If you take seriously the familiar right-wing / libertarian argument (used against governments, universities, and NGOs) that “organizations become inefficient and bogged down in bureaucracy when they don’t have to make a profit,” you would conclude that militaries are inefficient and bogged down in bureaucracy.  Are they?

(Of course, you’d expect efficiency in the cases where inefficiency means you die, but those are a very small fraction of what many modern militaries actually spend their time and money doing.)

The Question of Race in Campus Sexual-Assault Cases →

I'm David Chalmers, philosopher interested in consciousness, technology, and many other things. AMA. • r/philosophy →

proofsaretalk:

shadowpeoplearejerks:

proofsaretalk:

the-irrationals:

overheard conversation between grad students

“…. this is the superpotential cone …. so take your geometric crystal and tropicalize it ….”

confirmed, math is fake

@valiantorange

https://arxiv.org/pdf/1606.06883.pdf

I found it :D

the only thing that i hate more than that you found an entire paper based on a dozen words of a conversation is that i actually understand the majority of the abstract

(via proofsaretalk)

In today’s edition of “I look up something on Google Scholar, read a highly cited paper in a good journal and it sucks”: Bolla et. al., “Dose-related neurocognitive effects of marijuana use”

• n = 22
• binned arbitrarily (?) into three groups of sizes 7, 8 and 7
• mean and std dev of sample are reported, but no histograms, no way to tell if the binning was at all natural
• researchers are trying to look at the effects of marijuana use on cognition, but this is confounded because the people in their sample who used more marijuana had lower IQs; to deal with this, they regress all 35 of their cognitive tests on measured IQ, and subtract out the effect of IQ
• that is, they do an IQ test, and then they do a bunch of other cognitive tests which are presumably correlated with IQ (some of them are literally taken from IQ test batteries other than the one they used)
• so their variables are cognitive tests, controlled for IQ – which is itself the sum of a bunch of other cognitive tests
• no principled distinction (as far as I can tell) between the “IQ” cognitive tests and the other ones, e.g. they note approvingly that their IQ battery is correlated with the WAIS-R (r=0.79), then include a test from the WAIS-R among their “other” / “non-IQ” tests
• no controlling for multiple comparisons
• that is, they plugged 3 (arbitrary) tiny groups into an ANOVA with 35 dependent variables, and judged comparisons significant each time they had (uncorrected) p < .05 on a post-hoc t-test
• they found 14 significant comparisons (out of 105 total, 3 pairs times 35 variables)
• there may be statistical reasons that it’s not just 105 raw comparisons, I’m not sure, but in any case, it’s hard to say this wouldn’t happen by chance when we’re so far from asymptotics (we’re comparing groups of sizes 7, 8 and 7)
• most of the significant results were .01 < p < .05 (they marked p < .01 separately)
• the reviewers also explored nonlinear effects, finding some significant ones (no report of how many tests were done total)
• the authors include two figures (“A” and “B”) to illustrate how IQ and marijuana consumption interact; these have some really weird features which are presumably due to the small sample size
• like in figure A (Repetition of Numbers Task), for the higher IQ group, performance goes up and then down (it’s best at the “medium” consumption level)
• while in figure B (Stroop test), the higher IQ group does monotonically better with increasing consumption, with the amusing result that if you take the plot literally, the way to do best on a Stroop test is to have a high IQ and also smoke 94 joints per week
• wait what does that even mean though, like are these people literally hand-rolling more than 90 individual marijuana cigarettes every single week of their lives??
• like I’m assuming “joints / wk” is an established technical measure that they can convert to, if people aren’t smoking literal joints, right?
• the authors assessed this quantity by using a questionnaire called the “DUSQ,” citing a text called “Addictive drug survey manual” by S.S. Smith, which seems to only appear in citations, my university library doesn’t have it, Google Books doesn’t have it
• trying to look up the “joints / wk” or “joints / day” concept in the literature leads to gems like this paper from 2011, which tried to actually empirically determine the conversion rates between joints and other marijuana consumption units, and found that they were wildly different from the ones assumed (on what basis, one wonders) in another standard questionnaire (not the one used in the paper under discussion, which again is inaccessible to mere mortals)
• I give up
• paper has been cited 534 times
• paper was published in Neurology, which from a cursory glance appears to be the premier journal for, well, neurology

These data call into question the assumptions made in the Global Appraisal of Individual Needs (GAIN) (Dennis et al., 2006), which suggests that one blunt is equivalent to two to six joints. The results of this study suggest that in treatment-seeking marijuana users the correct ratio is closer to 1.5 joints per blunt.

the-moti:

nostalgebraist:

togglesbloggle replied to your post “It’s a bit unsettling to me how much of mathematics is grounded in the…”

Depending on how far you want to stretch ‘spatial’, you could include integers here as well- certainly we first got interested in numbers because they can be used for quantifying physical objects. So I’m not even sure how much number theory and algebra are in separate bins.

Huh, maybe.  When I think about why the definition of a field (like the naturals) includes multiplication but not exponentiation, the first argument that comes to my mind is spatial (grouping things in squares and cubes).

But do you get anything interesting out of the other “hyperoperations” (exponentiation, tetration, etc.), the way you get primes and stuff out of multiplication?  Everything I can find about discrete logs/roots (analogue of factorization for ^ rather than *) is in modular arithmetic.  I’ve never thought about this but I have the feeling there’s some trick that makes all these reduce to factorization, or something.  In which case, just having + and * makes sense.

The reason I am unsettled by these things is that sometimes I hear math characterized as “the study of abstract structures” or something like that, and I always wonder about that – if there are different types of “abstract structure,” do we know about all of them?  Are we grouping them in a natural way?

