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The Lost Art of Logarithms

lostartoflogarithms.com

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Re: The Lost Art of Logarithms

#131

Post by 7402 »

divbzero wrote: post #126
xelxebar wrote: post #94

How timely! I just learned how to use a slide rule yesterday. Looking to pick one up, and a bit overwhelmed by the plethora of choices, I went down a small rabbit hole[0]. Some slide rules produced are pure works of art! Lately, I've been rediscovering the surprising niceties that analog tools can provide over our everything-is-a-panel-of-glass interfaces these days. Recently, I have been enjoying pen and paper as my…

Where can I get the meter-long slide rule the man is holding in OP?

They show up on eBay. A search this minute revealed two:

https://www.ebay.com/itm/205220626817 https://www.ebay.com/itm/156686655356

They go for a bit more than the original price, according to this:

"Pricing varied by retailer, however Pickett did offer demonstration slide rules in 4 foot and 7 foot lengths: a 4 foot rule sold for $15 and the 7 foot rule was $25 in 1960. These were available with scales to match models N4, N803, and N1010 with the Ln scale added. These large rules were available free to schools which ordered 24 or more slide rules!"

[0] https://www.sphere.bc.ca/oldsite/test/pickett.html

Re: The Lost Art of Logarithms

#132

Post by kqr »

meta_ai_x wrote: post #75
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 actually prefer the straightforward log is an inverse of exponents. It's more intuitive that way because I automatically can understand 10^2 * 10^3 = 10^5. Hence if you are using log tables, addition makes sense. I didn't need an essay to explain that. Take logs, add 2 + 3 = 5 and then raise it back to get 10^5.

This is how I've always taught logarithms to students I've tutored. I photocopy a table of various powers of ten, we use it in all sorts of ways to solve problems, and then I sneakily present an "inverse power" problem where they need to make the lookup backwards.

Almost every student gets it right away, and then I tell them looking up things backwards in the power table is called taking a logarithm.

Re: The Lost Art of Logarithms

#133

Post by kqr »

xelxebar wrote: post #94

How timely! I just learned how to use a slide rule yesterday. Looking to pick one up, and a bit overwhelmed by the plethora of choices, I went down a small rabbit hole[0]. Some slide rules produced are pure works of art! Lately, I've been rediscovering the surprising niceties that analog tools can provide over our everything-is-a-panel-of-glass interfaces these days. Recently, I have been enjoying pen and paper as my…

I have several slide rules and use them daily. Especially in the kitchen where we deal a lot with scaling proportions they are the best tool available: you set them for the desired scale, and then you can just read off any proportion you need in the blink of an eye.

I'm honestly surprised they are not standard issue in kitchens.

Re: The Lost Art of Logarithms

#134

Post by Dunan »

meta_ai_x wrote: post #75
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 actually prefer the straightforward log is an inverse of exponents. It's more intuitive that way because I automatically can understand 10^2 * 10^3 = 10^5. Hence if you are using log tables, addition makes sense. I didn't need an essay to explain that. Take logs, add 2 + 3 = 5 and then raise it back to get 10^5.

That's how I mentally processed them when first learning them years ago. Doing operations on x and y with log(x) = y in the background somehow felt far less intuitive than thinking about 10^y = x.

I really enjoyed this author's work, BTW. Just spent several hours reading the entire first five chapters or so. What an excellent refresher for high school math in general.

Re: The Lost Art of Logarithms

#135

Post by kqr »

aquafox wrote: post #80
TrainedMonkey wrote: post #67

Earlier quoted context omitted.

All data is linear when plotted on a loglog scale with a thick marker.

But in my explanation, there is no x axis.

No but it holds more generally. Taking the log of data tends to make it look "more correct" even when it's not theoretically justified, and this can lead to very wrong conclusions.

Re: The Lost Art of Logarithms

#136

Post by kqr »

BinRoo wrote: post #69

One of my favorite tricks in elementary school was to convince people I can calculate any logarithm for any number of their choosing. > Me: Pick any number. > Friend: Ok, 149,135,151 > Me: The log is 8.2 Of course I'm simply counting the number of digits, using 10 as the base, and guessing the last decimal point, but it certainly impressed everyone.

> 149,135,151

This is 8-point-something as you say.

1.49 is in between 1.2 and 1.6 and I have memorised log(1.2)=0.1 and log(1.6)=0.2, so I would think log(1.5) is close to 0.17, using sloppy linear interpolation.

That would make log(149,135,151) approximately 8.17. My calculator also says 8.17. Your guess was good!

I have found linear interpolation such an intuitive approximation method that the tradeoff of having to memorise more logarithms is worth it.

Re: The Lost Art of Logarithms

#138

Post by spc476 »

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…

There is Mathematics for the Million by Lancelot Hogben, which not only covers math, but the history of math and why it was developed over the centuries. It starts with numbers, then geometry, arithmetic, trig, algebra, logarithms and calculus, in that order. It's a very cool book.

Re: The Lost Art of Logarithms

#139

Post by yujzgzc »

I have a few old math manuals at home, from late 19th / early 20th century. Many of them have a logarithm table as an appendix. It looked like the type of things that if you had a few extra sheets to print to make a booklet, you'd just add because it was bound to be very useful to someone.

Re: The Lost Art of Logarithms

#140

Post by xelxebar »

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

What reflections do you have putting this into action over the year since that post?

BTW, your blog is one of my absolute favorites!

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