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Unhappy Go Lucky!
- regularly publishes unofficial editorials for AtCoder
- also seems like an otaku >_>
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september 2019 by nhaliday
[Tutorial] A way to Practice Competitive Programming : From Rating 1000 to 2400+ - Codeforces
this guy really didn't take that long to reach red..., as of today he's done 20 contests in 2y to my 44 contests in 7y (w/ a long break)...>_>

tho he has 3 times as many submissions as me. maybe he does a lot of virtual rounds?

some snippets from the PDF guide linked:
1400-1900:
To be rating 1900, skills as follows are needed:
- You know and can use major algorithms like these:
Brute force DP DFS BFS Dijkstra
Binary Indexed Tree nCr, nPr Mod inverse Bitmasks Binary Search
- You can code faster (For example, 5 minutes for R1100 problems, 10 minutes for
R1400 problems)

If you are not good at fast-coding and fast-debugging, you should solve AtCoder problems. Actually, and statistically, many Japanese are good at fast-coding relatively while not so good at solving difficult problems. I think that’s because of AtCoder.

I recommend to solve problem C and D in AtCoder Beginner Contest. On average, if you can solve problem C of AtCoder Beginner Contest within 10 minutes and problem D within 20 minutes, you are Div1 in FastCodingForces :)

...

Interestingly, typical problems are concentrated in Div2-only round problems. If you are not good at Div2-only round, it is likely that you are not good at using typical algorithms, especially 10 algorithms that are written above.

If you can use some typical problem but not good at solving more than R1500 in Codeforces, you should begin TopCoder. This type of practice is effective for people who are good at Div.2 only round but not good at Div.1+Div.2 combined or Div.1+Div.2 separated round.

Sometimes, especially in Div1+Div2 round, some problems need mathematical concepts or thinking. Since there are a lot of problems which uses them (and also light-implementation!) in TopCoder, you should solve TopCoder problems.

I recommend to solve Div1Easy of recent 100 SRMs. But some problems are really difficult, (e.g. even red-ranked coder could not solve) so before you solve, you should check how many percent of people did solve this problem. You can use https://competitiveprogramming.info/ to know some informations.

1900-2200:
To be rating 2200, skills as follows are needed:
- You know and can use 10 algorithms which I stated in pp.11 and segment trees
(including lazy propagations)
- You can solve problems very fast: For example, 5 mins for R1100, 10 mins for
R1500, 15 mins for R1800, 40 mins for R2000.
- You have decent skills for mathematical-thinking or considering problems
- Strong mental which can think about the solution more than 1 hours, and don’t give up even if you are below average in Div1 in the middle of the contest

This is only my way to practice, but I did many virtual contests when I was rating 2000. In this page, virtual contest does not mean “Virtual Participation” in Codeforces. It means choosing 4 or 5 problems which the difficulty is near your rating (For example, if you are rating 2000, choose R2000 problems in Codeforces) and solve them within 2 hours. You can use https://vjudge.net/. In this website, you can make virtual contests from problems on many online judges. (e.g. AtCoder, Codeforces, Hackerrank, Codechef, POJ, ...)

If you cannot solve problem within the virtual contests and could not be able to find the solution during the contest, you should read editorial. Google it. (e.g. If you want to know editorial of Codeforces Round #556 (Div. 1), search “Codeforces Round #556 editorial” in google) There is one more important thing to gain rating in Codeforces. To solve problem fast, you should equip some coding library (or template code). For example, I think that equipping segment tree libraries, lazy segment tree libraries, modint library, FFT library, geometry library, etc. is very effective.

2200 to 2400:
Rating 2200 and 2400 is actually very different ...

To be rating 2400, skills as follows are needed:
- You should have skills that stated in previous section (rating 2200)
- You should solve difficult problems which are only solved by less than 100 people in Div1 contests

...

At first, there are a lot of educational problems in AtCoder. I recommend you should solve problem E and F (especially 700-900 points problem in AtCoder) of AtCoder Regular Contest, especially ARC058-ARC090. Though old AtCoder Regular Contests are balanced for “considering” and “typical”, but sadly, AtCoder Grand Contest and recent AtCoder Regular Contest problems are actually too biased for considering I think, so I don’t recommend if your goal is gain rating in Codeforces. (Though if you want to gain rating more than 2600, you should solve problems from AtCoder Grand Contest)

For me, actually, after solving AtCoder Regular Contests, my average performance in CF virtual contest increased from 2100 to 2300 (I could not reach 2400 because start was early)

If you cannot solve problems, I recommend to give up and read editorial as follows:
Point value 600 700 800 900 1000-
CF rating R2000 R2200 R2400 R2600 R2800
Time to editorial 40 min 50 min 60 min 70 min 80 min

If you solve AtCoder educational problems, your skills of competitive programming will be increased. But there is one more problem. Without practical skills, you rating won’t increase. So, you should do 50+ virtual participations (especially Div.1) in Codeforces. In virtual participation, you can learn how to compete as a purple/orange-ranked coder (e.g. strategy) and how to use skills in Codeforces contests that you learned in AtCoder. I strongly recommend to read editorial of all problems except too difficult one (e.g. Less than 30 people solved in contest) after the virtual contest. I also recommend to write reflections about strategy, learns and improvements after reading editorial on notebooks after the contests/virtual.

