[Sesquipedalian]

Originally posted by CP5670
Exactly. In fact, if the looped-time theory is to hold, a second time dimension would actually be required, and it wouldn't really be a curve at all but would be sort of like a point moving on a surface with an infinite number of directions to move to at every position.

Which may be a good reason to think the looped time theory doesn't hold.

That is partially correct, but the current hypothesis is that all of these realities are "actualized" into the same reality and that no one reality is any more "real" than another. Therefore, going back in time will just put you into a different form of the reality that already exists within the one we know. So in other words, a probabilistic set of particle movements exists wherein this guy got rich simultaneously along with a set of particle interactions that caused the guy not to get rich, and these probabilities are both part a larger reality.

So I'm in Fiji right now with you rubbing my feet?  Funny, I do not perceive that happening.  So I suppose in this particular location of possibility, there is only one reality being actualised.  If we want to shift possibilities, we need a "possibility travel" machine, not a time travel machine.

lol actually I might just be talking nonsense since I am a math guy and don't know much physics.

No comment.

[CP5670]

Which may be a good reason to think the looped time theory doesn't hold.

There are actually several other indications that point to the possible existence of a second time dimension as well (quantum tunneling, etc.), so it looks like people may end of accepting that regardless of this theory.

So I'm in Fiji right now with you rubbing my feet?  Funny, I do not perceive that happening.  So I suppose in this particular location of possibility, there is only one reality being actualised.  If we want to shift possibilities, we need a "possibility travel" machine, not a time travel machine.

Hey, I'm just repeating what I have been reading in science articles. (although it does makes sense) Basically there are an infinite number of these existences and possibilities, and any one "actualization" of human existence follows a curvilinear path through a multi-dimensional surface, but that does not make it any more "real" than another. This would allow the universe to not all move at the same speed through the time dimensions (as long as there are no "break" or "cuts," topologically speaking) and would also allow time travel due to the multiple directions, which would explain some of the quark movements predicted. (modern physics laws predict some small probability of a particle going back in time )

[Dark_4ce]

Originally posted by Sesquipedalian

 If we want to shift possibilities, we need a "possibility travel" machine, not a time travel machine.
No comment.

Aaah, the good ol' Heart of Gold could do that!

Yeah, the whole simultaneous reality thing is really fun to think about. Aaah, on one reality my toaster will somehow transform itself into Denise Richards in desperate need of intimate attention. And in another one I become the emperor of the world, develope über-tachyon technology for extra-galactic travel and conquer the known universe in the name of the Double-Whopper with Cheese Emperium.

[Sesquipedalian]

Originally posted by CP5670
There are actually several other indications that point to the possible existence of a second time dimension as well (quantum tunneling, etc.), so it looks like people may end of accepting that regardless of this theory.

There are a lot of interesting ideas out there in the scientific community.  But until someone can take these ideas and work them out into an experimentally testable theory, I'll not give much credence to them.

Hey, I'm just repeating what I have been reading in science articles. (although it does makes sense) Basically there are an infinite number of these existences and possibilities, and any one "actualization" of human existence follows a curvilinear path through a multi-dimensional surface, but that does not make it any more "real" than another. This would allow the universe to not all move at the same speed through the time dimensions (as long as there are no "break" or "cuts," topologically speaking) and would also allow time travel due to the multiple directions, which would explain some of the quark movements predicted. (modern physics laws predict some small probability of a particle going back in time )

That depends on how you define real, which is a very slippery word indeed.  We exist in this particular actualised possibility.  The course of history at this particular point of possibility is what it is, and travelling forward or backward along its timeline would not change that, as argued above.  Changing possibilities is something totally different.  

It also seems to me that the goings-on of other possibilities are of absolutely no consequence or concern to us, since they have absolutely no effect upon this one.  It may be that an À¥ number of possibilites have also be actualised, it may not.   But whether they have been actualised or not can make absolutely no difference to this actualised possibility.

[CP5670]

There are a lot of interesting ideas out there in the scientific community.  But until someone can take these ideas and work them out into an experimentally testable theory, I'll not give much credence to them.

Well, there are only really two major theories out there concerning this at the moment: either our time-path is a curve of constant (although infinite) length, or a dynamic surface-like configuration with an infinite number of distinct paths and directions and thus a variable length. Neither of these ideas can be directly confirmed by experiment; they follow from the math.

That depends on how you define real, which is a very slippery word indeed.  We exist in this particular actualised possibility.  The course of history at this particular point of possibility is what it is, and travelling forward or backward along its timeline would not change that, as argued above.  Changing possibilities is something totally different.

