"Creating a machine that would tell for every statement whether it's true or false."
Theoretically, that should be possible. It would be like some kind of really smart and wise human, who if you asked them something about the world, they would tell you about it, because they know so much.
Unlike with elephants being terrestrial now but evolving wings in the future, no parameters need to change for the coin flip example. It could happen the very next time someone attempts it. It's trivially plausible that I could flip a coin five times and get heads each time. From there, it's trivially plausible that the next five could also be heads--unlikely, but very realistic. If I continue to chain those together, at what point do you propose that it breaks down and enters the realm of the impossible, and what do you propose causes that?
Another way to say it.
1 is possible.
2 tails in a row is possible
3 tails in a row is possible
.
.
.
10,000 is not possible.
So this is arguing at some number, lets say 226 tails in a row, that there is a 100% chance the next flip is heads because 227 is impossible.
This is of course absurd. The next flip is always (roughly) 50% chance.
I mean, to defend mdinnerspace's perspective a little bit, you can do this sort of thing with hair as well. Where you say x amount of hairs counts as long hair, and just removing one hair does not make it short. But if you kept applying that logic you would eventually say a bald person had long hair, without being able to say at what exact point the logic broke down. So sometimes we think of things in chunks like that, where we don't need an exact cutoff for our terms to make sense.
But of course, coin flips and hair are very different things. The hair thing might just say more about when we like to call things bald or short or long, more of a psychological insight than anything rational. I'm just saying, maybe this is somewhere where mdinnerspace is coming from.
I actually saw a video once where a math/philosophy professor argued that infinity didn't exist. That people can't just assume that it keeps on going just because they can't point to where it stops. In some sense I can see why you might argue that it's hasty to just say "so far it doesn't end, so therefore it doesn't end period," as if you're trying to claim something that you might not even be able to humanly grasp, a non-ending thing, and just kind of postulate that it exists. I didn't agree with the man, but he wasn't a dumb guy, and mdinnerspace isn't a dumb guy, either.
I guess you could say, our understanding of "never ends" might be as deep as, we just say that when we don't want to discover the end, which is often the case. There might be a long, tedious chore we have to do and we'll say "it never ends!" and then just give up.
And then if they say infinity makes sense in math, just say that a mathematical postulation just isn't quite as good as something more concrete. Just to play devil's advocate. I dunno. Maybe I'll watch that video again just out of curiosity.
Lets say that nothing is impossible.
If so,
its impossible that I should win nothing against a super-GM
Unlike with elephants being terrestrial now but evolving wings in the future, no parameters need to change for the coin flip example. It could happen the very next time someone attempts it. It's trivially plausible that I could flip a coin five times and get heads each time. From there, it's trivially plausible that the next five could also be heads--unlikely, but very realistic. If I continue to chain those together, at what point do you propose that it breaks down and enters the realm of the impossible, and what do you propose causes that?
Another way to say it.
1 is possible.
2 tails in a row is possible
3 tails in a row is possible
.
.
.
10,000 is not possible.
So this is arguing at some number, lets say 226 tails in a row, that there is a 100% chance the next flip is heads because 227 is impossible.
This is of course absurd. The next flip is always (roughly) 50% chance.
I mean, to defend mdinnerspace's perspective a little bit, you can do this sort of thing with hair as well. Where you say x amount of hairs counts as long hair, and just removing one hair does not make it short. But if you kept applying that logic you would eventually say a bald person had long hair, without being able to say at what exact point the logic broke down. So sometimes we think of things in chunks like that, where we don't need an exact cutoff for our terms to make sense.
But of course, coin flips and hair are very different things. The hair thing might just say more about when we like to call things bald or short or long, more of a psychological insight than anything rational. I'm just saying, maybe this is somewhere where mdinnerspace is coming from.
I actually saw a video once where a math/philosophy professor argued that infinity didn't exist. That people can't just assume that it keeps on going just because they can't point to where it stops. In some sense I can see why you might argue that it's hasty to just say "so far it doesn't end, so therefore it doesn't end period," as if you're trying to claim something that you might not even be able to humanly grasp, a non-ending thing, and just kind of postulate that it exists. I didn't agree with the man, but he wasn't a dumb guy, and mdinnerspace isn't a dumb guy, either.
Yeah, infinity isn't a number, it's a concept. I think I heard some mathematicians made an argument for replacing infinity with some really big, but not infinite, number and it wouldn't hurt e.g. any calculus.
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As for not being a dumb guy, there's no way for me to know either way. My knowledge of his ideas is limited to what he's able to communicate to me by typing. I can't judge him, I can only judge what he's able to communicate to me. I'm aware our interaction is limited in this way.
"As for not being a dumb guy, there's no way for me to know either way. My knowledge of his ideas is limited to what he's able to communicate to me by typing. I can't judge him, I can only judge what he's able to communicate to me. I'm aware our interaction is limited in this way."
Well for example, I don't think he disagrees with the calculations you made, etc, but just thinks philosophically they are to be interpreted differently. I can kind of see where he's coming from. Math is reliant on logic, and logic can be pretty weird sometimes.
