> your brain can only work productively on a hard problem for 1 -3 hours before needing to reboot
This is very different from my experience. For advanced math or physics problems, it general takes at least a couple of hours to assemble the relevant mathematical structure in your head. Only once you are familiar with the "setting" can you really start to work.
I've heard similar things about writing code.
If I took a break every 2 hours, I'd never get anything done.
While that is true, sometimes stepping away from the problem will let it coalesce in my head and give clarity to what I wasn't making any headway on earlier. If you aren't getting anything done, working longer is probably not the path to victory. But if you are in the zone, you can sometimes work for hours straight and zip through.
Yep. In my experience the same is also true of writing good political science papers, solving information design problems, or really digging in to a photography project.
I solved most of my graduate algorithms problems while lying in bed in the morning, lying on the couch, or in the shower. I simply do not understand how some people can concentrate on problems like that while jogging. My thoughts while jogging are primarily about how much jogging sucks and how I just gotta keep going. If I could solve a technical problem in my head while exercising then either the problem is really easy or I'm not getting very much exercise.
If I could solve a technical problem in my head while exercising then either the problem is really easy or I'm not getting very much exercise.
Remember that walking is technically exercise. 5 miles walking is 5 miles jogging is 5 miles running, at least as far as your heart is concerned. Calorie burn is roughly equal too.
I won't pretend to know anything about you (You might run laps around me!) but if you think jogging sucks there's a chance you're making some classic mistakes re: not investing in slow base miles, not developing 'cellular piping' so your body can efficiently wick away waste, etc...
This topic strikes a chord with me because I hated running a few years ago. A marine friend of mine knocked it into my head that I was going about it all wrong, and I finally came around (kicking and screaming) to his way of thinking. I read Galloway's book (http://books.google.com/books?id=3kqUP3upHQ4C&printsec=f...) changed my approach and started running for pleasure. Now I log 20 to 30 miles a week for recreation, and formerly 'breakneck' paces feel comfortable (I think the charge from that natural pace is a positively excellent time to let the endorphins supercharge your thinking). And for the record I'm not blazing fast... my 5k PR is 20 minutes and change. But again speed doesn't really count for beans; It's really about following the fundamentals and letting the miles take care of themselves. BONUS: The boost to my fitness helped me earn a qualifying time for my fire department's Rapid Intervention Team, which was really gratifying.
You don't need to kill yourself to see awesome benefits from running, and I truly believe (moderate) physical exertion can plausibly yield higher order thinking.
Sure. The act of running creates waste, typically in the form of dead blood cells and lactic acid. It's natural, but if the muscle cells are ill-prepared to properly dispose of the waste it can create inefficiencies in the form of poorer performance.
It's important as a runner that you have a solid "highway system" of muscle fibers that can handle the waste throughput of your regimen. The most popular way competitve runners achieve this is by running lots of slow* comfortable base miles over several months. Increasing mileage 10% a week will break the cells down, while planned rest allows the body to regenerate 'heartier' cells capable of handling greater and greater loads. In the most relatable sense that burn you feel when you work out will start happening later and later; In physiological terms you've "increased your lactic threshold." The advantages of building an aerobic base transcend the muscle highway concept and seem to have really solid implications for cardiovascular health. Just something to think about.
*slow is relative and implies that you're running about 2 minutes off your tempo pace. A little huffing/puffing is okay, but it should feel natural to hold a conversation. Maintaining this slow pace - even when you feel you could run faster - is the hardest part of base building and therefore that piece which seems to pay the best dividends (for those who are disciplined).
Mitochondria development occurs when you're running - actually, doing aerobic exercise for long period of time. Mitochondria is responsible for intra cell energy exchange and utilization of "waste".
My trainer told me that professional runners, swimmers and skiers are pretty vulnerable for alcoholism, because mitochondrias greatly help to utilize products of alcohol metabolism. So there is buzz, but no hangover, you can do it over and over again. Until someone becomes physically dependent on alcohol.
There's a reason why academics prefer whiteboards and chalkboards to pen and paper. It's because they feel genuinely more productive and creative while working on them. I personally think that it comes down to improved blood flow, and it's one of the key tricks that my friends and I used to earn physics degrees from Caltech. We'd go camp out in empty lecture halls late at night, filling chalkboard after chalkboard with scrawl, and only sit down to copy finished problems in their final form.
I like standing up while reading and doing more free-form work like exploring ideas. But for concentrating on specific problems or focused study, I need to be sitting down. I just can't concentrate my efforts as well when standing.
Meat of the article: "Repeated fresh attacks are how hard problems are solved in the real world. ... Until you’ve approached a problem fresh, 3 – 4 times, you haven’t really yet tried to solve it."
There is more meat. Such as that you can't focus for extended periods of time. It is important to schedule time to work, preferably in the morning. It is useful to have a study partner around your level, but generally not useful to have a large study group. Get started early.
The same applies to any kind of reading with a deeper philosophical underpinning. Reading the words in no way means you truly understand what's being said.
> The ideal configuration for a problem set is a single partner who is at roughly your ability and is willing to meet earlier in the week.
I agree with everything he said, but in my experience, the part I've quoted is at least an order of magnitude more important than the rest. And don't forget the "roughly at your ability" part - if you work with someone much smarter, you may just get more confused and you certainly won't feel like you're contributing much; if you work with someone much less smart, it's a waste of time (which is not to say that helping people isn't a nice thing to do - it just won't help you complete the problem set).
This mostly matches up with my own experience. I always start several days early, and I always work with one or two other people if at all possible.
Starting several days early gives you a few days to think about a problem if you need it and ensures you don't have to pull any really late nights.
Working with people means that you won't get stuck on the easy problems if you didn't understand everything perfectly or forget one crucial fact/lemma exists (which I find is otherwise a real danger). It also gives you people to bounce ideas off of for the really hard problems,
The other thing I always do is to do my problem sets in two stages. In the first stage (which I do with other people), I figure out how to solve the problem and outline how I'm going to write it up. In the second stage (which I do alone and after solving everything), I write the problems up. As I do this, I walk through how we did the problems when we first solved them, and very often find mistakes we made.
>The ideal configuration for a problem set is a single partner who is at roughly your ability and is willing to meet earlier in the week.
There's really a lot of substance to this remark. I work with another guy in my class frequently and often come away feeling as though I've free-ridden somewhat.
But after looking more closely the results we get, it becomes apparent they are the product of our combined efforts and wouldn't have been achievable alone. The verbalisation is also highly conducive to understanding intuitively - a principle Salman Khan talks about and I can't agree with enough.
Ha! I didn't get my degree in engineering, but most of my friends did and this describes many classes they took in their field. Especially applied engineering physics.
I had two friends in AEP that were problem set partners, and they spent so much time working together her now-fiancé didn't ask her out for ages because he thought her problem set partner was her boyfriend.
And no, these kids were not dull buds. The girl is currently a grad student at MIT, and the not-boyfriend problem set partner is a grad student Harvard.
One tip I'd add: don't limit asking for prof/TA help to office hours. Knock and ask politely, and most (all, in my experience) will gladly answer questions on homeworks or lectures. Many seem to appreciate the chance to have a break from their work to talk with a student.
This is very different from my experience. For advanced math or physics problems, it general takes at least a couple of hours to assemble the relevant mathematical structure in your head. Only once you are familiar with the "setting" can you really start to work.
I've heard similar things about writing code.
If I took a break every 2 hours, I'd never get anything done.