Depreciation Calculator - Insurance Claims Tools & Databases - Claims Pages

12 weeks ago by nhaliday

depreciation calculator for different product categories/commodities (tbh I would prefer just a table of rates)

tools
calculator
personal-finance
money
increase-decrease
flux-stasis
cost-benefit
economics
time
correlation
manifolds
data
database
objektbuch
quality
12 weeks ago by nhaliday

Linus's Law - Wikipedia

october 2019 by nhaliday

Linus's Law is a claim about software development, named in honor of Linus Torvalds and formulated by Eric S. Raymond in his essay and book The Cathedral and the Bazaar (1999).[1][2] The law states that "given enough eyeballs, all bugs are shallow";

--

In Facts and Fallacies about Software Engineering, Robert Glass refers to the law as a "mantra" of the open source movement, but calls it a fallacy due to the lack of supporting evidence and because research has indicated that the rate at which additional bugs are uncovered does not scale linearly with the number of reviewers; rather, there is a small maximum number of useful reviewers, between two and four, and additional reviewers above this number uncover bugs at a much lower rate.[4] While closed-source practitioners also promote stringent, independent code analysis during a software project's development, they focus on in-depth review by a few and not primarily the number of "eyeballs".[5][6]

Although detection of even deliberately inserted flaws[7][8] can be attributed to Raymond's claim, the persistence of the Heartbleed security bug in a critical piece of code for two years has been considered as a refutation of Raymond's dictum.[9][10][11][12] Larry Seltzer suspects that the availability of source code may cause some developers and researchers to perform less extensive tests than they would with closed source software, making it easier for bugs to remain.[12] In 2015, the Linux Foundation's executive director Jim Zemlin argued that the complexity of modern software has increased to such levels that specific resource allocation is desirable to improve its security. Regarding some of 2014's largest global open source software vulnerabilities, he says, "In these cases, the eyeballs weren't really looking".[11] Large scale experiments or peer-reviewed surveys to test how well the mantra holds in practice have not been performed.

Given enough eyeballs, all bugs are shallow? Revisiting Eric Raymond with bug bounty programs: https://academic.oup.com/cybersecurity/article/3/2/81/4524054

https://hbfs.wordpress.com/2009/03/31/how-many-eyeballs-to-make-a-bug-shallow/

wiki
reference
aphorism
ideas
stylized-facts
programming
engineering
linux
worse-is-better/the-right-thing
correctness
debugging
checking
best-practices
security
error
scale
ubiquity
collaboration
oss
realness
empirical
evidence-based
multi
study
info-econ
economics
intricacy
plots
manifolds
techtariat
cracker-prog
os
systems
magnitude
quantitative-qualitative
number
threat-modeling
--

In Facts and Fallacies about Software Engineering, Robert Glass refers to the law as a "mantra" of the open source movement, but calls it a fallacy due to the lack of supporting evidence and because research has indicated that the rate at which additional bugs are uncovered does not scale linearly with the number of reviewers; rather, there is a small maximum number of useful reviewers, between two and four, and additional reviewers above this number uncover bugs at a much lower rate.[4] While closed-source practitioners also promote stringent, independent code analysis during a software project's development, they focus on in-depth review by a few and not primarily the number of "eyeballs".[5][6]

Although detection of even deliberately inserted flaws[7][8] can be attributed to Raymond's claim, the persistence of the Heartbleed security bug in a critical piece of code for two years has been considered as a refutation of Raymond's dictum.[9][10][11][12] Larry Seltzer suspects that the availability of source code may cause some developers and researchers to perform less extensive tests than they would with closed source software, making it easier for bugs to remain.[12] In 2015, the Linux Foundation's executive director Jim Zemlin argued that the complexity of modern software has increased to such levels that specific resource allocation is desirable to improve its security. Regarding some of 2014's largest global open source software vulnerabilities, he says, "In these cases, the eyeballs weren't really looking".[11] Large scale experiments or peer-reviewed surveys to test how well the mantra holds in practice have not been performed.

Given enough eyeballs, all bugs are shallow? Revisiting Eric Raymond with bug bounty programs: https://academic.oup.com/cybersecurity/article/3/2/81/4524054

https://hbfs.wordpress.com/2009/03/31/how-many-eyeballs-to-make-a-bug-shallow/

october 2019 by nhaliday

"Performance Matters" by Emery Berger - YouTube

october 2019 by nhaliday

Stabilizer is a tool that enables statistically sound performance evaluation, making it possible to understand the impact of optimizations and conclude things like the fact that the -O2 and -O3 optimization levels are indistinguishable from noise (sadly true).

Since compiler optimizations have run out of steam, we need better profiling support, especially for modern concurrent, multi-threaded applications. Coz is a new "causal profiler" that lets programmers optimize for throughput or latency, and which pinpoints and accurately predicts the impact of optimizations.

- randomize extraneous factors like code layout and stack size to avoid spurious speedups

- simulate speedup of component of concurrent system (to assess effect of optimization before attempting) by slowing down the complement (all but that component)

- latency vs. throughput, Little's law

video
presentation
programming
engineering
nitty-gritty
performance
devtools
compilers
latency-throughput
concurrency
legacy
causation
wire-guided
let-me-see
manifolds
pro-rata
tricks
endogenous-exogenous
control
random
signal-noise
comparison
marginal
llvm
systems
hashing
computer-memory
build-packaging
composition-decomposition
coupling-cohesion
local-global
dbs
direct-indirect
symmetry
research
models
metal-to-virtual
linux
measurement
simulation
magnitude
realness
hypothesis-testing
techtariat
Since compiler optimizations have run out of steam, we need better profiling support, especially for modern concurrent, multi-threaded applications. Coz is a new "causal profiler" that lets programmers optimize for throughput or latency, and which pinpoints and accurately predicts the impact of optimizations.

- randomize extraneous factors like code layout and stack size to avoid spurious speedups

- simulate speedup of component of concurrent system (to assess effect of optimization before attempting) by slowing down the complement (all but that component)

- latency vs. throughput, Little's law

october 2019 by nhaliday

Is there a common method for detecting the convergence of the Gibbs sampler and the expectation-maximization algorithm? - Quora

october 2019 by nhaliday

In practice and theory it is much easier to diagnose convergence in EM (vanilla or variational) than in any MCMC algorithm (including Gibbs sampling).

https://www.quora.com/How-can-you-determine-if-your-Gibbs-sampler-has-converged

There is a special case when you can actually obtain the stationary distribution, and be sure that you did! If your markov chain consists of a discrete state space, then take the first time that a state repeats in your chain: if you randomly sample an element between the repeating states (but only including one of the endpoints) you will have a sample from your true distribution.

One can achieve this 'exact MCMC sampling' more generally by using the coupling from the past algorithm (Coupling from the past).

Otherwise, there is no rigorous statistical test for convergence. It may be possible to obtain a theoretical bound for the convergence rates: but these are quite difficult to obtain, and quite often too large to be of practical use. For example, even for the simple case of using the Metropolis algorithm for sampling from a two-dimensional uniform distribution, the best convergence rate upper bound achieved, by Persi Diaconis, was something with an astronomical constant factor like 10^300.

In fact, it is fair to say that for most high dimensional problems, we have really no idea whether Gibbs sampling ever comes close to converging, but the best we can do is use some simple diagnostics to detect the most obvious failures.

nibble
q-n-a
qra
acm
stats
probability
limits
convergence
distribution
sampling
markov
monte-carlo
ML-MAP-E
checking
equilibrium
stylized-facts
gelman
levers
mixing
empirical
plots
manifolds
multi
fixed-point
iteration-recursion
heuristic
expert-experience
theory-practice
project
https://www.quora.com/How-can-you-determine-if-your-Gibbs-sampler-has-converged

There is a special case when you can actually obtain the stationary distribution, and be sure that you did! If your markov chain consists of a discrete state space, then take the first time that a state repeats in your chain: if you randomly sample an element between the repeating states (but only including one of the endpoints) you will have a sample from your true distribution.

One can achieve this 'exact MCMC sampling' more generally by using the coupling from the past algorithm (Coupling from the past).

Otherwise, there is no rigorous statistical test for convergence. It may be possible to obtain a theoretical bound for the convergence rates: but these are quite difficult to obtain, and quite often too large to be of practical use. For example, even for the simple case of using the Metropolis algorithm for sampling from a two-dimensional uniform distribution, the best convergence rate upper bound achieved, by Persi Diaconis, was something with an astronomical constant factor like 10^300.

In fact, it is fair to say that for most high dimensional problems, we have really no idea whether Gibbs sampling ever comes close to converging, but the best we can do is use some simple diagnostics to detect the most obvious failures.

october 2019 by nhaliday

Lindy effect - Wikipedia

june 2019 by nhaliday

The Lindy effect is a theory that the future life expectancy of some non-perishable things like a technology or an idea is proportional to their current age, so that every additional period of survival implies a longer remaining life expectancy.[1] Where the Lindy effect applies, mortality rate decreases with time. In contrast, living creatures and mechanical things follow a bathtub curve where, after "childhood", the mortality rate increases with time. Because life expectancy is probabilistically derived, a thing may become extinct before its "expected" survival. In other words, one needs to gauge both the age and "health" of the thing to determine continued survival.

wiki
reference
concept
metabuch
ideas
street-fighting
planning
comparison
time
distribution
flux-stasis
history
measure
correlation
arrows
branches
pro-rata
manifolds
aging
stylized-facts
age-generation
robust
technology
thinking
cost-benefit
conceptual-vocab
methodology
threat-modeling
efficiency
neurons
tools
track-record
ubiquity
june 2019 by nhaliday

Laryngeal nerve - RationalWiki

august 2018 by nhaliday

Giraffe neck nerve that takes circuitous route around heart ("evolution has no foresight")

wiki
examples
bio
evolution
neuro
counterexample
religion
theos
volo-avolo
degrees-of-freedom
selection
telos-atelos
local-global
unintended-consequences
optimization
manifolds
tip-of-tongue
embodied
eden-heaven
august 2018 by nhaliday

An adaptability limit to climate change due to heat stress

august 2018 by nhaliday

Despite the uncertainty in future climate-change impacts, it is often assumed that humans would be able to adapt to any possible warming. Here we argue that heat stress imposes a robust upper limit to such adaptation. Peak heat stress, quantified by the wet-bulb temperature TW, is surprisingly similar across diverse climates today. TW never exceeds 31 °C. Any exceedence of 35 °C for extended periods should induce hyperthermia in humans and other mammals, as dissipation of metabolic heat becomes impossible. While this never happens now, it would begin to occur with global-mean warming of about 7 °C, calling the habitability of some regions into question. With 11–12 °C warming, such regions would spread to encompass the majority of the human population as currently distributed. Eventual warmings of 12 °C are possible from fossil fuel burning. One implication is that recent estimates of the costs of unmitigated climate change are too low unless the range of possible warming can somehow be narrowed. Heat stress also may help explain trends in the mammalian fossil record.

