nhaliday + scholar   89

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.
ratty  learning  reading  studying  prioritizing  history  letters  philosophy  science  comparison  the-classics  canon  speculation  reflection  big-peeps  iron-age  mediterranean  roots  lens  core-rats  thinking  methodology  grad-school  academia  physics  giants  problem-solving  meta:research  scholar  the-trenches  explanans  crux  metameta  duplication  sociality  innovation 
june 2018 by nhaliday
What was the hardest part of doing your Ph.D.? - Quora
I think it’s a 5-way tie, each hard in its own way:
- Picking a good topic.
- Figuring out how to bound it.
- Actually getting started.
- Going on when nothing works as you had planned.
- Knowing when to stop.

A good advisor can make some of these things easier, but you’re the one who has to do them all.
q-n-a  qra  grad-school  phd  planning  scholar  success  advice  prioritizing 
january 2017 by nhaliday
Thinking Outside One’s Paradigm | Academically Interesting
I think that as a scientist (or really, even as a citizen) it is important to be able to see outside one’s own paradigm. I currently think that I do a good job of this, but it seems to me that there’s a big danger of becoming more entrenched as I get older. Based on the above experiences, I plan to use the following test: When someone asks me a question about my field, how often have I not thought about it before? How tempted am I to say, “That question isn’t interesting”? If these start to become more common, then I’ll know something has gone wrong.
ratty  clever-rats  academia  science  interdisciplinary  lens  frontier  thinking  rationality  meta:science  curiosity  insight  scholar  innovation  reflection  acmtariat  water  biases  heterodox  🤖  🎓  aging  meta:math  low-hanging  big-picture  hi-order-bits  flexibility  org:bleg  nibble  the-trenches  wild-ideas  metameta  courage  s:**  discovery  context  embedded-cognition  endo-exo  near-far  🔬  info-dynamics  allodium  ideas  questions  within-without 
january 2017 by nhaliday
soft question - Thinking and Explaining - MathOverflow
- good question from Bill Thurston
- great answers by Terry Tao, fedja, Minhyong Kim, gowers, etc.

Terry Tao:
- symmetry as blurring/vibrating/wobbling, scale invariance
- anthropomorphization, adversarial perspective for estimates/inequalities/quantifiers, spending/economy

fedja walks through his though-process from another answer

Minhyong Kim: anthropology of mathematical philosophizing

Per Vognsen: normality as isotropy
comment: conjugate subgroup gHg^-1 ~ "H but somewhere else in G"

gowers: hidden things in basic mathematics/arithmetic
comment by Ryan Budney: x sin(x) via x -> (x, sin(x)), (x, y) -> xy
I kinda get what he's talking about but needed to use Mathematica to get the initial visualization down.
To remind myself later:
- xy can be easily visualized by juxtaposing the two parabolae x^2 and -x^2 diagonally
- x sin(x) can be visualized along that surface by moving your finger along the line (x, 0) but adding some oscillations in y direction according to sin(x)
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january 2017 by nhaliday
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 
december 2016 by nhaliday
Fact Posts: How and Why
The most useful thinking skill I've taught myself, which I think should be more widely practiced, is writing what I call "fact posts." I write a bunch of these on my blog. (I write fact posts about pregnancy and childbirth here.)

To write a fact post, you start with an empirical question, or a general topic. Something like "How common are hate crimes?" or "Are epidurals really dangerous?" or "What causes manufacturing job loss?"

It's okay if this is a topic you know very little about. This is an exercise in original seeing and showing your reasoning, not finding the official last word on a topic or doing the best analysis in the world.

Then you open up a Google doc and start taking notes.

You look for quantitative data from conventionally reliable sources. CDC data for incidences of diseases and other health risks in the US; WHO data for global health issues; Bureau of Labor Statistics data for US employment; and so on. Published scientific journal articles, especially from reputable journals and large randomized studies.

