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British physicist Stephen Hawking may claim that extra dimensions provide the key to understanding the "grand design" of the universe, but it's Chinese-American mathematician Shing-Tung Yau who actually figured out how those extra dimensions work.
In his new book, "The Shape of Inner Space," Yau and his co-author, Steve Nadis, touch upon the work that led to the discovery of theoretical "Calabi-Yau spaces" — and the cosmic implications of multidimensional geometry.
The typical representation of a Calabi-Yau space looks like twisted web of a crumpled-up piece of paper. There's something elegant about its look — in fact, Calabi-Yau paperweights were voted the most popular gewgaw for holiday giving in last year's Cosmic Log Geek Gift Guide contest. But these shapes aren't just abstract art: String theorists believe that every single point in our universe is actually a compactified Calabi-Yau space in six dimensions.
Why would they think that? It's because the best theory they've been able to come up with for the universe's grand design requires 10 dimensions to make all the mathematics come out right. Because we can only perceive three dimensions of space and one dimension of time, they suggest that the other six dimensions curled up into near-nothingness when our universe took shape.
Yau was the one who worked out the mathematics for the curled-up spaces. At first, he was trying to disprove a conjecture about complex geometry that was proposed by another mathematician named Eugenio Calabi. But then Yau came around to the view that Calabi was actually right, and in 1976 he published the proof that laid the groundwork for the concept of Calabi-Yau spaces. String theorists eventually seized upon the concept in their explanations for the universe's 10-dimensional structure. Later, the theorists threw in an extra dimension to make it 11, because that helped make sense out of five different subtheories. It's that 11-dimensional view of the universe, known as M-theory, that Hawking is touting as the groundwork for the grand design.
"The Shape of Inner Space" delves deeply into the math behind M-theory. It also traces Yau's life story, which started with his birth in China in 1949 and and Hong Kong and eventually brought him to Harvard. There are plenty of career highlights along the way: In 1982 Yau won the math world's most prestigious prize, the Fields Medal, for proving the Calabi conjecture. In 2006 he played a role in the tale of Russian mathematician Grigory Perelman's refusal to accept the Fields Medal for proving the famous Poincare conjecture. And Yau is also known for his high-profile criticism of the Chinese educational system and scientific establishment.
You can read all about that and more (including Yau's early yen for kung-fu novels) in an extended interview on Discover magazine's website. During my telephone chat with Yau this week, we focused more on the cosmic perspective. Here's an edited transcript of the Q&A:
Cosmic Log: Recently there's been a lot of talk about multiple dimensions. Stephen Hawking also recently wrote a book, I hear ... and he talked about how M-theory was really the secret to the "grand design." But in your book, you point out that the grand design really has a lot to do with geometry. So a lot of people wonder what's going on with multiple dimensions that we can't directly perceive. What difference does it make for our understanding of the universe?
Shing-Tung Yau: We physicists always try to bridge two important discoveries in physics together. One is general relativity, and the other is quantum mechanics. There were many efforts to discover such a unification field, [but none was successful] until string theory came along. So far that's the only consistent theory. In order to make quantum mechanics consistent with general relativity, there is no other choice but to make space-time be 10-dimensional. On the other hand, we do have to try to understand the space-time that we perceive. So we make six dimensions very, very tiny.
We still see the four-dimensional space-time that we experience in general physics, special relativity and all that. This six-dimensional space is what we call "internal space." There are a lot of models for this, but the most effective and useful model is Calabi-Yau space, where We can do all the calculations. And in fact, if we can choose the right Calabi-Yau space, we should be able to calculate the properties of the particles in the universe. But the trouble is, right now, we have many candidates for these calculations. One day, if we have the fundamental physics that can lead us to know how to calculate such geometry, and if we pick the right geometry, we will be able to calculate the masses of all the particles in the universe.
In any case, a great number of important discoveries have been made, in terms of philosophical principles as well as mathematics. So as a mathematician I'm very excited about this.
Q: Some people say that our universe could be just one among 10 to the 500th power possibilities. I guess that has led some people to say that the study of the structure of our universe can do nothing more than catalog one of those possibilities, and that there's no particular reason why the laws of physics work one way rather than another way. The only answer would be, "Well, this is just the way it is." Just as one cave is more habitable than another because of the way it's laid out, it just so happens that the geometry of our universe makes it more suitable for life, and there's no use trying to figure out why that is.
A: That's one point of view. I do not necessarily take that point of view. The fact that we can already see that there is a finite number of possibilities is very exciting. There could have been an infinite number of possibilities for space-time. But right now we know of only a finite number, and that should be considered a good starting point.
Other people have called this the "cosmic landscape." Maybe that's what they think, but that's not what I believe. There must be some more fundamental principle in order to choose the right geometry to tell what the universe is supposed to be.
Q: What do you think are the most promising experimental avenues for determining the geometry of the universe?
A: If supersymmetry can be found, that would be very exciting for string theory. The whole theory is based on this supersymmetry. It may be possible to find supersymmetric partners in the Large Hadron Collider. If supersymmetry exists, most people would start to think that string theory has a strong foundation.
First, the experimental data have to come out. Then it will be time to look for more concrete statements about the geometry, and hopefully based on that, we can try to make more concrete statements about the geometry of the universe. Right now we don't have the experimental data, so we cannot say much. On the other hand, we can do a lot of theoretical calculations, using computers, and the calculations come out to be very beautiful. They have led to many important discoveries in math itself.
Some of the discoveries in mathematics are extraordinary. The calculations have solved problems that we didn't know how to solve for 100 years.
Q: Do you have particular solutions in mind?
A: Mathematicians have been looking at polynomial equations. You want to know how many solutions are there. We didn't know how to do this for a long, long time. In some important cases, string theory has inspired us to find the right formula. The formula is extremely complicated. If we didn't know much about string theory, I believe that even now, we still would not be able to find such a formula. But based on the inspiration and the intuition from string theory, we found the formula, and we also proved it. We proved it independently of whether string theory itself is right or wrong.
Q: So string theory already has yielded important scientific advances, even if it hasn't unraveled the deepest mysteries yet.
A: That's right. Many, many important problems in mathematics and geometry were solved, and that's why many mathematicians are actually looking to string theory, because it provides intuitions that we did not have before.