Trajectories of the Earth System in the Anthropocene: http://www.pnas.org/content/early/2018/07/31/1810141115

We explore the risk that self-reinforcing feedbacks could push the Earth System toward a planetary threshold that, if crossed, could prevent stabilization of the climate at intermediate temperature rises and cause continued warming on a “Hothouse Earth” pathway even as human emissions are reduced. Crossing the threshold would lead to a much higher global average temperature than any interglacial in the past 1.2 million years and to sea levels significantly higher than at any time in the Holocene. We examine the evidence that such a threshold might exist and where it might be.

study
org:nat
environment
climate-change
humanity
existence
risk
futurism
estimate
physics
thermo
prediction
temperature
nature
walls
civilization
flexibility
rigidity
embodied
multi
manifolds
plots
equilibrium
phase-transition
oscillation
comparison
complex-systems
earth
Trajectories of the Earth System in the Anthropocene: http://www.pnas.org/content/early/2018/07/31/1810141115

We explore the risk that self-reinforcing feedbacks could push the Earth System toward a planetary threshold that, if crossed, could prevent stabilization of the climate at intermediate temperature rises and cause continued warming on a “Hothouse Earth” pathway even as human emissions are reduced. Crossing the threshold would lead to a much higher global average temperature than any interglacial in the past 1.2 million years and to sea levels significantly higher than at any time in the Holocene. We examine the evidence that such a threshold might exist and where it might be.

august 2018 by nhaliday

Why would we think artists perform better on drugs ?

ratty lesswrong reflection essay analogy thinking metabuch metameta problem-solving optimization creative rationality order-disorder random mutation selection evolution deep-materialism drugs art track-record correlation causation biases endogenous-exogenous law analytical-holistic tradeoffs cybernetics nature reason humanity left-wing right-wing janus literature big-peeps old-anglo writing advice insight gradient-descent local-global extrema outcome-risk manifolds plots aphorism neurons inhibition direct-indirect ranking top-n telos-atelos values expectancy apollonian-dionysian

april 2018 by nhaliday

ratty lesswrong reflection essay analogy thinking metabuch metameta problem-solving optimization creative rationality order-disorder random mutation selection evolution deep-materialism drugs art track-record correlation causation biases endogenous-exogenous law analytical-holistic tradeoffs cybernetics nature reason humanity left-wing right-wing janus literature big-peeps old-anglo writing advice insight gradient-descent local-global extrema outcome-risk manifolds plots aphorism neurons inhibition direct-indirect ranking top-n telos-atelos values expectancy apollonian-dionysian

april 2018 by nhaliday

Ultimate fate of the universe - Wikipedia

april 2018 by nhaliday

The fate of the universe is determined by its density. The preponderance of evidence to date, based on measurements of the rate of expansion and the mass density, favors a universe that will continue to expand indefinitely, resulting in the "Big Freeze" scenario below.[8] However, observations are not conclusive, and alternative models are still possible.[9]

Big Freeze or heat death

Main articles: Future of an expanding universe and Heat death of the universe

The Big Freeze is a scenario under which continued expansion results in a universe that asymptotically approaches absolute zero temperature.[10] This scenario, in combination with the Big Rip scenario, is currently gaining ground as the most important hypothesis.[11] It could, in the absence of dark energy, occur only under a flat or hyperbolic geometry. With a positive cosmological constant, it could also occur in a closed universe. In this scenario, stars are expected to form normally for 1012 to 1014 (1–100 trillion) years, but eventually the supply of gas needed for star formation will be exhausted. As existing stars run out of fuel and cease to shine, the universe will slowly and inexorably grow darker. Eventually black holes will dominate the universe, which themselves will disappear over time as they emit Hawking radiation.[12] Over infinite time, there would be a spontaneous entropy decrease by the Poincaré recurrence theorem, thermal fluctuations,[13][14] and the fluctuation theorem.[15][16]

A related scenario is heat death, which states that the universe goes to a state of maximum entropy in which everything is evenly distributed and there are no gradients—which are needed to sustain information processing, one form of which is life. The heat death scenario is compatible with any of the three spatial models, but requires that the universe reach an eventual temperature minimum.[17]

physics
big-picture
world
space
long-short-run
futurism
singularity
wiki
reference
article
nibble
thermo
temperature
entropy-like
order-disorder
death
nihil
bio
complex-systems
cybernetics
increase-decrease
trends
computation
local-global
prediction
time
spatial
spreading
density
distribution
manifolds
geometry
janus
Big Freeze or heat death

Main articles: Future of an expanding universe and Heat death of the universe

The Big Freeze is a scenario under which continued expansion results in a universe that asymptotically approaches absolute zero temperature.[10] This scenario, in combination with the Big Rip scenario, is currently gaining ground as the most important hypothesis.[11] It could, in the absence of dark energy, occur only under a flat or hyperbolic geometry. With a positive cosmological constant, it could also occur in a closed universe. In this scenario, stars are expected to form normally for 1012 to 1014 (1–100 trillion) years, but eventually the supply of gas needed for star formation will be exhausted. As existing stars run out of fuel and cease to shine, the universe will slowly and inexorably grow darker. Eventually black holes will dominate the universe, which themselves will disappear over time as they emit Hawking radiation.[12] Over infinite time, there would be a spontaneous entropy decrease by the Poincaré recurrence theorem, thermal fluctuations,[13][14] and the fluctuation theorem.[15][16]

A related scenario is heat death, which states that the universe goes to a state of maximum entropy in which everything is evenly distributed and there are no gradients—which are needed to sustain information processing, one form of which is life. The heat death scenario is compatible with any of the three spatial models, but requires that the universe reach an eventual temperature minimum.[17]

april 2018 by nhaliday

The Future of Human Evolution

org:junk ratty bostrom study article letters futurism evolution philosophy formal-values values flux-stasis singularity number humanity malthus competition darwinian optimism pessimism definite-planning psychology cog-psych social-psych signaling cost-benefit art meaningness dennett within-without theory-of-mind farmers-and-foragers hanson equilibrium population ems civilization coordination cooperate-defect signal-noise coding-theory mutation property-rights intel leviathan authoritarianism antidemos moloch government social-choice frontier cybernetics evopsych EEA gender sex eden direction volo-avolo degrees-of-freedom anthropic ethics risk existence long-short-run manifolds direct-indirect complement-substitute neuro neuro-nitgrit composition-decomposition structure individualism-collectivism speed comparison selection fashun hidden-motives communication incentives taxes public-goodish markets civil-liberty coalitions politics EGT privacy trends eden-heaven fertility gedanken ideas ec

april 2018 by nhaliday

org:junk ratty bostrom study article letters futurism evolution philosophy formal-values values flux-stasis singularity number humanity malthus competition darwinian optimism pessimism definite-planning psychology cog-psych social-psych signaling cost-benefit art meaningness dennett within-without theory-of-mind farmers-and-foragers hanson equilibrium population ems civilization coordination cooperate-defect signal-noise coding-theory mutation property-rights intel leviathan authoritarianism antidemos moloch government social-choice frontier cybernetics evopsych EEA gender sex eden direction volo-avolo degrees-of-freedom anthropic ethics risk existence long-short-run manifolds direct-indirect complement-substitute neuro neuro-nitgrit composition-decomposition structure individualism-collectivism speed comparison selection fashun hidden-motives communication incentives taxes public-goodish markets civil-liberty coalitions politics EGT privacy trends eden-heaven fertility gedanken ideas ec

april 2018 by nhaliday

Prisoner's dilemma - Wikipedia

march 2018 by nhaliday

caveat to result below:

An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).[14]

Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is bigger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.[8]

https://alfanl.com/2018/04/12/defection/

Nature boils down to a few simple concepts.

Haters will point out that I oversimplify. The haters are wrong. I am good at saying a lot with few words. Nature indeed boils down to a few simple concepts.

In life, you can either cooperate or defect.

Used to be that defection was the dominant strategy, say in the time when the Roman empire started to crumble. Everybody complained about everybody and in the end nothing got done. Then came Jesus, who told people to be loving and cooperative, and boom: 1800 years later we get the industrial revolution.

Because of Jesus we now find ourselves in a situation where cooperation is the dominant strategy. A normie engages in a ton of cooperation: with the tax collector who wants more and more of his money, with schools who want more and more of his kid’s time, with media who wants him to repeat more and more party lines, with the Zeitgeist of the Collective Spirit of the People’s Progress Towards a New Utopia. Essentially, our normie is cooperating himself into a crumbling Western empire.

Turns out that if everyone blindly cooperates, parasites sprout up like weeds until defection once again becomes the standard.

The point of a post-Christian religion is to once again create conditions for the kind of cooperation that led to the industrial revolution. This necessitates throwing out undead Christianity: you do not blindly cooperate. You cooperate with people that cooperate with you, you defect on people that defect on you. Christianity mixed with Darwinism. God and Gnon meet.

This also means we re-establish spiritual hierarchy, which, like regular hierarchy, is a prerequisite for cooperation. It is this hierarchical cooperation that turns a household into a force to be reckoned with, that allows a group of men to unite as a front against their enemies, that allows a tribe to conquer the world. Remember: Scientology bullied the Cathedral’s tax department into submission.

With a functioning hierarchy, men still gossip, lie and scheme, but they will do so in whispers behind closed doors. In your face they cooperate and contribute to the group’s wellbeing because incentives are thus that contributing to group wellbeing heightens status.

Without a functioning hierarchy, men gossip, lie and scheme, but they do so in your face, and they tell you that you are positively deluded for accusing them of gossiping, lying and scheming. Seeds will not sprout in such ground.

Spiritual dominance is established in the same way any sort of dominance is established: fought for, taken. But the fight is ritualistic. You can’t force spiritual dominance if no one listens, or if you are silenced the ritual is not allowed to happen.

If one of our priests is forbidden from establishing spiritual dominance, that is a sure sign an enemy priest is in better control and has vested interest in preventing you from establishing spiritual dominance..

They defect on you, you defect on them. Let them suffer the consequences of enemy priesthood, among others characterized by the annoying tendency that very little is said with very many words.

https://contingentnotarbitrary.com/2018/04/14/rederiving-christianity/

To recap, we started with a secular definition of Logos and noted that its telos is existence. Given human nature, game theory and the power of cooperation, the highest expression of that telos is freely chosen universal love, tempered by constant vigilance against defection while maintaining compassion for the defectors and forgiving those who repent. In addition, we must know the telos in order to fulfill it.

In Christian terms, looks like we got over half of the Ten Commandments (know Logos for the First, don’t defect or tempt yourself to defect for the rest), the importance of free will, the indestructibility of evil (group cooperation vs individual defection), loving the sinner and hating the sin (with defection as the sin), forgiveness (with conditions), and love and compassion toward all, assuming only secular knowledge and that it’s good to exist.

Iterated Prisoner's Dilemma is an Ultimatum Game: http://infoproc.blogspot.com/2012/07/iterated-prisoners-dilemma-is-ultimatum.html

The history of IPD shows that bounded cognition prevented the dominant strategies from being discovered for over over 60 years, despite significant attention from game theorists, computer scientists, economists, evolutionary biologists, etc. Press and Dyson have shown that IPD is effectively an ultimatum game, which is very different from the Tit for Tat stories told by generations of people who worked on IPD (Axelrod, Dawkins, etc., etc.).

...

For evolutionary biologists: Dyson clearly thinks this result has implications for multilevel (group vs individual selection):

... Cooperation loses and defection wins. The ZD strategies confirm this conclusion and make it sharper. ... The system evolved to give cooperative tribes an advantage over non-cooperative tribes, using punishment to give cooperation an evolutionary advantage within the tribe. This double selection of tribes and individuals goes way beyond the Prisoners' Dilemma model.

implications for fractionalized Europe vis-a-vis unified China?

and more broadly does this just imply we're doomed in the long run RE: cooperation, morality, the "good society", so on...? war and group-selection is the only way to get a non-crab bucket civilization?

Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent:

http://www.pnas.org/content/109/26/10409.full

http://www.pnas.org/content/109/26/10409.full.pdf

https://www.edge.org/conversation/william_h_press-freeman_dyson-on-iterated-prisoners-dilemma-contains-strategies-that

https://en.wikipedia.org/wiki/Ultimatum_game

analogy for ultimatum game: the state gives the demos a bargain take-it-or-leave-it, and...if the demos refuses...violence?

The nature of human altruism: http://sci-hub.tw/https://www.nature.com/articles/nature02043

- Ernst Fehr & Urs Fischbacher

Some of the most fundamental questions concerning our evolutionary origins, our social relations, and the organization of society are centred around issues of altruism and selfishness. Experimental evidence indicates that human altruism is a powerful force and is unique in the animal world. However, there is much individual heterogeneity and the interaction between altruists and selfish individuals is vital to human cooperation. Depending on the environment, a minority of altruists can force a majority of selfish individuals to cooperate or, conversely, a few egoists can induce a large number of altruists to defect. Current gene-based evolutionary theories cannot explain important patterns of human altruism, pointing towards the importance of both theories of cultural evolution as well as gene–culture co-evolution.

