nhaliday + cartoons   47

Antinomia Imediata – experiments in a reaction from the left
https://antinomiaimediata.wordpress.com/lrx/
So, what is the Left Reaction? First of all, it’s reaction: opposition to the modern rationalist establishment, the Cathedral. It opposes the universalist Jacobin program of global government, favoring a fractured geopolitics organized through long-evolved complex systems. It’s profoundly anti-socialist and anti-communist, favoring market economy and individualism. It abhors tribalism and seeks a realistic plan for dismantling it (primarily informed by HBD and HBE). It looks at modernity as a degenerative ratchet, whose only way out is intensification (hence clinging to crypto-marxist market-driven acceleration).

How come can any of this still be in the *Left*? It defends equality of power, i.e. freedom. This radical understanding of liberty is deeply rooted in leftist tradition and has been consistently abhored by the Right. LRx is not democrat, is not socialist, is not progressist and is not even liberal (in its current, American use). But it defends equality of power. It’s utopia is individual sovereignty. It’s method is paleo-agorism. The anti-hierarchy of hunter-gatherer nomads is its understanding of the only realistic objective of equality.

...

In more cosmic terms, it seeks only to fulfill the Revolution’s side in the left-right intelligence pump: mutation or creation of paths. Proudhon’s antinomy is essentially about this: the collective force of the socius, evinced in moral standards and social organization vs the creative force of the individuals, that constantly revolutionize and disrupt the social body. The interplay of these forces create reality (it’s a metaphysics indeed): the Absolute (socius) builds so that the (individualistic) Revolution can destroy so that the Absolute may adapt, and then repeat. The good old formula of ‘solve et coagula’.

Ultimately, if the Neoreaction promises eternal hell, the LRx sneers “but Satan is with us”.

https://antinomiaimediata.wordpress.com/2016/12/16/a-statement-of-principles/
Liberty is to be understood as the ability and right of all sentient beings to dispose of their persons and the fruits of their labor, and nothing else, as they see fit. This stems from their self-awareness and their ability to control and choose the content of their actions.

...

Equality is to be understood as the state of no imbalance of power, that is, of no subjection to another sentient being. This stems from their universal ability for empathy, and from their equal ability for reason.

...

It is important to notice that, contrary to usual statements of these two principles, my standpoint is that Liberty and Equality here are not merely compatible, meaning they could coexist in some possible universe, but rather they are two sides of the same coin, complementary and interdependent. There can be NO Liberty where there is no Equality, for the imbalance of power, the state of subjection, will render sentient beings unable to dispose of their persons and the fruits of their labor[1], and it will limit their ability to choose over their rightful jurisdiction. Likewise, there can be NO Equality without Liberty, for restraining sentient beings’ ability to choose and dispose of their persons and fruits of labor will render some more powerful than the rest, and establish a state of subjection.

https://antinomiaimediata.wordpress.com/2017/04/18/flatness/
equality is the founding principle (and ultimately indistinguishable from) freedom. of course, it’s only in one specific sense of “equality” that this sentence is true.

to try and eliminate the bullshit, let’s turn to networks again:

any nodes’ degrees of freedom is the number of nodes they are connected to in a network. freedom is maximum when the network is symmetrically connected, i. e., when all nodes are connected to each other and thus there is no topographical hierarchy (middlemen) – in other words, flatness.

