Evolution of Understanding: Brain as a Predictive Model | March 18 2026, 13:29

An interesting philosophical thought came to my mind. What if evolution doesn’t exist in us (not in biological life), but in our system of understanding the laws of the world 🙂 That is, the system of understanding the laws of the world adapts itself so that everything more or less matches up. That is, the brain constructs an internal hallucination and constantly suppresses it in order to minimize the error of prediction. And there’s a big question — does our understanding system strive for truth (absolute correspondence to the world) or just for comfort (so that the picture in the head does not fall apart)?

With this approach, there’s a problem that if you don’t look into the future, then at each iteration, the understanding system adjusts its model so that the prediction works, but simultaneously creates problems for the next iteration, because it has to account for them already. As a result, this layered pie accumulates contradictions and constraints to such an extent that each subsequent theory becomes more and more complex and accreted with a multitude of unexplainable gaps. Dark matter, black hole radiation, gravitational waves, and so forth appear to somehow stretch the owl to fit the globe.

But yes, this is related to the question of whether mathematics was discovered or invented.

Navigating Without GPS: Understanding Cardinal Directions in Moscow | March 13 2026, 18:41

The spokesperson for the Phystech press service explains how to determine cardinal directions in Moscow when navigation systems are down. Find the North Star or use the sun: it rises in the east and sets in the west. Also reminds us how to determine directions using trees. Ziya, do you know how to find cardinal directions using trees? — What’s there to know? Fir tree points north, palm tree points south!

Overall, it seems the Phystech press service is not aware that in Moscow, the annual amplitude of sunrise point movement is almost 90 degrees. That means, it only sometimes (like now, in March) actually coincides with the east. But they do know the word “asterism”. I think most readers will place it somewhere near the word “flatulence”

When Cosines Defy Reality: Humor in the Trenches of Science and War | March 11 2026, 22:00

“Comrades cadets, in wartime the value of cosine can reach 2, and in exceptional cases, when the situation on the fronts demands it, even 3!”

Exploring the Mystical Connection Between π² and g in Defining a Meter | March 01 2026, 17:11

It turns out that π² ≈ g is not some mystical coincidence. When the first scientists contemplated the definition of the meter, there was one elegant proposal: to make the meter equal to the length of a pendulum that takes exactly one second to swing from one side to the other.

For a mathematical pendulum, the period of oscillation is calculated by the formula: T = 2π √(L / g). If we take the length L = 1 meter and set the full period T = 2 seconds (so that it takes exactly one second for each half swing), the equation implies: g = π² (m/s²).

The definition of the meter was later changed: it was tied to one ten-millionth of the distance from the equator to the North Pole along the meridian passing through Paris. However, this geodetic definition was inspired by the earlier idea with the pendulum. Notably, both approaches match up with an accuracy of 1%. Essentially, since the old “pendulum” definition was the main candidate for a long time, values were adjusted so that the new meter was convenient and close to the measurements customary at that time.

It is also interesting that the number of seconds in a year roughly corresponds to the number of pi * 10^7. Earth’s orbital speed is about v = 30 km/s. The distance from the Sun to Earth is approximately r = 150,000,000 km. Thus, over a year, Earth travels a path of about d = 2 * π * r. Then, the orbital period equals T = d/v = π * 2 * r/v = π * 10⁷ seconds.

Jet Trails as Weather Predictors: A Phenomenon of High Altitude Humidity | January 24 2026, 02:34

Walking with Yuki, I see across the sky a very distinct and narrow streak clearly (apparently, an airplane had passed by), and usually a contrail disappears quite quickly, but today it is unusually sharp and long.

I started to investigate and it turns out this is a reliable indicator of changing weather, specifically the arrival of snow or rain: as we are actually expecting a sudden knee-deep snowfall tomorrow. In short: the airplane trail acts as an indicator of humidity at high altitudes.

Here’s how it works:

For a contrail not to evaporate but to start “smearing”, the air at an altitude of 8–10 kilometers must be very humid (saturated with moisture). If the air is dry, the ice crystals from the engine quickly turn into invisible vapor (sublimate). If the air is moist, the crystals have nowhere to evaporate. Instead, they start attracting extra moisture from the surrounding environment and grow. High humidity at high altitudes is a sure sign of an approaching warm atmospheric front.

Unveiling Scientific Misnomers: A Cross-Cultural Exploration | January 14 2026, 04:46

Today I was surprised to learn that the Coriolis force is pronounced as CoriolIs force, not coriOlis force as we were taught in school. I started to investigate what else was wrong, and discovered something amazing.

It turns out what we called Gay-Lussac’s law is known as Charles’s Law in the rest of the world, and what we called Charles’s Law is known throughout the world as Gay-Lussac’s Law.

The Cartesian coordinate system here is Carthesian. Cartesius is just the Latinized name of René Descartes.

In our textbooks, the law of conservation of mass is called the Lomonosov-Lavoisier Law (what enters the chemical reaction = mass of the substances formed). In the rest of the world, it is exclusively the Law of Lavoisier (Lavoisier’s Law). Lomonosov got included here only because “whatever is taken from one body is added to another”.