...

Why are humans so unusual among animals in this respect? We propose that quantitatively, and probably even qualitatively, unique patterns of human altruism provide the answer to this question. Human altruism goes far beyond that which has been observed in the animal world. Among animals, fitness-reducing acts that confer fitness benefits on other individuals are largely restricted to kin groups; despite several decades of research, evidence for reciprocal altruism in pair-wise repeated encounters4,5 remains scarce6–8. Likewise, there is little evidence so far that individual reputation building affects cooperation in animals, which contrasts strongly with what we find in humans. If we randomly pick two human strangers from a modern society and give them the chance to engage in repeated anonymous exchanges in a laboratory experiment, there is a high probability that reciprocally altruistic behaviour will emerge spontaneously9,10.

However, human altruism extends far beyond reciprocal altruism and reputation-based cooperation, taking the form of strong reciprocity11,12. Strong reciprocity is a combination of altruistic rewarding, which is a predisposition to reward others for cooperative, norm-abiding behaviours, and altruistic punishment, which is a propensity to impose sanctions on others for norm violations. Strong reciprocators bear the cost of rewarding or punishing even if they gain no individual economic benefit whatsoever from their acts. In contrast, reciprocal altruists, as they have been defined in the biological literature4,5, reward and punish only if this is in their long-term self-interest. Strong reciprocity thus constitutes a powerful incentive for cooperation even in non-repeated interactions and when reputation gains are absent, because strong reciprocators will reward those who cooperate and punish those who defect.

...

We will show that the interaction between selfish and strongly reciprocal … [more]

concept
conceptual-vocab
wiki
reference
article
models
GT-101
game-theory
anthropology
cultural-dynamics
trust
cooperate-defect
coordination
iteration-recursion
sequential
axelrod
discrete
smoothness
evolution
evopsych
EGT
economics
behavioral-econ
sociology
new-religion
deep-materialism
volo-avolo
characterization
hsu
scitariat
altruism
justice
group-selection
decision-making
tribalism
organizing
hari-seldon
theory-practice
applicability-prereqs
bio
finiteness
multi
history
science
social-science
decision-theory
commentary
study
summary
giants
the-trenches
zero-positive-sum
🔬
bounded-cognition
info-dynamics
org:edge
explanation
exposition
org:nat
eden
retention
long-short-run
darwinian
markov
equilibrium
linear-algebra
nitty-gritty
competition
war
explanans
n-factor
europe
the-great-west-whale
occident
china
asia
sinosphere
orient
decentralized
markets
market-failure
cohesion
metabuch
stylized-facts
interdisciplinary
physics
pdf
pessimism
time
insight
the-basilisk
noblesse-oblige
the-watchers
ideas
l
An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).[14]

Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is bigger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.[8]

https://alfanl.com/2018/04/12/defection/

Nature boils down to a few simple concepts.

Haters will point out that I oversimplify. The haters are wrong. I am good at saying a lot with few words. Nature indeed boils down to a few simple concepts.

In life, you can either cooperate or defect.

Used to be that defection was the dominant strategy, say in the time when the Roman empire started to crumble. Everybody complained about everybody and in the end nothing got done. Then came Jesus, who told people to be loving and cooperative, and boom: 1800 years later we get the industrial revolution.

Because of Jesus we now find ourselves in a situation where cooperation is the dominant strategy. A normie engages in a ton of cooperation: with the tax collector who wants more and more of his money, with schools who want more and more of his kid’s time, with media who wants him to repeat more and more party lines, with the Zeitgeist of the Collective Spirit of the People’s Progress Towards a New Utopia. Essentially, our normie is cooperating himself into a crumbling Western empire.

Turns out that if everyone blindly cooperates, parasites sprout up like weeds until defection once again becomes the standard.

The point of a post-Christian religion is to once again create conditions for the kind of cooperation that led to the industrial revolution. This necessitates throwing out undead Christianity: you do not blindly cooperate. You cooperate with people that cooperate with you, you defect on people that defect on you. Christianity mixed with Darwinism. God and Gnon meet.

This also means we re-establish spiritual hierarchy, which, like regular hierarchy, is a prerequisite for cooperation. It is this hierarchical cooperation that turns a household into a force to be reckoned with, that allows a group of men to unite as a front against their enemies, that allows a tribe to conquer the world. Remember: Scientology bullied the Cathedral’s tax department into submission.

With a functioning hierarchy, men still gossip, lie and scheme, but they will do so in whispers behind closed doors. In your face they cooperate and contribute to the group’s wellbeing because incentives are thus that contributing to group wellbeing heightens status.

Without a functioning hierarchy, men gossip, lie and scheme, but they do so in your face, and they tell you that you are positively deluded for accusing them of gossiping, lying and scheming. Seeds will not sprout in such ground.

Spiritual dominance is established in the same way any sort of dominance is established: fought for, taken. But the fight is ritualistic. You can’t force spiritual dominance if no one listens, or if you are silenced the ritual is not allowed to happen.

If one of our priests is forbidden from establishing spiritual dominance, that is a sure sign an enemy priest is in better control and has vested interest in preventing you from establishing spiritual dominance..

They defect on you, you defect on them. Let them suffer the consequences of enemy priesthood, among others characterized by the annoying tendency that very little is said with very many words.

https://contingentnotarbitrary.com/2018/04/14/rederiving-christianity/

To recap, we started with a secular definition of Logos and noted that its telos is existence. Given human nature, game theory and the power of cooperation, the highest expression of that telos is freely chosen universal love, tempered by constant vigilance against defection while maintaining compassion for the defectors and forgiving those who repent. In addition, we must know the telos in order to fulfill it.

In Christian terms, looks like we got over half of the Ten Commandments (know Logos for the First, don’t defect or tempt yourself to defect for the rest), the importance of free will, the indestructibility of evil (group cooperation vs individual defection), loving the sinner and hating the sin (with defection as the sin), forgiveness (with conditions), and love and compassion toward all, assuming only secular knowledge and that it’s good to exist.

Iterated Prisoner's Dilemma is an Ultimatum Game: http://infoproc.blogspot.com/2012/07/iterated-prisoners-dilemma-is-ultimatum.html

The history of IPD shows that bounded cognition prevented the dominant strategies from being discovered for over over 60 years, despite significant attention from game theorists, computer scientists, economists, evolutionary biologists, etc. Press and Dyson have shown that IPD is effectively an ultimatum game, which is very different from the Tit for Tat stories told by generations of people who worked on IPD (Axelrod, Dawkins, etc., etc.).

...

For evolutionary biologists: Dyson clearly thinks this result has implications for multilevel (group vs individual selection):

... Cooperation loses and defection wins. The ZD strategies confirm this conclusion and make it sharper. ... The system evolved to give cooperative tribes an advantage over non-cooperative tribes, using punishment to give cooperation an evolutionary advantage within the tribe. This double selection of tribes and individuals goes way beyond the Prisoners' Dilemma model.

implications for fractionalized Europe vis-a-vis unified China?

and more broadly does this just imply we're doomed in the long run RE: cooperation, morality, the "good society", so on...? war and group-selection is the only way to get a non-crab bucket civilization?

Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent:

http://www.pnas.org/content/109/26/10409.full

http://www.pnas.org/content/109/26/10409.full.pdf

https://www.edge.org/conversation/william_h_press-freeman_dyson-on-iterated-prisoners-dilemma-contains-strategies-that

https://en.wikipedia.org/wiki/Ultimatum_game

analogy for ultimatum game: the state gives the demos a bargain take-it-or-leave-it, and...if the demos refuses...violence?

The nature of human altruism: http://sci-hub.tw/https://www.nature.com/articles/nature02043

- Ernst Fehr & Urs Fischbacher

Some of the most fundamental questions concerning our evolutionary origins, our social relations, and the organization of society are centred around issues of altruism and selfishness. Experimental evidence indicates that human altruism is a powerful force and is unique in the animal world. However, there is much individual heterogeneity and the interaction between altruists and selfish individuals is vital to human cooperation. Depending on the environment, a minority of altruists can force a majority of selfish individuals to cooperate or, conversely, a few egoists can induce a large number of altruists to defect. Current gene-based evolutionary theories cannot explain important patterns of human altruism, pointing towards the importance of both theories of cultural evolution as well as gene–culture co-evolution.

...

Why are humans so unusual among animals in this respect? We propose that quantitatively, and probably even qualitatively, unique patterns of human altruism provide the answer to this question. Human altruism goes far beyond that which has been observed in the animal world. Among animals, fitness-reducing acts that confer fitness benefits on other individuals are largely restricted to kin groups; despite several decades of research, evidence for reciprocal altruism in pair-wise repeated encounters4,5 remains scarce6–8. Likewise, there is little evidence so far that individual reputation building affects cooperation in animals, which contrasts strongly with what we find in humans. If we randomly pick two human strangers from a modern society and give them the chance to engage in repeated anonymous exchanges in a laboratory experiment, there is a high probability that reciprocally altruistic behaviour will emerge spontaneously9,10.

However, human altruism extends far beyond reciprocal altruism and reputation-based cooperation, taking the form of strong reciprocity11,12. Strong reciprocity is a combination of altruistic rewarding, which is a predisposition to reward others for cooperative, norm-abiding behaviours, and altruistic punishment, which is a propensity to impose sanctions on others for norm violations. Strong reciprocators bear the cost of rewarding or punishing even if they gain no individual economic benefit whatsoever from their acts. In contrast, reciprocal altruists, as they have been defined in the biological literature4,5, reward and punish only if this is in their long-term self-interest. Strong reciprocity thus constitutes a powerful incentive for cooperation even in non-repeated interactions and when reputation gains are absent, because strong reciprocators will reward those who cooperate and punish those who defect.

...

We will show that the interaction between selfish and strongly reciprocal … [more]

march 2018 by nhaliday

orbit - Best approximation for Sun's trajectory around galactic center? - Astronomy Stack Exchange

december 2017 by nhaliday

The Sun orbits in the Galactic potential. The motion is complex; it takes about 230 million years to make a circuit with an orbital speed of around 220 km/s, but at the same time it oscillates up and down with respect to the Galactic plane every ∼70∼70 million years and also wobbles in and out every ∼150∼150 million years (this is called epicyclic motion). The spatial amplitudes of these oscillations are around 100 pc vertically and 300 pc in the radial direction inwards and outwards around an average orbital radius (I am unable to locate a precise figure for the latter).

nibble
q-n-a
overflow
space
oscillation
time
cycles
spatial
trivia
manifolds
december 2017 by nhaliday

[1509.02504] Electric charge in hyperbolic motion: The early history and other geometrical aspects

november 2017 by nhaliday

We revisit the early work of Minkowski and Sommerfeld concerning hyperbolic motion, and we describe some geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material points are replaced by infinitesimal length elements.

SPACE AND TIME: An annotated, illustrated edition of Hermann Minkowski's revolutionary essay: http://web.mit.edu/redingtn/www/netadv/SP20130311.html

nibble
preprint
papers
org:mat
physics
electromag
relativity
exposition
history
mostly-modern
pre-ww2
science
the-trenches
discovery
intricacy
classic
explanation
einstein
giants
plots
manifolds
article
multi
liner-notes
org:junk
org:edu
absolute-relative
SPACE AND TIME: An annotated, illustrated edition of Hermann Minkowski's revolutionary essay: http://web.mit.edu/redingtn/www/netadv/SP20130311.html

november 2017 by nhaliday

Hyperbolic angle - Wikipedia

november 2017 by nhaliday

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.

nibble
math
trivia
wiki
reference
physics
relativity
concept
atoms
geometry
ground-up
characterization
measure
definition
plots
calculation
nitty-gritty
direction
metrics
manifolds
november 2017 by nhaliday

gn.general topology - Pair of curves joining opposite corners of a square must intersect---proof? - MathOverflow

october 2017 by nhaliday

In his 'Ordinary Differential Equations' (sec. 1.2) V.I. Arnold says "... every pair of curves in the square joining different pairs of opposite corners must intersect".

