6 ms·

About the origins of the equals sign

66 points by marketer 18y ago

michael_dorfman 18y ago
There was a nice documentary about the birth of the calculus, that focused on Newton and Leibniz's notebooks. It was cool to see them making up notation on the fly. (A quick check of YouTube finds it here: http://www.youtube.com/watch?v=dwZNg237x1M http://www.youtube.com/watch?v=dwZNg237x1M)
kcl 18y ago
An excellent article. Full of things I haven't seen. I will second his recommendation to read original works. They aren't always the best, but in many instances they can teach you a lot more than just the topic at hand. If you have your grammar school science textbooks at one end of the spectrum---nth hand knowledge echoed by an author with no understanding of the subject---then original works are at the opposite end---the idea in its first appearance, recorded by someone with the power necessary to understand and discover it for the first time. The advantage isn't only in that the author takes great pains to present his new discovery, it's in the countless unrepeatable ways he presents it dictated by the climate of his time. Just like there will never be another 17th century Italy to produce those particular violins, there will never be another Victorian Era to produce On the Origin of Species, in the way it was originally written. You can rewrite and distill the idea, but you can't recapture all the implications that originally flowed from it. Reinterpretations strip an idea of its historical context, and frequently these are as important as the idea itself.
- rflrob 18y ago
  After my (university) freshman physics class, we were all presented with a copy of Einstein's original papers on Brownian Motion. It's incredible how much he says things to the effect of, "well, I think this effect is the same thing that people are talking about, but I haven't actually seen it first hand, so I could be wrong".
- mechanical_fish 18y ago
  I will second his recommendation to read original works. Be aware, though, that this recommendation does have a flip side. I haven't tried to read Maxwell's original Treatise on Electricity and Magnetism, but I've heard it said that it's really, really difficult to get through. The fact that Maxwell's equations, the marvel of their era, are now a subject for second-year undergraduates is due to Oliver Heaviside's later work. From Wikipedia: In 1884 [Heaviside] recast Maxwell's mathematical analysis from its original cumbersome form (they had already been recast as quaternions) to its modern vector terminology, thereby reducing the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations. Just imagine Maxwell's equations as a system of 20 simultaneous equations. Now marvel at the fact that Maxwell was able to conclude anything at all while operating under such a heavy handicap. Similarly, one of the reasons that intelligent nonphysicists today find quantum mechanics terribly confusing is that the original formulators of quantum theory -- guys like Bohr, Heisenberg, Schroedinger, and Einstein -- were so influential and so well-spoken that their writings and ideas have refused to go quietly into the dustbin of history, where many of them arguably belong. The mental models used by these folks -- the cat in the box, the atom as a miniature solar system, the notion of "god playing dice" -- are largely obsolete. They reflect the viewpoint of classically-trained physicists desperately scrambling for a grip on quantum theory. Now that quantum theory is much better understood, there are probably better ways to approach the subject than the analogies and metaphors used by its original pioneers. Another example: While Darwin's Origin of Species is a great work, guys like Dennett and Dawkins and Gould have noted that one of Darwin's awesome literary talents is his ability to distract you from the fact that he didn't know about genetics. Without the notion of a gene it's rather hard to explain why the individual members of a species exhibit variation in the first place. Darwin, whose theory was already very difficult to sell, understood this problem but was careful not to call too much attention to it; it remained as a real hole in his theory until later work cemented it shut.
  - hhm 18y ago
    I was happy with Dawkins book until being told, by a geneticist if I remember right, that he wasn't very serious, that Gould was serious reading but Dawkins was not completely so. I'd be glad to know if it's right or not.
wave 18y ago
Robert Recorde wanted to make his math books clear and accessible. He was the first to write such books in English, rather than in the Latin or Greek of the educated elite. Also, little more about this subject on the PBS site: http://www.pbs.org/wgbh/nova/einstein/ance-equals.html http://www.pbs.org/wgbh/nova/einstein/ance-equals.html
- thomasmallen 18y ago
  "It doesn't seem that Recorde gained from his innovation, for it remained in bitter competition with the equally plausible "//" and even with the bizarre "[;" symbol, which the powerful German printing houses were trying to promote. But by Shakespeare's time a generation later Recorde's victory was finally certain." I think that sounds exactly like people defending bizarre syntax rules in modern languages.
thomasmallen 18y ago
So that's where the PHP guys got "===" from. Now it's obvious.
- nuclear_eclipse 18y ago
  Now I can feel much more dignified every time I have to use identity comparison!
vineetk 18y ago
It's very interesting to see the use of the tilde for nasalized vowels in an English text, the same as it is currently used in Portuguese today.

