nhaliday + meta:research   40

The Future of Mathematics? [video] | Hacker News
https://news.ycombinator.com/item?id=20909404
Kevin Buzzard (the Lean guy)

- general reflection on proof asssistants/theorem provers
- Kevin Hale's formal abstracts project, etc
- thinks of available theorem provers, Lean is "[the only one currently available that may be capable of formalizing all of mathematics eventually]" (goes into more detail right at the end, eg, quotient types)
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8 weeks ago by nhaliday
Learning to learn | jiasi
It might sound a bit stupid, but I just realized that a better reading strategy could help me learn faster, almost three times as fast as before.

To enter a research field, we sometimes have to read tens of research papers. We could alternatively read summaries like textbooks and survey papers, which are generally more comprehensive and more friendly for non-experts. But some fields don’t have good summaries out there, for reasons like the fields being too new, too narrow, or too broad.

...

Part 1. Taking good notes and keeping them organized.

Where we store information greatly affects how we access it. If we can always easily find some information — from Google or our own notes — then we can pick it up quickly, even after forgetting it. This observation can make us smarter.

Let’s do the same when reading papers. Now I keep searchable notes as follows:
- For every topic, create a document that contains the notes for all papers on this topic.[1]
- For each paper, take these notes: summaries, quotes, and sufficient bibliographic information for future lookup.[2, pages 95-99]
- When reading a new paper, if it cites a paper that I have already read, review the notes for the cited paper. Update the notes as needed.
This way, we won’t lose what we have read and learned.

Part 2. Skipping technical sections for 93% of the time.

Only 7% of readers of a paper will read its technical sections.[1] Thus, if we want to read like average, it might make sense to skip technical sections for roughly 93% of papers that we read. For example, consider reading each paper like this:
- Read only the big-picture sections — abstract, introduction, and conclusion;
- Scan the technical sections — figures, tables, and the first and the last paragraphs for each section[2, pages 76-77] — to check surprises;
- Take notes;
- Done!
In theory, the only 7% of the papers that we need to read carefully would be those that we really have to know well.
techtariat  scholar  academia  meta:research  notetaking  studying  learning  grad-school  phd  reflection  meta:reading  prioritizing  quality  writing  technical-writing  growth  checklists  metabuch  advice 
september 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?
nibble  q-n-a  overflow  academia  tcs  cs  meta:research  publishing  scholar  lens  properties  cost-benefit  analysis  impetus  increase-decrease  soft-question  motivation  proofs  search  complexity  analogy  problem-solving  elegance  synthesis  hi-order-bits  novelty  discovery 
june 2019 by nhaliday
Philip Guo - Research Design Patterns
List of ways to generate research directions. Some are pretty specific to applied CS.
techtariat  nibble  academia  meta:research  scholar  cs  systems  list  top-n  checklists  ideas  creative  frontier  memes(ew)  info-dynamics  innovation  novelty  the-trenches  tactics 
may 2019 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.
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  quixotic  meta:reading  classic 
june 2018 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
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  meta:research 
january 2017 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
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.
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june 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
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

bundles : abstractacadememetametaproblem-solving

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