Babel

The laryngeal nerve is the nerve that connects the brain to the larynx (the voice box).

Instead of connecting directly, the nerve goes all the way down through one side of the neck, through the heart, then back up the other side of the neck to connect to the voice box.

This evolutionary redundancy is more than prominent in giraffes, where the distance between the brain and the larynx is about 5cm apart. Yet, the nerve is about 15ft in length.

We get used to the idea that evolution is so good at producing beautiful elegant animals that look as though they’ve been designed. We forget that sometimes they’re not perfect and there are imperfections and the imperfections are very revealing because they’re exactly the kind of imperfections you’d expect from the accidents of history if there were no designer.

[…]

Remember that a designer [or] an engineer can go back to the drawing board, throw away the old design, start afresh with what looks more sensible. A designer has foresight. Evolution can’t go back to the drawing board. Evolution has no foresight.

— Richard Dawkins demonstrates laryngeal nerve of the giraffe

“Tower of Lire” is a cool-sounding name of the solution to the block-stacking problem.

Place N identical rigid rectangular blocks in a stable stack on a table edge in such a way as to maximize the overhang.

The solution looks like the following and basically, the overhang for N blocks has to start from ¹/_2N units:

If you add the total overhang, you get this:

¹/₂ + ¹/₄ + ¹/₆ + ¹/₈ + ¹/₁₀ + … = ¹/₂ + ¹/₂ (¹/₂ + ¹/₃ + ¹/₄ + ¹/₅ … )

That infinite sum inside the parentheses is the harmonic series. Famously divergent, meaning it adds to infinity.

So the sum of the overhangs also is technically infinite.

I came across this via a youtube short.

A play of the word “Ignoble”, it’s a satirical prize awarded to whimsical scientific achievements.

Winners are awarded 10 trillion Zimbabwean dollars ($0.40 USD).

Start your Wikipedia rabbit hole here.

When a resource or good becomes more efficient to consume, the consumption is expected to decrease. However, the consumption actually increases due to reduced costs resulting in increased demands.

This took me a while to understand because it seemed to be explained by simple price elasticity to me and I thought I was missing the “paradox” part of it. The “paradox” comes from directly relating efficiency and consumption without involving price elasticity at all.

But I still think it’s intuitive if you have a realistic world view.

Increasing number of lanes doesn’t lead to reduced traffic; just more people opting to use the traffic lanes because of perceived increased road availability, thereby increasing the traffic.

Increasing engine efficiency doesn’t need to lesser emissions. It leads to cheaper fuel which leads to more travel.

Interesting videos:

• Jevons Paradox & The Rebound Effect
• How To Fix Traffic Forever

The most magnetic thing in the universe is a special type of Neutron Star, called a Magnetar. Its magnetic field, is about 4 quadrillion T. It’s so magnetically corrosive that within 10000 km it will rip the atoms in your body apart by stretching them into needles.

Also sounds like a Pokemon.

Jesus wasn’t actually born in 1AD, and his actual birthdate is still debated.

In 525 AD, a monk named Dionysius Exiguus created the AD dating system, calculating that Jesus was born, well, 525 years earlier. However, modern scholars believe that he was around 4-22 years late. That means Jesus was likely born in 4-22 BC.

If the calculation had been correct, the current year would be somewhere between 2029 and 2047.

In islands, small species grow bigger (island gigantism) and large species go smaller (island dwarfism).

The scientific definition of glass is a something that’s amorphous (non-crystalline) and is formed by rapid cooling of something that was melted. There exists a whole category of naturally occurring Volcanic glass, an example of which is Obsidian. If you say obsidian is volcanic glass, I’ll believe you. They look glassy.

You might know about Pumice, which looks exactly opposite to “glass”.

But it is a volcanic glass because it has non-crystalline structure. (Also, I found out about Kutkhiny Baty while I was Googling around. Recommended Google.)

To add to the absurdity, what the hell is this?

This is called Pele’s hair. This is a type of volcanic glass. This very much looks crystalline but it’s not.

Nomenclature is hard.

If you’ve watched Bear Grylls you know what hypothermia is. In medical terms, it’s when body’s core temperature falls below 35 °C. I recently found out how scary moderate-to-severe hypothermia (body temperature at 20°C - 28 °C) can get.

Paradoxical undressing is when a person becomes disoriented and starts undressing which in turn lowers the body temperature even more. Explanations include a malfunctioning hypothalamus or the sudden surge of blood due to exhausted blood vessel muscles after excessive contraction, making the person feel overheated.

