nhaliday + convexity-curvature   115

Maybe America is simply too big | Eli Dourado
The classic economics paper on optimal country size is by Alesina and Spolare (1997). They advance a number of theoretical claims in the paper, but in my view the most important ones are on the relationship between political and economic integration.

Suppose that the world is full of trade barriers. Tariffs are high, and maybe also it’s just plain expensive to get goods across the ocean, so there’s not a lot of international competition. In this situation, there is a huge advantage to political integration: it buys you economic integration.

In a world of trade barriers, a giant internal free trade area is one of the most valuable public goods that a government can provide. Because many industries feature economies of scale, it’s better to live in a big market. If the only way to get a big market is to live in a big country, then megastates have a huge advantage over microstates.

On the other hand, if economic integration prevails regardless of political integration—say, tariffs are low and shipping is cheap—then political integration doesn’t buy you much. Many of the other public goods that governments provide—law and order, social insurance, etc.—don’t really benefit from large populations beyond a certain point. If you scale from a million people to 100 million people, you aren’t really better off.

As a result, if economic integration prevails, the optimal country size is small, maybe even a city-state.
econotariat  wonkish  2016-election  trump  contrarianism  politics  polisci  usa  scale  measure  convexity-curvature  government  exit-voice  polis  social-choice  diversity  putnam-like  cohesion  trade  nationalism-globalism  economics  alesina  american-nations 
4 days ago by nhaliday
The Existential Risk of Math Errors - Gwern.net
How big is this upper bound? Mathematicians have often made errors in proofs. But it’s rarer for ideas to be accepted for a long time and then rejected. But we can divide errors into 2 basic cases corresponding to type I and type II errors:

1. Mistakes where the theorem is still true, but the proof was incorrect (type I)
2. Mistakes where the theorem was false, and the proof was also necessarily incorrect (type II)

Before someone comes up with a final answer, a mathematician may have many levels of intuition in formulating & working on the problem, but we’ll consider the final end-product where the mathematician feels satisfied that he has solved it. Case 1 is perhaps the most common case, with innumerable examples; this is sometimes due to mistakes in the proof that anyone would accept is a mistake, but many of these cases are due to changing standards of proof. For example, when David Hilbert discovered errors in Euclid’s proofs which no one noticed before, the theorems were still true, and the gaps more due to Hilbert being a modern mathematician thinking in terms of formal systems (which of course Euclid did not think in). (David Hilbert himself turns out to be a useful example of the other kind of error: his famous list of 23 problems was accompanied by definite opinions on the outcome of each problem and sometimes timings, several of which were wrong or questionable5.) Similarly, early calculus used ‘infinitesimals’ which were sometimes treated as being 0 and sometimes treated as an indefinitely small non-zero number; this was incoherent and strictly speaking, practically all of the calculus results were wrong because they relied on an incoherent concept - but of course the results were some of the greatest mathematical work ever conducted6 and when later mathematicians put calculus on a more rigorous footing, they immediately re-derived those results (sometimes with important qualifications), and doubtless as modern math evolves other fields have sometimes needed to go back and clean up the foundations and will in the future.7

...

Isaac Newton, incidentally, gave two proofs of the same solution to a problem in probability, one via enumeration and the other more abstract; the enumeration was correct, but the other proof totally wrong and this was not noticed for a long time, leading Stigler to remark:

...

TYPE I > TYPE II?
“Lefschetz was a purely intuitive mathematician. It was said of him that he had never given a completely correct proof, but had never made a wrong guess either.”
- Gian-Carlo Rota13

Case 2 is disturbing, since it is a case in which we wind up with false beliefs and also false beliefs about our beliefs (we no longer know that we don’t know). Case 2 could lead to extinction.

...

Except, errors do not seem to be evenly & randomly distributed between case 1 and case 2. There seem to be far more case 1s than case 2s, as already mentioned in the early calculus example: far more than 50% of the early calculus results were correct when checked more rigorously. Richard Hamming attributes to Ralph Boas a comment that while editing Mathematical Reviews that “of the new results in the papers reviewed most are true but the corresponding proofs are perhaps half the time plain wrong”.

...

Gian-Carlo Rota gives us an example with Hilbert:

...

Olga labored for three years; it turned out that all mistakes could be corrected without any major changes in the statement of the theorems. There was one exception, a paper Hilbert wrote in his old age, which could not be fixed; it was a purported proof of the continuum hypothesis, you will find it in a volume of the Mathematische Annalen of the early thirties.

...

Leslie Lamport advocates for machine-checked proofs and a more rigorous style of proofs similar to natural deduction, noting a mathematician acquaintance guesses at a broad error rate of 1/329 and that he routinely found mistakes in his own proofs and, worse, believed false conjectures30.

[more on these "structured proofs":
https://academia.stackexchange.com/questions/52435/does-anyone-actually-publish-structured-proofs
https://mathoverflow.net/questions/35727/community-experiences-writing-lamports-structured-proofs
]

We can probably add software to that list: early software engineering work found that, dismayingly, bug rates seem to be simply a function of lines of code, and one would expect diseconomies of scale. So one would expect that in going from the ~4,000 lines of code of the Microsoft DOS operating system kernel to the ~50,000,000 lines of code in Windows Server 2003 (with full systems of applications and libraries being even larger: the comprehensive Debian repository in 2007 contained ~323,551,126 lines of code) that the number of active bugs at any time would be… fairly large. Mathematical software is hopefully better, but practitioners still run into issues (eg Durán et al 2014, Fonseca et al 2017) and I don’t know of any research pinning down how buggy key mathematical systems like Mathematica are or how much published mathematics may be erroneous due to bugs. This general problem led to predictions of doom and spurred much research into automated proof-checking, static analysis, and functional languages31.

[related:
https://mathoverflow.net/questions/11517/computer-algebra-errors
I don't know any interesting bugs in symbolic algebra packages but I know a true, enlightening and entertaining story about something that looked like a bug but wasn't.

Define sinc𝑥=(sin𝑥)/𝑥.

Someone found the following result in an algebra package: ∫∞0𝑑𝑥sinc𝑥=𝜋/2
They then found the following results:

...

So of course when they got:

∫∞0𝑑𝑥sinc𝑥sinc(𝑥/3)sinc(𝑥/5)⋯sinc(𝑥/15)=(467807924713440738696537864469/935615849440640907310521750000)𝜋

hmm:
Which means that nobody knows Fourier analysis nowdays. Very sad and discouraging story... – fedja Jan 29 '10 at 18:47

--

Because the most popular systems are all commercial, they tend to guard their bug database rather closely -- making them public would seriously cut their sales. For example, for the open source project Sage (which is quite young), you can get a list of all the known bugs from this page. 1582 known issues on Feb.16th 2010 (which includes feature requests, problems with documentation, etc).

That is an order of magnitude less than the commercial systems. And it's not because it is better, it is because it is younger and smaller. It might be better, but until SAGE does a lot of analysis (about 40% of CAS bugs are there) and a fancy user interface (another 40%), it is too hard to compare.

