10:35] Unbitwise: you ask to borrow your grandfather's
[10:36] Unbitwise: a slide rule is basically a pair of rulers with logarithmic scales written on them, so if you use one to find a distance along the other (starting from a point that isn't 1) then you've done multiplication(edited)
[10:37] timepoof: can you link to a video about that
[10:38] Unbitwise: (slide rules are cool but if they're not readily available then I wouldn't bother bringing them in as part of teaching how to algebra at logs)
[10:44] somni: you could also start out doing things by analogy to digit length of numbers like

"when you multiply two positive 1-digit numbers together you get either a 1 digit number or a 2 digit number because at min its 1x1=1 and at max its 9x9=81.

if we wanna see what 100x10000 is we dont actually have to calculate this out, we can look at the number of 0s and add them together to get 1000000. this trick can be used for other numbers! you can use their length to estimate what their product is.

if we want to estimate what 175x45 is we can say "okay 175 is between 100 which is 10^2 and 1000 which is 10^3 and 45 is between 10^1 and 10^2. so we will get a number between 10^3 and 10^5."

we can refine what sort of thing we are looking at when we estimate the size of a number 10s-wise. so that 23 and 82 get different numbers instead of both being "between 1 and 2" in the 10s-sense.

an advantage of this measurement system is that it converts multiplication to addition which makes computations easier.

so we want the measurement to make sense so that we can add two 10s-wise numbers, a + b, and get a new 10s-wise number which when translated back into normal numbers is axb.

like to make this work out, what 10s-wise number would you give the square root of 10?"
[10:44] Sonata▣: how i like to introduce logs it like -- here's some different ways of writing the same thing:

[10:45] somni: and then id add in notation after getting them comfy
[10:45] Sonata▣: so a log is the math way of asking the question "what's the exponent?"
[10:45] somni: memorizing notation straight away is terrible and confusing ime and makes noob humans parse the things as rules of grammar
[10:46] Sonata▣: oh yeah i get that
[10:46] Sonata▣: yeah, that is in fact how i was thinking of the thing
[10:46] Sonata▣: where's you're talking about a thing you can do for which logarithms are useful
[10:50] Unbitwise: notation is "here is a thing which I would like to be able to think about, how should I write it down" so it should be preceded by the concept but not too far
[10:53] somni: @timepoof

https://www.sliderule.ca/buy.htm

i actually did get my sliderule from my family. one of my friends got one from thinkgeek when they were selling them.

according to this site, ebay is the place to get them now
[10:53] Keltab: (you can also print flimsy ones from the internet onto paper or cardstock)
[10:54] somni: they look to be 15-25$ for good ones that i can press the "buy it now" button on
[10:54] somni: https://www.ebay.com/itm/Vintage-Relay-No-DB-517-Bamboo-Slide-Rule-7-inches-long/362478778100?hash=item54656b36f4:rk:1:pf:0

^ like this
eBay
Vintage Relay No. DB-517 Bamboo Slide Rule (7 inches long)
Vintage Relay No. DB-517 Bamboo Slide Rule (7 inches long) | Collectibles, Science & Medicine (1930-Now), Engineering | eBay!

[10:55] Unbitwise: caution: old slide rules may be bent out of smooth sliding shape
[10:56] Unbitwise: that said, I am proud to have my father's slide rule which is a Pickett N600-ES, a.k.a. the same model that went to the moon
[10:56] Manya (bluejay): I don't know that a slide rule will be helpful for learning how to think about logs
[10:56] somni: another thing you can do is pull out a book of log tables and go through that

um you can do other things, but its kind of hard to learn to use a tool dissociated from what the tool is for
[10:57] Manya (bluejay): uh, no its not? plenty of people learn to use tools by "I press these buttons and then it gives me an answer by magic", this can easily be the same
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[10:57] Unbitwise: if you're not already a nerd about this I think a slide rule is too much a weird thing, will be a distraction from actually learning the algebra
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[10:58] somni: like right now the tool is for making the teacher smile or something?

there are other ways to introduce optimization targets and this is one of them. but like if you dont have good ones i think it is hard to learn?

this seems to be a convergent conclusion among humans who unschool their kids and math circle humans and humans i know who special-interest pedagogy.
[10:59] Unbitwise: somni you seem to mean something unclear by 'optimization targets'
[10:59] Manya (bluejay): (13 comes from 9+4, 36 is both 9*4 and 6*6. They're doing the "let's throw random operations at these numbers, surely one of them will be right" thing)(edited)
[11:00] Unbitwise: perhaps some explanation would help
[11:01] somni: like i want to multiply numbers together well on my own, this is my goal. im trying to do well by this goal.

this is a nice optimization target for learning logs where "im trying to make my teacher smile" isnt a nice optimization target.
[11:01] somni: like optimization target is a thing-you-are-trying-to-do
[11:02] somni: i think if you need to like buy one or make one it might be a distraction to do days of planning, but if you have one around i dont think that using one to demostrate stuff is a distraction from learning logs!
[11:06] somni: like people learn best via solving puzzles and achieving goals and stuff

and they learn less well by memorizing sequences of things that are correct Just Because

and the things they learn via them being correct Just Because are more fragile and easier for them to forget over a change in context, like "how would you estimate the product of all these numbers in your head if you dont want to multiply them out?" might not ping "oh i know something that can help!" if you just learn how the formal symbol manipulation goes
[11:06] timepoof: i tried to explain it but i detected that they were picking up basically "oh so this is what the Correct Step is" and not the understanding
[11:07] Manya (bluejay): right, somni, which is why you shouldn't use a tool specifically designed to quickly and easily give you right answers by looking them up without thinking about the logic
[11:07] Manya (bluejay): poof, you basically can't avoid some degree of "this is what the correct step is" when someone's used to that approach
[11:07] timepoof: they have access to a calculator in the exam that is less than a week away
[11:08] timepoof: oh ok
[11:08] Manya (bluejay): but you can phrase the questions slightly differently all the time, so they don't have cached algorithms
[11:08] timepoof: how do you do that
[11:09] timepoof: also i think they are confused by the difference between a number and the log of a number
[11:09] timepoof: i tried to explain it with "function boxes"
[11:11] somni: yeaaah the Correct Step before the authority that decides what things are correct doesnt help them understand why the rules are that way and doesnt help them create a compact generator of how logs work.

um in my experience if you use slide rules you kind of have to think about the logic because you are seeing things turned into manipulation of physical distances which is something that humans can get? i disagree that using a sliderule dissociates you from thinking about how logs connect up to things structurally if you are claiming this?
[11:12] timepoof: you will be surprised to observe a high school math class then
[11:12] timepoof: i would probably see it but the relevant person probably wouldn't
[11:16] timepoof: i mean i would try it if it was a cheap test but as it stands i don't really posess one so
[11:19] timepoof: (i likely can't buy one online, for reasons manya will know and somni might not)
[11:21] somni: [
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claim is that high school math classes that work via approval from authority are useful for learning math?

but like most hs math classes make people be more like your friend wrt how they learn to absorb new topics? this is bad? people thinking and understanding things is good? it is good to help people learn things robustly so they arent addicted to grammar dictionaries and can think for themselves?
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idk how to help your friend while also being okay with needlessly hurting their ability to think about math.

like the thing i said about estimating lengths of things isnt about sliderules but is also a useful thing and enables them to use math-y relaitonal cognition instead of decorum social cognition.
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