Just watched a show on the Nat. Geo. channel about Stephen Hawking and his quest for a theory of everything, and it led to a discussion about string theory. Try as I might, I am simply unable to mentally visualize and thus fully comprehend the concept of nine dimensions. I understand what they are saying (sort of), but I simply can not visualize it. They even had little graphics to demonstrate the extra dimensions, yet that still looked two and three dimensional (for obvious reasons) and didn’t help me conceptualize nine dimensions at all.
I’m assuming my brain is just wired differently from those who grasp this.
I completely agree. Sometimes I will get lost while watching documentaries on the universe. It often humbles me to not be able to wrap my puny human brain around such ideas.
John, allow me to explain.
You see, reality is not a dump truck. It’s a series of tubes…
of course Obama thinks in 11 dimensions.
Man, I just got a depressing e-mail this evening:
I think if you talk to physicists, you’ll find they don’t really “visualize” more than four dimensions either. They can get very, very good at working through the math and logic of how things would relate at higher dimensions, but they can’t “picture” an “eight dimensional object” moving through time.
I know exactly what you mean. I consider myself a bit of a physics buff, but that is precisely where I lose comprehension.
I hear you, Cole. I love science, but the really cutting edge stuff… it’s like trying to imagine new colors.
I absolutely can’t wrap my mind around why they think that time slows down when you’re traveling the speed of light. People have tried to patiently explain it to me over and over and I just can’t get it. It’s like my brain plays with the parts for a minute, then squeaks in terror and runs to the back of its cave and hides.
Only two things are infinite, the universe and human stupidity, and I’m not sure about the former. Albert Einstein
Your superior intellect is no match for our puny weapons! The Simpsons. Also Too.
John, clarity of multi-dimensional realities requires many, many beers.
I don’t like string theory… something about theories where a hypothesis cannot be tested scientifically drives me nuts…. guess its the “experimental” scientist in me.
It starts with entropy, an idea that is used to describe the heat that we can not measure.
There are two kinds of truth: those that are defined and those that are determined. Of the kind that are determined, some are measured and some are determined by inference. String theory is an example, like entropy, of things that can not be directly measured but are only known to be true by logical inference. Imaginary numbers can not be measured, but we know them because of things like Euler’s identity:
e^i*pi + 1 = 0
We need to study and find ways to explain things like string theory because there are still people who think that the Flintstones was a documentary.
I can visualize an octopus playing with a volleyball.
At Snopes it says UNDETERMINED. In any case, are the other groups a part of this nefarious plot? Are the Amish and Muslims going to unite to force all of us to grow funky beards?
We are through the looking glass people!
Gozer + 80 + oz. beer (dunno how many single units that is)
EDIT: Sorry bruh. At first glance I though you were some kind of wingnut as the formatting was fucked on your post.
All physics at that level is beyond visualization. Quantum mechanics, relativity – it’s all wicked abstract shit. You learn to just go along with the math and stop trying to turn it into billiard balls. One thing that helps is to work downward – there’s a nice book written a century ago about how 2 dimensional creatures would interact with 3 dimensions. It doesn’t help with 9, but you start to get a sense of how utterly different additional dimensions would be compared to what we’re familiar with.
But string theory is bullshit at the moment. Science demands disprovability – string theory doesn’t have it. My .02.
While we’re discussing string theory, could someone please explain dark energy and dark matter? Dark energy must have something to do with the GOP but I’m not exactly sure how.
Also, our religions are completely inadequate for the universe we live in.
It must be an Obama plot to confuse us all.
Don’t worry about it. There are a large number of professional physicists, myself included, who don’t make any pretense about understanding string theory.
There are also quite a few who have the nagging suspicion that the whole field is the biggest waste of time since epicycles. Testable predictions would be nice to see, but we’re not really there yet in any useful sense.
So you’re in good company.
I’m waiting for BOB to weigh in, heavily, on the links between string theory and dhimmitude.
kommrade reproductive vigor
First you need a rubber sheet and some weights…
General Egali Tarian Stuck
I was very good at anything life sciences, or biological and got almost all A’s. My physics classes made me want to run away from home and join the circus.
Jeebus, I’m still trying to comprehend the lyrics to Louie, Louie.
this is just too confusing. thank goodness al gore invented internet porn to occupy our minds.
No one can really visualize more 3D, the dimensions come out of the math, and it is difficult if not impossible to translate math to words. That’s why quantum mechanics sounds all mystical and mysterious when it is really not.
ETA: Have to agree with Martin’s comment, and yes I don’t understand string theory either.
For a fun and interesting exposition to weirdness of relativity and quantum mechanics, try George Gamow’s Mr Tompkins in Wonderland series.
Don’t sweat it, John. One: string theorists do not understand string theory. A pair of Italian practical jokers earned a PhD in theoretical physics years ago and the field still cannot figure out whether or not their thesis was a joke.
Two, you can count the practical uses of string theory on one fist. Some better theory could supplant it completely, prove the whole thing wrong, and the whole mess would leave not one trace behind in the practical world. In terms of transistors and spaceships it is exactly as useful as TIMECUBE.
Reality is whatever Tunch thinks it is. He’s doing eleventy-billion dimension math in his sleep.
@beltane: Dark matter is pretty simple. It’s matter that doesn’t glow. Yes, really. Most of what we know about the universe comes from looking at the light (or other wavelengths, like radio or X-ray) emitted by objects such as stars, nebulae, and more exotic things like quasars. We know that dark matter is there because we can measure the effects of its gravitational pull, but we can’t see it because it’s …dark.
Dark energy is more exotic. It has to do with the very structure of the universe, the fabric of spacetime, and such things. We can measure things like how quickly the universe is expanding, and the history of that expansion, and compare that to what we know about things like gravity. If we try to mesh those two sets of facts, there’s a large quantity of …something which is needed to make the books balance. Call it dark energy, call it a cosmological constant, whatever. We don’t know what it is, just that there’s a really large unknown, which accounts for the great majority of the energy of the universe.
@Lockwood: I think this is pretty much right, especially with string theory. I was a mere physics undergrad, so I didn’t get close to actually learning string theory, but I did learn quantum mechanics, and at the end of the day, it’s just about the math. Physicists don’t have any particular power of visualization, they are just really good at math and at some point learn to let go and trust it.
There are any number of physicists who would tell you that string theorists trust the math too much, and aren’t even doing physics anymore. Most of their hypotheses are well beyond the capacity of current technology to test.
well….classical physics is observable….pulleys, wheels, force, temperature…
q-physics is just the physics of the very, very small.
You do have to rewire your brain a bit, because we can’t see quanta….homo sap. is highly vision oriented….superposition and quantum entanglement and multidimensional manifolds are not intuitive.
Some brains are more flexible than others….Hawking has an especially fine one.
It is good that Hawking has renounced his black hole heresy.
And that LHC is working again.
A really good book is Penrose’s Road to Reality.
If you are interested.
11 dimensions? Hell, it’s hard to “visualize” 2 dimensions (if you think of the dimensions in a plane, you’re most likely thinking of that plane existing in a larger 3-dimensional space).
Our brains simply are not wired for it. I don’t think anyone can really “visualize” less than or more than 3 spatial dimensions.
More than 3 dimensions only makes sense if you consider that a point “hides” an infinite array of other points, which are indexed using 8 additional co-ordinates, as opposed to just the x, y, z we are used to.
@dmsilev: Brains is weird stuff. I read your last two sentences too quickly, and thus at first glance I thought you wrote that “the whole field is the biggest waste of time since testicles”. ‘Cause of the following words, “testable predictions”. You know, plus epicycles. I can’t have been the only one.
I don’t get entropy. I can say that it’s about the degree of disorder in a system, and I can picture that if you took a box full of black and white marbles and shook it real hard, the marbles are more likely to be jumbled than to end up in neat lines of white, black, white, black. But then I get confused, because I figure if you have an infinite number of monkeys shaking an infinite number of boxes of black and white marbles, eventually you’d get a black and white marble depiction of the Mona Lisa.
I don’t get irony, either. I think I do, then it just squiggles away from me, and I flail around and say “sardonic” or “sarcastic” or “insipid” instead of risking “ironic”.
Not true. It would have left dozens of tenured theorists.
Instead of points, it’s useful to visualize some things as clouds (an electron probability cloud) or fields (an electromagnetic field – a gravity field – a nuclear field). Also, strings as membranes is a more useful image, with our universe existing within the membrane, a membrane that moves about in a higher dimension.
There’s a lot of truth to this. I once got into an argument with a cousin who (briefly) was a philosophy major. He wanted to know how I justified using quantum mechanics when nobody understood what it really was. I gave the pragmatist’s answer: The equations make predictions which can be checked, and those predictions have proven to be accurate, in some cases to incredible levels of detail. Therefore, we assume that the equations are useful for describing what’s going on.
That said, to make fundamental advances in theory, you really do have to have a intuitive grasp of the structure underlying the math. That’s a rare gift.
@dmsilev: if we find higgs bosons at CERN, parts of string theory will be proved.
But it is true that string theory originated as pure math.
My favorite Max Tegmark quote….
Well . . . it helps me to think that THEIR brains are wired differently.
But what I really want to say here is that, so far, this is the most entertaining thread I’ve ever read on BJ.
My lifelong position is that any concept that a genius can comprehend, so can a non-genius. There are cases, of course, where visualization fails–and I think this is one of them. The concepts, though, are available to me and you. This link is to Carl Sagan explaining a 4-cube, and I think it illustrates what I mean better than anything I can come up with:
My high school calculus teacher mentioned that he was able to envision multiple dimensions. The way he says it, the fourth was really the hump to get over. Once you can do that, going to eight (or more) is easy. Not that I ever managed four, of course.
