nhaliday + definition   71

Alon Amit's answer to Why is there no formal definition for a set in math? How can we make any statement about sets (and therefore all of math) if we don’t even know what it is? - Quora
In the realm of mathematics, an object is what it does (I keep quoting Tim Gowers with this phrase, and I will likely do so many more times). The only thing that matters about points, lines, real numbers, sets, functions, groups and tempered distributions is the properties and features and rules they obey. What they “are” is of no concern.

I've seen this idea in a lot of different places
q-n-a  qra  math  lens  abstraction  essence-existence  analytical-holistic  forms-instances  big-picture  aphorism  axioms  definition  characterization  zooming 
9 days ago by nhaliday
performance - What is the difference between latency, bandwidth and throughput? - Stack Overflow
Latency is the amount of time it takes to travel through the tube.
Bandwidth is how wide the tube is.
The amount of water flow will be your throughput

Vehicle Analogy:

Container travel time from source to destination is latency.
Container size is bandwidth.
Container load is throughput.

--

Note, bandwidth in particular has other common meanings, I've assumed networking because this is stackoverflow but if it was a maths or amateur radio forum I might be talking about something else entirely.
q-n-a  stackex  programming  IEEE  nitty-gritty  definition  jargon  network-structure  metrics  speedometer  time  stock-flow  performance 
8 weeks ago by nhaliday
Dividuals – The soul is not an indivisible unit and has no unified will
Towards A More Mature Atheism: https://dividuals.wordpress.com/2015/09/17/towards-a-more-mature-atheism/
Human intelligence evolved as a social intelligence, for the purposes of social cooperation, social competition and social domination. It evolved to make us efficient at cooperating at removing obstacles, especially the kinds of obstacles that tend to fight back, i.e. at warfare. If you ever studied strategy or tactics, or just played really good board games, you have probably found your brain seems to be strangely well suited for specifically this kind of intellectual activity. It’s not necessarily easier than studying physics, and yet it somehow feels more natural. Physics is like swimming, strategy and tactics is like running. The reason for that is that our brains are truly evolved to be strategic, tactical, diplomatic computers, not physics computers. The question our brains are REALLY good at finding the answer for is “Just what does this guy really want?”

...

Thus, a very basic failure mode of the human brain is to overdetect agency.

I think this is partially what SSC wrote about in Mysticism And Pattern-Matching too. But instead of mystical experiences, my focus is on our brains claiming to detect agency where there is none. Thus my view is closer to Richard Carrier’s definition of the supernatural: it is the idea that some mental things cannot be reduced to nonmental things.

...

Meaning actually means will and agency. It took me a while to figure that one out. When we look for the meaning of life, a meaning in life, or a meaningful life, we look for a will or agency generally outside our own.

...

I am a double oddball – kind of autistic, but still far more interested in human social dynamics, such as history, than in natural sciences or technology. As a result, I do feel a calling to religion – the human world, as opposed to outer space, the human city, the human history, is such a perfect fit for a view like that of Catholicism! The reason for that is that Catholicism is the pinnacle of human intellectual efforts dealing with human agency. Ideas like Augustine’s three failure modes of the human brain: greed, lust and desire for power and status, are just about the closest to forming correct psychological theories far earlier than the scientific method was discovered. Just read your Chesterbelloc and Lewis. And of course because the agency radars of Catholics run at full burst, they overdetect it and thus believe in a god behind the universe. My brain, due to my deep interest in human agency and its consequences, also would like to be religious: wouldn’t it be great if the universe was made by something we could talk to, like, everything else that I am interested in, from field generals to municipal governments are entities I could talk to?

...

I also dislike that atheists often refuse to propose a falsifiable theory because they claim the burden of proof is not on them. Strictly speaking it can be true, but it is still good form to provide one.

Since I am something like an “nontheistic Catholic” anyway (e.g. I believe in original sin from the practical, political angle, I just think it has natural, not supernatural causes: evolution, the move from hunting-gathering to agriculture etc.), all one would need to do to make me fully so is to plug a God concept in my mind.

If you can convince me that my brain is not actually overdetecting agency when I feel a calling to religion, if you can convince me that my brain and most human brains detect agency just about right, there will be no reason for me to not believe in God. Because if there would any sort of agency behind the universe, the smartest bet would be that this agency would be the God of Thomas Aquinas’ Summa. That guy was plain simply a genius.