In addition, about once a week, I recommend you to make time to think about much difficult problem (e.g. R2800 in Codeforces) for couple of hours. If you could not reach the solution after thinking couple of hours, I recommend you to read editorial because you can learn a lot. Solving high-level problems may give you chance to gain over 100 rating in a single contest, but also can give you chance to solve easier problems faster.
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august 2019 by nhaliday
The 'science' of training in competitive programming - Codeforces
"Hard problems" is subjective. A good rule of thumb for learning problem solving (at least according to me) is that your problem selection is good if you fail to solve roughly 50% of problems you attempt. Anything in [20%,80%] should still be fine, although many people have problems staying motivated if they fail too often. Read solutions for problems you fail to solve.

(There is some actual math behind this. Hopefully one day I'll have the time to write it down.)
- misof in a comment
--
I don't believe in any of things like "either you solve it in 30mins — few hours, or you never solve it at all". There are some magic at first glance algorithms like polynomial hashing, interval tree or FFT (which is magic even at tenth glance :P), but there are not many of them and vast majority of algorithms are possible to be invented on our own, for example dp. In high school I used to solve many problems from IMO and PMO and when I didn't solve a problem I tried it once again for some time. And I have solved some problems after third or sth like that attempt. Though, if we are restricting ourselves to beginners, I think that it still holds true, but it would be better to read solutions after some time, because there are so many other things which we can learn, so better not get stuck at one particular problem, when there are hundreds of other important concepts to be learnt.
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august 2019 by nhaliday
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"
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august 2019 by nhaliday
LeetCode - The World's Leading Online Programming Learning Platform
very much targeted toward interview prep
https://www.quora.com/Is-LeetCode-Online-Judges-premium-membership-really-worth-it
This data is especially valuable because you get to know a company's interview style beforehand. For example, most questions that appeared in Facebook interviews have short solution typically not more than 30 lines of code. Their interview process focus on your ability to write clean, concise code. On the other hand, Google style interviews lean more on the analytical side and is algorithmic heavy, typically with multiple solutions to a question - each with a different run time complexity.
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june 2019 by nhaliday
About - Project Euler
I've written my program but should it take days to get to the answer?
Absolutely not! Each problem has been designed according to a "one-minute rule", which means that although it may take several hours to design a successful algorithm with more difficult problems, an efficient implementation will allow a solution to be obtained on a modestly powered computer in less than one minute.
math  rec-math  math.NT  math.CO  programming  oly  database  community  forum  stream  problem-solving  accretion  puzzles  contest  🖥  👳 
june 2019 by nhaliday
What's the expected level of paper for top conferences in Computer Science - Academia Stack Exchange
Top. The top level.

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

...

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

- How surprising / novel / elegant / interesting is the result?
- How surprising / novel / elegant / interesting / general are the techniques?
- How technically difficult is the result? Ironically, FOCS and STOC committees have a reputation for ignoring the distinction between trivial (easy to derive from scratch) and nondeterministically trivial (easy to understand after the fact).
- What is the expected impact of this result? Is this paper going to change the way people do theoretical computer science over the next five years?
- Is the result of general interest to the theoretical computer science community? Or is it only of interest to a narrow subcommunity? In particular, if the topic is outside the STOC/FOCS mainstream—say, for example, computational topology—does the paper do a good job of explaining and motivating the results to a typical STOC/FOCS audience?
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june 2019 by nhaliday
Teach debugging
A friend of mine and I couldn't understand why some people were having so much trouble; the material seemed like common sense. The Feynman Method was the only tool we needed.

1. Write down the problem
2. Think real hard
3. Write down the solution

The Feynman Method failed us on the last project: the design of a divider, a real-world-scale project an order of magnitude more complex than anything we'd been asked to tackle before. On the day he assigned the project, the professor exhorted us to begin early. Over the next few weeks, we heard rumors that some of our classmates worked day and night without making progress.

...

And then, just after midnight, a number of our newfound buddies from dinner reported successes. Half of those who started from scratch had working designs. Others were despondent, because their design was still broken in some subtle, non-obvious way. As I talked with one of those students, I began poring over his design. And after a few minutes, I realized that the Feynman method wasn't the only way forward: it should be possible to systematically apply a mechanical technique repeatedly to find the source of our problems. Beneath all the abstractions, our projects consisted purely of NAND gates (woe to those who dug around our toolbox enough to uncover dynamic logic), which outputs a 0 only when both inputs are 1. If the correct output is 0, both inputs should be 1. The input that isn't is in error, an error that is, itself, the output of a NAND gate where at least one input is 0 when it should be 1. We applied this method recursively, finding the source of all the problems in both our designs in under half an hour.

How To Debug Any Program: https://www.blinddata.com/blog/how-to-debug-any-program-9
May 8th 2019 by Saketh Are

Start by Questioning Everything

...

When a program is behaving unexpectedly, our attention tends to be drawn first to the most complex portions of the code. However, mistakes can come in all forms. I've personally been guilty of rushing to debug sophisticated portions of my code when the real bug was that I forgot to read in the input file. In the following section, we'll discuss how to reliably focus our attention on the portions of the program that need correction.

Then Question as Little as Possible

Suppose that we have a program and some input on which its behavior doesn’t match our expectations. The goal of debugging is to narrow our focus to as small a section of the program as possible. Once our area of interest is small enough, the value of the incorrect output that is being produced will typically tell us exactly what the bug is.

In order to catch the point at which our program diverges from expected behavior, we must inspect the intermediate state of the program. Suppose that we select some point during execution of the program and print out all values in memory. We can inspect the results manually and decide whether they match our expectations. If they don't, we know for a fact that we can focus on the first half of the program. It either contains a bug, or our expectations of what it should produce were misguided. If the intermediate state does match our expectations, we can focus on the second half of the program. It either contains a bug, or our understanding of what input it expects was incorrect.

