power-law   57

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Overcoming Bias : Conformity Excuses
I picked my likes first, my group second.
I just couldn’t be happy elsewhere.
I actually like small differences.
In future, this will be more popular.
Second tier folks aren’t remotely as good. [isn't this kind of true because of power laws?]
Unpopular things are objectively defective.
ratty  hanson  rationality  neurons  biases  individualism-collectivism  info-dynamics  epistemic  mood-affiliation  preference-falsification  thinking  metabuch  embedded-cognition  water  social-norms  impetus  hidden-motives  homo-hetero  flux-stasis  power-law  heterodox  happy-sad 
june 2017 by nhaliday
Why does 'everything look correlated on a log-log scale'? - Quora
A correlation on a log log scale is meant to suggest the data follows a power law relationship of the form yy∝x−n.∝x−n.

A low R2R2 is suppose to suggest that the data either actually follows some other distribution like yy∝e−x∝e−xor is simply random noise. The problem is that log log correlation is a necessary but not sufficient condition to prove a power law relationship. While ruling out random noise is fairly easy, ruling out an alternate functional form is much harder- you can reject a power law hypothesis by a log log plot but you cannot prove it by one. As Aaron Brown answer points out, a lot of stuff that looks like it has a power law relationship does not actually follow it in reality. In particular, an exponential or log normal relationship might give similar results over most of the range but will diverge strongly at the tail end .[1] This difference can be difficult to detect if limited data is collected at the tail ends and deviations look like noise.

An example of a log normal distribution plotted on a normal and log-log scale. [2] Note the appearance of a straight line on the right tail that diverges strongly on the left tail. Using a power law relationship in this region will cause serious errors.
q-n-a  qra  data-science  correlation  regression  magnitude  dataviz  street-fighting  gotchas  nibble  plots  multiplicative  additive  power-law 
february 2017 by nhaliday
Information Processing: Success, Ability, and all that
Better to be Lucky than Good?: http://infoproc.blogspot.com/2018/03/better-to-be-lucky-than-good.html
The arXiv paper below looks at stochastic dynamical models that can transform initial (e.g., Gaussian) talent distributions into power law outcomes (e.g., observed wealth distributions in modern societies). While the models themselves may not be entirely realistic, they illustrate the potentially large role of luck relative to ability in real life outcomes.


Of course, it might be the case that better measurements would uncover a power law distribution of individual talents. But it's far more plausible to me that random fluctuations + nonlinear amplifications transform, over time, normally distributed talents into power law outcomes.
hsu  scitariat  meta:prediction  success  variance-components  correlation  signal-noise  street-fighting  methodology  multi  technocracy  quality  human-capital  money  wealth  compensation  distribution  inequality  winner-take-all  coming-apart  power-law  pareto  random  models  nonlinearity  roots  explanans 
january 2017 by nhaliday
The Life-Span of Empires
empires die but don't age

The author examined the distribution of imperial lifetimes using a data set that spans more than three millennia and found that it conforms to a memoryless exponential distribution in which the rate of collapse of an empire is independent of its age.

same is true for species apparently
but it's a power law for larger taxa
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december 2016 by nhaliday
Mandelbrot (and Hudson’s) The (mis)Behaviour of Markets: A Fractal View of Risk, Ruin, and Reward | EVOLVING ECONOMICS
If you have read Nassim Taleb’s The Black Swan you will have come across some of Benoit Mandelbrot’s ideas. However, Mandelbrot and Hudson’s The (mis)Behaviour of Markets: A Fractal View of Risk, Ruin, and Reward offers a much clearer critique of the underpinnings of modern financial theory (there are many parts of The Black Swan where I’m still not sure I understand what Taleb is saying). Mandelbrot describes and pulls apart the contributions of Markowitz, Sharpe, Black, Scholes and friends in a way likely understandable to the intelligent lay reader. I expect that might flow from science journalist Richard Hudson’s involvement in writing the book.

- interesting parable about lakes and markets (but power laws aren't memoryless...?)
- yeah I think that's completely wrong actually. the important property of power laws is the lack of finite higher-order moments.

based off http://www.iima.ac.in/~jrvarma/blog/index.cgi/2008/12/21/ I think he really did mean a power law (x = 100/sqrt(r) => pdf is p(x) ~ |dr/dx| = 2e4/x^3)

edit: ah I get it now, for X ~ p(x) = 2/x^3 on [1,inf), we have E[X|X > k] = 2k, so not memoryless, but rather subject to a "slippery slope"
books  summary  finance  map-territory  tetlock  review  econotariat  distribution  parable  blowhards  multi  risk  decision-theory  tails  meta:prediction  complex-systems  broad-econ  power-law 
november 2016 by nhaliday
Overcoming Bias : A Future Of Pipes
The future of computing, after about 2035, is adiabatic reservable hardware. When such hardware runs at a cost-minimizing speed, half of the total budget is spent on computer hardware, and the other half is spent on energy and cooling for that hardware. Thus after 2035 or so, about as much will be spent on computer hardware and a physical space to place it as will be spent on hardware and space for systems to generate and transport energy into the computers, and to absorb and transport heat away from those computers. So if you seek a career for a futuristic world dominated by computers, note that a career making or maintaining energy or cooling systems may be just as promising as a career making or maintaining computing hardware.

We can imagine lots of futuristic ways to cheaply and compactly make and transport energy. These include thorium reactors and superconducting power cables. It is harder to imagine futuristic ways to absorb and transport heat. So we are likely to stay stuck with existing approaches to cooling. And the best of these, at least on large scales, is to just push cool fluids past the hardware. And the main expense in this approach is for the pipes to transport those fluids, and the space to hold those pipes.

Thus in future cities crammed with computer hardware, roughly half of the volume is likely to be taken up by pipes that move cooling fluids in and out. And the tech for such pipes will probably be more stable than tech for energy or computers. So if you want a stable career managing something that will stay very valuable for a long time, consider plumbing.

Will this focus on cooling limit city sizes? After all, the surface area of a city, where cooling fluids can go in and out, goes as the square of city scale , while the volume to be cooled goes as the cube of city scale. The ratio of volume to surface area is thus linear in city scale. So does our ability to cool cities fall inversely with city scale?

Actually, no. We have good fractal pipe designs to efficiently import fluids like air or water from outside a city to near every point in that city, and to then export hot fluids from near every point to outside the city. These fractal designs require cost overheads that are only logarithmic in the total size of the city. That is, when you double the city size, such overheads increase by only a constant amount, instead of doubling.
hanson  futurism  prediction  street-fighting  essay  len:short  ratty  computation  hardware  thermo  structure  composition-decomposition  complex-systems  magnitude  analysis  urban-rural  power-law  phys-energy  detail-architecture  efficiency  economics  supply-demand  labor  planning  long-term  physics  temperature  flux-stasis  fluid  measure  technology  frontier  speedometer  career  cost-benefit  identity  stylized-facts  objektbuch  data  trivia  cocktail 
august 2016 by nhaliday
The Babe Ruth Effect in Venture Capital | cdixon blog
Building a portfolio that can deliver superior performance requires that you evaluate each investment using expected value analysis. What is striking is that the leading thinkers across varied fields — including horse betting, casino gambling, and investing — all emphasize the same point. We call it the Babe Ruth effect: even though Ruth struck out a lot, he was one of baseball’s greatest hitters. — ”The Babe Ruth Effect: Frequency vs Magnitude”
power-law  investing 
july 2015 by tonyyet

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