nhaliday + visual-understanding   98

How to come up with the solutions: techniques - Codeforces
Technique 1: "Total Recall"
Technique 2: "From Specific to General"
Let's say that you've found the solution for the problem (hurray!). Let's consider some particular case of a problem. Of course, you can apply the algorithm/solution to it. That's why, in order to solve a general problem, you need to solve all of its specific cases. Try solving some (or multiple) specific cases and then try and generalize them to the solution of the main problem.
Technique 3: "Bold Hypothesis"
Technique 4: "To solve a problem, you should think like a problem"
Technique 5: "Think together"
Technique 6: "Pick a Method"
Technique 7: "Print Out and Look"
Technique 8: "Google"
oly  oly-programming  problem-solving  thinking  expert-experience  retention  metabuch  visual-understanding  zooming  local-global  collaboration  tactics  debugging  bare-hands  let-me-see  advice 
august 2019 by nhaliday
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/
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march 2018 by nhaliday
Sequence Modeling with CTC
A visual guide to Connectionist Temporal Classification, an algorithm used to train deep neural networks in speech recognition, handwriting recognition and other sequence problems.
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december 2017 by nhaliday
The Earth-Moon system
nice way of expressing Kepler's law (scaled by AU, solar mass, year, etc.) among other things

1. PHYSICAL PROPERTIES OF THE MOON
2. LUNAR PHASES
3. ECLIPSES
4. TIDES
nibble  org:junk  explanation  trivia  data  objektbuch  space  mechanics  spatial  visualization  earth  visual-understanding  navigation  experiment  measure  marginal  gravity  scale  physics  nitty-gritty  tidbits  identity  cycles  time  magnitude  street-fighting  calculation  oceans  pro-rata  rhythm  flux-stasis 
august 2017 by nhaliday
Analysis of variance - Wikipedia
Analysis of variance (ANOVA) is a collection of statistical models used to analyze the differences among group means and their associated procedures (such as "variation" among and between groups), developed by statistician and evolutionary biologist Ronald Fisher. In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes the t-test to more than two groups. ANOVAs are useful for comparing (testing) three or more means (groups or variables) for statistical significance. It is conceptually similar to multiple two-sample t-tests, but is more conservative (results in less type I error) and is therefore suited to a wide range of practical problems.

good pic: https://en.wikipedia.org/wiki/Analysis_of_variance#Motivating_example

tutorial by Gelman: http://www.stat.columbia.edu/~gelman/research/published/econanova3.pdf

so one way to think of partitioning the variance:
y_ij = alpha_i + beta_j + eps_ij
Var(y_ij) = Var(alpha_i) + Var(beta_j) + Cov(alpha_i, beta_j) + Var(eps_ij)
and alpha_i, beta_j are independent, so Cov(alpha_i, beta_j) = 0

can you make this work w/ interaction effects?
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july 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
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may 2017 by nhaliday
Is Economic Activity Really “Distributed Less Evenly” Than It Used To Be?
http://xenocrypt.github.io/CountyIncomeHistory.html

First, imagine if you had a bar chart with every county in the United States sorted from lowest to highest by wages per capita, with the width of each bar proportional to the population of the county.

In fact, whenever anyone talks about “clustering” and “even distributions”, they’re mostly really talking about ways of comparing monotonic curves with integral one, whether they realize it or not.
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may 2017 by nhaliday
Origins of the brain networks for advanced mathematics in expert mathematicians
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.
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february 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
Principal Component Analysis explained visually
The PCA transformation ensures that the horizontal axis PC1 has the most variation, the vertical axis PC2 the second-most, and a third axis PC3 the least.

I think this is equivalent to variational characterization of singular values?
data-science  explanation  visual-understanding  visualization  techtariat  stats  methodology  exploratory  large-factor  better-explained  let-me-see  matrix-factorization 
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!"
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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.
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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)
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january 2017 by nhaliday
Fitness landscape - Wikipedia
Fitness landscapes are often conceived of as ranges of mountains. There exist local peaks (points from which all paths are downhill, i.e. to lower fitness) and valleys (regions from which many paths lead uphill). A fitness landscape with many local peaks surrounded by deep valleys is called rugged. If all genotypes have the same replication rate, on the other hand, a fitness landscape is said to be flat. An evolving population typically climbs uphill in the fitness landscape, by a series of small genetic changes, until a local optimum is reached.
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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".
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december 2016 by nhaliday
real analysis - Proof of "every convex function is continuous" - Mathematics Stack Exchange
bound above by secant and below by tangent, so graph of function is constrained to a couple triangles w/ common vertex at (x, f(x))
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november 2016 by nhaliday
Faster than Fisher | West Hunter
There’s a simple model of the spread of an advantageous allele:  You take σ, the typical  distance people move in one generation, and s,  the selective advantage: the advantageous allele spreads as a nonlinear wave at speed  σ * √(2s).  The problem is, that’s slow.   Suppose that s = 0.10 (a large advantage), σ = 10 kilometers, and a generation time of 30 years: the allele would take almost 7,000 years to expand out 1000 kilometers.

...

This big expansion didn’t just happen from peasants marrying the girl next door: it required migrations and conquests. This one looks as if it rode with the Indo-European expansion: I’ll bet it started out in a group that had domesticated only horses.

The same processes, migration and conquest, must explain the wide distribution of many geographically widespread selective sweeps and partial sweeps. They were adaptive, all right, but expanded much faster than possible from purely local diffusion. We already have reason to think that SLC24A5 was carried to Europe by Middle Eastern farmers; the same is probably true for the haplotype that carries the high-activity ergothioniene transporter and the 35delG connexin-26/GJB2 deafness mutation. The Indo-Europeans probably introduced the T-13910 LCT mutation and the delta-F508 cystic fibrosis mutation, so we should see delta-F508 in northwest India and Pakistan – and we do !

https://westhunt.wordpress.com/2014/11/22/faster-than-fisher/#comment-63067
To entertain a (possibly mistaken) physical analogy, it sounds like you’re suggested a sort genetic convection through space, as opposed to conduction. I.e. Entire masses of folks, carrying a new selected variant, are displacing others – as opposed to the slow gene flow process of “girl-next-door.” Is that about right? (Hopefully I haven’t revealed my ignorance of basic thermodynamics here…)

Has there been any attempt to estimate sigma from these time periods?

Genetic Convection: https://westhunt.wordpress.com/2015/02/22/genetic-convection/
People are sometimes interested in estimating the point of origin of a sweeping allele: this is probably effectively impossible even if diffusion were the only spread mechanism, since the selective advantage might well vary in both time and space. But that’s ok, since population movements – genetic convection – are real and very important. This means that the difficulties in estimating the origin of a Fisher wave are totally insignificant, compared to the difficulties of estimating the effects of past colonizations, conquests and Völkerwanderungs. So when Yuval Itan and Mark Thomas estimated that 13,910 T LCT allele originated in central Europe, in the early Neolithic, they didn’t just go wrong because of failing to notice that the same allele is fairly common in northern India: no, their whole notion was unsound in the first place. We’re talking turbulence on steroids. Hari Seldon couldn’t figure this one out from the existing geographic distribution.
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november 2016 by nhaliday
Probabilistic Filters By Example: Cuckoo Filter and Bloom Filters
Bloom filters have been in use since the 1970s and are well understood. Implementations are widely available. Variants exist that support deletion and counting, though with expanded storage requirements.

Cuckoo filters were described in Cuckoo Filter: Practically Better Than Bloom, a paper by researchers at CMU in 2014. Cuckoo filters improve on Bloom filters by supporting deletion, limited counting, and bounded FPP with similar storage efficiency as a standard Bloom filter.
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september 2016 by nhaliday
Noise: dinosaurs, syphilis, and all that | West Hunter
Generally speaking, I thought the paleontologists were a waste of space: innumerate, ignorant about evolution, and simply not very smart.

None of them seemed to understand that a sharp, short unpleasant event is better at causing a mass extinction, since it doesn’t give flora and fauna time to adapt.

Most seemed to think that gradual change caused by slow geological and erosion forces was ‘natural’, while extraterrestrial impact was not. But if you look at the Moon, or Mars, or the Kirkwood gaps in the asteroids, or think about the KAM theorem, it is apparent that Newtonian dynamics implies that orbits will be perturbed, and that sometimes there will be catastrophic cosmic collisions. Newtonian dynamics is as ‘natural’ as it gets: paleontologists not studying it in school and not having much math hardly makes it ‘unnatural’.

One of the more interesting general errors was not understanding how to to deal with noise – incorrect observations. There’s a lot of noise in the paleontological record. Dinosaur bones can be eroded and redeposited well after their life times – well after the extinction of all dinosaurs. The fossil record is patchy: if a species is rare, it can easily look as if it went extinct well before it actually did. This means that the data we have is never going to agree with a perfectly correct hypothesis – because some of the data is always wrong. Particularly true if the hypothesis is specific and falsifiable. If your hypothesis is vague and imprecise – not even wrong – it isn’t nearly as susceptible to noise. As far as I can tell, a lot of paleontologists [ along with everyone in the social sciences] think of of unfalsifiability as a strength.

Done Quickly: https://westhunt.wordpress.com/2011/12/03/done-quickly/
I’ve never seen anyone talk about it much, but when you think about mass extinctions, you also have to think about rates of change

You can think of a species occupying a point in a many-dimensional space, where each dimension represents some parameter that influences survival and/or reproduction: temperature, insolation, nutrient concentrations, oxygen partial pressure, toxin levels, yada yada yada. That point lies within a zone of habitability – the set of environmental conditions that the species can survive. Mass extinction occurs when environmental changes are so large that many species are outside their comfort zone.

The key point is that, with gradual change, species adapt. In just a few generations, you can see significant heritable responses to a new environment. Frogs have evolved much greater tolerance of acidification in 40 years (about 15 generations). Some plants in California have evolved much greater tolerance of copper in just 70 years.

As this happens, the boundaries of the comfort zone move. Extinctions occur when the rate of environmental change is greater than the rate of adaptation, or when the amount of environmental change exceeds the limit of feasible adaptation. There are such limits: bar-headed geese fly over Mt. Everest, where the oxygen partial pressure is about a third of that at sea level, but I’m pretty sure that no bird could survive on the Moon.

...

Paleontologists prefer gradualist explanations for mass extinctions, but they must be wrong, for the most part.
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september 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/
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september 2016 by nhaliday
Learn Difficult Concepts with the ADEPT Method – BetterExplained
Make explanations ADEPT: Use an Analogy, Diagram, Example, Plain-English description, and then a Technical description.
thinking  education  learning  teaching  tutoring  better-explained  analogy  visual-understanding  examples 
july 2016 by nhaliday
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