Question Things Efficiently

For practical purposes, inspecting intermediate state usually doesn't involve a complete memory dump. We'll typically print a small number of variables and check whether they have the properties we expect of them. Verifying the behavior of a section of code involves:

1. Before it runs, inspecting all values in memory that may influence its behavior.
2. Reasoning about the expected behavior of the code.
3. After it runs, inspecting all values in memory that may be modified by the code.

Reasoning about expected behavior is typically the easiest step to perform even in the case of highly complex programs. Practically speaking, it's time-consuming and mentally strenuous to write debug output into your program and to read and decipher the resulting values. It is therefore advantageous to structure your code into functions and sections that pass a relatively small amount of information between themselves, minimizing the number of values you need to inspect.

...

Finding the Right Question to Ask

We’ve assumed so far that we have available a test case on which our program behaves unexpectedly. Sometimes, getting to that point can be half the battle. There are a few different approaches to finding a test case on which our program fails. It is reasonable to attempt them in the following order:

1. Verify correctness on the sample inputs.
2. Test additional small cases generated by hand.
3. Adversarially construct corner cases by hand.
4. Re-read the problem to verify understanding of input constraints.
5. Design large cases by hand and write a program to construct them.
6. Write a generator to construct large random cases and a brute force oracle to verify outputs.
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may 2019 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
Why read old philosophy? | Meteuphoric
(This story would suggest that in physics students are maybe missing out on learning the styles of thought that produce progress in physics. My guess is that instead they learn them in grad school when they are doing research themselves, by emulating their supervisors, and that the helpfulness of this might partially explain why Nobel prizewinner advisors beget Nobel prizewinner students.)

The story I hear about philosophy—and I actually don’t know how much it is true—is that as bits of philosophy come to have any methodological tools other than ‘think about it’, they break off and become their own sciences. So this would explain philosophy’s lone status in studying old thinkers rather than impersonal methods—philosophy is the lone ur-discipline without impersonal methods but thinking.

This suggests a research project: try summarizing what Aristotle is doing rather than Aristotle’s views. Then write a nice short textbook about it.
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june 2018 by nhaliday
Introduction to Scaling Laws
https://betadecay.wordpress.com/2009/10/02/the-physics-of-scaling-laws-and-dimensional-analysis/
http://galileo.phys.virginia.edu/classes/304/scaling.pdf

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

An example of such an insight is “the surface of a small solid is comparatively greater than that of a large one” because the surface goes like the square of a linear dimension, but the volume goes like the cube.5 Thus as one scales down macroscopic objects, forces on their surfaces like viscous drag become relatively more important, and bulk forces like weight become relatively less important. Galileo uses this idea on the First Day in the context of resistance in free fall, as an explanation for why similar objects of different size do not fall exactly together, but the smaller one lags behind.
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august 2017 by nhaliday
Alzheimers | West Hunter
Some disease syndromes almost have to be caused by pathogens – for example, any with a fitness impact (prevalence x fitness reduction) > 2% or so, too big to be caused by mutational pressure. I don’t think that this is the case for AD: it hits so late in life that the fitness impact is minimal. However, that hardly means that it can’t be caused by a pathogen or pathogens – a big fraction of all disease syndromes are, including many that strike in old age. That possibility is always worth checking out, not least because infectious diseases are generally easier to prevent and/or treat.

There is new work that strongly suggests that pathogens are the root cause. It appears that the amyloid is an antimicrobial peptide. amyloid-beta binds to invading microbes and then surrounds and entraps them. ‘When researchers injected Salmonella into mice’s hippocampi, a brain area damaged in Alzheimer’s, A-beta quickly sprang into action. It swarmed the bugs and formed aggregates called fibrils and plaques. “Overnight you see the plaques throughout the hippocampus where the bugs were, and then in each single plaque is a single bacterium,” Tanzi says. ‘

obesity and pathogens: https://westhunt.wordpress.com/2016/05/29/alzheimers/#comment-79757
not sure about this guy, but interesting: https://westhunt.wordpress.com/2016/05/29/alzheimers/#comment-79748
http://perfecthealthdiet.com/2010/06/is-alzheimer%E2%80%99s-caused-by-a-bacterial-infection-of-the-brain/

https://westhunt.wordpress.com/2016/12/13/the-twelfth-battle-of-the-isonzo/
All too often we see large, long-lasting research efforts that never produce, never achieve their goal.

For example, the amyloid hypothesis [accumulation of amyloid-beta oligomers is the cause of Alzheimers] has been dominant for more than 20 years, and has driven development of something like 15 drugs. None of them have worked. At the same time the well-known increased risk from APOe4 has been almost entirely ignored, even though it ought to be a clue to the cause.

In general, when a research effort has been spinning its wheels for a generation or more, shouldn’t we try something different? We could at least try putting a fraction of those research dollars into alternative approaches that have not yet failed repeatedly.

Mostly this applies to research efforts that at least wish they were science. ‘educational research’ is in a special class, and I hardly know what to recommend. Most of the remedial actions that occur to me violate one or more of the Geneva conventions.