How to convince me my brain is not overdetecting agency? The simplest way is to convince me that magic, witchcraft, or superstition in general is real, and real in the supernatural sense (I do know Wiccans who cast spells and claim they are natural, not supernatural: divination spells make the brain more aware of hidden details, healing spells recruit the healing processes of the body etc.) You see, Catholics generally do believe in magic and witchcraft, as in: “These really do something, and they do something bad, so never practice them.”

The Strange Places the “God of the Gaps” Takes You: https://dividuals.wordpress.com/2018/05/25/the-strange-places-the-god-of-the-gaps-takes-you/
I assume people are familiar with the God of the Gaps argument. Well, it is usually just an accusation, but Newton for instance really pulled one.

But natural science is inherently different from humanities, because in natural science you build a predictive model of which you are not part of. You are just a point-like neutral observer.

You cannot do that with other human minds because you just don’t have the computing power to simulate a roughly similarly intelligent mind and have enough left to actually work with your model. So you put yourself into the predictive model, you make yourself a part of the model itself. You use a certain empathic kind of understanding, a “what would I do in that guys shoes?” and generate your predictions that way.

...

Which means that while natural science is relatively new, and strongly correlates with technological progress, this empathic, self-programming model of the humanities you could do millenia ago as well, you don’t need math or tools for this, and you probably cannot expect anything like straight-line progress. Maybe some wisdoms people figure out this way are really timeless and we just keep on rediscovering them.

So imagine, say, Catholicism as a large set of humanities. Sociology, social psychology, moral philosophy in the pragmatic, scientific sense (“What morality makes a society not collapse and actually prosper?”), life wisdom and all that. Basically just figuring out how people tick, how societies tick and how to make them tick well.

...

What do? Well, the obvious move is to pull a Newton and inject a God of the Gaps into your humanities. We tick like that because God. We must do so and so to tick well because God.

...

What I am saying is that we are at some point probably going to prove pretty much all of the this-worldy, pragmatic (moral, sociological, psychological etc.) aspect of Catholicism correct by something like evolutionary psychology.

And I am saying that while it will dramatically increase our respect for religion, this will also be probably a huge blow to theism. I don’t want that to happen, but I think it will. Because eliminating God from the gaps of natural science does not hurt faith much. But eliminating God from the gaps of the humanities and yes, religion itself?

My Kind of Atheist: http://www.overcomingbias.com/2018/08/my-kind-of-athiest.html
I think I’ve mentioned somewhere in public that I’m now an atheist, even though I grew up in a very Christian family, and I even joined a “cult” at a young age (against disapproving parents). The proximate cause of my atheism was learning physics in college. But I don’t think I’ve ever clarified in public what kind of an “atheist” or “agnostic” I am. So here goes.

The universe is vast and most of it is very far away in space and time, making our knowledge of those distant parts very thin. So it isn’t at all crazy to think that very powerful beings exist somewhere far away out there, or far before us or after us in time. In fact, many of us hope that we now can give rise to such powerful beings in the distant future. If those powerful beings count as “gods”, then I’m certainly open to the idea that such gods exist somewhere in space-time.

It also isn’t crazy to imagine powerful beings that are “closer” in space and time, but far away in causal connection. They could be in parallel “planes”, in other dimensions, or in “dark” matter that doesn’t interact much with our matter. Or they might perhaps have little interest in influencing or interacting with our sort of things. Or they might just “like to watch.”

But to most religious people, a key emotional appeal of religion is the idea that gods often “answer” prayer by intervening in their world. Sometimes intervening in their head to make them feel different, but also sometimes responding to prayers about their test tomorrow, their friend’s marriage, or their aunt’s hemorrhoids. It is these sort of prayer-answering “gods” in which I just can’t believe. Not that I’m absolutely sure they don’t exist, but I’m sure enough that the term “atheist” fits much better than the term “agnostic.”