For example the liar paradox. "This statement is false." Applying logic to it in one case might make it true, and in another, might make it false. If you figure out it's true, you can use that argument to show that it's false ("it's true that the statement is false"), etc.
Clearly the world doesn't work like the liar paradox. But I guess that would be a good point to make when questioning, how does something derived from a logical system actually relate to real life?
But I guess that would be a good point to make when questioning, how does something derived from a logical system actually relate to real life?
I invited him earlier to roll the dice himself. He can also flip coins.
I myself have done these just for fun. I've also cut up some numbers, shook them up in a bag, and drawn them to look at the results.
If you don't trust logic though... I mean... not to be rude, but it's not a matter of trust it's a matter of either you understand it or you don't.
That said, sure, you can doubt on philosophical grounds. Seems you're both telling me this is how it is... that it's more of a philosophical disagreement. That's fine, but someone like me is going to bring up practical things like "look, the sun really does rise every day even if I can't prove it." I don't do this to be rude though, I really meant that when I said it above (#4866).
Hmm. I think I have a pretty decent understanding of logic, such that I can talk about certain oddities about it. So I don't think that's the issue. It's just that sometimes you get strange results from it, as I showed. Remember that logic is a system. It tries to make itself so that if you apply its rules to the situation, you will get the right answer. It tries to represent how the world works. But in rare cases like the liar paradox, applying those rules might not do that, or just might have a different meaning than what you would typically get from applying logic.
That's kind of his angle, perhaps. I didn't say I agreed with him. Just that it's not impossible for the systems we have to be imperfect in describing the world, even if for most purposes and in most kinds of situations they work. I wouldn't consider 10,000 heads in a row to be one of those points where logic breaks down. But maybe he is taking some kind of philosophical approach for that sort of thing. Again, I didn't say I actually agreed with that, I'm just speculating on where he is coming from.
"but someone like me is going to bring up practical things like "look, the sun really does rise every day even if I can't prove it." I don't do this to be rude though, I really meant that when I said it above (#4866)."
That's fine as well. If you don't want to argue over the philosophy, no one will make you.
In #4842 I listed my reasoning making small steps and asked him to point out where he disagreed.
He said he agreed with all of it, but disagreed with the conclusion (I suppose the 11th step)
Unfortunately, 11 logically follows from 10, which follows from 9 etc, back to 1. So he needs to give me more detail.
By the way, 10 was "each possible outcome of flipping a coin 10,000 times is equally rare" so apparently he agreed with this, but disagreed that two of those results (all heads and all tails) were even possible at all.
He disagreed on the grounds of "the coin is multiple events" which is unlike e.g. drawing a single card. But my string of logic didn't distinguish between single and multiple events. It only asked him to agree to things like "flipping a coin twice has 4 possible outcomes, HH, HT, TH, and TT"
So tell me for yourself... what conclusion would you come to if someone said they agreed with your argument, but disagreed with the conclusion, and then disagreed on grounds that you didn't use?
Would you assume they didn't read your argument? They didn't understand it? Or they're lying about agreeing with it? I feel like there aren't many explanations to choose from here...
He seems to not be making any specific response, just kind of rehashing, at a certain point, math starts to separate itself from how it represents the physical world. I agree, he's way too unclear on what his problem is. He seems to just randomly talk about physics and philosophy without a lot of organization, haha.
It does kind of suck that you're taking the time to form your arguments so explicitly and he just dismisses them without giving you a clear idea of why.
It's fine. I thought it would be interesting if more people would discuss this way (presenting a string of statements then finding where the disagreement is) so it was fun to give it a try during an actual disagreement.
Haha, I actually did watch that infinity video again.
I would say after watching Carlsen blunder a full piece anything is possible.
I would also reference the Sack of Rome where Szofia Polgar had a tremendous performance at age fourteen if I recall correctly (2900 equivalent or something to that effect) by which I suggest there may be more than meets the eye.
bterranlong.wix.com/whitemates
This is the last infinity video I saw:
https://www.youtube.com/watch?v=SrU9YDoXE88
He goes over it pretty fast, I remember not following it the whole way.
Ah, I saw that one too. A few times actually. I enjoyed it a lot. It seems like you can always ask "why not go even further" no matter what you're talking about. Even with an infinite set, why can't there be something beyond that? And beyond that? You can even describe that phenomenon with some other number/concept, but why can't you even go beyond that? That seemed to be what he was getting at later in the video, but I dunno.
011 wrote:
If you don't trust logic though... I mean... not to be rude, but it's not a matter of trust it's a matter of either you understand it or you don't.
This is too the point and defines the difference of our individual positions. I can understand your logic without agreeing it is infallible. We all posses our own logic, but how open are we to accepting alternative explanations are possible? It goes well beyond the simple "it's not a matter of trust".
And you can try to argue that there is some kind of contradiction between being a 1300 and playing certain moves like binary has. That what it is to be a human 1300 involves learning to "never" consider certain moves, so that they will not be among possible games to play.