Other scary mental hypothermia symptoms include euphoria, impaired sense of time and place, hallucinations, and the most primitive, evolutionary slap of them all - terminal burrowing; wherein a person enters small enclosed spaces like wardrobes or under beds, like an animal going to hibernate.

Hypothermia Wikipedia article is scary.

Our body behaves differently to acceleration based on what direction it is being accelerated. This seems trivial if you think about it for more than 10 seconds but I never had done that so my shock when I learnt about it while watching a What If? video was not completely unwarranted.

Most tolerable direction is being accelerated forward. Least desirable is being accelerated downward and it has a limit of 2Gs which only makes free diving scarier than it already was.

Refers to the total area of the Arctic Ocean where sea ice covers at least 15% of the surface. Basically:

1. Divide the Arctic Ocean into uniform unit areas.
2. Identify all unit areas where at least 15% of the surface is covered in ice.
3. Sum all these unit areas, including both ice and water, to get the total ice extent.

This value ranges from a minimum of about 7 million km² in September to around 15 million km² in March. The long-term trend is a decline as ice is melting faster than it reforms in winter. This makes it a very strong indicator of global warming.

Recently, in March 2025, the extent reached a record low maximum of 14.33 million km². We can see how the median has decreased in this chart:

I came across an article that mentioned something called “superellipses” defined as:

Visually the shape is described as

[…] a rectangle with rounded corners [but] the change in curvature is continuous.

My first thought was “wait isn’t this a squircle?”. And indeed it is!

It’s a special case of the superellipse where r_a and r_b are equal and n > 2 (it’s a normal circle for n = 2). Wikipedia describes that it’s only a squircle when n = 4 but it’s subjective to me.

Mathematically, we can stop here. A squircle is a special case of the superellipse. But in the design world, squircles were — as per ritual — very minutely tweaked by Apple. The icons released with iOS 7 in 2013 were found to be superellipses of n = 5 by Marc Edwards.

But not quite:

Unfortunately, though, careful follow-up efforts showed that the superellipse formula wasn’t quite right (however, these days true superellipses are used as icons in other contexts). In fact, for all choices of n in the equation above, there is a small but systematic discrepancy when compared with the real icon shape.

[…] We have an elegantly simple equation for something that looks a lot like an iOS squircle, but it’s fundamentally incorrect.

— Desperately Seeking Squircles

The above excerpt is from a Figma blog which dives much deeper than it needs to^* about how an engineer tried to recreate the squircle. After trying out a lot of cool things (a lot of geometry I did not try to understand), they went ahead with a simpler and “good enough” modified bezier curves approach. The last paragraph is a pretty relatable conclusion to projects like this:

Intellectually, it’s somewhat unsatisfying to have gotten such a beautiful result as the clothoid series but not to have been able to at least see a reflection of that in the spline we shipped in the end. But there’s also the wider context — the constraints of time when working at a small company are very real — and a design which violates these cannot be considered good.

I’ll often come up with really cool stuff in my head for solving a problem only to realise that they can be solved much more simply so this was really nice to read.

The “crowns” of fully stocked trees (spaced almost evenly) don’t touch each other and it makes for very pretty patterns. This occurs in a few tree species.

It’s still uncertain as to why it happens. There are theories of course. Some say it’s due to branches colliding against each other which destroys bud tissues, hampering further growth. Some say that it’s due to shade avoidance — trees avoiding shade cast by other trees. Some species can sense neighbouring plants by sensing back-scattered light which allows them to do this.

I’d like to see and photograph this someday. Some species like Camphor, Eucalyptus and Pine trees exhibit this out of which only Eucalyptus is native to India. Tough luck.

Large crystal patterns found in iron meteorites. The presence of these patterns in a mineral is a very strong indicator of extraterrestrial origin since it’s impossible to achieve this artificially.

These meteorites are a mixture of iron-nickel alloys — Taenite (high nickel content) and Kamacite (low nickel content). The formation of these patterns takes place in the phase transition when it cools down from the former to latter, containing both of them. This cooling down is very, and I mean very slow — about 100-10,000 °C/million years for about 10 million years.

The patterns appear when you cut open the meteorites and treat them with an acid.

Until the late 1800s, calculus relied on the vague, geometric, non-rigid definitions of continuity and differentiability. Many mathematicians believed with “proofs” that there can only be a finite number of points where a continuous function cannot be differentiable. That every continuous function was differentiable at least somewhere.

