"If the universe (not in matters of space-time but in the context of scope) is truly infinite, and the true raw potential of everyone's imaginations are truly infinite (removal of environmental and other 'learned' limitations), then doesn't it stand to reason that anything (beings, places, times, etc) anyone has ever dreamed up, thought of, or in other ways created in their mind has to have existed, does exist, or will exist, and if so, does that mean that everyone takes a part in 'helping' to keep the universe's scale infinite?" ~Mark Feldman

While speaking with a friend about this quote (mine from 8th grade), I argued that if the above statement were in fact true, there must be a planet (in fact an infinite number of them) that rains jellybeans. His response was (to paraphrase), "Although there may be an infinite number of planets, all of those planets would have to conform to the rules of physics that we know (and the ones we don't) about our own universe, thus no, you could never physically have a world whose rain is made of jellybeans."

An example he used to describe to me the difference of infinite sets was:

The set of all even numbers vs the set of all numbers or all odd numbers; all infinite, non equal.

While I understand his argument, I am still unsatisfied with this outcome. Both the physical limitation and infinite number set difference arguments, to me, fall short. They are each a linear set of infinity whereas I view true infinity to have an infinite number of planes, dimensions and directions to branch from. Basically, I say that the universe (the true sense of the bucket that everything fits into) would hold every possible outcome, even if the physical limitations of our 'universe' wouldn't allow it. Do my arguments hold water to philosophical logic? Does infinity (not numbers) truly mean the sum of all outcomes?

Again please keep in mind that although I use the word universe, I'm not talking about space or matter. I simply have not found a better term for what I'm implying.

The concept of infinity also extends to the multiverse hypothesis, which, when explained by astrophysicists such as Michio Kaku, posits that there are an infinite number and variety of universes. Source

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  • In brief: no, it doesn't stand to reason since thinking about stuff doesn't make it happen. And infinity absolutely does not mean the sum of all outcomes. See the Wikipedia article for some standard usages. – Rex Kerr Aug 8 '14 at 9:23
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    It only means that anything you can potentially think of would be thought of. – Rex Kerr Aug 8 '14 at 9:38
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    You are able to think of impossible things and not realize it. – Rex Kerr Aug 8 '14 at 10:07
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    Close your eyes and imagine an infinite multiverse (or whathaveyou) where you can not state that such imagined places must exist because you were able to think of them. Now you have a big problem. – David H Aug 8 '14 at 10:24
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    Another point to be careful of here is that Wikipedia is not an authoritative source. There are issues around infinities and multiverse theories in physics, but these are primarily focused on addressing the problematic nature of the very small, and of the use of full real analysis in modelling it. That's not the kind of infinity you're thinking of, which would be something like Spinoza's concept of infinity. There's a useful discussion of that in the SEP: see plato.stanford.edu/entries/spinoza-attributes/#NumAtt and plato.stanford.edu/entries/spinoza-modal – Paul Ross Aug 8 '14 at 15:54

There are some people who believe our universe is contained within a "multiverse" which contains all possibilities (which personally I find a depressing prospect, since it would arguably reduce to meaninglessness any given event happening anywhere). The "multiverse" is highly speculative, however, and there are plenty of other people who disbelieve in it altogether.

On the other hand, as your friend pointed out, infinite doesn't necessarily mean encompassing all possibilities, even in the case that we do exist in a multiverse. Consider the decimal expansion of 1/3, which is 0.3333333... --infinite, yet without infinite novelty.

A tougher philosophical case is the number pi, which apparently does contain infinite novelty. Imagine mapping all possible two digit combinations to letters, numbers and punctuation. Surely, somewhere in the depths of pi, this exact paragraph you are now reading must be thus encoded --after all, if infinite variety is to be provided, it seems clear that all possibilities must someday be exhausted. And, from that point of view, couldn't we also imagine that all possible worlds must be described somewhere within pi (see also, Borges' Library of Babel, and the infinite monkey hypothesis)?

Yet is this another error? Consider also the Mandelbrot Set, the "most complex" object in mathematics. Upon expansion it presents graphs of infinite novelty --it never exactly repeats itself at any level of magnification. However, this doesn't mean that it will ever exactly resemble a picture of Kim Kardashian, or a dog wearing a hat, or so forth. Infinite novelty does not, in this case, mean the exhaustion of all possibilities, but rather an infinite exploration of variations upon a theme.

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    "And, from that point of view, couldn't we also imagine that all possible worlds must be described somewhere within pi" - sort of. You would need to consider your hypothetical map from digits of pi to worlds. If such a map is not surjective, then infinite variety does not mean all possibilities must be exhausted. – James Kingsbery Aug 8 '14 at 18:29
  • @JamesKingsbery - I think we're in agreement. It may not have been clear, but I didn't mean the statements in the second paragraph to stand as definitive. I'll edit to clarify. – Chris Sunami Aug 8 '14 at 18:57
  • A perceptive answer. It's not proven that pi contains all possible subsequences ("infinite variety"), even though it's conjectured. I'm guessing you used "apparently" to mean "it seems". A number which has this property in every number base is called a normal number. There exist (uncountably) infinitely many normal numbers and uncountably infinitely many numbers that are not normal, but the normal numbers outnumber the non-normal ones. We suspect that most of the irrational numbers we know are normal, but we don't know. – AndrewC Aug 31 '14 at 19:39

I think your reasoning is is begging the question. You define infinity like this: Infinity = a place where everything every human being ever thought of or will think of physically exists, no matter whether it defies the laws of physics or logic.