in this understanding, the maximization of freedom is the maximization of entropy production, that is, of intelligence. As Land puts it:

https://antinomiaimediata.wordpress.com/category/philosophy/mutualism/
gnon  blog  stream  politics  polisci  ideology  philosophy  land  accelerationism  left-wing  right-wing  paradox  egalitarianism-hierarchy  civil-liberty  power  hmm  revolution  analytical-holistic  mutation  selection  individualism-collectivism  tribalism  us-them  modernity  multi  tradeoffs  network-structure  complex-systems  cybernetics  randy-ayndy  insight  contrarianism  metameta  metabuch  characterization  cooperate-defect  n-factor  altruism  list  coordination  graphs  visual-understanding  cartoons  intelligence  entropy-like  thermo  information-theory  order-disorder  decentralized  distribution  degrees-of-freedom  analogy  graph-theory  extrema  evolution  interdisciplinary  bio  differential  geometry  anglosphere  optimate  nascent-state  deep-materialism  new-religion  cool  mystic  the-classics  self-interest  interests  reason  volo-avolo  flux-stasis  invariance  government  markets  paying-rent  cost-benefit  peace-violence  frontier  exit-voice  nl-and-so-can-you  war  track-record  usa  history  mostly-modern  world-war  military  justice  protestant-cathol 
march 2018 by nhaliday
Drude model - Wikipedia
The Drude model of electrical conduction was proposed in 1900[1][2] by Paul Drude to explain the transport properties of electrons in materials (especially metals). The model, which is an application of kinetic theory, assumes that the microscopic behavior of electrons in a solid may be treated classically and looks much like _a pinball machine_, with a sea of constantly jittering electrons bouncing and re-bouncing off heavier, relatively immobile positive ions.

The two most significant results of the Drude model are an electronic equation of motion,

d<p(t)>/dt = q(E + 1/m <p(t)> x B) - <p(t)>/τ

and a linear relationship between current density J and electric field E,

J = (nq^2τ/m) E

latter is Ohm's law
nibble  physics  electromag  models  local-global  stat-mech  identity  atoms  wiki  reference  ground-up  cartoons 
september 2017 by nhaliday
In the first place | West Hunter
We hear a lot about innovative educational approaches, and since these silly people have been at this for a long time now, we hear just as often about the innovative approaches that some idiot started up a few years ago and are now crashing in flames.  We’re in steady-state.

I’m wondering if it isn’t time to try something archaic.  In particular, mnemonic techniques, such as the method of loci.  As far as I know, nobody has actually tried integrating the more sophisticated mnemonic techniques into a curriculum.  Sure, we all know useful acronyms, like the one for resistor color codes, but I’ve not heard of anyone teaching kids how to build a memory palace.

https://westhunt.wordpress.com/2013/12/28/in-the-first-place/#comment-20106
I have never used formal mnemonic techniques, but life has recently tested me on how well I remember material from my college days. Turns out that I can still do the sorts of math and physics problems that I could then, in subjects like classical mechanics, real analysis, combinatorics, complex variables, quantum mechanics, statistical mechanics, etc. I usually have to crack the book though. Some of that material I have used from time to time, or even fairly often (especially linear algebra), most not. I’m sure I’m slower than I was then, at least on the stuff I haven’t used.

https://westhunt.wordpress.com/2013/12/28/in-the-first-place/#comment-20109
Long-term memory capacity must be finite, but I know of no evidence that anyone has ever run out of it. As for the idea that you don’t really need a lot of facts in your head to come up with new ideas: pretty much the opposite of the truth, in a lot of fields.

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

Mental Imagery > Ancient Imagery Mnemonics: https://plato.stanford.edu/entries/mental-imagery/ancient-imagery-mnemonics.html
In the Middle Ages and the Renaissance, very elaborate versions of the method evolved, using specially learned imaginary spaces (Memory Theaters or Palaces), and complex systems of predetermined symbolic images, often imbued with occult or spiritual significances. However, modern experimental research has shown that even a simple and easily learned form of the method of loci can be highly effective (Ross & Lawrence, 1968; Maguire et al., 2003), as are several other imagery based mnemonic techniques (see section 4.2 of the main entry).

The advantages of organizing knowledge in terms of country and place: http://marginalrevolution.com/marginalrevolution/2018/02/advantages-organizing-knowledge-terms-country-place.html

https://www.quora.com/What-are-the-best-books-on-Memory-Palace

fascinating aside:
US vs Nazi army, Vietnam, the draft: https://westhunt.wordpress.com/2013/12/28/in-the-first-place/#comment-20136
You think I know more about this than a retired major general and former head of the War College? I do, of course, but that fact itself should worry you.