In 1872, Karl Weierstrass came up with a horrific function that was continuous everywhere but differentiable nowhere:

It’s constructed from infinitely many cosine functions:

where 0 < a < 1, b is a positive odd integer, and ab > 1 + 3π/2.

This curve allowed Weierstrass to formally define continuity and differentiability with the famous epsilon-delta definition of the limit which I learnt in 11th class.

It’s also one of the earliest known fractals. I find it difficult to make sense of the fact that there are no straight lines between two jagged points even if it seems like it.

Another Quantamagazine find.

One of the coolest algorithms I’ve found. It generates random textures and patterns given a “miniature” of that particular pattern. More on GitHub.

A hypothesis that states that the universe is fine-tuned to support life and it is what it is because of the values. It would be much different from what it is right now if a few of the physical constants such as gravitational or electrostatic constant, etc. were even a little bit off.

It’s funny to think of a universe as some shader code with random parameters as global variables which change its behaviour and appearance.

Rare earth hypothesis is a similar one. It says that it’s extremely coincidental and rare that Earth supports life. It argues that life probably is very rare in this universe. Carl Sagan believes the opposite of this — that the universe is teeming with life. I do too. But I couldn’t give you reasons. I only hope that’s the case because that makes the universe more interesting and much less lonely.

Pictures that can give you permanent brain damage. They rewire your brain thinking red is green and vice versa.

I got this from a Tom Scott video. “Memetic hazard” is also an insanely scary phrase. As someone who has spent considerable time on the SCP wiki, I steer clear of these things.

There are two situations where this effect is stated.

First is to show the naivete and “undeserved” confidence of beginners. New people are overconfident at a thing. After spending a while on the thing, they are severely under-confident. After spending a lot more time on the thing, they gradually get more confident.

The other situation is when experienced people think something is so trivial when it actually isn’t.

Also called frequency bias. People become aware of the thing they have just come to know about. This is why you notice the word you just learnt about much more after you’ve learnt about it.

Also happens with pop culture references etc.

Also called bikeshedding. It says that people have a tendency to focus on irrelevant smaller details as opposed to ones they should be prioritising.

Chesterton’s fence refers to a thing in a system which seemingly serves no purpose and makes you question its relevance or role in the system. However, removing it would result in significant failures in the system.

For instance while coding, if you come across an if block that looks like it does nothing much and the case is already handled trivially, you might be tempted to remove it. But without context from the person who wrote and why it was written, you shouldn’t do it because there’s a good chance you’re missing something.

This also applies to places outside software engineering such as laws and economics. Context — both functional and historical, is important before changing systems.

I find it incredibly relaxing that the Italians have a phrase for “the sweetness of doing nothing”. Just the fact that there is such a philosophy calms my nerves a little bit when I’m overwhelmed.

Also acts as an excuse when I’m procrastinating.

A scary and controversial experiment conducted by Stanley Milgram which showed us how free will is basically a myth. I’m exaggerating of course, but that’s essentially how you feel after you get to know what it is. This is the experiment’s methodology.

The experimenter (E) orders the teacher (T), the subject of the experiment, to give what the teacher (T) believes are painful electric shocks to a learner (L), who is actually an actor and accomplice. The subject is led to believe that for each wrong answer, the learner was receiving actual electric shocks, though in reality there were no such punishments. Being separated from the subject, the accomplice set up a tape recorder integrated with the electro-shock generator, which played pre-recorded sounds for each shock level.

— Wikipedia

The shocks ranged from 15V to a life-threatening 450V. When a teacher expressed their concern and said that they didn’t want to do it, they were verbally forced to do it by the experimenter for 4 times with different prompts. The experiment was halted once they denied it for the 5th time or the 450V was given at least thrice in succession. The teachers were said to be shivering, having laughing fits, sweating and losing themselves. They believed they had no choice.

If you think the methodology was scary, which it was, the results are way scarier. Around 100% of the teachers gave at least a shock of 300V to the learners and around 65% of them went all the way to 450V.

It may be that we are puppets-puppets controlled by the strings of society. But at least we are puppets with perception, with awareness. And perhaps our awareness is the first step to our liberation.

— Stanley Milgram

Maybe being a little rebellious would be good for me.

A defense mechanism where someone loses all of their ability to think in nuances, seeing everything in binary. Commonly seen in people with BPD.