Of course, in this definition, everything you think of exists in "the void of infinity". But is this really the right definition? Or for that matter, a helpful definition? I'm no physicist, I'm not familiar with the multiverse-theory, so I cannot say whether this definition resembles the definition of multiverse. From a philosophically persepective, however, a definition that begs the question is not a very good one. How should you ever find out whether your definition is accurate? You cannot physically reach those other universes, so the criterion for accuracy must lie somewhere else. For example in logical consistency!

However, this line of thinking is somewhat similar to the thought, that with each decision you create another reality. If tomorrow at breakfast you have to decide between coffee and tea, either decision would cause reality to split, and henceforth there would be one reality where you had coffee, and one where you had tea. This thought is sometimes used in ethics to discuss the value of a decision. You would then argue, the world where I had tea is all together better then the world where I had coffee. It is highly debatable whether this line of thinking can really justify ethics.

The concept originally derives form modal logic and is discussed at length, e.g. here: http://plato.stanford.edu/entries/possible-worlds/

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    I like your example of coffee and tea, but I don't feel the rest of your answer pertains to the question. I don't <i>define infinity = a place where everything every human being ever thought of or will think of physically exists, no matter whether it defies the laws of physics or logic.</i> Conceptually I think of it as everything. The human thoughts simply being a subset of what is possible. (and impossible- as it was made aware to me in the comments) And yes, I did beg the question. Basically what I've learned today is... 8th grade thinking didn't hold up. – MegaMark Aug 8 '14 at 10:58
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    I believe, the definition of infinitiy that you are using, engulfs the definition I ascribed to you. As I read you, this was the implicit assumption underlying your reasoning. I was trying to make it explicit to you, where exactly the problem lies, and what "everything" could mean in context of your argument. So, basically, I used the fundamental philosophical tool for dealing with this kind of question: always clarify definitions of the concepts you're using, thats the name of the game ;) – Frederike Aug 11 '14 at 9:20

There is a compelling argument that says, if the universe is infinite, then anything that can exist will both exist and occur infinitely often.

What is meant by can exist is "has a non-zero probability" according the some probability measure.

That fact that you and I exist necessarily means that we exist infinitely often in a infinite universe. The fact that I am typing this text in response to your question means that we would have this exchange infinitely often. Etc.

This is obviously very unsettling.

The principle is best explained using a coin-flipping analogy. When flipping a fair coin, the probability of flipping one-million heads in a row is very small, but it is non-zero. Given enough time, this event will occur. Once it has occured it must occur again since an infinite amount of time remains.

In the context of your question, any finite volume of space can contain at most finitely many fundamental particles in various configurations. The fact that our galaxy exists means that it must exist infinitely many times in an infinite universe. Etc.

Whether or not a planet exists where it rains jelly beans is not clear.

  • It's obviously false. The sequence of numbers 1, 2, 3, ... is infinite, yet no number repeats. But ok, what if the number of possible states is bounded? The sequence 0, 1, 1, 1, 1, ... is infinite yet 0 does not recur. The idea that "in an infinite universe, everything must recur" is flat out false. – user4894 Sep 6 '14 at 23:08
  • @user4894 Have a look at [physics stack exchange] (physics.stackexchange.com/questions/132661/…) for a semi-formal argument. The accepted answer is the first listed. – Nick R Sep 6 '14 at 23:12
  • The argument is wrong, for the reason I gave. And we already know that if we attack the problem probabilistically, a state could still fail to recur, even though with zero probability (which in infinite probability spaces does NOT mean it's impossible). There's a lot of inaccurate information online, the link you gave is a great example. If someone accepted the answer, that doesn't mean it's right. In fact it is wrong twice. Once for the 0,1,1,1... reason and the other is for the measure zero reason. "Proof by somebody accepted it on Stackexchange." Aristotle would roll over in his grave. – user4894 Sep 6 '14 at 23:24
  • @user4894 All I can say is that the properties of the number system are not determined by probabilities. Interestingly, I too had the same issues that you have raised here. E.g., 2 is an even prime, but it doesn't mean there's another. The number-theoretic and analytic properties of numbers are determined by the axioms, they are not dependant on probability. – Nick R Sep 6 '14 at 23:31
  • @user4894 adding to my comment(above), current scientific theory says that reality is determined by probability. The accepted interpretation of Quantum Theory is that of probability. – Nick R Sep 6 '14 at 23:35

Regarding even numbers and odd numbers: If You take Natural numbers, then You have infinity power of set called Alef0, suppose it's also for integer. But real numbers, that with fractions, there is more numbers like this and its power is Continuum. So we can have many infinities and can compute on them. It's a bit mathematical point of view. Regarding thinking everything and it happen - suppose I think that there was no Big Bang. But I exist. It's safe to state that there is a Set of completed thoughts and a set of bounced thoughts. And the sum of it is that what @MegaMark described. Suppose also that the number of things in the universe is the maximum infinity we can have. So i think of number which is equal to this maximum infinity power of universe plus one jellybean. It shouldn't exist, because the maximum infinity number isn't maximum anymore… I know i don't know nothing.


Your friend's argument is basic and thus unsatifactory. The arbitrariness of the imagination cannot be doubted, however one can't concieve two contradictory notions simultaneously. This said one may assume reality is a fragment of the imagination,this said, we cannot have two contradicting realities existing simultaneously;your friend's argument. Thus if the universe is infinite,that is if the laws of physics differ from one terrain to the other,it follows we cannot have an interaction between this two terrain; thus there must be a planet raining jelly beans,and we cannot contact,let alone concieve such a world.

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