recentpopularlog in

nhaliday : hi-order-bits   144

« earlier  
What do executives do, anyway? - apenwarr
To paraphrase the book, the job of an executive is: to define and enforce culture and values for their whole organization, and to ratify good decisions.

That's all.

Not to decide. Not to break ties. Not to set strategy. Not to be the expert on every, or any topic. Just to sit in the room while the right people make good decisions in alignment with their values. And if they do, to endorse it. And if they don't, to send them back to try again.

There's even an algorithm for this.
techtariat  business  sv  tech  entrepreneurialism  management  startups  books  review  summary  culture  info-dynamics  strategy  hi-order-bits  big-picture  thinking  checklists  top-n  responsibility  organizing 
september 2019 by nhaliday
Philip Guo - A Five-Minute Guide to Ph.D. Program Applications
If you spend five minutes reading this article, you'll learn how to make your Ph.D. program application the strongest possible. Why five minutes? Because it's probably the longest that anyone will spend reading your application.
techtariat  grad-school  phd  advice  transitions  career  progression  hi-order-bits  cs  init 
september 2019 by nhaliday
Unix philosophy - Wikipedia
1. Make each program do one thing well. To do a new job, build afresh rather than complicate old programs by adding new "features".
2. Expect the output of every program to become the input to another, as yet unknown, program. Don't clutter output with extraneous information. Avoid stringently columnar or binary input formats. Don't insist on interactive input.
3. Design and build software, even operating systems, to be tried early, ideally within weeks. Don't hesitate to throw away the clumsy parts and rebuild them.
4. Use tools in preference to unskilled help to lighten a programming task, even if you have to detour to build the tools and expect to throw some of them out after you've finished using them.
wiki  concept  philosophy  lens  ideas  design  system-design  programming  engineering  systems  unix  subculture  composition-decomposition  coupling-cohesion  metabuch  skeleton  hi-order-bits  summary  list  top-n  quotes  aphorism  minimalism  minimum-viable  best-practices  intricacy  parsimony  protocol-metadata 
august 2019 by nhaliday
What's the expected level of paper for top conferences in Computer Science - Academia Stack Exchange
Top. The top level.

My experience on program committees for STOC, FOCS, ITCS, SODA, SOCG, etc., is that there are FAR more submissions of publishable quality than can be accepted into the conference. By "publishable quality" I mean a well-written presentation of a novel, interesting, and non-trivial result within the scope of the conference.

...

There are several questions that come up over and over in the FOCS/STOC review cycle:

- How surprising / novel / elegant / interesting is the result?
- How surprising / novel / elegant / interesting / general are the techniques?
- How technically difficult is the result? Ironically, FOCS and STOC committees have a reputation for ignoring the distinction between trivial (easy to derive from scratch) and nondeterministically trivial (easy to understand after the fact).
- What is the expected impact of this result? Is this paper going to change the way people do theoretical computer science over the next five years?
- Is the result of general interest to the theoretical computer science community? Or is it only of interest to a narrow subcommunity? In particular, if the topic is outside the STOC/FOCS mainstream—say, for example, computational topology—does the paper do a good job of explaining and motivating the results to a typical STOC/FOCS audience?
nibble  q-n-a  overflow  academia  tcs  cs  meta:research  publishing  scholar  lens  properties  cost-benefit  analysis  impetus  increase-decrease  soft-question  motivation  proofs  search  complexity  analogy  problem-solving  elegance  synthesis  hi-order-bits  novelty  discovery 
june 2019 by nhaliday
Information Processing: Moore's Law and AI
Hint to technocratic planners: invest more in physicists, chemists, and materials scientists. The recent explosion in value from technology has been driven by physical science -- software gets way too much credit. From the former we got a factor of a million or more in compute power, data storage, and bandwidth. From the latter, we gained (perhaps) an order of magnitude or two in effectiveness: how much better are current OSes and programming languages than Unix and C, both of which are ~50 years old now?

...

Of relevance to this discussion: a big chunk of AlphaGo's performance improvement over other Go programs is due to raw compute power (link via Jess Riedel). The vertical axis is ELO score. You can see that without multi-GPU compute, AlphaGo has relatively pedestrian strength.
hsu  scitariat  comparison  software  hardware  performance  sv  tech  trends  ai  machine-learning  deep-learning  deepgoog  google  roots  impact  hard-tech  multiplicative  the-world-is-just-atoms  technology  trivia  cocktail  big-picture  hi-order-bits 
may 2019 by nhaliday
Reverse salients | West Hunter
Edison thought in terms of reverse salients and critical problems.