You explicitly do not look for opinion, even expert opinion. You avoid news, and you're wary of think-tank white papers. You're looking for raw information. You are taking a sola scriptura approach, for better and for worse.

And then you start letting the data show you things.

You see things that are surprising or odd, and you note that.

You see facts that seem to be inconsistent with each other, and you look into the data sources and methodology until you clear up the mystery.

You orient towards the random, the unfamiliar, the things that are totally unfamiliar to your experience. One of the major exports of Germany is valves? When was the last time I even thought about valves? Why valves, what do you use valves in? OK, show me a list of all the different kinds of machine parts, by percent of total exports.

And so, you dig in a little bit, to this part of the world that you hadn't looked at before. You cultivate the ability to spin up a lightweight sort of fannish obsessive curiosity when something seems like it might be a big deal.

And you take casual notes and impressions (though keeping track of all the numbers and their sources in your notes).

You do a little bit of arithmetic to compare things to familiar reference points. How does this source of risk compare to the risk of smoking or going horseback riding? How does the effect size of this drug compare to the effect size of psychotherapy?

You don't really want to do statistics. You might take percents, means, standard deviations, maybe a Cohen's d here and there, but nothing fancy. You're just trying to figure out what's going on.

It's often a good idea to rank things by raw scale. What is responsible for the bulk of deaths, the bulk of money moved, etc? What is big? Then pay attention more to things, and ask more questions about things, that are big. (Or disproportionately high-impact.)

You may find that this process gives you contrarian beliefs, but often you won't, you'll just have a strongly fact-based assessment of why you believe the usual thing.
ratty  lesswrong  essay  rhetoric  meta:rhetoric  epistemic  thinking  advice  street-fighting  scholar  checklists  🤖  spock  writing  2016  info-foraging  rat-pack  clarity  systematic-ad-hoc  bounded-cognition  info-dynamics  let-me-see  nitty-gritty  core-rats  evidence-based  truth 
december 2016 by nhaliday
Information Processing: Advice to a new graduate student
first 3 points (tough/connected advisor, big picture, benchmarking) are key:

1. There is often a tradeoff between the advisor from whom you will learn the most vs the one who will help your career the most. Letters of recommendation are the most important factor in obtaining a postdoc/faculty job, and some professors are 10x as influential as others. However, the influential prof might be a jerk and not good at training students. The kind mentor with deep knowledge or the approachable junior faculty member might not be a mover and shaker.

2. Most grad students fail to grasp the big picture in their field and get too caught up in their narrowly defined dissertation project.

3. Benchmark yourself against senior scholars at a similar stage in their (earlier) careers. What should you have accomplished / mastered as a grad student or postdoc in order to keep pace with your benchmark?

4. Take the opportunity to interact with visitors and speakers. Don't assume that because you are a student they'll be uninterested in intellectual exchange with you. Even established scholars are pleased to be asked interesting questions by intelligent grad students. If you get to the stage where the local professors think you are really good, i.e., they sort of think of you as a peer intellect or colleague, you might get invited along to dinner with the speaker!

5. Understand the trends and bandwagons in your field. Most people cannot survive on the job market without chasing trends at least a little bit. But always save some brainpower for thinking about the big questions that most interest you.

6. Work your ass off. If you outwork the other guy by 10%, the compound effect over time could accumulate into a qualitative difference in capability or depth of knowledge.