APOe4 related to lymphatic system: https://en.wikipedia.org/wiki/Apolipoprotein_E

https://westhunt.wordpress.com/2012/03/06/spontaneous-generation/#comment-2236
Look,if I could find out the sort of places that I usually misplace my keys – if I did, which I don’t – I could find the keys more easily the next time I lose them. If you find out that practitioners of a given field are not very competent, it marks that field as a likely place to look for relatively easy discovery. Thus medicine is a promising field, because on the whole doctors are not terribly good investigators. For example, none of the drugs developed for Alzheimers have worked at all, which suggests that our ideas on the causation of Alzheimers are likely wrong. Which suggests that it may (repeat may) be possible to make good progress on Alzheimers, either by an entirely empirical approach, which is way underrated nowadays, or by dumping the current explanation, finding a better one, and applying it.

You could start by looking at basic notions of field X and asking yourself: How do we really know that? Is there serious statistical evidence? Does that notion even accord with basic theory? This sort of checking is entirely possible. In most of the social sciences, we don’t, there isn’t, and it doesn’t.

Hygiene and the world distribution of Alzheimer’s disease: Epidemiological evidence for a relationship between microbial environment and age-adjusted disease burden: https://academic.oup.com/emph/article/2013/1/173/1861845/Hygiene-and-the-world-distribution-of-Alzheimer-s

Amyloid-β peptide protects against microbial infection in mouse and worm models of Alzheimer’s disease: http://stm.sciencemag.org/content/8/340/340ra72

Fungus, the bogeyman: http://www.economist.com/news/science-and-technology/21676754-curious-result-hints-possibility-dementia-caused-fungal
Fungus and dementia
paper: http://www.nature.com/articles/srep15015

Porphyromonas gingivalis in Alzheimer’s disease brains: Evidence for disease causation and treatment with small-molecule inhibitors: https://advances.sciencemag.org/content/5/1/eaau3333
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july 2017 by nhaliday
Defection – quas lacrimas peperere minoribus nostris!
https://quaslacrimas.wordpress.com/2017/06/28/discussion-of-defection/

Kindness Against The Grain: https://srconstantin.wordpress.com/2017/06/08/kindness-against-the-grain/
I’ve heard from a number of secular-ish sources (Carse, Girard, Arendt) that the essential contribution of Christianity to human thought is the concept of forgiveness. (Ribbonfarm also has a recent post on the topic of forgiveness.)

I have never been a Christian and haven’t even read all of the New Testament, so I’ll leave it to commenters to recommend Christian sources on the topic.

What I want to explore is the notion of kindness without a smooth incentive gradient.

The Social Module: https://bloodyshovel.wordpress.com/2015/10/09/the-social-module/
Now one could propose that the basic principle of human behavior is to raise the SP number. Sure there’s survival and reproduction. Most people would forget all their socialization if left hungry and thirsty for days in the jungle. But more often than not, survival and reproduction depend on being high status; having a good name among your peers is the best way to get food, housing and hot mates.

The way to raise one’s SP number depends on thousands of different factors. We could grab most of them and call them “culture”. In China having 20 teenage mistresses as an old man raises your SP; in Western polite society it is social death. In the West making a fuss about disobeying one’s parents raises your SP, everywhere else it lowers it a great deal. People know that; which is why bureaucrats in China go to great lengths to acquire a stash of young women (who they seldom have time to actually enjoy), while teenagers in the West go to great lengths to be annoying to their parents for no good reason.

...

It thus shouldn’t surprise us that something as completely absurd as Progressivism is the law of the land in most of the world today, even though it denies obvious reality. It is not the case that most people know that progressive points are all bogus, but obey because of fear or cowardice. No, an average human brain has much more neurons being used to scan the social climate and see how SP are allotted, than neurons being used to analyze patterns in reality to ascertain the truth. Surely your brain does care a great deal about truth in some very narrow areas of concern to you. Remember Conquest’s first law: Everybody is Conservative about what he knows best. You have to know the truth about what you do, if you are to do it effectively.

But you don’t really care about truth anywhere else. And why would you? It takes time and effort you can’t really spare, and it’s not really necessary. As long as you have some area of specialization where you can make a living, all the rest you must do to achieve survival and reproduction is to raise your SP so you don’t get killed and your guts sacrificed to the mountain spirits.

SP theory (I accept suggestions for a better name) can also explains the behavior of leftists. Many conservatives of a medium level of enlightenment point out the paradox that leftists historically have held completely different ideas. Leftism used to be about the livelihood of industrial workers, now they agitate about the environment, or feminism, or foreigners. Some people would say that’s just historical change, or pull a No True Scotsman about this or that group not being really leftists. But that’s transparent bullshit; very often we see a single person shifting from agitating about Communism and worker rights, to agitate about global warming or rape culture.

...

The leftist strategy could be defined as “psychopathic SP maximization”. Leftists attempt to destroy social equilibrium so that they can raise their SP number. If humans are, in a sense, programmed to constantly raise their status, well high status people by definition can’t raise it anymore (though they can squabble against each other for marginal gains), their best strategy is to freeze society in place so that they can enjoy their superiority. High status people by definition have power, and thus social hierarchy during human history tends to be quite stable.

This goes against the interests of many. First of all the lower status people, who, well, want to raise their status, but can’t manage to do so. And it also goes against the interests of the particularly annoying members of the upper class who want to raise their status on the margin. Conservative people can be defined as those who, no matter the absolute level, are in general happy with it. This doesn’t mean they don’t want higher status (by definition all humans do), but the output of other brain modules may conclude that attempts to raise SP might threaten one’s survival and reproduction; or just that the chances of raising one’s individual SP is hopeless, so one might as well stay put.

...

