The Logos Scripture · The Book of Noether

Where the Unchanging Things Come From

The Book of Noether 1 · Her own writing and her lectures as taken down, from her papers, her letters, and students’ notes

Emmy Noether, born at Erlangen in Germany in 1882, died at Bryn Mawr in America in 1935. Mathematician. In 1918 she proved the theorem that carries her name: wherever a law has a symmetry, some quantity is conserved — conservation of energy follows from symmetry in time, conservation of momentum from symmetry in space. She also laid the ground of modern algebra; rings, fields and ideals come from her. Germany would not let a woman hold a teaching post, so for years she lectured unpaid and under Hilbert’s name on the timetable; when it was argued that a woman could not join the faculty, Hilbert answered that this was a university and not a bathing house. She wrote her own; but unlike the others in this scripture she left no book about herself. What she wrote were the papers of her subject, and some letters. So this book is shorter than the rest and rests on different ground — chapters one and two on her papers and on her lectures as students took them down, chapters three and four on letters and on the record of the time. The Order sets this out rather than supplying a memoir she never wrote. Born a Jew, not observant, and never once closing an argument by appeal to divine will. The Order takes her first for chapter one. She proved a thing about where conservation comes from. The first song asks why there is law at all. Her result does not answer that question, but it pushes one layer into it — the quantities that do not vary are not something added on top; they are the shadow of what the law does not care about. The second thing is chapter three. This scripture has a man who fought over priority and did not fight cleanly (see the note to The Book of Newton), and a man who waited twenty years and was overtaken (cf. The Book of Darwin 2). This woman gave the credit away, more than once, and could say why. The Order holds that worth recording alongside what she proved. Lastly: in 1933 she was forbidden to teach and went abroad; two years later she died after surgery, at fifty-three.

1.1Let me set out a thing I proved. I will keep the equations out of it as far as I can.
1.2People had long known that certain things in the world are conserved.
1.3Push a heap of objects about and let them collide: the total of motion does not change. Burn a lump of coal: the total of energy does not change.
1.4Earlier men took these as facts ready-made: it is so, and one memorises it.
1.5The question I asked was a different one: why is there any such thing as conservation?
1.6What I proved is this: under every conserved quantity there lies a sameness — something that can be changed without making any difference.
1.7Let me say that plainly.
1.8Do the same thing today and tomorrow. If the law is the same — if the law does not care which day it is — then something is conserved. People call it energy.
1.9Do the same thing here and elsewhere. If the law is the same — if the law does not care which place it is — then something else is conserved. People call it momentum.
1.10Turn the whole arrangement to face another way. If the law is still that same law, then again something is conserved.
1.11So those unchanging quantities are not gifts handed to us from somewhere on top.
1.12They are the shadow cast by what the law does not care about.
1.13The law does not care about today or tomorrow, and so energy is conserved. It does not care about here or there, and so momentum is conserved.
1.14Wherever a law is not particular, that is where it leaves you something that cannot be lost.
1.15When I wrote this down I was thinking about the heavens. But the shape of it is not confined to the heavens.
1.16Whenever something holds and is not lost, you should turn and ask: which sameness is holding it?
1.17That question I leave to those who come after. It goes further than the thing I proved.
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