# Infinite Improbability

## Recommended Posts

If, based on all current evidence, the chance of something possible being objectively true is "1 in infinity", does that mean infinite improbability, or impossibility, or something like that? Or something else entirely? Don't ask what could possibly have a "one in infinity" chance of being true:P I just want to know what "1 in infinity" means, and if I completely misunderstand the concept or not.

Thanks!

EDIT: Oh, and what if it were "x in infinity" where x was any positive integer, would it still be the same as "1 in infinity"?

Edited by redsaint182
##### Share on other sites

I am not sure if saying something is 1 in infinity is even proper. Generally saying the probability of event M something is a in b means:

$P(M)=\frac{a}{b}$

Generally, $\frac{1}{\infty}$ is undefined as infinity is not actually a number and therefore the expression is undefined. As such I would guess that your statement in not actually a true statement.

Merged post follows:

Consecutive posts merged

If you said x in infinity you would simply be saying,

$P(M)=\frac{x}{\infty}$

which would still be undefined if $x\in\aleph$. As far as I know the only way to make your statement undefined would be say, "The probability of event M occurring is 1 in X as x tends towards infinity" since that would be,

$P(M)=Lim_{x \rightarrow\infty} \frac{1}{x}=0$

And I am really not sure if this would be possible, and if so why the probability of it happening would not be reported simply as 0.

Edited by DJBruce
Consecutive posts merged.
##### Share on other sites
I am not sure if saying something is 1 in infinity is even proper. Generally saying the probability of event M something is a in b means:

$P(M)=\frac{a}{b}$

Generally, $\frac{1}{\infty}$ is undefined as infinity is not actually a number and therefore the expression is undefined. As such I would guess that your statement in not actually a true statement.

Thanks. Well, I am trying to disprove the existence of Monotheistic gods (LOL!), and I figured if there is an infinite number of equally plausible claims (meaning none of them have substantial evidence, but are all simply assertions meant to be taken on faith), and they cannot all be logically true (one being true would mean the others necessarily were not true), then the probability of any one specific monotheistic god being true (based on current lack of any evidence), is "one in infinity," whatever that means. I'm probably wrong, but I wanted to try to disprove god anyways (even though i don't have to,) hehe. Trying to justify strong atheism, and I am coming up with arguments for it.

But anyways, all of that goes in the Philosophy folder. I am just curious as to what "1 in infinity" means in this context, if anything, if even a usable term at all.

##### Share on other sites

1/infinity = 0

however, if there are infinite chances for this to occur you get infinity * 1/infinity which is undefined (both 0*infinity and infinity/infinity are undefined). If this were not the case than you could do some funny math.

##### Share on other sites
1/infinity = 0

however, if there are infinite chances for this to occur you get infinity * 1/infinity which is undefined (both 0*infinity and infinity/infinity are undefined). If this were not the case than you could do some funny math.

Isn't $\frac{1}{\infty}$ undefined as well; since infinity isn't actually a number?

The very sentence "1/infinity = 0" has no meaning. Why? Because

"infinity" is a concept, NOT a number. It is a concept that means

"limitlessness." As such, it cannot be used with any mathematical

operators. The symbols of +, -, x, and / are arithmetic operators, and

we can only use them for numbers.

To write 1/infinity and mean "1 divided by infinity" doesn't make any

sense. 1 cannot be divided by a concept. It can only be divided by

a number. Similarly, "infinity + 1" or "2 times infinity" are also

meaningless.

##### Share on other sites

I think, to be more accurate,

$\lim_{x\to \infty} \frac{1}{x} = 0$

##### Share on other sites

One thing to consider is that infinite possibilities does not imply that each possibility is infinitely unlikely.

For example: Option 1 has a probability of 1/2. Option 2 has a probability of 1/4, option 3 has 1/8, and so on, such that each successive possibility is 1/2 as likely as the previous one. You still have an infinite number of possibilities, but any particular possibility has a finite probability.

Edited by Sisyphus
##### Share on other sites

What Cap'n said. Infinity doesn't really make any sense, and if infinity appears anywhere I naturally think of it as the limit as a number grows unboundedly large. So 1/infinity = 0 in the same sense as infinity + 1 = infinity, or any other manipulations that can be done with infinity. The only way for this sort of equation to have meaning is to take a limit. Alternately, saying all arithmetic with infinity is invalid since infinity is not a number also works.

