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The Lost Art of Logarithms

lostartoflogarithms.com

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Re: The Lost Art of Logarithms

#161

Post by agumonkey »

BobbyTables2 wrote: post #90
agumonkey wrote: post #61

Earlier quoted context omitted.

I often wonder about this. I also believe that mathematical pedagogy strive to attract people that are very smart and think in the abstract like euler, and not operationally, meaning they will get it intuitively. For other people, you need to swim in the original problem for a while to see the light.

Math is rarely taught with practical problems in mind — that’s engineering !

Well, logarithms were made from physical entities (celestial bodies) but not on engineering per se.

I think this is already enough context to root the mental effort deeper.

Re: The Lost Art of Logarithms

#162

Post by meindnoch »

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…

By the way, there's another function that can be used to turn multiplication into addition: f(x) = x^2 / 2

a * b = f(a + b) - (f(a) + f(b))

Re: The Lost Art of Logarithms

#164

Post by meindnoch »

fenomas wrote: post #98
BobbyTables2 wrote: post #90

Earlier quoted context omitted.

Math is rarely taught with practical problems in mind — that’s engineering !

Agreed, and it's such a shame! A kid goes to math class and learns, say, derivatives as this weird set of transformations that have to be memorized, and it's only later in in physics class that they start to see why the transformations are useful. I mean, imagine a programming course where students spend the whole first year studying OpenGL, and then in the second year they learn that those APIs they've been memorizi…

I've never seen an introductory math textbook that didn't point out how position, velocity and acceleration are related by the derivative.

Re: The Lost Art of Logarithms

#165

Post by tmoertel »

lkuty wrote: post #154
tmoertel wrote: post #64

Earlier quoted context omitted.

For the particular case of the exponential distribution we can go further. By taking advantage of the theory of Poisson processes, we can take samples using a parallel algorithm. It even has a surprisingly succinct SQL translation: SELECT * FROM Population WHERE weight > 0 ORDER BY -LN(1.0 - RANDOM()) / weight LIMIT 100 -- Sample size. Notice our exponentially distributed random variable on prominent display in the O…

Quite off-topic, but do you know when you'll write the article about CPS, if ever?

Oops. I had quite forgotten that I need to write about that. I said I would over a decade ago, so that's a long time for you to wait. Sorry about that.

I mainly write for myself, so I need the time and the motivation. Until recently, my job at G took up my time and also provided an internal community where I could scratch the writing itch, which reduced the motivation for public writing on my blog. But now that I'm semi-retired, I'll try to write more frequently.

Thanks for the accountability!

Re: The Lost Art of Logarithms

#166

Post by codesuki »

madars wrote: post #97
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…

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 recently read mathematics for the nonmathematician. https://www.goodreads.com/book/show/281821.Mathematics_for_t...

Although the math in the book is relatively basic I enjoyed it tremendously because it gives the historical development for everything and even describes the characters of different mathematicians, etc. The historical context helps so much with understanding.

Re: The Lost Art of Logarithms

#168

Post by nkoren »

madars wrote: post #97
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…

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"

It's ontogeny recapitulating phylogeny, all the way down.

Re: The Lost Art of Logarithms

#169

Post by markstock »

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…

Here's one that starts with the concept of a straight line and builds all the way to string theory. It's a monumental book, and it still challenges me. Roger Penrose's The Road To Reality.

Re: The Lost Art of Logarithms

#170

Post by -__---____-ZXyw »

zwnow wrote: post #141
b0afc375b5 wrote: post #121

Earlier quoted context omitted.

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…

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.

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