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Math and the Tired Brain

  1. Jul 2, 2013 #1
    College students are notorious for cramming, late night or all night studying, having too-heavy course loads, skipping meals, etc. Much of this is to be expected and in many cases unavoidable.

    I'm a little bit older (36, I think...) and about to embark on my last year of undergraduate mathematics. While I don't have the brain plasticity of youth, I have a lot of motivation. Unfortunately, to do any work, I seem to require:

    a) lots of sleep
    b) to be well fed
    c) to be slightly caffeinated but not too much, or it raises my distractibility

    If any of these are missing, it's like I'm no good. (I also have reactive hypoglycemia, which makes me sensitive to diet. I really can't miss a meal or snack.)

    After a certain time of day my brain says "no more math." Right now I have my schedule set up so this is not that much of a problem. But I am afraid grad school will be less forgiving.

    Is there some other strategy for getting the most out of my day if I'm not having a "good brain day?" I suppose that even if I can't do any hardcore thinking, maybe lighter reading or just studying definitions or something. But also I just wonder if by "pushing through" I can train my brain to not be so dependent on external factors. Thoughts?

    -Dave K
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  3. Jul 2, 2013 #2


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    Music helps me a lot and I mean A LOT. I can stay up till 4AM studying and still manage to get up at 7 or 8AM for classes as long as I have music to listen to while studying. As far as eating goes, I'm afraid I can't help much there as I barely eat on a daily basis to begin with.
  4. Jul 2, 2013 #3
    Hi Dave K. You can check out Luminosity.com and sign up with them. They have "games" that improve elasticity, speed, and cut down on distraction.

    One thought in addition to your list. Walking is NOT listed. Having pre-diabeties, you should understand how important a walking program can be to stabilize your sugar and also help your concentration. In addition, if your sugars are off, they (on their own) will alter your ability to process data; exercise is the only way to burn off excess sugars.

    Also, cutting back on processed foods might help you to have more "clear" days. There is so much junk in our food chain now, that I have found this helps immensely as well.

    Best of luck in your endeavors.
  5. Jul 2, 2013 #4
    Thanks for the reply.

    I know about luminosity, but, two things..

    1) there's no convincing evidence that these types of things work, other than studies conducted by the company itself, and there are a few studies that show they do not work at all.

    2) If it works or if it doesn't, I think the work I'm doing (mathematics), etc. would be just as effective as doing luminosity type exercises. I think luminosity is basically math disguised as games. (Or maybe the converse is true!)

    Yes, I did not mention it. You're right to mention it. However I am a regular runner/cyclist, with the exception of the last month due to having my gallbladder removed. At minimum I bike 4 miles a day (to school and back) but I do either running or biking as well as yoga on top of that.

    All been done. This is kind of why I'm so frustrated. Between my wife and I we spend about $250 a week on groceries, since we don't eat boxed, processed, etc. We don't eat out. We spend 2-3 hours a day in the kitchen to make sure there are 3 good meals and at least 3 snacks for in between.

    So I have this whole blasted ritual (food prep, exercise, eat, hydrate...)I need to go through for hours a day to make sure I have "clear" days. That's hours that I can't actually be doing the work, of course. And if I miss one of those snacks, or a workout, miss a few hours of sleep, then it's like I'm no good.

    And by 9:00pm I'm pretty much out. (You can also see why I'd be hesitant to add luminosity to this task list).

    So that's the physical part.

    What I'm kind of asking is whether there is a strategy for studying that I can use when my "higher functions" don't work quite as well, or whether in general just "pushing through" might work, or if that would just lead to burnout. I try to just push through it sometimes, but it's as if there's a part of my brain that has clocked out.

    -Dave K
  6. Jul 2, 2013 #5
    Unfortunately music doesn't help me much, since I have a musical background, my minds tends to gravitate towards analysis of what's being played and it gets distracting.

    There are times when it works, if the work is very mechanical/computational , but I'm getting less and less of that type of work.