He’s not all wrong, but a lot of what he says is wrong. For example, the Germany Army was a conscript army, so conscription itself can’t explain why the Krauts were about 25% more effective than the average American unit. Nor is it true that the draft in WWII was corrupt.

The US had a different mix of armed forces – more air forces and a much larger Navy than Germany. Those services have higher technical requirements and sucked up a lot of the smarter guys. That was just a product of the strategic situation.

The Germans had better officers, partly because of better training and doctrine, partly the fruit of a different attitude towards the army. The US, much of the time, thought of the Army as a career for losers, but Germans did not.

The Germans had an enormous amount of relevant combat experience, much more than anyone in the US. Spend a year or two on the Eastern Front and you learn.

And the Germans had better infantry weapons.

The US tooth-to-tail ratio was , I think, worse than that of the Germans: some of that was a natural consequence of being an expeditionary force, but some was just a mistake. You want supply sergeants to be literate, but it is probably true that we put too many of the smarter guys into non-combat positions. That changed some when we ran into manpower shortages in late 1944 and combed out the support positions.

This guy is back-projecting Vietnam problems into WWII – he’s mostly wrong.

more (more of a focus on US Marines than Army): https://www.quora.com/Were-US-Marines-tougher-than-elite-German-troops-in-WW2/answer/Joseph-Scott-13
west-hunter  scitariat  speculation  ideas  proposal  education  learning  retention  neurons  the-classics  nitty-gritty  visuo  spatial  psych-architecture  multi  poast  history  mostly-modern  world-war  war  military  strategy  usa  europe  germanic  cold-war  visual-understanding  cartoons  narrative  wordlessness  comparison  asia  developing-world  knowledge  metabuch  econotariat  marginal-rev  discussion  world  thinking  government  local-global  humility  wire-guided  policy  iron-age  mediterranean  wiki  reference  checklists  exocortex  early-modern  org:edu  philosophy  enlightenment-renaissance-restoration-reformation  qra  q-n-a  books  recommendations  list  links  ability-competence  leadership  elite  higher-ed  math  physics  linear-algebra  cost-benefit  prioritizing  defense  martial  war-nerd 
may 2017 by nhaliday
254A, Supplement 4: Probabilistic models and heuristics for the primes (optional) | What's new
among others, the Cramér model for the primes (basically kinda looks like primality is independently distributed w/ Pr[n is prime] = 1/log n)
gowers  mathtariat  lecture-notes  exposition  math  math.NT  probability  heuristic  models  cartoons  nibble  org:bleg  pseudorandomness  borel-cantelli  concentration-of-measure  multiplicative  truth  guessing 
february 2017 by nhaliday
Oh, they were looking for their Missing Piece – spottedtoad
Assuming that the value of an offspring’s trait are determined by averaging the value of both parents and then adding some random error due to mutation or developmental noise, the ideal mate for each individual in the population isn’t the one that is closest to the ideal value, but one that is “complementary”- ie, equally distant from the ideal value, but from the opposite side.
ratty  unaffiliated  sapiens  evolution  sex  thinking  essay  genetic-load  speculation  spearhead  selection  models  equilibrium  parable  europe  mediterranean  history  literature  cartoons  wonkish  iron-age  myth  the-classics  assortative-mating  tails  extrema  matching  homo-hetero  complement-substitute  life-history  increase-decrease  signum  ecology  EGT 
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
pr.probability - What is convolution intuitively? - MathOverflow
I remember as a graduate student that Ingrid Daubechies frequently referred to convolution by a bump function as "blurring" - its effect on images is similar to what a short-sighted person experiences when taking off his or her glasses (and, indeed, if one works through the geometric optics, convolution is not a bad first approximation for this effect). I found this to be very helpful, not just for understanding convolution per se, but as a lesson that one should try to use physical intuition to model mathematical concepts whenever one can.

