Open thread, February 2018

3whpearson

3habryka

14Elo

9cousin_it

7gwillen

2Pattern

4EnterUsername

3habryka

2ChristianKl

4Qiaochu_Yuan

2[anonymous]

4Qiaochu_Yuan

3ChristianKl

2Qiaochu_Yuan

1Dr. Jamchie

3Said Achmiz

3cousin_it

1Dr. Jamchie

1PeterBorah

0Dr. Jamchie

2PeterBorah

1Dr. Jamchie

New Comment

Has anyone done work on a AI readiness index? This could track many things, like the state of AI safety research and the roll out of policy across the globe. It might have to be a bit dooms day clock-ish (going backwards and forwards as we understand more) but it might help to have a central place to collect the knowledge.

I am totally in favor of open threads, but I think the correct place in the current site hierarchy for that is your personal page, as opposed to the frontpage, so I moved it there. Happy to discuss whether to do something else with open threads, in meta, if people have opinions on that.

I love open threads. There are tons of questions I want to ask, which would just look pathetic and attention-grabby as blog posts.

One of my current interests is trinary reasoning as opposed to binary reasoning. IOTA for example is interesting because it tertiary in nature.

John Cottingham idea of moving from Cartesian dualism to trialism is also in that realm.

I'm not sure how to best think about trialist reasoning but if anyone has any pointers that would make me happy.

One thing ChristianKI is referencing is IOTA a cryptocurrency project that is apparently written using ternary rather than binary. I'm guessing the other two examples (which I'm unfamiliar with) are also places where this sort of triplet thing appears, and he's generalizing it as a way to think about things.

It sounds like this amounts to using a version of base 3. I don't understand what the conceptual significance of this is.

I think there's a cultural default to try to reason in base 2 for many issues and it would b interesting to think about more issues in base 3.

That default of thinking in base 2 for example leads to many people taking "The map is not the territory" to be a statement about there being two kinds of things when that wasn't Korzybski's intention at all.

Turning dichotomies into trichotomies seems useful but it seems unrelated to working in base 3 instead of base 2.

I think Conjunction Fallacy is not actually a fallacy.

Lets take water heater problem for example, which goes like this:

"Person X fixed my water heater. Which is more likely - A) he is mathematician or B) he is plumber AND mathematician?"

"A" answer is correct as P(A) >= P(A and B).

But lets rephrase the question:

"Which is more likely - A) he is a person randomly selected from mathematicians group or B) he is a person randomly selected from mathematicians who are also plumbers group?"

Now which one is correct?

Still A, obviously, because there are way more mathematicians than mathematicians who are also plumbers. Nothing about your rephrasing nullifies the fact of the vastly differing base rates.

The only way you could get B to be correct, is if you stipulated that there was an equal (or, at any rate, a greatly distorted) chance of either group being picked for X to be drawn from it. But ignorance of this fact—that such a stipulation is needed, and that otherwise B cannot be correct—*is precisely the fallacy*!

*Edit:* Did you have in mind the additional premise that only plumbers can fix toilets?

"Conjunction fallacy is not actually a fallacy" seems like overselling the result, but Dr. Jamchie has a point. Imagine I'm thinking of a person named Bob. You have two hypotheses:

1) "Bob is a mathematician" with probability 0.5

2) "Bob is a mathematician and a plumber" with probability 0.1

Then you receive evidence that Bob fixed my water heater, updating the probabilities to 0.4 and 0.2. The first one is still higher, as it should be, but the second one got a bigger boost from the evidence (aka "likelihood").

Still A, obviously, because there are way more mathematicians than mathematicians who are also plumbers. Nothing about your rephrasing nullifies the fact of the vastly differing base rates.

Let me give you an analogy: There are two bags of balls. 1st have 1000000 white balls and 10 black balls. 2nd have 5 black balls and no white balls. Bob took a ball from one of the bags and it was black. Which bag he took it from? There are more black balls in first bag, than in the second. As there are more mathematicians, who can fix water heater, that mathematicians who are plumbers. Still the correct answer would be 2nd bag obviously.

Did you have in mind the additional premise that only plumbers can fix toilets?

No, just that plumber have much higher probability of doing so.

This seems to be a problem of partitioning.

In your analogy, no ball that is in the second bag is also in the first bag. However, all mathematician-plumbers are also mathematicians.

In other words, your analogy is comparing these options:

1) Bob is a mathematician and Bob is not a plumber.

2) Bob is a mathematician and Bob is a plumber.

In that comparison, it is indeed possible that #2 is more likely.

But the actual problem asks you to compare these options:

1) Bob is a mathematician, and Bob either is a plumber or is not a plumber.

2) Bob is a mathematician, and Bob is a plumber.

Since all Bobs in #2 are also in #1, #2 cannot be more likely than #1.

" **In your analogy, no ball that is in the second bag is also in the first bag. However, all mathematician-plumbers are also mathematicians.** "

Most of balls in first bag are in fact not plumbers, as in real life, but whose who are - they are in the bag also. We could number the balls, and first 5 of 10 black balls in first bag would have same numbers as 5 balls in second bag.

Sure, so now there are two bags:

1) 1000000 white balls and 10 black balls, numbered 1-10.

2) 5 black balls, numbered 1-5.

And now the question is: Bob drew a ball from a bag. Which is more likely?

1) It was a black ball with a number between 1 and 5.

2) It was a black ball with a number between 1 and 10.

~~~

I considered submitting the above as my full response, but here is another approach.

You seem to be substituting a question about the *process of choosing* for the original question, which was about *outcomes*. An example where your approach would actually be correct:

"We know that Alice has access to two lists online: an exhaustive list of mathematicians, and an exhaustive list of mathematician-plumbers. We know that Alice invited Bob over for dinner by choosing him from one of those two lists. We know that, by complete coincidence, Alice's toilet broke while Bob was over. We know that Bob successfully fixed Alice's toilet. Which list did Alice originally choose Bob from?"

In that case, it's likely that the Bayesian calculation will say she probably used the Mathematician-Plumber list.

But notice that last question is *different* from the question of "which of the online lists is Bob most likely to be on?" We know that the answer to *that* is the Mathematicians list, because he has a 100% chance of being on that list, where he only has a high-probability chance of being on the Mathematician-Plumbers list.

Yes, but you see now, with enought details added, second question doesn`t seem to make a lot of sense. "Which" in the question implies that Bob is just on one of the lists, but most likely he isn't. That being said, natural language does not correspond 1:1 to math or statistics. Some ambiguities are expected and a lot of sentences are up for interpretation. Now who is to say that second question you prodived is the correct way to interpret the original problem, and first one is not? First is at least coherent, while second is condradicting itself.

Apologies if it's already there, but I just can't find the open thread.

In case it's not there, open thread for February 2018! Hurray!

In case it is, would it be difficult to check the title string for "open thread" and show a link to the current month's open thread, ask if that's what the person was looking for, and still have an option to post if not?