nhaliday + skeleton   58

How I Choose What To Read — David Perell
READING HEURISTICS
1. TRUST RECOMMENDATIONS — BUT NOT TOO MUCH
2. TAME THE THRILLERS
3. BLEND A BIZARRE BOWL
4. TRUST THE LINDY EFFECT
5. FAVOR BIOGRAPHIES OVER SELF-HELP
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28 days ago by nhaliday
Reasoning From First Principles: The Dumbest Thing Smart People Do
Most middle-class Americans at least act as if:
- Exactly four years of higher education is precisely the right level of training for the overwhelming majority of good careers.
- You should spend most of your waking hours most days of the week for the previous twelve+ years preparing for those four years. In your free time, be sure to do the kinds of things guidance counselors think are impressive; we as a society know that these people are the best arbiters of arete.
- Forty hours per week is exactly how long it takes to be reasonably successful in most jobs.
- On the margin, the cost of paying for money management exceeds the cost of adverse selection from not paying for it.
- You will definitely learn important information about someone’s spousal qualifications in years two through five of dating them.
-Human beings need about 50% more square feet per capita than they did a generation or two ago, and you should probably buy rather than rent it.
- Books are very boring, but TV is interesting.

All of these sound kind of dumb when you write them out. Even if they’re arguably true, you’d expect a good argument. You can be a low-risk contrarian by just picking a handful of these, articulating an alternative — either a way to get 80% of the benefit at 20% of the cost, or a way to pay a higher cost to get massively more benefits — and then living it.[1]
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6 weeks ago by nhaliday
Zettelkästen? | Hacker News
Here’s a LessWrong post that describes it (including the insight “I honestly didn’t think Zettelkasten sounded like a good idea before I tried it” which I also felt).

yeah doesn't sound like a good idea to me either. idk
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8 weeks ago by nhaliday
Unix philosophy - Wikipedia
1. Make each program do one thing well. To do a new job, build afresh rather than complicate old programs by adding new "features".
2. Expect the output of every program to become the input to another, as yet unknown, program. Don't clutter output with extraneous information. Avoid stringently columnar or binary input formats. Don't insist on interactive input.
3. Design and build software, even operating systems, to be tried early, ideally within weeks. Don't hesitate to throw away the clumsy parts and rebuild them.
4. Use tools in preference to unskilled help to lighten a programming task, even if you have to detour to build the tools and expect to throw some of them out after you've finished using them.
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august 2019 by nhaliday
Reconsidering epistemological scepticism – Dividuals
I blogged before about how I consider an epistemological scepticism fully compatible with being conservative/reactionary. By epistemological scepticism I mean the worldview where concepts, categories, names, classes aren’t considered real, just useful ways to categorize phenomena, but entirely mental constructs, basically just tools. I think you can call this nominalism as well. The nominalism-realism debate was certainly about this. What follows is the pro-empirical worldview where logic and reasoning is considered highly fallible: hence you don’t think and don’t argue too much, you actually look and check things instead. You rely on experience, not reasoning.

...

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

...

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

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

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

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

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

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

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

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

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

...

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

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

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

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

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

...

- Ultimate causation explains traits in terms of evolutionary forces acting on them.
- Proximate causation explains biological function in terms of immediate physiological or environmental factors.
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july 2018 by nhaliday
Jordan Peterson is Wrong About the Case for the Left
I suggest that the tension of which he speaks is fully formed and self-contained completely within conservatism. Balancing those two forces is, in fact, what conservatism is all about. Thomas Sowell, in A Conflict of Visions: Ideological Origins of Political Struggles describes the conservative outlook as (paraphrasing): “There are no solutions, only tradeoffs.”

The real tension is between balance on the right and imbalance on the left.

In Towards a Cognitive Theory of Polics in the online magazine Quillette I make the case that left and right are best understood as psychological profiles consisting of 1) cognitive style, and 2) moral matrix.