This is obvious geometrically but I was wondering how one could go about proving this rigorously. I have thought of a proof using Brouwer's Fixed Point Theorem which I describe below. I would greatly appreciate the group's comments on whether this proof is right and if a simpler proof is possible.

...

Since the full Jordan curve theorem is quite subtle, it might be worth pointing out that theorem in question reduces to the Jordan curve theorem for polygons, which is easier.

Suppose on the contrary that the curves A,BA,B joining opposite corners do not meet. Since A,BA,B are closed sets, their minimum distance apart is some ε>0ε>0. By compactness, each of A,BA,B can be partitioned into finitely many arcs, each of which lies in a disk of diameter <ε/3<ε/3. Then, by a homotopy inside each disk we can replace A,BA,B by polygonal paths A′,B′A′,B′ that join the opposite corners of the square and are still disjoint.

Also, we can replace A′,B′A′,B′ by simple polygonal paths A″,B″A″,B″ by omitting loops. Now we can close A″A″ to a polygon, and B″B″ goes from its "inside" to "outside" without meeting it, contrary to the Jordan curve theorem for polygons.

- John Stillwell

nibble
q-n-a
overflow
math
geometry
topology
tidbits
intricacy
intersection
proofs
gotchas
oly
mathtariat
fixed-point
math.AT
manifolds
intersection-connectedness
This is obvious geometrically but I was wondering how one could go about proving this rigorously. I have thought of a proof using Brouwer's Fixed Point Theorem which I describe below. I would greatly appreciate the group's comments on whether this proof is right and if a simpler proof is possible.

...

Since the full Jordan curve theorem is quite subtle, it might be worth pointing out that theorem in question reduces to the Jordan curve theorem for polygons, which is easier.

Suppose on the contrary that the curves A,BA,B joining opposite corners do not meet. Since A,BA,B are closed sets, their minimum distance apart is some ε>0ε>0. By compactness, each of A,BA,B can be partitioned into finitely many arcs, each of which lies in a disk of diameter <ε/3<ε/3. Then, by a homotopy inside each disk we can replace A,BA,B by polygonal paths A′,B′A′,B′ that join the opposite corners of the square and are still disjoint.

Also, we can replace A′,B′A′,B′ by simple polygonal paths A″,B″A″,B″ by omitting loops. Now we can close A″A″ to a polygon, and B″B″ goes from its "inside" to "outside" without meeting it, contrary to the Jordan curve theorem for polygons.

- John Stillwell

october 2017 by nhaliday

Is the U.S. Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution∗

july 2017 by nhaliday

world-wide: http://www.socsci.uci.edu/~duffy/papers/jeg2.pdf

https://www.weforum.org/agenda/2016/01/is-the-us-labour-share-as-constant-as-we-thought

https://www.economicdynamics.org/meetpapers/2015/paper_844.pdf

We find that IPP capital entirely explains the observed decline of the US labor share, which otherwise is secularly constant over the past 65 years for structures and equipment capital. The labor share decline simply reflects the fact that the US economy is undergoing a transition toward a larger IPP sector.

https://ideas.repec.org/p/red/sed015/844.html

http://www.robertdkirkby.com/blog/2015/summary-of-piketty-i/

https://www.brookings.edu/bpea-articles/deciphering-the-fall-and-rise-in-the-net-capital-share/

The Fall of the Labor Share and the Rise of Superstar Firms: http://www.nber.org/papers/w23396

The Decline of the U.S. Labor Share: https://www.brookings.edu/wp-content/uploads/2016/07/2013b_elsby_labor_share.pdf

Table 2 has industry disaggregation

Estimating the U.S. labor share: https://www.bls.gov/opub/mlr/2017/article/estimating-the-us-labor-share.htm

Why Workers Are Losing to Capitalists: https://www.bloomberg.com/view/articles/2017-09-20/why-workers-are-losing-to-capitalists

Automation and offshoring may be conspiring to reduce labor's share of income.

pdf
study
economics
growth-econ
econometrics
usa
data
empirical
analysis
labor
capital
econ-productivity
manifolds
magnitude
multi
world
🎩
piketty
econotariat
compensation
inequality
winner-take-all
org:ngo
org:davos
flexibility
distribution
stylized-facts
regularizer
hmm
history
mostly-modern
property-rights
arrows
invariance
industrial-org
trends
wonkish
roots
synthesis
market-power
efficiency
variance-components
business
database
org:gov
article
model-class
models
automation
nationalism-globalism
trade
news
org:mag
org:biz
org:bv
noahpinion
explanation
summary
methodology
density
polarization
map-territory
input-output
https://www.weforum.org/agenda/2016/01/is-the-us-labour-share-as-constant-as-we-thought

https://www.economicdynamics.org/meetpapers/2015/paper_844.pdf

We find that IPP capital entirely explains the observed decline of the US labor share, which otherwise is secularly constant over the past 65 years for structures and equipment capital. The labor share decline simply reflects the fact that the US economy is undergoing a transition toward a larger IPP sector.

https://ideas.repec.org/p/red/sed015/844.html

http://www.robertdkirkby.com/blog/2015/summary-of-piketty-i/

https://www.brookings.edu/bpea-articles/deciphering-the-fall-and-rise-in-the-net-capital-share/

The Fall of the Labor Share and the Rise of Superstar Firms: http://www.nber.org/papers/w23396

The Decline of the U.S. Labor Share: https://www.brookings.edu/wp-content/uploads/2016/07/2013b_elsby_labor_share.pdf

Table 2 has industry disaggregation

Estimating the U.S. labor share: https://www.bls.gov/opub/mlr/2017/article/estimating-the-us-labor-share.htm

Why Workers Are Losing to Capitalists: https://www.bloomberg.com/view/articles/2017-09-20/why-workers-are-losing-to-capitalists

Automation and offshoring may be conspiring to reduce labor's share of income.

july 2017 by nhaliday

No, research does not say that you produce more when working 40 hours per week | Meta Rabbit

scitariat rhetoric contrarianism regularizer labor career time-use time curvature plots manifolds human-bean embodied-pack embodied-cognition ego-depletion productivity convexity-curvature nonlinearity

july 2017 by nhaliday

scitariat rhetoric contrarianism regularizer labor career time-use time curvature plots manifolds human-bean embodied-pack embodied-cognition ego-depletion productivity convexity-curvature nonlinearity

july 2017 by nhaliday

On the Cobb–Douglas Production Function

june 2017 by nhaliday

- Kim Border

pdf
nibble
org:edu
exposition
explanation
economics
growth-econ
econ-productivity
synthesis
motivation
identity
characterization
arrows
labor
capital
atoms
article
🎩
distribution
compensation
magnitude
manifolds
stylized-facts
invariance
efficiency
input-output
june 2017 by nhaliday

PRE-INDUSTRIAL INEQUALITY*

june 2017 by nhaliday

Fig. 1: maximum possible Gini index still allowing subsistence of population (all surplus redistributed to 1 head honcho)

Fig. 2: scatter plot of Gini vs income, as well as possibility frontier

Ye Olde Inæqualitee Shoppe: https://pseudoerasmus.com/2014/10/01/inequality-possibility-frontier/

Gini indices, mean income, maximum feasible Gini, and "inequality extraction ratios" (gini2/max poss. inequality): https://pseudoerasmus.files.wordpress.com/2014/09/blwpg263.pdf

Growth and inequality in the great and little divergence debate: a Japanese perspective: http://onlinelibrary.wiley.com/doi/10.1111/ehr.12071/epdf

pdf
study
pseudoE
economics
growth-econ
broad-econ
inequality
industrial-revolution
agriculture
compensation
wealth-of-nations
wealth
britain
history
medieval
early-modern
europe
the-great-west-whale
🎩
cultural-dynamics
econ-metrics
data
multi
article
modernity
rent-seeking
vampire-squid
elite
india
asia
japan
civilization
time-series
plots
volo-avolo
malthus
manifolds
database
iron-age
mediterranean
the-classics
conquest-empire
germanic
gallic
latin-america
world
china
leviathan
usa
measurement
crosstab
pro-rata
MENA
africa
developing-world
distribution
archaeology
taxes
redistribution
egalitarianism-hierarchy
feudal
Fig. 2: scatter plot of Gini vs income, as well as possibility frontier

Ye Olde Inæqualitee Shoppe: https://pseudoerasmus.com/2014/10/01/inequality-possibility-frontier/

Gini indices, mean income, maximum feasible Gini, and "inequality extraction ratios" (gini2/max poss. inequality): https://pseudoerasmus.files.wordpress.com/2014/09/blwpg263.pdf

Growth and inequality in the great and little divergence debate: a Japanese perspective: http://onlinelibrary.wiley.com/doi/10.1111/ehr.12071/epdf

june 2017 by nhaliday

'Capital in the Twenty-First Century' by Thomas Piketty, reviewed | New Republic

april 2017 by nhaliday

by Robert Solow (positive)

The data then exhibit a clear pattern. In France and Great Britain, national capital stood fairly steadily at about seven times national income from 1700 to 1910, then fell sharply from 1910 to 1950, presumably as a result of wars and depression, reaching a low of 2.5 in Britain and a bit less than 3 in France. The capital-income ratio then began to climb in both countries, and reached slightly more than 5 in Britain and slightly less than 6 in France by 2010. The trajectory in the United States was slightly different: it started at just above 3 in 1770, climbed to 5 in 1910, fell slightly in 1920, recovered to a high between 5 and 5.5 in 1930, fell to below 4 in 1950, and was back to 4.5 in 2010.

The wealth-income ratio in the United States has always been lower than in Europe. The main reason in the early years was that land values bulked less in the wide open spaces of North America. There was of course much more land, but it was very cheap. Into the twentieth century and onward, however, the lower capital-income ratio in the United States probably reflects the higher level of productivity: a given amount of capital could support a larger production of output than in Europe. It is no surprise that the two world wars caused much less destruction and dissipation of capital in the United States than in Britain and France. The important observation for Piketty’s argument is that, in all three countries, and elsewhere as well, the wealth-income ratio has been increasing since 1950, and is almost back to nineteenth-century levels. He projects this increase to continue into the current century, with weighty consequences that will be discussed as we go on.

...

Now if you multiply the rate of return on capital by the capital-income ratio, you get the share of capital in the national income. For example, if the rate of return is 5 percent a year and the stock of capital is six years worth of national income, income from capital will be 30 percent of national income, and so income from work will be the remaining 70 percent. At last, after all this preparation, we are beginning to talk about inequality, and in two distinct senses. First, we have arrived at the functional distribution of income—the split between income from work and income from wealth. Second, it is always the case that wealth is more highly concentrated among the rich than income from labor (although recent American history looks rather odd in this respect); and this being so, the larger the share of income from wealth, the more unequal the distribution of income among persons is likely to be. It is this inequality across persons that matters most for good or ill in a society.

...

The data are complicated and not easily comparable across time and space, but here is the flavor of Piketty’s summary picture. Capital is indeed very unequally distributed. Currently in the United States, the top 10 percent own about 70 percent of all the capital, half of that belonging to the top 1 percent; the next 40 percent—who compose the “middle class”—own about a quarter of the total (much of that in the form of housing), and the remaining half of the population owns next to nothing, about 5 percent of total wealth. Even that amount of middle-class property ownership is a new phenomenon in history. The typical European country is a little more egalitarian: the top 1 percent own 25 percent of the total capital, and the middle class 35 percent. (A century ago the European middle class owned essentially no wealth at all.) If the ownership of wealth in fact becomes even more concentrated during the rest of the twenty-first century, the outlook is pretty bleak unless you have a taste for oligarchy.

