oly   193

« earlier    

Vladimir Novakovski's answer to What financial advice would you give to a 21-year-old? - Quora
Learn economics and see that investment and consumption levels (as percentages) depend only marginally on age and existing net worth and mostly on your risk preferences and utility function.
qra  q-n-a  oly  advice  reflection  personal-finance  ORFE  outcome-risk  investing  time-preference  age-generation  dependence-independence  economics 
11 weeks ago by nhaliday
gn.general topology - Pair of curves joining opposite corners of a square must intersect---proof? - MathOverflow
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 
october 2017 by nhaliday
Best Topology Olympiad ***EVER*** - Affine Mess - Quora
Most people take courses in topology, algebraic topology, knot theory, differential topology and what have you without once doing anything with a finite topological space. There may have been some quirky questions about such spaces early on in a point-set topology course, but most of us come out of these courses thinking that finite topological spaces are either discrete or only useful as an exotic counterexample to some standard separation property. The mere idea of calculating the fundamental group for a 4-point space seems ludicrous.

Only it’s not. This is a genuine question, not a joke, and I find it both hilarious and super educational. DO IT!!
nibble  qra  announcement  math  geometry  topology  puzzles  rec-math  oly  links  math.AT  ground-up  finiteness  math.GN 
october 2017 by nhaliday
What is the best way to parse command-line arguments with Python? - Quora
- Anders Kaseorg

Use the standard optparse library.

It’s important to uphold your users’ expectation that your utility will parse arguments in the same way as every other UNIX utility. If you roll your own parsing code, you’ll almost certainly break that expectation in obvious or subtle ways.

Although the documentation claims that optparse has been deprecated in favor of argparse, which supports more features like optional option arguments and configurable prefix characters, I can’t recommend argparse until it’s been fixed to parse required option arguments in the standard UNIX way. Currently, argparse uses an unexpected heuristic which may lead to subtle bugs in other scripts that call your program.

consider also click (which uses the optparse behavior)
q-n-a  qra  oly  best-practices  programming  terminal  unix  python  libraries  protocol  gotchas  howto  pls  yak-shaving  integration-extension 
august 2017 by nhaliday
Links 6/15: URLing Toward Freedom | Slate Star Codex
Why do some schools produce a disproportionate share of math competition winners? May not just be student characteristics.

My post The Control Group Is Out Of Control, as well as some of the Less Wrong posts that inspired it, has gotten cited in a recent preprint article, A Skeptical Eye On Psi, on what psi can teach us about the replication crisis. One of the authors is someone I previously yelled at, so I like to think all of that yelling is having a positive effect.

A study from Sweden (it’s always Sweden) does really good work examining the effect of education on IQ. It takes an increase in mandatory Swedish schooling length which was rolled out randomly at different times in different districts, and finds that the districts where people got more schooling have higher IQ; in particular, an extra year of education increases permanent IQ by 0.75 points. I was previously ambivalent about this, but this is a really strong study and I guess I have to endorse it now (though it’s hard to say how g-loaded it is or how linear it is). Also of note; the extra schooling permanently harmed emotional control ability by 0.5 points on a scale identical to IQ (mean 100, SD 15). This is of course the opposite of past studies suggest that education does not improve IQ but does help non-cognitive factors. But this study was an extra year tacked on to the end of education, whereas earlier ones have been measuring extra education tacked on to the beginning, or just making the whole educational process more efficient. Still weird, but again, this is a good experiment (EDIT: This might not be on g)
ratty  yvain  ssc  links  commentary  study  summary  economics  education  oly  math  success  tails  endo-exo  roots  causation  regularizer  environmental-effects  psychology  social-psych  replication  social-science  europe  nordic  iq  cog-psych  intervention  effect-size  marginal  tradeoffs  cost-benefit  large-factor  multi  personality  serene  growth  stress  psych-architecture  emotion  endogenous-exogenous 
march 2017 by nhaliday