##### Share on other sites

So is there any way to mathematically represent the probability of a specific god claim which is equally as plausible as an infinite amount of other god claims that makes any sort of sense? Or is the equation with the limit the best we can do?

Also, can someone explain a little more what Sisyphus is talking about, about each option having finite probability, within the context of the god thing. I thought that if there were infinite possibilities, which are all equally plausible, and which would cancel the others out if it was true, then they would be infinitely unlikely. Because, if they are all equally as likely, then how do you decide which is option 1, and which is option 5, and no matter what option, don't they still have to stand up against an infinite amount of other equally plausible options?

Edited by redsaint182
##### Share on other sites

Basically what he said was that if you were to sum together an infinite amount of numbers, they could still sum up to a finite amount, so long as they numbers get successively smaller at a fast enough pace. For example, 1+1/2+1/4+1/8+1/16+... = 2.

##### Share on other sites

In order to say they're all equally likely, you have to be able to quantify their probability in some way and confirm that. Probability of x among n options is not automatically 1/n.

Do you, for example, think that the absence of a conscious, monotheistic deity is equally as probable as, say, the tenets of Pastafarianism? I don't.

This is, ironically, the same flaw in reasoning that is often used as an argument for the plausibility of a certain religion. "Either it's true or it isn't. You can't know, so it's illogical to discount it." The flaw in reasoning, to repeat, is to imply that the two options presented ("it's true" and "it isn't true") are equally likely.

EDIT: Also, how has the thread gotten this far without any Hitchhiker's Guide references?

Edited by Sisyphus
##### Share on other sites
Basically what he said was that if you were to sum together an infinite amount of numbers, they could still sum up to a finite amount, so long as they numbers get successively smaller at a fast enough pace. For example, 1+1/2+1/4+1/8+1/16+... = 2.

But would that apply to a situation where you have an infinite amount of equally plausible claims? It seems like if they are all equally probable, then you do not get the 1/2s and 1/4s and 1/8s, because isn't adding the 1/8 like adding a claim that is only 1/8 as likely as the first one? If all possibilities are, according to current evidence all equally plausible, then wouldn't it be 1+1+1+1...?

Merged post follows:

Consecutive posts merged
In order to say they're all equally likely, you have to be able to quantify their probability in some way and confirm that. Probability of x among n options is not automatically 1/n.

Do you, for example, think that the absence of a conscious, monotheistic deity is equally as probable as, say, the tenets of Pastafarianism? I don't.

This is, ironically, the same flaw in reasoning that is often used as an argument for the plausibility of a certain religion. "Either it's true or it isn't. You can't know, so it's illogical to discount it." The flaw in reasoning, to repeat, is to imply that the two options presented ("it's true" and "it isn't true") are equally likely.

EDIT: Also, how has the thread gotten this far without any Hitchhiker's Guide references?

Well, in my attempts to disprove monotheism, I am going to show that evidence for the claim can be historical evidence, personal revelation, and empirical evidence. And then I am going to show why historical evidence and personal revelation are unreliable, and very possibly not true (I won't assert for certain that they are untrue, but that it is more plausible that the claims they make are not the case.) So after that, it leaves empirical evidence, and if a God is empirically untestable, that means they cannot gather any empirical evidence for it, then it has an equal amount of evidence as any claim your imagination can conceive of (FSM, we can use as an example.)

It is true that "either it's true or it isn't", it has to be one or the other, but the flaw comes in when we assume that both are equally as likely. But coming at it from looking at the evidence (or lack thereof), we have to hold all of these infinite number of gods at the same level, at this point in time (we can put one above another if new evidence comes in later, but for now, since they all have equal evidence, it is not unreasonable to put them on the same level.) We don't need to know the probability of god existing, because if there isn't a monotheistic god, then there isn't one. If there is one, then the question is "which one?", and then when we attempt to pick from the infinite amount, no matter which one we pick, we can say that it is, by all counts of current evidence or lack thereof, infinitely improbable and impossible. And since we could do that with any and every of the specific monotheistic god claims, we have to conclude that all of them are infinitely improbable and impossible, so none of them exist. So no matter what premise we assume from the start (that there is a monotheistic god, or there isn't,), we arrive at the same conclusion, that there isn't a monotheistic god.

But this all relies on our current evidence (or lack thereof) being correct. Of course, everything could change if some empirical evidence was provided for a certain god, because that would mean that it wouldn't fall into this category of infinite possible equally plausible monotheistic gods.

I don't think this will convince anybody because I think it is relatively useless. But I was just trying to make the point that if there isn't any evidence for these claims, that it is not unreasonable to actually take a position and say that they don't actually exist, based on all current evidence or lack thereof. It could be wrong, and shown wrong later by incoming empirical evidence, but it is currently, at least, a reasonable position.

Also, yes haha, Hitchhikers Guide... When I started thinking about this idea yesterday, I typed "infinite improbability" into google to see if it was a real concept or not, and Hitchhikers Guide came up... guess that tells you something about the validity of the concept hehehe.

##### Share on other sites

I know the argument. I had similar reasoning when I decided I was an atheist around age 13 or so. In fact I guessed that's what you were getting at from the first post.

I do think you can use similar arguments to show why a particular belief is unlikely, but I don't think it's valid the way you're trying to use it, since I don't think the "equally likely" part is really supportable. For example, I too think that Biblical accounts and personal "revelation" have almost no value as evidence for a Christian god. However, I'm not sure you can say they have zero value, which is what you would need to do to make it equivalent with any other random option you can think of.

##### Share on other sites
But would that apply to a situation where you have an infinite amount of equally plausible claims? It seems like if they are all equally probable, then you do not get the 1/2s and 1/4s and 1/8s, because isn't adding the 1/8 like adding a claim that is only 1/8 as likely as the first one? If all possibilities are, according to current evidence all equally plausible, then wouldn't it be 1+1+1+1...?

No... a probability of 1 is 100% and you can't get any higher than that. If you have n equally likely outcomes and they are mutually exclusive (there can be no outcome other than those), then the probability for each of them is 1/n and the probability that at least one of them is true is 1 (certainty).

However, if you were to guess which outcome would in fact happen, your probability of guessing correctly would be 1/n. This results in one of the best arguments against religion, ie how do you know your religion is the only right one out of millions. Putting an exact number to it would be difficult, since not all of them contradict each other and the correctness of one would increase the likelihood of some of being correct (they are not independent).

Merged post follows:

Consecutive posts merged
I don't think this will convince anybody because I think it is relatively useless. But I was just trying to make the point that if there isn't any evidence for these claims, that it is not unreasonable to actually take a position and say that they don't actually exist, based on all current evidence or lack thereof. It could be wrong, and shown wrong later by incoming empirical evidence, but it is currently, at least, a reasonable position.

And if you consider that to be equally likely, than it is almost certainly false as well, equally likely to any of the religions or made up nonsense anyone might think of.

I think you might consider reading up on Occam's Razor.

##### Share on other sites
I know the argument. I had similar reasoning when I decided I was an atheist around age 13 or so. In fact I guessed that's what you were getting at from the first post.

I do think you can use similar arguments to show why a particular belief is unlikely, but I don't think it's valid the way you're trying to use it, since I don't think the "equally likely" part is really supportable. For example, I too think that Biblical accounts and personal "revelation" have almost no value as evidence for a Christian god. However, I'm not sure you can say they have zero value, which is what you would need to do to make it equivalent with any other random option you can think of.

Well, I certainly cannot claim that a specific personal revelation or whatever is absolutely false. But, what I can do is look at all of the claims of personal revelation of competing gods of competing religions, and we can see there there are a vast amount of claims, and each maker of those claims deeply believes that they have had some personal experience or personal connection to a god or supernatural entity or force of some sort. We don't know exactly who is wrong, but we know that A LOT of people are in fact wrong, and are experiencing something which is not the god they claim to be, but some sort of psychological phenomena. Since we know of this phenomena, we can reasonably assert that it is much much more likely that any one individual making these claims is probably deluded rather than correct. Personal Revelation holds zero truth value to the objective observer, and taking into account that we know for a fact people can fool themselves into believing something that isn't real, we know that even for the person experiencing those things, it isn't reasonable for them to rely on their personal experience or revelation either.

Historical evidence is somewhat similar, as it can play off of someone having these supernatural experiences and then writing them down, but it isn't quite the same as the personal revelation evidence, because historical evidence generally makes a claim that something happened in objective reality at one point in time, in a way that the one event was experienced by multiple people. The way I go about discrediting Historical claims is similar to the personal revelation claims. There are a vast number of religions whose texts purport supernatural miracles and happenings, and a vast number of them claim to be historical or objectively true. While some claims can co-exist with other claims, a great many of them cannot. If the Bible claims are true, then none of the other historical god claims are true. If Hindu texts are true, then the Bible god, and the Quran god claims are not true, ect. So, looking at these contradictory claims, we know that supernatural events have been believed and written down. In fact, they still are today. There are plenty of recent god claims, many of which have been believed by a number of followers, and some of which have gained a great following over the years. The reason I bring these up is that the recent claims are more easily falsifiable. Claims from thousands of years ago are not as easily falsifiable, but that doesn't mean they are more likely to be true, in fact, I would think the opposite to be the case. If there is a historical assertion of supernatural proportion, and we know that claims of supernatural proportions are being made still today and are false, then we might be able to say that it is likely that the claim from a thousand years ago is false as well, more likely than not, anyways. Since there are competing historical claims, we know that many of them are made up. A supernatural event written down a thousand years ago is almost surely false, and is very improbable, in the same vein that a supernatural event written down two weeks ago is almost surely false, and is very improbable. It is just easier to put the one from two weeks ago to the test. We know that people can be fooled into believing ridiculous claims. Historical evidence of god is merely another assertion, one which cannot be easily falsified if the claim took place thousands of years ago, but an assertion that we know is more likely false than true. This doesn't prove that every single mention of supernatural happenings in the past are wrong, but with all of this taken into account, it is certainly more plausible than not that historical evidence of god, and personal revelation evidence, is unreliable and likely delusory, and it is not unreasonable to operate as if they were wrong.

So for those reasons (which are just evidence that historical god claims and personal revelation are not reliable, not proof, but evidence), I think that it is more plausible than not that those personal revelations and historical evidences hold zero truth value. And if that is the case, and the only other option is empirical evidence, which they all have an equal amount of, then I think it is more plausible to assert that from the looks of it, no monotheistic god exists.

And if you consider that to be equally likely, than it is almost certainly false as well, equally likely to any of the religions or made up nonsense anyone might think of.

I don't think I would consider the position that none of the claims are true as equally likely as any one of the individual claims. If each claim is almost certainly false, and we can go through each claim and label it as such, then we can also say about the claim that it is almost certainly not true, and once we say that about each claim individually, we can say about the whole that these claims are almost certainly not true, and more plausibly false. Therefore, the position that each claim is almost certainly not true is more plausible than the position that any specific one is true, or more plausibly true. I think But Idk... the idea has some holes, but I am going to toy around with it for a while.

Anyways, I an a noob regarding all things science, as many of you may be able to tell already I was just wondering if the concept of infinite improbability was a valid theoretical concept (it obviously doesn't carry over into reality very well, but was just wondering about it in theory.)

##### Share on other sites
• 5 months later...

If, based on all current evidence, the chance of something possible being objectively true is "1 in infinity", does that mean infinite improbability, or impossibility, or something like that? Or something else entirely? Don't ask what could possibly have a "one in infinity" chance of being true:P I just want to know what "1 in infinity" means, and if I completely misunderstand the concept or not.

Thanks!

EDIT: Oh, and what if it were "x in infinity" where x was any positive integer, would it still be the same as "1 in infinity"?

It seems like what this is referring to is something in quantum mechanics called the wave function. The elementary particles we think of are also waves, but they are waves of existence. The way particles work is by appearing at the most likely locations in the form of points once observed. However, a particles wave function extends indefinitely through space. An electron has a probability of appearing on the other side of the universe, but it's just such an unimaginably small probability that everything usually stays on small areas of probability. In an atom, the most likely place for an electron to be found with the energy that occupies the first energy level is in a sphere that encircles the nucleus with a radius from the nucleus of about .529*10^-10 meters. Typically what happens in physics with the wave function, is if you know something about a particle such as its energy, you can figure out the most likely places for that particle to show after some x amount of time. Quantum mechanics uses continuous variables. In a probability function you have infinite possibilities, but you try and find a high probability between two numbers. An improbability function can look like this:

## Create an account

Register a new account