More generally, if one thinks of functions as fuzzy versions of points, then convolution is the fuzzy version of addition (or sometimes multiplication, depending on the context). The probabilistic interpretation is one example of this (where the fuzz is a a probability distribution), but one can also have signed, complex-valued, or vector-valued fuzz, of course.
q-n-a  overflow  math  concept  atoms  intuition  motivation  gowers  visual-understanding  aphorism  soft-question  tidbits  👳  mathtariat  cartoons  ground-up  metabuch  analogy  nibble  yoga  neurons  retrofit  optics  concrete  s:*  multiplicative  fourier 
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
gt.geometric topology - Intuitive crutches for higher dimensional thinking - MathOverflow
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 
december 2016 by nhaliday
The Castle and the Forest Sauvage – spottedtoad
So meritocracy might rule when it comes to who ends up nearer or further from the castle (or then it might again not), but it will never determine who is allowed to come over the drawbridge, in through the gate, and allowed to see the Castle’s inside.
thinking  ratty  government  speculation  parable  essay  unaffiliated  gedanken  metabuch  analogy  cartoons  wonkish  inequality  mobility  winner-take-all  managerial-state  s-factor  chart 
november 2016 by nhaliday
Why Information Grows – Paul Romer
thinking like a physicist:

The key element in thinking like a physicist is being willing to push simultaneously to extreme levels of abstraction and specificity. This sounds paradoxical until you see it in action. Then it seems obvious. Abstraction means that you strip away inessential detail. Specificity means that you take very seriously the things that remain.

Abstraction vs. Radical Specificity: https://paulromer.net/abstraction-vs-radical-specificity/
books  summary  review  economics  growth-econ  interdisciplinary  hmm  physics  thinking  feynman  tradeoffs  paul-romer  econotariat  🎩  🎓  scholar  aphorism  lens  signal-noise  cartoons  skeleton  s:**  giants  electromag  mutation  genetics  genomics  bits  nibble  stories  models  metameta  metabuch  problem-solving  composition-decomposition  structure  abstraction  zooming  examples  knowledge  human-capital  behavioral-econ  network-structure  info-econ  communication  learning  information-theory  applications  volo-avolo  map-territory  externalities  duplication  spreading  property-rights  lattice  multi  government  polisci  policy  counterfactual  insight  paradox  parallax  reduction  empirical  detail-architecture  methodology  crux  visual-understanding  theory-practice  matching  analytical-holistic  branches  complement-substitute  local-global  internet  technology  cost-benefit  investing  micro  signaling  limits  public-goodish  interpretation  elegance  meta:reading  intellectual-property  writing 
september 2016 by nhaliday
soft question - How do you not forget old math? - MathOverflow
Terry Tao:
I find that blogging about material that I would otherwise forget eventually is extremely valuable in this regard. (I end up consulting my own blog posts on a regular basis.) EDIT: and now I remember I already wrote on this topic: terrytao.wordpress.com/career-advice/write-down-what-youve-d‌​one

fedja:
The only way to cope with this loss of memory I know is to do some reading on systematic basis. Of course, if you read one paper in algebraic geometry (or whatever else) a month (or even two months), you may not remember the exact content of all of them by the end of the year but, since all mathematicians in one field use pretty much the same tricks and draw from pretty much the same general knowledge, you'll keep the core things in your memory no matter what you read (provided it is not patented junk, of course) and this is about as much as you can hope for.