A totally unserious serious glossary book by Mort Walker which coined (made up) a bunch of new terms for many of the artistic and literary devices used in comic books. Some of my favorite ones are:

If you take a corpus of text and arrange all the words in descending order according to their frequency, you’ll see that the nth ranking word’s frequency is approximately equal to 1/n of the frequency of the most used word. This is the most famous example of Zipf’s law:

an empirical law stating that when a list of measured values is sorted in decreasing order, the value of the n-th entry is often approximately inversely proportional to n.

— WikiPedia

It is also a discrete form of the Pareto distribution which says 20% of the causes are responsible for 80% of the effects.

The fascinating thing about this law is how much it occurs naturally literally everywhere.

It’s also found in city populations, solar flare intensities, protein sequences and immune receptors, the amount of traffic websites get, earthquake magnitudes, the number of times academic papers are cited, last names, the firing patterns of neural networks, ingredients used in cookbooks, the number of phone calls people received, the diameter of Moon craters, the number of people that die in wars, the popularity of opening chess moves, even the rate at which we forget.

— The Zipf Mystery - VSauce (must watch)

Typing random text with spaces explains Zipf’s law mathematically i.e., it’s more probable to write short words than long words. But why it occurs in all of these places is non-trivial if not a complete mystery.

A common explanation for Zipf-ian distributions is preferential attachment processes.

They occur when something - money, views, attention, variation, friends, jobs, anything really is given out according to how much is already possessed.

— The Zipf Mystery - VSauce

Viral things go more viral. Used things are used more.

It’s just weird that it rules so much around us. The world doesn’t feel predictable but this somehow tells me it is? That all our life amounts to a few moments even if we live for years. All the knowledge we gather, all the media we consume, all the moments we live, we are going to forget most of it because as stated above, our forgetting curve is Zipf-ian.

I look at all the books I’ve read and realize that I can’t remember every detail from them, it’s a little disappointing. I mean, why even bother if the Pareto Principle dictates that my ‘Zipf-ian’ mind will consciously remember pretty much only the titles and a few basic reactions years later.

Ralph Waldo Emerson makes me feel better. He once said, “I cannot remember the books I’ve read any more than the meals I have eaten. Even so, they have made me.”

— The Zipf Mystery - VSauce

Take a natural number and apply this function recursively.

Basically, if it is even, divide it by 2. If not, multiply it by 3 and add 1. Repeat this until you get 1. At this point, you’ll get a loop of 1-4-2-1.

Collatz conjecture states that any natural number always finishes in this loop.

It is still a conjecture because it hasn’t been proven yet although it has been tested up to a really large number.

The trisectors of angles in any triangle form an equilateral triangle. This theorem was later generalized to The lighthouse theorem. It has little-to-no practical usage but I found it cool.

I even made an interactive thingy for this with Geogebra.

Flowers exhibit some pretty patterns and colors when viewed under UV light. Craig Burrows photographed a bunch of them and they look insane.

“It’s definitely not an especially easy type of photography,” says Burrows. Typically, he’ll mount his floral subject to a metal stand and use a remote trigger to sound off a 10 to 20 second exposure—holding his breath while the shutter is open. Even the smallest air movement or petal droop will result in motion blur.

— National Geographic (email-walled)

Pollinators such as Bees can see this since they can see in the UV spectrum. This is a type of co-evolution. Also, the patterns/colors are generally around anthers and filaments where the bees actually get the pollen from, making them more effective.

The Perseverance & Curiosity rovers have a 5 kg plutonium cube as their energy source. That’s like 20 million USD of plutonium.

The generators are called the Multi-mission radioisotope thermoelectric generator or MMRTG which convert the heat generated by the radioactive decay of plutonium-238 into electricity.

An open flow wind turbine can only harness a maximum of 16/27 (~59.26%) of kinetic energy from wind.

This only applies to open flow wind turbines that look like fans without any extra configurations like shrouds, “wind lenses”, diffusers, or secondary actuators. All of which I didn’t quite understand but they basically ignore a few assumptions made by Betz’s law to go over the limit (like exploiting the fact that wind is not fully non-transverse to the blades).

Practically, the general wind turbines reach 75-80% of this limit. Advanced wind turbines with extra stuff on them can reach more than the limit.

There are special locations between the sun and the earth’s orbit where the effective gravitational force on a body is zero. The body stays suspended and locked in orbit in these points.

There are 5 different points — L1 through L5.