I once ran a graduate course whose core topic was studying the fundamental disconnect between the algebraic nature of CAS and the analytic nature of the what it is mostly used for. There are issues of logic -- CASes work more or less in an intensional logic, while most of analysis is stated in a purely extensional fashion. There is no well-defined 'denotational semantics' for expressions-as-functions, which strongly contributes to the deeper bugs in CASes.]

...

Should such widely-believed conjectures as P≠NP or the Riemann hypothesis turn out be false, then because they are assumed by so many existing proofs, a far larger math holocaust would ensue38 - and our previous estimates of error rates will turn out to have been substantial underestimates. But it may be a cloud with a silver lining, if it doesn’t come at a time of danger.

https://mathoverflow.net/questions/338607/why-doesnt-mathematics-collapse-down-even-though-humans-quite-often-make-mista

more on formal methods in programming:
https://www.quantamagazine.org/formal-verification-creates-hacker-proof-code-20160920/
https://intelligence.org/2014/03/02/bob-constable/

https://softwareengineering.stackexchange.com/questions/375342/what-are-the-barriers-that-prevent-widespread-adoption-of-formal-methods
Update: measured effort
In the October 2018 issue of Communications of the ACM there is an interesting article about Formally verified software in the real world with some estimates of the effort.

Interestingly (based on OS development for military equipment), it seems that producing formally proved software requires 3.3 times more effort than with traditional engineering techniques. So it's really costly.

On the other hand, it requires 2.3 times less effort to get high security software this way than with traditionally engineered software if you add the effort to make such software certified at a high security level (EAL 7). So if you have high reliability or security requirements there is definitively a business case for going formal.

WHY DON'T PEOPLE USE FORMAL METHODS?: https://www.hillelwayne.com/post/why-dont-people-use-formal-methods/
You can see examples of how all of these look at Let’s Prove Leftpad. HOL4 and Isabelle are good examples of “independent theorem” specs, SPARK and Dafny have “embedded assertion” specs, and Coq and Agda have “dependent type” specs.6

If you squint a bit it looks like these three forms of code spec map to the three main domains of automated correctness checking: tests, contracts, and types. This is not a coincidence. Correctness is a spectrum, and formal verification is one extreme of that spectrum. As we reduce the rigour (and effort) of our verification we get simpler and narrower checks, whether that means limiting the explored state space, using weaker types, or pushing verification to the runtime. Any means of total specification then becomes a means of partial specification, and vice versa: many consider Cleanroom a formal verification technique, which primarily works by pushing code review far beyond what’s humanly possible.

...

The question, then: “is 90/95/99% correct significantly cheaper than 100% correct?” The answer is very yes. We all are comfortable saying that a codebase we’ve well-tested and well-typed is mostly correct modulo a few fixes in prod, and we’re even writing more than four lines of code a day. In fact, the vast… [more]
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july 2019 by nhaliday
How Many Keystrokes Programers Type a Day?
I was quite surprised how low my own figure is. But thinking about it… it makes sense. Even though we sit in front of computer all day, but the actual typing is a small percentage of that. Most of the time, you have to lunch, run errands, browse web, read docs, chat on phone, run to the bathroom. Perhaps only half of your work time is active coding or writing email/docs. Of that duration, perhaps majority of time you are digesting the info on screen.
techtariat  convexity-curvature  measure  keyboard  time  cost-benefit  data  time-use  workflow  efficiency  prioritizing  editors 
june 2019 by nhaliday
Complexity no Bar to AI - Gwern.net
Critics of AI risk suggest diminishing returns to computing (formalized asymptotically) means AI will be weak; this argument relies on a large number of questionable premises and ignoring additional resources, constant factors, and nonlinear returns to small intelligence advantages, and is highly unlikely. (computer science, transhumanism, AI, R)
created: 1 June 2014; modified: 01 Feb 2018; status: finished; confidence: likely; importance: 10
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april 2018 by nhaliday
The Hanson-Yudkowsky AI-Foom Debate - Machine Intelligence Research Institute
How Deviant Recent AI Progress Lumpiness?: http://www.overcomingbias.com/2018/03/how-deviant-recent-ai-progress-lumpiness.html
I seem to disagree with most people working on artificial intelligence (AI) risk. While with them I expect rapid change once AI is powerful enough to replace most all human workers, I expect this change to be spread across the world, not concentrated in one main localized AI system. The efforts of AI risk folks to design AI systems whose values won’t drift might stop global AI value drift if there is just one main AI system. But doing so in a world of many AI systems at similar abilities levels requires strong global governance of AI systems, which is a tall order anytime soon. Their continued focus on preventing single system drift suggests that they expect a single main AI system.

The main reason that I understand to expect relatively local AI progress is if AI progress is unusually lumpy, i.e., arriving in unusually fewer larger packages rather than in the usual many smaller packages. If one AI team finds a big lump, it might jump way ahead of the other teams.

However, we have a vast literature on the lumpiness of research and innovation more generally, which clearly says that usually most of the value in innovation is found in many small innovations. We have also so far seen this in computer science (CS) and AI. Even if there have been historical examples where much value was found in particular big innovations, such as nuclear weapons or the origin of humans.

Apparently many people associated with AI risk, including the star machine learning (ML) researchers that they often idolize, find it intuitively plausible that AI and ML progress is exceptionally lumpy. Such researchers often say, “My project is ‘huge’, and will soon do it all!” A decade ago my ex-co-blogger Eliezer Yudkowsky and I argued here on this blog about our differing estimates of AI progress lumpiness. He recently offered Alpha Go Zero as evidence of AI lumpiness:

...

In this post, let me give another example (beyond two big lumps in a row) of what could change my mind. I offer a clear observable indicator, for which data should have available now: deviant citation lumpiness in recent ML research. One standard measure of research impact is citations; bigger lumpier developments gain more citations that smaller ones. And it turns out that the lumpiness of citations is remarkably constant across research fields! See this March 3 paper in Science:

I Still Don’t Get Foom: http://www.overcomingbias.com/2014/07/30855.html
All of which makes it look like I’m the one with the problem; everyone else gets it. Even so, I’m gonna try to explain my problem again, in the hope that someone can explain where I’m going wrong. Here goes.

“Intelligence” just means an ability to do mental/calculation tasks, averaged over many tasks. I’ve always found it plausible that machines will continue to do more kinds of mental tasks better, and eventually be better at pretty much all of them. But what I’ve found it hard to accept is a “local explosion.” This is where a single machine, built by a single project using only a tiny fraction of world resources, goes in a short time (e.g., weeks) from being so weak that it is usually beat by a single human with the usual tools, to so powerful that it easily takes over the entire world. Yes, smarter machines may greatly increase overall economic growth rates, and yes such growth may be uneven. But this degree of unevenness seems implausibly extreme. Let me explain.

