Mage246
Two options does not mean that those 2 options are equally likely. Would you like to be shot in the face, yes or no?
Infinite Debates
- 主题发起人 Splintert
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Okay, as Mage wrote, relationships between sets. Sets A and B got equal amount of elements, if there's a relationship between them that for EACH element of set A assigns EXACTLY ONE element from set B. Simple example: you've got set of two apples, yellow and red, and set of two children, boy and girl. Relation assigns red apples to girls and yellow to boys, SHAZAM, you can clearly see sets are equal in elements.
Harder example, natural (classical way, without 0) and integer numbers sets. You can make a relation between them, like that:
n is natural number, if it's pair, then assign to it n/2, if it's odd then assign -((n-1)/2). Let's see how it works:
n=1, -((n-1)/2)=0
n=2, n/2=1
n=3, -((n-1)/2)=-1
n=4, n/2=2
n=5, -((n-1)/2)=-2
and so on. In simple words, you can "number" all the integer with 1st, 2nd, 3rd and so on. Similarly you can "number" all the rational numbers.
The problem is, similar relation doesn't exist between natural and real numbers, so there are effectively more real numbers.
Harder example, natural (classical way, without 0) and integer numbers sets. You can make a relation between them, like that:
n is natural number, if it's pair, then assign to it n/2, if it's odd then assign -((n-1)/2). Let's see how it works:
n=1, -((n-1)/2)=0
n=2, n/2=1
n=3, -((n-1)/2)=-1
n=4, n/2=2
n=5, -((n-1)/2)=-2
and so on. In simple words, you can "number" all the integer with 1st, 2nd, 3rd and so on. Similarly you can "number" all the rational numbers.
The problem is, similar relation doesn't exist between natural and real numbers, so there are effectively more real numbers.
Mage246
Dryvus 说:
We're not looking at a set of infinite numbers where we are trying to compare infinity to infinity, we're looking at an infinite set of finite numbers with a defined relationship with each other. This is what I've been trying to communicate with my examples, but my notation is extremely rusty and after looking back I screwed up the explanations a few times.
This has already been explained by Do not look here.
Splintert 说:
Yes, and for every one of those universes, there are also a certain number of universes in which it was not chosen. The relationship between those universes being determined by the probability of that option being chosen.
Mage246
They're not connected, but they are related to each other via probabilities. Parallel universes are an expression of probabilities. A probability is a statement saying that for every situation X, there is a possibility of A or B happening, and that the relationship between the occurrences of either of those possibilities is A/(A+B) for A, and B/(A+B) for B. Each occurrence is not connected to the next, but taken as a whole the complete set of all occurrences (in other words, as the number of occurrences approaches infinity) must relate to that probability.
Mage246
A 1:1 split is a 50/50 probability. You are the one assuming that you know the probability, not me. Based on what? Nothing.
It could be a 1:2 split or a 2:1 split or anything in between or outside of that. There's no reason whatsoever to assume that it's a 1:1 split.
It could be a 1:2 split or a 2:1 split or anything in between or outside of that. There's no reason whatsoever to assume that it's a 1:1 split.
If we have our infinite set of universes, and a finite set of two possibilities, there is simply no other conclusion you can come to.
As the number of coin flips approaches infinity, the number of heads to tails approaches 1:1.
And, reply to your edit:
If its a 2:1 or 1:2 probability that's not fair chance.
As the number of coin flips approaches infinity, the number of heads to tails approaches 1:1.
And, reply to your edit:
If its a 2:1 or 1:2 probability that's not fair chance.
About probability with yes-no, 0-1, pink and fluffy unicorns exist-don't exist...
In math, there's something called random variable. It has probability distribution of kind. Let's say, this specific random variable has two values 1 and 0.
Now, in probability there's probability space - all of what can happen is included there. As each space, this one can be divided into sets, and as all sets, these can be "measured".
So if you take our random variable, you can measure the set of happenings, for which its value is 1. Now something called "expected value" kicks in, for ordinary variables, that's integral, but for 0-1 variables it's also comfortably showing how much of probability space is "covered" by values 1 (it's any number from 0 - meaning there's no "1" value - to 1 - meaning it's always "1").
EXAMPLE: random variable counting wins in the "three-gates" kind of tv-show. There are three gates, but only one covers the prize, contestants have no effing idea which one. Expected value of this variable is 1/3, as they will guess right only 1/3 of times.