Q: The mathematics of string theory is beautiful, but there's also a beauty to these depictions of Calabi-Yau spaces. How do you feel about those representations? Are they simplications of what you've done, or do you see them as tributes to what you've done?
A: Those pictures are grossly simplified versions of what we know. We cannot really draw a Calabi-Yau space, because it is a six-dimensional space. We use computers to make some slice of these Calabi-Yau spaces. What we see is far away from being the original picture of what we think in our heads, but it's useful, I think, even to look at the slice. In our original philosophical description for the space, we can do a huge amount of things — in algebra and number theory, many problems can go back to this space.
I constructed this space eight years before string theory became an important subject. I just thought that it was exotic and beautiful. I couldn't imagine that any other space could be more beautiful. We went on to many discoveries in math. And then, to my great surprise, the string theorists came along, and all these great people in string theory came to ask me how this space was constructed. I was really excited by the possibility that such spaces could be used to understand nature.
Q: In the past, you've talked a lot about China's status in science, math and technology, so I can't let you go without asking at least one question about global competitiveness and the worries that people have about American innovation.
A: There is absolutely no question that America will be the leader for a very long time. I think it would take a long time for any Chinese universities to be as good as our top universities. It may take 50 years, it may take a century. So America's science and technology is really far ahead of China's. I don't think Americans should worry about it. But on the other hand, of course, there are a lot of good Chinese scientists coming up, and they are very competitive. I wish that they would be as original as our American colleagues.
So it's very interesting to have a good group of Chinese scientists competing with us. They will make us better. I always feel it is important to have challenges — to have people competing with us. Otherwise we'll think that we are just great and will not evolve toward a better scientific world. So I don't think there'll be any negative effect from this competition. It will be positive — for both sides.
Update for 7 p.m. ET Oct. 3: Toward the latter part of the book, Yau and Nadis take the concept of a 10-dimensional (or 11-dimensional) universe into some speculative frontiers. For example, what would happen if those rolled-up dimensions were to "un-scrunch" themselves? That phenomenon, known as decompactification, would be a very bad thing for the universe as we know it. It's the kind of stuff that science-fiction nightmares are made of.
Where would you look for evidence of extra dimensions? On the widest scale, you might look for anomalous areas in the cosmic microwave background (the so-called "big bang afterglow") that could be seen as signs that our bubble universe has bumped into a neighboring bubble. You might also look for evidence of cosmic strings at work. Yau and Nadis say cosmic strings could be detected by instruments to come such as the Gaia satellite or the Large Synoptic Survey Telescope.
On the smallest scale, you might look for supersymmetric particles in the Large Hadron Collider, as Yau said in the Q&A, or you could look for special types of particles leaking back and forth through extra dimensions. Kaluza-Klein particles would have unusual masses or spins due to their sojourn through the multidimensional realm.
More about extra dimensions:
- Physicists probe the fifth dimension
- The quest for a theory of everything
- Black strings: Black holes with extra dimensions
- Hey, it's only a string theory (scroll down to Oct. 25, 2005)
- One of the best-known popularizers of string theory and extra dimensions is Columbia physicist Brian Greene, whose book "The Elegant Universe" has been made into a public-TV documentary series. You can read my review of the documentary and my extended Q&A with Greene, but for the whole shebang, you simply have to watch the full three-hour series online at the PBS "Nova" website. If you're intrigued by unseen dimensions, this is must-see free TV.
Visit the brand-spanking-new Cosmic Log page on Facebook and hit the "Like" button. You can also follow @boyle on Twitter. And if you really want to be friendly, ask me about "The Case for Pluto."
Leave a Comment:
What does it mean for other dimensions to be "scrunched" up? Does it mean that measured along one of those dimensions, the distance to the next galaxy (or anywhere else in the universe) is very short? Or is that the wrong interpretation of these small dimensions?
Why is attributing the universe to imagined dimensions any less likely than attributing it to imagined gods? At least these guys have some math to show for it, even if only 10 people can understand it. Which brings up the question: how do you kow it's wrong?
Oh, and this has nothign to do with evolution; you're getting your obsessions mixed up again.
Mike: "Scrunched up" is a poor choice of words, sorry Alan. In math it is called compactification. Think of it more like a knot tied in a rope, a really complex knot. This knot is so small that we currently have no means of detecting it. They are smaller than planck's length 1.6 X 10^-35 m. Whereas a proton is 2.5 X 10^-15 which means that there is easily more than 10^20 of these knots across the diameter of a proton. Hopefully this helps in showing how small these knots are. Some string theorists believe that if one of the curled dimensions uncurled then a new universe would open up and break away from our universe. Another point of view, since string theorists like 11 dimensions, try to imagine this knot with all 11 dimensions curled up. Whatever may have caused it, there is 3 + 1 spacetime dimensions uncurling. This in effect is the big bang theory.
@MikeMaxwell,
I like your question. In the article, they theorize that these other dimensions shrunk down to almost nothingness. What if that's not really true? What if we just don't normally perceive them?
I've heard of people who can experience these other dimensions during ceremonies using DMT and other natural substances.
This begs another question. What if when we die, we just move into another dimension? That would explain why we can sometimes see ghosts. They can sometimes move into ours if they have enough energy.
I'm just sayin'
:)
No problem, TReed ... in this case I was going for something that could attract the casual reader's attention, rather than the more precise term "compactified." Hope you can forgive me for that. ;-)
Alan : Just trying to help. Sometimes with very complex and difficult topics, it becomes nearly impossible to describe the elegance of the math in words for a casual reader to truly appreciate, but kudos for the effort. Its more difficult for me to exlpain than to understand.
Whew, Much knowledge beyond my comprehension. I believe only the authors understand it!
I do not believe our Universe is a reality unto itself. That is to say, I do not believe our Universe is independent of a higher or greater reality. I believe it to be dimensionally dependent on a higher reality, in which case we cannot develop a Theory of Everything without taking into account a higher reality, or hyperspace. Furthermore, I do not see time in our Universe as a true dimension. I believe our Universe is actually a contiguum, and not a continuum, which is to say that time in our Universe only exists as a single moment, the moment "Now". I believe our Universe continuously updates much like a television screen updates, on the basis of Universal laws. It is basically a chain reaction of contiguous moments, which at any given moment constitutes the moment "Now". - Rick Carter
Yes, time is not a dimension, but an artifact of the speed of light being finite. Your postulate of the Universal Moment known as "Now" doesn't jibe very well with General Relativity, though. The only way for a Universal "Now" to exist would involve the speed of light being infinite, and that would be a Bad Thing, because we wouldn't exist, and couldn't exist, in any universe where that was true.
it can be argued that the theory of relativity is also mainly influenced by gravity though. What we really need is zero G physics studies in deadspace.
Okay. We're back to Yau's argument.
Rick: So how would you disprove Minkowski space-time proofs?
Hon. Rick-- et al., Metaphysically plausible, scientifically Currently unprovable, but, since you call that higher/(faster)/stronger(greater) reality possibily hyperspace, I'll grant that it could perhaps be. However, that said, when one has to Use the term believe, rather than postulate, you are still out there in Faith Territory from where I stand. I like your Taoist conceptualizing of Time as a Factor of Now. On the other Hand, Some of Us do need to (knowingly) plant ourselves out there for the Good of the Group & In Order to Visuallize the Big(ger) picture.
As always, thanks to e.e. cummings and Piglet (Te of) for the use of the Caps and Parentheses.
In other Words, Metaphysics is meritorious but not morally essential;therefore Needs to be kept Within the boundries (small "b") -- of Science.
Because Metaphysics without Science is merely Superstition. Or optimistically known as Mythos. Or Faith in a Super-Natural.
@Mike:
As I recall the explanation from other texts, you can think of it this way: the x axis goes one way toward infinity, and 180 degrees the other way to infinity. 90 degrees from that is the y axis, and it does the infinite thing in both directions as well. Finally, 90 degrees to both of those lies the z axis, with the same properties. (Time does not enter into this.) When we draw this on paper we usually just draw axes intersecting at (0,0,0)--the "origin"--but every point on the x axis (leaving aside the definition of "point" for a moment) has a y and z axis associated with it. For the purposes of this illustration, a geometric plane is a very dense "weave" of x and y lines; space is a very dense aggregate of intersecting planes (x/y, x/z, y/z).
Now, according to the theories Dr. Yau talks about, there are also other axes of direction--call them "a" through "f", and instead of extending off into infinity, they begin and end right on each point on the x axis we were talking about. (Also y and z, but let's not get a headache just yet.) These extra dimensions are very, very small, but not infinitely small; following their curves takes at least one Planck time unit. (A Planck time unit is about 5.4 times 10 to the -44th power seconds. That's really, really, short. The shortest time interval we've ever measured is about 32,600,000,000,000,000,000,000,000 times longer than a Planck time unit.)
So, every point in space time, instead of being specified by (x,y,z,t), is specified by (x,y,z,a,b,c,d,e,f,t) [at least I think it is--I've never quite figured out how time gets into this], but you can only travel "easily" to locations specified by (x,y,z). The other dimensions you just "skip over" because your smallest increment of movement far exceeds their "length;" for all practical purposes their length is zero, and calculating the length of a travel vector in only three dimensions plus time is sufficient. Trying to utilize the hidden or "compact" dimensions to travel to the next galaxy won't work because you can only "go somewhere" in x, y, and z. Trying to go somewhere along the "a" axis takes you precisely nowhere.
Quote:
"The other dimensions you just "skip over" because your smallest increment of movement far exceeds their "length;" for all practical purposes their length is zero, and calculating the length of a travel vector in only three dimensions plus time is sufficient. Trying to utilize the hidden or "compact" dimensions to travel to the next galaxy won't work because you can only "go somewhere" in x, y, and z. Trying to go somewhere along the "a" axis takes you precisely nowhere."
end quote :)**************
ok:)
help me here, I am slow. :)
If you are speaking of knowledge of these things as they relate to "travel"...ok. I have little to ask or say then.
on the other hand :)
If you are speaking of how this knowledge explains things about the way "life is", from either a "physical" or "metaphysical" perspective...
then let us say, "for the sake of conversation"...
To say that the the "other dimensions" are "inconsequential?"
That does not make sense.
That is just another way of saying that we do not know what they are for, or what they do.
So.
What do people speculate are the "purposes and functions" of these "inconsequential" dimensions?If they actually exist then there must be a purpose.
If they had "no purpose" then they would not exist.
What are your thoughts?
Remember that just a "short time ago" doctors did not know of germs. And people would die from an infected cut on a finger. No one imagined that something microscopic even exixted. Much less that it was something that could kill you.
now we know better.
SO with regard to these "excess, inconsequential, meaningless," aspects of this convo, (that is way above my head mathematically btw :)).
Just because something seems meaningless, doesnt mean that it is...
(like turning a knob on your stereo that you don't understand and afterwards saying, "well, it does not do anything." Well duh, it does SOMETHING. YOU just don't know what.)
Fascinating article and comments.
Be Well All.
Thomas Gabriel Grey.
Sorry for the typos. I can't even spell my own silly name right. lol.
But I would value anyones comments on my post and questions.
Be Well.
Think of responding to this as, "Teach a Dummy something today," Day.
Later. T.G.G
TG : If the string theorists are correct, then the curled dimensions do have meaning in the scheme of the 11 dimensions, the meaning is just not shown in our universe. By this I mean the dimensions define the universe, the 3 + 1 spacetime dimensions of our universe defines how things work, the physics. A 4 + 1 or 7 + 1 spacetime universe would have a different set of physics, something at this time we cannot predict.
To back up T.G. Gray, germs would have been considered 'Supernatural' only a few centuries ago, as they were beyond the boundaries of science At That Time, same for the way DNA works, which we are still unraveling, having only discovered it fairly recently, although we have seen the effects for milenia. It is entirely possible that a LOT of things that we consider to be 'Metaphysical' or 'Supernatural' now will become known quantities at some future point in time once we develop the proper theories and equipment to measure them. There is a large body of data showing some correlations between such things as telepathy and our body's electrical fields and the idea of biofields that help guide an organism's growth and development and such things as regeneration in some of the lower life forms. The more data we acquire, the more questions and ideas that it opens up, things that frankly, we do not know!
Just because we do not know it NOW does not mean that it is beyond the physical or above the natural, which is what Metaphysical and Supernatural mean, it just means that we do not have the right equipment to positively measure or see it Now, NOT that it does not exist.
