nhaliday : discrete   30

Anti-hash test. - Codeforces
- Thue-Morse sequence
In general, polynomial string hashing is a useful technique in construction of efficient string algorithms. One simply needs to remember to carefully select the modulus M and the variable of the polynomial p depending on the application. A good rule of thumb is to pick both values as prime numbers with M as large as possible so that no integer overflow occurs and p being at least the size of the alphabet.
2.2. Upper Bound on M
[stuff about 32- and 64-bit integers]
2.3. Lower Bound on M
On the other side Mis bounded due to the well-known birthday paradox: if we consider a collection of m keys with m ≥ 1.2√M then the chance of a collision to occur within this collection is at least 50% (assuming that the distribution of fingerprints is close to uniform on the set of all strings). Thus if the birthday paradox applies then one needs to choose M=ω(m^2)to have a fair chance to avoid a collision. However, one should note that not always the birthday paradox applies. As a benchmark consider the following two problems.

I generally prefer to use Schwartz-Zippel to reason about collision probabilities w/ this kind of thing, eg, https://people.eecs.berkeley.edu/~sinclair/cs271/n3.pdf.

A good way to get more accurate results: just use multiple primes and the Chinese remainder theorem to get as large an M as you need w/o going beyond 64-bit arithmetic.

more on this: https://codeforces.com/blog/entry/60442
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august 2019 by nhaliday
Reconsidering epistemological scepticism – Dividuals
I blogged before about how I consider an epistemological scepticism fully compatible with being conservative/reactionary. By epistemological scepticism I mean the worldview where concepts, categories, names, classes aren’t considered real, just useful ways to categorize phenomena, but entirely mental constructs, basically just tools. I think you can call this nominalism as well. The nominalism-realism debate was certainly about this. What follows is the pro-empirical worldview where logic and reasoning is considered highly fallible: hence you don’t think and don’t argue too much, you actually look and check things instead. You rely on experience, not reasoning.

...

Anyhow, the argument is that there are classes, which are indeed artificial, and there are kinds, which are products of natural forces, products of causality.

...

And the deeper – Darwinian – argument, unspoken but obvious, is that any being with a model of reality that does not conform to such real clumps, gets eaten by a grue.

This is impressive. It seems I have to extend my one-variable epistemology to a two-variable epistemology.

My former epistemology was that we generally categorize things according to their uses or dangers for us. So “chair” is – very roughly – defined as “anything we can sit on”. Similarly, we can categorize “predator” as “something that eats us or the animals that are useful for us”.

The unspoken argument against this is that the universe or the biosphere exists neither for us nor against us. A fox can eat your rabbits and a lion can eat you, but they don’t exist just for the sake of making your life difficult.

Hence, if you interpret phenomena only from the viewpoint of their uses or dangers for humans, you get only half the picture right. The other half is what it really is and where it came from.

Copying is everything: https://dividuals.wordpress.com/2015/12/14/copying-is-everything/
Philosophy professor Ruth Millikan’s insight that everything that gets copied from an ancestor has a proper function or teleofunction: it is whatever feature or function that made it and its ancestor selected for copying, in competition with all the other similar copiable things. This would mean Aristotelean teleology is correct within the field of copyable things, replicators, i.e. within biology, although in physics still obviously incorrect.

Darwinian Reactionary drew attention to it two years ago and I still don’t understand why didn’t it generate a bigger buzz. It is an extremely important insight.

I mean, this is what we were waiting for, a proper synthesis of science and philosophy, and a proper way to rescue Aristotelean teleology, which leads to so excellent common-sense predictions that intuitively it cannot be very wrong, yet modern philosophy always denied it.

The result from that is the briding of the fact-value gap and burying the naturalistic fallacy: we CAN derive values from facts: a thing is good if it is well suitable for its natural purpose, teleofunction or proper function, which is the purpose it was selected for and copied for, the purpose and the suitability for the purpose that made the ancestors of this thing selected for copying, instead of all the other potential, similar ancestors.

...

What was humankind selected for? I am afraid, the answer is kind of ugly.

Men were selected to compete between groups, the cooperate within groups largely for coordinating for the sake of this competition, and have a low-key competition inside the groups as well for status and leadership. I am afraid, intelligence is all about organizing elaborate tribal raids: “coalitionary arms races”. The most civilized case, least brutal but still expensive case is arms races in prestige status, not dominance status: when Ancient Athens buildt pretty buildings and modern France built the TGV and America sent a man to the Moon in order to gain “gloire” i.e. the prestige type respect and status amongst the nations, the larger groups of mankind. If you are the type who doesn’t like blood, you should probably focus on these kinds of civilized, prestige-project competitions.

Women were selected for bearing children, for having strong and intelligent sons therefore having these heritable traits themselves (HBD kind of contradicts the more radically anti-woman aspects of RedPillery: marry a weak and stupid but attractive silly-blondie type woman and your son’s won’t be that great either), for pleasuring men and in some rarer but existing cases, to be true companions and helpers of their husbands.

https://en.wikipedia.org/wiki/Four_causes
- Matter: a change or movement's material cause, is the aspect of the change or movement which is determined by the material that composes the moving or changing things. For a table, that might be wood; for a statue, that might be bronze or marble.
- Form: a change or movement's formal cause, is a change or movement caused by the arrangement, shape or appearance of the thing changing or moving. Aristotle says for example that the ratio 2:1, and number in general, is the cause of the octave.
- Agent: a change or movement's efficient or moving cause, consists of things apart from the thing being changed or moved, which interact so as to be an agency of the change or movement. For example, the efficient cause of a table is a carpenter, or a person working as one, and according to Aristotle the efficient cause of a boy is a father.
- End or purpose: a change or movement's final cause, is that for the sake of which a thing is what it is. For a seed, it might be an adult plant. For a sailboat, it might be sailing. For a ball at the top of a ramp, it might be coming to rest at the bottom.

https://en.wikipedia.org/wiki/Proximate_and_ultimate_causation
A proximate cause is an event which is closest to, or immediately responsible for causing, some observed result. This exists in contrast to a higher-level ultimate cause (or distal cause) which is usually thought of as the "real" reason something occurred.

...

- Ultimate causation explains traits in terms of evolutionary forces acting on them.
- Proximate causation explains biological function in terms of immediate physiological or environmental factors.
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july 2018 by nhaliday
Is the human brain analog or digital? - Quora
The brain is neither analog nor digital, but works using a signal processing paradigm that has some properties in common with both.

Unlike a digital computer, the brain does not use binary logic or binary addressable memory, and it does not perform binary arithmetic. Information in the brain is represented in terms of statistical approximations and estimations rather than exact values. The brain is also non-deterministic and cannot replay instruction sequences with error-free precision. So in all these ways, the brain is definitely not "digital".

At the same time, the signals sent around the brain are "either-or" states that are similar to binary. A neuron fires or it does not. These all-or-nothing pulses are the basic language of the brain. So in this sense, the brain is computing using something like binary signals. Instead of 1s and 0s, or "on" and "off", the brain uses "spike" or "no spike" (referring to the firing of a neuron).
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april 2018 by nhaliday
Prisoner's dilemma - Wikipedia
caveat to result below:
An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).[14]

Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is bigger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.[8]

https://alfanl.com/2018/04/12/defection/
Nature boils down to a few simple concepts.

Haters will point out that I oversimplify. The haters are wrong. I am good at saying a lot with few words. Nature indeed boils down to a few simple concepts.

In life, you can either cooperate or defect.

Used to be that defection was the dominant strategy, say in the time when the Roman empire started to crumble. Everybody complained about everybody and in the end nothing got done. Then came Jesus, who told people to be loving and cooperative, and boom: 1800 years later we get the industrial revolution.

Because of Jesus we now find ourselves in a situation where cooperation is the dominant strategy. A normie engages in a ton of cooperation: with the tax collector who wants more and more of his money, with schools who want more and more of his kid’s time, with media who wants him to repeat more and more party lines, with the Zeitgeist of the Collective Spirit of the People’s Progress Towards a New Utopia. Essentially, our normie is cooperating himself into a crumbling Western empire.

Turns out that if everyone blindly cooperates, parasites sprout up like weeds until defection once again becomes the standard.

The point of a post-Christian religion is to once again create conditions for the kind of cooperation that led to the industrial revolution. This necessitates throwing out undead Christianity: you do not blindly cooperate. You cooperate with people that cooperate with you, you defect on people that defect on you. Christianity mixed with Darwinism. God and Gnon meet.

This also means we re-establish spiritual hierarchy, which, like regular hierarchy, is a prerequisite for cooperation. It is this hierarchical cooperation that turns a household into a force to be reckoned with, that allows a group of men to unite as a front against their enemies, that allows a tribe to conquer the world. Remember: Scientology bullied the Cathedral’s tax department into submission.

With a functioning hierarchy, men still gossip, lie and scheme, but they will do so in whispers behind closed doors. In your face they cooperate and contribute to the group’s wellbeing because incentives are thus that contributing to group wellbeing heightens status.

Without a functioning hierarchy, men gossip, lie and scheme, but they do so in your face, and they tell you that you are positively deluded for accusing them of gossiping, lying and scheming. Seeds will not sprout in such ground.

Spiritual dominance is established in the same way any sort of dominance is established: fought for, taken. But the fight is ritualistic. You can’t force spiritual dominance if no one listens, or if you are silenced the ritual is not allowed to happen.

If one of our priests is forbidden from establishing spiritual dominance, that is a sure sign an enemy priest is in better control and has vested interest in preventing you from establishing spiritual dominance..

They defect on you, you defect on them. Let them suffer the consequences of enemy priesthood, among others characterized by the annoying tendency that very little is said with very many words.

https://contingentnotarbitrary.com/2018/04/14/rederiving-christianity/
To recap, we started with a secular definition of Logos and noted that its telos is existence. Given human nature, game theory and the power of cooperation, the highest expression of that telos is freely chosen universal love, tempered by constant vigilance against defection while maintaining compassion for the defectors and forgiving those who repent. In addition, we must know the telos in order to fulfill it.

In Christian terms, looks like we got over half of the Ten Commandments (know Logos for the First, don’t defect or tempt yourself to defect for the rest), the importance of free will, the indestructibility of evil (group cooperation vs individual defection), loving the sinner and hating the sin (with defection as the sin), forgiveness (with conditions), and love and compassion toward all, assuming only secular knowledge and that it’s good to exist.

Iterated Prisoner's Dilemma is an Ultimatum Game: http://infoproc.blogspot.com/2012/07/iterated-prisoners-dilemma-is-ultimatum.html
The history of IPD shows that bounded cognition prevented the dominant strategies from being discovered for over over 60 years, despite significant attention from game theorists, computer scientists, economists, evolutionary biologists, etc. Press and Dyson have shown that IPD is effectively an ultimatum game, which is very different from the Tit for Tat stories told by generations of people who worked on IPD (Axelrod, Dawkins, etc., etc.).

...

For evolutionary biologists: Dyson clearly thinks this result has implications for multilevel (group vs individual selection):
... Cooperation loses and defection wins. The ZD strategies confirm this conclusion and make it sharper. ... The system evolved to give cooperative tribes an advantage over non-cooperative tribes, using punishment to give cooperation an evolutionary advantage within the tribe. This double selection of tribes and individuals goes way beyond the Prisoners' Dilemma model.

implications for fractionalized Europe vis-a-vis unified China?

and more broadly does this just imply we're doomed in the long run RE: cooperation, morality, the "good society", so on...? war and group-selection is the only way to get a non-crab bucket civilization?

Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent:
http://www.pnas.org/content/109/26/10409.full
http://www.pnas.org/content/109/26/10409.full.pdf
https://www.edge.org/conversation/william_h_press-freeman_dyson-on-iterated-prisoners-dilemma-contains-strategies-that

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

analogy for ultimatum game: the state gives the demos a bargain take-it-or-leave-it, and...if the demos refuses...violence?

The nature of human altruism: http://sci-hub.tw/https://www.nature.com/articles/nature02043
- Ernst Fehr & Urs Fischbacher

Some of the most fundamental questions concerning our evolutionary origins, our social relations, and the organization of society are centred around issues of altruism and selfishness. Experimental evidence indicates that human altruism is a powerful force and is unique in the animal world. However, there is much individual heterogeneity and the interaction between altruists and selfish individuals is vital to human cooperation. Depending on the environment, a minority of altruists can force a majority of selfish individuals to cooperate or, conversely, a few egoists can induce a large number of altruists to defect. Current gene-based evolutionary theories cannot explain important patterns of human altruism, pointing towards the importance of both theories of cultural evolution as well as gene–culture co-evolution.

...

Why are humans so unusual among animals in this respect? We propose that quantitatively, and probably even qualitatively, unique patterns of human altruism provide the answer to this question. Human altruism goes far beyond that which has been observed in the animal world. Among animals, fitness-reducing acts that confer fitness benefits on other individuals are largely restricted to kin groups; despite several decades of research, evidence for reciprocal altruism in pair-wise repeated encounters4,5 remains scarce6–8. Likewise, there is little evidence so far that individual reputation building affects cooperation in animals, which contrasts strongly with what we find in humans. If we randomly pick two human strangers from a modern society and give them the chance to engage in repeated anonymous exchanges in a laboratory experiment, there is a high probability that reciprocally altruistic behaviour will emerge spontaneously9,10.

However, human altruism extends far beyond reciprocal altruism and reputation-based cooperation, taking the form of strong reciprocity11,12. Strong reciprocity is a combination of altruistic rewarding, which is a predisposition to reward others for cooperative, norm-abiding behaviours, and altruistic punishment, which is a propensity to impose sanctions on others for norm violations. Strong reciprocators bear the cost of rewarding or punishing even if they gain no individual economic benefit whatsoever from their acts. In contrast, reciprocal altruists, as they have been defined in the biological literature4,5, reward and punish only if this is in their long-term self-interest. Strong reciprocity thus constitutes a powerful incentive for cooperation even in non-repeated interactions and when reputation gains are absent, because strong reciprocators will reward those who cooperate and punish those who defect.

...

We will show that the interaction between selfish and strongly reciprocal … [more]
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march 2018 by nhaliday
GALILEO'S STUDIES OF PROJECTILE MOTION
During the Renaissance, the focus, especially in the arts, was on representing as accurately as possible the real world whether on a 2 dimensional surface or a solid such as marble or granite. This required two things. The first was new methods for drawing or painting, e.g., perspective. The second, relevant to this topic, was careful observation.

With the spread of cannon in warfare, the study of projectile motion had taken on greater importance, and now, with more careful observation and more accurate representation, came the realization that projectiles did not move the way Aristotle and his followers had said they did: the path of a projectile did not consist of two consecutive straight line components but was instead a smooth curve. [1]

Now someone needed to come up with a method to determine if there was a special curve a projectile followed. But measuring the path of a projectile was not easy.

Using an inclined plane, Galileo had performed experiments on uniformly accelerated motion, and he now used the same apparatus to study projectile motion. He placed an inclined plane on a table and provided it with a curved piece at the bottom which deflected an inked bronze ball into a horizontal direction. The ball thus accelerated rolled over the table-top with uniform motion and then fell off the edge of the table Where it hit the floor, it left a small mark. The mark allowed the horizontal and vertical distances traveled by the ball to be measured. [2]

By varying the ball's horizontal velocity and vertical drop, Galileo was able to determine that the path of a projectile is parabolic.

https://www.scientificamerican.com/author/stillman-drake/

Galileo's Discovery of the Parabolic Trajectory: http://www.jstor.org/stable/24949756

Galileo's Experimental Confirmation of Horizontal Inertia: Unpublished Manuscripts (Galileo
Gleanings XXII): https://sci-hub.tw/https://www.jstor.org/stable/229718
- Drake Stillman

MORE THAN A DECADE HAS ELAPSED since Thomas Settle published a classic paper in which Galileo's well-known statements about his experiments on inclined planes were completely vindicated.' Settle's paper replied to an earlier attempt by Alexandre Koyre to show that Galileo could not have obtained the results he claimed in his Two New Sciences by actual observations using the equipment there described. The practical ineffectiveness of Settle's painstaking repetition of the experiments in altering the opinion of historians of science is only too evident. Koyre's paper was reprinted years later in book form without so much as a note by the editors concerning Settle's refutation of its thesis.2 And the general literature continues to belittle the role of experiment in Galileo's physics.

More recently James MacLachlan has repeated and confirmed a different experiment reported by Galileo-one which has always seemed highly exaggerated and which was also rejected by Koyre with withering sarcasm.3 In this case, however, it was accuracy of observation rather than precision of experimental data that was in question. Until now, nothing has been produced to demonstrate Galileo's skill in the design and the accurate execution of physical experiment in the modern sense.

Pant of a page of Galileo's unpublished manuscript notes, written late in 7608, corroborating his inertial assumption and leading directly to his discovery of the parabolic trajectory. (Folio 1 16v Vol. 72, MSS Galileiani; courtesy of the Biblioteca Nazionale di Firenze.)

...

(The same skeptical historians, however, believe that to show that Galileo could have used the medieval mean-speed theorem suffices to prove that he did use it, though it is found nowhere in his published or unpublished writings.)

...

Now, it happens that among Galileo's manuscript notes on motion there are many pages that were not published by Favaro, since they contained only calculations or diagrams without attendant propositions or explanations. Some pages that were published had first undergone considerable editing, making it difficult if not impossible to discern their full significance from their printed form. This unpublished material includes at least one group of notes which cannot satisfactorily be accounted for except as representing a series of experiments designed to test a fundamental assumption, which led to a new, important discovery. In these documents precise empirical data are given numerically, comparisons are made with calculated values derived from theory, a source of discrepancy from still another expected result is noted, a new experiment is designed to eliminate this, and further empirical data are recorded. The last-named data, although proving to be beyond Galileo's powers of mathematical analysis at the time, when subjected to modern analysis turn out to be remarkably precise. If this does not represent the experimental process in its fully modern sense, it is hard to imagine what standards historians require to be met.

The discovery of these notes confirms the opinion of earlier historians. They read only Galileo's published works, but did so without a preconceived notion of continuity in the history of ideas. The opinion of our more sophisticated colleagues has its sole support in philosophical interpretations that fit with preconceived views of orderly long-term scientific development. To find manuscript evidence that Galileo was at home in the physics laboratory hardly surprises me. I should find it much more astonishing if, by reasoning alone, working only from fourteenth-century theories and conclusions, he had continued along lines so different from those followed by profound philosophers in earlier centuries. It is to be hoped that, warned by these examples, historians will begin to restore the old cautionary clauses in analogous instances in which scholarly opinions are revised without new evidence, simply to fit historical theories.

In what follows, the newly discovered documents are presented in the context of a hypothetical reconstruction of Galileo's thought.

...

As early as 1590, if we are correct in ascribing Galileo's juvenile De motu to that date, it was his belief that an ideal body resting on an ideal horizontal plane could be set in motion by a force smaller than any previously assigned force, however small. By "horizontal plane" he meant a surface concentric with the earth but which for reasonable distances would be indistinguishable from a level plane. Galileo noted at the time that experiment did not confirm this belief that the body could be set in motion by a vanishingly small force, and he attributed the failure to friction, pressure, the imperfection of material surfaces and spheres, and the departure of level planes from concentricity with the earth.5

It followed from this belief that under ideal conditions the motion so induced would also be perpetual and uniform. Galileo did not mention these consequences until much later, and it is impossible to say just when he perceived them. They are, however, so evident that it is safe to assume that he saw them almost from the start. They constitute a trivial case of the proposition he seems to have been teaching before 1607-that a mover is required to start motion, but that absence of resistance is then sufficient to account for its continuation.6

In mid-1604, following some investigations of motions along circular arcs and motions of pendulums, Galileo hit upon the law that in free fall the times elapsed from rest are as the smaller distance is to the mean proportional between two distances fallen.7 This gave him the times-squared law as well as the rule of odd numbers for successive distances and speeds in free fall. During the next few years he worked out a large number of theorems relating to motion along inclined planes, later published in the Two New Sciences. He also arrived at the rule that the speed terminating free fall from rest was double the speed of the fall itself. These theorems survive in manuscript notes of the period 1604-1609. (Work during these years can be identified with virtual certainty by the watermarks in the paper used, as I have explained elsewhere.8)