    And 3 hours of sleep just will not cut it.
  7. Jul 2, 2013 #6


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    I agree with you that Lumosity (not Luminosity) is trumped up quackery. But there are some puzzles online that are surely very good. I recommend this loop puzzle as being surely on of the best logic puzzles online. At the bottom you will see more puzzles, the circles and bridges puzzle is also very nice. These could definitely be good practice because one must look all around the puzzle to see the next deducible fact. The Hard difficulty is pretty difficult, you will probably need weeks of practice to solve > 50% of them. I truly think these are the best free non-verbal logic puzzles online.

    Best of luck.

    PS. If you practice until you can solve 50% of the 15x15 Hard Loop puzzles, I'll bet your concentration has improved, it can hardly not have.
  8. Jul 2, 2013 #7
    Hi Dave

    From what you've said it seems more like a physiological/medical/stress management problem than anything to do with learning maths. Exhaustion could certainly be part of it, too - sometimes 'mathematical exhaustion' is hard to detect, and tends to accumulate.

    I can't really give you rock solid advice on this - but one thing that often helps me reset my brain for 'higher functions' is to have a 15-20 minute 'coffee nap'. That is, when you're feeling really tired, have a small coffee quickly (i.e. don't take 10 minutes drinking it), set a timer and try to have a nap for about that much time. The caffeine will take effect just about when you've paid back a bit of sleep debt - but if you exceed the time limit too much, grogginess will take over. Over several years I've tested this trick extensively: it almost always lets me rescue 'bad' days and even elevate the good days, in terms of productivity and use of higher functions.
    There even seems to be some scientific support for this, given certain conditions.

    Of course, this may not work for you (e.g. I don't know how hypoglycemia is related to this, and I don't know if you react to caffeine differently than me), and obviously it can't typically be done when you're tired while not being physically at home.

    Maybe you can make it work, though. Failing that, there's also the 'many small meals' method - i.e. above and beyond having a healthy diet in terms of choice, eat & drink before you get hungry or thirsty, respectively. Prof Dan Bernardot makes a pretty convincing case for this.

    (Again, hypoglycemia might make this more complicated. It might be worth the time to get medical advice on this.)

    I hope you find something that helps - if it were up to me, every maths student would live each month with 100% 'good brain days.' =)
  9. Jul 2, 2013 #8
    I can't really nap for some reason. I do meditate for 20-30 minutes a day. (Been practicing meditation for about 10 years) It helps. Sometimes I sneak a coffee in during. (We drink espresso here, so it doesn't take long.)

    I have. I eat every two hours, low carb, higher fat/protein content. That's kind of what I meant before. I have all the physical stuff taken care of. There's nothing else in terms of physicality/stress reduction/diet that I can possibly do. I sometimes spend more time doing that stuff than studying.

    That's why I'm wondering if there's an actual study skill/strategy that I can work on. I may just have to accept that I can only do so much at my age and with my physical limitations. I am just a little worried about the pace of grad school not being as merciful.

    The only next step is to start getting medicated for ADD, which I've been trying to avoid. That's why I'm focusing on study skills.

    Thanks. I may just have to accept that I can only do so much at my age and with my physical limitations. I am just a little worried about the pace of grad school not being as merciful.

    The only next step is to start getting medicated for ADD, which I've been trying to avoid. That's why I'm focusing on study skills.

    -Dave K
  10. Jul 2, 2013 #9
    Maybe this could be part of the problem?
    http://www.fi.edu/learn/brain/carbs.html [Broken]
    Last edited by a moderator: May 6, 2017
  11. Jul 2, 2013 #10
    ^^ Sorry, just realized you said you have reactive hypoglycemia :redface:
  12. Jul 2, 2013 #11
    No worries. Yeah, it's weird, and not a lot of people have it. Carbs actually make me stupider! It's quite frustrating.
  13. Jul 2, 2013 #12
    I have noticed that I have the "tired brain" happen lately also. For me, I think I have pinpointed it to a shifting sleep schedule. If I can go to sleep at the same time and wake up at the same time, 10pm-5:30am I always feel alert throughout the day. Although, if I shift those times even about an hour later I'll get that foggy mind feeling the next day.