You can’t blame people for being logically inconsistent; because they can’t possibly know anything about all these issues. Few have any experience or knowledge about evolution and human races, or about the history of black people to make an informed judgment on HBD. Few have time to learn about sex differences, and stuff like the climate is as close to unknowable as there is. Opinions about anything but a very narrow area of expertise are always output of your SP module, not any judgment of fact. People don’t know the facts. And even when they know; I mean most people have enough experience with sex differences and black dysfunction to be quite confident that progressive ideas are false. But you can never be sure. As Hume said, the laws of physics are a judgment of habit; who is to say that a genie isn’t going to change all you know the next morning? At any rate, you’re always better off toeing the line, following the conventional wisdom, and keeping your dear SP. Perhaps you can even raise them a bit. And that is very nice. It is niceness itself.

Leftism is just an easy excuse: https://bloodyshovel.wordpress.com/2015/03/01/leftism-is-just-an-easy-excuse/
Unless you’re not the only defector. You need a way to signal your intention to defect, so that other disloyal fucks such as yourself (and they’re bound to be others) can join up, thus reducing the likely costs of defection. The way to signal your intention to defect is to come up with a good excuse. A good excuse to be disloyal becomes a rallying point through which other defectors can coordinate and cover their asses so that the ruling coalition doesn’t punish them. What is a good excuse?

Leftism is a great excuse. Claiming that the ruling coalition isn’t leftist enough, isn’t holy enough, not inclusive enough of women, of blacks, of gays, or gorillas, of pedophiles, of murderous Salafists, is the perfect way of signalling your disloyalty towards the existing power coalition. By using the existing ideology and pushing its logic just a little bit, you ensure that the powerful can’t punish you. At least not openly. And if you’re lucky, the mass of disloyal fucks in the ruling coalition might join your banner, and use your exact leftist point to jump ship and outflank the powerful.

...

The same dynamic fuels the flattery inflation one sees in monarchical or dictatorial systems. In Mao China, if you want to defect, you claim to love Mao more than your boss. In Nazi Germany, you proclaim your love for Hitler and the great insight of his plan to take Stalingrad. In the Roman Empire, you claimed that Caesar is a God, son of Hercules, and those who deny it are treacherous bastards. In Ancient Persia you loudly proclaimed your faith in the Shah being the brother of the Sun and the Moon and King of all Kings on Earth. In Reformation Europe you proclaimed that you have discovered something new in the Bible and everybody else is damned to hell. Predestined by God!

...

And again: the precise content of the ideological point doesn’t matter. Your human brain doesn’t care about ideology. Humans didn’t evolve to care about Marxist theory of class struggle, or about LGBTQWERTY theories of social identity. You just don’t know what it means. It’s all abstract points you’ve been told in a classroom. It doesn’t actually compute. Nothing that anybody ever said in a political debate ever made any actual, concrete sense to a human being.

So why do we care so much about politics? What’s the point of ideology? Ideology is just the water you swim in. It is a structured database of excuses, to be used to signal your allegiance or defection to the existing ruling coalition. Ideology is just the feed of the rationalization Hamster that runs incessantly in that corner of your brain. But it is immaterial, and in most cases actually inaccessible to the logical modules in your brain.

Nobody ever acts on their overt ideological claims if they can get away with it. Liberals proclaim their faith in the potential of black children while clustering in all white suburbs. Communist party members loudly talk about the proletariat while being hedonistic spenders. Al Gore talks about Global Warming while living in a lavish mansion. Cognitive dissonance, you say? No; those cognitive systems are not connected in the first place.

...

And so, every little step in the way, power-seekers moved the consensus to the left. And open societies, democratic systems are by their decentralized nature, and by the size of their constituencies, much more vulnerable to this sort of signalling attacks. It is but impossible to appraise and enforce the loyalty of every single individual involved in a modern state. There’s too many of them. A Medieval King had a better chance of it; hence the slow movement of ideological innovation in those days. But the bigger the organization, the harder it is to gather accurate information of the loyalty of the whole coalition; and hence the ideological movement accelerates. And there is no stopping it.

Like the Ancients, We Have Gods. They’ll Get Greater: http://www.overcomingbias.com/2018/04/like-the-ancients-we-have-gods-they-may-get… [more]
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june 2017 by nhaliday
Edge.org: 2017 : WHAT SCIENTIFIC TERM OR CONCEPT OUGHT TO BE MORE WIDELY KNOWN?
highlights:
- the genetic book of the dead [Dawkins]
- complementarity [Frank Wilczek]
- relative information
- effective theory [Lisa Randall]
- affordances [Dennett]
- spontaneous symmetry breaking
- relatedly, equipoise [Nicholas Christakis]
- case-based reasoning
- population reasoning (eg, common law)
- criticality [Cesar Hidalgo]
- Haldan's law of the right size (!SCALE!)
- polygenic scores
- non-ergodic
- ansatz
- state [Aaronson]: http://www.scottaaronson.com/blog/?p=3075
- transfer learning
- effect size
- satisficing
- scaling
- the breeder's equation [Greg Cochran]
- impedance matching

soft:
- reciprocal altruism
- life history [Plomin]
- intellectual honesty [Sam Harris]
- coalitional instinct (interesting claim: building coalitions around "rationality" actually makes it more difficult to update on new evidence as it makes you look like a bad person, eg, the Cathedral)
basically same: https://twitter.com/ortoiseortoise/status/903682354367143936

more: https://www.edge.org/conversation/john_tooby-coalitional-instincts

interesting timing. how woke is this dude?
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may 2017 by nhaliday
Educational Romanticism & Economic Development | pseudoerasmus
https://twitter.com/GarettJones/status/852339296358940672
deleeted

https://twitter.com/GarettJones/status/943238170312929280
https://archive.is/p5hRA

Did Nations that Boosted Education Grow Faster?: http://econlog.econlib.org/archives/2012/10/did_nations_tha.html
On average, no relationship. The trendline points down slightly, but for the time being let's just call it a draw. It's a well-known fact that countries that started the 1960's with high education levels grew faster (example), but this graph is about something different. This graph shows that countries that increased their education levels did not grow faster.