Income from wealth is probably even more concentrated than wealth itself because, as Piketty notes, large blocks of wealth tend to earn a higher return than small ones. Some of this advantage comes from economies of scale, but more may come from the fact that very big investors have access to a wider range of investment opportunities than smaller investors. Income from work is naturally less concentrated than income from wealth. In Piketty’s stylized picture of the United States today, the top 1 percent earns about 12 percent of all labor income, the next 9 percent earn 23 percent, the middle class gets about 40 percent, and the bottom half about a quarter of income from work. Europe is not very different: the top 10 percent collect somewhat less and the other two groups a little more.

You get the picture: modern capitalism is an unequal society, and the rich-get-richer dynamic strongly suggest that it will get more so. But there is one more loose end to tie up, already hinted at, and it has to do with the advent of very high wage incomes. First, here are some facts about the composition of top incomes. About 60 percent of the income of the top 1 percent in the United States today is labor income. Only when you get to the top tenth of 1 percent does income from capital start to predominate. The income of the top hundredth of 1 percent is 70 percent from capital. The story for France is not very different, though the proportion of labor income is a bit higher at every level. Evidently there are some very high wage incomes, as if you didn’t know.

This is a fairly recent development. In the 1960s, the top 1 percent of wage earners collected a little more than 5 percent of all wage incomes. This fraction has risen pretty steadily until nowadays, when the top 1 percent of wage earners receive 10–12 percent of all wages. This time the story is rather different in France. There the share of total wages going to the top percentile was steady at 6 percent until very recently, when it climbed to 7 percent. The recent surge of extreme inequality at the top of the wage distribution may be primarily an American development. Piketty, who with Emmanuel Saez has made a careful study of high-income tax returns in the United States, attributes this to the rise of what he calls “supermanagers.” The very highest income class consists to a substantial extent of top executives of large corporations, with very rich compensation packages. (A disproportionate number of these, but by no means all of them, come from the financial services industry.) With or without stock options, these large pay packages get converted to wealth and future income from wealth. But the fact remains that much of the increased income (and wealth) inequality in the United States is driven by the rise of these supermanagers.

and Deirdre McCloskey (p critical): https://ejpe.org/journal/article/view/170

nice discussion of empirical economics, economic history, market failures and statism, etc., with several bon mots

Piketty’s great splash will undoubtedly bring many young economically interested scholars to devote their lives to the study of the past. That is good, because economic history is one of the few scientifically quantitative branches of economics. In economic history, as in experimental economics and a few other fields, the economists confront the evidence (as they do not for example in most macroeconomics or industrial organization or international trade theory nowadays).

...

Piketty gives a fine example of how to do it. He does not get entangled as so many economists do in the sole empirical tool they are taught, namely, regression analysis on someone else’s “data” (one of the problems is the word data, meaning “things given”: scientists should deal in capta, “things seized”). Therefore he does not commit one of the two sins of modern economics, the use of meaningless “tests” of statistical significance (he occasionally refers to “statistically insignificant” relations between, say, tax rates and growth rates, but I am hoping he does not suppose that a large coefficient is “insignificant” because R. A. Fisher in 1925 said it was). Piketty constructs or uses statistics of aggregate capital and of inequality and then plots them out for inspection, which is what physicists, for example, also do in dealing with their experiments and observations. Nor does he commit the other sin, which is to waste scientific time on existence theorems. Physicists, again, don’t. If we economists are going to persist in physics envy let us at least learn what physicists actually do. Piketty stays close to the facts, and does not, for example, wander into the pointless worlds of non-cooperative game theory, long demolished by experimental economics. He also does not have recourse to non-computable general equilibrium, which never was of use for quantitative economic science, being a branch of philosophy, and a futile one at that. On both points, bravissimo.

...

Since those founding geniuses of classical economics, a market-tested betterment (a locution to be preferred to “capitalism”, with its erroneous implication that capital accumulation, not innovation, is what made us better off) has enormously enriched large parts of a humanity now seven times larger in population than in 1800, and bids fair in the next fifty years or so to enrich everyone on the planet. [Not SSA or MENA...]

...

Then economists, many on the left but some on the right, in quick succession from 1880 to the present—at the same time that market-tested betterment was driving real wages up and up and up—commenced worrying about, to name a few of the pessimisms concerning “capitalism” they discerned: greed, alienation, racial impurity, workers’ lack of bargaining strength, workers’ bad taste in consumption, immigration of lesser breeds, monopoly, unemployment, business cycles, increasing returns, externalities, under-consumption, monopolistic competition, separation of ownership from control, lack of planning, post-War stagnation, investment spillovers, unbalanced growth, dual labor markets, capital insufficiency (William Easterly calls it “capital fundamentalism”), peasant irrationality, capital-market imperfections, public … [more]

news
org:mag
big-peeps
econotariat
economics
books
review
capital
capitalism
inequality
winner-take-all
piketty
wealth
class
labor
mobility
redistribution
growth-econ
rent-seeking
history
mostly-modern
trends
compensation
article
malaise
🎩
the-bones
whiggish-hegelian
cjones-like
multi
mokyr-allen-mccloskey
expert
market-failure
government
broad-econ
cliometrics
aphorism
lens
gallic
clarity
europe
critique
rant
optimism
regularizer
pessimism
ideology
behavioral-econ
authoritarianism
intervention
polanyi-marx
politics
left-wing
absolute-relative
regression-to-mean
legacy
empirical
data-science
econometrics
methodology
hypothesis-testing
physics
iron-age
mediterranean
the-classics
quotes
krugman
world
entrepreneurialism
human-capital
education
supply-demand
plots
manifolds
intersection
markets
evolution
darwinian
giants
old-anglo
egalitarianism-hierarchy
optimate
morality
ethics
envy
stagnation
nl-and-so-can-you
expert-experience
courage
stats
randy-ayndy
reason
intersection-connectedness
detail-architect
The data then exhibit a clear pattern. In France and Great Britain, national capital stood fairly steadily at about seven times national income from 1700 to 1910, then fell sharply from 1910 to 1950, presumably as a result of wars and depression, reaching a low of 2.5 in Britain and a bit less than 3 in France. The capital-income ratio then began to climb in both countries, and reached slightly more than 5 in Britain and slightly less than 6 in France by 2010. The trajectory in the United States was slightly different: it started at just above 3 in 1770, climbed to 5 in 1910, fell slightly in 1920, recovered to a high between 5 and 5.5 in 1930, fell to below 4 in 1950, and was back to 4.5 in 2010.

The wealth-income ratio in the United States has always been lower than in Europe. The main reason in the early years was that land values bulked less in the wide open spaces of North America. There was of course much more land, but it was very cheap. Into the twentieth century and onward, however, the lower capital-income ratio in the United States probably reflects the higher level of productivity: a given amount of capital could support a larger production of output than in Europe. It is no surprise that the two world wars caused much less destruction and dissipation of capital in the United States than in Britain and France. The important observation for Piketty’s argument is that, in all three countries, and elsewhere as well, the wealth-income ratio has been increasing since 1950, and is almost back to nineteenth-century levels. He projects this increase to continue into the current century, with weighty consequences that will be discussed as we go on.

...

Now if you multiply the rate of return on capital by the capital-income ratio, you get the share of capital in the national income. For example, if the rate of return is 5 percent a year and the stock of capital is six years worth of national income, income from capital will be 30 percent of national income, and so income from work will be the remaining 70 percent. At last, after all this preparation, we are beginning to talk about inequality, and in two distinct senses. First, we have arrived at the functional distribution of income—the split between income from work and income from wealth. Second, it is always the case that wealth is more highly concentrated among the rich than income from labor (although recent American history looks rather odd in this respect); and this being so, the larger the share of income from wealth, the more unequal the distribution of income among persons is likely to be. It is this inequality across persons that matters most for good or ill in a society.

...

The data are complicated and not easily comparable across time and space, but here is the flavor of Piketty’s summary picture. Capital is indeed very unequally distributed. Currently in the United States, the top 10 percent own about 70 percent of all the capital, half of that belonging to the top 1 percent; the next 40 percent—who compose the “middle class”—own about a quarter of the total (much of that in the form of housing), and the remaining half of the population owns next to nothing, about 5 percent of total wealth. Even that amount of middle-class property ownership is a new phenomenon in history. The typical European country is a little more egalitarian: the top 1 percent own 25 percent of the total capital, and the middle class 35 percent. (A century ago the European middle class owned essentially no wealth at all.) If the ownership of wealth in fact becomes even more concentrated during the rest of the twenty-first century, the outlook is pretty bleak unless you have a taste for oligarchy.

Income from wealth is probably even more concentrated than wealth itself because, as Piketty notes, large blocks of wealth tend to earn a higher return than small ones. Some of this advantage comes from economies of scale, but more may come from the fact that very big investors have access to a wider range of investment opportunities than smaller investors. Income from work is naturally less concentrated than income from wealth. In Piketty’s stylized picture of the United States today, the top 1 percent earns about 12 percent of all labor income, the next 9 percent earn 23 percent, the middle class gets about 40 percent, and the bottom half about a quarter of income from work. Europe is not very different: the top 10 percent collect somewhat less and the other two groups a little more.

You get the picture: modern capitalism is an unequal society, and the rich-get-richer dynamic strongly suggest that it will get more so. But there is one more loose end to tie up, already hinted at, and it has to do with the advent of very high wage incomes. First, here are some facts about the composition of top incomes. About 60 percent of the income of the top 1 percent in the United States today is labor income. Only when you get to the top tenth of 1 percent does income from capital start to predominate. The income of the top hundredth of 1 percent is 70 percent from capital. The story for France is not very different, though the proportion of labor income is a bit higher at every level. Evidently there are some very high wage incomes, as if you didn’t know.

This is a fairly recent development. In the 1960s, the top 1 percent of wage earners collected a little more than 5 percent of all wage incomes. This fraction has risen pretty steadily until nowadays, when the top 1 percent of wage earners receive 10–12 percent of all wages. This time the story is rather different in France. There the share of total wages going to the top percentile was steady at 6 percent until very recently, when it climbed to 7 percent. The recent surge of extreme inequality at the top of the wage distribution may be primarily an American development. Piketty, who with Emmanuel Saez has made a careful study of high-income tax returns in the United States, attributes this to the rise of what he calls “supermanagers.” The very highest income class consists to a substantial extent of top executives of large corporations, with very rich compensation packages. (A disproportionate number of these, but by no means all of them, come from the financial services industry.) With or without stock options, these large pay packages get converted to wealth and future income from wealth. But the fact remains that much of the increased income (and wealth) inequality in the United States is driven by the rise of these supermanagers.

and Deirdre McCloskey (p critical): https://ejpe.org/journal/article/view/170

nice discussion of empirical economics, economic history, market failures and statism, etc., with several bon mots

Piketty’s great splash will undoubtedly bring many young economically interested scholars to devote their lives to the study of the past. That is good, because economic history is one of the few scientifically quantitative branches of economics. In economic history, as in experimental economics and a few other fields, the economists confront the evidence (as they do not for example in most macroeconomics or industrial organization or international trade theory nowadays).

...

Piketty gives a fine example of how to do it. He does not get entangled as so many economists do in the sole empirical tool they are taught, namely, regression analysis on someone else’s “data” (one of the problems is the word data, meaning “things given”: scientists should deal in capta, “things seized”). Therefore he does not commit one of the two sins of modern economics, the use of meaningless “tests” of statistical significance (he occasionally refers to “statistically insignificant” relations between, say, tax rates and growth rates, but I am hoping he does not suppose that a large coefficient is “insignificant” because R. A. Fisher in 1925 said it was). Piketty constructs or uses statistics of aggregate capital and of inequality and then plots them out for inspection, which is what physicists, for example, also do in dealing with their experiments and observations. Nor does he commit the other sin, which is to waste scientific time on existence theorems. Physicists, again, don’t. If we economists are going to persist in physics envy let us at least learn what physicists actually do. Piketty stays close to the facts, and does not, for example, wander into the pointless worlds of non-cooperative game theory, long demolished by experimental economics. He also does not have recourse to non-computable general equilibrium, which never was of use for quantitative economic science, being a branch of philosophy, and a futile one at that. On both points, bravissimo.