These sort of gods supposedly intervene in our world millions of times daily to respond positively to particular prayers, and yet they do not noticeably intervene in world affairs. Not only can we find no physical trace of any machinery or system by which such gods exert their influence, even though we understand the physics of our local world very well, but the history of life and civilization shows no obvious traces of their influence. They know of terrible things that go wrong in our world, but instead of doing much about those things, these gods instead prioritize not leaving any clear evidence of their existence or influence. And yet for some reason they don’t mind people believing in them enough to pray to them, as they often reward such prayers with favorable interventions.
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june 2018 by nhaliday
Land, history or modernization? Explaining ethnic fractionalization: Ethnic and Racial Studies: Vol 38, No 2
Ethnic fractionalization (EF) is frequently used as an explanatory tool in models of economic development, civil war and public goods provision. However, if EF is endogenous to political and economic change, its utility for further research diminishes. This turns out not to be the case. This paper provides the first comprehensive model of EF as a dependent variable.
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december 2017 by nhaliday
Is the speed of light really constant?
So what if the speed of light isn’t the same when moving toward or away from us? Are there any observable consequences? Not to the limits of observation so far. We know, for example, that any one-way speed of light is independent of the motion of the light source to 2 parts in a billion. We know it has no effect on the color of the light emitted to a few parts in 1020. Aspects such as polarization and interference are also indistinguishable from standard relativity. But that’s not surprising, because you don’t need to assume isotropy for relativity to work. In the 1970s, John Winnie and others showed that all the results of relativity could be modeled with anisotropic light so long as the two-way speed was a constant. The “extra” assumption that the speed of light is a uniform constant doesn’t change the physics, but it does make the mathematics much simpler. Since Einstein’s relativity is the simpler of two equivalent models, it’s the model we use. You could argue that it’s the right one citing Occam’s razor, or you could take Newton’s position that anything untestable isn’t worth arguing over.

SPECIAL RELATIVITY WITHOUT ONE-WAY VELOCITY ASSUMPTIONS:
https://sci-hub.bz/https://www.jstor.org/stable/186029
https://sci-hub.bz/https://www.jstor.org/stable/186671
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november 2017 by nhaliday
Equilibrium thermodynamics - Wikipedia
Equilibrium Thermodynamics is the systematic study of transformations of matter and energy in systems in terms of a concept called thermodynamic equilibrium. The word equilibrium implies a state of balance. Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle. Here, typically a system, as cylinder of gas, initially in its own state of internal thermodynamic equilibrium, is set out of balance via heat input from a combustion reaction. Then, through a series of steps, as the system settles into its final equilibrium state, work is extracted.

In an equilibrium state the potentials, or driving forces, within the system, are in exact balance. A central aim in equilibrium thermodynamics is: given a system in a well-defined initial state of thermodynamic equilibrium, subject to accurately specified constraints, to calculate, when the constraints are changed by an externally imposed intervention, what the state of the system will be once it has reached a new equilibrium. An equilibrium state is mathematically ascertained by seeking the extrema of a thermodynamic potential function, whose nature depends on the constraints imposed on the system. For example, a chemical reaction at constant temperature and pressure will reach equilibrium at a minimum of its components' Gibbs free energy and a maximum of their entropy.

Equilibrium thermodynamics differs from non-equilibrium thermodynamics, in that, with the latter, the state of the system under investigation will typically not be uniform but will vary locally in those as energy, entropy, and temperature distributions as gradients are imposed by dissipative thermodynamic fluxes. In equilibrium thermodynamics, by contrast, the state of the system will be considered uniform throughout, defined macroscopically by such quantities as temperature, pressure, or volume. Systems are studied in terms of change from one equilibrium state to another; such a change is called a thermodynamic process.
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november 2017 by nhaliday
Hyperbolic angle - Wikipedia
A unit circle {\displaystyle x^{2}+y^{2}=1} x^2 + y^2 = 1 has a circular sector with an area half of the circular angle in radians. Analogously, a unit hyperbola {\displaystyle x^{2}-y^{2}=1} {\displaystyle x^{2}-y^{2}=1} has a hyperbolic sector with an area half of the hyperbolic angle.
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november 2017 by nhaliday
Culture, Ethnicity, and Diversity - American Economic Association
We investigate the empirical relationship between ethnicity and culture, defined as a vector of traits reflecting norms, values, and attitudes. Using survey data for 76 countries, we find that ethnic identity is a significant predictor of cultural values, yet that within-group variation in culture trumps between-group variation. Thus, in contrast to a commonly held view, ethnic and cultural diversity are unrelated. Although only a small portion of a country’s overall cultural heterogeneity occurs between groups, we find that various political economy outcomes (such as civil conflict and public goods provision) worsen when there is greater overlap between ethnicity and culture. (JEL D74, H41, J15, O15, O17, Z13)

definition of chi-squared index, etc., under:
II. Measuring Heterogeneity

Table 5—Incidence of Civil Conflict and Diversity
Table 6—Public Goods Provision and Diversity

https://twitter.com/GarettJones/status/924002043576115202
https://archive.is/oqMnC
https://archive.is/sBqqo
https://archive.is/1AcXn
χ2 diversity: raising the risk of civil war. Desmet, Ortuño-Ortín, Wacziarg, in the American Economic Review (1/N)