Where has all the education gone?: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1016.2704&rep=rep1&type=pdf

https://twitter.com/GarettJones/status/948052794681966593
https://archive.is/kjxqp

https://twitter.com/GarettJones/status/950952412503822337
https://archive.is/3YPic

https://twitter.com/pseudoerasmus/status/862961420065001472
http://hanushek.stanford.edu/publications/schooling-educational-achievement-and-latin-american-growth-puzzle

The Case Against Education: What's Taking So Long, Bryan Caplan: http://econlog.econlib.org/archives/2015/03/the_case_agains_9.html

The World Might Be Better Off Without College for Everyone: https://www.theatlantic.com/magazine/archive/2018/01/whats-college-good-for/546590/
Students don't seem to be getting much out of higher education.
- Bryan Caplan

College: Capital or Signal?: http://www.economicmanblog.com/2017/02/25/college-capital-or-signal/
After his review of the literature, Caplan concludes that roughly 80% of the earnings effect from college comes from signalling, with only 20% the result of skill building. Put this together with his earlier observations about the private returns to college education, along with its exploding cost, and Caplan thinks that the social returns are negative. The policy implications of this will come as very bitter medicine for friends of Bernie Sanders.

Doubting the Null Hypothesis: http://www.arnoldkling.com/blog/doubting-the-null-hypothesis/

Is higher education/college in the US more about skill-building or about signaling?: https://www.quora.com/Is-higher-education-college-in-the-US-more-about-skill-building-or-about-signaling
ballpark: 50% signaling, 30% selection, 20% addition to human capital
more signaling in art history, more human capital in engineering, more selection in philosophy

Econ Duel! Is Education Signaling or Skill Building?: http://marginalrevolution.com/marginalrevolution/2016/03/econ-duel-is-education-signaling-or-skill-building.html
Marginal Revolution University has a brand new feature, Econ Duel! Our first Econ Duel features Tyler and me debating the question, Is education more about signaling or skill building?

Against Tulip Subsidies: https://slatestarcodex.com/2015/06/06/against-tulip-subsidies/

https://www.overcomingbias.com/2018/01/read-the-case-against-education.html

https://nintil.com/2018/02/05/notes-on-the-case-against-education/

https://www.nationalreview.com/magazine/2018-02-19-0000/bryan-caplan-case-against-education-review

https://spottedtoad.wordpress.com/2018/02/12/the-case-against-education/
Most American public school kids are low-income; about half are non-white; most are fairly low skilled academically. For most American kids, the majority of the waking hours they spend not engaged with electronic media are at school; the majority of their in-person relationships are at school; the most important relationships they have with an adult who is not their parent is with their teacher. For their parents, the most important in-person source of community is also their kids’ school. Young people need adult mirrors, models, mentors, and in an earlier era these might have been provided by extended families, but in our own era this all falls upon schools.

Caplan gestures towards work and earlier labor force participation as alternatives to school for many if not all kids. And I empathize: the years that I would point to as making me who I am were ones where I was working, not studying. But they were years spent working in schools, as a teacher or assistant. If schools did not exist, is there an alternative that we genuinely believe would arise to draw young people into the life of their community?

...

It is not an accident that the state that spends the least on education is Utah, where the LDS church can take up some of the slack for schools, while next door Wyoming spends almost the most of any state at $16,000 per student. Education is now the one surviving binding principle of the society as a whole, the one black box everyone will agree to, and so while you can press for less subsidization of education by government, and for privatization of costs, as Caplan does, there’s really nothing people can substitute for it. This is partially about signaling, sure, but it’s also because outside of schools and a few religious enclaves our society is but a darkling plain beset by winds.

This doesn’t mean that we should leave Caplan’s critique on the shelf. Much of education is focused on an insane, zero-sum race for finite rewards. Much of schooling does push kids, parents, schools, and school systems towards a solution ad absurdum, where anything less than 100 percent of kids headed to a doctorate and the big coding job in the sky is a sign of failure of everyone concerned.

But let’s approach this with an eye towards the limits of the possible and the reality of diminishing returns.

https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/
https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/#comment-101293
The real reason the left would support Moander: the usual reason. because he’s an enemy.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/
I have a problem in thinking about education, since my preferences and personal educational experience are atypical, so I can’t just gut it out. On the other hand, knowing that puts me ahead of a lot of people that seem convinced that all real people, including all Arab cabdrivers, think and feel just as they do.

One important fact, relevant to this review. I don’t like Caplan. I think he doesn’t understand – can’t understand – human nature, and although that sometimes confers a different and interesting perspective, it’s not a royal road to truth. Nor would I want to share a foxhole with him: I don’t trust him. So if I say that I agree with some parts of this book, you should believe me.

...

Caplan doesn’t talk about possible ways of improving knowledge acquisition and retention. Maybe he thinks that’s impossible, and he may be right, at least within a conventional universe of possibilities. That’s a bit outside of his thesis, anyhow. Me it interests.