...

Since those founding geniuses of classical economics, a market-tested betterment (a locution to be preferred to “capitalism”, with its erroneous implication that capital accumulation, not innovation, is what made us better off) has enormously enriched large parts of a humanity now seven times larger in population than in 1800, and bids fair in the next fifty years or so to enrich everyone on the planet. [Not SSA or MENA...]

...

Then economists, many on the left but some on the right, in quick succession from 1880 to the present—at the same time that market-tested betterment was driving real wages up and up and up—commenced worrying about, to name a few of the pessimisms concerning “capitalism” they discerned: greed, alienation, racial impurity, workers’ lack of bargaining strength, workers’ bad taste in consumption, immigration of lesser breeds, monopoly, unemployment, business cycles, increasing returns, externalities, under-consumption, monopolistic competition, separation of ownership from control, lack of planning, post-War stagnation, investment spillovers, unbalanced growth, dual labor markets, capital insufficiency (William Easterly calls it “capital fundamentalism”), peasant irrationality, capital-market imperfections, public … [more]

april 2017 by nhaliday

Noahpinion: Robuts takin' jerbs

april 2017 by nhaliday

https://www.reddit.com/r/badeconomics/comments/6hp7yi/counter_r1_automation_can_actually_hurt_workers/

simple Cobb-Douglas analysis

https://www.bloomberg.com/view/articles/2017-07-26/in-a-robot-economy-all-humans-will-be-marketers

econotariat
noahpinion
technology
automation
ai
labor
malaise
stagnation
compensation
trends
market-power
winner-take-all
krugman
autor
models
stylized-facts
economics
econ-productivity
🎩
intervention
thinking
big-picture
innovation
plots
capital
roots
manifolds
cost-disease
info-dynamics
chart
zeitgeist
speedometer
class-warfare
multi
reddit
social
discussion
micro
distribution
street-fighting
analysis
ratty
ssc
news
org:mag
org:bv
org:biz
marginal-rev
the-bones
complement-substitute
simple Cobb-Douglas analysis

https://www.bloomberg.com/view/articles/2017-07-26/in-a-robot-economy-all-humans-will-be-marketers

april 2017 by nhaliday

Riemannian manifold - Wikipedia

february 2017 by nhaliday

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.

concept
definition
math
differential
geometry
manifolds
inner-product
norms
measure
nibble
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.

february 2017 by nhaliday

Deadweight loss - Wikipedia

february 2017 by nhaliday

example:

Deadweight loss created by a binding price ceiling. Producer surplus is necessarily decreased, while consumer surplus may or may not increase; however the decrease in producer surplus must be greater than the increase (if any) in consumer surplus.

economics
concept
efficiency
markets
micro
metabuch
regulation
taxes
wiki
reference
models
things
manifolds
plots
supply-demand
intersection
intersection-connectedness
Deadweight loss created by a binding price ceiling. Producer surplus is necessarily decreased, while consumer surplus may or may not increase; however the decrease in producer surplus must be greater than the increase (if any) in consumer surplus.

february 2017 by nhaliday

interpretation - How to understand degrees of freedom? - Cross Validated

january 2017 by nhaliday

From Wikipedia, there are three interpretations of the degrees of freedom of a statistic:

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom (df). In general, the degrees of freedom of an estimate of a parameter is equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself (which, in sample variance, is one, since the sample mean is the only intermediate step).

Mathematically, degrees of freedom is the dimension of the domain of a random vector, or essentially the number of 'free' components: how many components need to be known before the vector is fully determined.

...

This is a subtle question. It takes a thoughtful person not to understand those quotations! Although they are suggestive, it turns out that none of them is exactly or generally correct. I haven't the time (and there isn't the space here) to give a full exposition, but I would like to share one approach and an insight that it suggests.

Where does the concept of degrees of freedom (DF) arise? The contexts in which it's found in elementary treatments are:

- The Student t-test and its variants such as the Welch or Satterthwaite solutions to the Behrens-Fisher problem (where two populations have different variances).

- The Chi-squared distribution (defined as a sum of squares of independent standard Normals), which is implicated in the sampling distribution of the variance.

- The F-test (of ratios of estimated variances).

- The Chi-squared test, comprising its uses in (a) testing for independence in contingency tables and (b) testing for goodness of fit of distributional estimates.

In spirit, these tests run a gamut from being exact (the Student t-test and F-test for Normal variates) to being good approximations (the Student t-test and the Welch/Satterthwaite tests for not-too-badly-skewed data) to being based on asymptotic approximations (the Chi-squared test). An interesting aspect of some of these is the appearance of non-integral "degrees of freedom" (the Welch/Satterthwaite tests and, as we will see, the Chi-squared test). This is of especial interest because it is the first hint that DF is not any of the things claimed of it.

...

Having been alerted by these potential ambiguities, let's hold up the Chi-squared goodness of fit test for examination, because (a) it's simple, (b) it's one of the common situations where people really do need to know about DF to get the p-value right and (c) it's often used incorrectly. Here's a brief synopsis of the least controversial application of this test:

...

This, many authorities tell us, should have (to a very close approximation) a Chi-squared distribution. But there's a whole family of such distributions. They are differentiated by a parameter νν often referred to as the "degrees of freedom." The standard reasoning about how to determine νν goes like this

I have kk counts. That's kk pieces of data. But there are (functional) relationships among them. To start with, I know in advance that the sum of the counts must equal nn. That's one relationship. I estimated two (or pp, generally) parameters from the data. That's two (or pp) additional relationships, giving p+1p+1 total relationships. Presuming they (the parameters) are all (functionally) independent, that leaves only k−p−1k−p−1 (functionally) independent "degrees of freedom": that's the value to use for νν.

The problem with this reasoning (which is the sort of calculation the quotations in the question are hinting at) is that it's wrong except when some special additional conditions hold. Moreover, those conditions have nothing to do with independence (functional or statistical), with numbers of "components" of the data, with the numbers of parameters, nor with anything else referred to in the original question.

...

Things went wrong because I violated two requirements of the Chi-squared test:

1. You must use the Maximum Likelihood estimate of the parameters. (This requirement can, in practice, be slightly violated.)

2. You must base that estimate on the counts, not on the actual data! (This is crucial.)

...

The point of this comparison--which I hope you have seen coming--is that the correct DF to use for computing the p-values depends on many things other than dimensions of manifolds, counts of functional relationships, or the geometry of Normal variates. There is a subtle, delicate interaction between certain functional dependencies, as found in mathematical relationships among quantities, and distributions of the data, their statistics, and the estimators formed from them. Accordingly, it cannot be the case that DF is adequately explainable in terms of the geometry of multivariate normal distributions, or in terms of functional independence, or as counts of parameters, or anything else of this nature.

We are led to see, then, that "degrees of freedom" is merely a heuristic that suggests what the sampling distribution of a (t, Chi-squared, or F) statistic ought to be, but it is not dispositive. Belief that it is dispositive leads to egregious errors. (For instance, the top hit on Google when searching "chi squared goodness of fit" is a Web page from an Ivy League university that gets most of this completely wrong! In particular, a simulation based on its instructions shows that the chi-squared value it recommends as having 7 DF actually has 9 DF.)

q-n-a
overflow
stats
data-science
concept
jargon
explanation
methodology
things
nibble
degrees-of-freedom
clarity
curiosity
manifolds
dimensionality
ground-up
intricacy
hypothesis-testing
examples
list
ML-MAP-E
gotchas
grokkability-clarity
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom (df). In general, the degrees of freedom of an estimate of a parameter is equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself (which, in sample variance, is one, since the sample mean is the only intermediate step).

Mathematically, degrees of freedom is the dimension of the domain of a random vector, or essentially the number of 'free' components: how many components need to be known before the vector is fully determined.

...

This is a subtle question. It takes a thoughtful person not to understand those quotations! Although they are suggestive, it turns out that none of them is exactly or generally correct. I haven't the time (and there isn't the space here) to give a full exposition, but I would like to share one approach and an insight that it suggests.

Where does the concept of degrees of freedom (DF) arise? The contexts in which it's found in elementary treatments are:

- The Student t-test and its variants such as the Welch or Satterthwaite solutions to the Behrens-Fisher problem (where two populations have different variances).

- The Chi-squared distribution (defined as a sum of squares of independent standard Normals), which is implicated in the sampling distribution of the variance.

- The F-test (of ratios of estimated variances).

- The Chi-squared test, comprising its uses in (a) testing for independence in contingency tables and (b) testing for goodness of fit of distributional estimates.

In spirit, these tests run a gamut from being exact (the Student t-test and F-test for Normal variates) to being good approximations (the Student t-test and the Welch/Satterthwaite tests for not-too-badly-skewed data) to being based on asymptotic approximations (the Chi-squared test). An interesting aspect of some of these is the appearance of non-integral "degrees of freedom" (the Welch/Satterthwaite tests and, as we will see, the Chi-squared test). This is of especial interest because it is the first hint that DF is not any of the things claimed of it.

...

Having been alerted by these potential ambiguities, let's hold up the Chi-squared goodness of fit test for examination, because (a) it's simple, (b) it's one of the common situations where people really do need to know about DF to get the p-value right and (c) it's often used incorrectly. Here's a brief synopsis of the least controversial application of this test:

...

This, many authorities tell us, should have (to a very close approximation) a Chi-squared distribution. But there's a whole family of such distributions. They are differentiated by a parameter νν often referred to as the "degrees of freedom." The standard reasoning about how to determine νν goes like this

I have kk counts. That's kk pieces of data. But there are (functional) relationships among them. To start with, I know in advance that the sum of the counts must equal nn. That's one relationship. I estimated two (or pp, generally) parameters from the data. That's two (or pp) additional relationships, giving p+1p+1 total relationships. Presuming they (the parameters) are all (functionally) independent, that leaves only k−p−1k−p−1 (functionally) independent "degrees of freedom": that's the value to use for νν.

The problem with this reasoning (which is the sort of calculation the quotations in the question are hinting at) is that it's wrong except when some special additional conditions hold. Moreover, those conditions have nothing to do with independence (functional or statistical), with numbers of "components" of the data, with the numbers of parameters, nor with anything else referred to in the original question.

...

Things went wrong because I violated two requirements of the Chi-squared test:

1. You must use the Maximum Likelihood estimate of the parameters. (This requirement can, in practice, be slightly violated.)

2. You must base that estimate on the counts, not on the actual data! (This is crucial.)

...

The point of this comparison--which I hope you have seen coming--is that the correct DF to use for computing the p-values depends on many things other than dimensions of manifolds, counts of functional relationships, or the geometry of Normal variates. There is a subtle, delicate interaction between certain functional dependencies, as found in mathematical relationships among quantities, and distributions of the data, their statistics, and the estimators formed from them. Accordingly, it cannot be the case that DF is adequately explainable in terms of the geometry of multivariate normal distributions, or in terms of functional independence, or as counts of parameters, or anything else of this nature.

We are led to see, then, that "degrees of freedom" is merely a heuristic that suggests what the sampling distribution of a (t, Chi-squared, or F) statistic ought to be, but it is not dispositive. Belief that it is dispositive leads to egregious errors. (For instance, the top hit on Google when searching "chi squared goodness of fit" is a Web page from an Ivy League university that gets most of this completely wrong! In particular, a simulation based on its instructions shows that the chi-squared value it recommends as having 7 DF actually has 9 DF.)

january 2017 by nhaliday

soft question - Thinking and Explaining - MathOverflow

january 2017 by nhaliday

- good question from Bill Thurston

- great answers by Terry Tao, fedja, Minhyong Kim, gowers, etc.

