Hard Light Productions Forums
Off-Topic Discussion => General Discussion => Topic started by: HotSnoJ on August 02, 2002, 04:34:28 pm
-
http://www.timetravelfund.com/
This sites a laugh! Just like this :headz:.
-
A time travel fund? While time travel may well become practical in the future, a whole organization dedicated to it seems a bit silly... :wtf: :p
-
Well, i'm tempted, but i'm sure i'll die for a good enough reason, here's not much point resurecting me in the future... And what if nobody invents time travel? Then you loose your $10. And what if you discover the secret of eternal youth, and never die. Yet again, a waste of $10.
I'm thinking about this too much already.
-
Random time travel thoughts:
Time travel is not possible. If it was someone would have come back and told us about it.
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.
-
...You've gotta be sh***ing me...
-
useing the time machine some old guy gave, me along with some good advice, I will go back in time and give my yonger self the time machine and a few... stock tips ;7
-
Originally posted by GalacticEmperor
Random time travel thoughts:
Time travel is not possible. If it was someone would have come back and told us about it.
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.
yeah but by changing something, you may create a whole new dimension...
-
Originally posted by Zeronet
yeah but by changing something, you may create a whole new dimension...
In which case YOU wouldn't be in that dimension, it would be ANOTHER you! So this whole thing is a waste of money!
*gets confused*
What did I just say?
:wakka:
-
Time travel is not possible. If it was someone would have come back and told us about it.
Time travel into the past might still be possible if there is a second time dimension, allowing for closed curves, but time travel into the future only would still work fine regardless.
In which case YOU wouldn't be in that dimension, it would be ANOTHER you! So this whole thing is a waste of money!
yeah, but there is no one "real" you, since all the yous correspond to you. :D
-
Actually my theory, and a few others i think (scientists and stuff) is this: (in my own words)
Since everything we see we're not actually seeing the way most people commonly think of it... It's been proven that we see reflection of light waves. Everything we see is in light.
Light reflects... and therefore (to cut it short) reflects ... (!?) and if we can travel faster than the speed of LIGHT, we could travel back in time and SEE (not experience) what happened, without sound... cause we'd move back and see the reflection of the light in space, if you know what i mean
i'm no scientist, it's very vague... can't explain, i'm sure you understand (hopefully) :) lol
-
:no: SCAM ALERT!! SCAM ALERT!!
I can't believe this bull****. I read in some scientific magazine that if a time machine was built, u can only go back to when the machine was built and not before. They gave a host of reasons, but who knows who to believe. This is all highly theorhetical and IMO totally fraudulent. It might work as well if we all contribute $10 for FS3 to be made (which BTW won't work).
Catch my drift?
-
Originally posted by Megadude
:no: SCAM ALERT!! SCAM ALERT!!
Catch my drift?
you're not talking about my post, are you?
-
actually, i was replying when u posted so i didn't see it till i posted. I was referring to the whole thing. They claim it's not a scam, but if its too good to be true well...
-
I had an idea to do something like this. it's the same idea, but people would be donating to my "sick" mother...
-
I had an idea to do something like this. it's the same idea, but people would be donating to my "sick" mother...
That's what it sounded like to me as well; time travel is good, but a time travel institution? :p
Light reflects... and therefore (to cut it short) reflects ... (!?) and if we can travel faster than the speed of LIGHT, we could travel back in time and SEE (not experience) what happened, without sound... cause we'd move back and see the reflection of the light in space, if you know what i mean
That makes sense, but since we're not made of tachyons, it is thought to be impossible to reach the light speed in the first place (relative to anything) since that would require an infinite amount of energy. There might be ways of getting around that using gravity though...
-
Originally posted by GalacticEmperor
Random time travel thoughts:
Time travel is not possible. If it was someone would have come back and told us about it.
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.
You can jump foward in time the close to the speed of light you go.
-
i didn't say we could travel the speed of light, i said it would probably be POSSIBLE...
they say you can stop aging by traveling the speed of light too!
-
u don't move forward in time. the closer u get to the speed of light, the slower time passes for u. So while u experience 1 day, stationary people may move forward 1 year.
-
well well, isn't something strange happening:D
i post but someone always beats me to it :looks at stealth:
-
You cant travel at or faster then the speed of light, as proved by Einstein (sp?)