66 points by marketer 18y ago

There was a nice documentary about the birth of the calculus, that focused on Newton and Leibniz's notebooks. It was cool to see them making up notation on the fly. (A quick check of YouTube finds it here: http://www.youtube.com/watch?v=dwZNg237x1M http://www.youtube.com/watch?v=dwZNg237x1M)

kcl 18y ago

An excellent article. Full of things I haven't seen. I will second his recommendation to read original works. They aren't always the best, but in many instances they can teach you a lot more than just the topic at hand. If you have your grammar school science textbooks at one end of the spectrum---nth hand knowledge echoed by an author with no understanding of the subject---then original works are at the opposite end---the idea in its first appearance, recorded by someone with the power necessary to understand and discover it for the first time. The advantage isn't only in that the author takes great pains to present his new discovery, it's in the countless unrepeatable ways he presents it dictated by the climate of his time. Just like there will never be another 17th century Italy to produce those particular violins, there will never be another Victorian Era to produce On the Origin of Species, in the way it was originally written. You can rewrite and distill the idea, but you can't recapture all the implications that originally flowed from it. Reinterpretations strip an idea of its historical context, and frequently these are as important as the idea itself.

rflrob 18y ago
After my (university) freshman physics class, we were all presented with a copy of Einstein's original papers on Brownian Motion. It's incredible how much he says things to the effect of, "well, I think this effect is the same thing that people are talking about, but I haven't actually seen it first hand, so I could be wrong".
mechanical_fish 18y ago
I will second his recommendation to read original works. Be aware, though, that this recommendation does have a flip side. I haven't tried to read Maxwell's original Treatise on Electricity and Magnetism, but I've heard it said that it's really, really difficult to get through. The fact that Maxwell's equations, the marvel of their era, are now a subject for second-year undergraduates is due to Oliver Heaviside's later work. From Wikipedia: In 1884 [Heaviside] recast Maxwell's mathematical analysis from its original cumbersome form (they had already been recast as quaternions) to its modern vector terminology, thereby reducing the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations. Just imagine Maxwell's equations as a system of 20 simultaneous equations. Now marvel at the fact that Maxwell was able to conclude anything at all while operating under such a heavy handicap. Similarly, one of the reasons that intelligent nonphysicists today find quantum mechanics terribly confusing is that the original formulators of quantum theory -- guys like Bohr, Heisenberg, Schroedinger, and Einstein -- were so influential and so well-spoken that their writings and ideas have refused to go quietly into the dustbin of history, where many of them arguably belong. The mental models used by these folks -- the cat in the box, the atom as a miniature solar system, the notion of "god playing dice" -- are largely obsolete. They reflect the viewpoint of classically-trained physicists desperately scrambling for a grip on quantum theory. Now that quantum theory is much better understood, there are probably better ways to approach the subject than the analogies and metaphors used by its original pioneers. Another example: While Darwin's Origin of Species is a great work, guys like Dennett and Dawkins and Gould have noted that one of Darwin's awesome literary talents is his ability to distract you from the fact that he didn't know about genetics. Without the notion of a gene it's rather hard to explain why the individual members of a species exhibit variation in the first place. Darwin, whose theory was already very difficult to sell, understood this problem but was careful not to call too much attention to it; it remained as a real hole in his theory until later work cemented it shut.
- hhm 18y ago
  I was happy with Dawkins book until being told, by a geneticist if I remember right, that he wasn't very serious, that Gould was serious reading but Dawkins was not completely so. I'd be glad to know if it's right or not.

wave 18y ago

Robert Recorde wanted to make his math books clear and accessible. He was the first to write such books in English, rather than in the Latin or Greek of the educated elite. Also, little more about this subject on the PBS site: http://www.pbs.org/wgbh/nova/einstein/ance-equals.html http://www.pbs.org/wgbh/nova/einstein/ance-equals.html

thomasmallen 18y ago
"It doesn't seem that Recorde gained from his innovation, for it remained in bitter competition with the equally plausible "//" and even with the bizarre "[;" symbol, which the powerful German printing houses were trying to promote. But by Shakespeare's time a generation later Recorde's victory was finally certain." I think that sounds exactly like people defending bizarre syntax rules in modern languages.

thomasmallen 18y ago

So that's where the PHP guys got "===" from. Now it's obvious.

nuclear_eclipse 18y ago
Now I can feel much more dignified every time I have to use identity comparison!

vineetk 18y ago

It's very interesting to see the use of the tilde for nasalized vowels in an English text, the same as it is currently used in Portuguese today.