Programmer, rationalist, chess player, father, altruist.
cata
I’m inclined to participate. I have some baseline knowledge of various discrete math but not much probability theory.
I’m in West Michigan, within forty-five minutes of Grand Rapids and two and a half hours of Chicago. I learn better face-to-face than online, so I’d be happy to meet.
Even when I am perfectly capable of understanding something myself, I find it extremely helpful to learn with other interested people in a “study, study, then discuss” kind of format. I come to my own conclusions about the text while I study, just as I would if I were working by myself, but then I additionally get to compare the details of my conclusions with those of other minds working independently. Also, having participants with diverse intellectual backgrounds means that they may be able to identify and share interesting tangential ideas that would not have occurred to me alone.
I also find that communicating my thoughts to other people forces me to clarify them to a greater degree, often revealing small gaps in understanding that I had papered over in my own mind.
I believe Jaynes was implying that since the experimenters didn’t have a threshold model in mind, the experiment did not measure a broad enough range of doses to distinguish between a linear response and a threshold. For example, if the only tests of the sweetener were at doses which produced harmful effects, then it might be impossible to derive the correct model based on only that data.
It occurs to me that Jaynes is missing a desideratum that I might have included. I can’t decide if it’s completely trivial, or if perhaps it’s covered implicitly in his consistency rule 3c; I expect it will become clear as the discussion becomes more formal—and of course, he did promise that the rules given would turn out to be sufficient. To wit:
The robot should not assign plausibilities arbitrarily. If the robot has plausibilities for propositions A and B such that the plausibility of A is independent of the plausibility of B, and the plausibility of A is updated, then the degree of plausibility for B should remain constant barring other updates.
One more thing. The footnote on page 12 wonders: Does it follow that AND and NOT (or NAND alone) are sufficient to write any computer program?
Isn’t this trivial? Since AND and NOT can together be composed to represent any logic function, and a logic function can be interpreted as a function from some number of bits (the truth values of the variable propositions) to one result bit, it follows that we can write programs with AND and NOT that make any bits in our computer an arbitrary function of any of the other bits. Is there some complication I’m missing?
(Edited slightly for clarity.)
- 22 Jun 2010 7:37 UTC; 1 point) 's comment on Book Club Update and Chapter 1 by (
I agree that you are correct. Thank you.
I think I was unclear. Here’s what I mean:
Suppose our robot takes these two propositions:
A = “It’s going to rain tonight in Michigan.” B = “England will win the World Cup.”
And suppose it thinks that the plausibility of A is 40, and the plausibility of B is 25.
As far as our robot knows, these propositions are not related. That is, in Jaynes’ notation (I’ll use a bang for “not,”) (A|B) = (A|!B) = 40, and (B|A) = (B|!A) = 25. Is that correct?
Now suppose that the plausibility of A jumps to 80, because it’s looking very cloudy this afternoon. I suggest that the plausibility of B should remain unchanged. I’m not sure whether the current set of rules is sufficient to ensure that, although I suspect it is. I think it might be impossible to come up with a consistent system breaking this rule that still obeys the (3c) “consistency over equivalent problems” rule.
After 2.9 in the text: “Furthermore, the function F(x, y) must be continuous; for otherwise an arbitrarily small increase in one of the plausibilities on the right-hand side of (2-1) could result in a large increase in AB|C.”
Is there some particular reason that’s an unacceptable outcome, or is it just generally undesirable?
(I suppose we might be in trouble later if it weren’t necessarily continuous, since it wouldn’t be necessarily differentiable (although he waves this off in a footnote with reference to some other papers and proofs) so this seems like an important statement.)
I don’t know if this counts, but when I was about 9 or 10 and learning C (my first exposure to programming) I understood input/output, loops, functions, variables, but I really didn’t get pointers. I distinctly remember my dad trying to explain the relationship between the * and & operators with box-and-pointer diagrams and I just absolutely could not figure out what was going on. I don’t know whether it was the notation or the concept that eluded me. I sort of gave up on it and stopped programming C for a while, but a few years later (after some Common Lisp in between), when I revisited C and C++ in high school programming classes, it seemed completely trivial.
So there might be some kind of level of abstract-thinking-ability which is a prerequisite to understanding such things. No comment on whether everyone can develop it eventually or not.
I did read the rest of chapter 2. I solved the first part of 2.3 without difficulty (proving the inequalities) but I was surprised to work for half an hour on the second part without solving it; I intend to come back to it still with a clear head.
From your text: “If we think that probabilities are transcendal [sic] the principle of indifference offers us a free lunch. We get knowledge about the real world, merely by being ignorant of it. That is absurd.”
Can you clarify what you mean by this?
I don’t find your words very different from Jaynes’ words. He makes it clear that his standard of “objectivity” is encapsulated in the consistency and completeness desiderata 3b and 3c, which ensure that two people reasoning independently from the same background information come to the same conclusions.
The difference is that you frame people’s differences in background information as “different viewpoints” on the same situation, which I find a little confusing; logically, they’re simply different situations that need to be reasoned out independently. There’s no reason to be surprised when they yield different results.
Jaynes certainly agrees that probability is “situational” in your categorization. It can’t be “individual”, since that violates 3c consistency, unless you’re considering people’s mental states to be part of their background information (in which case it’s just “situational.”) “Transcendental” is just the special case of “situational” where everyone has perfect information.
I loved “The Mathematical Experience” when I was 13-ish, and I re-read it recently; still good! I strongly second this recommendation.
Thank you.
This might be old hat for the crowd here, but I’ve just discovered Karl Popper and I’m working through his collection of talks and essays, “Conjectures and Refutations.” It contains a lot of very clear insights about the philosophy of science and its application to political and historical questions; the two most interesting pieces to me so far were one on Hume’s problem of induction, discussing the difference between acceptance and logical certainty, and one on the development of the scientific mindset in Greek-era philosophers. I strongly recommend it if you’re interested in such topics.
I also recently read Marvin Minsky’s “Society of Mind”, which is just a fantastic book. It’s a very fleshed out introduction to some of Minsky’s ideas about how surface-level phenomena of the mind like memory, learning, and volition can be explained through a model of the mind as a hierarchy of tiny agents with very specific goals that communicate among themselves. It’s amazingly written; completely accessible, written in simple language, but every paragraph has a thought-provoking concept about something or other. (The single flaw is that it doesn’t really reference a lot of actual research or data; it’s more or less just laying out some food for thought based on our intuitive understanding of our mind.) I would pretty much recommend it to anyone at all.
Finally, I read Hermann Hesse’s “The Glass Bead Game”—although Hesse has been a favorite of mine for a long time, I never got around to that one—and I found it to be the best fiction I’ve read in a year or two. You can head to wherever for a summary, but I highly recommend it to anyone. I suspect the premise will especially appeal to the sort of systematizing, truth-seeking folks around here.
I also have a pretty jaded opinion of that same category of dabblers in science fiction, but I didn’t really perceive Hesse in that light.
I identify “science-fictiony” books as being not only about technology, but about unusual, daring ideas taken to their logical conclusions; e.g. Borges and Calvino would usually qualify. But I didn’t find Glass Bead Game to be focused on that; I found the most gripping parts of the book to be Knecht’s intellectual and spiritual development, and how each of the characters negotiated the balance between a life of the mind and the rest of the world. Not very SF.
However, it’s true that the big “idea”, the Game itself, was immensely attractive to me, in a science-fictiony way, and maybe in a narcissistic way. I wish Hesse had been alive to learn computer programming; perhaps he would have had something to say about that.
This is a lovely book. What a shame that Blogspot sort of munges the formatting. It’s worth buying.
Glenn Greenwald!
That’s the only book I can think of that has ever made me cry.
Oh, hi. I’m an autodidact programmer in my early 20s working for a small company. A lot of programmers tend to be hacker sorts who like making things, but I mostly only care about achieving a deeper and more intuitive understanding of the world. I am interested in a lot of things, but I tend to concentrate alternately on math, CS, linguistics, philosophy, history, and literature.
I don’t identify as a rationalist or make very rational decisions, but I share a lot of intellectual interests with the community, and there aren’t really any other public spots on the web where smart people are discussing a variety of topics without a ton of noise and bullshit.
I don’t have enough background in some of the jargon and shared historical discussion here to contribute to many of the more topical discussions, but hopefully as I catch up on the archives I’ll be able to comment more often.
I agree with this, and in particular, although there are generally smart people on Hacker News, there are a ton of people who are interested in talking about business and startups 24⁄7, a topic I find extremely boring.
I’m a big fan of MetaFilter (http://www.metafilter.com/). The commenters there are charming and often pretty smart, but the spirit of discussion is usually somewhat less serious.
Might you be open to a carpool? I’m in Holland and I’d enjoy attending, if the weather’s nice.