Math without Tech - Reject Calculators Return to SlideRules

[N Space]

Math is a fun hobby, and a while back, I wondered how they were doing complex matrices before we had computers or even personal calculators in the late 60s/early 70s. (those earlier "personal calculators" don't count; they were enormous and didn't use solid state/integrated circuits until the 60s, so weren't handheld/portable)

Meet Classical Matrix Algebra, calculating Eigenvalues as they did 100 years ago and beyond. Fucking wild. From Modern Algebra and Matrices, 1951

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They were just manually transforming everything and checking to ensure everything was correct manually. We don't consider the amount of math we outsource to computers today and how much of what we learn now has been simplified; past curriculums are fucking insane to take a look at.

We built the atomic bomb and the first computers with this kind of math. It's amazing!

Disclaimer, I'm a bit rusted so correct me if I'm wrong.

Don't know exactly what algorithm is being used here since there are many and I'm not entirely familiar with the notation or theorems used in the book, but the algorithm I recall was to obtain the characteristic polynomial of the matrix and then find its roots to find all eigenvalues. The characteristic polynomial is simply the determinant of the matrix λI - A. To compute such determinants in a reasonable amount of time, Gaussian Elimination can be used to obtain an upper triangular matrix B. When you swap two rows in a matrix, the determinant changes its sign and when you multiply a row by a scalar a, the determinant is also multiplied by a, therefore, the determinant of A is the determinant of B (which is just the product of its diagonal components) divided by (-1)^n*a_1*a_2...*a_k where n is the number of row swaps you performed and a_1,...,a_k are the scalars you used to multiply rows of A.

 

[gagabobo1997]

Mechanical calculators are great but good ones capable of advanced arithmetic are large, expensive, rare, and very complex.
Solar calculators are cool but cheap ones are often fake. Can't go wrong with a ti-83 and a solar panel to charge your AAA batteries.
The ti-30XIIS is the only solar calculator I would recommend, I have a few in my collection and they work well.
Slide rules are fun but in a SHTF scenario I see no reason why you shouldn't be able to use a good graphing calculator; electricity is relatively easy to produce if you prepare well.

 

[VIPPER?]

If you want a book req, "Math for the Non-Mathematician" is quite good imo. Originally written as a textbook for early college students, it got a stendo version with extra hot maths lore inbetween chapters that covers the use cases and history of that math. I have a weatherbeaten hard copy somewhere I thumb through when I get back into autism games like gmod or stormwanks when I need more than basic trig. I don't have a link to a pirate copy on this computer but it was easy to find last time I had to.

For SHTF I don't see a huge call for advanced math but it would be worthwhile to look into compass-and-straightedge tricks. IMO the main draw of being good at math for any SHTF reason would mostly relate to construction/carpentry/etc, or for navigation. And for navigation there's a million physical tools from sextants to specially marked slide rules made just for it that you can get at any nautical or outdoorsman store. But for drafting/marking up wood, if you have a compass and straightedge you can very easily get precise parallel/perpendicular lines against a circle and from there it's easy to get easy 30/45/60/90 angles. As a bonus, once you do the major tricks once each, you can just do them again all together in colored pencil and keep that in your notebook.

I guess maybe if you're doing hick chemistry some math might be important but I feel like "practical o-chem"(meth and bombs) doesn't require math so much as logic.

And of course, just like do long division once in a while.

Any advice on getting better at math when you also have dyscalculia? I struggle with math, but I’d love to become more proficient without relying on tech as much as I have to.

Do it on paper. Unless you're a cashier or something, being proud of handling huge numbers in your head is jeet shit. Even ancient peoples carved that shit into tablets or used an abacus. Even with dyscalculia you should be able to add numbers not bigger than 9.
And again a lot of practical math comes down to geometry, which can be done mostly visually. Even calculus ends up being a lot of "line goes what way now?" stuff.

I use regular printing paper but this is something I would love

https://en.m.wikipedia.org/wiki/Kraft_paper

If you don't want to get an account at Uline or something to just get giant rolls of packing paper, you can often buy this in art stores. People like to use grease pencils on it.

 

[YazeePro]

...wait, this isn't taught in US universities? We learned this in linear algebra in 2003 and I'm 140% sure it's still in the curriculum.

We had this taught in a class about quantitative methodologies. Our professor insisted on doing some matrix calculations manually to get a better understanding of how the methods (like regression analysis) worked and to develop an appreciation for how much complexity computers are handling for us. To be honest, it was really beneficial.

We can all do at least some math in our head, but if you don't have a computer, phone, or calculator on hand, and need to crunch something complex, how would you do it? lets discuss various methods and tools to do calculations, preferably in a context where electricity wasn't readily accessible.

I distinctly remember a trick I was taught when I was in elementary school and which really made me realize how factorization and powers work. Looking back I am amazed nobody taught me that earlier... But that's maybe due to the fact that a big focus was on memorizing the 'times table'. Or maybe I just didn't pay attention.

The trick was to think of powers of 2 when multiplying by 4 or 8. So, instead of solving 7*8=56 directly, it's easier to think of it as doubling 7 three times (because 2*2*2=8 ). So, double 7, then double 14, and laatly double 28 = 56.
Sure, it's slower than memorizing the solution, but it really helped me to understand how multiplication and factorization works.

Since, obviously, the concept is extendable, I tend to do apply this trick even nowadays then multiplying larger numbers.

 

[Strangolapreti]

Here's a funny little Math thing I found:
Let's take the basic 2 + 2 = 4, let's replace the numbers with incognitas (a + b = c) and the "+" with any operation that results in a < c and b < c (addition, multiplication, exponent...), with the resulting math problem being something that I like to write down as (a |?| b = c).
Without recurring to immaginary numbers, this problem can only be solved with a = b = 2 and c = 4.
Let's evolve this problem to a |?| b |?| c = d, again, I don't think this problem is actually solvable unless we assume that the 2 operations performed are always the same (so a + b + c = d or a × b × c = d, a ^ b ^ c = d and so on), but otherwise, the only possible solution there becomes a = b = c = √3 and d = 3(√3).
If we add more letterns, a pattern generates: the solution is n values with nth as the solution, the number you seek is always n-2√n-1 for all but the last one and n-1(n-2√n-1) for the final value.
Just thought it was funny math thingy to learn.

 

[The Real Slim Shady]

For integer solutions of a+b = c and a*b = c there are only two possibilites, either all zero (trivial) or a = b = 2. But in general for a, b in reals you get b = a / (a - 1) and c = a^2 / (a - 1)