“Reverse salients are areas of research and development that are lagging in some obvious way behind the general line of advance. Critical problems are the research questions, cast in terms of the concrete particulars of currently available knowledge and technique and of specific exemplars or models that are solvable and whose solutions would eliminate the reverse salients. ”

What strikes you as as important current example of a reverse salient, and the associated critical problem or problems?
west-hunter  scitariat  discussion  science  technology  innovation  low-hanging  list  top-n  research  open-problems  the-world-is-just-atoms  marginal  definite-planning  frontier  🔬  speedometer  ideas  the-trenches  hi-order-bits  prioritizing  judgement 
may 2019 by nhaliday
Theory of Self-Reproducing Automata - John von Neumann
Fourth Lecture: THE ROLE OF HIGH AND OF EXTREMELY HIGH COMPLICATION

Comparisons between computing machines and the nervous systems. Estimates of size for computing machines, present and near future.

Estimates for size for the human central nervous system. Excursus about the “mixed” character of living organisms. Analog and digital elements. Observations about the “mixed” character of all componentry, artificial as well as natural. Interpretation of the position to be taken with respect to these.

Evaluation of the discrepancy in size between artificial and natural automata. Interpretation of this discrepancy in terms of physical factors. Nature of the materials used.

The probability of the presence of other intellectual factors. The role of complication and the theoretical penetration that it requires.

Questions of reliability and errors reconsidered. Probability of individual errors and length of procedure. Typical lengths of procedure for computing machines and for living organisms--that is, for artificial and for natural automata. Upper limits on acceptable probability of error in individual operations. Compensation by checking and self-correcting features.

Differences of principle in the way in which errors are dealt with in artificial and in natural automata. The “single error” principle in artificial automata. Crudeness of our approach in this case, due to the lack of adequate theory. More sophisticated treatment of this problem in natural automata: The role of the autonomy of parts. Connections between this autonomy and evolution.

- 10^10 neurons in brain, 10^4 vacuum tubes in largest computer at time
- machines faster: 5 ms from neuron potential to neuron potential, 10^-3 ms for vacuum tubes

https://en.wikipedia.org/wiki/John_von_Neumann#Computing
pdf  article  papers  essay  nibble  math  cs  computation  bio  neuro  neuro-nitgrit  scale  magnitude  comparison  acm  von-neumann  giants  thermo  phys-energy  speed  performance  time  density  frequency  hardware  ems  efficiency  dirty-hands  street-fighting  fermi  estimate  retention  physics  interdisciplinary  multi  wiki  links  people  🔬  atoms  duplication  iteration-recursion  turing  complexity  measure  nature  technology  complex-systems  bits  information-theory  circuits  robust  structure  composition-decomposition  evolution  mutation  axioms  analogy  thinking  input-output  hi-order-bits  coding-theory  flexibility  rigidity  automata-languages 
april 2018 by nhaliday
National Defense Strategy of the United States of America
National Defense Strategy released with clear priority: Stay ahead of Russia and China: https://www.defensenews.com/breaking-news/2018/01/19/national-defense-strategy-released-with-clear-priority-stay-ahead-of-russia-and-china/