There are two predominant cognitive styles and two predominant moral matrices.

The two cognitive styles are described by Arthur Herman in his book The Cave and the Light: Plato Versus Aristotle, and the Struggle for the Soul of Western Civilization, in which Plato and Aristotle serve as metaphors for them. These two quotes from the book summarize the two styles:

Despite their differences, Plato and Aristotle agreed on many things. They both stressed the importance of reason as our guide for understanding and shaping the world. Both believed that our physical world is shaped by certain eternal forms that are more real than matter. The difference was that Plato’s forms existed outside matter, whereas Aristotle’s forms were unrealizable without it. (p. 61)

The twentieth century’s greatest ideological conflicts do mark the violent unfolding of a Platonist versus Aristotelian view of what it means to be free and how reason and knowledge ultimately fit into our lives (p.539-540)

The Platonic cognitive style amounts to pure abstract reason, “unconstrained” by reality. It has no limiting principle. It is imbalanced. Aristotelian thinking also relies on reason, but it is “constrained” by empirical reality. It has a limiting principle. It is balanced.

The two moral matrices are described by Jonathan Haidt in his book The Righteous Mind: Why Good People Are Divided by Politics and Religion. Moral matrices are collections of moral foundations, which are psychological adaptations of social cognition created in us by hundreds of millions of years of natural selection as we evolved into the social animal. There are six moral foundations. They are:

Care/Harm
Fairness/Cheating
Liberty/Oppression
Loyalty/Betrayal
Authority/Subversion
Sanctity/Degradation
The first three moral foundations are called the “individualizing” foundations because they’re focused on the autonomy and well being of the individual person. The second three foundations are called the “binding” foundations because they’re focused on helping individuals form into cooperative groups.

One of the two predominant moral matrices relies almost entirely on the individualizing foundations, and of those mostly just care. It is all individualizing all the time. No balance. The other moral matrix relies on all of the moral foundations relatively equally; individualizing and binding in tension. Balanced.

The leftist psychological profile is made from the imbalanced Platonic cognitive style in combination with the first, imbalanced, moral matrix.

The conservative psychological profile is made from the balanced Aristotelian cognitive style in combination with the balanced moral matrix.

It is not true that the tension between left and right is a balance between the defense of the dispossessed and the defense of hierarchies.

It is true that the tension between left and right is between an imbalanced worldview unconstrained by empirical reality and a balanced worldview constrained by it.

A Venn Diagram of the two psychological profiles looks like this:
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july 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
Books I suggest you read so you won’t be misled as often – Gene Expression
People often ask me for history books on a very specific topics often, assuming I’ve read something on an issue because I exhibit some fluency discussing something that might seem abstruse or arcane. The thing is that I haven’t always read a monograph on a singular topic even if I know a fair amount on it. It’s just that I’ve read a larger number of history books, so the union of my knowledge set is quite wide and expansive.

...

In any case, what books should you read? It’s useful to read big general surveys because they allow you to frame and interpret narrower monographs.

...

What is my goal with providing you this list? I want you to be able to iterate through historical assertions people in the media and politics make against your internal data set. See if they are full of shit. They often are.

There are two classes of bullshit. The first class are the nakedly mendacious. This is more common in the political class, where lying is a form of art. The second class are just ignorant and don’t know any better. This is more common in the pundit class.

