The Math of When to Self-Improve

It's rational to be motivated entirely by the net present value of one's future earnings.

There might be other relevant sources of utility for the developer, but did you really want me to complicate the post by discussing them?

Programmers are immortal (and never switch career.)

I think your discount rate is supposed to take the probability of your dying each year into account. Ditto the above regarding career switching/retirement.

A programmer's skill increases in a smooth, deterministic, predictable and exponential manner over time.

Not necessary. For my model to be useful, you just need to know the expected rate at which the programmer's wealth-creation ability will improve. The formula gives the programmer's expected rate of instantaneous value creation.

A programmer's skill is a scalar-valued quantity proportional to their (potential) income.

Taboo skill.

Anyway, the real question is whether using this model or some approximation of it produces better results than relying on one's native intuition. Relevant link.

The context was optimizing job earnings, not transhumanist brain modifications. I think the model is reasonable in that context, if a bit hard to apply.

I think I have a simpler utility function than you do :)

I think it comes from the units in the definition of g:

(For example, if working on improving their tools currently offers the software developer the opportunity to improve their wealth creation skills at a rate of a 50% increase in their ability per year, their growth factor would be 1.5.) We'll call that g for growth.

At that point, you've accounted for current present value of your current skills, but now you want to add in the value of future growth. The '1' in '1.5' is what you have now, and is always what you have now by definition; the '.5' is additional growth. To remove what you already have, you do '-1'. Hence you multiply by 'g-1'

Deja Vu:

http://lesswrong.com/lw/28e/the_math_of_when_to_selfimprove/2100?c=1

I'm pretty sure you'd be crazy to value the time and energy you spend on these activities at only $8/hour.

Another way of thinking the cards would be "if it takes me 30-40 seconds to memorize this card for 3 years, how many seconds do I expect to spend looking up the information on this card if I don't bother to memorize it?" Would you really spend 30-40 seconds looking up information on the median card you'd consider memorizing?

As for dual-n-back, first there's the critique you mention in your FAQ, which seems very damning. Second it's quite unpleasant in my experience at least, and therefore uses up a lot of energy. And third, I'm inherently skeptical that simple mental activities like dual-n-back and nintendo brain age could increase your IQ faster than complex activities like writing software that someone might be willing to pay for or becoming proficient in economics--and these last activities have significant side benefits above and beyond possible IQ increase.

If you just want to increase your income I suspect there are much more efficient and direct ways of doing it. I have a few arbitrage-type ideas I can share via private message with anyone who expresses a desire to donate a lot of their income to preventing human existential risk.

For what it's worth, when I first wrote this post many months ago, I thought time spent on pure self-improvement activities was generally time well spent. Now I think it's generally not time well spent unless you're at the point where you spend eight hours a day browsing reddit or something like that. My view is that if you're able to spend a decent chunk of the day working on worthwhile projects, you should do that, and your self-improvement efforts should be limited to running day-long or week-long self-experiments on yourself that don't cost you many productive hours and recording the results of those. (Example of such a self-experiment: if you're a programmer, write down every bug you have, estimate how long it takes to solve, and once it's solved record how long it actually took to solve and the details of your solution. Then periodically review for trends. I've done a little bit of this; it was highly unpleasant/boring but it seems intuitively like it could be quite beneficial so I'm planning to do it more.)

They are notoriously short-term planners in many cases, and uncertainty is the reason why. Most think that improvements should pay off in 3-5 years, or they aren't worth doing.

Corporations also have many issues that a truly unitary immortal entity might not; the principle-agent conflict is everywhere in corporations, especially the financial industry types you excoriate.

You seem to have gotten through to a couple of people on the strength of your math

That's a danger I hadn't thought of. Thanks. Maybe it's best to discuss new methods of using math only with those who think they're super-competent at it, so they won't be impressed if you do something tricky and will shoot down anything that doesn't make sense to them (instead of assuming you're just more clever).

there's no such thing as the "instantaneous annual value" of self-improvement in the real world.

Could you be a little more precise here? I'm talking about someone's rate of value production in terms of dollars per year. I used the word instantaneous to emphasize the fact that this rate isn't necessarily going to hold steady over even one year.

The idea is there are two ways of creating value: directly, or by self-improving. To know how much value you are creating by self-improving, you could start by estimating the percentage increase in your effectiveness as a result of your self-improvement efforts. This seems like something that one could possibly estimate. But that still wouldn't be enough to compare the two sorts of value creation if you weren't able to value yourself as an asset. If you value yourself as an asset using net present value, then you can treat the value produced through self-improvement just like the value you create directly.

What was your intention when you decided to compute the instantaneous annual value of different strategies?