What predicts higher χ2 diversity? The authors tell us that, too. Here are all of the variables that have a correlation > 0.4: (7/N)

one of them is UK legal origin...

online appendix (with maps, Figures B1-3): http://www.anderson.ucla.edu/faculty_pages/romain.wacziarg/downloads/2017_culture_appendix.pdf
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september 2017 by nhaliday
Reynolds number - Wikipedia
The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities, in what is known as a boundary layer in the case of a bounding surface such as the interior of a pipe. A similar effect is created by the introduction of a stream of higher velocity fluid, such as the hot gases from a flame in air. This relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which as it increases, progressively inhibits turbulence, as more kinetic energy is absorbed by a more viscous fluid. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation.[6]

Re = ρuL/μ

(inertial forces)/(viscous forces)
= (mass)(acceleration) / (dynamic viscosity)(velocity/distance)(area)
= (ρL^3)(v/t) / μ(v/L)L^2
= Re

NB: viscous force/area ~ μ du/dy is definition of viscosity
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september 2017 by nhaliday
Correlated Equilibria in Game Theory | Azimuth
Given this, it’s not surprising that Nash equilibria can be hard to find. Last September a paper came out making this precise, in a strong way:

• Yakov Babichenko and Aviad Rubinstein, Communication complexity of approximate Nash equilibria.

The authors show there’s no guaranteed method for players to find even an approximate Nash equilibrium unless they tell each other almost everything about their preferences. This makes finding the Nash equilibrium prohibitively difficult to find when there are lots of players… in general. There are particular games where it’s not difficult, and that makes these games important: for example, if you’re trying to run a government well. (A laughable notion these days, but still one can hope.)

Klarreich’s article in Quanta gives a nice readable account of this work and also a more practical alternative to the concept of Nash equilibrium. It’s called a ‘correlated equilibrium’, and it was invented by the mathematician Robert Aumann in 1974. You can see an attempt to define it here:
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july 2017 by nhaliday
Gnosticism - Wikipedia
https://en.wikipedia.org/wiki/Eric_Voegelin#Voegelin_on_gnosticism

Faith and other Epistemic Categories: https://quaslacrimas.wordpress.com/2017/03/10/faith-and-other-epistemic-categories/
In response to Bonald’s excellent little piece Faith is honesty in doubt, I wanted to offer a parallel thesis (or, if you like, a friendly amendment): faith is a matter of whom, not what.

I can have faith in a man (I believe him). Maybe I have faith in him in a general sense, or maybe I have only heard him recite one particular narrative (in which case when I say I believe him I mean I have faith in that particular narrative). I can also have faith in groups and communities, and in their reports, publications, traditions, in the names they put forward as trustworthy authorities on certain questions, and so on.

Faith (or belief) is a matter of trust; fundamentally it is your confidence in the man that makes you confident his words will ring true. (Indeed, confidence is a Latin word meaning with faith.)

You can trust a man, or a group; you can always trust every word that comes out of his mouth, or just in one incident; you can trust him on account of his honesty, his accuracy, or both; you can trust him absolutely or only casually; but wherever you say you trust, the question whom it is that you trust arises. You can’t trust things, states of affairs, trees…

...

As Christians, we believe Christ and his Apostles. When Mr. Smith tells us something that conflicts with our Christian creed, we withhold our assent from Mr. Smith’s claims because we have greater faith in Christ than in Mr. Smith. If later on Mr. Thompson tells us something that conflicts with some other rumor we heard from Mr. Smith, this conflict will cause us to experience some uncertainty and confusion; but we will have a much more vivid understanding of what is going on if we have recently had some reason to reflect on Mr. Smith and how much (or how little) we trust him.

...

Perhaps we could say that this is the difference between faith and conviction. Conviction refers to something that you have been convinced is true (and only implicitly, if at all, to those who convinced you), whereas faith refers to someone you trust (and only implicitly to opinions you hold as a result of this trust). To restate a point using this new conceptual contrast: everyone has convictions, but a Christian has faith as well.

Faith and Gullibility: https://quaslacrimas.wordpress.com/2018/05/09/faith-and-gullibility/
But Chesterton’s point is in a certain sense a petty one to score: which of the trendy superstitions in circulation today is half as trendy as barren, godless materialism?

The vulgar errors of the plebs have actually become part of the metabolism of our godless society. As the Cathedral and its choirboys have gradually improved message-discipline on science and superstition (yes, they “freaking love science”), the contrast between the amusingly rustic ignorance of the commoners and the smug confidence of the overclass has become part of the status-structure that draws ambitious youngsters into the Cathedral’s cold embrace. Abandoning the poor to the torment of demons is now part of the Left’s plan; more room to tut-tut and demonstrate that you are a reasonable bugman, more misery to justify the next stage in the revolution.