PS - By the way, I do see gravity as a dimension, or an expression of a (4th) dimension. - Rick Carter
Gravity is a force and through Enstein's theories, this force is a result of the curving of spacetime around a mass.
Gravity is one of the four elements of physics: weak force, strong force, electromagnetism and gravity.
The Calabi-Yau space is a multi-dimensional mathematical expression of what sci-fi and fantasy/paranormal writers have been speculating on for decades.
Now that we are conscious of the existence of the additional dimensions, their presence will begin to become demonstrative before our human senses and we will begin to perceive them. It was merely five to six hundred years ago that mankind could finally perceive more than 2 dimensions - one of the reasons mankind thought the earth was flat. Once it was proven the earth was NOT flat because the concept was revealed and was finally accepted, mankind slowly began perceiving the world in 3 dimensions. Once time was accepted as the 4th dimension, it's impact was recognized and abe to be perceived.
Now that mankind's awareness has been exposed to the additional dimensons, once it is fully accepted and recognized (maybe a generation or two), those dimensions will be so obviously apparent toour human senses that those of that future generation will look upon us with the same arrogance and intonations we use when describing our ancestors who believed the earth was flat and refused to acknowledge anything different.
PS: we have had the knowledge and use of the mathematics of our multidimensional world, but it is, and has been for some time, something ost foreign to the average person. This discovery makes it closer to reality for many ... but the reality of "what is" versus what we "believed" will take time to break through the paradigms of our lives that we have so carefully chosen to believed in.
There was a time people could NOT imagine something three-dimensionlly, we now understand 4 dimensions. Soon we will understand and sense 10 dimensions. It is inevitable since it has been brought to our consciousness - however the reality paradigm accepted by humanity currently will take 1 to 2 generations to change and the new reality paradigm be accepted so that human senses can perceive its existence - unless of course, religion or some other dogma attacks it and hinders it's reality from being accepted like the concept of the earth being round vs flat and the concept of an earth centered vs sun centered universe.
There was a time people laughed at the concept of "germs" and something so tiny that it couldnt be seen, but could be deadly was considered lunacy - now we can sense when those germs are invading, have a good clue what it might be and have a doctor diagnose it so that we can get the proper medications for it.
So many different examples ... so little space and time for many of them.
Those times are NOT that very long ago ... we have come a very long way in a very few centuries, and we are still only taking baby steps.
Well Spoken Recycled. The only phrase I take issue to is the assumption that we look down with arrogance on our Pre-Enlightenment or Pre-Reformation ancestors. A true philosopher or scientist does well to not look at any prior concept with arrogance.
Remember that Metaphysics and Philosophies are separate Endeavors in Academe...
Just sayin...
so, people in 1491 couldn't look up or down ?
Dicks-1891035: you must be right, I guess when Abbot wrote Flatland, he must have read pre-Columbian stories to get the background right. Are you a circle, or a triangle?
I guess another question would be...are we assuming (hoping) these extra dimensions (extraneous solutions) are real (valid) in order to resolve the indeterminate polynominals (mortal human fustration)?
I am sure the devoted string theorists would respond with a resounding NO!
So my next question would be...would the math developed under the M-theory progression of equations hold if applied solely in each of the physics, general relativity, and quantum mechanics? In other words is it possible to the same solutions (11 dimensions) without using terms from one into the other?
My suspicion is maybe the solution is not in conjecturing eigenspaces to complete the polynominals but to search for a the existance of cycles of preponderance between the symmetry partners (particles). And maybe supersymmetry can never occur because of the randomness of space. In other words no point in space can have zero mass because of the randomance interaction between the symmetry partners in both phases of time (matter creation, antimatter prepondance, and matter annihilation, matter prepondance).
W.r.t mass measurements we should be around 1/4 ways before next Big Bang and 1/2 ways before the big crunch starts. So based on this assumption do we have enough physics (or observations) to deduce and evidence of a cycle?
Point being, I would readily trust the simplest of solutions as opposed to most complicated deduced by man-made math. Mass, keep track and measure the masses, i.e bigger telescopes and bigger colliders!
A couple of things:
- Scrunched up means the extra dimensions are rolled up. I suppose it's possible there's a universe right next door, but you couldn't use the scrunchiness to get from one place to another quickly in our universe (I don't think!) ... I'll add a couple of links that will help a little bit there.
- Oaktree, I may have lost you somewhere in there, but you're basically right. The point of this is to come up with a set of equations that would hold for both general relativity (realm of the very big) and quantum mechanics (realm of the very small). Such equations might explain what happens inside a black hole, or how the big bang took place.
Mr. Boyle, first thank you for your quick response and for you responding period, I have enjoyed your articles very much.
I do understand the methodolgies of conjecturing the hypothesis (assumptions of most convience that require observations to falsify, lol) between the two physics. The point implied in my second question was that in order to maintain validity in our formulations (understanding of our universe) the progression of equations (extrapolations) of each of the two physics must and can only cross (unified) through common observations.
My fear has always been that the analytical search for solutions has impeded our progress when ever it overshoots our experiements. We should not run too far ahead of nature or we will lose our way.
well...
use some imagination... Perhaps the 'scrunched up' dimensions, once perceived from the vantage point of the spaces that they inhabit, will have our dimentions as scrunched up, and hence, are only scrunched up in principle because we cannot interact with them. Hence, they may very well be 'scrunched out' and scrunched up, meaning we are scrunched up to the 'higher' dimensions as they are to us. Forming a sort of perfect higher dimensional doughnut and paradox where the only thing defining things is the point of reference (like the speed of light, the only absolute is the speed....and by implication, the absolute makes everything else relative...).
Perhaps.....our mind is at the cross-roads of these dimentions, since our mind in itself is higher dimentional. And also perhaps, this gives our memories the ability to 'ground' us in the universe we seek or are afraid to seek (unintended fates)....and assign it from the multiverse....'creating our reality' based on our memories. The outside world would not be inconsistent because it would be consistent with our biases and memories...So everything is relative to the absolute of preconceptions and memories, reality adapts to us...But if we knew this, we would immediately try to change reality by changing our memories..then that would ceaze to be the absolute, but a dynamic, and the absolute would simply be our desire to create, the absolute would be the reality we choose, and we would change to create it (like in any entangled system, one cannot get information if not one amongst the entangled pair changes as well). But that would mean we would have to leap our confined respective programs, with its neural precepts and logical hierarchies, which is impossible to do at our current stage of evolution....Hence, it spins and spins and we will never know.....but does it matter? would our existence not be the same either way? we are happy or unhappy, irrespective of it...
exactly, and thats why its possible.
