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@futurebird
I work in tech, not physics or more classical engineering, but I can say that the number of times I've wished staff knew calculus when they didn't? Zero in twenty years. The number of times I've wished they knew basic statistics when they didn't? At least once a month, for twenty years.
@whknott

@dymaxion @whknott

When you've wished you knew more about stats what was it that you wanted to do, find out, or know?

@futurebird
Hmm. Often, really just basic statistical numeracy so they could understand data they seeing in papers, etc. Sometimes, more the ability to reason about what is and isn't good data for quantitative decision-making — folks really love to make up meaningless numbers to let them avoid qualitative decisions when quant data isn't there. Sometimes data analysis to understand things like perf impact from log data for edge cases. So in some ways, not really statistics itself, but all things that I find that folks who made it through at least one real stats course are likely to be better at, if that makes sense?
@whknott

@dymaxion @whknott

So, more experience with the creation of data visualizations and summary statistics (where do they come from?) Methods to access their quality and predictive value?

I ask because I've had many people say something along these lines "why did I learn so much calculus, everything I need to do with math is statistics?"

This can confuse me a little because understanding distributions is so much easier if you know calculus. (To find maximums and areas under curves.)

@futurebird
Yeah, largely in that kind of space. Also rigor around what it means to measure something, etc. Like, obviously calculus is useful — if nothing else, not having the conceptual tools of first and second derivatives makes looking at a line on a graph or the area under it less intuitively useful — but I think it's more about the things that you learn along the way.
@whknott

@dymaxion @whknott

I realize that mathematicians can make everyone very tired because we are more interested in the foundations and shape of the containers than their contents.

We teach students how to complete the square to solve quadratics ... mostly so they can prove the quadratic formula for themselves.

But often these students don't even really understand that if a*b=0 that means a, b or both must be 0 or how that is at all relevant to "finding x"

1/

@dymaxion @whknott

Because what mathematics really is are the *proofs* not the solutions, not the algorithms, but that unbroken chain from a minimal set of assumptions to the solution.

Over and over we work to demonstrate this unbroken chain, though in most undergrad statistics courses this is just something we give up on in favor of getting the students competent enough with the algorithms to mostly apply them correctly. And that's part of why such courses aren't seen as "real math." 2/2

@futurebird @dymaxion @whknott

Indeed the emphasis of math teaching, in high school and early college, is in the sort of logic that enables one to gain trust in a mathematical statement C from facts A and B that one trusts are true.

And that is a good thing, because most problems the student will require algorithms or formulas that he did not learn at school.

‍>

@futurebird @dymaxion @whknott

‍> But, as you say, math teaching at school indeed tries more: it tries to derive every math statement all the way from a few "fundamental axioms". That is a leftover from the days when the only serious math taught at school was geometry, and geometry meant Euclid's book.

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@futurebird @dymaxion @whknott

‍> I don't see THAT -- going all the way to "fundamental axioms" -- as a good thing. On one hand, the choice of axioms is arbitrary: one could take any sufficiently large set of theorems from Euclid, declare them to be the axioms, and then derive his axioms from these.‍>

@futurebird @dymaxion @whknott

‍> Furthermore, over the last couple of centuries we have realized that those "fundamental axioms" are not as "true" as Euclid assumed. General relativity and the Heisenberg principle make Euclid statements wholly unreal -- like axioms about gods, ghosts or dragons. The foundations of set theory are a mess. ‍>

@JorgeStolfi @dymaxion @whknott

The foundations of set theory are a mess? This is news to me.

There have always been mathematicians interested in pipe dreams like universal axioms or more minimal sets of axioms. But if you need to get things done you *can* ... you just need to be honest about what you are assuming, and it might not be as minimal as some want.

Different assumptions create different mathematics that have their own uses.

Maybe I'm not understanding what you are saying.

@futurebird @dymaxion @whknott

"Let X be the set of all elements that don't belong to X" That definition of the set X is *obviously* invalid; but how do you define rigorously what is a valid definition?

The complement C of a set X is supposed to be all the elements that do not belong to X. But since sets can be elements of other sets, the set C is itself an element of C. Is that okay? if not, how do we fix that?‍>

@JorgeStolfi @dymaxion @whknott

At the base of every axiomatic system are terms that cannot be defined using the system itself. Terms that require consensus and should be recognized as such. And these are always worth re-examining and removing, changing to see what other systems we may develop.

It is still a human endeavor, based on language. And I think that's a feature not a bug.

@futurebird @dymaxion @whknott

It is not just that the axioms are arbitrary, but that they cannot be specified precisely without contradiction. If you can't define what a "set" is, how can you expect everybody to agree on whether something is a set of not?

Euclid himself assumed a couple of things that should have been explicitly stated as axioms, such as "If a line, not passing through any vertex of a triangle, meets one side of the triangle then it meets another side."

@futurebird @JorgeStolfi @dymaxion @whknott Because it was the last hope for those who wanted fundamental certainty in their worldview. Religion struck out, physics was finding fundamental limits. If you yearned for completeness and certainty, it was distressing.

@randomgeek @futurebird Right?

Also, Alan Watts must be among the most sampled philosopher of all time! There are dozens of songs with bits of his talks.

One of my favorites is Golden Light, by STRFKR

https://open.spotify.com/track/1rPYEWQfIRo5A4fvLgFbBe?si=6-nU6genQZurpSrs8VCUow