He dismisses objections from educational psychologists who claim that studying a subject improves you in subtle ways even after you forget all of it. I too find that hard to believe. On the other hand, it looks to me as if poorly-digested fragments of information picked up in college have some effect on public policy later in life: it is no coincidence that most prominent people in public life (at a given moment) share a lot of the same ideas. People are vaguely remembering the same crap from the same sources, or related sources. It’s correlated crap, which has a much stronger effect than random crap.

These widespread new ideas are usually wrong. They come from somewhere – in part, from higher education. Along this line, Caplan thinks that college has only a weak ideological effect on students. I don’t believe he is correct. In part, this is because most people use a shifting standard: what’s liberal or conservative gets redefined over time. At any given time a population is roughly half left and half right – but the content of those labels changes a lot. There’s a shift.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/#comment-101492
I put it this way, a while ago: “When you think about it, falsehoods, stupid crap, make the best group identifiers, because anyone might agree with you when you’re obviously right. Signing up to clear nonsense is a better test of group loyalty. A true friend is with you when you’re wrong. Ideally, not just wrong, but barking mad, rolling around in your own vomit wrong.”
--
You just explained the Credo quia absurdum doctrine. I always wondered if it was nonsense. It is not.
--
Someone on twitter caught it first – got all the way to “sliding down the razor blade of life”. Which I explained is now called “transitioning”

What Catholics believe: https://theweek.com/articles/781925/what-catholics-believe
We believe all of these things, fantastical as they may sound, and we believe them for what we consider good reasons, well attested by history, consistent with the most exacting standards of logic. We will profess them in this place of wrath and tears until the extraordinary event referenced above, for which men and women have hoped and prayed for nearly 2,000 years, comes to pass.

https://westhunt.wordpress.com/2018/02/05/bright-college-days-part-ii/
According to Caplan, employers are looking for conformity, conscientiousness, and intelligence. They use completion of high school, or completion of college as a sign of conformity and conscientiousness. College certainly looks as if it’s mostly signaling, and it’s hugely expensive signaling, in terms of college costs and foregone earnings.

But inserting conformity into the merit function is tricky: things become important signals… because they’re important signals. Otherwise useful actions are contraindicated because they’re “not done”. For example, test scores convey useful information. They could help show that an applicant is smart even though he attended a mediocre school – the same role they play in college admissions. But employers seldom request test scores, and although applicants may provide them, few do. Caplan says ” The word on the street… [more]
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april 2017 by nhaliday
Main Page - Competitive Programming Algorithms: E-Maxx Algorithms in English
original russian version: http://e-maxx.ru/algo/

some notable stuff:
- O(N) factorization sieve
- discrete logarithm
- factorial N! (mod P) in O(P log N)
- flow algorithms
- enumerating submasks
- bridges, articulation points
- Ukkonen algorithm
- sqrt(N) trick, eg, for range mode query
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february 2017 by nhaliday
Information Processing: Learn to solve every problem that has been solved
While it may be impossible to achieve Feynman's goal, I'm surprised that more people don't attempt the importance threshold-modified version. Suppose we set the importance bar really, really high: what are the most important results that everyone should try to understand? Here's a very biased partial list: basic physics and mathematics (e.g., to the level of the Feynman Lectures); quantitative theory of genetics and evolution; information, entropy and probability; basic ideas about logic and computation (Godel and Turing?); ... What else? Dynamics of markets? Complex Systems? Psychometrics? Descriptive biology? Organic chemistry?
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february 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
ExtraTricky - On Taking Notes in Math Class
Perhaps this fictional story convinced you, and perhaps it didn't. I'm not going to claim I have proof that notes are detrimental to every student, or even on average. I don't know about any research in that area. But if you want to try out not taking notes for yourself, here are my recommendations for how to do it.
- During lecture, try to find the main new ideas being presented. If something is just algebraic manipulation, trust yourself to be able to do that on the homework if you need to.
- If the course doesn't have written materials available, do write down definitions. Keep these very short. Most definitions are only a single sentence. If you're writing more than that you're probably writing something that's not included in the definition.
- Be ready to struggle with the homework. Being stuck on a problem for hours is extremely common for mathematicians, even though it doesn't always seem that way. On one of my problem sets at MIT I was stuck near the end of a solution for around ten hours before realizing that it could be finished in a reasonably simple manner.
- When you get your homework back, make sure you have a complete and correct solution. If it's the one you turned in, great. If the teacher posts homework solutions, read through and keep that. Those solutions are now your notes.
- When exam time comes, go through those homework problems as study materials. If you end up getting stuck on one of those problems again, chances are it'll be in the same place you got stuck the first time, and your mind will connect the dots.
extratricky  oly  math  advice  notetaking  learning  reflection  checklists  metabuch  problem-solving  ground-up  scholar  the-trenches  studying  s:*  org:bleg  nibble  contrarianism  regularizer  hmm  cost-benefit  hi-order-bits 
december 2016 by nhaliday
Books | West Hunter
The Princeton Companion to Mathematics
From Alexander to Actium
Stalingrad: The Fateful Siege
The Decline and Fall of Practically Everybody
The Conquest of New Spain
The Anubis Gates:
The Sleepwalkers
Coup D’Etat: A Practical Handbook
The Penguin Atlas of Ancient History
The Great Siege:
Song of the Sky
How to Solve It
The Double-Cross System
In Search of the Indo-Europeans
The Washing of the Spears
Eagle Against the Sun
The Steel Bonnets
Kim
Rats, Lice, and History
The Great Impostor
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december 2016 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
Wizard War | West Hunter
Some of his successes were classically thin, as when he correctly analyzed the German two-beam navigation system (Knickebein). He realize that the area of overlap of two beams could be narrow, far narrower than suggested by the Rayleigh criterion.