Why?... prime directive.
www.youtube.com/watch?v=BlcJ-fDmDhA
If extra dimensions are scrunched up and out, then there is nothing stopping us from creating our own geometry simply by 'growing' the scrunched up ones with sufficiently advanced technology..perhaps....after all, reality is based on a seed, and the mathematical implications and complexity from such a seed...we can create our own 'artificial reality'/enviroment by creating our own geometry.perhaps...by manipulating gravity. If the dimensions are scrunched up by our perspective, then they can be accessed, and if they can be accessed, they can be manipulated and grown, and if that is the case, then we could travel around our own created artificial environment that would pay no respect to the rules of our current universe, but allow us to travel anywhere whithin it once we re-emerged from our own artificially created environment...created reality...
after all, we are made in God's image, so we can create. Who knows, this may just be a dream, and us, a program, confined by our constraints of reality whithin a larger operating system. Kind of like the matrix but far more complicated. For reality itself is a computer. Atoms are just embedded computation, its dispersed computation, not centrally processed. The atoms are the processors, and they remmember through resonance and re-enforcement their own properties (dimentions are self-justifying "the universe is the way it is because the universe is the way it is" arguements...in other words, a self-contained resonant wave resonates on 'itself' to self-justify its existance). For ask yourself, the disk remmembers holes for a computer to process the binary 1's and 0's, but how do atoms remmember? How does reality remmember? Through the resonance mechanism. The computation arises from their interaction, and the complexity that arises a consequence of trying to stabilize instabilities at higher levels (noble gases stabilize quickly, so they do not emerge into complexity...the opposite is true for carbon, it needs 4 electrons to be stable, so it stabilizes in complexity...carbon nanotubes). So the whole universe is a computer, and the real matter is information, a contruct, a program. Any program can be manipulated and changed. And hence, in a very real, hyper-dimensional way, we may just be like neo, waiting to be awakened, and upon the realization that there is no actual spoon but in our minds, we can change it, and follow in the footsteps of our creator.
Perhaps matter is not the real substance of the universe, but information. The more complex the pattern, the more it can contain whithin it, the more it can change whithin its hierarchy. We are the apex of the computation ...perhaps...because we are the most complex pattern, hence, we contain all whithin it, and we can change it. Perhaps not entirely now, but later, when we evolve further.
So there is no fundamental but logic, for we are the apex of the hierarchy. The only thing we must abide by is the seed, the fundamental that allows all complexity thereafter in a system. Everything else can be changed to our whim. After all, the more we understand, the more access we gain...not bychanging matter, but changing the information construct and the mind...augmented reality is just the beginning of this.
We are simply in a greater mind. And the result of us, was the purpose of the universe, an unending equation trying to reach for greater complexity, to stabilize all instability, and the most complex pattern, is one that repeats itself the least...intelligence.
Have a good day.
the greatest priests are mathematicians...They seek truth through painstaking discipline, resolve, and absolute logic through purity of thought. And hence, the purest form of morality, for to reach to perfect the human mind only leads to the tyranny of logic, and hence only the perfect, only the worthy shall pass [Moral U logical]. The essence of God. A church of mathematics.
-unknown.
In the end, it may spin and spin, and you may never know, but really, does it matter?
If you knew everyone's thoughts and they knew yours, you would all merge into one, but then you would be lonely, for what is more boring than yourself? poker is only fun if you don't know other people's cards. you may know the optimum strategy to chess, but then it becomes like tic tac toe..boring
You may screw others to get everything you want, but at the end of the day, you may have all the material in the world but with no one to share it with, will you truely really be happy? You become a machine, and you only value the material, but then you make no intimate bonds, and you get a reflection of your priorities, a world full of material, but devoid of beings....for you have died long ago...you look in that mirror, but only a machine remains...
The person that has, gets more. The person that has less, usually gets punished. But the challenge is what makes the difference. Someone who is poor will get happier with simple things, or someone who is not as intelligent. A person that has more, the challenges are greater. Sometimes ignorance protects those that cannot see their fate...but by doing so, makes their life just as much worth living (if not more) than those who do not have..
if you had everything you wanted, and everyone else did as well, things would be meaningless, you would feel worthless, you would degenerate, appreciate nothing, there would be no standard bearer. No challenges to face, no wars to fight....nothing but a monotonous perfection. The saddest and ugliest of all. Nothing to define you, to make you rise to the ocassion and challenge. Why must someone take that from you? why must someone prevent you from reaching for glory? the glory of the struggle?...for there is a purpose to this struggle, have you no doubt. God may be benevolent, but he is not stupid...
you givce up, you see things and conclude there is nothing there, you don't notice the other signs, because YOU have created your reality, your memories have grounded you in your own pity party, and since you do not arise to the occassion, to be all that you can be, you punish yourself,...
for there are higher manifestations of ourselves....the subconcious and you, are your biggest and harshest critics. For if there are no wars outside, why does it feel like we are in one?
You are your ultimate judgement day machine, you simply do not realize it. But thats the point, if you did, you would be perfect, but again, that would be boring..
and so it spins and spins, but does it really, truly matter?
;)
The math that is the basis for relativity, quantum mechanics and string theory is differential geometry. The differences come in the different geomteries that each theory has. The most interesting geometry that might unite relativity and quantum field theory is the E8 Lie group.
yes...
Sounds like Chaos theory, where nothing reoccurs. Just hope they don't try to teach this garbage in college physics.
Nate, Nate, Nate~~ Teach is such a Parochial term. In college physics, I would imagine and would certainly be beyond "teach" and and into enlightened and honest debate. (and, no, I don't understand it either). I do know the Difference and the Value in being able to sort out the Meta data and know which is which.
Jonah:
> since our mind in itself is higher dimentional.
Only if you're demented :-)
Soooo....if other dimensions exist does that mean other planets and stars exist in those dimensions? And when they say other dimensions do they mean entire universes similar to our own??
