A book I’d like (someone) to write

Posted on 5 February 2013 by John

Here’s an idea I had for a book. Maybe someone has already written it. If you know of such a book, please let me know.

Differential geometry has a huge ratio of definitions to theorems. It seems like you do nothing but study definitions for a semester or two in preparation for proving something later. It’s easy to lose sight of the geometry. I’d like to see a book that is a concrete complement more typical abstract books.

My suggestion is for someone to write a book that goes through a standard differential geometry book, like Spivak’s, and compute everything for a small number of example manifolds: at least a sphere and an ellipsoid, maybe a torus. The book would first go through everything on a sphere where things are simplest, then generalize to an ellipsoid. There would be a lot of applications to geodesy: to first approximation the earth is a sphere, to second approximation it is an ellipsoid.

Sometimes a calculation, such as arc length, is very simple on a sphere. It can be done just using trig. Then the analogous calculation on an ellipsoid is much harder. It is complicated enough to illustrate the machinery of differential geometry. However, we know the answers shouldn’t be much different from those for a sphere, so we have a way to see whether the results are reasonable. This book would not shy away from computational difficulties.

I imagine this book would have lots of illustrations. It might even come with physical models, such as a globe with an exaggerated equatorial bulge. The idea is to be as tangible as other books are abstract.

I don’t plan to write this book, at least not any time soon. Maybe if my consulting goes well I would have the time to work on it in the future, but now is not the time for me to write a book. In the mean time, if someone wants to scoop my idea, please do!

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Here are a couple other book ideas I’ve blogged about: R: The Good Parts and a rigorous elementary statistics text.

And here are some posts on geodesy: What is the shape of the earth? and Latitude doesn’t exactly mean what I thought.

And finally a few posts on spherical geometry: Napier’s mnemonic, The Sydney Opera House, and Mercator projection.

Four hours of concentration a day

Posted on 4 February 2013 by John

Man concentrating

As I’ve blogged about before, and mentioned again in my previous post, the great mathematician and physicist Henri Poincaré put in two hours of work in the morning and two in the evening.

Apparently this is a common pattern. Cal Newport mentions this in his interview with Todd Henry.

Now we also know that if you study absolute world class, best virtuoso violin players, none of them put in more than about four or so hours of practice in a day, because that’s the cognitive limit. And this limit actually shows up in a lot of different fields where people do intense training, that you really can’t do about more than four or so hours of this type of really mental strain.

And they often break this into two sessions, of two hours and then two hours. So there’s huge limits here. I think if you’re able to do three, maybe four hours of this sort of deep work in a typical day, you’re hitting basically the mental speed limit, the amount of concentration your brain is actually able to give.

He goes on to say that you may be able to work 15 hours a day processing email and doing other less demanding work, but nobody can sustain more than about four hours of intense concentration per day.

Update: The comments add examples of authors and physicists who had a similar work schedule.

Related post: Increasing your chances of entering flow

Increasing your chances of entering flow

Posted on 1 February 2013 by John

I recently ran across a tip from Mark Hepburn that caught my eye. The content of the tip isn’t important here but rather his justification of the tip:

It sounds trivial, but it can really help keep you in the flow.

This line jumped out at me because I’ve been thinking about my work habits lately. Now that I’m self-employed, I have the opportunity to develop new habits. My excuses for not trying different ways of working have been stripped away. Maybe my excuses weren’t valid before, but it’s obvious that they are not valid now.

Small customizations like Mark mentioned are under-appreciated in part because they are trivial, at least when viewed one at a time. But the cumulative effect of numerous trivial customizations could be substantial. Together they increase the probability that you can act on an idea before it slips your mind and before you lose the will to pursue it.

Small customizations are also very personal, and so they don’t make good blog posts. I suspect that productivity bloggers primarily write about things they don’t actually do. They write about things that a wide audience will find entertaining if not useful. The little things that make a difference to the blogger may be boring or embarrassing to write about.

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Instead of giving a simple list of related links at the bottom as I usually do, I’ll give some links along with commentary.

Henri Poincaré had a radical work schedule: one two-hour sprint in the morning and another in the afternoon. Some people look at that and think he put in half a normal work day. But if he had four hours of concentrated focus, I imagine he put in four times a typical work day.

Here are posts on changing how you type and how you use a text editor.

And here are a three posts on how mundane things are undervalued:

And finally, here’s a post on customizing conventional wisdom to your circumstances.