During the early struggle with the Germans, the “Battle of the Beams”, he personally read all the relevant Enigma messages. They piled up on his desk, but he could almost always pull out the relevant message, since he remembered the date, which typewriter it had been typed on, and the kind of typewriter ribbon or carbon. When asked, he could usually pick out the message in question in seconds. This system was deliberate: Jones believed that the larger the field any one man could cover, the greater the chance of one brain connecting two facts – the classic approach to a ‘thick’ problem, not that anyone seems to know that anymore.

All that information churning in his head produced results, enough so that his bureaucratic rivals concluded that he had some special unshared source of information. They made at least three attempts to infiltrate his Section to locate this great undisclosed source. An officer from Bletchley Park was offered on a part-time basis with that secret objective. After a month or so he was called back, and assured his superiors that there was no trace of anything other than what they already knew. When someone asked ‘Then how does Jones do it? ‘ he replied ‘Well, I suppose, Sir, he thinks!’
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november 2016 by nhaliday
Thick and thin | West Hunter
There is a spectrum of problem-solving, ranging from, at one extreme, simplicity and clear chains of logical reasoning (sometimes long chains) and, at the other, building a picture by sifting through a vast mass of evidence of varying quality. I will give some examples. Just the other day, when I was conferring, conversing and otherwise hobnobbing with my fellow physicists, I mentioned high-altitude lighting, sprites and elves and blue jets. I said that you could think of a thundercloud as a vertical dipole, with an electric field that decreased as the cube of altitude, while the breakdown voltage varied with air pressure, which declines exponentially with altitude. At which point the prof I was talking to said ” and so the curves must cross!”. That’s how physicists think, and it can be very effective. The amount of information required to solve the problem is not very large. I call this a ‘thin’ problem’.

...

In another example at the messy end of the spectrum, Joe Rochefort, running Hypo in the spring of 1942, needed to figure out Japanese plans. He had an an ever-growing mass of Japanese radio intercepts, some of which were partially decrypted – say, one word of five, with luck. He had data from radio direction-finding; his people were beginning to be able to recognize particular Japanese radio operators by their ‘fist’. He’d studied in Japan, knew the Japanese well. He had plenty of Navy experience – knew what was possible. I would call this a classic ‘thick’ problem, one in which an analyst needs to deal with an enormous amount of data of varying quality. Being smart is necessary but not sufficient: you also need to know lots of stuff.

...

Nimitz believed Rochefort – who was correct. Because of that, we managed to prevail at Midway, losing one carrier and one destroyer while the the Japanese lost four carriers and a heavy cruiser*. As so often happens, OP-20-G won the bureaucratic war: Rochefort embarrassed them by proving them wrong, and they kicked him out of Hawaii, assigning him to a floating drydock.

The usual explanation of Joe Rochefort’s fall argues that John Redman’s ( head of OP-20-G, the Navy’s main signals intelligence and cryptanalysis group) geographical proximity to Navy headquarters was a key factor in winning the bureaucratic struggle, along with his brother’s influence (Rear Admiral Joseph Redman). That and being a shameless liar.

Personally, I wonder if part of the problem is the great difficulty of explaining the analysis of a thick problem to someone without a similar depth of knowledge. At best, they believe you because you’ve been right in the past. Or, sometimes, once you have developed the answer, there is a ‘thin’ way of confirming your answer – as when Rochefort took Jasper Holmes’s suggestion and had Midway broadcast an uncoded complaint about the failure of their distillation system – soon followed by a Japanese report that ‘AF’ was short of water.

Most problems in the social sciences are ‘thick’, and unfortunately, almost all of the researchers are as well. There are a lot more Redmans than Rocheforts.
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november 2016 by nhaliday
Low-hanging fruit | West Hunter
Think about it: peptic and duodenal ulcer were fairly common, and so were effective antibiotics, starting in the mid-40s. . Every internist in the world – every surgeon – every GP was accidentally curing ulcers – not just one or twice, but again and again. For decades. Almost none of them noticed it, even though it was happening over and over, right in front of their eyes. Those who did notice were ignored until the mid-80s, when Robin Warren and Barry Marshall finally made the discovery stick. Even then, it took something like 10 years for antibiotic treatment of ulcers to become common, even though it was cheap and effective. Or perhaps because it was cheap and effective.

This illustrates an important point: doctors are lousy scientists, lousy researchers. They’re memorizers, not puzzle solvers. Considering that Western medicine was an ineffective pseudoscience – actually, closer to a malignant pseudoscience – for its first two thousand years, we shouldn’t be surprised. Since we’re looking for low-hanging fruit, this is good news. It means that the great discoveries in medicine are probably not mined out. From our point of view, past incompetence predicts future progress. The worse, the better!
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november 2016 by nhaliday
COS597C: How to solve it
- Familiarity with tools. You have to know the basic mathematical and conceptuatl tools, and over the semester we will encounter quite a few of them.
- Background reading on your topic. What is already known and how was it proven? Research involves figuring out how to stand on the shoulders of others (could be giants, midgets, or normal-sized people).
- Ability to generate new ideas and spot the ones that dont work. I cannot stress the second part enough. The only way you generate new ideas is by shooting down the ones you already have.
- Flashes of genius. Somewhat overrated; the other three points are more important. Insights come to the well-prepared.
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october 2016 by nhaliday
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