The main difficulties in giving an accurate and brief statement of what physics is for someone who’s never seen anything like it are (1) that physics is a very big subject and (2) that your stipulation about the audience seems to be intended to assume they don’t know any mathematics to speak of either.
Are you claiming that DI is a hugely varied subject like physics? (If so: How is that even possible, given how recent it apparently is?)
Are you claiming that DI depends on a large and conceptually very difficult substrate, as physics does with mathematics? (If so: What is that substrate?)
If the answers are both “no”, then I’ll adjust your question to fix those two mismatches, and attempt to give a brief summary of (not all of physics, but) Newtonian particle mechanics for (not someone completely ignorant of mathematics, but) someone who has college-level mathematics but has somehow managed not to hear that it can be applied to understanding the physical world.
“This is a theory about the motion of small rigid objects such as rocks. The same theory can actually handle large objects by considering them as aggregates of smaller ones, but for the moment we’ll only consider objects that are very small. So, suppose we have a bunch of small objects. At any instant we can describe the state of the universe by saying (1) where these objects are—we specify this by giving three coordinates for each object—and (2) how fast and in what direction each object is moving—we specify this by another set of three coordinates, which collectively we call the velocity. And the only other thing there is to know about each object is its mass, a single positive number that in some sense describes how much of it there is; it’s closely related to how heavy it feels when you hold it.
“Now the basic rules are as follows. First: the derivative of position with respect to time is the velocity. Second: the derivative of velocity with respect to time, which we call the acceleration, is completely determined by a set of rules that care only about the positions, velocities, and masses of the objects. (As long as they don’t actually crash into one another. We’ll talk about that in a moment.)
“Third: the rule for finding the acceleration is as follows. The acceleration of each object is a sum of vectors, one for each other object. What’s happening here is that all the objects are pulling on one another; objects with more mass pull harder. More precisely, the formula goes like this: the acceleration of an object with mass m is the sum over all the other objects of Mr/|r|^3 where r is the vector from our object to the other object and M is the mass of the other object. So the further away the other object is, the less effect it has; in practice this means we can mostly ignore objects very far away.
“Here’s an exercise, to give you a feeling for what the theory lets you do. Define the momentum of an object to be the mass times the velocity. Then prove that the sum of all the momenta in the system never changes.
“This system takes some getting used to, although basically it’s just fairly elementary mathematics. Let me mention a few of the things that follow from it. We just saw a “conservation law”: the total momentum is constant. There are a whole lot of other conservation laws, and in many cases one can make detailed predictions using only those. If you have one object whose mass is very large and all other nearby objects have much smaller mass and don’t get too close to one another, then you can pretend that the first object stays fixed in place, and that the others’ motions are affected only by it, and in that case it turns out that their paths are always conic sections. In particular, our solar system is like this, and the planets move in near-perfect ellipses. If you do the calculations more carefully, taking into account the planets’ influence on one another, you can get very accurate results, and in fact someone once found a previously unknown planet by noticing that another already known planet wasn’t moving quite as expected and working out where another planet would have to be to produce the observed deviations.
“That’ll do for now. If you want a more difficult challenge, try to prove the statement I made about conic sections.”
...Okay, that is honestly an impressively rapid bit of writing in its own unusual context (as a summary of newtonian particle mechanics to someone who had college math but had somehow never heard about physics, like you said.)
But my original analogy was never meant to be expanded, because it was never an argument by analogy in the first place, as I told Jem
OK, so the only point of your analogy was to explain how you feel about being asked to explain what DI is? Fair enough. Then all I can say is: It doesn’t seem to me that you’ve successfully communicated how you feel about that, since apparently you find it unreasonable to be asked to explain what DI is, whereas if I try to imagine myself in any genuinely-analogous situation then I don’t find it unreasonable to be asked the corresponding question.
I’m also rather confused about what your actual problem with explaining what DI is is. You say it’s kinda like the problem someone has who’s asked to explain what physics is. But (see above) it seems to me to be highly unlike that problem in a couple of respects that (for me) seem to be central to the difficulty of the problem. So what, in fact, is it about DI that makes it so difficult for you to say what it is?
An uncharitable explanation suggests itself: Perhaps you cannot say just what DI is because you don’t know what DI is; you’ve read things saying how wonderful it is, and you’ve experienced something that purports to be DI and found that it works well, and concluded: DI is great—without actually pinning down just what DI is. I don’t think this is terribly likely (though I suspect that situations of roughly that sort are quite common, and for sure I have been in them myself), but it might be useful for you to try explaining why you don’t think that’s what’s going on. (Assuming that you don’t.)
Yeah, this analogy-laden meta-digression is getting a bit ridiculous, I agree. Forget the physics stuff, at least for now.
Yeah, I am just a student of DI theory myself, largely just reciting outlines of my own mental notes.
If you could possibly find the time to check the online catalogs of any university libraries near you to see if they have the book… because if you could easily get your hands on a copy, it wouldn’t be too hard to just try skimming the section and chapter summaries.
An uncharitable explanation suggests itself: Perhaps you cannot say just what DI is because you don’t know what DI is; you’ve read things saying how wonderful it is, and you’ve experienced something that purports to be DI and found that it works well, and concluded: DI is great—without actually pinning down just what DI is. I don’t think this is terribly likely (though I suspect that situations of roughly that sort are quite common, and for sure I have been in them myself), but it might be useful for you to try explaining why you don’t think that’s what’s going on. (Assuming that you don’t.)
Quite honestly, yes, that is how it started.
But I was actually explicitly aware of it at the time, that my emotional experience with the Michel Thomas lessons was almost surely biasing me in my initial tentative vague estimate that there was a somewhere more than 50% chance that the results from Project Follow-Through were pretty much representative of something true about DI’s effectiveness in practice.
Although just because the experience with the Michel Thomas lessons was emotional doesn’t mean it should have been discarded as evidence, does it? Especially considering that I also had some evidence that many other people had had similar experiences (my vague impression that the ‘marketing anecdotes’ surrounding them as a product were slightly more numerous and slightly more gushing than usual, especially given how the lessons were in surface appearance much less polished compared to their competitors)… so maybe the bias wasn’t so bad, but I knew I had a general human bias to underestimate my biases, and might therefore overcompensate for it… which is a line of thought that just goes into insanity, so at the time the sanest thing I could do was accept my feelings of how good my experience with the audio lessons was as evidence as valid, right? As the best working level at the time?
Anyway, yeah, my estimate of the probability of there being something to DI theory, even though I found it just as mystifyingly vague as you did at first, was obviously bumped up a lot by my slightly stronger faith in the Project Follow-Through graphs as representing something true about DI’s practical effectiveness.
And as I found that bits of DI theory that had just seemed like techno-babble at first started to actually become meaningful to me, in recursive layers, I started to get really quite sure.
...And from that story you could probably give me some great feedback on my current level of general strength as a rationalist. How’s my epistemic driving? (Although I realize you’re in a position where you should probably expect that if you keep looking into DI theory your probability estimate of it being valid will more than likely move from ‘somewhere in the middle?’(?) to a position much closer to either 0 or 1, and that might complicate things… or not? I’d have to think about that.)
...This is me working on less than four hours of sleep a night for three days in a row, by the way. I’ma go to bed now.
The main difficulties in giving an accurate and brief statement of what physics is for someone who’s never seen anything like it are (1) that physics is a very big subject and (2) that your stipulation about the audience seems to be intended to assume they don’t know any mathematics to speak of either.
Are you claiming that DI is a hugely varied subject like physics? (If so: How is that even possible, given how recent it apparently is?)
Are you claiming that DI depends on a large and conceptually very difficult substrate, as physics does with mathematics? (If so: What is that substrate?)
If the answers are both “no”, then I’ll adjust your question to fix those two mismatches, and attempt to give a brief summary of (not all of physics, but) Newtonian particle mechanics for (not someone completely ignorant of mathematics, but) someone who has college-level mathematics but has somehow managed not to hear that it can be applied to understanding the physical world.
“This is a theory about the motion of small rigid objects such as rocks. The same theory can actually handle large objects by considering them as aggregates of smaller ones, but for the moment we’ll only consider objects that are very small. So, suppose we have a bunch of small objects. At any instant we can describe the state of the universe by saying (1) where these objects are—we specify this by giving three coordinates for each object—and (2) how fast and in what direction each object is moving—we specify this by another set of three coordinates, which collectively we call the velocity. And the only other thing there is to know about each object is its mass, a single positive number that in some sense describes how much of it there is; it’s closely related to how heavy it feels when you hold it.
“Now the basic rules are as follows. First: the derivative of position with respect to time is the velocity. Second: the derivative of velocity with respect to time, which we call the acceleration, is completely determined by a set of rules that care only about the positions, velocities, and masses of the objects. (As long as they don’t actually crash into one another. We’ll talk about that in a moment.)
“Third: the rule for finding the acceleration is as follows. The acceleration of each object is a sum of vectors, one for each other object. What’s happening here is that all the objects are pulling on one another; objects with more mass pull harder. More precisely, the formula goes like this: the acceleration of an object with mass m is the sum over all the other objects of Mr/|r|^3 where r is the vector from our object to the other object and M is the mass of the other object. So the further away the other object is, the less effect it has; in practice this means we can mostly ignore objects very far away.
“Here’s an exercise, to give you a feeling for what the theory lets you do. Define the momentum of an object to be the mass times the velocity. Then prove that the sum of all the momenta in the system never changes.
“This system takes some getting used to, although basically it’s just fairly elementary mathematics. Let me mention a few of the things that follow from it. We just saw a “conservation law”: the total momentum is constant. There are a whole lot of other conservation laws, and in many cases one can make detailed predictions using only those. If you have one object whose mass is very large and all other nearby objects have much smaller mass and don’t get too close to one another, then you can pretend that the first object stays fixed in place, and that the others’ motions are affected only by it, and in that case it turns out that their paths are always conic sections. In particular, our solar system is like this, and the planets move in near-perfect ellipses. If you do the calculations more carefully, taking into account the planets’ influence on one another, you can get very accurate results, and in fact someone once found a previously unknown planet by noticing that another already known planet wasn’t moving quite as expected and working out where another planet would have to be to produce the observed deviations.
“That’ll do for now. If you want a more difficult challenge, try to prove the statement I made about conic sections.”
...Okay, that is honestly an impressively rapid bit of writing in its own unusual context (as a summary of newtonian particle mechanics to someone who had college math but had somehow never heard about physics, like you said.)
But my original analogy was never meant to be expanded, because it was never an argument by analogy in the first place, as I told Jem
OK, so the only point of your analogy was to explain how you feel about being asked to explain what DI is? Fair enough. Then all I can say is: It doesn’t seem to me that you’ve successfully communicated how you feel about that, since apparently you find it unreasonable to be asked to explain what DI is, whereas if I try to imagine myself in any genuinely-analogous situation then I don’t find it unreasonable to be asked the corresponding question.
I’m also rather confused about what your actual problem with explaining what DI is is. You say it’s kinda like the problem someone has who’s asked to explain what physics is. But (see above) it seems to me to be highly unlike that problem in a couple of respects that (for me) seem to be central to the difficulty of the problem. So what, in fact, is it about DI that makes it so difficult for you to say what it is?
An uncharitable explanation suggests itself: Perhaps you cannot say just what DI is because you don’t know what DI is; you’ve read things saying how wonderful it is, and you’ve experienced something that purports to be DI and found that it works well, and concluded: DI is great—without actually pinning down just what DI is. I don’t think this is terribly likely (though I suspect that situations of roughly that sort are quite common, and for sure I have been in them myself), but it might be useful for you to try explaining why you don’t think that’s what’s going on. (Assuming that you don’t.)
Yeah, this analogy-laden meta-digression is getting a bit ridiculous, I agree. Forget the physics stuff, at least for now.
Yeah, I am just a student of DI theory myself, largely just reciting outlines of my own mental notes.
If you could possibly find the time to check the online catalogs of any university libraries near you to see if they have the book… because if you could easily get your hands on a copy, it wouldn’t be too hard to just try skimming the section and chapter summaries.
Quite honestly, yes, that is how it started.
But I was actually explicitly aware of it at the time, that my emotional experience with the Michel Thomas lessons was almost surely biasing me in my initial tentative vague estimate that there was a somewhere more than 50% chance that the results from Project Follow-Through were pretty much representative of something true about DI’s effectiveness in practice.
Although just because the experience with the Michel Thomas lessons was emotional doesn’t mean it should have been discarded as evidence, does it? Especially considering that I also had some evidence that many other people had had similar experiences (my vague impression that the ‘marketing anecdotes’ surrounding them as a product were slightly more numerous and slightly more gushing than usual, especially given how the lessons were in surface appearance much less polished compared to their competitors)… so maybe the bias wasn’t so bad, but I knew I had a general human bias to underestimate my biases, and might therefore overcompensate for it… which is a line of thought that just goes into insanity, so at the time the sanest thing I could do was accept my feelings of how good my experience with the audio lessons was as evidence as valid, right? As the best working level at the time?
Anyway, yeah, my estimate of the probability of there being something to DI theory, even though I found it just as mystifyingly vague as you did at first, was obviously bumped up a lot by my slightly stronger faith in the Project Follow-Through graphs as representing something true about DI’s practical effectiveness.
And as I found that bits of DI theory that had just seemed like techno-babble at first started to actually become meaningful to me, in recursive layers, I started to get really quite sure.
At this point, I would be very surprised if any evidence I found that contradicted DI actually held up under scrutiny (and yes, give it a correspondingly greater weight if it did!)
...And from that story you could probably give me some great feedback on my current level of general strength as a rationalist. How’s my epistemic driving? (Although I realize you’re in a position where you should probably expect that if you keep looking into DI theory your probability estimate of it being valid will more than likely move from ‘somewhere in the middle?’(?) to a position much closer to either 0 or 1, and that might complicate things… or not? I’d have to think about that.)
...This is me working on less than four hours of sleep a night for three days in a row, by the way. I’ma go to bed now.