One trick that the pundit class pulls sincerely because they are often ignorant is that they cite a historian to buttress an assertion, even getting a quote from that historian. But quite often the historian is clearly misleading the audience…the historian may not utter a lie, but in their presentation they allow the reader to have a takeaway that aligns with the normative bias of the pundit, and the historian that has prostituted themselves to some cause. Obviously you will never master a specific area of history like an academic with a command of another language, but if you know enough you can easily smell bullshit when it’s being injected into the information stream.

https://gnxp.nofe.me/2017/06/15/the-system-of-the-world-by-william-h-mcneill/

other: http://gapersblock.com/airbags/archives/22_books_to_get_you_up_to_speed_on_the_entire_world_part_6_the_whole_world/
military history: https://www.gnxp.com/WordPress/2017/06/12/books-i-suggest-you-read-so-you-wont-be-misled-as-often/#comment-2518
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june 2017 by nhaliday
How is Chinese history organized? - Quora
Typically, in my mind, this is how I structure history:
1. Dinosaurs
2. Cavemen
3. Pre-Christian
4. Roman (500 BC to 500 AD)
5. Dark Ages
6. Middle Ages
7. Renaissance (Machiavelli and the Tudors go here.)
8. Reformation
9. Industrial Age (WWI & WWII go here.)
10. Information Age

First two are the same.
3. Dawn of civilization.
4. Loose united, feudal lords fighting each other.
5. United by first emperor of Qin, centralised government.
6. Warlords fighting for uniting.
7. United.
8. Repeat 6&7 for several times.
9. Last empire Qing.
10. Moderation, struggling from foreign invading force, revolution.
11. Revolution of revolution, communism take over.
12. Reform, non-communism.
13. Economic powerhouse, world factory.
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june 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
Overcoming Bias : On the goodness of Beeminder
There is a lot of leeway in what indicators you measure, and some I tried didn’t help much. The main things I measure lately are:

- number of 20 minute blocks of time spent working. They have to be continuous, though a tiny bit of interruption is allowed if someone else causes it
- time spent exercising weighted by the type of exercise e.g. running = 2x dancing = 2 x walking
- points accrued for doing tasks on my to-do list. When I think of anything I want to do I put it on the list, whether it’s watching a certain movie or figuring out how to make the to do list system better. Some things stay there permanently, e.g. laundry. I assign each task a number of points, which goes up every Sunday if it’s still on the list. I have to get 15 points per day or I lose.
ratty  core-rats  hanson  rationality  money-for-time  akrasia  productivity  workflow  webapp  tools  review  software  exocortex  decision-making  working-stiff  the-monster  🦉  beeminder  skeleton  summary  gtd  time-use  quantified-self  procrastination 
january 2017 by nhaliday
Thought Patterns: Marginal · Alex Guzey
Problem: you have a certain action you want to be doing but when the moment comes you forget about it or the trigger just never fully comes to your attention.

Example: Instead of postponing small tasks (e.g. taking out the trash) I want to do them immediately, but when they actually come, I forget about this intention and continue with whatever I was doing before i.e. telling myself I’ll do them later.

How to solve? Make these if-else action plans to always be somewhere at the back of the mind, preferably not far from the working memory, always on the edge of awareness.

Solution: Anki deck with the maximum card interval of 1 day and long initial learning curve.
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december 2016 by nhaliday
Thoughts on graduate school | Secret Blogging Seminar
I’ll organize my thoughts around the following ideas.

- Prioritize reading readable sources
- Build narratives
- Study other mathematician’s taste
- Do one early side project
- Find a clump of other graduate students
- Cast a wide net when looking for an advisor
- Don’t just work on one thing
- Don’t graduate until you have to
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september 2016 by nhaliday
Why Information Grows – Paul Romer
thinking like a physicist:

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

Abstraction vs. Radical Specificity: https://paulromer.net/abstraction-vs-radical-specificity/
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september 2016 by nhaliday
soft question - How do you not forget old math? - MathOverflow
Terry Tao:
I find that blogging about material that I would otherwise forget eventually is extremely valuable in this regard. (I end up consulting my own blog posts on a regular basis.) EDIT: and now I remember I already wrote on this topic: terrytao.wordpress.com/career-advice/write-down-what-youve-d‌​one

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

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

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

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

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

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

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

his description of Aumann's agreement theorem seems to be incorrect/miss the point
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january 2016 by nhaliday

bundles : metametametavague

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