    If I do have that feeling I usually can take a 10-15 minute nap in the afternoon and I'm back to normal. The nap usually happens when I'm reading something technical, lol. It's like my brain just can't process anything and needs to shut down. Unfortunately, you said you can't nap :frown: but I just wanted to throw in my two cents.
  14. Jul 2, 2013 #13
    Maybe I should read the actual thread and not just the OP before responding. =)

    Alright, it looks like you need some way to get the most out of your mind when it's already exhausted (or just partly 'clocked out' as you put it).

    Just off the top of my head, here's what worked for me in these kinds of situations: try breaking your study pattern. For instance, if you usually a) follow a mathematical text for a bit, b) do the exercises, c) compare with solutions; break that pattern - e.g. read definitions for a bit instead. Then try simply writing down functions or concepts - maybe do a bit of memorization. Don't feel as though you need to have a sense of accomplishment at the end.

    You can call it low-intensity work, but that may be the wrong way to think about it. It may sound strange, but by doing things that don't feel like actual mathematical work, you can often do the groundwork for future mathematical insights (which you can have when you're on a good brain day). We get at least a fair fraction of our ideas from our subconscious minds, so it's only reasonable to suspect that a lot of subtle logical connections are made there even when you don't consciously attempt to make them.

    (I know a bunch of good books on mathematical problem solving, study skills and such that have relevant stuff on this - let me know if you'd like some links.)

    From my own experience, 'pushing through' works - for a while. Then after some point, your health magically takes a nosedive, and you can't do anything anymore. That short burst of performance is probably not worth it. I'd say you're better off if you don't ignore mental exhaustion for too long.
    Last edited: Jul 2, 2013
  15. Jul 3, 2013 #14
    This may be different for you and me since I only have about half the years as you, but I usually need a healthy social life in order to be on top of my math game.
    I generally try to check Maslow's hierarchy of needs (http://en.m.wikipedia.org/wiki/Maslow's_hierarchy_of_needs) when I feel like I'm having an off day. I find that good 3rd and 4th levels can really boost my performance. Of course this is just a theory with known limitations.
  16. Jul 3, 2013 #15
    In my experience most of people that work/studies 12 hour days study sloppily, bad, unfocused and crash from time to time. In my opinion I feel you learn more with 7-8 hours of focused study than 12 hour days.
  17. Jul 9, 2013 #16
    I personally avoid cramming, all nighters, and et cetera. If I have math test the next day and I'm too tired to study, I go to bed and wake up early in the morning to study. As a general rule, I always study ahead of time to avoid the chaos of changing my sleeping schedule. I'm prone to forget to eat anyways, but going to college won't make you suddenly have a bad diet. For most people that has to do with budget. If you need extra energy, take a B-12 vitamin instead of an extra serving of coffee. The B-12 works better anyways. Good Luck.
  18. Jul 11, 2013 #17


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    Do you have a demanding job?
  19. Jul 11, 2013 #18
    I eat a low carb diet (fully ketogenic) since I find it just gives me constant energy throughout the day, no spikes/troughs, but after a little while I started losing the ability to concentrate and I couldn't really sit down and do a lot of maths work at once like I usually could.

    I did 3 things which have helped a lot:

    - Taking magnesium and vitamin D supplements. I did a bit of reading and apparently the cloudiness and inability to concentrate is pretty common with low carbs, and magnesium supplements are encouraged. I just grabbed some vitamin D as well because it's commonly deficient (and it's pretty cheap), I haven't tried taking either of the two exclusively so I don't actually know if both are necessary. I didn't feel an immediate difference but then after a few days I could certainly concentrate much better.

    - High intensity, short duration exercise (mostly early in the morning). Granted, I am barely 20, so sprinting and weights training didn't pose an issue for my body (joints etc.) and I appreciate that the older you get the harder this may be, so YMMV. Weights training shouldn't be an issue though unless you have somehow really stuffed your body. It's nice to push yourself to the limit in such a way, and it's as much mental as it is physical.

    - Break up the routine! Doing the same thing week after week can be taxing and make you stagnate a bit, so at least once a fortnight I try to do something to kind of 'reset' and refresh my mind. Something like going for a big bike ride (200km+), a random overnight camping trip in the middle of nowhere, go for a hike, spend a day drawing/painting or playing music and so on... This works wonders for me.
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