimate Priority

While having some bottled water stored is essential for the first hours, relying solely on pre-bottled water for days or weeks is often impractical due to storage space and weight. When the taps are dry or the water supply is compromised, finding and purifying water becomes the single most critical task for long-term survival. You can only last a few days without it.

This is why, in Hard Mode, a reliable water filter or purification method is non-negotiable. This could be a high-quality portable filter. Knowing how to safely collect and treat water is a skill, and having the right tool makes it possible to access a potentially life-saving resource that clean, running water in the city is now denying you.2

Sustenance: Food for Days

Remember that supermarket rush for non-perishables we talked about? In Hard Mode, you need enough food to avoid having to rely on potentially empty stores or competing with others. We touched on non-perishable food for the first hours, but for a prolonged event, you need a sufficient quantity – think a minimum of three days' supply per person, ideally more if possible.

Focus on calorie-dense, easy-to-prepare items that don't require refrigeration or much water for cooking. Canned goods (with that all-important manual can opener!), energy bars, dried fruits, nuts, and ready-to-eat meals are good candidates.

Staying Healthy: First Aid & Hygiene

In a prolonged crisis, minor injuries can easily become infected without proper care, and sanitation systems failing significantly increases the risk of illness spreading. Staying healthy becomes an active survival task.

A comprehensive first aid kit is absolutely vital. This isn't just for dramatic injuries, but for cuts, burns, sprains, and general health issues. Your kit should include bandages, sterile gauze, medical tape, antiseptic wipes, pain relievers, anti-diarrhea medication, any necessary prescription medications (with a good supply), and tools like scissors and tweezers.

Beyond the first aid kit, don't underestimate the importance of basic hygiene. Items like hand sanitizer, wet wipes, garbage bags, and perhaps even a portable toilet solution become critical for preventing disease when normal facilities aren't available.

Shelter, Warmth, and Practicality

Often forgotten, maintaining body temperature will be key. If your home loses heat in cold weather, or if you needed to seek alternative shelter, a temperature-resistant cover is essential. This could be lightweight Mylar emergency blankets (they reflect body heat) or even a robust wool blanket. The goal is to prevent hypothermia.

In Hard Mode, having the right tools for tasks beyond information and light is also crucial. This includes things like a sturdy knife or multi-tool, duct tape, and potentially a wrench to turn off utilities if needed.

Finally, navigating a crisis often involves proving who you are or accessing important personal information. Keeping copies of important documents (like ID, insurance papers, deeds, birth certificates, and a list of emergency contacts) in a waterproof bag is a simple step that can save immense hassle and stress in a chaotic situation. Having some cash on hand remains important, as electronic payments may be down for a long time. Lastly, a compass may become useful again in a world without GPS.

Summary: Building Your Kit

Before I’ve shown a not so far fetched chain of situations that highlighted the importance of different objects. By preparing a survival kit tailored to these different situations (the chaotic "First Hours" and the challenging "Hard Mode" that follows) we can significantly improve our ability to stay safe, informed, and sustained.

Hence, below I’ve written a checklist of essential items, categorized by the phase they primarily address, though many are crucial throughout:

First Hours

• Analog Radio: Your link to official information when other communication fails.

• Batteries: Power for your radio and other essential devices.

• Flashlight or Headlamp: Safe navigation in the dark.

• Non-perishable food: An initial supply to avoid immediate panic buying.

• Initial Water Supply: Some bottled water to cover immediate needs.

Hard Mode

• Water Filter or Purification Method: For accessing safe drinking water long-term.

• Substantial Non-perishable Food Supply: Enough for multiple days or weeks.

• Comprehensive First Aid Kit: To manage health and injuries without medical services.

• Hygiene Essentials: Hand sanitizer, wipes, etc. for sanitation.

• Temperature Resistant Cover (e.g., Emergency Blanket): For warmth and basic shelter.

• Copies of Important Documents: Identification and critical information.

• Cash: For potential transactions if electronic payment is impossible.

• Multi-tool or Knife: Versatile for various tasks.

• Plenty of Patience: An intangible but essential element for enduring uncertainty and difficulty.

For those visual learners out there, check this infography made by the French governemnt. It tells the same story.

If you are thinking about starting your own kit, you check here.

👋That’s all for today! Be safe. Thanks for reading.