There is a proposal for putting up a mirror as a “shade” for the earth at the L1 Lagrangian point to prevent global warming:

[…] in 1989, James Early of the Lawrence Livermore National Laboratory noted the harbingers of global warming and proposed deflecting a measure of sunlight with a “space shade” located at Lagrangian Point L1 […] 2,000 kilometers in diameter and about 10 microns thick, with a weight of about 100 megatons under Earth’s gravity […] in the form of a Fresnel lens […] estimated the cost at $1 to $10 trillion

— Source

Geoengineering solutions like these are usually last resorts as they tend to be obscenely expensive. To quote again from the article,

[…] if bad things start to happen quickly, then people will demand something be done quickly.

A cool identity I learnt about in a climate economics course I took in college.

Where:

• F is global CO₂ emissions from human sources
• P is global population
• G is world GDP
• E is global energy consumption

So,

• ^G/_P is the GDP per capita
• ^E/_G is the energy intensity of the GDP
• ^F/_E is the emission intensity of energy

In computation, erasing one bit of information requires some energy which is proportional to the temperature of the computing system. The minimum energy is called the Landauer’s limit and is given by:

where k_B is the Boltzmann constant and T is the temperature in Kelvin. This is around 0.018 eV (2.9 × 10^-21 J) at room temperature.

Funny thing is modern computers use about a billion times as much energy per operation. So we’re nowhere near efficient computing. Efforts in “reversible” computing have been shown to reach really close to this limit but it’s all in theory anyway.

Related:

the amount of battery needed for a fixed computing load will fall by a factor of 100 every decade

— Koomey’s Law

If you take a sphere and “squish” it to a 2D plane in any way you can, there will always be two points that fall on the same point on the plane. These points are called antipodal points. These are basically diametrically opposite points since we’re talking about 3D spheres here.

If you have a continuous function f(p), where p is a point on a sphere, that gives out a point on a 2D plane, there will be f(p) = f(-p).

I did not fully comprehend the proof for this or the general case for higher dimensional n-spheres (as one does with topology) but what I found interesting was a common usage/example of this. Two diametrically opposite points on earth will always have approximately the same pressure and temperature. This is because we are mapping the 3D coordinate on earth to 2 parameters — temperature and pressure with a continuous function.

Here’s the 3b1b video which I learned this from. Here’s a fun interactive thing. Both of them explain this much better than I’m doing here.

The space and arms race that was going between the Soviet Union and the US in the late 50s to early 60s was getting heated year after year. Intercontinental ballistic missiles were being developed which were capable of reaching targets through outer space. Developments like these scared the UN and led to the drafting of the Outer Space treaty in January 1967.

This is the treaty that made countries come on the same page that space was not anyone’s to own. The full provisions or “rules” of the treaty can be found on the UNOOSA website but I’m just copying them here because link rot is real:

• The exploration and use of outer space shall be carried out for the benefit and in the interests of all countries and shall be the province of all mankind
• Outer space shall be free for exploration and use by all States
• Outer space is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means
• States shall not place nuclear weapons or other weapons of mass destruction in orbit or on celestial bodies or station them in outer space in any other manner
• The Moon and other celestial bodies shall be used exclusively for peaceful purposes; prohibits their use for testing weapons of any kind, conducting military maneuvers, or establishing military bases, installations, and fortifications
• Astronauts shall be regarded as the envoys of mankind
• States shall be responsible for national space activities whether carried out by governmental or non-governmental entities
• States shall be liable for damage caused by their space objects
• States shall avoid harmful contamination of space and celestial bodies.

These are pretty important. Without these, there wouldn’t be ISS; astronauts stuck in space would not be saved by any of the other national space agencies; and there would be another thing for billionaires to fight over.

As of today (Feb 2025), 115 countries have signed this treaty while more and more countries keep signing and increasing the number.

Related: The Antarctic Treaty is a similar treaty that was entered into force in 1961 to do the same thing for Antarctica. It declares Antarctica as unsovereignable and disallows nuclear and military activities.

I took an Econ 101 course during college which I quite enjoyed. Price elasticity was quite intuitive to grasp until I found out about these.

Giffen and Veblen goods are special kinds of goods where the demand increases with price.

The demand for Giffen goods increases with price due to the income effect overpowering the substitution effect. Often observed in low-income, staple food markets.

Veblen goods are luxury items where higher prices boost demand as they symbolize wealth and status. Overpriced trashy looking sneakers and bananas taped to walls are examples of these.