https://twitter.com/AngloRemnant/status/985341571410341893
https://archive.is/RhBdG
https://archive.is/wRzRN
A saner allocation of US 'defense' funds would be something like 10% nuclear trident, 10% border patrol, & spend the rest innoculating against cyber & biological attacks.
and since the latter 2 are hopeless, just refund 80% of the defense budget.
--
Monopoly on force at sea is arguably worthwhile.
--
Given the value of the US market to any would-be adversary, id be willing to roll the dice & let it ride.
--
subs are part of the triad, surface ships are sitting ducks this day and age
--
But nobody does sink them, precisely because of the monopoly on force. It's a path-dependent equilibirum where (for now) no other actor can reap the benefits of destabilizing the monopoly, and we're probably drastically underestimating the ramifications if/when it goes away.
--
can lethal autonomous weapon systems get some
pdf  white-paper  org:gov  usa  government  trump  policy  nascent-state  foreign-policy  realpolitik  authoritarianism  china  asia  russia  antidemos  military  defense  world  values  enlightenment-renaissance-restoration-reformation  democracy  chart  politics  current-events  sulla  nuclear  arms  deterrence  strategy  technology  sky  oceans  korea  communism  innovation  india  europe  EU  MENA  multi  org:foreign  war  great-powers  thucydides  competition  twitter  social  discussion  backup  gnon  🐸  markets  trade  nationalism-globalism  equilibrium  game-theory  tactics  top-n  hi-order-bits  security  hacker  biotech  terrorism  disease  parasites-microbiome  migration  walls  internet 
january 2018 by nhaliday
What are the Laws of Biology?
The core finding of systems biology is that only a very small subset of possible network motifs is actually used and that these motifs recur in all kinds of different systems, from transcriptional to biochemical to neural networks. This is because only those arrangements of interactions effectively perform some useful operation, which underlies some necessary function at a cellular or organismal level. There are different arrangements for input summation, input comparison, integration over time, high-pass or low-pass filtering, negative auto-regulation, coincidence detection, periodic oscillation, bistability, rapid onset response, rapid offset response, turning a graded signal into a sharp pulse or boundary, and so on, and so on.

These are all familiar concepts and designs in engineering and computing, with well-known properties. In living organisms there is one other general property that the designs must satisfy: robustness. They have to work with noisy components, at a scale that’s highly susceptible to thermal noise and environmental perturbations. Of the subset of designs that perform some operation, only a much smaller subset will do it robustly enough to be useful in a living organism. That is, they can still perform their particular functions in the face of noisy or fluctuating inputs or variation in the number of components constituting the elements of the network itself.
scitariat  reflection  proposal  ideas  thinking  conceptual-vocab  lens  bio  complex-systems  selection  evolution  flux-stasis  network-structure  structure  composition-decomposition  IEEE  robust  signal-noise  perturbation  interdisciplinary  graphs  circuits  🌞  big-picture  hi-order-bits  nibble  synthesis 
november 2017 by nhaliday
What is the connection between special and general relativity? - Physics Stack Exchange
Special relativity is the "special case" of general relativity where spacetime is flat. The speed of light is essential to both.
nibble  q-n-a  overflow  physics  relativity  explanation  synthesis  hi-order-bits  ground-up  gravity  summary  aphorism  differential  geometry 
november 2017 by nhaliday
What is the difference between general and special relativity? - Quora
General Relativity is, quite simply, needed to explain gravity.

Special Relativity is the special case of GR, when the metric is flat — which means no gravity.

You need General Relativity when the metric gets all curvy, and when things start to experience gravitation.
nibble  q-n-a  qra  explanation  physics  relativity  synthesis  hi-order-bits  ground-up  gravity  summary  aphorism  differential  geometry 
november 2017 by nhaliday
If Quantum Computers are not Possible Why are Classical Computers Possible? | Combinatorics and more
As most of my readers know, I regard quantum computing as unrealistic. You can read more about it in my Notices AMS paper and its extended version (see also this post) and in the discussion of Puzzle 4 from my recent puzzles paper (see also this post). The amazing progress and huge investment in quantum computing (that I presented and update  routinely in this post) will put my analysis to test in the next few years.
tcstariat  mathtariat  org:bleg  nibble  tcs  cs  computation  quantum  volo-avolo  no-go  contrarianism  frontier  links  quantum-info  analogy  comparison  synthesis  hi-order-bits  speedometer  questions  signal-noise 
november 2017 by nhaliday
The Constitutional Economics of Autocratic Succession on JSTOR
Abstract. The paper extends and empirically tests Gordon Tullock’s public choice theory of the nature of autocracy. A simple model of the relationship between constitutional rules governing succession in autocratic regimes and the occurrence of coups against autocrats is sketched. The model is applied to a case study of coups against monarchs in Denmark in the period ca. 935–1849. A clear connection is found between the specific constitutional rules governing succession and the frequency of coups. Specifically, the introduction of automatic hereditary succession in an autocracy provides stability and limits the number of coups conducted by contenders.