E = MC^2
The only way the speed of light can be reached is through pure energy (E). To do this, you would have to take mass (M) out of the equation. And since we have to be composed of mass to exist, you would be taking us out of the 'speed of light' equation. Therefor, only pure energy can travel at the speed of light (photons). - E = C^2 (energy equals the speed of light squared)
-
yeah well i never said we could travel faster!
i didn't say we could travel the speed of light, i said it would probably be POSSIBLE...
:)
-
even energyhas mass right?
-
Originally posted by Megadude
well well, isn't something strange happening:D
i post but someone always beats me to it :looks at stealth:
lol, what's even funnier is what you say i already said in my previous posts almost exactly :) we must think alike
great minds think alike
;)
EDIT: Forgot to close the 'color' tag :)
-
Originally posted by Megadude
even energyhas mass right?
I'm no physics expert, but i'd say no. Try to get the mass of a flame and let me know how you make out...:D
-
Clicky, sil vous plait (http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html)
It is massless, yet, it isn't. What a paradox. If anyone care enough to read an understand the article, perhaps u can tell us lay men what it's all about.
-
The only way the speed of light can be reached is through pure energy (E). To do this, you would have to take mass (M) out of the equation. And since we have to be composed of mass to exist, you would be taking us out of the 'speed of light' equation. Therefor, only pure energy can travel at the speed of light (photons). - E = C^2 (energy equals the speed of light squared)
uh...the c speed limit is not related to e=mc²; it can be derived from the lorentz speed equation, vT = (v1 + v2)/Ö(1 + v1v2/c²). (this holds for all 0 < v1 < c and 0 < v2 < c)
eh...pure mathematics is better than this... :headz:
If anyone care enough to read an understand the article, perhaps u can tell us lay men what it's all about.
Makes sense to me, but it basically says that the question has not been answered yet and probably cannot easily be by experimentation alone.
i didn't say we could travel the speed of light, i said it would probably be POSSIBLE...
It is actually quite possible to travel very close to the speed of light, just not at that speed. ;)
-
I read the article...didn't cesinarily undertand it...but hey im only 16...
-
well I'm 15 and it seemed fine to me... :p
-
Im also not a genious and I barely passed algebra II in school...of course i hate math but dag yo...
-
Originally posted by CP5670
uh...the c speed limit is not related to e=mc²; it can be derived from the lorentz speed equation, vT = (v1 + v2)/Ö(1 + v1v2/c²). (this holds for all 0 < v1 < c and 0 < v2 < c)
My hero! Now I'm no longer left alone with having to explain this :D
The idea of outpacing light to see our past derives from a common astronomical concept. Light from the edge of the universe takes its time to reach us, on the order of billions of years i.e. we are currently seeing those objects as they were billions of years ago. I'm sure most people know that deal. In the same respect, light emitted from ourselves is also racing away to some (all) corners of the universe - if we were to get there first by whatever means someone wants to dream up, then we'd see that light and our former selves.
Another form of time travel would be to travel at high relatavistic speeds for a while and let the rest of the universe pass by a few million years. However both these forms don't fit into the classical interpretation of time travel, which more or less implies jumping to any point in time on little more than a whim, and possibly some petrol fumes. That, for the most part, still lies in the realm of hypothesis, and can't really be proven or disproven with current knowledge. There are bound to be many more paradigm-shattering discoveries remaining that will change current understanding.
*Mr Obvious takes off his thinking cap...*
-
let's take a bet:
in 20 years, scientists will have rendered all your theories and all your pretty equations false, and will have replaced them with new ones that will be proven false in 40 years, and will widen the range of possibilities, and in 60 years...
-
Or alternative, we can just tell more jokes instead of debating creation and it's working....
= = = = = =
During his wedding rehearsal, the groom approached his pastor with an unusual offer. "I'll give you $100 if you'll change the wedding vows, and leave out the 'love, honor, obey, and forsake all others' part." He pressed a $100 bill in the pastor's hand and walked away with a satisfied smile.
On the day of the wedding, the groom was feeling pretty pleased when the pastor got to the part where the vows are exchanged. The pastor looked him in the eye and asked, "Will you promise to bow before her, obey whatever command she gives, fulfill her every wish, serve her breakfast each morning, and swear before God that you'll not look at another woman as long as you both shall life?"
The groom gulped and looked astonished, but he finally said "Yes" in a tiny voice. He then leaned in toward the pastor and whispered, "I thought we had a deal!"