But still, this fails to get at the root of the fairies and the séances and the horoscopes, which is neither faith’s relation to superstition, nor to the arrogance of those who lift themselves up above the superstitions they despise in others, but rather faith’s relation to gullibility.

Gullibility is a more general concept than superstition. Let us define superstition as gullibility with respect to opinions and possibilities that are held in contempt by the powerful, while gullibility itself is the epistemic equivalent of pettiness — an inability to dismiss highly improbable hypotheses.

...

Not because of any special piety or zeal, but simply because it was barely yesterday that I was an atheist, I had a vivid impression of the changes in my thinking process. It was not impossible that supernatural agency was involved, of course, but it was very implausible — because it seemed too trivial and indistinct to be worth the effort of a self-respecting angel. So I set that aside immediately, and stayed focused on thinking about what might actually be going on.

Putting aside the insignificant possibility lightened my mind almost in the way pouring water out of a jug would. I seem to remember that when I was an atheist confronting this type of “superstition”, I would keep the supernatural hypothesis in front of my mind, regulating my thoughts, considering the case from every angle but only from the perspective of what might disprove the superstitious opinion.

But a superstition is the opinion of a crackpot. Why was I worried about what crackpots believe? If Eddington has a hypothesis or Einstein has a hypothesis, then falsifying the hypothesis is science. Falsifying a crackpot’s hypothesis is proof that you place a low value on your time.

...

Here is another possibility: I don’t know why the appliance turns on when it does. I wasn’t able to figure it out. It would be odd if I could, since I’m not an electrician or an engineer. The world would be a boring place if you could just suss out the answer to arbitrarily unusual questions without making any special study of the topic. Sometimes we don’t know. And often when we don’t know we don’t care. In fact, most of the time we don’t care about what we don’t know precisely because the insignificance of the topic is the very reason we never prepared ourselves to answer that type of question in the first place.
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july 2017 by nhaliday
Harmonic mean - Wikipedia
The harmonic mean is a Schur-concave function, and dominated by the minimum of its arguments, in the sense that for any positive set of arguments, {\displaystyle \min(x_{1}\ldots x_{n})\leq H(x_{1}\ldots x_{n})\leq n\min(x_{1}\ldots x_{n})} . Thus, the harmonic mean cannot be made arbitrarily large by changing some values to bigger ones (while having at least one value unchanged).

more generally, for the weighted mean w/ Pr(x_i)=t_i, H(x1,...,xn) <= x_i/t_i
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july 2017 by nhaliday
Riemannian manifold - Wikipedia
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real smooth manifold M equipped with an inner product {\displaystyle g_{p}} on the tangent space {\displaystyle T_{p}M} at each point {\displaystyle p} that varies smoothly from point to point in the sense that if X and Y are vector fields on M, then {\displaystyle p\mapsto g_{p}(X(p),Y(p))} is a smooth function. The family {\displaystyle g_{p}} of inner products is called a Riemannian metric (tensor). These terms are named after the German mathematician Bernhard Riemann. The study of Riemannian manifolds constitutes the subject called Riemannian geometry.

A Riemannian metric (tensor) makes it possible to define various geometric notions on a Riemannian manifold, such as angles, lengths of curves, areas (or volumes), curvature, gradients of functions and divergence of vector fields.
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february 2017 by nhaliday
Neurodiversity | West Hunter
Having an accurate evaluation of a syndrome as a generally bad thing isn’t equivalent to attacking those with that syndrome. Being a leper is a bad thing, not just another wonderful flavor of humanity [insert hot tub joke] , but that doesn’t mean that we have to spend our spare time playing practical jokes on lepers, tempting though that is.. Leper hockey. We can cure leprosy, and we are right to do so. Preventing deafness through rubella vaccination was the right thing too – deafness sucks. And so on. As we get better at treating and preventing, humans are going to get more uniform – and that’s a good thing. Back to normalcy!