I suppose "reality" can be taken to mean all that which exists in the universe that we exist in; it is a pretty inexact definition, but I can't think of anything better at the moment. The thing is, the whole concept of I/we/us/etc. is poorly defined and I am not sure whether or not, if alternate reality systems exist, we are any different from the we's in the other realities (which in turn leads to a necessity of defining "existence") despite our sensory experience, since these experiences could be said to form a wavefunction of sorts in themselves, one which collapses when a time causality violation is made and possibly changes around the past. Also, strictly speaking, even history itself and past events are not completely 100% deterministic if the quantum theory is fully correct, and while causality still holds to some extent, it isn't really the original Newtonian type that we normally think of.

It also seems to me that the goings-on of other possibilities are of absolutely no consequence or concern to us, since they have absolutely no effect upon this one.  It may be that an À¥ number of possibilites have also be actualised, it may not.   But whether they have been actualised or not can make absolutely no difference to this actualised possibility.

While it is true that we do not have to worry about these things in our daily lives, they do become a significant factor at the elementary particle level, where particles can go through all kinds of time loops (the spontaneous appearance/disappearance that is sometimes seen). What is À_¥? I think there is only À₀ and À₁, which correspond to the countably and uncountably transfinite number sets.

I'm not very well acquianted with this stuff, so I will let one of our physics people here explain this more thoroughly.

[Sesquipedalian]

After a conversation of ours in another thread awhile ago, CP5670, I became interested in the transfinite number sets.  It turns out that they work differently than you think.

The different orders of transfinites represent different "intensities," if you will, of infinitude, and can range in the series À₀, À₁, À₂, ... À_¥.

À₀ is the lowest, or rather, least intense order of infinity, and is the one generally refered to using the ¥ symbol.  This represents the infinite number of integers.  It is worth noting that the set of all rational numbers can be put into a one-to-one correspondence with the set of integers, and so there are an ¥ number of rationals.  The same holds true of the irrationals.

When we put the rationals and irrationals together we obtain the set of real numbers.  The thing is, it can be shown that the set of real numbers cannot be put into a one-to-one correspondence with the series of integers!  No matter how one arranges things, no matter what system one uses, an endless number of real numbers will be left out.  The conclusion is that there are more real numbers than there are integers, producing an infinitude that is more intense than that of the integers.

Since the symbol ¥ is all tied up with the integers and rationals generally, another is used for the reals, C, standing for continuum (because all the reals can, of course, be put into a one-to-one correspondence with all of the points on a line, which is a continuum).  This new level of endlessness C is different and more intensely endless than the set of "ordinary infinity," ¥.  It is believed that C is equivalent to À₁, but it has also been shown that this is impossible to prove.

Now, one of the interesting properties of the transfinites is that the only way to produce any change in a transfinite is to raise it by the power of of a transfinite equal or greater value.  Raising a transfinite by a power equal to itself causes the transfinite to be raised to the next transfinite level.  Thus:
À₀^À₀=À₁, À₁^À₁=À₂, ...

If C does equal À₁, that makes ¥^¥=C.

Finally, it has been shown that the number of curves that can be drawn on a plane is even more intensely endless than the number of points in a line (i.e. the number of x-y axis functions is of a higher transfinite value than the number of reals).  In other words, there is no way to match up all the curves in a one-to-one correspondence with the points on a line; an endless series of curves will always be left out.  The endlessness of the functions may be equal to À₂, but that cannot be proven either.

No one has even taken a stab at what À₃ might correspond to, let alone À_132723762.  Neither does anyone know where x-y-z functions could fit in.

Btw, any set of finite numbers is not part of a set of transfinites numbers.  In order to be a transfinite, it has to be uncountable.

[CP5670]

Hey cool, you're getting interested in math! You're right about the existence of a transfinite set with an infinite cardinality actually; it's just that I had not ever seen anything aside from the usual À₀ and À₁ in analysis textbooks, but I guess those only cover the set theory necessary for analysis proofs and don't go too in depth.

Since the symbol ¥ is all tied up with the integers and rationals generally, another is used for the reals, C, standing for continuum (because all the reals can, of course, be put into a one-to-one correspondence with all of the points on a line, which is a continuum).  This new level of endlessness C is different and more intensely endless than the set of "ordinary infinity," ¥.  It is believed that C is equivalent to À₁, but it has also been shown that this is impossible to prove.