The pastor pressed the $100 bill back into his hand and whispered in return, "She made me a much better offer."
:D
-
I'm not exactly stupid in areas of math and physics (I'm taking advanced precal this year); i was just being sarcastic. I got to as far as photon is massless yet it has mass. Then I lost interest.
-
Ah, Time Travel. I remember it well.
Why, it was only last yea...no wait, maybe it wasn't. Maybe it was next Tuesday - no, Thursday week. Or the year 2042. May 11th. Yesterday! Tomorrow! Today! AIIIEEEEEEEEEEEEEEE!!! :eek2:
Anyhoo, yeah, I thought it was always that you couldn't enact the grandfather paradox or anything like that because you just create a new parallel universe in doing so, therefore you can't change your reality but only create others.
I was also under the impression that travel into the future was easier because there were a potentially infinite number of universes to travel into. Which, of course would make travel into the future completely pointless except as a curio. It couldn't actually 'predict' anything meaningful. :)
-
Actually it is plausible to go faster than time using the ST warp idea (aka curve spacetime around you to push you foreward. It's like when your in a big airport, and there's one of those moving walkways. There's a limit to how fast you can walk normally, but if your on the walkway you can move faster than you can normally.
-
You will not be retrieved if you die by suicide. Sorry, but we don't want your family blaming us for you killing yourself because you think you will get to the future sooner
:lol:
-
If time travel in the "jumping to any point in time on little more than a whim, and possibly some petrol fumes" sense were ever to become a possibility, we still could never do anything that would change the course of history, past or future.
Travelling to the past would not introduce anything new into the course of history. It is the past; you were already there, and the actions you performed then are part of the events leading up to your going back.
A traveller to the future is faced with the same situation. There are, as Kellan said, an infinite number of possibilites (in fact, an infinitely infinite number), but only one of those possibilites is ever actualised in the past, present, or future. So the traveller to the future could certainly go and get reliable stock market information if he wanted, and he could bring it back and use it to get rich. If he does this successfully, he will also have found himself to be a rich man when he arrives in the future in the first place. Moreover, if upon his arrival in the future he finds his future self not to have gotten rich from the stock trade, he may as well give up his plan, since the evidence is standing right there in front of him that it will not work.
-
Originally posted by Sesquipedalian
If time travel in the "jumping to any point in time on little more than a whim, and possibly some petrol fumes" sense were ever to become a possibility, we still could never do anything that would change the course of history, past or future.
Travelling to the past would not introduce anything new into the course of history. It is the past; you were already there, and the actions you performed then are part of the events leading up to your going back.
A traveller to the future is faced with the same situation. There are, as Kellan said, an infinite number of possibilites (in fact, an infinitely infinite number), but only one of those possibilites is ever actualised in the past, present, or future. So the traveller to the future could certainly go and get reliable stock market information if he wanted, and he could bring it back and use it to get rich. If he does this successfully, he will also have found himself to be a rich man when he arrives in the future in the first place. Moreover, if upon his arrival in the future he finds his future self not to have gotten rich from the stock trade, he may as well give up his plan, since the evidence is standing right there in front of him that it will not work.
One thing that gets me about this line of reasoning is that it accepts time as being forever linear. Wouldn't time travel in the sense mentioned require the interpretation of time as just another dimension as manipulable as the physical 3 dimensions we hold to? By adding the dimension of time to that which can be controlled, it loses its sense of linearity which is so firmly entrenched in our life because we can know no other way in our current way.
-
I read somewhere of a crackpot theory in which time travel could be possible into to the past. Basically, the theory hypothesises that space and time is circular. That the big bang and the big crunch are one in the same. So if you would go futher enough into the future to the end of the universe. It would end and start all over again. Hence you'd be back in time. So you just keep going forward until you reached you're favored time. Now I don't remember how the theory stated that it could do this in a reasonable time span, but it had something to do with reaching almost the the speed of light then doing a quantum leap into tachyon speed. Something like that. Like I said, it's a crackpot theory. :D
-
One thing that gets me about this line of reasoning is that it accepts time as being forever linear. Wouldn't time travel in the sense mentioned require the interpretation of time as just another dimension as manipulable as the physical 3 dimensions we hold to? By adding the dimension of time to that which can be controlled, it loses its sense of linearity which is so firmly entrenched in our life because we can know no other way in our current way.