focus: https://westhunt.wordpress.com/2017/02/22/neurodiversity/#comment-88691
interesting discussion of mutational load: https://westhunt.wordpress.com/2017/02/22/neurodiversity/#comment-88793

https://westhunt.wordpress.com/2013/04/30/blurry/
I was thinking again about the consequences of having more small-effect deleterious mutations than average. I don’t think that they would push hard in a particular direction in phenotype space – I don’t believe they would make you look weird, but by definition they would be bad for you, reduce fitness. I remembered a passage in a book by Steve Stirling, in which our heroine felt as if her brain ‘was moving like a mechanism of jewels and steel precisely formed.’ It strikes me that a person with an extra dollop of this kind of genetic load wouldn’t feel like that. And of course that heroine did have low genetic load, being the product of millennia of selective breeding, not to mention an extra boost from the Invisible Crown.

https://westhunt.wordpress.com/2013/04/30/blurry/#comment-12769
Well, what does the distribution of fitness burden by frequency look like for deleterious mutations of a given fitness penalty?
--
It’s proportional to the mutation rate for that class. There is reason to believe that there are more ways to moderately or slightly screw up a protein than to really ruin it, which indicates that mild mutations make up most load in protein-coding sequences. More of the genome is made up of conserved regulatory sequences, but mutations there probably have even milder effects, since few mutations in non-coding sequences cause a serious Mendelian disease.

https://westhunt.wordpress.com/2013/04/30/blurry/#comment-12803
I have wondered if there was some sort of evolutionary tradeoff between muscles and brains over the past hundred thousand years through dystrophin’s dual role. There is some evidence of recent positive selection among proteins that interact with dystrophin, such as DTNBP1 and DTNA.

Any novel environment where higher intelligence can accrue more caloric energy than brute strength alone (see: the invention of the bow) should relax the selection pressure for muscularity. The Neanderthals didn’t fare so well with the brute strength strategy.
--
Sure: that’s what you might call an inevitable tradeoff, a consequence of the laws of physics. Just as big guys need more food. But because of the way our biochemistry is wired, there can be tradeoffs that exist but are not inevitable consequences of the laws of physics – particularly likely when a gene has two fairly different functions, as they often do.
west-hunter  discussion  morality  philosophy  evolution  sapiens  psychology  psychiatry  disease  neuro  scitariat  ideology  rhetoric  diversity  prudence  genetic-load  autism  focus  👽  multi  poast  mutation  equilibrium  scifi-fantasy  rant  🌞  paternal-age  perturbation  nibble  ideas  iq  quotes  aphorism  enhancement  signal-noise  blowhards  dysgenics  data  distribution  objektbuch  tradeoffs  embodied  speculation  metabolic  volo-avolo  degrees-of-freedom  race  africa  genetics  genomics  bio  QTL  population-genetics  stylized-facts  britain  history  early-modern  pre-ww2  galton  old-anglo  giants  industrial-revolution  neuro-nitgrit  recent-selection  selection  medicine  darwinian  strategy  egalitarianism-hierarchy  CRISPR  biotech  definition  reflection  poetry  deep-materialism  EGT  discrimination  conceptual-vocab 
february 2017 by nhaliday
Mixing (mathematics) - Wikipedia
One way to describe this is that strong mixing implies that for any two possible states of the system (realizations of the random variable), when given a sufficient amount of time between the two states, the occurrence of the states is independent.

Mixing coefficient is
α(n) = sup{|P(A∪B) - P(A)P(B)| : A in σ(X_0, ..., X_{t-1}), B in σ(X_{t+n}, ...), t >= 0}
for σ(...) the sigma algebra generated by those r.v.s.

So it's a notion of total variational distance between the true distribution and the product distribution.
concept  math  acm  physics  probability  stochastic-processes  definition  mixing  iidness  wiki  reference  nibble  limits  ergodic  math.DS  measure  dependence-independence 
february 2017 by nhaliday
Difference between off-policy and on-policy learning - Cross Validated
The reason that Q-learning is off-policy is that it updates its Q-values using the Q-value of the next state s′ and the greedy action a′. In other words, it estimates the return (total discounted future reward) for state-action pairs assuming a greedy policy were followed despite the fact that it's not following a greedy policy.

The reason that SARSA is on-policy is that it updates its Q-values using the Q-value of the next state s′ and the current policy's action a″. It estimates the return for state-action pairs assuming the current policy continues to be followed.

The distinction disappears if the current policy is a greedy policy. However, such an agent would not be good since it never explores.
q-n-a  overflow  machine-learning  acm  reinforcement  confusion  jargon  generalization  nibble  definition  greedy  comparison 
february 2017 by nhaliday
general topology - What should be the intuition when working with compactness? - Mathematics Stack Exchange
http://math.stackexchange.com/questions/485822/why-is-compactness-so-important

The situation with compactness is sort of like the above. It turns out that finiteness, which you think of as one concept (in the same way that you think of "Foo" as one concept above), is really two concepts: discreteness and compactness. You've never seen these concepts separated before, though. When people say that compactness is like finiteness, they mean that compactness captures part of what it means to be finite in the same way that shortness captures part of what it means to be Foo.

