Growing up, they told us about continuity like it was gonna save our souls, never have to use rationals again... Never have to approximate. Calculus was the grail! (It was mine; I sought it for years. Never take the books away.) They never told us that 1 and 0 and + and * were enough to break your mind. My teachers enthused at wiping away complexity with the unblemished surface of complex numbers and analytic functions... but crystal don't grow without a seed.

The thing with number theory is, 'can you do that' is never a question. Of course you can do that! Does it make any sense, does it land you in a useful field, does it have any non-trivial properties you can exploit to pull a rabbit out of your hat? That's the question. But can you do that? Of course! It's just adding and multiplying, you can do whatever you want. Most things, however, won't get you anywhere.

Kim Reece boosted

I still find it faintly incredible that no group of scientists has gotten together and just made a damn set of free textbooks to cover the whole standard curriculum of their field. For uni physics, you'd need, roughly speaking and allowing for bits of overlap:

1. Classical mechanics
2. Single-variable calculus
3. Electromagnetism
4. Multivariable and vector calculus
5. Statistical physics
6. Quantum physics
7. Special relativity
8. Data analysis (a text most likely used as reference in a lab course)
9. Differential equations
10. Linear algebra

Education reform went haring off into MOOCs without really contemplating the possibility of making better resources for more traditional in-person teaching.

Kim Reece boosted

... Some open textbooks have been written, but to my knowledge, nobody has organized a "depth-first" drive. For example, the OpenStax products look fine, but they really only cover about 1 to 1.5 academic years of a physics program:

openstax.org/subjects/science

openstax.org/subjects/math

What I'd like to see is more comprehensive (and with a lighter-weight website, for heaven's sake).

Kim Reece boosted

Technology, thought experiment; stated clearly 

Kim Reece boosted

being a math student of the European tradition is a lot like being a wizard or something.

You get told that nothing is really what you thought it was, and you have to perform menial labor and pass gruelling tests for years as an acolyte, memorizing and internalizing thousands of years' worth of esoteric knowledge. When you finally pass the final test(defending a dissertation), you're a full wizard.

Kim Reece boosted

ok I think I have maybe reached a new low of nerdism, but,

John Gustafson's 'posits' floating point format is a thing of beauty and I am in awe

the bits! they align!

also, exponents of exponents of exponents

when your numbers aren't quite numbery enough? MOAR EXPONENTS is definitely what you need.

posithub.org/docs/Posits4.pdf

via nextplatform.com/2019/07/08/ne

via @enkiv2

I feel like I'm missing a fundamental level of comfort with moving these objects in my head. :(

But what if .. The Other Complex Conjugation?!

[Twilight Zone theme plays]

Kim Reece boosted
Kim Reece boosted

I threaded some math madness.

hackers.town/@feonixrift/10237

There's a lot more where that came from. The inside of my head looks like this.

Kim Reece boosted

Turkey has charged over 700 academics with terrorism for signing a peace petition: insidehighered.com/news/2019/0

Among the most severely penalized among them is Tuna Altınel, a mathematician in France who was arrested visiting family in Turkey, and who has now been imprisoned for over 50 days. For more see math.univ-lyon1.fr/SoutienTuna (via cameroncounts.wordpress.com/20)

I'm hungry, I'm sad. I'm trying to calculate a special case of an explicit bound, when the paper it's from was only interested in it being finite. So 'some constant can be determined from this information' and on it goes, when I need the constant (or a bound on it). It's really likely to be too big to be useful, but due diligence... Mostly the norm method I was using before fell apart so I'm doing this while I get up the courage to localize at a prime.

Current status: Viscerally disturbed by 1 and 0.

From comparing this to the answers of others, I conclude that I am part abacus, as my method is to build tens out of small components, then consider the tens as a separate counter.

Kim Reece boosted

What happens in your head when you do 27+48?

I do
7 + 8 = 15; 20 + 40 + 10 = 70; 70 + 5 = 75

[If you want to do this yourself please copy the question and make your own post] #27plus48

What happens in your head when you do 27+48?

I do
10-8=2, 7-2=5, 22+48=60+10=70, 70+5=75

[If you want to do this yourself please copy the question and make your own post]

The desire to pair-program a thesis so I quit wasting time on dead ends...

I haven't felt like this since Caltech. I didn't know I still could feel this... I missed it so much.

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