Actually, I’m not sure it does. You seem to have gotten through to a couple of people on the strength of your math, but one way of wording a critique I see repeated in the comments is that there’s no such thing as the “instantaneous annual value” of self-improvement in the real world. I tend to agree.
What was your intention when you decided to compute the instantaneous annual value of different strategies? Sometimes it makes sense to let a model deviate from reality in order to make it simpler, clearer, or more tractable. I don’t see how your model accomplishes this. On the contrary, it seems to me like computing the value of different strategies on an instantaneous basis complicates your model by requiring the use of integrals.
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, and (b) easier to understand, in that it would have required less math.
I do hope you publish the ‘practical’ half of your article, but I urge you to be careful not to let your ability to do math get in the way of your ability to develop and teach useful models.
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.
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
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.
Sure! I’ll try to distinguish between 3 concepts:
(1) is average value production over a meaningfully long period of time, e.g. twelve months. Even if we don’t know how productive you are on any given day, we can get a decent estimate of your productivity over twelve months by extrapolating from past performance and from your honest statements about what you plan to do next. If you say you plan to write code for immediate profit, and, in the past, that activity has earned you between $2,000 and $9,000 a month, then we might crunch the numbers and estimate that you’ll make something like $57,500 a year, with wide error bars.
(2) is the net present value of (1). If you figure that after coding for twelve months, you’ll have earned $57,500, and your discount rate is 1.15, then your net present value of coding for twelve months is $50,000. Unless you get paid on a biweekly basis, in which case your net present value might be more like $54,000.
(3) is the slope of the curve used to estimate (1). The units are expressed in $ per year, but the quantity itself is fundamentally connected with a very short period of time. If you assume, as a trivial and obviously inaccurate example, that the formula for a pure code-writing strategy is Income(t) = ($2750 t t) + $52,000, then the “instantaneous value” of Income(t) is $0 when you start out, $2750 six months into the year, and $5500 at the end of the year.
My point is that (3) is not a very useful metric, because we are very unlikely to have anywhere near enough information about the typical person’s production curve to start calculating derivatives. Extrapolating future income based on past income already taxes the predictive powers of our data set to the limit. If you want to put yourself in a reference class of similarly situated programmers, fine, but that raises a host of other theoretical issues, e.g. which reference classes are most relevant.
Obviously I agree that (2) is an interesting metric—that’s why I want to read your next article. I’m just confused about what good you think (3) is accomplishing.
Perhaps you didn’t mean to refer to (3) at all. Perhaps you just used the phrase “instantaneous value” to mean “net present value.” That would be somewhat confusing. Especially in a post making heavy use of simple integrals, I associate the word “instantaneous” with the idea of derivatives and slopes.
My high discount rate might have been what caused me think the term you suggested was unimportant.
I’m curious as to how accurate your self-estimate of your discount rate is. Are you heavily in debt or otherwise deeply leveraged? You should be able to find all kinds of opportunities to borrow at less than 15% interest.
OK, so maybe the question/answer should just go in italics between sections.
That would certainly be easier for me to read. Knowing how the LW community works, I suspected you weren’t actually making a ploy for higher status. It’s a mental energy drain, though, to have to sit there reminding myself that you’re just using a funny register, and not actually trying to be an authority figure. The energy drain takes away from my ability to read and enjoy and learn from your post, and I suspect at least some other people would feel the same way. And, yes, rot13 is a clue that you’re not actually full of yourself. :-)
I’m curious as to how accurate your self-estimate of your discount rate is. Are you heavily in debt or otherwise deeply leveraged? You should be able to find all kinds of opportunities to borrow at less than 15% interest.
I appreciate you said that, because I realized that despite my claim of a high discount rate, I haven’t actually borrowed any money. Probably if I had a steady stream of income I would.
I really did mean (3), and I’m not ashamed of it. My thinking is that if you’re an individual who’s trying to be as effective as possible, you’re going to want to guess what you can do to be maximally effective right now, and I might as well fit my formulas for you.
Edit: It’s true that there is higher variance in a person’s output over a short time period. But I’m not sure we should avoid a question just because it’s hard to answer.
Probably if I had a steady stream of income I would.
Makes sense. Just because you have a high discount rate doesn’t mean you have a high tolerance for risk; there’s a fine line between wanting to redirect your future income toward the present and wanting to spend now at the cost of going bankrupt later
.>I really did mean (3), and I’m not ashamed of it.
Well, at least that clears up your motives—they’re pure. Sorry I doubted you. I thought maybe for a moment that you just liked showing off calculus, but I guess you were just trying to attack a really hard problem. This comment is sincere, not sarcastic.
But I’m not sure we should avoid a question just because it’s hard to answer.
Avoid, no. Save for slightly later, yes. In my opinion, the much easier and nearly as useful problem of calculating medium-term net present value should have been solved first, and then once we all understand that and have begun to apply it to our everyday lives, then it’s time to try to solve the much harder and only marginally more useful problem of calculating instantaneous net present value. But, you know, you’re the one doing the work, and (not knowing you) I have no reason to distrust your estimate of your ability to solve a really hard problem. So, good luck!
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.
Actually, I’m not sure it does. You seem to have gotten through to a couple of people on the strength of your math, but one way of wording a critique I see repeated in the comments is that there’s no such thing as the “instantaneous annual value” of self-improvement in the real world. I tend to agree.
What was your intention when you decided to compute the instantaneous annual value of different strategies? Sometimes it makes sense to let a model deviate from reality in order to make it simpler, clearer, or more tractable. I don’t see how your model accomplishes this. On the contrary, it seems to me like computing the value of different strategies on an instantaneous basis complicates your model by requiring the use of integrals.
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, and (b) easier to understand, in that it would have required less math.
I do hope you publish the ‘practical’ half of your article, but I urge you to be careful not to let your ability to do math get in the way of your ability to develop and teach useful models.
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.
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).
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.
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.
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.
Well the ending formula would have been more complicated:
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.
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 :)
Sure! I’ll try to distinguish between 3 concepts:
(1) is average value production over a meaningfully long period of time, e.g. twelve months. Even if we don’t know how productive you are on any given day, we can get a decent estimate of your productivity over twelve months by extrapolating from past performance and from your honest statements about what you plan to do next. If you say you plan to write code for immediate profit, and, in the past, that activity has earned you between $2,000 and $9,000 a month, then we might crunch the numbers and estimate that you’ll make something like $57,500 a year, with wide error bars.
(2) is the net present value of (1). If you figure that after coding for twelve months, you’ll have earned $57,500, and your discount rate is 1.15, then your net present value of coding for twelve months is $50,000. Unless you get paid on a biweekly basis, in which case your net present value might be more like $54,000.
(3) is the slope of the curve used to estimate (1). The units are expressed in $ per year, but the quantity itself is fundamentally connected with a very short period of time. If you assume, as a trivial and obviously inaccurate example, that the formula for a pure code-writing strategy is Income(t) = ($2750 t t) + $52,000, then the “instantaneous value” of Income(t) is $0 when you start out, $2750 six months into the year, and $5500 at the end of the year.
My point is that (3) is not a very useful metric, because we are very unlikely to have anywhere near enough information about the typical person’s production curve to start calculating derivatives. Extrapolating future income based on past income already taxes the predictive powers of our data set to the limit. If you want to put yourself in a reference class of similarly situated programmers, fine, but that raises a host of other theoretical issues, e.g. which reference classes are most relevant.
Obviously I agree that (2) is an interesting metric—that’s why I want to read your next article. I’m just confused about what good you think (3) is accomplishing.
Perhaps you didn’t mean to refer to (3) at all. Perhaps you just used the phrase “instantaneous value” to mean “net present value.” That would be somewhat confusing. Especially in a post making heavy use of simple integrals, I associate the word “instantaneous” with the idea of derivatives and slopes.
I’m curious as to how accurate your self-estimate of your discount rate is. Are you heavily in debt or otherwise deeply leveraged? You should be able to find all kinds of opportunities to borrow at less than 15% interest.
That would certainly be easier for me to read. Knowing how the LW community works, I suspected you weren’t actually making a ploy for higher status. It’s a mental energy drain, though, to have to sit there reminding myself that you’re just using a funny register, and not actually trying to be an authority figure. The energy drain takes away from my ability to read and enjoy and learn from your post, and I suspect at least some other people would feel the same way. And, yes, rot13 is a clue that you’re not actually full of yourself. :-)
I appreciate you said that, because I realized that despite my claim of a high discount rate, I haven’t actually borrowed any money. Probably if I had a steady stream of income I would.
I really did mean (3), and I’m not ashamed of it. My thinking is that if you’re an individual who’s trying to be as effective as possible, you’re going to want to guess what you can do to be maximally effective right now, and I might as well fit my formulas for you.
Edit: It’s true that there is higher variance in a person’s output over a short time period. But I’m not sure we should avoid a question just because it’s hard to answer.
Makes sense. Just because you have a high discount rate doesn’t mean you have a high tolerance for risk; there’s a fine line between wanting to redirect your future income toward the present and wanting to spend now at the cost of going bankrupt later
.>I really did mean (3), and I’m not ashamed of it.
Well, at least that clears up your motives—they’re pure. Sorry I doubted you. I thought maybe for a moment that you just liked showing off calculus, but I guess you were just trying to attack a really hard problem. This comment is sincere, not sarcastic.
Avoid, no. Save for slightly later, yes. In my opinion, the much easier and nearly as useful problem of calculating medium-term net present value should have been solved first, and then once we all understand that and have begun to apply it to our everyday lives, then it’s time to try to solve the much harder and only marginally more useful problem of calculating instantaneous net present value. But, you know, you’re the one doing the work, and (not knowing you) I have no reason to distrust your estimate of your ability to solve a really hard problem. So, good luck!
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.