Also, it turns out that if you have to explain Pythagoras’ theorem to someone in English, without a hint, it’s absolutely impossible to guess that it’s Pythagoras. Greek names are generally a mess. Thales here is pronounced as Teelis.

For some reason, in physics Roentgen is called RentgEnom, although it’s Röntgen with the emphasis on ö.

In Russia, a trapezoid is a quadrilateral with two sides parallel and two not. In the USA, our trapezoid is known as Trapezoid, and the word Trapezium here refers to a quadrilateral with no parallel sides at all. In the UK, it’s the opposite. Our trapezoid is Trapezium, and the “skewed” quadrilateral is Trapezoid.

Exploring the Fascinating Properties of Glass | November 21 2025, 23:58

I got carried away with the topic of glass and learned so many interesting things, so I’m sharing. It all started when I read about the supercritical state of matter – it turns out that the line separating liquid and gaseous states on a pressure and temperature graph at some point breaks off, and beyond that lies a state of matter that is neither here nor there. I started reading about states (phases) of matter and stumbled upon the fact that glass is essentially a state between liquid and solid. It flows, just very slowly. This myth is popular thanks to observations of medieval windows, where the glass is often thicker at the bottom, which was attributed to “flowing” under the influence of gravity, and it was even mentioned in school textbooks. In reality, glass is an amorphous solid with extremely high viscosity at room temperature, and it does not flow noticeably even over billions of years; the uneven thickness of old glass panes is explained by production technologies, when the thicker edge was installed at the bottom for stability.

I delved into the topic of glass further. It turned out that the reason why glass can be transparent is rooted in quantum mechanics, specifically in the electronic structure of the material, not because of the density of particles. The essence is that for an electron to absorb a photon, it must transition from one energy level to another, but in silicon dioxide, the width of the band gap is so large that the energy of visible light photons is physically insufficient to make this “jump.” As a result, light simply cannot interact with the electrons and goes straight through the material, while higher-energy ultraviolet radiation can overcome this barrier and is thus absorbed by glass.

It also turned out that melted glass conducts electricity. Moreover, the mechanism of conductivity fundamentally differs from how metals conduct electricity. In a copper wire, current is a flow of free electrons. In cold glass (an insulator), electrons are tightly bound, and ions are locked in the solid lattice. But when you heat glass to the molten state (usually above 1000 degrees for silicates), thermal energy breaks the rigid bonds of the lattice, and glass becomes a liquid, with ions gaining freedom of movement. The current in molten glass is the physical movement of charged atoms (ionic conductivity), not just “flowing” electrons.

The green tint you see on the edge of regular glass (as seen in the attached picture) turns out to be caused by iron ions, present as impurities (~0.1%). Sand is a natural material, and removing all the iron from it is difficult and costly. Low-iron glass, which has tens of times fewer iron ions, is used in solar panels, not just because it is more transparent. Iron greedily absorbs the infrared spectrum (thermal energy), reducing the efficiency of the panel. By removing iron, we allow maximum energy to reach the silicon cells.

And finally, the most “mind-blowing” (literally). There are these things called “Prince Rupert’s drops.” If you drop molten glass into icy water, the outer shell of the drop cools and hardens instantly, while the inner part remains liquid. As it cools, the core tries to contract, but the hardened shell doesn’t allow it. As a result, the inside of the drop preserves colossal mechanical stress (up to 700 MPa).

The physics of this process creates a paradox: the “head” of such a drop can withstand being struck by a hammer because the compression of the surface makes it incredibly strong (the same principle is used in tempered glass for smartphones). But just nick the thin tail, and the balance of forces is disrupted, and a wave of destruction moves through the drop at the speed of a bullet (about 1.5 km/s), turning it into glass dust right in your hands.

There’s also something in physics called “metallic glasses” (amorphous metals). If you cool the molten metal at a rate of a million degrees per second, atoms do not have time to arrange into a crystalline lattice and freeze in chaos. Such “glassy metal” possesses unique magnetic permeability and is stronger than titanium, because it lacks crystal lattice defects, which are usually the points of destruction. So glass is a much broader concept than just transparent substance in our windows 🙂

The only example of an object made from this material, amorphous metal, that I’ve encountered is, believe it or not, the iPhone clip.

By the way, that same amorphous structure of glass, which I mentioned earlier, gives it an unexpected advantage — supernatural sharpness. If you take a scalpel made of the best surgical steel and look at it under an electron microscope, its edge will look like a jagged saw. This is inevitable: steel is made up of crystalline grains, and it’s impossible to sharpen it any smoother than the grain size allows.

But obsidian (volcanic glass) when fractured provides an edge only about 3 nanometers thick (about 1/30000 the thickness of a human hair). There’s no magic here, just that glass lacks a crystalline lattice, which would otherwise prevent achieving a perfectly smooth fracture down to the molecular level. That’s why obsidian scalpels are still used in the most complex eye surgeries — the cut is so clean that tissue cells are minimally traumatized, and healing occurs faster.

