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To be perfectly frank, this sounds like some sort of new-agey claptrap to me, but from a purely physical standpoint we cananswer this question.

First, let's define our terms. Infinite means infinite, not some arbitrarily large but finite number. And for "universe", let's be pragmatic and say we mean the observable universe, that portion of the universe that we can ever reach or that can ever affect us in any way, including by us just being able to see it. And finally, let's replace "intelligence", which is a pretty nebulous term, with "information", which we can define more precisely.

The most densely we can even imagine information being packed is one bit (yes/no, on/off, 1/0) per Planck volume... in practice, we are nowhere near being able to store information at that density; Planck volumes are much, much smaller than the smallest subatomic particles we know. There are a large but finite number of Planck volumes in the universe. So, there cannot be an infinite amount of information in the universe. In fact, the amount of information there can possibly be in the universe is pretty small as far as big numbers go; there are only about 8 x 10184 Planck volumes in the observable universe, a number so small that I could write it in full in a couple of minutes.

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