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[silverspawn]

So Set is a card game I always hated because I'm terrible at it.

It works like this. You have cards that show geometric things. They vary in four dimensions: shape, color, number, and texture. Each dimension can take three different values (1/2/3 for number; solid/dotted/empty for texture, etc.). E.g., a card may show three solid red ovals.

To play, put a bunch of cards face up on the table. The goal is to find three cards such that, for each dimension, [either all cards are different or all cards are alike]; such three cards are called a set. E.g., [one solid green oval, two solid green ovals, three solid green ovals] passes (different in number, identical in rest), or [one dotted magenta squigglything, two empty red ovals, three solid green rectangles] (different in all four).

Any mathematically inclined person can now conclude that (a) there are 81 possible cards, and (b) for any two cards, exactly one other card makes them a set.

If you were to program an algorithm to solve this problem, I don't believe (though I'm not sure) that it's possible to do better than brute force. Since considering a set of two is never useful, you just have to look at all sets of triples among the revealed cards. Or, well, depending on which operation is cheaper, you can look at all sets of two, compute the third card, and check all other cards for equality with that third.

[silverspawn]

The question is how, how are humans so good at this.

You play with 12 cards, so there are (12 choose 3) many triples; that's 220. The chance for a triple to be a set is 1/79. So there are about three sets in the first collection of cards. But people often find the first after 15 seconds or something. This would require considering at least two triples per second. What's going on here?

[silverspawn]

If A) what the brain is doing is clearly *not* looking at random triples and checking for the set-property, and B) there doesn't exist a better algorithm to do this, then that is a contradiction.

[silverspawn]

Wikipedia:

Using a natural generalization of Set, where the number of properties and values vary, it was shown that determining whether a set exists from a collection of dealt cards is NP-complete.[8]

[MiX]

Since considering a set of two is never useful

I think this is the mistake you make, and how our brains can work at 2 triples per second. As someone that has played Set casually, I mainly look at pairs, and then scan the board for a card that could fit that pair.

The question is how, how are humans so good at this.

You play with 12 cards, so there are (12 choose 3) many triples; that's 220. The chance for a triple to be a set is 1/79. So there are about three sets in the first collection of cards. But people often find the first after 15 seconds or something. This would require considering at least two triples per second. What's going on here?

Is two triples per second too fast? I'm sure if my fingers were fast enough, I could classify random trios of cards as being a set and not a set faster than that. Surely I'd get some wrong, but if you don't count those, I think I would still get 2 triples right per second, and most likely more.

[MiX]

I guess I just said two contradictory statements, but I don't agree with "considering a set of two is never useless" and also don't agree with "two triples per second is too fast".

[Awaclus]

Forget everything you know about the additive or subtractive color model, go to this website:

https://www.canva.com/colors/color-wheel/

and rotate the color picker around the circumference of the circle. How many phenomenologically distinct colors do you think there are? How many that add a new phenomenological tone rather than mixing two existing ones?

I think I'm going to run this experiment the next time I see my niece.

I think there are red, purple, blue, cyan, green, yellow, and orange.

[silverspawn]

How long do you need to find a set? Is 15 seconds roughly accurate?

"considering a set of two is never use[ful]".

The point I was making here is that looking at two doesn't give you information about how likely they are to be complete-able to a set. This means that in terms of number of algorithmic complexity, it doesn't get better than brute force. It's just a question of which primitives (checking a triple, cheecking whether a card is a specific one) is cheaper. Although, yes, if the latter is cheaper, then it's literally useful to look at pairs first

[silverspawn]

I think this is the mistake you make, and how our brains can work at 2 triples per second. As someone that has played Set casually, I mainly look at pairs, and then scan the board for a card that could fit that pair.

if you really do this, the example may be less interesting than I had hoped. I was expecting more that you do something that you can't defined well at all; i.e., just sort of scanning the entire board

[silverspawn]

Forget everything you know about the additive or subtractive color model, go to this website:

https://www.canva.com/colors/color-wheel/

and rotate the color picker around the circumference of the circle. How many phenomenologically distinct colors do you think there are? How many that add a new phenomenological tone rather than mixing two existing ones?

