Infinity and unique don’t mix. Theory

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    Infinity Theory
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Discussion Overview

The discussion revolves around the implications of infinity in relation to uniqueness in space and time. Participants explore whether the infinite nature of the universe allows for the existence of identical or similar planets, and the philosophical and mathematical ramifications of these ideas.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that if space and time are infinite, it implies there are an infinite number of identical and varied versions of Earth existing simultaneously and across time.
  • Others argue against the notion of infinite space and time, suggesting they are likely finite.
  • A participant introduces mathematical considerations, noting that while infinities exist in mathematics, they do not necessarily imply the existence of all possible values within a given context.
  • Another participant discusses the implications of a flat universe and the potential for calculating identical states of matter within arbitrary volumes, referencing the work of Max Tegmark on the multiverse and quantum states.
  • There is a reiteration of the idea that if the universe is spatially infinite, it could lead to identical copies of regions of space, but this is contested by those who doubt the infinite nature of space and time.

Areas of Agreement / Disagreement

Participants express differing views on the finiteness or infiniteness of space and time, with no consensus reached on whether these concepts allow for true uniqueness. The discussion remains unresolved with competing perspectives on the implications of infinity.

Contextual Notes

Participants reference mathematical concepts and theories related to infinity, but the discussion includes assumptions about the nature of the universe that remain unverified. The implications of these assumptions on the uniqueness of objects in the universe are not fully explored.

Alestair
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Because space and time are infinite, doesn’t that make it impossible for anything to be truly unique. I propose there are an infinite number of this planet right now in this universe. The distance between each planet is probably unconceivable. Also there is an infinite number of this planet in the past and in the future. Not only is there an infinite number of Earth's exactly the same as this one, there are also an infinite number of this planet with slight differences and infinite number with extreme differences. This possibility is opened up because time and space are infinite. Nothing can ever be unique.
 
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So your saying both have a start point and an end point? Well I believe otherwise. So humor me and pretend they are. Open your mind a little.
 
I am far from an expert in these matters, but two fairly basic points come to mind.

#1 - While infinities seem to have a functional place in mathematics, infinite quantities and values tend to have a rather dyspeptic relationship with physics.

#2 - Just from the standpoint of mathematics, an infinite quantity of values does not imply all possible values for the class or variable in question. For example, if you imagine a number line, marked off in both directions with integer values, you have an infinite sequence of numbers, but you are hardly expressing _all possible_ numbers. Far from it, in fact. The same statement could be said for the rational numbers, the real numbers, etc... with each expressing an infinite sequence, yet containing 'more' numbers. Similarly, counting numbers and whole numbers are both infinite sequences, yet containing fewer numbers than the integers. FWIW, this has been a historical issue in mathematics of some controversy that involves some mind bending counter-intuitive thinking.

An interesting popular/mid-level book on the subject and history of 'Infinity' is A Brief History of Infinity. Constable & Robinson. 2003. ISBN 1-84119-650-9

http://www.brianclegg.net/infinity.html

By author Brian Clegg

http://en.wikipedia.org/wiki/Brian_Clegg

--diogenesNY
 
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Alestair said:
Because space and time are infinite, doesn’t that make it impossible for anything to be truly unique. I propose there are an infinite number of this planet right now in this universe. The distance between each planet is probably unconceivable. Also there is an infinite number of this planet in the past and in the future. Not only is there an infinite number of Earth's exactly the same as this one, there are also an infinite number of this planet with slight differences and infinite number with extreme differences. This possibility is opened up because time and space are infinite. Nothing can ever be unique.
Yes, these would all be logical consequences of a spatially infinite, infinitely old universe.
 
Alestair said:
Because space and time are infinite, doesn’t that make it impossible for anything to be truly unique. I propose there are an infinite number of this planet right now in this universe. The distance between each planet is probably unconceivable. Also there is an infinite number of this planet in the past and in the future. Not only is there an infinite number of Earth's exactly the same as this one, there are also an infinite number of this planet with slight differences and infinite number with extreme differences. This possibility is opened up because time and space are infinite. Nothing can ever be unique.

Let's leave time aside, and focus on space. Spatial geometry of universe is flat as far as we can measure it. That implies that universe is either spatially infinite, or that it is really, really big (radius of curvature is so big that it simply can't be detected).

So, you can take any arbitrary volume, and calculate all possible states and arrangement of matter in that volume, and then if physics is same everywhere, you can calculate how far is identical copy of that volume. Simple as that.

Here is what famous multiverse guy Max Tegmark has to say about it. You can read whole paper at http://arxiv.org/abs/0905.1283" :

This is an extremely conservative estimate, simply counting all possible quantum states that a Hubble volume can have that are no hotter than 108K. 10^115 is roughly the number of protons that the Pauli exclusion principle would allow you to pack into a Hubble volume at this temperature (our own Hubble volume contains only about 10^80 protons). Each of these 10^115 slots can be either occupied or unoccupied, giving N = 2^(10^115) ~ 10^(10^115) possibilities, so the expected distance to the nearest identical Hubble volume is N^(1/3) ~ 10^(10^115) Hubble radii ~ 10^(10^115) meters. Your nearest copy is likely to be much closer than 10^(10^29) meters, since the planet formation and evolutionary processes that have tipped the odds in your favor are at work everywhere. There are probably at least 10^20 habitable planets in our own Hubble volume alone.

russ_watters said:
Neither space nor time are likely infinite.

Is this your personal feeling, or is it based on some scientific argument?
 
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