--

As many have said, compactness is sort of a topological generalization of finiteness. And this is true in a deep sense, because topology deals with open sets, and this means that we often "care about how something behaves on an open set", and for compact spaces this means that there are only finitely many possible behaviors.

--

Compactness does for continuous functions what finiteness does for functions in general.

If a set A is finite then every function f:A→R has a max and a min, and every function f:A→R^n is bounded. If A is compact, the every continuous function from A to R has a max and a min and every continuous function from A to R^n is bounded.

If A is finite then every sequence of members of A has a subsequence that is eventually constant, and "eventually constant" is the only kind of convergence you can talk about without talking about a topology on the set. If A is compact, then every sequence of members of A has a convergent subsequence.
q-n-a  overflow  math  topology  math.GN  concept  finiteness  atoms  intuition  oly  mathtariat  multi  discrete  gowers  motivation  synthesis  hi-order-bits  soft-question  limits  things  nibble  definition  convergence  abstraction  span-cover 
january 2017 by nhaliday
D-separation
collider C = A->C<-B
A, B d-connected (resp. conditioned on Z) iff path A~>B or B~>A w/o colliders (resp. path excluding vertices in Z)
A,B d-separated conditioned on Z iff not d-connected conditioned on Z

http://bayes.cs.ucla.edu/BOOK-2K/d-sep.html
concept  explanation  causation  bayesian  graphical-models  cmu  org:edu  stats  methodology  tutorial  jargon  graphs  hypothesis-testing  confounding  🔬  direct-indirect  philosophy  definition  volo-avolo  multi  org:junk 
january 2017 by nhaliday
Shtetl-Optimized » Blog Archive » Why I Am Not An Integrated Information Theorist (or, The Unconscious Expander)
In my opinion, how to construct a theory that tells us which physical systems are conscious and which aren’t—giving answers that agree with “common sense” whenever the latter renders a verdict—is one of the deepest, most fascinating problems in all of science. Since I don’t know a standard name for the problem, I hereby call it the Pretty-Hard Problem of Consciousness. Unlike with the Hard Hard Problem, I don’t know of any philosophical reason why the Pretty-Hard Problem should be inherently unsolvable; but on the other hand, humans seem nowhere close to solving it (if we had solved it, then we could reduce the abortion, animal rights, and strong AI debates to “gentlemen, let us calculate!”).

Now, I regard IIT as a serious, honorable attempt to grapple with the Pretty-Hard Problem of Consciousness: something concrete enough to move the discussion forward. But I also regard IIT as a failed attempt on the problem. And I wish people would recognize its failure, learn from it, and move on.

In my view, IIT fails to solve the Pretty-Hard Problem because it unavoidably predicts vast amounts of consciousness in physical systems that no sane person would regard as particularly “conscious” at all: indeed, systems that do nothing but apply a low-density parity-check code, or other simple transformations of their input data. Moreover, IIT predicts not merely that these systems are “slightly” conscious (which would be fine), but that they can be unboundedly more conscious than humans are.

To justify that claim, I first need to define Φ. Strikingly, despite the large literature about Φ, I had a hard time finding a clear mathematical definition of it—one that not only listed formulas but fully defined the structures that the formulas were talking about. Complicating matters further, there are several competing definitions of Φ in the literature, including ΦDM (discrete memoryless), ΦE (empirical), and ΦAR (autoregressive), which apply in different contexts (e.g., some take time evolution into account and others don’t). Nevertheless, I think I can define Φ in a way that will make sense to theoretical computer scientists. And crucially, the broad point I want to make about Φ won’t depend much on the details of its formalization anyway.

We consider a discrete system in a state x=(x1,…,xn)∈Sn, where S is a finite alphabet (the simplest case is S={0,1}). We imagine that the system evolves via an “updating function” f:Sn→Sn. Then the question that interests us is whether the xi‘s can be partitioned into two sets A and B, of roughly comparable size, such that the updates to the variables in A don’t depend very much on the variables in B and vice versa. If such a partition exists, then we say that the computation of f does not involve “global integration of information,” which on Tononi’s theory is a defining aspect of consciousness.
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january 2017 by nhaliday
Ethnic fractionalization and growth | Dietrich Vollrath
Garett Jones did a podcast with The Economics Detective recently on the costs of ethnic diversity. It is particularly worth listening to given that racial identity has re-emerged as a salient element of politics. A quick summary - and the link above includes a nice write-up of relevant sources - would be that diversity within workplaces does not appear to improve outcomes (however those outcomes are measured).

