Recorded my productivity for 1000 days, here’s what I found

In 2011, I started my PhD and also started recording every minute I spent working line-by-line through graduate texts and research papers in mathematics. At that time, the majority of my work was spent understanding various branches of mathematics necessary to do research.

I recorded this data in a spreadsheet. It’s important to realize what kind of time I recorded. I recorded only time spent going through books and papers line-by-line. I did not record any time searching the literature, skimming through papers I needed to read, or going to class. In other words, I only recorded highly focused time where I was actively engaging with the material.

I wanted to understand the limits of my mind in terms of how quickly I can absorb new mathematics. Other work is important too, but in my experience tasks like searching the literature or typesetting my thesis require very little effort compared to reading new mathematics line-by-line.

In my measurement, I tried to be precise. During the time intervals I measured, I worked constantly. I did not take any breaks to check email or do anything else. In fact, I did not even have the internet at home during my entire PhD. I always worked at home with no distractions. If any break was required, I stopped the timer, but usually I worked in short intervals of 45-90 minutes where no breaks were required.

Here are the results in terms of hours spent over the past fourteen days in a graph, recorded for about a thousand days (click to enlarge):

Here is what I learned in this exercise of fairly precise measurement:

  1. Periods of high mental productivity come in cycles. There would always come a period of 2-3 weeks where I just wasn’t very productive. I tried to recognize when that happened and just do other things instead of being upset that I could not work.
  2. There is a hard limit to how much work your mind can do. In the long run (that is averaged over a period of years including days where I did nothing), I averaged one hour a day.
  3. On any given day I could do a very hard maximum of 3 hours of intense reading, usually less.

The bottom line is that work comes in phases, and the mind has an upper limit to what it can do. It is like lifting weights. After a certain number of reps at the bench press, you just won’t able to do any more. And moreover, after doing an intense weight workout, you need to take a break to let your muscles recover. It does not make sense to have it uniformly done day after day. When your mind is at its peak power, it will do a lot more than the average per day. Intense mental work like understanding math is much more like anaerobic exercise, rather than aerobic exercise like running.

Everyone has a different level of intensity they can handle. For me, it seemed to come out to a long-term average of an hour a day but other people are different and could average two hours a day. (Remember, this average is over all days of the year.) Also, one hour for some person might mean getting farther in the book with even more understanding than another person can do in two hours.

The mind is a complex machine and if you are going to use it for very intense intellectual work, you need to understand the subtlety of its power, and how to use it well. It needs a combination of a strong effort together without any harshness and it can do amazing things.

3 Comments

  • Elizabeth Henning says:

    Did you also track the hard work of thinking up and working out new mathematics for research? How do you feel this compares with learning mathematics by working through texts and papers?

    Also, what about consolidation work for learning like review and self-testing?

    • Jason Polak says:

      Thank you for the questions!

      > Did you also track the hard work of thinking up and working out new mathematics for research?

      I didn’t do that with these observations. Part of the reason for that is that during the beginning of my degree, I really spent much more of my time working through papers and books rather than working on research. I mean, although I was reading about techniques I needed, I did very little ‘original work’ at that time. That accounts for the “working out” part.

      In terms of the “thinking up” part, that seems to just come spontaneously when I am reading about math, so actually the main way I come up with ideas is just reading and waiting for ideas to randomly appear.

      > How do you feel this compares with learning mathematics by working through texts and papers?

      I think it’s very similar to working through existing math except there is the additional component of calculating/proving stuff you feel to be true. But because there are such huge gaps between the conjectures you make and what exists, there is a lot more just “staring into space”. With reading, the “staring into space” only lasts for seconds or minutes and then you just keep going onto new stuff. With research, the “staring into space” might last much longer, and persists around similar ideas for much longer because sometimes it can take hours or days before the correct “next step” appears in your mind. Whereas, with reading existing math, the next steps are much more guided, like a well-worn trail.

      That is one reason why I never tried to measure time doing research later when I started to focus more on writing papers as opposed to learning new math. With learning new math, the progress is fairly predictable and what to do is mostly obvious, so thirty minutes one day is roughly the same as thirty minutes the next week. But with research, the correct breakthrough might just come randomly when you’re not even doing math so one hour thinking might not actually do very much whereas one minute the next day might be way more mentally productive and also mentally taxing. In other words, with research, the mental strain is harder to measure with time whereas with reading it is fairly easy.

      > Also, what about consolidation work for learning like review and self-testing?

      When I am actually reading, I don’t tend to do much review, but I do work out a lot of examples and of course in math further material depends on past material quite strongly so review happens in that way.

      Of course when I do things like give a talk or write a blog post, I am in some ways reviewing the material. However, I don’t feel like doing that stuff requires much effort in comparison to reading through books/papers line-by-line, so I wasn’t that interested in recording that.

      Personally, I don’t find straight review or repetition very helpful. On the other hand, I do love to do problems and usually I try to work out all the exercises, but most of the time doing exercises was not recorded in this data either. The reason for that is mainly that I do not find doing exercises to require the same kind of mental technique as reading and understanding proofs.

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