First Principles
School

Does the eye reach out to the world, or does the world arrive at the eye?

Everyone from Euclid onward says rays leave the eye. But stare at the sun and the eye is hurt — the damage travels inward. So build a dark room with one small hole and let the world paint itself upside down on the far wall. The image arrives without any eye present at all. Light comes in. Settle it by making the world answer, not by arguing.

Is the force that drops an apple the same force that bends the Moon?

Fire a cannonball level from a high enough mountain and it falls the whole way — but the ground curves away beneath it just as fast, so it never lands. It is in free fall forever. That is all an orbit is. Then the Moon is simply falling, and falling is a single law that thins out as the square of the distance. One rule for the orchard and the sky. To write it down I need a mathematics of instantaneous change, so I will have to invent that too.

A current makes a magnetic field. Can a magnetic field be made to give a current back?

I have no mathematics, so I will think in pictures. Iron filings around a magnet arrange into lines — treat those lines as real things filling space, not as bookkeeping. A steady magnet next to a coil does nothing. But push the magnet *through* and the needle kicks, then dies. So it is not the field that drives the current, it is the *cutting* of those lines — the change. Nature charges for motion, not for presence.

If Faraday's pictures are true, what do they look like as equations — and are they complete?

Write down everything known about electricity and magnetism and the set is inconsistent: charge would not be conserved inside a charging capacitor. Patch it with one extra term — a changing electric field must itself count as a current. Now the equations close. And when I solve them in empty space, they give a wave whose speed is built from two numbers measured in a laboratory with no light in it. That speed is the speed of light. Light is not *like* an electromagnetic wave. It is one.

These rays never weaken. What reservoir are they drawing on?

Measure the rays with an electrometer rather than a photographic plate, so the answer is a number and not an impression. The intensity tracks only the quantity of uranium present — not its compound, not its temperature, not its crystal form. Chemistry cannot reach it. So the source is inside the atom itself, and the atom is therefore not indivisible. And pitchblende is more active than its uranium content allows, which means something far stronger is hiding in it.

What would I see if I ran alongside a beam of light?

I should see a frozen wave standing still — but Maxwell's equations have no such solution, and no experiment has ever caught light moving at anything but c. So the fault is not in the light. It is in my assumption that time is the same for everyone. Keep the speed of light fixed and let simultaneity break instead. Ten years later, the falling man: a person in free fall feels no weight at all, so gravity is not a force pulling on him — it is the shape of the spacetime he is coasting through.

Schrödinger's equation is first order in time and second in space. Relativity will not accept that. Can I take the square root?

To make the equation first order in both, the coefficients cannot be ordinary numbers — they must be matrices that anticommute. Force that and two things fall out uninvited: the electron's spin, which nobody put in, and a second set of solutions with negative energy. I can either discard half my own equation or believe it. I will believe it. There is another particle, identical in mass and opposite in charge.

How much of a message is actually information, and how much is noise the channel can be made to ignore?

The meaning of a message is irrelevant to the engineering problem. What matters is how surprised the receiver is. A symbol you could have predicted carries nothing; a symbol you could not carries a lot. Measure that surprise in bits and the whole thing becomes arithmetic — and the same formula Boltzmann wrote for a gas reappears, unchanged, for English text. Then the shock: a noisy channel still has a hard, finite capacity, and below it you can push the error rate to as near zero as you like.

What shape must a molecule have if its job is to copy itself?

Do not guess the structure and then look for support. Control the humidity, get the fibre to hold one crystalline form, and let X-rays report the geometry directly. The pattern comes back as a cross of spots — the diffraction signature of a helix — and the spacings fix the pitch and the diameter. The phosphate backbone is on the outside, where the water is. Whatever the bases do, they do it facing inward, in pairs.

Why must you ask permission before one document can point at another?

Every system here wants to own its own data and impose its own hierarchy, so knowledge sits in silos and dies with the project. Drop the hierarchy. Give every document a single global address, let any document link to any other without the target's consent or knowledge, and accept that some links will break. The tolerance for broken links is the feature — it is what lets the thing grow without a coordinator. Then give it away, unpatented.

If spacetime is a physical thing, it should be able to ripple. Can we feel one pass?

A passing wave stretches one direction while squeezing the perpendicular one — so build an L, send the same laser down both arms, and watch the interference pattern breathe. The catch is the size of the effect: a thousandth of the width of a proton over four kilometres. Everything else on Earth is louder. So build two detectors three thousand kilometres apart and accept only signals that arrive at both within the light-travel time. A century after the prediction, two black holes merge and both arms ring.