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A VERY BRIEF REVIEW OF MEASURE THEORY
A brief philosophical discussion:
Measure theory, as much as any branch of mathematics, is an area where it is important to be acquainted with the basic notions and statements, but not desperately important to be acquainted with the detailed proofs, which are often rather unilluminating. One should always have in a mind a place where one could go and look if one ever did need to understand a proof: for me, that place is Rudin’s Real and Complex Analysis (Rudin’s “red book”).
gowers  pdf  math  math.CA  math.FA  philosophy  measure  exposition  synthesis  big-picture  hi-order-bits  ergodic  ground-up  summary  roadmap  mathtariat  proofs  nibble  unit  integral  zooming  p:whenever 
february 2017 by nhaliday
Shtetl-Optimized » Blog Archive » Logicians on safari
So what are they then? Maybe it’s helpful to think of them as “quantitative epistemology”: discoveries about the capacities of finite beings like ourselves to learn mathematical truths. On this view, the theoretical computer scientist is basically a mathematical logician on a safari to the physical world: someone who tries to understand the universe by asking what sorts of mathematical questions can and can’t be answered within it. Not whether the universe is a computer, but what kind of computer it is! Naturally, this approach to understanding the world tends to appeal most to people for whom math (and especially discrete math) is reasonably clear, whereas physics is extremely mysterious.

the sequel: http://www.scottaaronson.com/blog/?p=153
tcstariat  aaronson  tcs  computation  complexity  aphorism  examples  list  reflection  philosophy  multi  summary  synthesis  hi-order-bits  interdisciplinary  lens  big-picture  survey  nibble  org:bleg  applications  big-surf  s:*  p:whenever  ideas  elegance 
january 2017 by nhaliday
Home Page << Autobiographical writing software designed to stimulate psychological growth; Self Authoring
http://well.blogs.nytimes.com/2015/01/19/writing-your-way-to-happiness/

http://www.overcomingbias.com/2011/12/easy-job-fix.html
I’ve been slowly working my way through Triver’s book Folly of Fools. Chapter six reviews the many amazing benefits that appear to arise from having people write about their troubles. For example:

>Writing about job loss improves one’s chance of reemployment. This sort of writing appears to be cathartic – people immediately feel better. More striking, at least in one study, is a sharply increased chance of getting a job. After six months, 53 percent of writers had found a new job, compared with only 18 percent of non writers. One effect of writing is that it helps you work through your anger so it is not displaced onto a new, prospective employer or, indeed, revealed to the employer in any form.

...

This suggests an easy way to increase employment, at least if the problem is employee attitudes. Digging more, I found this ’01 review, which seems to confirm the benefits of writing therapy. It all does seem a bit hard to believe, but stranger things have been true.

https://www.lesswrong.com/posts/o7nRiBP9W8xR5E4v5/meta-analysis-of-writing-therapy

Not Learning From Failure—the Greatest Failure of All: https://journals.sagepub.com/doi/abs/10.1177/0956797619881133
Our society celebrates failure as a teachable moment. Yet in five studies (total N = 1,674), failure did the opposite: It undermined learning.
...
Why does failure undermine learning? Failure is ego threatening, which causes people to tune out. Participants learned less from personal failure than from personal success, yet they learned just as much from other people’s failure as from others’ success. Thus, when ego concerns are muted, people tune in and learn from failure.
psychology  thinking  growth  productivity  reflection  lifehack  skunkworks  akrasia  money-for-time  habit  discipline  cog-psych  hmm  multi  org:rec  meaningness  optimate  decision-making  clarity  the-monster  org:health  🦉  humility  virtu  prioritizing  p:**  p:whenever  self-control  allodium  wire-guided  spearhead  volo-avolo  bootstraps  quixotic  albion  canada  journos-pundits  ratty  hanson  lesswrong  commentary  gwern  analysis  critique  effect-size  cost-benefit  career  intervention  solid-study  psycho-atoms  grokkability-clarity  failure  study  social-psych 
july 2016 by nhaliday
Talagrand’s concentration inequality | What's new
Proposition 1 follows easily from the following statement, that asserts that if a convex set {A \subset {\bf R}^n} occupies a non-trivial fraction of the cube {\{-1,+1\}^n}, then the neighbourhood {A_t := \{ x \in {\bf R}^n: \hbox{dist}(x,A) \leq t \}} will occupy almost all of the cube for {t \gg 1}:
exposition  math.CA  math  gowers  concentration-of-measure  mathtariat  random-matrices  levers  estimate  probability  math.MG  geometry  boolean-analysis  nibble  org:bleg  high-dimension  p:whenever  dimensionality  curvature  convexity-curvature 
may 2016 by nhaliday

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