Yes, it's possible that there are other stars and planets that exist in other "bubble universes" ... and the existence of extra dimensions could imply that another universe could exist not that far away, only in the direction of that rolled-up dimension. The metaphor that's usually used relates to ants on a power line. A power line is very long in one dimension, but it's very small and rolled up in another dimension (the dimension going around the power line). A near-sighted ant walking on the power line might think that there's just one dimension ... not realizing that there are other ants walking on other power lines nearby. This is illustrated in part 2 of the "Elegant Universe" documentary:
http://www.pbs.org/wgbh/nova/physics/elegant-universe-string.html
HOWEVER, according to the "landscape" theory that Yau referred to, not all universes are equal. In fact, most of the bubble universes could be unsuitable for life, or they might just fizzle out as soon as they take shape. So there aren't necessarily planets and stars next door, even if other bubble universes exist.
You spoke of bubble universe can they collide and if they did what would that mean. what if it collided with our universe.
Bubble Universes, as far as we can tell, are each separate and in generally no danger of collision due to the differing numbers that formed them. Even in our Universe, there is tons of space even within each atom, let alone the spaces between the atoms that are pure vacuum and if the bubble universe's vibrations or charge were slightly different than ours then it would be able to co-exist within the same 'space' as ours but we would never even notice it at all. Especially if it occupied a different axis of dimensions, say X,Y A dimensions instead of X,Y,Z dimensions, it would, presumably, never come into "contact" with our own unique universe.
This is just great. This is beyond great. This will give the kids something to think about.
Yet another scientific(?) theorist who implies his speculations, based upon other, very shakey, speculations, are factual (e.g. , " ... actually figured out how these extra dimensions work". When, in fact, all he's done is, very conveniently, made all his calculations around the figure 10. It's so easy to just add the odd nought, or move the decimal point about. If he had invented '7.5' universes instead, he'd have been in the poo (not that, in reallity, he isn't anyway!).
It's time for a big shake-up of the people, who's decisions affect us all and our future and the future of our planet and for them to stop this, now, very irritating and damaging habit of stating 'theories' (scientifically derived, or not) as 'fact', which has the destructive effect of 'blocking' other, probably better fitting, theories being discovered and offered.
With which you prove you have NO CONCEPT of the scientific method. A theory is only as good as it contains NO CONTRADICTIONS. Once a contradiction is PROVED, usually mathematically, the theory falls apart, or is modified to meet the newly proven conditions.
Unlike foolish people who WISH, and BELIEVE, and HOPE, scientific methods DO NOT blindly accept a theory as fact without rigorous and constant testing against FACT.
Quit betting on ignorance.
I should point out that Yau figured out how multidimensional geometry works for this case, but that doesn't necessarily mean our "multiverse" is actually 10- or 11-dimensional. But scientists are trying to figure out a way to look for evidence for or against this. So it's not exactly voodoo. If you want to learn more ... and "The Shape of Inner Space" or "The Grand Design" doesn't catch your fancy ... there's a new book from John Gribbin titled "In Search of the Multiverse" that might ring your chimes.
Ron : Actually Yau is a Mathematican. He proved the Calabi conjecture. No theory. The string theorists came to him to learn the math. The Calabi-Yau manifold, the picture in the story above, can be created for many different dimensions not just the 10 or 11 dimensions for string theory.
I agree that this string theory is a very elegant mathematical concept, but it has been custom-built to fit the prevailing views of the cosmologists. In that sense, it is exactly like the Ptolemaic (earth-centered) model of the solar system, which is a very good model for predictive purposes, but just plain wrong in reality - the earth is not the center of the solar system. Clear up until Copernicus disproved it, astronomers kept "refining" the Ptolemaic model by adding more epicycles, as if the solar system were a vast, clockwork collection of gears spinning around the earth. I fear that string theory and M-theory may be falling into that same trap - if the model doesn't fit the data, well then, we'll just add some more epicycles to make it work. Where's the proof?
Would you rather we call our Facts--- Theories? Maybe put a little Tremor into our Voices?
couldnt you say mass would be a dimension in itself? Mass of one object effects mass of other objects within its gravity well? This applies to everything from microbes to planets and stars.
Actually, mass and space-time affect each other. Mass is something that gives the "shape" to space-time, and that shape may be reflected in other dimensions as well. In fact, some theories suggest that gravity works the way it does because it exerts its force in other dimensions as well as its own. But first scientists have to figure out the workings of "gravitons" ... the force-carrying particles for gravity, which have not yet been detected.
The big crunch? I thought it was determined that a collapse of the universe was not possible? Something to do with the perfect balance of gravity. Can anyone assist me in understanding this?
OK, the big crunch is a scenario for the far future of the universe. Current theory suggests that the universe will not end in a "big crunch," but in a "big chill" instead. Because the expansion of the universe is accelerating, eventually all matter will just spread out into nothingness. This is different from the idea that dimensions are "scrunched up." There might come a time when extra dimensions "un-scrunch" ... and theorists are thinking that would be a very bad thing. With all this in mind ... have a good weekend. ;-)
Thankyou allen
ALSO : Did the 10 dimensions all start with separate 'Big Bangs', 13 or 14 or 15 bullion years ago (they can't get the timing right - still, what's two billion years?), or was it just one, fairly largish 'Big Bang', then the dimensions sorted themselves out from that? No! I'm not laughing (much)!
Yes, this hypothesis would say that the rolled-up dimensions "compactified" in the big bang 13.7 billion years ago or so.
Alan. Recent arguments (centering upon the "Crisis in Cosmology" meeting in Portgal) and, apparently, reported in this month's 'Physics World' magazine, about differing constants, dimensions and certain properties of the cosmic microwave background, not matching predictions from the theory of the 'big bang', alters the use of the value of the constant by 15%, suggesting that the Umay actually be 15.8 billions years old??
Ron : A large part of the discussion in the meeting dealt with the concepts of dark matter and dark energy and how much they are used in current big bang theories. Even though this group doesn't like the use of the dark concepts when explaining big bang. However, this group has not come up with a viable theory to compete against the current one. This is how science works, some agree, some disagree and sometimes improvements occur to the existing theory or whole new theory comes about.
Yau right about that!
Theories are made up of ideas because the universe doesn't seem to work right with the facts as we know them. Math is made up so the theories look right. Sometimes it's right. Sometimes it's not. Even our math may be wrong about what we think are facts since things don't work right with our present math and facts. No one will ever know for sure. I'm happy for that.
