I can't help but think his examples are symbolic manipulation and not actual mathematics.
These maybe of interest to physicists without access to a computer algebra system, but to actual mathematicians they are as meaningless today as being able to do your 12 times table in your head.
Not all of them mind you, the last 10 questions are still interesting, but again mainly to physicists.
Edit: which makes sense since he states the questions are a "mathematical minimum for a physics student", which is different to the minimum mathematics needed for a mathematics student.
Filters allow rather large families of wavelengths through. You don't have just red, you have a fraction of green. Because your eyes only have three types of photoreceptors they can be fooled by playing back a similarly large family of wavelengths back.
Slav surnames are gendered. * ski is male, * ska is female, * sko is neutral. Using gender neutral in this case is as insulting as calling him a dog.
Other cases where using gender neutral pronouns insults everyone speaking the language is using Latinx for Latino. If you want to butcher every other languages genders like they are in English, use Latin instead - the gender neutral form of Latino in English since only the middle ages.
I think it will when we finally have a language that is useful for all of: jotting down expressions, manipulating them by hand, and being consistent enough that automated theorem provers/proof helpers can use as their internal representation.
The issue right now is that the impressionistic maths notation works well for humans and there is no computer language that:
1). has good notation
2). is useful to mathematicians out of the box
Mathematica, sage, axiom, etc all have internal representations that are essentially the system I'm talking about but the user facing language is a mess in all cases. It's not a simple problem and I don't even know what the solution looks like.
It will have a lispy notation (tree serialization), and use rewrite rules (generalized macros) and types (some type of type inference with explicit typing annotations), but other than that I feel like someone trying to invent Algol in 1947.
Being a republican doesn't make you part of some gestalt consciousness. I imagine the reactions will be the same as those of democrats I've seen so far: everything from bemused indifference to posting about a coup every day on social media.
It's all part of the 2024 election campaign. I will be shocked if Trump doesn't run again.
God help the Democrats if Biden dies during his first term. It will be a blood bath after how close this election was despite everything that had gone wrong this year for Trump.
>This dynamic isn't unique to ECE 352, or even Wisconsin – I saw the same thing when TA'ed EE 202, a second year class on signals and systems at Purdue. The problems were FFTs and Laplace transforms instead of dividers and Boolean2, but the avoidance of teaching fundamental skills was the same. It was clear, from the questions students asked me in office hours, that those who were underperforming weren't struggling with the fundamental concepts in the class, but with algebra: the problems were caused by not having an intuitive understanding of, for example, the difference between f(x+a) and f(x)+a.
>When I suggested to the professor that he spend half an hour reviewing algebra for those students who never had the material covered cogently in high school, I was told in no uncertain terms that it would be a waste of time because some people just can't hack it in engineering. I was told that I wouldn't be so naive once the semester was done, because some people just can't hack it in engineering. I was told that helping students with remedial material was doing them no favors; they wouldn't be able to handle advanced courses anyway because some students just can't hack it in engineering. I was told that Purdue has a loose admissions policy and that I should expect a high failure rate, because some students just can't hack it in engineering.
I think that fundamentally the problem is in mathematics.
Our notation is from the 18th century at best, yet because it is hard people think it's meaningful.
Standard maths notation makes sense for polynomials: a_0 x^n+a_1 x^(n-1)+ ... + a_n = k is the only type of general expression one can write without the need to use parens. Everything else is a kludge added on top of that notation to fix one problem with it, but only in one specific field. Which leaves you with dozens of dsls to specific types of areas of maths/engineering/physics/etc
I'm a big fan of lispified typed lambda calculus. There are no exceptions, and any specific notation is defined in terms of rewrite rules. The fact that types are required also makes it clear what you're talking about.
Unfortunately I'm in a minority of one whenever I've talked to working mathematicians, even though I can tear through papers and proofs an order of magnitude faster than when I try and use standard notation.
I've been on the board of three community tech orgs (user group, hacker space and coop).
Each was pathologically mismanaged to the point of embezzlement (literally) using consensus rules. I managed to force Roberts rules to be adopted in two of them.
The end result was that the user group that didn't adopt them stagnated and no new members have stayed for longer than three months in the last 5 years. The other two grew to the point where they were self sustaining. The coop managed to negotiate a 50 year lease on a property from the city council at $1 a year, the hacker space ended up expelling the whole board for mismanagement and reduced the monthly fees to a quarter of what they were because we were drowning in cash.
Consensus is a way to run therapy groups, if you want to get anything done peoples feelings only get in the way.
We call the wind whistle-y past our whale-y ears "progress".