Ah, that's the famous continuum hypothesis; as you said, this is a decidedly indeterminate proposition, and at least one more axiom is needed to add to the conventional zermelo-fraenkel axioms to prove or disprove this. Cantor thought that it should be true, but the general consensus today among the mathematical community seems to be that the hypothesis is false and that there exist sets with cardinalities greater than that of the usual continuum that cannot be put to a one-to-one correspondence with the real numbers. Do you think this should be true or not?

Now, one of the interesting properties of the transfinites is that the only way to produce any change in a transfinite is to raise it by the power of of a transfinite equal or greater value.  Raising a transfinite by a power equal to itself causes the transfinite to be raised to the next transfinite level.  Thus:
À₀^À₀=À₁, À₁^À₁=À₂, ...

If C does equal À₁, that makes ¥^¥=C.

I didn't know any of that before; thanks for bringing it to my attention. So the continuum hypothesis could be restated as C^C=C.


On a side note, since you seem to know some stuff about transfinite set theory, do you know if the equinumerability of all sets with cardinality À₀ is another of those undecidable Gödel statements? For example, a special case of this is that the number of natural numbers is equal to the number of perfect squares. We all know of the one-to-one correspondence proof, but the following statement also appears to hold:

Let N denote the set of natural numbers, S denote the set of perfect squares of natural numbers and E(s) be a general function that returns the number of elements in a set.

E( x | xÎN /\ xÏS ) ¹ E( x | xÎS /\ xÏN )

In other words, the set of all numbers that are in N but not in S should be equal to the set of all numbers that are in S but not in N, and this property obviously holds for any two equinumberable finite sets. Of course, there are pairs of sets that have different numbers of elements and still satisfy that property, but it can be shown that all equinumerable sets must satisfy it, and so this is a necessary but not a sufficient condition for the sets to have any equal number of elements. However, we also know that there exist natural numbers that are not squares, and also that there are no squares that are not naturals as well. Therefore, N and S would not be equinumerable, because the E( x | xÎN /\ xÏS ) set will have more elements than the E( x | xÎS /\ xÏN ) (which would be equal to Æ), but this contradicts the original assumption.

Additionally, there is a result from analysis that the average asymptotic density of the squares over the real line is less that of the natural numbers and also continuously decreases while going to infinity.

I'm not all that familiar with this set theory stuff (I am more of a pure analysis guy ), so you might know what is going on here.

[Stryke 9]

The math geeks are multiplying! Head for the hills! Women and children second, me first!

[Alikchi]

Originally posted by GalacticEmperor

If you had a time machine, you could theoretically go back and change the course of history. But you wouldn't. Because you didn't.

How do you know they didn't? Maybe we would have lost World War I if Time Traveler Man hadn't gone back in time and made the Lusitania get torpedoed. Hmm? HMMM?



Oh, and Stryke..that doesn't work out..how can you be first AND second?

/me is in an evil mood tonight.

[Alikchi]

*deleted*

[Kellan]

In amongst all this maths, I would like to know one thing: does current theory suppose that all the infinite possible realities combine into the one existing one, averaging out good/bad events and so on - or are there an infinite number of realities progressing as we speak.

In other words, is there one 'real me' that all possibility feeds into, or are there infinite me's?

[CP5670]

Infinite yous, I think. (each reality has its own you)

[Kellan]

Okay; that's what I thought made more sense.

Presumably there are then infinite pasts, radiating out from the Big Bang or whatever. I don't see how a rule that applies to the future cannot apply to what we perceive as the past, particularly if time is circular.

[Sesquipedalian]

Originally posted by CP5670
Ah, that's the famous continuum hypothesis; as you said, this is a decidedly indeterminate proposition, and at least one more axiom is needed to add to the conventional zermelo-fraenkel axioms to prove or disprove this. Cantor thought that it should be true, but the general consensus today among the mathematical community seems to be that the hypothesis is false and that there exist sets with cardinalities greater than that of the usual continuum that cannot be put to a one-to-one correspondence with the real numbers. Do you think this should be true or not?

If I'm understanding you correctly, there is something wrong here.  The continuum C is the set of real numbers, and the hypothesis is that C is À₁.  The question is whether there is some endless set between ¥ and C to which À₁ would correspond.  If there is such a set, then it would be À₁, and C might be À₂.  

Transfinite sets with cardinalities greater than whichever one C really is would of course not be able to be put into a one-to-one correspondence with the real numbers, because there are not enough real numbers to fill a higher-level transfinite set.

If you are asking me whether I think C is À₁, I'd say it makes sense to me running on intuition.  Removing any endless series of numbers from C, by whatever pattern, should produce two sets correspondent to ¥.  How anything else could be true defies my imagination, but I cannot prove it, and neither, it seems, can any better minds.