If we count by economic value, humans now do most of the mental tasks worth doing. Evolution has given us a brain chock-full of useful well-honed modules. And the fact that most mental tasks require the use of many modules is enough to explain why some of us are smarter than others. (There’d be a common “g” factor in task performance even with independent module variation.) Our modules aren’t that different from those of other primates, but because ours are different enough to allow lots of cultural transmission of innovation, we’ve out-competed other primates handily.

We’ve had computers for over seventy years, and have slowly build up libraries of software modules for them. Like brains, computers do mental tasks by combining modules. An important mental task is software innovation: improving these modules, adding new ones, and finding new ways to combine them. Ideas for new modules are sometimes inspired by the modules we see in our brains. When an innovation team finds an improvement, they usually sell access to it, which gives them resources for new projects, and lets others take advantage of their innovation.

...

In Bostrom’s graph above the line for an initially small project and system has a much higher slope, which means that it becomes in a short time vastly better at software innovation. Better than the entire rest of the world put together. And my key question is: how could it plausibly do that? Since the rest of the world is already trying the best it can to usefully innovate, and to abstract to promote such innovation, what exactly gives one small project such a huge advantage to let it innovate so much faster?

...

In fact, most software innovation seems to be driven by hardware advances, instead of innovator creativity. Apparently, good ideas are available but must usually wait until hardware is cheap enough to support them.

Yes, sometimes architectural choices have wider impacts. But I was an artificial intelligence researcher for nine years, ending twenty years ago, and I never saw an architecture choice make a huge difference, relative to other reasonable architecture choices. For most big systems, overall architecture matters a lot less than getting lots of detail right. Researchers have long wandered the space of architectures, mostly rediscovering variations on what others found before.

Some hope that a small project could be much better at innovation because it specializes in that topic, and much better understands new theoretical insights into the basic nature of innovation or intelligence. But I don’t think those are actually topics where one can usefully specialize much, or where we’ll find much useful new theory. To be much better at learning, the project would instead have to be much better at hundreds of specific kinds of learning. Which is very hard to do in a small project.

What does Bostrom say? Alas, not much. He distinguishes several advantages of digital over human minds, but all software shares those advantages. Bostrom also distinguishes five paths: better software, brain emulation (i.e., ems), biological enhancement of humans, brain-computer interfaces, and better human organizations. He doesn’t think interfaces would work, and sees organizations and better biology as only playing supporting roles.

...

Similarly, while you might imagine someday standing in awe in front of a super intelligence that embodies all the power of a new age, superintelligence just isn’t the sort of thing that one project could invent. As “intelligence” is just the name we give to being better at many mental tasks by using many good mental modules, there’s no one place to improve it. So I can’t see a plausible way one project could increase its intelligence vastly faster than could the rest of the world.

Takeoff speeds: https://sideways-view.com/2018/02/24/takeoff-speeds/
Futurists have argued for years about whether the development of AGI will look more like a breakthrough within a small group (“fast takeoff”), or a continuous acceleration distributed across the broader economy or a large firm (“slow takeoff”).

I currently think a slow takeoff is significantly more likely. This post explains some of my reasoning and why I think it matters. Mostly the post lists arguments I often hear for a fast takeoff and explains why I don’t find them compelling.

(Note: this is not a post about whether an intelligence explosion will occur. That seems very likely to me. Quantitatively I expect it to go along these lines. So e.g. while I disagree with many of the claims and assumptions in Intelligence Explosion Microeconomics, I don’t disagree with the central thesis or with most of the arguments.)
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april 2018 by nhaliday
Moral Transposition – neocolonial
- Every morality inherently has a doctrine on that which is morally beneficial and that which is morally harmful.
- Under the traditional, absolute, eucivic moral code of Western Civilisation these were termed Good and Evil.
- Under the modern, relative, dyscivic moral code of Progressivism these are called Love and Hate.
- Good and Evil inherently reference the in-group, and seek its growth in absolute capability and glory.  Love and Hate inherently reference the out-group, and seek its relative growth in capability and privilege.
- These combinations form the basis of the Frame through which individuals aligned with those moralities view the world.  They are markedly distinct; although both Good serves the moral directive of absolutely strengthening the in-group and Hate counters the moral directive of relatively weakening the in-group, they do not map to one another. This failure to map, as well as the overloading of terms, is why it is generally (intentionally, perniciously) difficult to discern the differences between the two world views.

You Didn’t Join a Suicide Cult: http://www.righteousdominion.org/2018/04/13/you-didnt-join-a-suicide-cult/
“Thomas Aquinas discusses whether there is an order to charity. Must we love everyone in outward effects equally? Or do we demonstrate love more to our near neighbors than our distant neighbors? His answers: No to the first question, yes to the second.”

...

This is a perfect distillation of the shaming patriotic Christians with a sense of national identity face. It is a very Alinsky tactic whose fourth rule is “Make the enemy live up to their own book of rules. You can kill them with this, for they can no more obey their own rules than the Christian church can live up to Christianity.” It is a tactic that can be applied to any idealistic movement. Now to be fair, my friend is not a disciple of Alinsky, but we have been bathed in Alinsky for at least two generations. Reading the Gospels alone and in a vacuum one could be forgiven coming away with that interpretation of Christ’s teachings. Take for example Luke 6:27-30:

...

Love as Virtue and Vice
Thirdly, Love is a virtue, the greatest, but like all virtues it can be malformed with excessive zeal.

Aristotle taught that virtues were a proper balance of behavior or feeling in a specific sphere. For instance, the sphere of confidence and fear: a proper balance in this sphere would be the virtue of courage. A deficit in this sphere would be cowardice and an excess would be rashness or foolhardiness. We can apply this to the question of charity. Charity in the bible is typically a translation of the Greek word for love. We are taught by Jesus that second only to loving God we are to love our neighbor (which in the Greek means those near you). If we are to view the sphere of love in this context of excess and deficit what would it be?

Selfishness <—- LOVE —-> Enablement

Enablement here is meant in its very modern sense. If we possess this excess of love, we are so selfless and “others focused” that we prioritize the other above all else we value. The pathologies of the target of our enablement are not considered; indeed, in this state of enablement they are even desired. The saying “the squeaky wheel gets the grease” is recast as: “The squeaky wheel gets the grease, BUT if I have nothing squeaking in m y life I’ll make sure to find or create something squeaky to “virtuously” burden myself with”.