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. ;)
If time travel in the "jumping to any point in time on little more than a whim, and possibly some petrol fumes" sense were ever to become a possibility, we still could never do anything that would change the course of history, past or future.
Travelling to the past would not introduce anything new into the course of history. It is the past; you were already there, and the actions you performed then are part of the events leading up to your going back.
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.
I read somewhere of a crackpot theory in which time travel could be possible into to the past. Basically, the theory hypothesises that space and time is circular. That the big bang and the big crunch are one in the same. So if you would go futher enough into the future to the end of the universe. It would end and start all over again. Hence you'd be back in time.
Actually, that is one of the two dominant science theories out there today. :D It makes sense to me, but the alternative of an infinite open curve (instead of a closed curve) is equally plausible judging from what we know so far.
My hero! Now I'm no longer left alone with having to explain this
:D
lol actually I might just be talking nonsense since I am a math guy and don't know much physics. :p :D
-
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. :p :D
No comment. ;7
-
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. :D (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 :D)
-
Originally posted by Sesquipedalian
If we want to shift possibilities, we need a "possibility travel" machine, not a time travel machine.
No comment. ;7
Aaah, the good ol' Heart of Gold could do that! :D
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. :D :p
-
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. :D (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 :D)
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 ˴ 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.
-
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. :D
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. :p 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 ˴ 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¥? :wtf: 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. :D
-
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 À132723762. 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.
-
Hey cool, you're getting interested in math! :D 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 :D), so you might know what is going on here.
-
The math geeks are multiplying! Head for the hills! Women and children second, me first!
-
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.
-
*deleted*
-
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? :confused:
-
Infinite yous, I think. (each reality has its own you)
-
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.
-
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 :D), 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.
-
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.
-
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?
-
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.
-
I was gonna post something here about how you cant change the past, but i got confused.
Sorry i cant be much help
-
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"?
:D
-
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.
-
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.
There are actually two (related) continuum hypotheses out there; one is simply the contiuum hypothesis, that À1 = C, and the other one is called the generalized continuum hypothesis, which says that xÀn = Àn+1 for all finite x. I was referring to the generalized one here, since the other one immediately follows from that as a special case.
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.
Interesting; I personally think it actually should not be true. It has been proven that the transcendental numbers are what make up the continuum, since the algebraic numbers make up a À0 set while the transcendentals are a À1 set, which means that there are infinitely more transcendentals than algebraics. Unlike algebraics, transcendentals have not really been classified into more subgroups (i.e. integers, rationals, etc.), so it is quite possible that the À1 cardinality of the continuum comes from several of these subgroups and not just one.
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.
ack...I actually meant À1 = C there. It was 2 in the morning and I had only gotten five hours of sleep the previous night, so I probably made some errors...yeah, uh, that's my excuse! :D
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.
I also think that S should be only a subset of N, but apparently Cantor (the same guy who proposed the continuum hypothesis) proved that all sets of the same cardinality are equinumerable. This would mean that there are just as many squares, cubes or primes, etc. as natural numbers. This also implies that the set of points on any continuum is equal to that of any other continuum, so something like, say, a line segment of length 1 will have the same number of points as an infinite-dimensional cube with infinite edges. While this could well be true, I personally find the proof of it a bit dodgy, and the implications of it would be quite far-reaching; for example, all of analysis, one of the largest and most developed branches of pure mathematics, would be rendered completely meaningless, since all infinite sums and integrals would be equal.
-
if some one could find that master equation to einsteins unifed core theory it would explain lots of things including
time travel einsteins unifed theory is like a manual for the universe
think about it
-
if some one could find that master equation to einsteins unifed core theory it would explain lots of things including
time travel einsteins unifed theory is like a manual for the universe
think about it
yeah, that's been one of the major pursuits in physics for the last 40 or so years: to find a unified equation that combines quantum theory and general relativity. (the Dirac equation comes close, but that is only special relativity)
-
Meh, they'll probably find at some point that Einstein was wrong and an0n was by far the more correct. :p
-
Originally posted by Kellan
Meh, they'll probably find at some point that Einstein was wrong and an0n was by far the more correct. :p
I'm not even going to ask...