7. Don't be afraid to seek out professors with questions. Occasionally you will get a gem of an explanation. Most things, even the most conceptually challenging, can be explained in a very clear and concise way after enough thought. A real expert in the field will have accumulated many such explanations, which are priceless.
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november 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
reflection  math  grad-school  phd  advice  expert  strategy  long-term  growth  🎓  aphorism  learning  scholar  hi-order-bits  tactics  mathtariat  metabuch  org:bleg  nibble  the-trenches  big-picture  narrative  meta:research  info-foraging  skeleton  studying  prioritizing  s:*  info-dynamics  chart  expert-experience  explore-exploit 
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/
books  summary  review  economics  growth-econ  interdisciplinary  hmm  physics  thinking  feynman  tradeoffs  paul-romer  econotariat  🎩  🎓  scholar  aphorism  lens  signal-noise  cartoons  skeleton  s:**  giants  electromag  mutation  genetics  genomics  bits  nibble  stories  models  metameta  metabuch  problem-solving  composition-decomposition  structure  abstraction  zooming  examples  knowledge  human-capital  behavioral-econ  network-structure  info-econ  communication  learning  information-theory  applications  volo-avolo  map-territory  externalities  duplication  spreading  property-rights  lattice  multi  government  polisci  policy  counterfactual  insight  paradox  parallax  reduction  empirical  detail-architecture  methodology  crux  visual-understanding  theory-practice  matching  analytical-holistic  branches  complement-substitute  local-global  internet  technology  cost-benefit  investing  micro  signaling  limits  public-goodish  interpretation 
september 2016 by nhaliday
The capacity to be alone | Quomodocumque
In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still from the perspective or thirty or thirty five years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve done all things, often beautiful things in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have to rediscover in themselves that capability which was their birthright, as it was mine: The capacity to be alone.
math  reflection  quotes  scholar  mathtariat  lens  optimate  serene  individualism-collectivism  the-monster  humility  the-trenches  virtu  courage  emotion  extra-introversion  allodium  ascetic 
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 
june 2016 by nhaliday
10 reasons Ph.D. students fail
Once a student has two good publications, if she convinces her committee that she can extrapolate a third, she has a thesis proposal.

Once a student has three publications, she has defended, with reasonable confidence, that she can repeatedly conduct research of sufficient quality to meet the standards of peer review. If she draws a unifying theme, she has a thesis, and if she staples her publications together, she has a dissertation.
advice  grad-school  phd  techtariat  planning  gotchas  scholar  🎓 
may 2016 by nhaliday
For potential Ph.D. students
Ravi Vakil's advice for PhD students

General advice:
Think actively about the creative process. A subtle leap is required from undergraduate thinking to active research (even if you have done undergraduate research). Think explicitly about the process, and talk about it (with me, and with others). For example, in an undergraduate class any Ph.D. student at Stanford will have tried to learn absolutely all the material flawlessly. But in order to know everything needed to tackle an important problem on the frontier of human knowledge, one would have to spend years reading many books and articles. So you'll have to learn differently. But how?

Don't be narrow and concentrate only on your particular problem. Learn things from all over the field, and beyond. The facts, methods, and insights from elsewhere will be much more useful than you might realize, possibly in your thesis, and most definitely afterwards. Being broad is a good way of learning to develop interesting questions.

When you learn the theory, you should try to calculate some toy cases, and think of some explicit basic examples.

Talk to other graduate students. A lot. Organize reading groups. Also talk to post-docs, faculty, visitors, and people you run into on the street. I learn the most from talking with other people. Maybe that's true for you too.

Specific topics:
- seminars
- giving talks
- writing
- links to other advice
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may 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)
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may 2016 by nhaliday
Discrete Analysis
each paper is given a nice write-up + links to any talks. useful for getting the background
research  papers  aggregator  math  gowers  math.CO  stream  scholar  scholar-pack  👳  org:mat  accretion  discrete  additive-combo 
april 2016 by nhaliday
Work hard | What's new
Similarly, to be a “professional” mathematician, you need to not only work on your research problem(s), but you should also constantly be working on learning new proofs and techniques, going over important proofs and papers time and again until you’ve mastered them. Don’t stay in your mathematical comfort zone, but expand your horizon by also reading (relevant) papers that are not at the heart of your own field. You should go to seminars to stay current and to challenge yourself to understand math in real time. And so on. All of these elements have to find their way into your daily work routine, because if you neglect any of them it will ultimately affect your research output negatively.
- from the comments
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april 2016 by nhaliday
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