Now, if you'll try and try and try, number of wins compared to loses won't become equal to 1/2, although it's simple 0-1 choice, you win or lose.
Coming closer and closer to infinity number of trials, you'll get equally 1/3 wins to loses ratio, so expected value.
In math, there's something called random variable. It has probability distribution of kind. Let's say, this specific random variable has two values 1 and 0.
Now, in probability there's probability space - all of what can happen is included there. As each space, this one can be divided into sets, and as all sets, these can be "measured".
So if you take our random variable, you can measure the set of happenings, for which its value is 1. Now something called "expected value" kicks in, for ordinary variables, that's integral, but for 0-1 variables it's also comfortably showing how much of probability space is "covered" by values 1 (it's any number from 0 - meaning there's no "1" value - to 1 - meaning it's always "1").
EXAMPLE: random variable counting wins in the "three-gates" kind of tv-show. There are three gates, but only one covers the prize, contestants have no effing idea which one. Expected value of this variable is 1/3, as they will guess right only 1/3 of times.
Now, if you'll try and try and try, number of wins compared to loses won't become equal to 1/2, although it's simple 0-1 choice, you win or lose.
Coming closer and closer to infinity number of trials, you'll get equally 1/3 wins to loses ratio, so expected value.
Mage246
Splintert 说:
A choice is not a coin toss. Choosing to have clipping or choosing to fix it is not a coin toss. Just because something is a yes/no decision does not mean that it is a coin toss. If one choice is clearly preferable to the other, and a rational actor is able to choose between them, a 1:1 split is extremely unlikely.
If you were tossing a coin and you could choose whether it lands on heads or tails, and heads get you a dollar while tails gets you nothing, would it be reasonable to expect that the probability of the coin landing on heads or tails to be a 1:1 split? NO.
Do not look here 说:
In your example they have a 2/3 chance to lose and a 1/3 chance to win, so its not the same. It would have to be a two-door type of thing.
Mage246 说:
Yes, in our universe LOD clipping is undesirable. But since we're talking about parallel universes, its totally irrelevant which option is "right", every possible permutation of options exists.
Mage246
Now you're assuming that the probability of a universe in which clipping is desirable is equal in probability to a universe in which clipping is undesirable. Another unsubstantiated assumption.
It's not an assumption. It's a fact.
I mentioned earlier about a tree.
x
undesirable / \ desirable
y z
more variables /\ /\
For all the universes on the left side of X, LOD clipping is undesirable. For all the universes on the right, it is desirable. All of the other variables can be exactly identical for each respective universe down the tree, but because the first variable in question is different they are distinct universes.
I mentioned earlier about a tree.
x
undesirable / \ desirable
y z
more variables /\ /\
For all the universes on the left side of X, LOD clipping is undesirable. For all the universes on the right, it is desirable. All of the other variables can be exactly identical for each respective universe down the tree, but because the first variable in question is different they are distinct universes.
Well, to be honest, if you take it so far, then you have to take in account two different variables, one saying it is desirable and one saying it's undesirable. In both cases, they're expected value is 0.
Because in infinite numbers of yes-no choices you're taking only those which lead to occurrence of that one specific yes-no choice, ignoring the fact of existence of tremendous portion of parallel universes which never had that choice.
Because in infinite numbers of yes-no choices you're taking only those which lead to occurrence of that one specific yes-no choice, ignoring the fact of existence of tremendous portion of parallel universes which never had that choice.
Mage246
Splintert 说:
That doesn't even mean that the chances of it being desirable are equal. That's just plotting out the choices, not their probability. Return to my coin-tossing example-
If you can choose whether a coin lands on heads or tails, and heads is clearly superior in outcome for you, the probability of the coin landing on heads is much higher than the probability of the coin landing on tails. Sub-optimal outcomes have lower probabilities when either a rational actor or a natural law are involved.
But if I were to display things as you have, it would look like this:
x
tails / \ heads
y z
more variables /\ /\
Because your example isn't actually telling us anything about the probability.
Mage246 说:
It seems like a pretty ridiculous argument to say that I don't know the probability because the universes aren't sentient objects capable of controlling everything inside of them.
The probability doesn't particularly matter. The fact that there are choices means there exists a universe for that choice. Because there are two possible choices, half are yes and half are no. As Do not look here said there are also infinitely many universes in which it is neither yes or no.
Mage246
Splintert 说:
This is just plain flat out wrong. The first half of the sentence is completely unconnected to the second half. I don't know why you can't understand this.
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