Funny how logarithms shaped navigation, astronomy, and music—yet now they're mostly a forgotten button gathering dust on our calculators. Hidden tech history right there.
The Lost Art of Logarithms
191–200 of 204 posts
Re: The Lost Art of Logarithms
#192Earlier quoted context omitted.
Ironically, that notation, which I just discovered, confuses me more than anything else. Logs clicked for me when someone online said "amongst all the definitions we have for logs, the most useful and less taught is that log() is just a power". At that exact instant, it's like if years of arcane and foreign language just disappeared in front of my eyes to leave only obviousness and poetry.
That is not without humour :) I don't understand the comment about it just being a power, but, for me, knowing that it's filling in the third vertice on the triangle with exponents at the top, and n on the other is what makes it work for me - I now know in my head when I am looking for the log of n, I am looking for the exponent that would turn the log into n. I don't go looking for the exact log, I only look for who…
I said "power" as in "exponent", so we basically have the same understanding, I just do without the triangle.
Re: The Lost Art of Logarithms
#193Earlier quoted context omitted.
I've been doing a math course and occasionally think of picking up these analogue tools. Someone on Hacker News had me interested in the Soroban, the Japanese abacus [1], which is still used to train insane mental math speeds to this day [2]. 1. https://en.wikipedia.org/wiki/Soroban 2. https://www.youtube.com/watch?v=s6OmqXCsYt8
We're definitely on a similar wavelength. I actually own a couple Japanese abaci and know the basics. Top performers feel near magical: double-fisters[0] and blazingly fast mental arithmetic [1]. [0]: https://www.youtube.com/watch?v=EK6uIjjkrGE [1]: https://youtu.be/-kjUCtqSWlw?feature=shared&t=451
Have you used it much? I'd like one, but I can imagine it sitting on my desk for years unused. I have "Secrets of Mental Math" by Arthur Benjamin and have wanted to practice some of those mental math skills, and I wonder if learning the soroban will interfere with my existing mental calculation framework (which is admittedly weak at the moment).
Re: The Lost Art of Logarithms
#194Earlier 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 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.
Devlins book - "Mathematics: The Science of Patterns" was similar for me and you might enjoy it in addition to what you previously read.
Much better than how I was taught in my schooling.
Re: The Lost Art of Logarithms
#195Earlier 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). The only reason that "logarithm" sounds like advanced math is because it was so useful that mathematicians, well, used it. Since this terminology is just log…
It's written like ^6 and said like "mag 6", which sounds like an earthquake (and this is basically the Richter scale writ large). One syllable, sounds cool, easy to type/spell, evokes largeness. "Logarithm" is 3-4 syllables, hard to pronounce, hard to spell, sounds jargon-y.
People virtually never say “logarithm” in use though. They either say “log” or they say “lun” for natural log. Notice that both log and lun are one syllable, easy to pronounce etc.
Magnitude is an existing and important concept in maths - it would be extremely confusing to just overload it to mean something else.
Re: The Lost Art of Logarithms
#196Earlier 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 !
As someone who is studying maths at the moment I don’t recognise this picture at all. Every resource I learn from stresses the practical motivation for things. My book of odes is full of problems involving liquids mixing, pollution dispersing through lakes, etc, my analysis book has a whole big thing about heat diffusion to justify Fourier analysis, the course I’m following online uses differential equations in population dynamics to justify eigenvalues etc.
Re: The Lost Art of Logarithms
#197Earlier quoted context omitted.
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.
Right, I'm not saying it's for no reason, but the asymmetry makes it harder to keep track of which undoes exponentiation in which way.
And logs are frankly more confusing than the other operations because more than anything else they feel like an algebraic expression in the form of an operation. Other operations intuitively feel like a process, whereas logs feel like more like a question.
Maybe that's just because I never learned them super well though, maybe they're not actually that inherently different ¯\_(ツ)_/¯
Re: The Lost Art of Logarithms
#198Earlier quoted context omitted.
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...
Wait let me make sure I understand, you want to skip the notation all together, or you want more support in understanding it?
Re: The Lost Art of Logarithms
#199Earlier quoted context omitted.
It's written like ^6 and said like "mag 6", which sounds like an earthquake (and this is basically the Richter scale writ large). One syllable, sounds cool, easy to type/spell, evokes largeness. "Logarithm" is 3-4 syllables, hard to pronounce, hard to spell, sounds jargon-y.
People virtually never say “logarithm” in use though. They either say “log” or they say “lun” for natural log. Notice that both log and lun are one syllable, easy to pronounce etc. Magnitude is an existing and important concept in maths - it would be extremely confusing to just overload it to mean something else.
The log of 3.1m is 6.5. How do you say "10^6.5"? I say "mag 6.5" and it is clear. The Richter scale famously uses "mag 6.5" exactly like this. If that was ever confusing, then we've managed to work past it, and this just expands the Richter scale to cover basically everything.
Re: The Lost Art of Logarithms
#200Earlier quoted context omitted.
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...
Wait let me make sure I understand, you want to skip the notation all together, or you want more support in understanding it?
I want to learn the notation. Just not everything at once. I need to be able to see real world usecases, otherwise I wont be able to remember and apply the notation.
What I meant is learning the notation step by step, topic related.