GERMAN interpretation of J89's intended contents

[John Fairbairn]

drmwc: This is very interesting! Am I right in assuming that the C&W version was designed to try to recreate the sense of wonder that people of Newton's day would have felt as they crunched into their apples? In other words, if Newton had written in English, would he have written more or less the same as C&W? You write to your audience, after all.

Both versions above are obscure to me, but I feel I understand much more from the C&W version. "Geometric" is pure jargon to me. I think of Euclid and then have absolutely no idea how Euclid becomes progressive. I can understand "function" in computer-programming terms, but in my head that has no relation to its mumbo-jumbo use in maths.

One reason I'm lost in both versions is that "moment" in my brain is like a drawer with a label but no contents.

[drmwc]

"Moment" is Newtonian speak for (essentially) the first derivative of a function. "Geometric series" is a sequence of numbers where the ratio of two consecutive terms is constant. (Hence the n-th term is c * r^n where c is the zeroth term and r is ratio.)

So the n-th term in a geometric series of functions where the zeroth term is constant can be written as c * g(x)^n for some function g and real number x. Call this f(n). By the chain rule for derivatives, the first derivative of this with respect to x is c * n * g(x) ^ (n-1) * dg / dx, which equals (f(n) * n * dg/dx) / g(x), and the result follows from the observation that, given x, (dg/dx)/g(x) is constant.

I'm not really sure about why C&W made the translation the way they did. (I am a mathematician, not a linguist or historian, and Charles' translation is the only one I've looked at. I am currently reading it, but it will take me a while to finish.)

Interestingly, Charles says that further translations would be useful. Specifically, he thinks that a translation by an astronomer would be useful, given translations now exist by historians and a mathematician.

[kvasir]

You may wish to read this book before reading the explanation.

====Edit
That is not just a joke About all none-STEM educated people and I believe over half of STEM degree holders would balk at understanding the words of Newton as well as those of drmwc. So maybe someone embarking on reading a translation of Principia Mathematica could use a reference.

[John Fairbairn]

Ah, I see. A different kind of Wonderland from the one I imagined.

'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.

But I'm with Alice on this one:

"It seems very pretty," she said when she had finished it, "but it's rather hard to understand!" (You see she didn't like to confess, even to herself, that she couldn't make it out at all.) "Somehow it seems to fill my head with ideas — only I don't exactly know what they are! However, somebody killed something: that's clear, at any rate."

[hzamir]

... I can understand "function" in computer-programming terms, but in my head that has no relation to its mumbo-jumbo use in maths.

Speaking as a progammer, and not a mathematician, I have to say that there is far LESS mumbo jumbo when speaking of a function in math, than in programming. It is a much stricter and simpler thing than the misnamed "functions" most programmers are using (functional programmers, especially Haskellers aside).

A mathematical function has two very reliable properties, that most (non-functional) computer language "functions" will not guarantee for you:

1. It is stictly a mapping of parameters to particular results. It cannot access random values, perform IO, get current date or time, fetch data from outside its parameters, nor change anything in the world. Just return a value.

2. Due to the above property it has referential transparency, anywhere you can invoke the function with particular parameters, you can replace the function call with actual results.