At the same time, there is a parallel literature, touched on in the podcast, about ethnic diversity (or fractionalization, as it is termed in that literature) and economic growth. But one has to be careful drawing a bright line between the two literatures. It does not follow that the results for workplace diversity imply the results regarding economic growth. And this is because the growth results, to the extent that you believe they are robust, all operate through political systems.

So here let me walk through some of the core empirical relationships that have been found regarding ethnic fractionalization and economic growth, and then talk about why you need to take care with over-interpreting them. This is not a thorough literature review, and I realize there are other papers in the same vein. What I’m after is characterizing the essential results.

--

- objection about sensitivity of measure to definition of clusters seems dumb to me (point is to fix definitions than compare different polities. as long as direction and strength of correlation is fairly robust to changes in clustering, this is a stupid critique)
- also, could probably define a less arbitrary notion of fractionalization (w/o fixed clustering or # of clusters) if using points in a metric/vector/euclidean space (eg, genomes)
- eg, A Generalized Index of Ethno-Linguistic Fractionalization: http://www-3.unipv.it/webdept/prin/workpv02.pdf
So like -E_{A, B ~ X} d(A, B). Or maybe -E_{A, B ~ X} f(d(A, B)) for f an increasing function (in particular, f(x) = x^2).

Note that E ||A - B|| = Θ(E ||E[A] - A||), and E ||A - B||^2 = 2Var A,
for A, B ~ X, so this is just quantifying deviation from mean for Euclidean spaces.

In the case that you have a bunch of difference clusters w/ centers equidistant (so n+1 in R^n), measures p_i, and internal variances σ_i^2, you get E ||A - B||^2 = -2∑_i p_i^2σ_i^2 - ∑_{i≠j} p_ip_j(1 + σ_i^2 + σ_j^2) = -2∑_i p_i^2σ_i^2 - ∑_{i≠j} p_ip_j(1 + σ_i^2 + σ_j^2) = -∑_i p_i^2(1 + 2σ_i^2) - ∑_i 2p_i(1-p_i)σ_i^2
(inter-center distance scaled to 1 wlog).
(in general, if you allow _approximate_ equidistance, you can pack in exp(O(n)) clusters via JL lemma)
econotariat  economics  growth-econ  diversity  spearhead  study  summary  list  survey  cracker-econ  hive-mind  stylized-facts  🎩  garett-jones  wonkish  populism  easterly  putnam-like  metric-space  similarity  dimensionality  embeddings  examples  metrics  sociology  polarization  big-peeps  econ-metrics  s:*  corruption  cohesion  government  econ-productivity  religion  broad-econ  social-capital  madisonian  chart  article  wealth-of-nations  the-bones  political-econ  public-goodish  microfoundations  alesina  🌞  multi  pdf  concept  conceptual-vocab  definition  hari-seldon 
december 2016 by nhaliday
Genetic Ancestry and Natural Selection Drive Population Differences in Immune Responses to Pathogens: Cell
Skin Deep: https://westhunt.wordpress.com/2016/10/30/skin-deep/
There are a couple of new papers out in Cell about demonstrated immunological differences between Africans and Europeans. We already knew that the course of various infectious diseases can be quite different in people from those two different races, while autoimmune risks are also different (lupus for example is considerably more common in blacks). Researchers found that inflammatory responses were considerably stronger in Africans than Europeans. African macrophages zapped bacteria three times faster than European macrophages.

I wonder if this increased inflammatory tendency is behind the increased risk for sarcoidosis in blacks (12-fold higher death rate). If so, maybe you could help the clinical course by damping down inflammation.

The African pattern almost certainly worked better in Africa (chock-full o’ of pathogens, including many adapted to man or close relatives), while the European pattern worked better outside of Africa – on the whole cooler and less of a microbial playpen.

Henry and I, along with others, put out a paper on this subject a few years ago.

Some of the milder-inflammation alleles in Europeans originated in Neanderthals. Logical, since they too had adapted to the lower pathogen load in ice-age Europe and Central Asia. This probably meant that Neanderthals couldn’t have returned to Africa.

This is all impossible if race does not exist, or if Lewontin had had anything to valid to say on the subject. Of course race does exist, while Lewontin is a fountain of nonsense.
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october 2016 by nhaliday

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