-
Originally posted by CP5670
Interesting; I personally think it actually should not be true. It has been proven that the transcendental numbers are what make up the continuum, since the algebraic numbers make up a À0 set while the transcendentals are a À1 set, which means that there are infinitely more transcendentals than algebraics. Unlike algebraics, transcendentals have not really been classified into more subgroups (i.e. integers, rationals, etc.), so it is quite possible that the À1 cardinality of the continuum comes from several of these subgroups and not just one.
But the transcendentals are still a subset of the real numbers, which are what C is supposed to be the totality of. If it were proven that the transcendentals were of a higher transfinite cardinality than the algebraics, that would also be a proof that C¹À1, for it would bump C up to at least À2.
I also think that S should be only a subset of N, but apparently Cantor (the same guy who proposed the continuum hypothesis) proved that all sets of the same cardinality are equinumerable. This would mean that there are just as many squares, cubes or primes, etc. as natural numbers.
This is true. There are as many rationals as irrationals, for another example. The snag in the problem you proposed before is that we were not comparing two comparable sets: the one was an empty set, while the other was not. If we were simply comparing squares to naturals, they are of course equinumerable, but we were comparing naturals to squares of naturals that are not themselves naturals, which is comparing an infinite set to one that is obviously not infinite, because it is empty. Finite (or more generally, non-infinite) sets do not register on the transfinite scale at all, and thus S is an invalid set to use in the equation.
The set of points on any continuum is equal to that of any other continuum, so something like, say, a line segment of length 1 will have the same number of points as an infinite-dimensional cube with infinite edges.
It is true that there are as many points in an infinitely large cube as in a single line segment, and that makes perfect sense to me. I don't know if it would have quite the horrible implications that you fear it would, however. Obviously all operations that involve ¥ end in ¥, and all that involve C end in C, and this has been known for a long time. The fact that this is true has not impeded the development of analysis.
Take a square, for example. Its area is calculated by x*y. A cube is x*y*z. The operation involved is multiplication, and as we mentioned previously, the only way to change any transfinite set is to raise it by a transfinite set not less than itself. So an infinite square is just C*C, which equals C. An infinite cube is C*C*C, which equals C. None of these produces any change in the number of points being discussed. If one one considered an object of infinite size that existed in infinite (C, not merely ¥) dimensions, that would change things I suppose, since it would have C^C many points in it, but so long as we are dealing with a finite number of dimensions, no difference is made. Thus we have nothing to worry about insofar as the self-destruction of mathematics is concerned, because no matter what, ¥, C, etc. are still ¥, C, etc.
-
But the transcendentals are still a subset of the real numbers, which are what C is supposed to be the totality of. If it were proven that the transcendentals were of a higher transfinite cardinality than the algebraics, that would also be a proof that C¹À1, for it would bump C up to at least À2.
Well, that has actually been proven, but the cardinality of the reals would still be À1 because in this case, À0+À1 = À1.
Finite (or more generally, non-infinite) sets do not register on the transfinite scale at all, and thus S is an invalid set to use in the equation.
Thing is, S is actually infinite, just as N is infinite, but neither one is continuous. Now what this theory says is that they are equinumerable, but that leads to the contradiction I posted before.
Take a square, for example. Its area is calculated by x*y. A cube is x*y*z. The operation involved is multiplication, and as we mentioned previously, the only way to change any transfinite set is to raise it by a transfinite set not less than itself. So an infinite square is just C*C, which equals C. An infinite cube is C*C*C, which equals C. None of these produces any change in the number of points being discussed. If one one considered an object of infinite size that existed in infinite (C, not merely ¥) dimensions, that would change things I suppose, since it would have C^C many points in it, but so long as we are dealing with a finite number of dimensions, no difference is made.
That sounds fine, but suppose we do this: ¥ - ¥, which is obviously an indeterminate quantity in that form, but we are assuming it is equal to zero if the two terms are truly equal. Basically, the problem here is that ¥ = ¥ is being assumed, and this does not necessarily have to be true; for example, just because the functions 1/x² and e1/x both have a limit of infinity as x->0 does not mean that they are equal. One thing that might solve this problem is to use a different, "weaker" definition of equality, something like the order O(f(x)) used in analysis.
Although a continously infinite-dimensional object (i.e. existing in 2.31 dimensions, p dimensions, etc.) and having infinite sides, or the C^C you mentioned, would also apparently have an equal number points as any line segment with unit length from what I have read.