The formula is for the instantaneous rate of value creation because you only need to know what you can do to maximize the rate at which you're creating value right now.

A model that confined itself to calculating the net present value of a finite # of months or years of various strategies would have been both (a) more accurate, in the sense of better reflecting real-world concerns

Perhaps, although there is a probability distribution over the time at which a person stops producing. So there might be a better way to correct for this.

(b) easier to understand, in that it would have required less math.

Well the ending formula would have been more complicated:

(g%20-%201))

Fooling around with a calculator, you can see that if a person's discount rate is 1.05 and z = 20, then the term you suggest is almost 40% of the size of the term it's being subtracted from, which is significant. However, if you change the person's discount rate to 1.15, the term you suggest is 6% of the first term's size. My high discount rate might have been what caused me think the term you suggested was unimportant.

You also may wish to avoid mimicking the formal style of textbooks, e.g., "exercise for the reader," "question to confirm understanding." This tone of voice can be easy to use, but it's odd and unpleasant for me to read it, given that (in theory) we're all peers here.

OK, so maybe the question/answer should just go in italics between sections, like

Who is John Galt? Answer in rot13: fhcrezna.

so you wouldn't think I was making a ploy for high status. (Heh, I can't see how using rot13 mimicks the formal style of textbooks :)

You also may wish to avoid mimicking the formal style of textbooks, e.g., "exercise for the reader," "question to confirm understanding." This tone of voice can be easy to use, but it's odd and unpleasant for me to read it, given that (in theory) we're all peers here. You may have something to teach us, but you're not exactly my professor.

I would add that this is another reason to simplify the math - doing so eliminates the need for exercises by making the answers less confusing.

f and p appear to be the same thing: the annual income they would get from coding full-time.

If they're doing some self-improvement activity that requires that they stop wealth-creation altogether, p = 0. If they're coding half-time, p = 0.5f. Etc. You're right about f.

Also, if you can grow your wealth-creation skills faster than your discount rate, then obviously you should put all your effort into growing those skills and none into earning money now. Obvious within the terms of the model, at least. In practice, you have to use the skills as you develop them -- that's part of learning the skills. Choose a project that you need some new skill to complete. A real project, creating a product that that you are going to sell.

OK, but what if you have one project that's a little more educational and one that's a little more profitable? The equation should help you decide between them.

BTW, you've done a good job of explaining why I think college for programmers is stupid. (But I'm going anyway, for the friends/prestige.)

I believe this applies generally to any form of self-improvement: doing stuff, and learning to do stuff better, cannot be separated.

Hm. I tend to think that someone can often improve their skill faster per minute by reading advice than doing. The things I learned from my last project (~1 month of work) would easily fit in a blog post.

Plus what about reading about a subject like probability, game theory, or history that could potentially transform the way you look at things?

One hole in my model is it has no way of taking in to account self-improvement effects that are temporary, such as spending the time necessary to think of a really good idea for a project (significantly helps your wealth creation skill, but only until you finish that project).

Thank you for daring to use math! (How did you make the equations?)

If you put LaTeX code after "http://www.codecogs.com/png.latex?", you should get a png of the equation the code represents that you can insert in the post editor using the image insertion tool. Codecogs' own equation editor is good if you don't know LaTeX. Use this thing I coded just today if you want to insert LaTeX in a comment, as there's a lot of nasty escaping that needs to go on.

You might be interested in John Holland's theorem showing that the genetic algorithm optimizes (on average) the tradeoff between exploration (trying out new things) and exploitation (doing things you already know work pretty well).

Sounds interesting, but wouldn't one's definition of "optimized" depend on one's discount rate? I guess in Holland's model exploration requires resources? That's not a factor in my model, but maybe it should be. Even if my independent software developer had all their living expenses covered, they might still be able to "explore" faster with more resources by hiring software developers in third-world countries to read blogs for them :)

There is a good reason that the discount rate (r) is assumed to be constant: if your discount rate is not constant, you are a money pump. For more, look for web pages that contain "discount rate" and "preference reversal".

Hm, interesting.

Also, I forgot to mention that it approximates by making the software developer's product release continuous, when in reality they might be releasing a product, say, every few months.

I think you could just compare sums of money. Would you trade 10$ now for 20$ in a year? I would, so your discount is <2. Would you trade 10$ for 15$ in a year? Then your discount is <1.5. And so on.

If you just have trouble comparing dollars, then maybe you could compare coffee, or books, or something.

I don't think constant g is important. If your g changes you can just recompute the formula. Remember, the formula gives your instantaneous rate of value creation.

Glad you liked it. I decided on two posts in case some people didn't know integrals or weren't concerned with the derivation of the equation and were willing to take my word that it made sense.

It doesn't for me. Can you read this version?