Terry Tao:

- symmetry as blurring/vibrating/wobbling, scale invariance

- anthropomorphization, adversarial perspective for estimates/inequalities/quantifiers, spending/economy

fedja walks through his though-process from another answer

Minhyong Kim: anthropology of mathematical philosophizing

Per Vognsen: normality as isotropy

comment: conjugate subgroup gHg^-1 ~ "H but somewhere else in G"

gowers: hidden things in basic mathematics/arithmetic

comment by Ryan Budney: x sin(x) via x -> (x, sin(x)), (x, y) -> xy

I kinda get what he's talking about but needed to use Mathematica to get the initial visualization down.

To remind myself later:

- xy can be easily visualized by juxtaposing the two parabolae x^2 and -x^2 diagonally

- x sin(x) can be visualized along that surface by moving your finger along the line (x, 0) but adding some oscillations in y direction according to sin(x)

q-n-a
soft-question
big-list
intuition
communication
teaching
math
thinking
writing
thurston
lens
overflow
synthesis
hi-order-bits
👳
insight
meta:math
clarity
nibble
giants
cartoons
gowers
mathtariat
better-explained
stories
the-trenches
problem-solving
homogeneity
symmetry
fedja
examples
philosophy
big-picture
vague
isotropy
reflection
spatial
ground-up
visual-understanding
polynomials
dimensionality
math.GR
worrydream
scholar
🎓
neurons
metabuch
yoga
retrofit
mental-math
metameta
wisdom
wordlessness
oscillation
operational
adversarial
quantifiers-sums
exposition
explanation
tricki
concrete
s:***
manifolds
invariance
dynamical
info-dynamics
cool
direction
elegance
heavyweights
analysis
guessing
grokkability-clarity
technical-writing
- great answers by Terry Tao, fedja, Minhyong Kim, gowers, etc.

Terry Tao:

- symmetry as blurring/vibrating/wobbling, scale invariance

- anthropomorphization, adversarial perspective for estimates/inequalities/quantifiers, spending/economy

fedja walks through his though-process from another answer

Minhyong Kim: anthropology of mathematical philosophizing

Per Vognsen: normality as isotropy

comment: conjugate subgroup gHg^-1 ~ "H but somewhere else in G"

gowers: hidden things in basic mathematics/arithmetic

comment by Ryan Budney: x sin(x) via x -> (x, sin(x)), (x, y) -> xy

I kinda get what he's talking about but needed to use Mathematica to get the initial visualization down.

To remind myself later:

- xy can be easily visualized by juxtaposing the two parabolae x^2 and -x^2 diagonally

- x sin(x) can be visualized along that surface by moving your finger along the line (x, 0) but adding some oscillations in y direction according to sin(x)

january 2017 by nhaliday

gt.geometric topology - Intuitive crutches for higher dimensional thinking - MathOverflow

december 2016 by nhaliday

Terry Tao:

I can't help you much with high-dimensional topology - it's not my field, and I've not picked up the various tricks topologists use to get a grip on the subject - but when dealing with the geometry of high-dimensional (or infinite-dimensional) vector spaces such as R^n, there are plenty of ways to conceptualise these spaces that do not require visualising more than three dimensions directly.

For instance, one can view a high-dimensional vector space as a state space for a system with many degrees of freedom. A megapixel image, for instance, is a point in a million-dimensional vector space; by varying the image, one can explore the space, and various subsets of this space correspond to various classes of images.

One can similarly interpret sound waves, a box of gases, an ecosystem, a voting population, a stream of digital data, trials of random variables, the results of a statistical survey, a probabilistic strategy in a two-player game, and many other concrete objects as states in a high-dimensional vector space, and various basic concepts such as convexity, distance, linearity, change of variables, orthogonality, or inner product can have very natural meanings in some of these models (though not in all).

It can take a bit of both theory and practice to merge one's intuition for these things with one's spatial intuition for vectors and vector spaces, but it can be done eventually (much as after one has enough exposure to measure theory, one can start merging one's intuition regarding cardinality, mass, length, volume, probability, cost, charge, and any number of other "real-life" measures).

For instance, the fact that most of the mass of a unit ball in high dimensions lurks near the boundary of the ball can be interpreted as a manifestation of the law of large numbers, using the interpretation of a high-dimensional vector space as the state space for a large number of trials of a random variable.

More generally, many facts about low-dimensional projections or slices of high-dimensional objects can be viewed from a probabilistic, statistical, or signal processing perspective.

Scott Aaronson:

Here are some of the crutches I've relied on. (Admittedly, my crutches are probably much more useful for theoretical computer science, combinatorics, and probability than they are for geometry, topology, or physics. On a related note, I personally have a much easier time thinking about R^n than about, say, R^4 or R^5!)

1. If you're trying to visualize some 4D phenomenon P, first think of a related 3D phenomenon P', and then imagine yourself as a 2D being who's trying to visualize P'. The advantage is that, unlike with the 4D vs. 3D case, you yourself can easily switch between the 3D and 2D perspectives, and can therefore get a sense of exactly what information is being lost when you drop a dimension. (You could call this the "Flatland trick," after the most famous literary work to rely on it.)

2. As someone else mentioned, discretize! Instead of thinking about R^n, think about the Boolean hypercube {0,1}^n, which is finite and usually easier to get intuition about. (When working on problems, I often find myself drawing {0,1}^4 on a sheet of paper by drawing two copies of {0,1}^3 and then connecting the corresponding vertices.)

3. Instead of thinking about a subset S⊆R^n, think about its characteristic function f:R^n→{0,1}. I don't know why that trivial perspective switch makes such a big difference, but it does ... maybe because it shifts your attention to the process of computing f, and makes you forget about the hopeless task of visualizing S!

4. One of the central facts about R^n is that, while it has "room" for only n orthogonal vectors, it has room for exp(n) almost-orthogonal vectors. Internalize that one fact, and so many other properties of R^n (for example, that the n-sphere resembles a "ball with spikes sticking out," as someone mentioned before) will suddenly seem non-mysterious. In turn, one way to internalize the fact that R^n has so many almost-orthogonal vectors is to internalize Shannon's theorem that there exist good error-correcting codes.

5. To get a feel for some high-dimensional object, ask questions about the behavior of a process that takes place on that object. For example: if I drop a ball here, which local minimum will it settle into? How long does this random walk on {0,1}^n take to mix?

Gil Kalai:

This is a slightly different point, but Vitali Milman, who works in high-dimensional convexity, likes to draw high-dimensional convex bodies in a non-convex way. This is to convey the point that if you take the convex hull of a few points on the unit sphere of R^n, then for large n very little of the measure of the convex body is anywhere near the corners, so in a certain sense the body is a bit like a small sphere with long thin "spikes".

q-n-a
intuition
math
visual-understanding
list
discussion
thurston
tidbits
aaronson
tcs
geometry
problem-solving
yoga
👳
big-list
metabuch
tcstariat
gowers
mathtariat
acm
overflow
soft-question
levers
dimensionality
hi-order-bits
insight
synthesis
thinking
models
cartoons
coding-theory
information-theory
probability
concentration-of-measure
magnitude
linear-algebra
boolean-analysis
analogy
arrows
lifts-projections
measure
markov
sampling
shannon
conceptual-vocab
nibble
degrees-of-freedom
worrydream
neurons
retrofit
oscillation
paradox
novelty
tricki
concrete
high-dimension
s:***
manifolds
direction
curvature
convexity-curvature
elegance
guessing
I can't help you much with high-dimensional topology - it's not my field, and I've not picked up the various tricks topologists use to get a grip on the subject - but when dealing with the geometry of high-dimensional (or infinite-dimensional) vector spaces such as R^n, there are plenty of ways to conceptualise these spaces that do not require visualising more than three dimensions directly.

For instance, one can view a high-dimensional vector space as a state space for a system with many degrees of freedom. A megapixel image, for instance, is a point in a million-dimensional vector space; by varying the image, one can explore the space, and various subsets of this space correspond to various classes of images.

One can similarly interpret sound waves, a box of gases, an ecosystem, a voting population, a stream of digital data, trials of random variables, the results of a statistical survey, a probabilistic strategy in a two-player game, and many other concrete objects as states in a high-dimensional vector space, and various basic concepts such as convexity, distance, linearity, change of variables, orthogonality, or inner product can have very natural meanings in some of these models (though not in all).

It can take a bit of both theory and practice to merge one's intuition for these things with one's spatial intuition for vectors and vector spaces, but it can be done eventually (much as after one has enough exposure to measure theory, one can start merging one's intuition regarding cardinality, mass, length, volume, probability, cost, charge, and any number of other "real-life" measures).

For instance, the fact that most of the mass of a unit ball in high dimensions lurks near the boundary of the ball can be interpreted as a manifestation of the law of large numbers, using the interpretation of a high-dimensional vector space as the state space for a large number of trials of a random variable.

More generally, many facts about low-dimensional projections or slices of high-dimensional objects can be viewed from a probabilistic, statistical, or signal processing perspective.

Scott Aaronson:

Here are some of the crutches I've relied on. (Admittedly, my crutches are probably much more useful for theoretical computer science, combinatorics, and probability than they are for geometry, topology, or physics. On a related note, I personally have a much easier time thinking about R^n than about, say, R^4 or R^5!)

1. If you're trying to visualize some 4D phenomenon P, first think of a related 3D phenomenon P', and then imagine yourself as a 2D being who's trying to visualize P'. The advantage is that, unlike with the 4D vs. 3D case, you yourself can easily switch between the 3D and 2D perspectives, and can therefore get a sense of exactly what information is being lost when you drop a dimension. (You could call this the "Flatland trick," after the most famous literary work to rely on it.)

2. As someone else mentioned, discretize! Instead of thinking about R^n, think about the Boolean hypercube {0,1}^n, which is finite and usually easier to get intuition about. (When working on problems, I often find myself drawing {0,1}^4 on a sheet of paper by drawing two copies of {0,1}^3 and then connecting the corresponding vertices.)

3. Instead of thinking about a subset S⊆R^n, think about its characteristic function f:R^n→{0,1}. I don't know why that trivial perspective switch makes such a big difference, but it does ... maybe because it shifts your attention to the process of computing f, and makes you forget about the hopeless task of visualizing S!

4. One of the central facts about R^n is that, while it has "room" for only n orthogonal vectors, it has room for exp(n) almost-orthogonal vectors. Internalize that one fact, and so many other properties of R^n (for example, that the n-sphere resembles a "ball with spikes sticking out," as someone mentioned before) will suddenly seem non-mysterious. In turn, one way to internalize the fact that R^n has so many almost-orthogonal vectors is to internalize Shannon's theorem that there exist good error-correcting codes.

5. To get a feel for some high-dimensional object, ask questions about the behavior of a process that takes place on that object. For example: if I drop a ball here, which local minimum will it settle into? How long does this random walk on {0,1}^n take to mix?

Gil Kalai:

This is a slightly different point, but Vitali Milman, who works in high-dimensional convexity, likes to draw high-dimensional convex bodies in a non-convex way. This is to convey the point that if you take the convex hull of a few points on the unit sphere of R^n, then for large n very little of the measure of the convex body is anywhere near the corners, so in a certain sense the body is a bit like a small sphere with long thin "spikes".

december 2016 by nhaliday

Psychological comments: Does Age make us sage or sag?

december 2016 by nhaliday

Khan on Twitter: "figure on right from @tuckerdrob lab is depressing (the knowledge plateau). do i read in vain??? https://t.co/DZzBD8onEv": https://twitter.com/razibkhan/status/809439911627493377

- reasoning rises then declines after age ~20

- knowledge plateaus by age 35-40

- different interpretation provided by study authors w/ another graph (renewal)

- study (can't find the exact graph anywhere): http://www.iapsych.com/wj3ewok/LinkedDocuments/McArdle2002.pdf

School’s out: https://westhunt.wordpress.com/2016/12/29/schools-out/

I saw a note by Razib Khan, in which he mentioned that psychometric research suggests that people plateau in their knowledge base as adults. I could believe it. But I’m not sure it’s true in my case. One might estimate total adult knowledge in terms of BS equivalents…

Age-related IQ decline is reduced markedly after adjustment for the Flynn effect: https://www.ncbi.nlm.nih.gov/m/pubmed/20349385/

Twenty-year-olds outperform 70-year-olds by as much as 2.3 standard deviations (35 IQ points) on subtests of the Wechsler Adult Intelligence Scale (WAIS). We show that most of the difference can be attributed to an intergenerational rise in IQ known as the Flynn effect.

