Most people think they understand the world they live in. They understand the surface. Underneath that surface are a handful of ideas — from mathematics, physics, technology and the brain — that are publicly available, taught in universities, and yet deeply understood by only a tiny fraction of people. This article collects them, short and plain, so you do not need a degree to follow them. The 0.01% figure in the title is illustrative, not a measured census: it is a way of saying “very few people understand this deeply”, not a claim that exactly 800,000 people were counted.
Maths: infinity is not just “very big”
Most people think infinity is just “very big”. In reality there are different sizes of infinity. The infinity of real numbers is strictly larger than the infinity of natural numbers — a result proved by Georg Cantor’s diagonal argument. Almost no one outside mathematics truly internalises this, because it breaks the everyday intuition that infinity is a single thing.
There exist mathematical statements that are true but cannot be proven within standard mathematics. This is not philosophy — it is Kurt Gödel’s incompleteness theorems, a proven result. And you can have a shape with finite volume but infinite surface area: Gabriel’s Horn, also called Torricelli’s trumpet. It is the kind of result that sounds like a trick, until you work through the maths and find it is not.
Physics: time, quantum and empty space are not what they seem
Time does not pass at the same rate everywhere. GPS satellites have to correct for both special and general relativity every day, otherwise your phone’s location would drift by kilometres. Your satnav works because Einstein was right, not in the abstract, but in the device in your pocket.
Quantum entanglement does not allow faster-than-light communication. The correlation is real, but no usable information can be sent this way. This confuses even many educated people, because popular explanations often imply a kind of instant messaging across space. It is not that.
The vacuum of space is not empty. It has energy, called zero-point energy, and this has measurable effects, including the Casimir effect, where two uncharged plates in a vacuum attract each other. And the sunlight you see left the Sun about eight minutes ago — you are always looking at the Sun as it was eight minutes in the past.
Technology: AI, encryption and the old internet
Modern AI systems, including large language models, do not “understand” in the human sense. They are extremely sophisticated statistical pattern machines. The gap between performance and actual comprehension is still poorly understood by the public — which is why fluent output is so often mistaken for understanding.
Most encryption that protects the internet relies on the difficulty of factoring very large numbers. If a practical quantum computer with enough stable qubits is built, much of current encryption breaks. This is why post-quantum cryptography is being developed right now, before that day arrives.
The majority of the internet’s routing still depends on protocols designed in the 1980s and 1990s that were never meant for today’s scale or security threats. The internet works, in part, because later layers were built on top of foundations that were never designed for what they now carry.
Body and mind: your brain is an editor, not a camera
Your brain continuously predicts the world and mostly shows you its predictions, not raw sensory data. What you experience as “reality” is heavily constructed. That is why optical illusions work, and why two people can witness the same event and remember it differently.
Many of your decisions are made before you become consciously aware of them, in the line of Libet-style experiments and later replications. The feeling of conscious control is partly retrospective — though how far this interpretation goes is still debated by neuroscientists, and this article does not claim the debate is settled.
Your brain runs on roughly 20 watts of electricity — about the power of a dim light bulb — yet it does work that still challenges the most powerful computers. Efficiency, not raw power, is the brain’s real trick.
Hidden history and nature: the timeline is backwards from what you expect
Sharks are older than trees. Sharks have existed for around 450 million years, while trees appeared around 390 million years ago. Cleopatra lived closer in time to the Moon landing than to the building of the pyramids. Oxford University is older than the Aztec Empire. Each of these sounds wrong on first hearing, and each is a reminder that historical intuition is a poor guide to actual dates.
A teaspoon of neutron star material would weigh about a billion tonnes. A neutron star packs more mass than the Sun into a sphere roughly the size of a city, so its density is beyond everyday imagination — and the teaspoon figure, while an extrapolation, is the standard way physicists convey just how extreme that density is.
Probability: where even professionals go wrong
The majority of people, including many professionals, systematically misunderstand base rates and conditional probability — Bayesian reasoning. This leads to large errors in medicine, law and finance, where a test result or a statistic is read without asking how common the underlying condition actually is.
In many real-world systems, extreme events — black swans — dominate outcomes far more than the “average” case. Most risk models still underweight this. The average hides the event that matters most, which is why planning for the average alone so often fails.
None of this knowledge is hidden behind a paywall or a secret society. It is in textbooks, papers and public lectures. What makes it rare is not access, but attention: very few people ever sit with these ideas long enough for them to change how they see the world. If you have read this far, you have already done the part most people skip.
Is the 0.01% figure a real survey result?
No. It is illustrative, meaning “deeply understood by a tiny fraction of people”, not a counted census of who knows what.
Is any of this secret or classified?
No. Every fact here is publicly available. It is rare because it is rarely understood deeply, not because it is hidden.
Which fact should I remember if I remember only one?
That your brain predicts the world and shows you its prediction. Once you know that, you start questioning your own certainty — which is the point of all the rest.