I didn't know any of that before; thanks for bringing it to my attention. So the continuum hypothesis could be restated as C^C=C.

Um, is that a typo?  C^C should give the set of functions on a two-dimensional plain, not just C again.  I presume that that set of functions raised by itself gives the set of three dimensional functions, but I don't know.

On a side note, since you seem to know some stuff about transfinite set theory, do you know if the equinumerability of all sets with cardinality À₀ is another of those undecidable Gödel statements? For example, a special case of this is that the number of natural numbers is equal to the number of perfect squares. We all know of the one-to-one correspondence proof, but the following statement also appears to hold:

Let N denote the set of natural numbers, S denote the set of perfect squares of natural numbers and E(s) be a general function that returns the number of elements in a set.

E( x | xÎN /\ xÏS ) ¹ E( x | xÎS /\ xÏN )

In other words, the set of all numbers that are in N but not in S should be equal to the set of all numbers that are in S but not in N, and this property obviously holds for any two equinumberable finite sets. Of course, there are pairs of sets that have different numbers of elements and still satisfy that property, but it can be shown that all equinumerable sets must satisfy it, and so this is a necessary but not a sufficient condition for the sets to have any equal number of elements. However, we also know that there exist natural numbers that are not squares, and also that there are no squares that are not naturals as well. Therefore, N and S would not be equinumerable, because the E( x | xÎN /\ xÏS ) set will have more elements than the E( x | xÎS /\ xÏN ) (which would be equal to Æ), but this contradicts the original assumption.

Well, the big problem in this question is that N and S are not mutually exclusive at all; S is a subset of N.  Thus they are not equinumerable, and never were claimed to be.  S and -S will be (where -S is the set of naturals that are not squares of naturals), but N contains them both.

Additionally, there is a result from analysis that the average asymptotic density of the squares over the real line is less that of the natural numbers and also continuously decreases while going to infinity.

I'm not all that familiar with this set theory stuff (I am more of a pure analysis guy ), so you might know what is going on here.

I have no idea about that.

I must confess I'm not a mathematician at all, and haven't taken any since high school.  I'm a philospher and theologian.  Everything in my first post came from my doing some reading into the subject, and in this post just by the application of logic, rather than actual math.

[Sesquipedalian]

Originally posted by Kellan
Okay; that's what I thought made more sense.

Presumably there are then infinite pasts, radiating out from the Big Bang or whatever. I don't see how a rule that applies to the future cannot apply to what we perceive as the past, particularly if time is circular.

The only thing is, what sort of "reality" do these endless other possibilites have?  This particular possibility (in which Caeser crossed the Rubicon in 49 B.C., my dog walked into the room just as I was typing this post, and tomorrow I do whatever it is that I actually end up doing) has been actualised and thus exists as more than only possibility.  Whether any of the other infinitely infinitely infinite (that's not a typo) number of possibilities has been actualised is another question entirely.

[Unknown Target]

Think of it this way: If time travel were actually invented, where are all the time travelers?

I'm getting a lot of this info from Popular Science, and they said that many scientists believe that you cannot travel farther back in time from when you first made the machine. So, how could they come back to get you?

[beatspete]

I was gonna post something here about why you cant change the past, but i got confused.
Then i tried to think about parallel universes and i got confused.  Maybe its for the best.

And if some person came up to you on the street and said, "hi, i'm a time traveller from 2348"  would you beleive him?
Thats why you dont see many time travelers.

Could someone delete the post after this, it accidentally double posted.

[beatspete]

I was gonna post something here about how you cant change the past, but i got confused.

Sorry i cant be much help

[Stealth]

Originally posted by beatspete
I was gonna post something here about why you cant change the past, but i got confused.
Then i tried to think about parallel universes and i got confused.  Maybe its for the best.

And if some person came up to you on the street and said, "hi, i'm a time traveller from 2348"  would you beleive him?
Thats why you dont see many time travelers.

has anyone read a book called "Sound of Thunder" (it MAY be called "Roar of Thunder"... one of the two!) ?  about these travelers that go back in time and change something or something like that, and it changes everything.

wasn't really a book, might be though... there was a part of it in one of my 9th grade textbooks in English... i remember clearly!

Oh, and about those "parallel universes"... anyone ever seen a Jet Li movie called "The One"?

[Galemp]

Another random time travel thought:

Perhaps all the time travellers' time machines only moved in time, but not space. So Earth and the universe move in their diurnal courses while a time traveller pops out in the exact same place as he left, 100 years earlier, and spins off into the void of space.