...

For these verbal subtests, the Flynn effect masked a modest increase in ability as individuals grow older.

Predictors of ageing-related decline across multiple cognitive functions: http://www.sciencedirect.com/science/article/pii/S0160289616302707

Cognitive ageing is likely a process with few large-effect predictors

A strong link between speed of visual discrimination and cognitive ageing: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4123160/

Results showed a moderate correlation (r = 0.460) between inspection time performance and intelligence, and a strong correlation between change in inspection time and change in intelligence from 70 to 76 (r = 0.779). These results support the processing speed theory of cognitive ageing. They go beyond cross-sectional correlation to show that cognitive change is accompanied by changes in basic visual information processing as we age.

albion
psychology
cog-psych
psychometrics
aging
iq
objektbuch
long-term
longitudinal
study
summary
variance-components
scitariat
multi
gnxp
learning
metabuch
twitter
social
discussion
pic
data
planning
tradeoffs
flux-stasis
volo-avolo
west-hunter
studying
knowledge
age-generation
flexibility
rigidity
plots
manifolds
universalism-particularism
being-becoming
essence-existence
intelligence
stock-flow
large-factor
psych-architecture
visuo
correlation
time
speed
short-circuit
roots
flynn
trends
dysgenics
language
explanans
direction
chart
- reasoning rises then declines after age ~20

- knowledge plateaus by age 35-40

- different interpretation provided by study authors w/ another graph (renewal)

- study (can't find the exact graph anywhere): http://www.iapsych.com/wj3ewok/LinkedDocuments/McArdle2002.pdf

School’s out: https://westhunt.wordpress.com/2016/12/29/schools-out/

I saw a note by Razib Khan, in which he mentioned that psychometric research suggests that people plateau in their knowledge base as adults. I could believe it. But I’m not sure it’s true in my case. One might estimate total adult knowledge in terms of BS equivalents…

Age-related IQ decline is reduced markedly after adjustment for the Flynn effect: https://www.ncbi.nlm.nih.gov/m/pubmed/20349385/

Twenty-year-olds outperform 70-year-olds by as much as 2.3 standard deviations (35 IQ points) on subtests of the Wechsler Adult Intelligence Scale (WAIS). We show that most of the difference can be attributed to an intergenerational rise in IQ known as the Flynn effect.

...

For these verbal subtests, the Flynn effect masked a modest increase in ability as individuals grow older.

Predictors of ageing-related decline across multiple cognitive functions: http://www.sciencedirect.com/science/article/pii/S0160289616302707

Cognitive ageing is likely a process with few large-effect predictors

A strong link between speed of visual discrimination and cognitive ageing: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4123160/

Results showed a moderate correlation (r = 0.460) between inspection time performance and intelligence, and a strong correlation between change in inspection time and change in intelligence from 70 to 76 (r = 0.779). These results support the processing speed theory of cognitive ageing. They go beyond cross-sectional correlation to show that cognitive change is accompanied by changes in basic visual information processing as we age.

december 2016 by nhaliday

Hidden Games | West Hunter

november 2016 by nhaliday

Since we are arguably a lot smarter than ants or bees, you might think that most adaptive personality variation in humans would be learned (a response to exterior cues) rather than heritable. Maybe some is, but much variation looks heritable. People don’t seem to learn to be aggressive or meek – they just are, and in those tendencies resemble their biological parents. I wish I (or anyone else) understood better why this is so, but there are some notions floating around that may explain it. One is that jacks of all trades are masters of none: if you play the same role all the time, you’ll be better at it than someone who keep switching personalities. It could be the case that such switching is physiologically difficult and/or expensive. And in at least some cases, being predictable has social value. Someone who is known to be implacably aggressive will win at ‘chicken’. Being known as the sort of guy who would rush into a burning building to save ugly strangers may pay off, even though actually running into that blaze does not.

...

This kind of game-theoretic genetic variation, driving distinct behavioral strategies, can have some really odd properties. For one thing, there can be more than one possible stable mix of behavioral types even in identical ecological situations. It’s a bit like dropping a marble onto a hilly landscape with many unconnected valleys – it will roll to the bottom of some valley, but initial conditions determine which valley. Small perturbations will not knock the marble out of the valley it lands in. In the same way, two human populations could fall into different states, different stable mixes of behavioral traits, for no reason at all other than chance and then stay there indefinitely. Populations are even more likely to fall into qualitatively different stable states when the ecological situations are significantly different.

...

What this means, think, is that it is entirely possible that human societies fall into fundamentally different patterns because of genetic influences on behavior that are best understood via evolutionary game theory. Sometimes one population might have a psychological type that doesn’t exist at all in another society, or the distribution could be substantially different. Sometimes these different social patterns will be predictable results of different ecological situations, sometimes the purest kind of chance. Sometimes the internal dynamics of these genetic systems will produce oscillatory (or chaotic!) changes in gene frequencies over time, which means changes in behavior and personality over time. In some cases, these internal genetic dynamics may be the fundamental reason for the rise and fall of empires. Societies in one stable distribution, in a particular psychological/behavioral/life history ESS, may simply be unable to replicate some of the institutions found in peoples in a different ESS.

Evolutionary forces themselves vary according to what ESS you’re in. Which ESS you’re in may be the most fundamental ethnic fact, and explain the most profound ethnic behavioral differences

Look, everyone is always looking for the secret principles that underlie human society and history, some algebra that takes mounds of historical and archaeological data – the stuff that happens – and explains it in some compact way, lets us understand it, just as continental drift made a comprehensible story out of geology. On second thought, ‘everyone’ mean that smallish fraction of researchers that are slaves of curiosity…

This approach isn’t going to explain everything – nothing will. But it might explain a lot, which would make it a hell of a lot more valuable than modern sociology or cultural anthropology. I would hope that an analysis of this sort might help explain fundamental long-term flavor difference between different human societies, differences in life-history strategies especially (dads versus cads, etc). If we get particularly lucky, maybe we’ll have some notions of why the Mayans got bored with civilization, why Chinese kids are passive at birth while European and African kids are feisty. We’ll see.

Of course we could be wrong. It’s going to have be tested and checked: it’s not magic. It is based on the realization that the sort of morphs and game-theoretic balances we see in some nonhuman species are if anything more likely to occur in humans, because our societies are so complex, because the effectiveness of a course of action so often depends on the psychologies of other individuals – that and the obvious fact that people are not the same everywhere.

west-hunter
sapiens
game-theory
evolution
personality
thinking
essay
adversarial
GT-101
EGT
scitariat
tradeoffs
equilibrium
strategy
distribution
sociality
variance-components
flexibility
rigidity
diversity
biodet
behavioral-gen
nature
within-without
roots
explanans
psychology
social-psych
evopsych
intricacy
oscillation
pro-rata
iteration-recursion
insight
curiosity
letters
models
theory-practice
civilization
latin-america
farmers-and-foragers
age-of-discovery
china
asia
sinosphere
europe
the-great-west-whale
africa
developmental
empirical
humanity
courage
virtu
theory-of-mind
reputation
cybernetics
random
degrees-of-freedom
manifolds
occam
parsimony
turchin
broad-econ
deep-materialism
cultural-dynamics
anthropology
cliometrics
hari-seldon
learning
ecology
context
leadership
cost-benefit
apollonian-dionysian
detail-architecture
history
antiquity
pop-diff
comparison
plots
being-becoming
number
uniqueness
...

This kind of game-theoretic genetic variation, driving distinct behavioral strategies, can have some really odd properties. For one thing, there can be more than one possible stable mix of behavioral types even in identical ecological situations. It’s a bit like dropping a marble onto a hilly landscape with many unconnected valleys – it will roll to the bottom of some valley, but initial conditions determine which valley. Small perturbations will not knock the marble out of the valley it lands in. In the same way, two human populations could fall into different states, different stable mixes of behavioral traits, for no reason at all other than chance and then stay there indefinitely. Populations are even more likely to fall into qualitatively different stable states when the ecological situations are significantly different.

...

What this means, think, is that it is entirely possible that human societies fall into fundamentally different patterns because of genetic influences on behavior that are best understood via evolutionary game theory. Sometimes one population might have a psychological type that doesn’t exist at all in another society, or the distribution could be substantially different. Sometimes these different social patterns will be predictable results of different ecological situations, sometimes the purest kind of chance. Sometimes the internal dynamics of these genetic systems will produce oscillatory (or chaotic!) changes in gene frequencies over time, which means changes in behavior and personality over time. In some cases, these internal genetic dynamics may be the fundamental reason for the rise and fall of empires. Societies in one stable distribution, in a particular psychological/behavioral/life history ESS, may simply be unable to replicate some of the institutions found in peoples in a different ESS.

Evolutionary forces themselves vary according to what ESS you’re in. Which ESS you’re in may be the most fundamental ethnic fact, and explain the most profound ethnic behavioral differences

Look, everyone is always looking for the secret principles that underlie human society and history, some algebra that takes mounds of historical and archaeological data – the stuff that happens – and explains it in some compact way, lets us understand it, just as continental drift made a comprehensible story out of geology. On second thought, ‘everyone’ mean that smallish fraction of researchers that are slaves of curiosity…

This approach isn’t going to explain everything – nothing will. But it might explain a lot, which would make it a hell of a lot more valuable than modern sociology or cultural anthropology. I would hope that an analysis of this sort might help explain fundamental long-term flavor difference between different human societies, differences in life-history strategies especially (dads versus cads, etc). If we get particularly lucky, maybe we’ll have some notions of why the Mayans got bored with civilization, why Chinese kids are passive at birth while European and African kids are feisty. We’ll see.

Of course we could be wrong. It’s going to have be tested and checked: it’s not magic. It is based on the realization that the sort of morphs and game-theoretic balances we see in some nonhuman species are if anything more likely to occur in humans, because our societies are so complex, because the effectiveness of a course of action so often depends on the psychologies of other individuals – that and the obvious fact that people are not the same everywhere.

november 2016 by nhaliday

Useful Math | Academically Interesting

math academia list roadmap machine-learning tcs yoga acm synthesis metabuch clever-rats ratty scholar-pack top-n hi-order-bits levers 🎓 👳 pre-2013 acmtariat big-picture org:bleg nibble metameta impact meta:math skeleton s:*** p:*** applications chart knowledge studying prioritizing ideas track-record checklists tricki problem-solving optimization differential linear-algebra probability stochastic-processes martingale estimate math.CA series approximation deep-learning graphs graph-theory graphical-models model-class pigeonhole-markov linearity atoms distribution entropy-like dimensionality homogeneity spectral fourier arrows finiteness math.GN topology smoothness measure manifolds curvature concept conceptual-vocab convexity-curvature confluence toolkit apollonian-dionysian pragmatic telos-atelos ends-means quixotic

february 2016 by nhaliday

math academia list roadmap machine-learning tcs yoga acm synthesis metabuch clever-rats ratty scholar-pack top-n hi-order-bits levers 🎓 👳 pre-2013 acmtariat big-picture org:bleg nibble metameta impact meta:math skeleton s:*** p:*** applications chart knowledge studying prioritizing ideas track-record checklists tricki problem-solving optimization differential linear-algebra probability stochastic-processes martingale estimate math.CA series approximation deep-learning graphs graph-theory graphical-models model-class pigeonhole-markov linearity atoms distribution entropy-like dimensionality homogeneity spectral fourier arrows finiteness math.GN topology smoothness measure manifolds curvature concept conceptual-vocab convexity-curvature confluence toolkit apollonian-dionysian pragmatic telos-atelos ends-means quixotic

february 2016 by nhaliday

Copy this bookmark: