nhaliday + coarse-fine   20

Software Testing Anti-patterns | Hacker News
I haven't read this but both the article and commentary/discussion look interesting from a glance

hmm: https://news.ycombinator.com/item?id=16896390
In small companies where there is no time to "waste" on tests, my view is that 80% of the problems can be caught with 20% of the work by writing integration tests that cover large areas of the application. Writing unit tests would be ideal, but time-consuming. For a web project, that would involve testing all pages for HTTP 200 (< 1 hour bash script that will catch most major bugs), automatically testing most interfaces to see if filling data and clicking "save" works. Of course, for very important/dangerous/complex algorithms in the code, unit tests are useful, but generally, that represents a very low fraction of a web application's code.
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9 weeks ago by nhaliday
Lateralization of brain function - Wikipedia
Language
Language functions such as grammar, vocabulary and literal meaning are typically lateralized to the left hemisphere, especially in right handed individuals.[3] While language production is left-lateralized in up to 90% of right-handers, it is more bilateral, or even right-lateralized, in approximately 50% of left-handers.[4]

Broca's area and Wernicke's area, two areas associated with the production of speech, are located in the left cerebral hemisphere for about 95% of right-handers, but about 70% of left-handers.[5]:69

Auditory and visual processing
The processing of visual and auditory stimuli, spatial manipulation, facial perception, and artistic ability are represented bilaterally.[4] Numerical estimation, comparison and online calculation depend on bilateral parietal regions[6][7] while exact calculation and fact retrieval are associated with left parietal regions, perhaps due to their ties to linguistic processing.[6][7]

...

Depression is linked with a hyperactive right hemisphere, with evidence of selective involvement in "processing negative emotions, pessimistic thoughts and unconstructive thinking styles", as well as vigilance, arousal and self-reflection, and a relatively hypoactive left hemisphere, "specifically involved in processing pleasurable experiences" and "relatively more involved in decision-making processes".

Chaos and Order; the right and left hemispheres: https://orthosphere.wordpress.com/2018/05/23/chaos-and-order-the-right-and-left-hemispheres/
In The Master and His Emissary, Iain McGilchrist writes that a creature like a bird needs two types of consciousness simultaneously. It needs to be able to focus on something specific, such as pecking at food, while it also needs to keep an eye out for predators which requires a more general awareness of environment.

These are quite different activities. The Left Hemisphere (LH) is adapted for a narrow focus. The Right Hemisphere (RH) for the broad. The brains of human beings have the same division of function.

The LH governs the right side of the body, the RH, the left side. With birds, the left eye (RH) looks for predators, the right eye (LH) focuses on food and specifics. Since danger can take many forms and is unpredictable, the RH has to be very open-minded.

The LH is for narrow focus, the explicit, the familiar, the literal, tools, mechanism/machines and the man-made. The broad focus of the RH is necessarily more vague and intuitive and handles the anomalous, novel, metaphorical, the living and organic. The LH is high resolution but narrow, the RH low resolution but broad.

The LH exhibits unrealistic optimism and self-belief. The RH has a tendency towards depression and is much more realistic about a person’s own abilities. LH has trouble following narratives because it has a poor sense of “wholes.” In art it favors flatness, abstract and conceptual art, black and white rather than color, simple geometric shapes and multiple perspectives all shoved together, e.g., cubism. Particularly RH paintings emphasize vistas with great depth of field and thus space and time,[1] emotion, figurative painting and scenes related to the life world. In music, LH likes simple, repetitive rhythms. The RH favors melody, harmony and complex rhythms.

...

Schizophrenia is a disease of extreme LH emphasis. Since empathy is RH and the ability to notice emotional nuance facially, vocally and bodily expressed, schizophrenics tend to be paranoid and are often convinced that the real people they know have been replaced by robotic imposters. This is at least partly because they lose the ability to intuit what other people are thinking and feeling – hence they seem robotic and suspicious.

Oswald Spengler’s The Decline of the West as well as McGilchrist characterize the West as awash in phenomena associated with an extreme LH emphasis. Spengler argues that Western civilization was originally much more RH (to use McGilchrist’s categories) and that all its most significant artistic (in the broadest sense) achievements were triumphs of RH accentuation.

The RH is where novel experiences and the anomalous are processed and where mathematical, and other, problems are solved. The RH is involved with the natural, the unfamiliar, the unique, emotions, the embodied, music, humor, understanding intonation and emotional nuance of speech, the metaphorical, nuance, and social relations. It has very little speech, but the RH is necessary for processing all the nonlinguistic aspects of speaking, including body language. Understanding what someone means by vocal inflection and facial expressions is an intuitive RH process rather than explicit.

...

RH is very much the center of lived experience; of the life world with all its depth and richness. The RH is “the master” from the title of McGilchrist’s book. The LH ought to be no more than the emissary; the valued servant of the RH. However, in the last few centuries, the LH, which has tyrannical tendencies, has tried to become the master. The LH is where the ego is predominantly located. In split brain patients where the LH and the RH are surgically divided (this is done sometimes in the case of epileptic patients) one hand will sometimes fight with the other. In one man’s case, one hand would reach out to hug his wife while the other pushed her away. One hand reached for one shirt, the other another shirt. Or a patient will be driving a car and one hand will try to turn the steering wheel in the opposite direction. In these cases, the “naughty” hand is usually the left hand (RH), while the patient tends to identify herself with the right hand governed by the LH. The two hemispheres have quite different personalities.

The connection between LH and ego can also be seen in the fact that the LH is competitive, contentious, and agonistic. It wants to win. It is the part of you that hates to lose arguments.

Using the metaphor of Chaos and Order, the RH deals with Chaos – the unknown, the unfamiliar, the implicit, the emotional, the dark, danger, mystery. The LH is connected with Order – the known, the familiar, the rule-driven, the explicit, and light of day. Learning something means to take something unfamiliar and making it familiar. Since the RH deals with the novel, it is the problem-solving part. Once understood, the results are dealt with by the LH. When learning a new piece on the piano, the RH is involved. Once mastered, the result becomes a LH affair. The muscle memory developed by repetition is processed by the LH. If errors are made, the activity returns to the RH to figure out what went wrong; the activity is repeated until the correct muscle memory is developed in which case it becomes part of the familiar LH.

Science is an attempt to find Order. It would not be necessary if people lived in an entirely orderly, explicit, known world. The lived context of science implies Chaos. Theories are reductive and simplifying and help to pick out salient features of a phenomenon. They are always partial truths, though some are more partial than others. The alternative to a certain level of reductionism or partialness would be to simply reproduce the world which of course would be both impossible and unproductive. The test for whether a theory is sufficiently non-partial is whether it is fit for purpose and whether it contributes to human flourishing.

...

Analytic philosophers pride themselves on trying to do away with vagueness. To do so, they tend to jettison context which cannot be brought into fine focus. However, in order to understand things and discern their meaning, it is necessary to have the big picture, the overview, as well as the details. There is no point in having details if the subject does not know what they are details of. Such philosophers also tend to leave themselves out of the picture even when what they are thinking about has reflexive implications. John Locke, for instance, tried to banish the RH from reality. All phenomena having to do with subjective experience he deemed unreal and once remarked about metaphors, a RH phenomenon, that they are “perfect cheats.” Analytic philosophers tend to check the logic of the words on the page and not to think about what those words might say about them. The trick is for them to recognize that they and their theories, which exist in minds, are part of reality too.

The RH test for whether someone actually believes something can be found by examining his actions. If he finds that he must regard his own actions as free, and, in order to get along with other people, must also attribute free will to them and treat them as free agents, then he effectively believes in free will – no matter his LH theoretical commitments.

...

We do not know the origin of life. We do not know how or even if consciousness can emerge from matter. We do not know the nature of 96% of the matter of the universe. Clearly all these things exist. They can provide the subject matter of theories but they continue to exist as theorizing ceases or theories change. Not knowing how something is possible is irrelevant to its actual existence. An inability to explain something is ultimately neither here nor there.

If thought begins and ends with the LH, then thinking has no content – content being provided by experience (RH), and skepticism and nihilism ensue. The LH spins its wheels self-referentially, never referring back to experience. Theory assumes such primacy that it will simply outlaw experiences and data inconsistent with it; a profoundly wrong-headed approach.

...

Gödel’s Theorem proves that not everything true can be proven to be true. This means there is an ineradicable role for faith, hope and intuition in every moderately complex human intellectual endeavor. There is no one set of consistent axioms from which all other truths can be derived.

Alan Turing’s proof of the halting problem proves that there is no effective procedure for finding effective procedures. Without a mechanical decision procedure, (LH), when it comes to … [more]
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september 2018 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
Heretics -- On Certain Modern Writers and the Institution of the Family
It is not fashionable to say much nowadays of the advantages of the small community. We are told that we must go in for large empires and large ideas. There is one advantage, however, in the small state, the city, or the village, which only the wilfully blind can overlook. The man who lives in a small community lives in a much larger world. He knows much more of the fierce varieties and uncompromising divergences of men. The reason is obvious. In a large community we can choose our companions. In a small community our companions are chosen for us. Thus in all extensive and highly civilized societies groups come into existence founded upon what is called sympathy, and shut out the real world more sharply than the gates of a monastery. There is nothing really narrow about the clan; the thing which is really narrow is the clique. The men of the clan live together because they all wear the same tartan or are all descended from the same sacred cow; but in their souls, by the divine luck of things, there will always be more colours than in any tartan. But the men of the clique live together because they have the same kind of soul, and their narrowness is a narrowness of spiritual coherence and contentment, like that which exists in hell. A big society exists in order to form cliques. A big society is a society for the promotion of narrowness. It is a machinery for the purpose of guarding the solitary and sensitive individual from all experience of the bitter and bracing human compromises. It is, in the most literal sense of the words, a society for the prevention of Christian knowledge.
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april 2017 by nhaliday
bounds - What is the variance of the maximum of a sample? - Cross Validated
- sum of variances is always a bound
- can't do better even for iid Bernoulli
- looks like nice argument from well-known probabilist (using E[(X-Y)^2] = 2Var X), but not clear to me how he gets to sum_i instead of sum_{i,j} in the union bound?
edit: argument is that, for j = argmax_k Y_k, we have r < X_i - Y_j <= X_i - Y_i for all i, including i = argmax_k X_k
- different proof here (later pages): http://www.ism.ac.jp/editsec/aism/pdf/047_1_0185.pdf
Var(X_n:n) <= sum Var(X_k:n) + 2 sum_{i < j} Cov(X_i:n, X_j:n) = Var(sum X_k:n) = Var(sum X_k) = nσ^2
why are the covariances nonnegative? (are they?). intuitively seems true.
- for that, see https://pinboard.in/u:nhaliday/b:ed4466204bb1
- note that this proof shows more generally that sum Var(X_k:n) <= sum Var(X_k)
- apparently that holds for dependent X_k too? http://mathoverflow.net/a/96943/20644
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february 2017 by nhaliday
Mikhail Leonidovich Gromov - Wikipedia
Gromov's style of geometry often features a "coarse" or "soft" viewpoint, analyzing asymptotic or large-scale properties.

Gromov is also interested in mathematical biology,[11] the structure of the brain and the thinking process, and the way scientific ideas evolve.[8]
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january 2017 by nhaliday
Soft analysis, hard analysis, and the finite convergence principle | What's new
It is fairly well known that the results obtained by hard and soft analysis respectively can be connected to each other by various “correspondence principles” or “compactness principles”. It is however my belief that the relationship between the two types of analysis is in fact much closer[3] than just this; in many cases, qualitative analysis can be viewed as a convenient abstraction of quantitative analysis, in which the precise dependencies between various finite quantities has been efficiently concealed from view by use of infinitary notation. Conversely, quantitative analysis can often be viewed as a more precise and detailed refinement of qualitative analysis. Furthermore, a method from hard analysis often has some analogue in soft analysis and vice versa, though the language and notation of the analogue may look completely different from that of the original. I therefore feel that it is often profitable for a practitioner of one type of analysis to learn about the other, as they both offer their own strengths, weaknesses, and intuition, and knowledge of one gives more insight[4] into the workings of the other. I wish to illustrate this point here using a simple but not terribly well known result, which I shall call the “finite convergence principle” (thanks to Ben Green for suggesting this name; Jennifer Chayes has also suggested the “metastability principle”). It is the finitary analogue of an utterly trivial infinitary result – namely, that every bounded monotone sequence converges – but sometimes, a careful analysis of a trivial result can be surprisingly revealing, as I hope to demonstrate here.
gowers  mathtariat  math  math.CA  expert  reflection  philosophy  meta:math  logic  math.CO  lens  big-picture  symmetry  limits  finiteness  nibble  org:bleg  coarse-fine  metameta  convergence  expert-experience 
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.

...

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

bundles : abstractmathpatternsproblem-solvingthinkingvague

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