Table 2. General constitutional rules of succession, Denmark ca. 935–1849

To see this the data may be divided into three categories of constitutional rules of succession: One of open succession (for the periods 935–1165 and 1326–40), one of appointed succession combined with election (for the periods 1165–1326 and 1340–1536), and one of more or less formalized hereditary succession (1536–1849). On the basis of this categorization the data have been summarized in Table 3.

validity of empirics is a little sketchy

https://twitter.com/GarettJones/status/922103073257824257
https://archive.is/NXbdQ
The graphic novel it is based on is insightful, illustrates Tullock's game-theoretic, asymmetric information views on autocracy.

Conclusions from Gorton Tullock's book Autocracy, p. 211-215.: https://astro.temple.edu/~bstavis/courses/tulluck.htm
study  polisci  political-econ  economics  cracker-econ  big-peeps  GT-101  info-econ  authoritarianism  antidemos  government  micro  leviathan  elite  power  institutions  garett-jones  multi  econotariat  twitter  social  commentary  backup  art  film  comics  fiction  competition  europe  nordic  empirical  evidence-based  incentives  legacy  peace-violence  order-disorder  🎩  organizing  info-dynamics  history  medieval  law  axioms  stylized-facts  early-modern  data  longitudinal  flux-stasis  shift  revolution  correlation  org:junk  org:edu  summary  military  war  top-n  hi-order-bits  feudal  democracy  sulla  leadership  nascent-state  protocol-metadata 
october 2017 by nhaliday
“Editor’s Introduction to The New Economic History and the Industrial Revolution,” J. Mokyr (1998) | A Fine Theorem
I taught a fun three hours on the Industrial Revolution in my innovation PhD course this week. The absolutely incredible change in the condition of mankind that began in a tiny corner of Europe in an otherwise unremarkable 70-or-so years is totally fascinating. Indeed, the Industrial Revolution and its aftermath are so important to human history that I find it strange that we give people PhDs in social science without requiring at least some study of what happened.

My post today draws heavily on Joel Mokyr’s lovely, if lengthy, summary of what we know about the period. You really should read the whole thing, but if you know nothing about the IR, there are really five facts of great importance which you should be aware of.

1) The world was absurdly poor from the dawn of mankind until the late 1800s, everywhere.
2) The average person did not become richer, nor was overall economic growth particularly spectacular, during the Industrial Revolution; indeed, wages may have fallen between 1760 and 1830.
3) Major macro inventions, and growth, of the type seen in England in the late 1700s and early 1800s happened many times in human history.
4) It is hard for us today to understand how revolutionary ideas like “experimentation” or “probability” were.
5) The best explanations for “why England? why in the late 1700s? why did growth continue?” do not involve colonialism, slavery, or famous inventions.
econotariat  broad-econ  economics  growth-econ  cjones-like  summary  divergence  industrial-revolution  list  top-n  mokyr-allen-mccloskey  hi-order-bits  aphorism  wealth  wealth-of-nations  malthus  revolution  innovation  the-trenches  science  europe  the-great-west-whale  britain  conceptual-vocab  history  early-modern  technology  long-short-run  econ-metrics  data  time-series  conquest-empire  india  asia  scale  attaq  enlightenment-renaissance-restoration-reformation  roots  cycles  flux-stasis  whiggish-hegelian 
october 2017 by nhaliday
Benedict Evans on Twitter: ""University can save you from the autodidact tendency to overrate himself. Democracy depends on people who know they don’t know everything.""
“The autodidact’s risk is that they think they know all of medieval history but have never heard of Charlemagne” - Umberto Eco

Facts are the least part of education. The structure and priorities they fit into matters far more, and learning how to learn far more again
techtariat  sv  twitter  social  discussion  rhetoric  info-foraging  learning  education  higher-ed  academia  expert  lens  aphorism  quotes  hi-order-bits  big-picture  synthesis  expert-experience 
october 2017 by nhaliday
New Theory Cracks Open the Black Box of Deep Learning | Quanta Magazine
A new idea called the “information bottleneck” is helping to explain the puzzling success of today’s artificial-intelligence algorithms — and might also explain how human brains learn.

sounds like he's just talking about autoencoders?
news  org:mag  org:sci  popsci  announcement  research  deep-learning  machine-learning  acm  information-theory  bits  neuro  model-class  big-surf  frontier  nibble  hmm  signal-noise  deepgoog  expert  ideas  wild-ideas  summary  talks  video  israel  roots  physics  interdisciplinary  ai  intelligence  shannon  giants  arrows  preimage  lifts-projections  composition-decomposition  characterization  markov  gradient-descent  papers  liner-notes  experiment  hi-order-bits  generalization  expert-experience  explanans  org:inst  speedometer 
september 2017 by nhaliday
All models are wrong - Wikipedia
Box repeated the aphorism in a paper that was published in the proceedings of a 1978 statistics workshop.[2] The paper contains a section entitled "All models are wrong but some are useful". The section is copied below.