I think I'm going to run this experiment the next time I see my niece.

I think there are red, purple, blue, cyan, green, yellow, and orange.

very interesting, thanks. Mostly surprised about orange; to me that feels super like yellow and red and not like something new

[MiX]

Forget everything you know about the additive or subtractive color model, go to this website:

https://www.canva.com/colors/color-wheel/

and rotate the color picker around the circumference of the circle. How many phenomenologically distinct colors do you think there are? How many that add a new phenomenological tone rather than mixing two existing ones?

I think I'm going to run this experiment the next time I see my niece.

I think there are red, purple, blue, cyan, green, yellow, and orange.

very interesting, thanks. Mostly surprised about orange; to me that feels super like yellow and red and not like something new

After seeing the colors Awaclus did, I looked closer and also saw Pink. But I had to specifically click on the color picker and it was much less distinguished from the other 7.

[faust]

The question is how, how are humans so good at this.

You play with 12 cards, so there are (12 choose 3) many triples; that's 220. The chance for a triple to be a set is 1/79. So there are about three sets in the first collection of cards. But people often find the first after 15 seconds or something. This would require considering at least two triples per second. What's going on here?

I don't have the answer but this reminded me of a fun maths talk I heard about creating more mathsy versions of SET. Unfortunately that talk isn't available online, but the rules for mathsy SET variants are here.

[faust]

If A) what the brain is doing is clearly *not* looking at random triples and checking for the set-property, and B) there doesn't exist a better algorithm to do this, then that is a contradiction.

silverspawn: A proof that P=NP using Set. f.ds, 2022.

[silverspawn]

computational complexity was not what I was going for. Rather that the brain is using consciousness for computation speed-up

[Awaclus]

After seeing the colors Awaclus did, I looked closer and also saw Pink. But I had to specifically click on the color picker and it was much less distinguished from the other 7.

I can see pink, and also e.g. azure. But they feel like subcategories of the 7 rather than fundamentally different colors. Like, if someone refers to an azure car as a blue car, or a pink car as a purple car, it doesn't feel contradictory to how I experience the car's color the same way it does if someone refers to a cyan car as green or an orange car as yellow.

[silverspawn]

ok poker is back to being incredibly hard and unfair. this feels more normal

[silverspawn]

It's not been my experience that all emotions pass away after at most one minute if not reinforced by thought, as Sam Harris claims a lot. It's been a few minutes since listening to the interview with Jeff Hawkins and I'm still very angry. But it is true that being mindful of the anger robs it of its power; it's just an interesting pattern of energy

[silverspawn]

imagine believing both that

(a) suffering is the most important problem in the world
(b) consciousness isn't real

It seems contradictory on its face -- and it is contradictory on its face -- but this is where many EA people are. That's what I want to fight against.

[silverspawn]

It may be a reasonable idea to only take cold showers from now on to cultivate equanimity. Let see if I can do it

[silverspawn]

ow. this is extremely tough.

[silverspawn]

Alright, the last two days have been very tough for poker. Let's see if today goes better.

[silverspawn]

Third and fourth place, which is the best possible worse-than-even result, which also happened in the most frustrating way possible in both cases

[silverspawn]

ok one more try

[silverspawn]

2nd and 8th, well this does make the day 0.5$ net positive

this is theoretically something I have the data for, but very hard to verify. It feels like my preflop allin luck is another one of those << 1% things. I had kings against aces so many times. It happens so often that whenever I go all-in preflop with KK, I get anxiety about my opponent having aces. Twice since I started playing, idk how many times before

[silverspawn]

it's definitely not a mistake to go all-in, all the good players and websites tell you to go all-in with KK whenever you can, and other people do it with hands t hat are much worse than KK on average. It feels like everyone except me does it with AA-QQ, most people with AK and JJ, and many people with ridiculous things like 99 or AQ