Also, in this state of excessive love even those natural and healthy extensions of yourself must be sacrificed to the other. There was one mother I was acquainted with that embodies this excess of love. She had two biological children and anywhere from five to six very troubled adopted/foster kids at a time. She helped many kids out of terrible situations, but in turn her natural children were constantly subject to high levels of stress, drama, and constant babysitting of very troubled children. There was real resentment. In her efforts to help troubled foster children, she sacrificed the well-being of her biological children. Needless to say, her position on the refugee crisis was predictable.
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march 2018 by nhaliday
Open Thread, 11/26/2017 – Gene Expression
A few days ago there was a Twitter thing about top five books that have influenced you. It’s hard for me to name five, but I put three books down for three different reasons:

- Principles of Population Genetics, because it gives you a model for how to analyze and understand evolutionary processes. There are other books out there besides Principles of Population Genetics. But if you buy this book you don’t need to buy another (at SMBE this year I confused Andy Clark with Mike Lynch for a second when introducing myself. #awkward)
- The Fall of Rome. A lot of historical writing can be tendentious. I’ve also noticed an unfortunate tendency of historians dropping into contemporary arguments and pretty much lying through omission or elision to support their political side (it usually goes “actually, I’m a specialist in this topic and my side is 100% correct because of obscure-stuff where I’m shading the facts”). The Fall of Rome illustrates the solidity that an archaeological and materialist take can give the field. This sort of materialism isn’t the final word, but it needs to be the start of the conversation.
- From Dawn to Decadence: 1500 to the Present: 500 Years of Western Cultural Life. To know things is important in and of itself. My own personal experience is that the returns to knowing things in a particular domain or area do not exhibit a linear return. Rather, it exhibits a logistic curve. Initially, it’s hard to make sense of anything from the facts, but at some point comprehension and insight increase rapidly, until you reach the plateau of diminishing marginal returns.

If you haven’t, I recommend you subscribe to Patrick Wyman’s Tides of History podcast. I pretty much wait now for every new episode.
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november 2017 by nhaliday
Social Animal House: The Economic and Academic Consequences of Fraternity Membership by Jack Mara, Lewis Davis, Stephen Schmidt :: SSRN
We exploit changes in the residential and social environment on campus to identify the economic and academic consequences of fraternity membership at a small Northeastern college. Our estimates suggest that these consequences are large, with fraternity membership lowering student GPA by approximately 0.25 points on the traditional four-point scale, but raising future income by approximately 36%, for those students whose decision about membership is affected by changes in the environment. These results suggest that fraternity membership causally produces large gains in social capital, which more than outweigh its negative effects on human capital for potential members. Alcohol-related behavior does not explain much of the effects of fraternity membership on either the human capital or social capital effects. These findings suggest that college administrators face significant trade-offs when crafting policies related to Greek life on campus.

- III. Methodology has details
- it's an instrumental variable method paper

Table 5: Fraternity Membership and Grades

Do High School Sports Build or Reveal Character?: http://ftp.iza.org/dp11110.pdf
We examine the extent to which participation in high school athletics has beneficial effects on future education, labor market, and health outcomes. Due to the absence of plausible instruments in observational data, we use recently developed methods that relate selection on observables with selection on unobservables to estimate bounds on the causal effect of athletics participation. We analyze these effects in the US separately for men and women using three different nationally representative longitudinal data sets that each link high school athletics participation with later-life outcomes. We do not find consistent evidence of individual benefits reported in many previous studies – once we have accounted for selection, high school athletes are no more likely to attend college, earn higher wages, or participate in the labor force. However, we do find that men (but not women) who participated in high school athletics are more likely to exercise regularly as adults. Nevertheless, athletes are no less likely to be obese.

Online Social Network Effects in Labor Markets: Evidence From Facebook's Entry into College Campuses: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3381938
My estimates imply that access to Facebook for 4 years of college causes a 2.7 percentile increase in a cohort's average earnings, relative to the earnings of other individuals born in the same year.

https://marginalrevolution.com/marginalrevolution/2019/05/might-facebook-boost-wages.html
What Clockwork_Prior said. I was a college freshman when facebook first made its appearance and so I know that facebook's entry/exit cannot be treated as a quasi-random with respect to earnings. Facebook began at harvard, then expanded to other ivy league schools + places like stanford/MIT/CMU, before expanding into a larger set of universities.

Presuming the author is using a differences-in-differences research design, the estimates would be biased as they would essentially be calculating averaging earnings difference between Elite schools and non elite schools. If the sample is just restricted to the period where schools were simply elite, the problem still exist because facebook originated at Harvard and this becomes a comparison of Harvard earnings v.s. other schools.
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september 2017 by nhaliday
Subgradients - S. Boyd and L. Vandenberghe
If f is convex and x ∈ int dom f, then ∂f(x) is nonempty and bounded. To establish that ∂f(x) ≠ ∅, we apply the supporting hyperplane theorem to the convex set epi f at the boundary point (x, f(x)), ...
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august 2017 by nhaliday
The Determinants of Trust
Both individual experiences and community characteristics influence how much people trust each other. Using data drawn from US localities we find that the strongest factors that reduce trust are: i) a recent history of traumatic experiences, even though the passage of time reduces this effect fairly rapidly; ii) belonging to a group that historically felt discriminated against, such as minorities (black in particular) and, to a lesser extent, women; iii) being economically unsuccessful in terms of income and education; iv) living in a racially mixed community and/or in one with a high degree of income disparity. Religious beliefs and ethnic origins do not significantly affect trust. The latter result may be an indication that the American melting pot at least up to a point works, in terms of homogenizing attitudes of different cultures, even though racial cleavages leading to low trust are still quite high.

Understanding Trust: http://www.nber.org/papers/w13387
In this paper we resolve this puzzle by recognizing that trust has two components: a belief-based one and a preference based one. While the sender's behavior reflects both, we show that WVS-like measures capture mostly the belief-based component, while questions on past trusting behavior are better at capturing the preference component of trust.

MEASURING TRUST: http://scholar.harvard.edu/files/laibson/files/measuring_trust.pdf
We combine two experiments and a survey to measure trust and trustworthiness— two key components of social capital. Standard attitudinal survey questions about trust predict trustworthy behavior in our experiments much better than they predict trusting behavior. Trusting behavior in the experiments is predicted by past trusting behavior outside of the experiments. When individuals are closer socially, both trust and trustworthiness rise. Trustworthiness declines when partners are of different races or nationalities. High status individuals are able to elicit more trustworthiness in others.

What is Social Capital? The Determinants of Trust and Trustworthiness: http://www.nber.org/papers/w7216
Using a sample of Harvard undergraduates, we analyze trust and social capital in two experiments. Trusting behavior and trustworthiness rise with social connection; differences in race and nationality reduce the level of trustworthiness. Certain individuals appear to be persistently more trusting, but these people do not say they are more trusting in surveys. Survey questions about trust predict trustworthiness not trust. Only children are less trustworthy. People behave in a more trustworthy manner towards higher status individuals, and therefore status increases earnings in the experiment. As such, high status persons can be said to have more social capital.

Trust and Cheating: http://www.nber.org/papers/w18509
We find that: i) both parties to a trust exchange have implicit notions of what constitutes cheating even in a context without promises or messages; ii) these notions are not unique - the vast majority of senders would feel cheated by a negative return on their trust/investment, whereas a sizable minority defines cheating according to an equal split rule; iii) these implicit notions affect the behavior of both sides to the exchange in terms of whether to trust or cheat and to what extent. Finally, we show that individual's notions of what constitutes cheating can be traced back to two classes of values instilled by parents: cooperative and competitive. The first class of values tends to soften the notion while the other tightens it.