Now it would be very remarkable if any system existing in the real world could be exactly represented by any simple model. However, cunningly chosen parsimonious models often do provide remarkably useful approximations. For example, the law PV = RT relating pressure P, volume V and temperature T of an "ideal" gas via a constant R is not exactly true for any real gas, but it frequently provides a useful approximation and furthermore its structure is informative since it springs from a physical view of the behavior of gas molecules.

For such a model there is no need to ask the question "Is the model true?". If "truth" is to be the "whole truth" the answer must be "No". The only question of interest is "Is the model illuminating and useful?".
thinking  metabuch  metameta  map-territory  models  accuracy  wire-guided  truth  philosophy  stats  data-science  methodology  lens  wiki  reference  complex-systems  occam  parsimony  science  nibble  hi-order-bits  info-dynamics  the-trenches  meta:science  physics  fluid  thermo  stat-mech  applicability-prereqs  theory-practice  elegance  simplification-normalization 
august 2017 by nhaliday
Introduction to Scaling Laws
https://betadecay.wordpress.com/2009/10/02/the-physics-of-scaling-laws-and-dimensional-analysis/
http://galileo.phys.virginia.edu/classes/304/scaling.pdf

Galileo’s Discovery of Scaling Laws: https://www.mtholyoke.edu/~mpeterso/classes/galileo/scaling8.pdf
Days 1 and 2 of Two New Sciences

An example of such an insight is “the surface of a small solid is comparatively greater than that of a large one” because the surface goes like the square of a linear dimension, but the volume goes like the cube.5 Thus as one scales down macroscopic objects, forces on their surfaces like viscous drag become relatively more important, and bulk forces like weight become relatively less important. Galileo uses this idea on the First Day in the context of resistance in free fall, as an explanation for why similar objects of different size do not fall exactly together, but the smaller one lags behind.
nibble  org:junk  exposition  lecture-notes  physics  mechanics  street-fighting  problem-solving  scale  magnitude  estimate  fermi  mental-math  calculation  nitty-gritty  multi  scitariat  org:bleg  lens  tutorial  guide  ground-up  tricki  skeleton  list  cheatsheet  identity  levers  hi-order-bits  yoga  metabuch  pdf  article  essay  history  early-modern  europe  the-great-west-whale  science  the-trenches  discovery  fluid  architecture  oceans  giants  tidbits  elegance 
august 2017 by nhaliday
A sense of where you are | West Hunter
Nobody at the Times noticed it at first. I don’t know that they ever did notice it by themselves- likely some reader brought it to their attention. But this happens all the time, because very few people have a picture of the world in their head that includes any numbers. Mostly they don’t even have a rough idea of relative size.

In much the same way, back in the 1980s,lots of writers were talking about 90,000 women a year dying of anorexia nervosa, another impossible number. Then there was the great scare about 1,000,000 kids being kidnapped in the US each year – also impossible and wrong. Practically all the talking classes bought into it.

You might think that the people at the top are different – but with a few exceptions, they’re just as clueless.
west-hunter  scitariat  commentary  discussion  reflection  bounded-cognition  realness  nitty-gritty  calculation  fermi  quantitative-qualitative  stories  street-fighting  mental-math  being-right  info-dynamics  knowledge  hi-order-bits  scale  dysgenics  drugs  death  coming-apart  opioids  elite  ability-competence  rant  decision-making 
may 2017 by nhaliday
New studies show the cost of student laptop use in lecture classes - Daniel Willingham
In-lecture media use and academic performance: Does subject area matter: http://www.sciencedirect.com/science/article/pii/S0747563217304983
The study found that while a significant negative correlation exists between in-lecture media use and academic performance for students in the Arts and Social Sciences, the same pattern is not observable for students in the faculties of Engineering, Economic and Management Sciences, and Medical and Health Sciences.

hmm

Why you should take notes by hand — not on a laptop: https://www.vox.com/2014/6/4/5776804/note-taking-by-hand-versus-laptop
Presumably, they're using the computers to take notes, so they better remember the course material. But new research shows that if learning is their goal, using a laptop during class is a terrible idea.