In the autumn of 1608, after a summer at Florence, Galileo seems to have interested himself in the question whether the actual slowing of a body moving horizontally followed any particular rule. On folio 117i of the manuscripts just mentioned, the numbers 196, 155, 121, 100 are noted along the horizontal line near the middle of the page (see Fig. 1). I believe that this was the first entry on this leaf, for reasons that will appear later, and that Galileo placed his grooved plane in the level position and recorded distances traversed in equal times along it. Using a metronome, and rolling a light wooden ball about 4 3/4 inches in diameter along a plane with a groove 1 3/4 inches wide, I obtained similar relations over a distance of 6 feet. The figures obtained vary greatly for balls of different materials and weights and for greatly different initial speeds.9 But it suffices for my present purposes that Galileo could have obtained the figures noted by observing the actual deceleration of a ball along a level plane. It should be noted that the watermark on this leaf is like that on folio 116, to which we shall come presently, and it will be seen later that the two sheets are closely connected in time in other ways as well.

The relatively rapid deceleration is obviously related to the contact of ball and groove. Were the ball to roll right off the end of the plane, all resistance to horizontal motion would be virtually removed. If, then, there were any way to have a given ball leave the plane at different speeds of which the ratios were known, Galileo's old idea that horizontal motion would continue uniformly in the absence of resistance could be put to test. His law of free fall made this possible. The ratios of speeds could be controlled by allowing the ball to fall vertically through known heights, at the ends of which it would be deflected horizontally. Falls through given heights … [more]
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august 2017 by nhaliday
Diophantine approximation - Wikipedia
- rationals perfectly approximated by themselves, badly approximated (eps>1/bq) by other rationals
- irrationals well-approximated (eps~1/q^2) by rationals:
https://en.wikipedia.org/wiki/Dirichlet%27s_approximation_theorem
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august 2017 by nhaliday
Kolmogorov's zero–one law - Wikipedia
In probability theory, Kolmogorov's zero–one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, called a tail event, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one.

tail events include limsup E_i
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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.
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january 2017 by nhaliday
Ehrhart polynomial - Wikipedia
In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem in the Euclidean plane.
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january 2017 by nhaliday
(Gil Kalai) The weak epsilon-net problem | What's new
This is a problem in discrete and convex geometry. It seeks to quantify the intuitively obvious fact that large convex bodies are so “fat” that they cannot avoid “detection” by a small number of observation points.
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january 2017 by nhaliday
Overcoming Bias : In Praise of Low Needs
We humans have come a long way since we first became human; we’ve innovated and grown our ability to achieve human ends by perhaps a factor of ten million. Not at all shabby, even though it may be small compared to the total factor of growth and innovation that life achieved before humans arrived. But even if humanity’s leap is a great achievement, I fear that we have much further to go than we have come.

The universe seems almost entirely dead out there. There’s a chance it will eventually be densely filled with life, and that our descendants may help to make that happen. Some worry about the quality of that life filling the universe, and yes there are issues there. But I worry mostly about the difference between life and death. Our descendants may kill themselves or stop growing, and fail to fill the universe with life. Any life.

To fill the universe with life requires that we grow far more than our previous leap factor of ten million. More like three to ten factors that big still to go. (See Added below.) So think of all the obstacles we’ve overcome so far, obstacles that appeared when we reached new scales of size and levels of ability. If we were lucky to make it this far, we’ll have to be much more lucky to make it all the way.

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Added 28Oct: Assume humanity’s leap factor is 107. Three of those is 1021. As there are 1024 stars in observable universe, that much growth could come from filling one in a thousand of those stars with as many rich humans as Earth now has. Ten of humanity’s leap is 1070, and there are now about 1010 humans on Earth. As there are about 1080 atoms in the observable universe, that much growth could come from finding a way to implement one human like creature per atom.
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october 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.

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Paleontologists prefer gradualist explanations for mass extinctions, but they must be wrong, for the most part.
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september 2016 by nhaliday
Discrete Analysis
each paper is given a nice write-up + links to any talks. useful for getting the background
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april 2016 by nhaliday

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