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bsaul

i'm looking forward to the day calculus gets rewritten using more intuitive notations.

Everytime i manipulate dx i feel like walking on a minefield.

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You can always try infinitesimal analysis[1]

[1] https://people.math.wisc.edu/~hkeisler/calc.html

I honestly don't know why infitesimals aren't widespread. It can basically have the same basis/justification can't it? But with the bonus of being more intuitive.

You don't even need to use "infinity", it starts out as just a variable representing some unknown quantity, then you "round to zero" on output.

I actually collected a bunch of old Infinitesimal calculus math books.

> I honestly don't know why infitesimals aren't widespread. It can basically have the same basis/justification can't it? But with the bonus of being more intuitive.

Indeed they are more intuitive, people like Newton and Leibniz invented/discovered calculus by thinking in terms of infinitesimals, but it took time to be made rigorous, in the XX century. By then network effects got we stuck with epsilons and deltas, given that was the approach made rigorous earlier, and broadly adopted, despite being more cumbersome.

Would you mind giving us the titles of those books?

They are in the attic at the moment, but they are all fairly old books (and terse, dry, basic formatting/illustration), seemingly from a period in time when infitesimals were apparently more popular.

There are a few similar ones on IA, e.g.

https://archive.org/details/in.ernet.dli.2015.148501/page/n8...

On that page the 'h' term is the infitesimal, as in

  d(x^2) / dx = 2x + h

Though I prefer something like 'Δx' to make the link to x more explicit. Would love to see a more modern book on the topic.

Or, for the Knuth-included, surreal numbers: https://people.math.harvard.edu/~knill/teaching/mathe320_201...

(Seriously though, learn to love the minefield. ~~~~Another physicist)

Keisler book is excellent.

> Everytime i manipulate dx i feel like walking on a minefield.

Embrace the minefield, love the minefield!

  Signed
  a physicist

Newtonian notation certainly feels more elegant to me. But kind of painful to work with in LaTeX. Langrangian notation is almost the same, and much eaiser to type too.

It has been argued before [0] that Leibniz notation being embraced in mainland Europe and not adopted in England/UK was the reason England fell about a century behind. First heard of this in MIT Calc undergrad course on YouTube, but would be too tedious to find which video, hence ran a search on the Internet.

[0] https://hsm.stackexchange.com/questions/7704/was-english-mat...

Newtonian notation is just doing time derivatives with a dot above them, so in Latex that is just \dot{x} = v . Which means dx/dt = v, or \ddot{x} = a.

Did you mean "Leibniz's" notation[1]? If so, if you use the esdiff package[2] it's just \diffp{y}{x} for partials or \diff{x}{y} for regular derivatives.

Lagrange's notation is when people do x' = v or x'' = a and Like the Newton's notation you kinda have to know from context that you are differentiating with respect to time unless they write it properly as a function with arguments which people often tend not to (at least I often tend not to I guess).

Sometimes people call the partial derivative notation where you use subscripts "Lagrange's notation" also[3]. So like f_x(x,y) = blah is the partial derivative of f with respect to x.

[1] Actually invented by Euler, or maybe some other guy called Arbogast or something[?sp]

[2] https://ctan.math.illinois.edu/macros/latex/contrib/esdiff/e...

[3] Even though that was also actually invented by Euler apparently.

\dot {} is not convenient to write everytime, and I suck at remembering to use macros. On the other hand, just writeing f' is far faster.

I’d be thrilled if mathematicians would just use multicharacter variable names instead of getting overly fancy with diacritics and italic/bold/capital/Greek variations.

The XKCD about unifying standards under a new standard is how I feel every single time I learn anew piece of math notation.

"This is ridiculous! We need a better, more intuitive notation that's also easier to do math at."

That's xkcd 927,a mnemonic for that is 3^2 * 100 + 3^3

SICM?

If you liked the "functional" style of calculus in SICM, or want a calculus only book in this vein I recommend Baby Spivak: https://en.wikipedia.org/wiki/Calculus_on_Manifolds_(book)

(And obviously Functional Differential Geometry by the authors of SICM)

Certainly Gerry Sussman's frustrations with ambiguous notation were a big reason for his decision to create SICM! https://youtu.be/arMH5GjBwUQ?t=236

never seen this talk before, thanks ! i feel less lonely.

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