Relating abstract things to "real life stuff" (and vice versa) is automatic when you work as a mathematician. For me, the proof of the Chacon-Ornstein ergodic theorem is just a sandpile moving over a pit with the sand falling down after every shift. I often tell my students that every individual term in the sequence doesn't matter at all for the limit but somehow together they determine it like no individual human is of any real importance while together they keep this civilization running, etc. No special effort is needed here and, moreover, if the analogy is not natural but contrived, it'll not be helpful or memorable. The standard mnemonic techniques are pretty useless in math. IMHO (the famous "foil" rule for the multiplication of sums of two terms is inferior to the natural "pair each term in the first sum with each term in the second sum" and to the picture of a rectangle tiled with smaller rectangles, though, of course, the foil rule sounds way more sexy).

One thing that I don't think the other respondents have emphasized enough is that you should work on prioritizing what you choose to study and remember.

Timothy Chow:
As others have said, forgetting lots of stuff is inevitable. But there are ways you can mitigate the damage of this information loss. I find that a useful technique is to try to organize your knowledge hierarchically. Start by coming up with a big picture, and make sure you understand and remember that picture thoroughly. Then drill down to the next level of detail, and work on remembering that. For example, if I were trying to remember everything in a particular book, I might start by memorizing the table of contents, and then I'd work on remembering the theorem statements, and then finally the proofs. (Don't take this illustration too literally; it's better to come up with your own conceptual hierarchy than to slavishly follow the formal hierarchy of a published text. But I do think that a hierarchical approach is valuable.)

Organizing your knowledge like this helps you prioritize. You can then consciously decide that certain large swaths of knowledge are not worth your time at the moment, and just keep a "stub" in memory to remind you that that body of knowledge exists, should you ever need to dive into it. In areas of higher priority, you can plunge more deeply. By making sure you thoroughly internalize the top levels of the hierarchy, you reduce the risk of losing sight of entire areas of important knowledge. Generally it's less catastrophic to forget the details than to forget about a whole region of the big picture, because you can often revisit the details as long as you know what details you need to dig up. (This is fortunate since the details are the most memory-intensive.)

Having a hierarchy also helps you accrue new knowledge. Often when you encounter something new, you can relate it to something you already know, and file it in the same branch of your mental tree.
thinking  math  growth  advice  expert  q-n-a  🎓  long-term  tradeoffs  scholar  overflow  soft-question  gowers  mathtariat  ground-up  hi-order-bits  intuition  synthesis  visual-understanding  decision-making  scholar-pack  cartoons  lens  big-picture  ergodic  nibble  zooming  trees  fedja  reflection  retention  meta:research  wisdom  skeleton  practice  prioritizing  concrete  s:***  info-dynamics  knowledge  studying  the-trenches  chart  expert-experience  quixotic  elegance  heavyweights 
june 2016 by nhaliday
Answer to What is it like to understand advanced mathematics? - Quora
thinking like a mathematician

some of the points:
- small # of tricks (echoes Rota)
- web of concepts and modularization (zooming out) allow quick reasoning
- comfort w/ ambiguity and lack of understanding, study high-dimensional objects via projections
- above is essential for research (and often what distinguishes research mathematicians from people who were good at math, or majored in math)
math  reflection  thinking  intuition  expert  synthesis  wormholes  insight  q-n-a  🎓  metabuch  tricks  scholar  problem-solving  aphorism  instinct  heuristic  lens  qra  soft-question  curiosity  meta:math  ground-up  cartoons  analytical-holistic  lifts-projections  hi-order-bits  scholar-pack  nibble  the-trenches  innovation  novelty  zooming  tricki  virtu  humility  metameta  wisdom  abstraction  skeleton  s:***  knowledge  expert-experience  elegance  judgement  advanced  heavyweights  guessing 
may 2016 by nhaliday

bundles : abstractspthinkingworrydream

related tags

:)  aaronson  ability-competence  abstraction  accelerationism  acm  additive  additive-combo  advanced  adversarial  advice  agriculture  ai  ai-control  algebra  alignment  allodium  altruism  amazon  analogy  analysis  analytical-holistic  anglosphere  anthropology  antidemos  aphorism  apollonian-dionysian  apple  applications  aristos  arrows  art  asia  assortative-mating  atmosphere  atoms  authoritarianism  axelrod  axioms  barons  bayesian  behavioral-econ  being-becoming  benevolence  best-practices  better-explained  biases  big-list  big-peeps  big-picture  big-surf  bio  biodet  bioinformatics  biotech  bits  blog  boltzmann  books  boolean-analysis  borel-cantelli  bounded-cognition  branches  brands  broad-econ  brunn-minkowski  business  business-models  california  cancer  canon  capital  capitalism  cartoons  characterization  chart  checklists  china  civil-liberty  clarity  class  classic  clever-rats  climate-change  closure  coarse-fine  coding-theory  cohesion  cold-war  collaboration  comics  commentary  communication  comparison  compensation  competition  compilers  complement-substitute  complex-systems  composition-decomposition  computation  computer-vision  concentration-of-measure  concept  conceptual-vocab  concrete  contrarianism  convexity-curvature  cool  cooperate-defect  coordination  correlation  cost-benefit  counter-revolution  counterexample  counterfactual  courage  course  creative  crime  crooked  crux  cs  cultural-dynamics  curiosity  curvature  cybernetics  cycles  cynicism-idealism  dark-arts  darwinian  data  death  debt  decentralized  decision-making  decision-theory  deep-materialism  defense  definite-planning  definition  degrees-of-freedom  democracy  dependence-independence  detail-architecture  developing-world  differential  dimensionality  direction  dirty-hands  discussion  distribution  drugs  duality  duplication  duty  dynamic  dynamical  early-modern  ecology  economics  econotariat  education  efficiency  egalitarianism-hierarchy  EGT  einstein  electromag  elegance  elite  embeddings  emergent  empirical  ems  energy-resources  engineering  enhancement  enlightenment-renaissance-restoration-reformation  entrepreneurialism  entropy-like  environment  envy  equilibrium  ergodic  error  essay  essence-existence  estimate  ethics  europe  evolution  examples  exit-voice  exocortex  expert  expert-experience  explanans  explanation  exploratory  exposition  externalities  extra-introversion  extrema  facebook  fashun  FDA  fedja  feudal  feynman  fiction  finance  finiteness  fisher  flexibility  flux-stasis  focus  form-design  formal-values  fourier  frontier  futurism  gallic  games  gbooks  gedanken  genetic-load  genetics  genomics  geoengineering  geography  geometry  germanic  giants  gnon  gnosis-logos  god-man-beast-victim  good-evil  google  gotchas  government  gowers  grad-school  graph-theory  graphs  gravity  grokkability-clarity  ground-up  growth  growth-econ  GT-101  guessing  hard-tech  harvard  heavyweights  heterodox  heuristic  hi-order-bits  hidden-motives  high-dimension  high-variance  higher-ed  history  hmm  homo-hetero  homogeneity  honor  human-capital  human-ml  humility  hypocrisy  hypothesis-testing  ideas  identity  ideology  impetus  increase-decrease  individualism-collectivism  inequality  inference  info-dynamics  info-econ  infographic  information-theory  inner-product  innovation  insight  instinct  institutions  intel  intellectual-property  intelligence  interdisciplinary  interests  internet  interpretation  interview  intuition  invariance  investing  iron-age  isotropy  iteration-recursion  janus  japan  judgement  justice  knowledge  land  latin-america  lattice  law  leadership  learning  lecture-notes  left-wing  len:short  lens  lesswrong  let-me-see  levers  leviathan  life-history  lifts-projections  limits  linear-algebra  links  list  literature  local-global  logic  long-term  longevity  love-hate  machine-learning  macro  magnitude  management  managerial-state  manifolds  map-territory  marginal  marginal-rev  market-power  markets  markov  martial  martingale  matching  math  math.AG  math.CA  math.CO  math.FA  math.GN  math.GR  math.MG  math.NT  mathtariat  measure  measurement  mechanics  media  medicine  mediterranean  mental-math  meta:math  meta:reading  meta:research  meta:science  metabuch  metameta  methodology  metric-space  michael-nielsen  micro  microfoundations  microsoft  military  minimum-viable  miri-cfar  mobile  mobility  models  modernity  moments  monetary-fiscal  morality  mostly-modern  motivation  multi  multiplicative  musk  mutation  mystic  myth  n-factor  narrative  nascent-state  nationalism-globalism  nature  network-structure  neuro  neurons  new-religion  news  nibble  nietzschean  nihil  nitty-gritty  nl-and-so-can-you  noble-lie  norms  northeast  notetaking  novelty  nuclear  nutrition  nyc  occam  occident  old-anglo  oly  open-closed  open-problems  operational  optics  optimate  optimism  order-disorder  orders  ORFE  org:anglo  org:bleg  org:edge  org:edu  org:inst  org:mag  org:mat  org:sci  organizing  orient  oscillation  outcome-risk  outliers  overflow  p:whenever  parable  paradox  parallax  patience  paul-romer  paying-rent  peace-violence  people  personality  perturbation  pessimism  phalanges  pharma  philosophy  phys-energy  physics  pic  plots  poast  polanyi-marx  polarization  policy  polisci  politics  polynomials  popsci  population-genetics  postrat  power  power-law  practice  pragmatic  pre-ww2  presentation  primitivism  princeton  prioritizing  pro-rata  probabilistic-method  probability  problem-solving  productivity  profile  proofs  properties  property-rights  proposal  protestant-catholic  pseudorandomness  psych-architecture  public-goodish  q-n-a  qra  quantifiers-sums  quantum  questions  quixotic  quotes  random  randy-ayndy  ranking  rationality  ratty  realness  reason  recommendations  recruiting  redistribution  reduction  reference  reflection  regulation  relaxation  religion  rent-seeking  responsibility  retention  retrofit  review  revolution  rhythm  right-wing  rigor  risk  ritual  robotics  roots  russia  s-factor  s:*  s:**  s:***  s:null  sampling  sapiens  scale  scholar  scholar-pack  science  scifi-fantasy  scitariat  search  securities  selection  self-interest  separation  sex  shakespeare  shalizi  shannon  shift  signal-noise  signaling  signum  sinosphere  skeleton  skunkworks  smoothness  social  social-capital  social-choice  social-norms  sociality  socs-and-mops  soft-question  space  spatial  spearhead  spectral  speculation  speed  speedometer  spreading  stackex  stagnation  stanford  startups  stat-mech  statesmen  stats  status  stereotypes  stochastic-processes  stock-flow  stories  strategy  stream  street-fighting  structure  studying  stylized-facts  success  summary  sv  symmetry  synchrony  synthesis  szabo  tactics  tails  tcs  tcstariat  teaching  tech  technical-writing  technology  techtariat  telos-atelos  tensors  the-classics  the-devil  the-founding  the-great-west-whale  the-self  the-trenches  the-watchers  the-west  the-world-is-just-atoms  theory-of-mind  theory-practice  theos  thermo  thick-thin  thiel  things  thinking  thurston  tidbits  time  time-preference  top-n  topology  track-record  trade  tradeoffs  transportation  trees  tribalism  tricki  tricks  troll  trust  truth  twitter  unaffiliated  uncertainty  unintended-consequences  urban-rural  us-them  usa  vague  values  venture  video  virtu  visual-understanding  visualization  visuo  vitality  volo-avolo  war  war-nerd  water  waves  wealth  welfare-state  west-hunter  whole-partial-many  wiki  wild-ideas  winner-take-all  wire-guided  wisdom  within-without  wonkish  wordlessness  world  world-war  wormholes  worrydream  writing  X-not-about-Y  yoga  zero-positive-sum  zooming  🌞  🎓  🎩  👳  🔬 

Copy this bookmark:



description:


tags: