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Infinite Earths? Scientific Fantasy?

One of the most depressing ideas of modern times is that of infinity. Recent work in multiverse physics represents another destructive, dehumanising and incoherent use of this idea.
Multiverse physics: there are infinite earths and infinite yous and mes and everything else.

A popular book: Hidden Reality (Greene (HRG)) argues for this hypothesis.

The concept of infinity is obscure and incomprehensible. Its use in language destabilises, decoheres and incapacitates healthy truth preserving thought processes no matter what the context.

Does the hypothesis of infinite earths and everything make sense? How does it impact on our attitude to our own earth?

There is no evidence for infinite earths. But HRG uses a mathematical argument to prove that it must be so.

Physicists often boast that they are good at math "if weez weren't such good mathos then weez wouldn't be such good physicists" (for example Greene and Spengler (myth of fine tuning).

But the argument from math-infinity to infinite earths is incorrect.

Sadly, many scientists start jabbering about infinity, quickly degenerate into a maniacal rave about evolution and the collapse completely with a solemn sermon about god.

Thankfully HRG stops at stage 2 in these three stages of mental deterioration.

However if HRG's discussion of infinity is bad the discussion of evolution is worse, but I will focus on infinity.

The concept of infinity is formalized in only one branch of science and math: transfinite set theory (TST).

In TST infinity is defined as a correspondence relation (a set and a proper subset). This definition/axiom is used to derive theorems in TST. The definition makes no mention of space, no mention of particles, no mention of time. One of the theorems derived from infinity is that infinity plus or minus an arbitrarily large number still equals infinity.

This theorem is used by HRG as a foundation (first 4 chapters of HR) for the argument for infinite universes, earths etc.

In short, no matter how many possible particle combinations (let's say X = you) even a zillion to the power zillion, this number will still be trumped (sorry) by infinity.

But outside of TST this theorem is nonsensical. It is only a theorem inside TST and it is not based on a physical conception of infinity.
But rather an abstract math operation which has one main virtue: consistency within the system.

When I first studied logic our tutor (LH, now a world class logician) asked us to prove something unusual. We proved that there are only two objects in the universe. We had a great laugh, it was funny, because outside of the system of axioms used to prove it the theorem just couldn't be accepted.

We must treat each other and the earth as unique for very practical reasons. The insidious ideas of misguided science and unreserved exploitation of the earth and each other have to be refuted.