Nationalism and Ethnic-Based Trust: Evidence from an African Border Region: https://u.osu.edu/robinson.1012/files/2015/12/Robinson_NationalismTrust-1q3q9u1.pdf
These results offer microlevel evidence that a strong and salient national identity can diminish ethnic barriers to trust in diverse societies.

One Team, One Nation: Football, Ethnic Identity, and Conflict in Africa: http://conference.nber.org/confer//2017/SI2017/DEV/Durante_Depetris-Chauvin.pdf
Do collective experiences that prime sentiments of national unity reduce interethnic tensions and conflict? We examine this question by looking at the impact of national football teams’ victories in sub-Saharan Africa. Combining individual survey data with information on over 70 official matches played between 2000 and 2015, we find that individuals interviewed in the days after a victory of their country’s national team are less likely to report a strong sense of ethnic identity and more likely to trust people of other ethnicities than those interviewed just before. The effect is sizable and robust and is not explained by generic euphoria or optimism. Crucially, national victories do not only affect attitudes but also reduce violence. Indeed, using plausibly exogenous variation from close qualifications to the Africa Cup of Nations, we find that countries that (barely) qualified experience significantly less conflict in the following six months than countries that (barely) did not. Our findings indicate that, even where ethnic tensions have deep historical roots, patriotic shocks can reduce inter-ethnic tensions and have a tangible impact on conflict.

Why Does Ethnic Diversity Undermine Public Goods Provision?: http://www.columbia.edu/~mh2245/papers1/HHPW.pdf
We identify three families of mechanisms that link diversity to public goods provision—–what we term “preferences,” “technology,” and “strategy selection” mechanisms—–and run a series of experimental games that permit us to compare the explanatory power of distinct mechanisms within each of these three families. Results from games conducted with a random sample of 300 subjects from a slum neighborhood of Kampala, Uganda, suggest that successful public goods provision in homogenous ethnic communities can be attributed to a strategy selection mechanism: in similar settings, co-ethnics play cooperative equilibria, whereas non-co-ethnics do not. In addition, we find evidence for a technology mechanism: co-ethnics are more closely linked on social networks and thus plausibly better able to support cooperation through the threat of social sanction. We find no evidence for prominent preference mechanisms that emphasize the commonality of tastes within ethnic groups or a greater degree of altruism toward co-ethnics, and only weak evidence for technology mechanisms that focus on the impact of shared ethnicity on the productivity of teams.

does it generalize to first world?

Higher Intelligence Groups Have Higher Cooperation Rates in the Repeated Prisoner's Dilemma: https://ideas.repec.org/p/iza/izadps/dp8499.html
The initial cooperation rates are similar, it increases in the groups with higher intelligence to reach almost full cooperation, while declining in the groups with lower intelligence. The difference is produced by the cumulation of small but persistent differences in the response to past cooperation of the partner. In higher intelligence subjects, cooperation after the initial stages is immediate and becomes the default mode, defection instead requires more time. For lower intelligence groups this difference is absent. Cooperation of higher intelligence subjects is payoff sensitive, thus not automatic: in a treatment with lower continuation probability there is no difference between different intelligence groups

Why societies cooperate: https://voxeu.org/article/why-societies-cooperate
Three attributes are often suggested to generate cooperative behaviour – a good heart, good norms, and intelligence. This column reports the results of a laboratory experiment in which groups of players benefited from learning to cooperate. It finds overwhelming support for the idea that intelligence is the primary condition for a socially cohesive, cooperative society. Warm feelings towards others and good norms have only a small and transitory effect.

individual payoff, etc.:

Trust, Values and False Consensus: http://www.nber.org/papers/w18460
Trust beliefs are heterogeneous across individuals and, at the same time, persistent across generations. We investigate one mechanism yielding these dual patterns: false consensus. In the context of a trust game experiment, we show that individuals extrapolate from their own type when forming trust beliefs about the same pool of potential partners - i.e., more (less) trustworthy individuals form more optimistic (pessimistic) trust beliefs - and that this tendency continues to color trust beliefs after several rounds of game-play. Moreover, we show that one's own type/trustworthiness can be traced back to the values parents transmit to their children during their upbringing. In a second closely-related experiment, we show the economic impact of mis-calibrated trust beliefs stemming from false consensus. Miscalibrated beliefs lower participants' experimental trust game earnings by about 20 percent on average.

The Right Amount of Trust: http://www.nber.org/papers/w15344
We investigate the relationship between individual trust and individual economic performance. We find that individual income is hump-shaped in a measure of intensity of trust beliefs. Our interpretation is that highly trusting individuals tend to assume too much social risk and to be cheated more often, ultimately performing less well than those with a belief close to the mean trustworthiness of the population. On the other hand, individuals with overly pessimistic beliefs avoid being cheated, but give up profitable opportunities, therefore underperforming. The cost of either too much or too little trust is comparable to the income lost by forgoing college.

...

This framework allows us to show that income-maximizing trust typically exceeds the trust level of the average person as well as to estimate the distribution of income lost to trust mistakes. We find that although a majority of individuals has well calibrated beliefs, a non-trivial proportion of the population (10%) has trust beliefs sufficiently poorly calibrated to lower income by more than 13%.

Do Trust and … [more]
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august 2017 by nhaliday
Stages of Diversification
This paper studies the evolution of sectoral concentration in relation to the level of per capita income. We show that various measures of sectoral concentration follow a U-shaped pattern across a wide variety of data sources: countries first diversify, in the sense that economic activity is spread more equally across sectors, but there exists, relatively late in the development process, a point at which they start specializing again. We discuss this finding in light of existing theories of trade and growth, which generally predict a monotonic relationship between income and diversification. (JEL F43, F15, O40)

seems unhealthy to me (complacency)
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june 2017 by nhaliday
There Is No Such Thing as Decreasing Returns to Scale — Confessions of a Supply-Side Liberal
Besides pedagogical inertia—enforced to some extent by textbook publishers—I am not quite sure what motivates the devotion in so many economics curricula to U-shaped average cost curves. Let me make one guess: there is a desire to explain why firms are the size they are rather than larger or smaller. To my mind, such an explanation should proceed in one of three ways, appropriate to three different situations.
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may 2017 by nhaliday
Estimating the number of unseen variants in the human genome
To find all common variants (frequency at least 1%) the number of individuals that need to be sequenced is small (∼350) and does not differ much among the different populations; our data show that, subject to sequence accuracy, the 1000 Genomes Project is likely to find most of these common variants and a high proportion of the rarer ones (frequency between 0.1 and 1%). The data reveal a rule of diminishing returns: a small number of individuals (∼150) is sufficient to identify 80% of variants with a frequency of at least 0.1%, while a much larger number (> 3,000 individuals) is necessary to find all of those variants.

A map of human genome variation from population-scale sequencing: http://www.internationalgenome.org/sites/1000genomes.org/files/docs/nature09534.pdf

Scientists using data from the 1000 Genomes Project, which sequenced one thousand individuals from 26 human populations, found that "a typical [individual] genome differs from the reference human genome at 4.1 million to 5.0 million sites … affecting 20 million bases of sequence."[11] Nearly all (>99.9%) of these sites are small differences, either single nucleotide polymorphisms or brief insertion-deletions in the genetic sequence, but structural variations account for a greater number of base-pairs than the SNPs and indels.[11]

Human genetic variation: https://en.wikipedia.org/wiki/Human_genetic_variation

Singleton Variants Dominate the Genetic Architecture of Human Gene Expression: https://www.biorxiv.org/content/early/2017/12/15/219238
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may 2017 by nhaliday
Concentration and Growth | Dietrich Vollrath
Ultimately, and this is my impression, not some kind of established fact, concentration likely lowers innovative activity. Put it this way, the null hypothesis should probably be that concentration lowers innovation. An individual industry needs to provide evidence they are on the “right side of the curve” in the first AAH figure to believe concentration would be good for productivity growth in the long run.
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may 2017 by nhaliday
Educational Romanticism & Economic Development | pseudoerasmus
https://twitter.com/GarettJones/status/852339296358940672
deleeted

https://twitter.com/GarettJones/status/943238170312929280
https://archive.is/p5hRA

Did Nations that Boosted Education Grow Faster?: http://econlog.econlib.org/archives/2012/10/did_nations_tha.html
On average, no relationship. The trendline points down slightly, but for the time being let's just call it a draw. It's a well-known fact that countries that started the 1960's with high education levels grew faster (example), but this graph is about something different. This graph shows that countries that increased their education levels did not grow faster.

Where has all the education gone?: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1016.2704&rep=rep1&type=pdf

https://twitter.com/GarettJones/status/948052794681966593
https://archive.is/kjxqp

https://twitter.com/GarettJones/status/950952412503822337
https://archive.is/3YPic

https://twitter.com/pseudoerasmus/status/862961420065001472
http://hanushek.stanford.edu/publications/schooling-educational-achievement-and-latin-american-growth-puzzle

The Case Against Education: What's Taking So Long, Bryan Caplan: http://econlog.econlib.org/archives/2015/03/the_case_agains_9.html

The World Might Be Better Off Without College for Everyone: https://www.theatlantic.com/magazine/archive/2018/01/whats-college-good-for/546590/
Students don't seem to be getting much out of higher education.
- Bryan Caplan

College: Capital or Signal?: http://www.economicmanblog.com/2017/02/25/college-capital-or-signal/
After his review of the literature, Caplan concludes that roughly 80% of the earnings effect from college comes from signalling, with only 20% the result of skill building. Put this together with his earlier observations about the private returns to college education, along with its exploding cost, and Caplan thinks that the social returns are negative. The policy implications of this will come as very bitter medicine for friends of Bernie Sanders.

Doubting the Null Hypothesis: http://www.arnoldkling.com/blog/doubting-the-null-hypothesis/

Is higher education/college in the US more about skill-building or about signaling?: https://www.quora.com/Is-higher-education-college-in-the-US-more-about-skill-building-or-about-signaling
ballpark: 50% signaling, 30% selection, 20% addition to human capital
more signaling in art history, more human capital in engineering, more selection in philosophy

Econ Duel! Is Education Signaling or Skill Building?: http://marginalrevolution.com/marginalrevolution/2016/03/econ-duel-is-education-signaling-or-skill-building.html
Marginal Revolution University has a brand new feature, Econ Duel! Our first Econ Duel features Tyler and me debating the question, Is education more about signaling or skill building?

Against Tulip Subsidies: https://slatestarcodex.com/2015/06/06/against-tulip-subsidies/

https://www.overcomingbias.com/2018/01/read-the-case-against-education.html

https://nintil.com/2018/02/05/notes-on-the-case-against-education/

https://www.nationalreview.com/magazine/2018-02-19-0000/bryan-caplan-case-against-education-review

https://spottedtoad.wordpress.com/2018/02/12/the-case-against-education/
Most American public school kids are low-income; about half are non-white; most are fairly low skilled academically. For most American kids, the majority of the waking hours they spend not engaged with electronic media are at school; the majority of their in-person relationships are at school; the most important relationships they have with an adult who is not their parent is with their teacher. For their parents, the most important in-person source of community is also their kids’ school. Young people need adult mirrors, models, mentors, and in an earlier era these might have been provided by extended families, but in our own era this all falls upon schools.

Caplan gestures towards work and earlier labor force participation as alternatives to school for many if not all kids. And I empathize: the years that I would point to as making me who I am were ones where I was working, not studying. But they were years spent working in schools, as a teacher or assistant. If schools did not exist, is there an alternative that we genuinely believe would arise to draw young people into the life of their community?

...

It is not an accident that the state that spends the least on education is Utah, where the LDS church can take up some of the slack for schools, while next door Wyoming spends almost the most of any state at $16,000 per student. Education is now the one surviving binding principle of the society as a whole, the one black box everyone will agree to, and so while you can press for less subsidization of education by government, and for privatization of costs, as Caplan does, there’s really nothing people can substitute for it. This is partially about signaling, sure, but it’s also because outside of schools and a few religious enclaves our society is but a darkling plain beset by winds.

This doesn’t mean that we should leave Caplan’s critique on the shelf. Much of education is focused on an insane, zero-sum race for finite rewards. Much of schooling does push kids, parents, schools, and school systems towards a solution ad absurdum, where anything less than 100 percent of kids headed to a doctorate and the big coding job in the sky is a sign of failure of everyone concerned.

But let’s approach this with an eye towards the limits of the possible and the reality of diminishing returns.

https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/
https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/#comment-101293
The real reason the left would support Moander: the usual reason. because he’s an enemy.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/
I have a problem in thinking about education, since my preferences and personal educational experience are atypical, so I can’t just gut it out. On the other hand, knowing that puts me ahead of a lot of people that seem convinced that all real people, including all Arab cabdrivers, think and feel just as they do.

One important fact, relevant to this review. I don’t like Caplan. I think he doesn’t understand – can’t understand – human nature, and although that sometimes confers a different and interesting perspective, it’s not a royal road to truth. Nor would I want to share a foxhole with him: I don’t trust him. So if I say that I agree with some parts of this book, you should believe me.

...

Caplan doesn’t talk about possible ways of improving knowledge acquisition and retention. Maybe he thinks that’s impossible, and he may be right, at least within a conventional universe of possibilities. That’s a bit outside of his thesis, anyhow. Me it interests.

He dismisses objections from educational psychologists who claim that studying a subject improves you in subtle ways even after you forget all of it. I too find that hard to believe. On the other hand, it looks to me as if poorly-digested fragments of information picked up in college have some effect on public policy later in life: it is no coincidence that most prominent people in public life (at a given moment) share a lot of the same ideas. People are vaguely remembering the same crap from the same sources, or related sources. It’s correlated crap, which has a much stronger effect than random crap.

These widespread new ideas are usually wrong. They come from somewhere – in part, from higher education. Along this line, Caplan thinks that college has only a weak ideological effect on students. I don’t believe he is correct. In part, this is because most people use a shifting standard: what’s liberal or conservative gets redefined over time. At any given time a population is roughly half left and half right – but the content of those labels changes a lot. There’s a shift.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/#comment-101492
I put it this way, a while ago: “When you think about it, falsehoods, stupid crap, make the best group identifiers, because anyone might agree with you when you’re obviously right. Signing up to clear nonsense is a better test of group loyalty. A true friend is with you when you’re wrong. Ideally, not just wrong, but barking mad, rolling around in your own vomit wrong.”
--
You just explained the Credo quia absurdum doctrine. I always wondered if it was nonsense. It is not.
--
Someone on twitter caught it first – got all the way to “sliding down the razor blade of life”. Which I explained is now called “transitioning”

What Catholics believe: https://theweek.com/articles/781925/what-catholics-believe
We believe all of these things, fantastical as they may sound, and we believe them for what we consider good reasons, well attested by history, consistent with the most exacting standards of logic. We will profess them in this place of wrath and tears until the extraordinary event referenced above, for which men and women have hoped and prayed for nearly 2,000 years, comes to pass.

https://westhunt.wordpress.com/2018/02/05/bright-college-days-part-ii/
According to Caplan, employers are looking for conformity, conscientiousness, and intelligence. They use completion of high school, or completion of college as a sign of conformity and conscientiousness. College certainly looks as if it’s mostly signaling, and it’s hugely expensive signaling, in terms of college costs and foregone earnings.

But inserting conformity into the merit function is tricky: things become important signals… because they’re important signals. Otherwise useful actions are contraindicated because they’re “not done”. For example, test scores convey useful information. They could help show that an applicant is smart even though he attended a mediocre school – the same role they play in college admissions. But employers seldom request test scores, and although applicants may provide them, few do. Caplan says ” The word on the street… [more]
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april 2017 by nhaliday
Fertility trends by social status
The study reveals that as fertility declines, there is a general shift from a positive to a negative or neutral status-fertility relation. Those with high income/wealth or high occupation/social class switch from having relatively many to fewer or the same number of children as others. Education, however, depresses fertility for as long as this relation is observed (from early in the 20th century).

- good survey with trends for different regions, including UK+North America
- Figure 4: quadratic for UK+NA, crossing zero around 1800 or so and quickly leveling off
http://imgur.com/a/xjwO1
- also Figure 5: fertility differential by total TFR (quadratic trend), so worst dysgenics in middle of demographic transition
- dataset: http://www.demographic-research.org/volumes/vol18/5/files/StatusFertilityDataset.xls

This article discusses how fertility relates to social status with the use of a new dataset, several times larger than the ones used so far. The status-fertility relation is investigated over several centuries, across world regions and by the type of status-measure. The study reveals that as fertility declines, there is a general shift from a positive to a negative or neutral status-fertility relation. Those with high income/wealth or high occupation/social class switch from having relatively many to fewer or the same number of children as others. Education, however, depresses fertility for as long as this relation is observed (from early in the 20th century).
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march 2017 by nhaliday
Was the Wealth of Nations Determined in 1000 BC?
Our most interesting, strong, and robust results are for the association of 1500 AD technology with per capita income and technology adoption today. We also find robust and significant technological persistence from 1000 BC to 0 AD, and from 0 AD to 1500 AD.

migration-adjusted ancestry predicts current economic growth and technology adoption today

https://economix.blogs.nytimes.com/2010/08/02/was-todays-poverty-determined-in-1000-b-c/

Putterman-Weil:
Post-1500 Population Flows and the Long Run Determinants of Economic Growth and Inequality: http://www.nber.org/papers/w14448
Persistence of Fortune: Accounting for Population Movements, There Was No Post-Columbian Reversal: http://sci-hub.tw/10.1257/mac.6.3.1
Extended State History Index: https://sites.google.com/site/econolaols/extended-state-history-index
Description:
The data set extends and replaces previous versions of the State Antiquity Index (originally created by Bockstette, Chanda and Putterman, 2002). The updated data extends the previous Statehist data into the years before 1 CE, to the first states in Mesopotamia (in the fourth millennium BCE), along with filling in the years 1951 – 2000 CE that were left out of past versions of the Statehist data.
The construction of the index follows the principles developed by Bockstette et al (2002). First, the duration of state existence is established for each territory defined by modern-day country borders. Second, this duration is divided into 50-year periods. For each half-century from the first period (state emergence) onwards, the authors assign scores to reflect three dimensions of state presence, based on the following questions: 1) Is there a government above the tribal level? 2) Is this government foreign or locally based? 3) How much of the territory of the modern country was ruled by this government?

Creators: Oana Borcan, Ola Olsson & Louis Putterman

State History and Economic Development: Evidence from Six Millennia∗: https://drive.google.com/file/d/1cifUljlPpoURL7VPOQRGF5q9H6zgVFXe/view
The presence of a state is one of the most reliable historical predictors of social and economic development. In this article, we complete the coding of an extant indicator of state presence from 3500 BCE forward for almost all but the smallest countries of the world today. We outline a theoretical framework where accumulated state experience increases aggregate productivity in individual countries but where newer or relatively inexperienced states can reach a higher productivity maximum by learning from the experience of older states. The predicted pattern of comparative development is tested in an empirical analysis where we introduce our extended state history variable. Our key finding is that the current level of economic development across countries has a hump-shaped relationship with accumulated state history.

nonlinearity confirmed in this other paper:
State and Development: A Historical Study of Europe from 0 AD to 2000 AD: https://ideas.repec.org/p/hic/wpaper/219.html
After addressing conceptual and practical concerns on its construction, we present a measure of the mean duration of state rule that is aimed at resolving some of these issues. We then present our findings on the relationship between our measure and local development, drawing from observations in Europe spanning from 0 AD to 2000 AD. We find that during this period, the mean duration of state rule and the local income level have a nonlinear, inverse U-shaped relationship, controlling for a set of historical, geographic and socioeconomic factors. Regions that have historically experienced short or long duration of state rule on average lag behind in their local wealth today, while those that have experienced medium-duration state rule on average fare better.

