

About the origins of the equals sign - marketer
http://blog.plover.com/math/recorde.html

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kcl
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.

~~~
mechanical_fish
_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
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.

~~~
Eliezer
Wow, you asked the WRONG geneticist. Gould is regarded as worthless and
possibly dishonest by many/most professional _evolutionary biologists_ (which
is _not_ quite the same thing as genetics).

John Maynard Smith, possibly the preeminent evolutionary theorist of our era:

"Gould occupies a rather curious position, particularly on his side of the
Atlantic. Because of the excellence of his essays, he has come to be seen by
non-biologists as the preeminent evolutionary theorist. In contrast, the
evolutionary biologists with whom I have discussed his work tend to see him as
a man whose ideas are so confused as to be hardly worth bothering with, but as
one who should not be publicly criticized because he is at least on our side
against the creationists. All this would not matter, were it not that he is
giving non-biologists a largely false picture of the state of evolutionary
theory."

<http://www.overcomingbias.com/2007/11/beware-of-gould.html>

~~~
mechanical_fish
Thanks. I was thinking about dropping stronger hints of this, actually -- I
distinctly recall seeing various arguments of Gould's being torn to shreds by
Dawkins and/or Dennett, and I have gradually developed the habit of taking my
extensive collection of Gould's books (given to me as gifts), stacking them in
a little pile on my shelf, and then actually _reading_ something else -- but I
am neither educated enough in evolutionary biology nor recent enough in my
reading to pull a specific quote, and the last thing we need is more heat and
less light from a total non-biologist like myself.

Also, I haven't read an essay that is quite so direct as this one that you
link to. I'd point out that this link illustrates my point: When scientists
get down to business and talk about each other's work, they do not mince
words. It's kind of refreshing, actually.

~~~
hhm
Thanks a lot, both of you for your replies. I hadn't imagined that Gould could
be on that position. I might have asked the wrong geneticist indeed!

------
michael_dorfman
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>)

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thomasmallen
So _that's_ where the PHP guys got "===" from. Now it's obvious.

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

------
wave
_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>

~~~
thomasmallen
"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.

------
vineetk
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.

