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The Lost Art of Logarithms

lostartoflogarithms.com

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Re: The Lost Art of Logarithms

#171

Post by pipes »

dkislyuk wrote: post #45

I found that looking at the original motivation of logarithms has been more elucidating than the way the topic is presented in grade-school. Thinking through the functional form that can solve the multiplication problem that Napier was facing (how to simplify multiplying large astronomical observations), f(ab) = f(a) + f(b), and why that leads to a unique family of functions, resonates a lot better with me for why lo…

Coincidentally I watched this last night https://m.youtube.com/watch?v=7TWKSMtKCmU

It gives the history / motivation behind logarithms and suddenly it became so much clearer to me. Pretty much multipling huge numbers by adding exponents , well I think I've understood that correctly?

I think why I'm so interested in programming and computing is because I fascinated by the history of it all. It somehow acts as a motivation to understand it.

Re: The Lost Art of Logarithms

#172

Post by blame-troi »

twbarr wrote: post #142
madars wrote: post #97

Earlier quoted context omitted.

Toeplitz wrote "Calculus: The Genetic Approach" and his approach of explaining math via its historical development is apparently more widely used: https://en.wikipedia.org/wiki/Genetic_method . Felix Klein remarked: "on a small scale, a learner naturally and always has to repeat the same developments that the sciences went through on a large scale"

We could really take a page from this style for teaching advanced computing. We try to imagine that architectures just kind of come out of nowhere. Starting with mechanical computing and unit record equipment makes so much make more sense. Plus, unit record equipment was cool.

Very cool. But so many of us paid not enough attention to the details. Only two of the people in my first shop attempted channel programming.

Re: The Lost Art of Logarithms

#173

Post by zwnow »

-__---____-ZXyw wrote: post #170
zwnow wrote: post #141

Earlier quoted context omitted.

A book without expecting any knowledge of mathematical notation would be a good start. I've bought 3 math books to get into it and quit all of them within the first chapter.

In a roundabout way, I wonder does this one fit what you're after: https://bogart.openmathbooks.org/ctgd/ctgd.html And more directly, a quick browse showed up a book called: "Mathematical Notation: A Guide for Engineers and Scientists" which looks like it addresses your issue directly.

The issue is that I dont want to explicily learn all of the notation but step by step, topic related with usecases in the real world...

Re: The Lost Art of Logarithms

#174

Post by kccqzy »

BobaFloutist wrote: post #113
kccqzy wrote: post #89

Earlier quoted context omitted.

From a teaching perspective it goes like this: first we learn additions, and to undo additions we have subtractions; then we learn repeated additions i.e. multiplications, and to undo multiplications we have divisions; finally we learn repeated multiplications, i.e. exponentiation, and to undo exponentiation we have logarithms and roots.

You see how one of those isn't like the others?

You mean we have both logarithms and roots to undo exponentiation? That's because exponentiation is non-commutative.

Re: The Lost Art of Logarithms

#175

Post by vonneumannstan »

b0afc375b5 wrote: post #121
madars wrote: post #97

Earlier quoted context omitted.

Toeplitz wrote "Calculus: The Genetic Approach" and his approach of explaining math via its historical development is apparently more widely used: https://en.wikipedia.org/wiki/Genetic_method . Felix Klein remarked: "on a small scale, a learner naturally and always has to repeat the same developments that the sciences went through on a large scale"

I always longed for a book/course on mathematics where topics are in chronological order: 1. ... (mathematical topics at the beginning of history of which I am ignorant of) 2. pythagoras theorem 3. ... 4. euclid geometry 5. ... 6. algebra 7. ... 8. calculus 9. ... 10. set theory 11. ... 12. number theory 13. etc. etc. (you get the point) Maybe there's already something that lays out topics like this. I haven't search…

This one was just discussed on HN yesterday with pretty good reviews: https://www.amazon.com/Math-Through-Ages-Teachers-Mathematic...

Re: The Lost Art of Logarithms

#178

Post by tim333 »

dkislyuk wrote: post #45

I found that looking at the original motivation of logarithms has been more elucidating than the way the topic is presented in grade-school. Thinking through the functional form that can solve the multiplication problem that Napier was facing (how to simplify multiplying large astronomical observations), f(ab) = f(a) + f(b), and why that leads to a unique family of functions, resonates a lot better with me for why lo…

I rather like Feynman's approach in the lecture Algebra from the Feynman Lectures https://www.feynmanlectures.caltech.edu/I_22.html

He covers the inverse of the exponential, Henry Briggs' log tables and goes on to e^ix = cos x + i sin x

The audio is also available https://www.feynmanlectures.caltech.edu/flptapes.html

Re: The Lost Art of Logarithms

#179

Post by vanderZwan »

Related: in a reaction to a comment I wrote about logarithms about a month ago[0], saulpw recently linked his own idea of making logarithms more "accessible" to the masses by introducing magnitude-based notation:

https://saul.pw/mag/

I think it is a really nice idea that should be spread more widely. It might be Pi day, and while I traditionally complain that Tau is better for contrarian reasons (hey at least I'm honest), we might as well co-opt the extra attention maths gets for other mathematical causes.

[0] https://news.ycombinator.com/item?id=43036094

Re: The Lost Art of Logarithms

#180

Post by saulpw »

kzrdude wrote: post #148
saulpw wrote: post #57

Earlier quoted context omitted.

I think this should be front and center. To that end I propose "magnitude notation"[0] (and I don't think we should use the word logarithm, which sounds like advanced math and turns people away from the basic concept, which does make math easier and more fun). https://saul.pw/mag

If logarithm sounds too advanced, just say log and logs. I think it could work!

Mag is the inverse of log10. e.g. log10 ^6 = 6. We have no current shorthand for inverse log10 except "tentothe" which might be serviceable but is not as punchy.
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