Figure 1 shows all borders that existed during this period
Figure 4 shows quadratic fit

I wonder if U-shape is due to Ibn Kaldun-Turchin style effect on asabiya? They suggest sunk costs and ossified institutions.
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march 2017 by nhaliday
List of games in game theory - Wikipedia
https://twitter.com/BretWeinstein/status/961503023854833665
https://archive.is/qLsD4
The most important patterns:

1. Prisoner's Dilemma
2. Race to the Bottom
3. Free Rider Problem / Tragedy of the Commons / Collective Action
4. Zero Sum vs. Non-Zero Sum
5. Externalities / Principal Agent
6. Diminishing Returns
7. Evolutionarily Stable Strategy / Nash Equilibrium
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february 2017 by nhaliday
inequalities - Is the Jaccard distance a distance? - MathOverflow
Steinhaus Transform
the referenced survey: http://kenclarkson.org/nn_survey/p.pdf

It's known that this transformation produces a metric from a metric. Now if you take as the base metric D the symmetric difference between two sets, what you end up with is the Jaccard distance (which actually is known by many other names as well).
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february 2017 by nhaliday
Prékopa–Leindler inequality | Academically Interesting
Consider the following statements:
1. The shape with the largest volume enclosed by a given surface area is the n-dimensional sphere.
2. A marginal or sum of log-concave distributions is log-concave.
3. Any Lipschitz function of a standard n-dimensional Gaussian distribution concentrates around its mean.
What do these all have in common? Despite being fairly non-trivial and deep results, they all can be proved in less than half of a page using the Prékopa–Leindler inequality.

ie, Brunn-Minkowski
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february 2017 by nhaliday
The Brunn-Minkowski Inequality | The n-Category Café
For instance, this happens in the plane when A is a horizontal line segment and B is a vertical line segment. There’s obviously no hope of getting an equation for Vol(A+B) in terms of Vol(A) and Vol(B). But this example suggests that we might be able to get an inequality, stating that Vol(A+B) is at least as big as some function of Vol(A) and Vol(B).

The Brunn-Minkowski inequality does this, but it’s really about linearized volume, Vol^{1/n}, rather than volume itself. If length is measured in metres then so is Vol^{1/n}.

...

Nice post, Tom. To readers whose background isn’t in certain areas of geometry and analysis, it’s not obvious that the Brunn–Minkowski inequality is more than a curiosity, the proof of the isoperimetric inequality notwithstanding. So let me add that Brunn–Minkowski is an absolutely vital tool in many parts of geometry, analysis, and probability theory, with extremely diverse applications. Gardner’s survey is a great place to start, but by no means exhaustive.

I’ll also add a couple remarks about regularity issues. You point out that Brunn–Minkowski holds “in the vast generality of measurable sets”, but it may not be initially obvious that this needs to be interpreted as “when A, B, and A+B are all Lebesgue measurable”, since A+B need not be measurable when A and B are (although you can modify the definition of A+B to work for arbitrary measurable A and B; this is discussed by Gardner).
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february 2017 by nhaliday
mg.metric geometry - Pushing convex bodies together - MathOverflow
- volume of intersection of colliding, constant-velocity convex bodies is unimodal
- pf by Brunn-Minkowski inequality
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january 2017 by nhaliday
Ehrhart polynomial - Wikipedia
In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem in the Euclidean plane.
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january 2017 by nhaliday
Dvoretzky's theorem - Wikipedia
In mathematics, Dvoretzky's theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering a question of Alexander Grothendieck. In essence, it says that every sufficiently high-dimensional normed vector space will have low-dimensional subspaces that are approximately Euclidean. Equivalently, every high-dimensional bounded symmetric convex set has low-dimensional sections that are approximately ellipsoids.

http://mathoverflow.net/questions/143527/intuitive-explanation-of-dvoretzkys-theorem
http://mathoverflow.net/questions/46278/unexpected-applications-of-dvoretzkys-theorem
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january 2017 by nhaliday
Carathéodory's theorem (convex hull) - Wikipedia
- any convex combination in R^d can be pared down to at most d+1 points
- eg, in R^2 you can always fit a point in convex hull in a triangle
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january 2017 by nhaliday
(Gil Kalai) The weak epsilon-net problem | What's new
This is a problem in discrete and convex geometry. It seeks to quantify the intuitively obvious fact that large convex bodies are so “fat” that they cannot avoid “detection” by a small number of observation points.
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january 2017 by nhaliday
A Systematic Review of Personality Trait Change Through Intervention
gwern: https://plus.google.com/103530621949492999968/posts/6kFWRkUTXSV
Messy (noticeable levels of publication bias, high heterogeneity), but results look plausible: 8-week+ interventions can improve emotional stability and neuroticism, change Openness and Extraversion somewhat, but leave Conscientiousness largely unaffected.

hbd chick/murray: https://twitter.com/hbdchick/status/818138228553302017

- 8-week intervention -> d=.37 after (an average of) 24 weeks
- after 8 weeks, strong diminishing returns
- pretty much entirely self-report
- good page-length discussion of limitations at end
- there was actually a nonzero effect for conscientiousness (~.2). not sure it would remain w/o publication bias.
- what's the difference between Table 2 and 3? I guess RCT vs. something else? why highlight Table 2 in abstract then?
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january 2017 by nhaliday
Mental rotation and real-world wayfinding. - PubMed - NCBI
r ≈ .3

The results indicate that mental rotation skills are significantly correlated with wayfinding performance on an orienteering task. The findings also replicate sex differences in spatial ability as found in laboratory-scale studies. However, the findings complicate the discussion of mental rotation skills and sex because women often performed as well as men despite having lower mean test scores. This suggests that mental rotation ability may not be as necessary for some women's wayfinding as it is for men's navigation.

Sex Differences in Furniture Assembly Performance: An Experimental Study: http://onlinelibrary.wiley.com/doi/10.1002/acp.3182/abstract
fucking lol

Sex hormones predict the sensory strength and vividness of mental imagery: https://www.ncbi.nlm.nih.gov/pubmed/25703930
- not in the direction I would expect (women have more vivid mental imagery)
- visual working memory is different

Sex hormones and mental rotation: An intensive longitudinal investigation: http://www.sciencedirect.com.sci-hub.tw/science/article/pii/S0018506X12003066
For males and females, estradiol and testosterone were significantly linearly and quadratically related to interindividual variation in performance at the beginning of the study (progesterone was linearly related to performance for females). The association between testosterone and performance differed across sexes: for males, it had an inverse U-shape, for females it was U-shaped. Towards the end of the study, none of the hormones were significantly related to performance anymore. Thus, the relationship between hormones and mental rotation performance disappeared with repeated testing.

very confusing study. seems sketchy.

Is There a Relationship Between the Performance in a Chronometric Mental-Rotations Test and Salivary Testosterone and Estradiol Levels in Children Aged 9–14 Years?: http://sci-hub.tw/10.1002/dev.21333
Results showed a significant gender difference in reaction time and rotational speed in favor of boys, and a significant age, but no gender difference in testosterone and estradiol levels. We found no significant relationships between hormonal levels and any measure of mental-rotation performance.

Having a Male Co-Twin Masculinizes Mental Rotation Performance in Females: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4438761/
There were 351 females from same-sex pairs, 223 males from same-sex pairs, 120 females from opposite-sex pairs, and 110 males from opposite-sex pairs.

hmm:
Sex Differences in Mental Rotation Ability Are a Consequence of Procedure and Artificiality of Stimuli: https://link.springer.com/article/10.1007/s40806-017-0120-x
Our results suggest that the sex difference found on this test is not due to a male advantage in spatial ability, but is an artifact of the stimuli.
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december 2016 by nhaliday
Convex Optimization Applications
there was a problem in ACM113 related to this (the portfolio optimization SDP stuff)
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december 2016 by nhaliday
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