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Re: Largest number using 5 symbols

25 Jul 2022 15:33

The argument can be made that if the universe/multiverse is mathematical than rather than the Big Bang, there must be a Big Bounce because if the universe/multiverse is mathematical than all numbers must be able to be described within the entirety of its existence.  So would say Max Tegmark.  We could apply a recursive function to the multiverse also, as you can envision universes existing inside black holes inside universes, and so on (and on and on lol)
That doesn't make sense to me.  I don't see why a "mathematical" universe couldn't be a subset of mathematics. If "mathematical" universe means that the universe can be fully described by mathematics, why couldn't mathematics also describe abstract, non-physical things?
Because then it would be a question of why those abstract non physical things didn't exist in reality.  We always have to be cautious about that-- there was a time that imaginary numbers were thought of as abstract and non physical, but it turns out they are absolutely essential in describing our universe.  Even beyond them, quaternions are essential to relativity and for a unified theory of everything combining both relativity and quantum mechanics, 8 dimensional octonion numbers seem to be required.  According to Tegmark, anything that is mathematically possible should be reality somewhere within the multiverse.
 
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midtskogen
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Re: Largest number using 5 symbols

26 Jul 2022 01:23

Because then it would be a question of why those abstract non physical things didn't exist in reality.  We always have to be cautious about that-- there was a time that imaginary numbers were thought of as abstract and non physical, but it turns out they are absolutely essential in describing our universe.  Even beyond them, quaternions are essential to relativity and for a unified theory of everything combining both relativity and quantum mechanics, 8 dimensional octonion numbers seem to be required.  According to Tegmark, anything that is mathematically possible should be reality somewhere within the multiverse.
That sounds like a respin of platonism.
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Re: Largest number using 5 symbols

27 Jul 2022 10:09

Because then it would be a question of why those abstract non physical things didn't exist in reality.  We always have to be cautious about that-- there was a time that imaginary numbers were thought of as abstract and non physical, but it turns out they are absolutely essential in describing our universe.  Even beyond them, quaternions are essential to relativity and for a unified theory of everything combining both relativity and quantum mechanics, 8 dimensional octonion numbers seem to be required.  According to Tegmark, anything that is mathematically possible should be reality somewhere within the multiverse.
That sounds like a respin of platonism.
It definitely is common amongst mathematicians.  Especially those who seek a unification of the infinite with the finite.  Godel was one its vocal proponents.

https://plato.stanford.edu/entries/platonism/

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and non-mental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this question, the term ‘platonism’ is spelled with a lower-case ‘p’. (See entry on Plato.) The most important figure in the development of modern platonism is Gottlob Frege (1884, 1892, 1893–1903, 1919). The view has also been endorsed by many others, including Kurt Gödel (1964), Bertrand Russell (1912), and W.V.O. Quine (1948, 1951).
 
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Re: Largest number using 5 symbols

28 Jul 2022 05:49

Mathematics does not know an upper limit for a number, so this idea would imply that the universe is infinite.  This is getting too deductive to my taste.  We would need some observational support for an infinite universe.  But what needs to be infinite?  Is the universe infinite if space and time are infinite but matter is finite?
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Re: Largest number using 5 symbols

29 Jul 2022 05:47

Mathematics does not know an upper limit for a number, so this idea would imply that the universe is infinite.  This is getting too deductive to my taste.  We would need some observational support for an infinite universe.  But what needs to be infinite?  Is the universe infinite if space and time are infinite but matter is finite?
I completely agree about infinite universe/multiverse.  Also we can redefine multiverse to universe if we allow for regions where the physical laws and constants are different.  I am trying to find this fascinating article I read a few months ago-- it was about the discovery of a function that describes both finite and infinite numbers-- the first of its kind.  It was stated that Godel would be proud because this was something he had been searching for his entire later life.
If the universe itself (that is just our universe not the whole multiverse of course) is inside the singularity of a black hole inside a higher dimensional parent universe, does that in a sense imply that our universe is infinite but bounded (by the singularity-- which is itself infinite?)  An infinity inside an infinity?  I guess this can be possible, since there are different kinds of infinity?  Quantum gravity will perhaps sort out the singularity infinity, but you can still have a universe inside it that is infinite but bounded by the inner horizon of that black hole.  Infinite but bounded would mean that at however great the distance the universe would curve back in on itself.  So infinite as in endless, but at some point it would repeat and you'd end up back where you started.
 
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Re: Largest number using 5 symbols

04 Dec 2022 11:32

Image

The Church–Kleene ordinal, i think, is it acceptable?
more: https://en.wikipedia.org/wiki/Nonrecurs ... d_variants

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