i was talking to opus the other night about the polio vaccine related stuff (i had been arguing with one of those people who claims the polio vaccine didn't work so i figured i'd use it as an excuse to brush up on some bio/history). i asked it to explain how polio virus was isolated pre PCR and claude hard killed my session citing security reasons (it was talking about stool samples ffs LOL)
Hell i’m working on ai for board games as a hobby (tfmbot.com) and one of the cards is ‘microbes’. Sent straight back to 4.8 for having that in my code.
- lean proofs are hard, and a lot of the time there is so much mathematical machinery that folks are working on that you would need to not only prove your result, but also all of the machinery that your subfield it is built on. it would be infeasible for many authors to do all of this work (this might be a major part of multiple careers, and when there are 5 folks in your entire subfield, the payoff is not really worth it)
- human proofs are readable, and can illustrate concepts better than lean proofs. human proofs give insights into how to think about a type of problem, and this is often the most valuable part of a proof/result.
- lean proofs are often very difficult to read; while they give you a "verified" check mark, they do not necessarily improve the bounds of human understanding if that makes sense.
i can kinda get how a glp-1 can be a miracle drug for weight: if we assume that simple molecular fixes to problems will eventually be found by evolution, then when we change our environment rapidly (e.g., with cheap bountiful calories) then this presents an opportunity for a miracle drug, since evolution will take some time to find the fix.
but for something like reducing disease infection, i find it a lot harder to understand why we don't create this naturally unless there is some equal-but-opposite cost that we'd incur, or if there is not actually as big of a benefit as we believe (or if this is all just colinear with the weight loss stuff).
note: i have no background in any of this and have no idea what i'm talking about
I'm not a doctor or biologist, but remember that bacteria is a far simpler organism with a much shorter individual lifespan than a human. Depending on the species and their environment, they might divide every 12 minutes or every 24 hours. A new human generation will be more 15 to 35 years. Their reproduction is also simpler. Genes are inherited or mutated mostly at the time of reproduction. Selection is mostly therefore over the course of generations.
These things together mean their microevolution is on a different timescale than ours.
these might not be 100% complete, but i think this does a reaaalllly good job at capturing the vast majority of mathematics.
i'm sure you could come up with another breakdown, but these also have the benefit of tracking roughly with history. numbers and geometry (euclid), then eventually algebra. probability was a fundamentally new way of looking at the world. analysis comes via newton/leibniz and then dynamics tries to tackle complex systems (kinda where newton left off, e.g., 3-body problem type stuff).
also: dimension reduction is not a bad thing. this is like a decomposition: we can decompose so much of what research mathematics is doing into 6 different basis elements. that's pretty darn neat.
agreed! it's funny, i'm returning to some of the maths i studied in undergrad with a bit more "worldly" knowledge (if you can call comp sci academia knowledge "worldly"), and i'm seeing that so so much of the stuff that was confusing was actually just trying to frame really intuitive properties. of course, the language to do so rigorously can be very dense and terse and difficult to get through, but at the end of the day, mathematicians are often trying to do some very simple things.
for example, intuitively, i and j are _basically_ the same "shape" as one another, and f and c and s and v are _basically_ the same "shape" as each other, but the two sets of shapes are definitely _not_ the same as one another...to quantify this and actually capture it in math you gotta do topology, and once you get past the point set stuff it gets real abstract real fast. but they really just wanna say "hey, my donut kinda looks like my coffee mug".
It seems like you might be inventing a form of non-monotonic logic. Check out answer set programming, it actually does exactly what you want of "unlearning" facts that you've learned. Not sure if it helps in your particular instance, but it's very cool stuff and IIRC there is an implementation that extends datalog. https://en.wikipedia.org/wiki/Answer_set_programming
yeah, i've studied a lot of math and a lot of cs, and stats is tough. part of the problem is the terminology, and just giving a ton of complex machinery without telling you what it's actually doing. i've never learned that way, and it is very easy to feel like you're doing some sort of dark magic.
also, probability theory vs statistics is an important distinction: prob theory is a nice clean mathematical subject, while statistics is almost the philosophy of applying probability theory to the world.
Statistical reasoning isn't really motivated when it's taught, at least in the US. My schooling (I did jump around a bunch) assumed the student to have picked it up through vague balls-and-bins style problems taught in various units in various grade levels.
By the time I took my statistics class in undergrad math, coming from a similar background to you, they just sort of assumed you had a head for combinatorics and used that to develop everything else. I was a really good student in undergrad and statistics was my hardest class, I spent like 2x time on that class than any other class.
In grad school I took a class on complex system failure analysis and was quite apprehensive. My hope was that I could team up with a classmate to help with the math while I could work on the systems levels analysis. Turns out that because I understood systems really well, system failure offered me the intuition I needed to really understand statistics. I aced the class, published a moderately popular paper in distributed systems using what I learned, then went and took our graduate level statistics class widely known to be very difficult and aced it.
I think tacking statistical thinking on as an afterthought in curriculum is a huge mistake in the school system, especially so in the age of machine learning. I think for the average student statistical thinking is even more important than a lot of trigonometry.
Ugh no. You and the sibling commenter pushed me to do some searching but it looks like that class isn't offered anymore. It was a special class anyway (which is kinda common in grad schools.) I'll see if I can dig up some lecture notes from a long time ago.
i mean, the headline statistic can be misleading, but you gotta dig in and wrestle with the details. just like anything, we cannot boil down complex things to single numbers and expect any sort of meaningful signal. we gotta roll up our sleeves, look at definitions, think about what our actual questions are, how we might answer those questions through measurements and observations, and what the confounders are. i think a common issue folks have with stats is that they expect a tidy answer, and it just doesn't do that: it's more of a way to prove the world...the results still need some interpretation.
> At the time, my professor closed the final lecture with dramatic words (I'm paraphrasing slightly):
>>> And now you've learned that almost all interesting problems are undecidable and of the remaining ones, almost all are NP-hard. For the project of computer science, that puts the final nail in the coffin.
> Sheesh. Not sure if everyone got such a dire framing but that would explain.
Honestly, this is what makes computer science fun.
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