« earlier    

related tags

2013  2016-election  abstraction  academia  accretion  acm  additive-combo  advice  age-generation  aggregator  ai  akrasia  alg-combo  algebra  algorithms  ama  amt  analysis  announcement  aphorism  applications  arrows  atoms  automation  axioms  bare-hands  barons  best-practices  better-explained  bias-variance  big-list  big-picture  binomial  biodet  bitcoin  blog  books  boolean-analysis  brexit  brunn-minkowski  business  c(pp)  calculation  caltech  canada  cartoons  causation  characterization  chart  cheatsheet  checklists  clarity  clever-rats  closure  cmu  coarse-fine  coding-theory  cog-psych  coloring  combo-optimization  commentary  commutativity  comparison  complexity  computation  concentration-of-measure  concept  conceptual-vocab  contradiction  convergence  convexity-curvature  cool  core-rats  cost-benefit  counterexample  course  crime  critique  crooked  crypto  cryptocurrency  cs  curiosity  curvature  data-science  data-structures  database  dataviz  debt  debugging  decision-making  deep-learning  deepgoog  definition  dennett  dependence-independence  design  devtools  differential  dimensionality  discrete  discussion  distribution  divide-and-conquer  documentation  duty  dynamic  dynamical  economics  education  effect-size  emotion  endo-exo  endogenous-exogenous  engineering  ensembles  environmental-effects  epistemic  erdos  error  estimate  europe  evergreen  examples  expert-experience  expert  explanation  exposition  extratricky  extrema  facebook  fedja  fields  finance  finiteness  fixed-point  flexibility  foreign-lang  fourier  frontier  games  gender-diff  gender  geometry  gotchas  government  gowers  graph-theory  graphs  ground-up  growth  hanson  hashing  heuristic  hi-order-bits  high-dimension  history  howto  identity  impact  induction  info-dynamics  info-foraging  information-theory  inner-product  insight  integration-extension  intersection-connectedness  intersection  intervention  intricacy  intuition  invariance  investing  iq  jargon  journal  knowledge  large-factor  learning  lecture-notes  lens  lesswrong  levers  libraries  limits  linear-algebra  links  list  logic  long-short-run  machine-learning  magazine  magnitude  male-variability  manifolds  map-territory  marginal  markov  matching  math.ac  math.ag  math.at  math.ca  math.co  math.ct  math.cv  math.fa  math.gn  math.gr  math.mg  math.nt  math.rt  math  mathtariat  matrix-factorization  measure  media  meta:research  meta:rhetoric  metabuch  metameta  methodology  metrics  michael-nielsen  mihai  mit  models  moments  money  monotonicity  motivation  multi  multiplicative  naturality  neurons  news  nibble  nonlinearity  nordic  norms  notetaking  novelty  occam  off-convex  oly-programming  open-problems  optimization  orders  orfe  org:biz  org:bleg  org:bv  org:mag  organization  orourke  outcome-risk  overflow  oxbridge  p:**  p:whenever  pdf  people  personal-finance  personality  persuasion  physics  pigeonhole-markov  plots  pls  poast  politics  polynomials  positivity  postmortem  pragmatic  prediction  pro-rata  probabilistic-method  probability  problem-solving  productivity  profile  programming  proof-systems  proofs  protocol  psych-architecture  psychology  psychometrics  puzzles  python  q-n-a  qra  quantum-info  quantum  questions  quixotic  rand-approx  random-matrices  random  rationality  ratty  reading  realness  rec-math  recommendations  reference  reflection  regression-to-mean  regression  regularity  regularizer  reinforcement  replication  research  retention  rhetoric  rigidity  rigorous-crypto  roadmap  roots  russia  ryan-odonnell  s:**  s:*  s:null  scholar  scitariat  seminar  separation  sequential  serene  series  shift  signum  simplex  singularity  skeleton  smoothness  social-choice  social-psych  social-science  social  soft-question  software  space-complexity  spatial  spectral  ssc  stackex  state-of-art  stats  status  stream  stress  strings  structure  study  studying  subculture  sublinear  success  summary  sv  symmetry  synthesis  tails  tcs  tcstariat  tech  techtariat  tensors  terminal  tetlock  texas  the-prices  the-trenches  things  thinking  tidbits  time-preference  time  toolkit  tools  top-n  topology  toxoplasmosis  track-record  tradeoffs  trees  tricki  tricks  trivia  trump  turing  uniqueness  unit  unix  usaco-ioi  vague  visual-understanding  visualization  west-hunter  wiki  wire-guided  wisdom  wormholes  yak-shaving  yoga  yvain  zooming  👳  🖥  🤖 

Copy this bookmark:



description:


tags: