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The Lost Art of Logarithms

lostartoflogarithms.com

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Re: The Lost Art of Logarithms

#141

Post by zwnow »

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…

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.

Re: The Lost Art of Logarithms

#142

Post by twbarr »

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"

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.

Re: The Lost Art of Logarithms

#143

Post by nakedneuron »

kqr wrote: post #63

I can strongly recommend memorising some logarithms for use in mental maths. It's given me powers I did not expect to have! Here's what I wrote about it when I started: https://entropicthoughts.com/learning-some-logarithms

Great blog!

Interesting fact that memory decay also is inherently logarithmic/exponential.

Learning logs with SRS is so meta.

Re: The Lost Art of Logarithms

#144

Post by hansmayer »

Wow, I thought it was just some random guy, but was then quite surprised to see this was being authored by none other than the legendary Charles Petzold. I'd buy this book - just to put it next to my copy of "Programming Windows 95" (who remembers?) :)

Re: The Lost Art of Logarithms

#146

Post by jamalaramala »

There was an interesting text, by Isaac Asimov, where he explained in a very clear way the historical importance of logarithms -- they allowed Kepler to finalize his work by replacing tables of multiplications (which were difficult and error-prone) with sums.

Re: The Lost Art of Logarithms

#147

Post by PaulRobinson »

twelvechairs wrote: post #129
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…

I'm sympathetic but there's no clear historic chronology. For instance the ancient egyptians dealt with both algebra and calculus (at least in part) long before Pythagoras. And thats not starting on China and India which had very different chronologies.

Choose a chronology that makes sense. We can see how Western ideas build, we have less clarity on how the ancient Egyptians or Chinese ideas developed, and therefore it's harder to explain to a learner.

If you're sensitive to that singular world view warping the learner's prospect, you could at each point explain similar ideas from other cultures that pre-date that chronology.

For example, once you've introduced calculus and helped a student understand it, you can then jump back and point out that ancient Egyptians seemed to have a take on it, explain it, ask the student to reason did they get there in the same way as the Western school of ideas did, is there an interesting insight to that way of thinking about the World?

Another ideas is how ideas evolved. We know Newton and Leibniz couldn't have had access to direct Egyptian sources (hieroglyphs were a lost language in their life times), but Greek ideas would have been rolling around in their heads.

Re: The Lost Art of Logarithms

#148

Post by kzrdude »

saulpw wrote: post #57
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 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!

Re: The Lost Art of Logarithms

#149

Post by ForOldHack »

BobaFloutist wrote: post #112
II2II wrote: post #107

Earlier quoted context omitted.

I think it is a combination of factors. Mathematical pedagogy is legitimate if the end goal is to train mathematicians, so yes it is geared towards those who think in the abstract. (I'm going to ignore the comment about very smart, since I don't think mathematical ability should be used as a proxy for intelligence.) On the other side, I don't think those who are involved in curriculum development are very skilled in…

Frankly I wish I had known integral calculus going into geometry, I could tell there was a pattern behind formulas for areas and volumes but I couldn't for the life of me figure it out. There are worse ways to remember the formula for the volume of a sphere than banging out a quick integral!

I had known it. Thanks Dr Steven Giavat. The geometric shapes gave the patterns meaning. I read 'mathematics and the imagination' and mathematics a human endever' while I was starting algebra. Also the time-life book on math. All very brilliant because they used the methods that were used to investigate it, to show how it was discovered. These allowed me to fly ahead in math until I got to trig. Which took a long year to get facile, until I was able to finish my degree.

I had brilliant teachers.

Napier's bones, were for adding exponents, hense multiplication. Brilliant and nessary for the development of the slide rule, and the foundation of modern engineering, until the pocket calculator.

Re: The Lost Art of Logarithms

#150

Post by vismit2000 »

jamalaramala wrote: post #146

There was an interesting text, by Isaac Asimov, where he explained in a very clear way the historical importance of logarithms -- they allowed Kepler to finalize his work by replacing tables of multiplications (which were difficult and error-prone) with sums.

Realm of Algebra by Isaac Asimov: https://archive.org/stream/RealmOfAlgebra-English-IsaacAsimo...
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