The difference between math and "science" (such as physics) is that when it's properly done, math is rock-solid. It's the only scientific discipline where proofs can be absolute. So I don't think it's the case that mathematics is simply "made up" ... although mathematicians start out with a hypothesis (such as the Poincare conjecture) and see whether they can prove it.
"It's the only scientific discipline where proofs can be absolute."
Notwithstanding Goedel's incompleteness theorem, though....
Assuming the underlying mathematical assumptions are correct, of course.
Yes, thanks for the caveat, folks.
I went and looked at Godel's Incompleteness theory, the first thing that stood out was it's basis was on Natural number set. That's the set of positive numbers and sometimes zero, depending on which definition is used. The set of numbers that you build you basis matters tremendously. I didn't see any mention of the real set. If I am wrong on this, can you show me a link?
SacramentoMike
> Assuming the underlying mathematical assumptions are correct, of course.
*Correct* refers to the question of whether the mathematical assumptions fit reality; this is a scientific question, not a mathematical one. A mathematician is more or less free to make any assumptions, so long as they're not mutually *contradictory* (or don't lead to contradictions, which is more or less the same thing).
The only true "element" or in this case if they want to use the word "dimension" in the universe is "thought." Via "thought," I percieve a fundamental flaw in science/mathmatics/astronomy/physics if it is foundationally based upon a theory that Copernicus was correct. If the universe is infinate then where ever you are is the center of the universe. H. Tod Taylor
But the universe is not infinite.
What 'irrefuteable' evidence do you have that makes you so sure, j-son?
It's supposedly a theory of existence, a grand design, of everything. To me that's infinate but I will admit that I am still flushing out my "thought" process on all of this in my latter yrs of this pecieved existence.
Since the universe is still expanding this would imply finiteness.
Hmmm.... So, the equation is: (A complex mathematical model of an unobservable, untestable hypothesis) + (then a miracle happens) = Theory of Everything. Honestly, needs a bit more work.
True that, DMHewey
Best comment yet. Personally, I'm still working on my unified theory of mysticism.
"... but it's Chinese-American mathematician Shing-Tung Yau who actually figured out how those extra dimensions work ..."
I hate to be the critic, because I do believe that Alan Boyle means very well in his reporting. However, there exists a burden upon science journalists to point out to the public that this is a mathematical model which lacks any supportive observation. To be clear, there exists NO OBSERVATIONAL EVIDENCE for 11 dimensional space. He should also be much clearer on the fact that this model absolutely depends upon all of the assumptions inherent to the conventional theories. Every single one of those assumptions must be correct, or we are all wasting our time here. These assumptions include:
(a) That electric fields do not occur in cosmic plasmas like they do in laboratory plasmas.
(b) That double layers do not occur in cosmic plasmas like they do in laboratory plasmas.
(c) That galactic-scale magnetic fields are NOT the result of electric currents or time-varying electric fields, as is taught in any electromagnetics class, and as is true inside of every single piece of electronics ever created by mankind (which electrically works).
Alan unknowingly tosses aside the computer revolution which created the very computer he writes his articles on in order to suggest that a highly speculative computer simulation can resolve the failures of the Big Bang Theory. After all, were the conventional models functioning properly to begin with, we would not be here pretending as though a discussion of invisible hypothetical cosmic objects somehow represents a scientific topic. And his reporting, were the conventional theories not in need of these invisible objects, would be more properly termed "PSEUDO-SCIENCE."
Only in conventional cosmology does laboratory physics (like plasma physics principles) take a backseat to some guy playing with equations on his computer. Alan Boyle is a smart man, but I just don't understand why he thinks it's sufficient as a science journalist to simply adopt the opinion of the scientific consensus. It's as if he's never put any thought into even the possibility that the consensus might possibly be wrong. Is there not a burden in science journalism to formulate your own independent opinion, based upon a review of the critics?
Criticisms of the conventional theories abound outside of MSNBC's cosmic log. So, why is the public not told of ANY of them?
http://www.electric-cosmos.org/indexOLD.htm
It's long past due for Mr. Boyle to do an article on the Electric Universe. There is simply no philosophical justification for focusing more upon such abstract hypotheses than upon a group of laboratory plasma physicists who are trying their hardest to tell us that the objects we are seeing through our telescopes can be completely explained (without ANY hypothetical, invisible particles) using fundamental laboratory plasma physics principles.
One need only to fix the cosmic plasma models to more properly match the behavior of plasmas which we observe in the laboratory in order to create a fully functional, and highly predictive, model for the universe. So, why are we talking about alternate dimensions?
What a waste of thought and money that Alan inspires amongst us all! It's the never-ending barrage of reporting which fails to ask important, critical questions which keeps us all in a holding pattern, waiting for a better theory. Alan, please stop drinking the Kool-Aid, and for once read something written by a critic.
People--including Chris Reeve--keep complaining about this:
"... but it's Chinese-American mathematician Shing-Tung Yau who actually figured out how those extra dimensions work ..."
saying that there is no evidence for the theory. Yau is a mathematician, not a scientist; and yes, he did figure out how these dimensions work *in the mathematical theory.* If we some day discover that the universe doesn't follow this theory, that won't change the math; Yau will still have shown how the dimensions work in math. The math just won't be describing our universe.
Just want to say to Alan and all of you who have contributed...
For those of us who are endlessly intrigued by this, but have no hope of ever ever ever actually understanding it, this is pure porn.
And what's not to like about that?
G-rated infoporn ... the best kind
I like Larry's comment equating the perennial inability to understand the complexity of these mathematics to porn. Porn fits into the category of all these theories because it is, in effect, not comprehensible to anyone save possibly the ones who create it. Since male and female attitudes towards pornography are quite different, it would be interesting to know if the fundamentals of string theory, M theory, and supersymmetry differ between the sexes of the mathematicians who are studying them. Anybody got information about that ?
No. Trust me, I'm a Librarian. Talk about a leap of Faith.
Maybe they can use these breakthroughs to make us better TV sets to watch Star Trek reruns on :P
Seriously though, this is amazing and I wish I had the intellectual horsepower and comprehension to get this. Ah well, that's what makes the interview subject special - he's one of the few who can.
During his short life, Evariste Galois (1811-1832) developed some quite obscure and impractical mathematical theories, such as group theory, Galois fields, etc.
These theories are used as a foundation for error correcting codes (Reed-Solomon codes), used these days in every hard disk in most every computer.
I always have suspected that forces are representations of matter in higher dimensions, which lends itself to the duality of certain particles like photons. Both a particle and a wave.....depending on which dimension is exerting influence or being observed.
you know, I agree with this guys last statement very much, you always need a challenge. We may discover the 'theory of everything'...but then what? Its like reaching the peak of mount everest or alexander the great's great quote "for alexander weeped, for there were not worlds left to conquer".....
we must always challenge ourselves to perfect not only ourselves but the world. And if we, god forbid, reach perfection, then let us get our happiness by guiding and experiencing the lives of those who haven't....for through a million eyes and experiences we relive our journey to perfection, and are in constant happiness. Nirvana.
maybe reality is like a game. Once you know the optimum strategy perfectly..it is not entertaining to play it...
lol, ' a silly game, the only winning move is not to play'...
The separation between art, the creative, and mathematics...exists only in the mind.
Jonah- The urge to conquer, explore, research, etc, etc, can never end for the truly, open minded, intelligent human. When all the mountains have been climbed, the climber, if he's not dogmatically obsessed with climbing, should become, say a naturalist, or a pot-holer. There are endless new games to play and when they run, invent some more, and the fantacy world of your nirvana can never be likened to the reality of life. Still, I would not want to spoil the enjoyment some people get from their dreams and beliefs, but, imo, it's no advanatge to the progress of the human race and all other life on this planet, nor discovering the mysteries of the universe (and what's beyond it!!).
ron james..
surely, somewhere along our technological perfection, there could come a time where we know certain things in such a wya that we stop enjoying them, now?
Atari used to be really cool during its time, but now it would be scoffed at.
Obvcourse there are boundaries. However, such an explanation seeks to calm human frustration more than reveal any insight (why things are this way rather than another way). However...never say never.
All boundaries can be broken, except those set by logic...and the noble heart.
The noble heart is defined by the one that sets out to seek a greater more perfect reality, a justice. And by doing so, he is defined by his struggle...Not by his victory, but by his endless perseverance against all odds....even if he knows he will surely fail.
www.youtube.com/watch?v=35UC2Jdsyic
after all, it is only beautiful if you don't know you will win, or even if you think you will surely lose. There is no point in fighting if the outcome is known.
a person is defined by the challenges he/she faces. Sometimes you don't need to solve everything to destroy the intellect and heart of a society. Sometimes all you need to do is take away desire, a desire for the betterment of mankind, or to aspire to something loftier than the ugly motivations that underly daily life, to destroy a society. It doesn't always have to come by being so perfectly perfect as to necessitate no struggle. By seeing that life and struggle has its purpose, one learns to make peace with it, and to cherish it. For it grows the creative expression to an almost divine form. Hence, the noble heart gains meaning. Struggle serves its purpose.
many forget what struggle really means, they turn to ugly motivation. And their world loses meaning. like many before them, they also meet their fate. God and the logical embedded intelligence that self-assembles and premeates all reality (like the 'force' in star wars), strikes them down from the darkness, and as abruptly and as surely as they rose to power, they disappear from the pages of history. ...
but only insidiously....if we knew of the overall presence we would delegate responsibility..there would be no purpose in the struggle, we would degenerate...
only by being faced with the darkness of the unknown, is man really defined. Defined forever.
I have got some questions. Like why does seem like gravity is reversed and the dimensions are here? Not hidden, or unattainable or magic like. And what is someone supposed to do with all that information of Crushed dimensions? Are we a non-crushed dimension How do you touch one of these dimensions do they move away? Are they what gravity is? Is gravity controllable in these dimensions. Are their galaxies in these dimensions. What particles are moving between them, and how often? Is a frictionless dimension theory or friction here friction their? How can we keep from being crushed into these dimensions? Is the universe breathing in and out and how many times does it breath? What is it breathing in,and what does it breath out? Does time go both ways in these dimensions, and do these dimensions have memory? How can you make contact with these dimensions, and will you be sure that it wasn't just an imagination gone wild? Does one dimension try to corrupt the other dimensions or are working with each other? Does one dimension know that the other dimension exists? Are they self aware or are they dumb particles? Not retarded particles but programed particles make up our universe do they hold the same forces?
Wow, so many questions ... I'm definitely adding links to other stories above so that people can at least get a wider sense of what's out there.
- When you say gravity is reversed, are you meaning perhaps dark energy, which some folks initially referred to as an "anti-gravity effect"? Dark energy appears to be built into the parameters of our particular universe, and I suppose a case could be made that this universe needs dark energy in order to exist. But it doesn't directly speak to what's going on in the extra dimensions. As I said before, some folks think gravity may be "leaking" into extradimensional space, which would explain why it's so weak compared with the other fundamental forces. Hypothetically, there could be galaxies in other "bubble universes" separated by extradimensional space. When you talk of a universe "breathing," that reminds me of the ekpyrotic universe model. (Do a search on "ekpyrotic" for more.) People are trying to figure out how we know these extra dimensions exist ... and one possible way is to look for signs that energy is going out into the extra dimensions in the form of what scientists call "Kaluza Klein particles" or KK particles.
Yes Dark Energy... Thanks I will do the searching.
If you were to draw circular spheres of non competing matter and then draw lines intersecting them causing fluctuations of motion does that not cause gravity All particles must move freely through them setting up random sizes of spherical space
I would think that with so many different dimensions 'scrunched' into infitisimal points and the idea that other universes may well exist within these other dimensions, perhaps within each individual point, that it would give some impetus to the study of Zero Point energy sources, whereby energy may well be tapped from these other universes/dimensions and given the huge number of points even within a Planck length radius that this energy would be, for all intensive purposes, infinite.
Just an idea...
Also, who is to say that individual universes cannot occupy, say, X,Y,A axis, X,A,B Axis, Y,A,F Axis and so on perhaps each of them operating on different dimensions of time, such as an "X,Y,Z" Axis for time whereupon time may travel in these different directions and in both directions (although in different universes) for each time dimension. This would give 6 different time directions for each of the 3 Dimension Axis universes leading to a HUGE number of possible universes just using the 11 dimensions projected.
Certainly some food for thought!