It's not just because internet-connected laptops are so distracting. It's because even if students aren't distracted, the act of taking notes on a computer actually seems to interfere with their ability to remember information.

Pam Mueller and Daniel Oppenheimer, the psychologists who conducted the new research, believe it's because students on laptops usually just mindlessly type everything a professor says. Those taking notes by hand, though, have to actively listen and decide what's important — because they generally can't write fast enough to get everything down — which ultimately helps them learn.

The Pen Is Mightier Than the Keyboard: Advantages of Longhand Over Laptop Note Taking: https://linguistics.ucla.edu/people/hayes/Teaching/papers/MuellerAndOppenheimer2014OnTakingNotesByHand.pdf
scitariat  education  higher-ed  learning  data  study  summary  intervention  internet  attention  field-study  effect-size  studying  regularizer  aversion  the-monster  multi  cost-benefit  notetaking  evidence-based  news  org:lite  org:data  hi-order-bits  synthesis  spreading  contiguity-proximity 
april 2017 by nhaliday
Paperscape
- includes physics, cs, etc.
- CS is _a lot_ smaller, or at least has much lower citation counts
- size = number citations, placement = citation network structure
papers  publishing  science  meta:science  data  visualization  network-structure  big-picture  dynamic  exploratory  🎓  physics  cs  math  hi-order-bits  survey  visual-understanding  preprint  aggregator  database  search  maps  zooming  metameta  scholar-pack  🔬  info-dynamics  scale  let-me-see  chart 
february 2017 by nhaliday
Information Processing: Learn to solve every problem that has been solved
While it may be impossible to achieve Feynman's goal, I'm surprised that more people don't attempt the importance threshold-modified version. Suppose we set the importance bar really, really high: what are the most important results that everyone should try to understand? Here's a very biased partial list: basic physics and mathematics (e.g., to the level of the Feynman Lectures); quantitative theory of genetics and evolution; information, entropy and probability; basic ideas about logic and computation (Godel and Turing?); ... What else? Dynamics of markets? Complex Systems? Psychometrics? Descriptive biology? Organic chemistry?
hsu  scitariat  feynman  giants  stories  aphorism  curiosity  interdisciplinary  frontier  signal-noise  top-n  discussion  caltech  problem-solving  big-picture  vitality  🎓  virtu  big-surf  courage  🔬  allodium  nietzschean  ideas  quixotic  accretion  learning  hi-order-bits 
february 2017 by nhaliday
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
What is the relationship between information theory and Coding theory? - Quora
basically:
- finite vs. asymptotic
- combinatorial vs. probabilistic (lotsa overlap their)
- worst-case (Hamming) vs. distributional (Shannon)

Information and coding theory most often appear together in the subject of error correction over noisy channels. Historically, they were born at almost exactly the same time - both Richard Hamming and Claude Shannon were working at Bell Labs when this happened. Information theory tends to heavily use tools from probability theory (together with an "asymptotic" way of thinking about the world), while traditional "algebraic" coding theory tends to employ mathematics that are much more finite sequence length/combinatorial in nature, including linear algebra over Galois Fields. The emergence in the late 90s and first decade of 2000 of codes over graphs blurred this distinction though, as code classes such as low density parity check codes employ both asymptotic analysis and random code selection techniques which have counterparts in information theory.

They do not subsume each other. Information theory touches on many other aspects that coding theory does not, and vice-versa. Information theory also touches on compression (lossy & lossless), statistics (e.g. large deviations), modeling (e.g. Minimum Description Length). Coding theory pays a lot of attention to sphere packing and coverings for finite length sequences - information theory addresses these problems (channel & lossy source coding) only in an asymptotic/approximate sense.
q-n-a  qra  math  acm  tcs  information-theory  coding-theory  big-picture  comparison  confusion  explanation  linear-algebra  polynomials  limits  finiteness  math.CO  hi-order-bits  synthesis  probability  bits  hamming  shannon  intricacy  nibble  s:null  signal-noise 
february 2017 by nhaliday
general topology - What should be the intuition when working with compactness? - Mathematics Stack Exchange
http://math.stackexchange.com/questions/485822/why-is-compactness-so-important

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

--

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

--

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

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

If A is finite then every sequence of members of A has a subsequence that is eventually constant, and "eventually constant" is the only kind of convergence you can talk about without talking about a topology on the set. If A is compact, then every sequence of members of A has a convergent subsequence.
q-n-a  overflow  math  topology  math.GN  concept  finiteness  atoms  intuition  oly  mathtariat  multi  discrete  gowers  motivation  synthesis  hi-order-bits  soft-question  limits  things  nibble  definition  convergence  abstraction  span-cover 
january 2017 by nhaliday
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
ho.history overview - Proofs that require fundamentally new ways of thinking - MathOverflow
my favorite:
Although this has already been said elsewhere on MathOverflow, I think it's worth repeating that Gromov is someone who has arguably introduced more radical thoughts into mathematics than anyone else. Examples involving groups with polynomial growth and holomorphic curves have already been cited in other answers to this question. I have two other obvious ones but there are many more.

I don't remember where I first learned about convergence of Riemannian manifolds, but I had to laugh because there's no way I would have ever conceived of a notion. To be fair, all of the groundwork for this was laid out in Cheeger's thesis, but it was Gromov who reformulated everything as a convergence theorem and recognized its power.

Another time Gromov made me laugh was when I was reading what little I could understand of his book Partial Differential Relations. This book is probably full of radical ideas that I don't understand. The one I did was his approach to solving the linearized isometric embedding equation. His radical, absurd, but elementary idea was that if the system is sufficiently underdetermined, then the linear partial differential operator could be inverted by another linear partial differential operator. Both the statement and proof are for me the funniest in mathematics. Most of us view solving PDE's as something that requires hard work, involving analysis and estimates, and Gromov manages to do it using only elementary linear algebra. This then allows him to establish the existence of isometric embedding of Riemannian manifolds in a wide variety of settings.
q-n-a  overflow  soft-question  big-list  math  meta:math  history  insight  synthesis  gowers  mathtariat  hi-order-bits  frontier  proofs  magnitude  giants  differential  geometry  limits  flexibility  nibble  degrees-of-freedom  big-picture  novelty  zooming  big-surf  wild-ideas  metameta  courage  convergence  ideas  innovation  the-trenches  discovery  creative  elegance 
january 2017 by nhaliday
Thinking Outside One’s Paradigm | Academically Interesting
I think that as a scientist (or really, even as a citizen) it is important to be able to see outside one’s own paradigm. I currently think that I do a good job of this, but it seems to me that there’s a big danger of becoming more entrenched as I get older. Based on the above experiences, I plan to use the following test: When someone asks me a question about my field, how often have I not thought about it before? How tempted am I to say, “That question isn’t interesting”? If these start to become more common, then I’ll know something has gone wrong.
ratty  clever-rats  academia  science  interdisciplinary  lens  frontier  thinking  rationality  meta:science  curiosity  insight  scholar  innovation  reflection  acmtariat  water  biases  heterodox  🤖  🎓  aging  meta:math  low-hanging  big-picture  hi-order-bits  flexibility  org:bleg  nibble  the-trenches  wild-ideas  metameta  courage  s:**  discovery  context  embedded-cognition  endo-exo  near-far  🔬  info-dynamics  allodium  ideas  questions  within-without  meta:research 
january 2017 by nhaliday
"Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character ... - Richard P. Feynman - Google Books
Actually, there was a certain amount of genuine quality to my guesses. I had a scheme, which I still use today when somebody is explaining something that l’m trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terrific theorem, and they’re all excited. As they’re telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball)—disjoint (two balls). Then the balls tum colors, grow hairs, or whatever, in my head as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, “False!"
physics  math  feynman  thinking  empirical  examples  lens  intuition  operational  stories  metabuch  visual-understanding  thurston  hi-order-bits  geometry  topology  cartoons  giants  👳  nibble  the-trenches  metameta  meta:math  s:**  quotes  gbooks  elegance 
january 2017 by nhaliday
soft question - Thinking and Explaining - MathOverflow
- 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 
january 2017 by nhaliday
« earlier      
per page:    204080120160

Copy this bookmark:





to read