And one more powerful engineering case — vitrification (glassification). Mankind has chosen glass as the most reliable “safe” for nuclear waste. Liquid radioactive waste is mixed with special additives, melted, and cooled into blocks. The trick is that dangerous isotopes are not just poured inside, they are chemically embedded into the atomic grid of the glass. Glass is chemically inert, it doesn’t rust like metal or decompose for thousands of years. This is perhaps the only material that engineers trust to store hazardous substances on a geological time scale. Yes, it takes about a million years for a discarded bottle to decompose.

And finally. Digging into history, it turns out that the Romans were engaged in nanotechnology 1600 years before we even invented the word. In the British Museum stands the “Lycurgus Cup” (4th century AD). If you look at it under normal lighting, it’s greenish and opaque. But if you place a light source inside the cup, the glass flashes bright rubin red.

Until the 1990s, scientists could not understand how this was achieved. An electron microscope showed: Roman craftsmen added gold and silver, ground to nanoparticles about 50 nanometers in size (about 1000-1800 times thinner than a hair). This size of particles triggers a quantum effect known as surface plasmon resonance: electrons in the metal begin to oscillate such that they absorb some wavelengths of light and let others pass depending on the angle of incidence. The funniest thing is that the Romans did this empirically, “by eye,” and we’ve only just learned to replicate this consciously in photonics. It’s crazy to think you could handle 50 nm gold dust by eye. This moment required additional googling.

It’s unlikely the Romans mechanically crushed the metal to 50 nanometers — they had no such mills.

More likely, they added gold and silver in the form of salts or foil to the molten glass mass. The nanoparticles formed not by crushing, but by crystallization and sedimentation from the melt under very precise temperature conditions (“glass prescription”). This is even more complex chemistry than simple grinding.

The most astonishing thing is not that they did it, but that the ratio of gold to silver was maintained perfectly. Changing the concentration of gold by just 1% would alter the color to something other than pure ruby red. This indicates that the craftsmen mastered the technology incredibly accurately, although they likely did not understand the mechanism. And that they had a heck of a lot of time for all kinds of nonsense;) probably many generations dedicated their lives to experimenting. Because it’s hard to see why all this was necessary.

There’s a beautiful hypothesis (unproven, but popular) that the cup could have been used as a detector. If you pour a different liquid into it (for example, alcohol with impurities or poison), the refractive index changes, and the color of the “flash” might vary.

Exploring the Chaos Game: Creating Fractals From Randomness | October 04 2025, 15:32

I read something interesting today. About fractals. If you take any three points that form a triangle, and then a fourth point anywhere, and subsequently throw a dice, the faces of which are assigned to the first three points. Next, you move from the current point towards the point corresponding to the result on the dice and place a new point halfway; this becomes the new current point. After many iterations, the points start to form the Sierpinski triangle – the one shown in the attached picture. Intuitively, you would think the triangle should be fully filled because it involves random movements in three directions from a randomly chosen point, but no. Moreover, it works even if the starting point is inside the future empty triangle (yes, a few points will disrupt the picture, but that’s it). If you start our experiment with five or six points instead of three, different shapes will form – see the attached picture. This graphical method is called the Chaos Game.

By the way, it may seem obvious, but in case you wondered — all the presented figures have zero area.

If you take two triangles and with a probability p move towards random vertices of the first, and with (1-p) towards random vertices of the second, you end up forming a Barnsley fern (picture №2).

I love such things because they seem like magic at first glance 🙂

(It’s a kind of problem from the same class as the synchronization of metronomes)

The Optical Illusion of the Changing Purple Dots | September 27 2025, 23:44

An interesting trick. To color the circle dark purple, you simply need to look at it and it will instantly change color. However, to revert it back, you just need to stop looking at it, and it will return to its original appearance (though you’re likely to look at another circle instead)

The Maunder Minimum’s Impact on Stradivari’s Unique Violins | September 18 2025, 21:20

I stumbled upon an interesting scientific hypothesis from 2003 regarding why Stradivari violins (and those of his contemporaries) are so unique. Traditional hypotheses—about the secrets of the varnish or the aging of the wood—prove insufficient. According to this hypothesis, the entire blame lies with the Maunder Minimum, a period of reduced solar activity occurring from 1645–1715, during which the tree growth rate slowed down due to the climate, meaning the wood was denser. The hypothesis suggests that amidst the perfect combination of altitude, humidity, and temperature, this environmental shift provided material with unique properties, ideal for resonant soundboards.

Stradivari was born a year before the Maunder Minimum began. His “Amati Period” (1666–1690), “Experimentation Period” (1690–1700), and “Golden Period” (1700–1720), during which he perfected and produced his best instruments (see Henley 1961), all coincided with the Maunder Minimum. Cremona’s craftsmen during this period used the only wood available to them, i.e., from trees growing during the Maunder Minimum. Neither before nor after this period was such wood available. And, probably, it is nowhere to be found in the world even now.

But really, modern violins are also quite something. Two-three hundred years ago, musicians extracted the maximum from an instrument through trial and error, whereas now it is done through meticulous calculation of sound. It is almost impossible to differentiate violins by their sound anymore, and the difference lies in the realm of individual preferences, rather than an undisputed objective worse-better.