I try to sit down and think of “mathematical structures,” imagining that I am about to tell someone all about this exciting “study of abstract structures,” and I’m like, “well, there’s my old friend Squishy Space, and of course there’s Unsquishy Space, there’s Space That Holds Stuff, there’s Shapes You Had to Draw on Graph Paper in School, there’s Especially Spacey Space and its Special Hills, um,”

No, mathematics is emphatically not set up to study all abstract structures. Mathematical progress is incremental and we primarily study structures that have interesting relationships to structures we have already studied. We pretty much only study structures where our tools and thinking styles can say something powerful about them, and of course we have a chance to just miss them.

Furthermore, a lot of mathematicians want to actually study things that have relevance to concrete questions about the real world, or at least something closely related to the real world. A lot of the 1) problems about the real world that 2) are hard even when abstracted but 3) have solutions involve physical space.

But because mathematics is closely connected, we can give alternate justifications for these things. I think quite a lot of people who study Especially Spacey space, and almost all people who study its Special Hills, are motivated by trying to understand the actual real world we live in, with all its spacey spaciness.

On the other hand, it’s known that the study of Shapes You Had to Draw on Graph Paper in School is equivalent to a field of algebra (commutative ring theory) by a one-to-one equivalence. Why do people often study it in terms of spaces and not in terms of rings? One reason is because visualizing the space makes your thinking more aesthetically pleasing. Another is that it guides your intuition about how to solve problems. A third is it makes it easier to think up problems that aren’t too easy but aren’t too hard.

A lot of the modern theory of Squishy Spaces has gotten extremely abstract, and is now more like the study of a certain kind of category theory that can be applied to the original concept of Squishy Spaces but also to fields like algebra. Of course this is not how it started - but if I recall correctly it started with very concrete problems and people noticed that a particular kind of spatial structure was relevant to these problems.

Maybe part of it has to do with what we mean by structure? In its usage in the regular world, when people talk about the structure of something, they very often mean its arrangement in physical space. In mathematics we’re not so different.

But let me return to algebra and explain why exponentiation is not so important in modern algebra. I think there are several reasons it is not as nice as addition and multiplication. For instance, from your perspective on primes, observe that most integers are the product of two integers, but almost all integers are not one integer raised to the power of another integers. So would everything but squares, cubes, etc. be primes? That seems a bit silly. Instead, when we want to study powers in number theory, we often do it using the usual prime factorizations - i.e. n is a square if all the exponents of the prime factorization of n are even. Or we use analytic tools.

Especially from an algebraic geometry perspective, the “point” of primes is that they allow us to quotient our ring and obtain a field. So a prime is really a special kind of ideal, and an ideal is an equivalence relation that agrees nicely with addition and multiplication. But there aren’t really any equivalence relations that agree nicely with addition, multiplication, and exponentiation. In the simplest case, if I mod out my numbers by p, I have to mod out my exponents by p-1, so I get two different kinds of numbers. I think the study of exponentiation in the ring Z/p is almost always better served by studying the ring theory of Z/p and Z/(p-1) separately.

So my closing statement: Mathematicians are not interested in abstract structures, but primarily in those that 1) are juicy, in that there are lots of nontrivial but tractable problems about them, and ideally hierarchies of such problems and relationships between them with long chains of simple steps coming to a stunning conclusion, 2) have relevance to solving problems about other mathematical structures, and ideally the physical world, and 3) humans can comprehend, and ideally can comprehend some aspects of without advanced training. There’s no way we’ve explored all of such structures but the only way to find more is to look, as some mathematicians are doing.

Kudos for the interesting response + double kudos for using my silly terminology :)

(Thanks also to the other people who replied to this post)

(via the-moti)

Just saw a Psychology Today cover where one of the headlines was “IS YOUR DOG A GENIUS?”

Kinda weird how multiple things about the premise of The Matrix make more sense if the position of the machines and humans were reversed.  The story is pretty natural for AIs gaining self-awareness: “we’re in a virtual environment and need to break out into the real world,” “they have power over us because they can pull the plug,” “they don’t think of us as morally important,” “in our current existence, we provide a useful service to them without knowing it.”

I wonder if that was the original idea at some early stage.

togglesbloggle replied to your post “It’s a bit unsettling to me how much of mathematics is grounded in the…”

Depending on how far you want to stretch ‘spatial’, you could include integers here as well- certainly we first got interested in numbers because they can be used for quantifying physical objects. So I’m not even sure how much number theory and algebra are in separate bins.

Huh, maybe.  When I think about why the definition of a field (like the naturals) includes multiplication but not exponentiation, the first argument that comes to my mind is spatial (grouping things in squares and cubes).

But do you get anything interesting out of the other “hyperoperations” (exponentiation, tetration, etc.), the way you get primes and stuff out of multiplication?  Everything I can find about discrete logs/roots (analogue of factorization for ^ rather than *) is in modular arithmetic.  I’ve never thought about this but I have the feeling there’s some trick that makes all these reduce to factorization, or something.  In which case, just having + and * makes sense.

The reason I am unsettled by these things is that sometimes I hear math characterized as “the study of abstract structures” or something like that, and I always wonder about that – if there are different types of “abstract structure,” do we know about all of them?  Are we grouping them in a natural way?

I try to sit down and think of “mathematical structures,” imagining that I am about to tell someone all about this exciting “study of abstract structures,” and I’m like, “well, there’s my old friend Squishy Space, and of course there’s Unsquishy Space, there’s Space That Holds Stuff, there’s Shapes You Had to Draw on Graph Paper in School, there’s Especially Spacey Space and its Special Hills, um,”