I also remember him once taking that e^pi*i^ + 1 = 0 equation and using it to demonstrate that i^i^ is a real number. Now THAT was a mindfuck.
(edit: I’m breaking formatting and trying to fix it)
@dmsilev: Thank you. That did help clarify things somewhat. It is incredible to think that only a century ago we were not even certain of the existence of other galaxies.
@beltane: There are a number of cosmological measurements which don’t make sense, particularly two. One is that the outer limits of the observable universe are moving too slowly — at some point in the past, the Universe was expanding more slowly than it is now. The other is that the large spiral galaxies don’t have the correct rotational profile — their outer rims are rotating too fast, and they should fly apart. They clearly don’t.
The first of these two requires some sort of energy to be present which makes the Universe grow faster than it should. It can’t be electromagnetic, as we’d be able to detect that — in fact, the sky would glow at night — and it can’t be nuclear, as those forms are strictly range bound. So there’s some mysterious “energy field” that fills space with “extra energy”…and we can’t see it. That’s “dark energy”.
The second of these requires that there be a bunch of gravitationally interacting mass which isn’t electromagnetically active. Some part of this “stuff” could be the mass-equivalent of dark energy, but calculations show that there’s too much missing mass. This stuff, which we also can’t detect directly, is “dark matter”.
@Larkspur: Entropy isn’t too bad. To use your example, while it is true that an infinite number of monkeys shaking a set of black and white balls will eventually reproduce the Mona Lisa, for any given trial, you’re much more likely to just get a random mess. Entropy is, in it’s simplest sense, a measure of how much more likely the random mess is than the da Vinci.
@matoko_chan: And we aren’t going to. The lower bound on the Higgs Boson’s mass-energy keeps rising; the CERN collider is no more going to find that particle than the earliest synchrotrons could.
I once had a boyfriend who was a physicist. He claimed that mathematics was the most perfect and pure language. We eventually broke up because his idea of fun was good wine (that part I liked) and long discussions of chaos theory…
Your own perception of time never changes. You will observe other people’s time slow down as their speed relative to you approaches the speed of light. They will also get redder and seem to flatten out.
The effects occur because light has a finite speed. You don’t see things as they are, but as they were the moment the light left them on its way to your eyes. Light coming from one part of an object gets out of sync with light coming from another part due to the speed of the object – thus the image you perceive is distorted due to the motion.
Probably doesn’t help much, but at least I tried.
Until marijuana is legalized nobody is ever going to understand this shit.
@matoko_chan: Depends on what they see. The Higgs is part of the Standard Model, so that in and of itself wouldn’t say much about string theories. If they find the Higgs at some unexpected energy range, or see evidence of supersymmetry, or something like that, then we’d be getting somewhere.
Science is really all about generating a set of testable predictions about the real world that are known to work out in all cases. It’s easier to do this if you have a way of generating them that ties together into a whole unified framework.
Relativity and (basic) quantum mechanics are both very weird relative to everyday intuition, but both lead to very accurate predictions (in different situations) that have been tested and confirmed experimentally. Just the same way as Newtonian gravitation did; relativity explains situations to extraordinary accuracy where Newtonian predictions turn out to be inaccurate (meaning wrong). FWIW the semiconductors that are allowing us to post are here by virtue of the extraordinary accuracy of quantum mechanics’s explanation of nature.
String theory (and various others) are new ideas that might bring both these worlds together with further refinement of accuracy, etc, but until they can offer predictions that are subject to a Popperian falsifiable experimental test they’re still in the kitchen and not yet out on the buffet line.
This is not the same thing. But you don’t have a problem with a linear programming problem in 8 dimensions, right?
I mean, if you are trying to optimize the process of building an automobile, it is not hard to see that you would have multiple equations involving labor hours, management hours, raw materials, machine time and so forth that would require multiple “dimensions.”
Itis not the dimensions per se that bug you. It is the idea that physical reality can be described at this degree of abstraction. But, shit, that is what an atom was at the turn of the century.
It doesn’t bother you, intellectually, to know that you are mostly empty space, or, even worse, that there really is no good understanding of how it is that you (or Lily) are conscious. (That she is conscious is itself controversial for some people who have not lived with a dog.)
Whether a quark actually exists, and is not a mathematical abstraction that happens to work in some weird ass equations is (as far as my amateur understanding gets) still an open question.
As has been mentioned upthread, there are, AFAIK, no testable hypotheses have been generated by string theory. And it has been a remarkably unproductive couple of decades. We still have three paradigms–the deterministic theory of gravity, the quantum probabilistic theory of the other three forces, and the empirical laws of thermodynamics.
So don’t worry about it.
@Annie: can I have his number?
And, regarding the math:
@Sentient Puddle: Picture a soccer ball. The ball rolls down the street and into a sunlit patch of macadam, stops and loses air from a slow leak until it’s flat. You just visualized the ball changing in five dimensions: time, color and space x3.
Speaking as a theoretical physicist, I can assure you that physicists aren’t any better at visualizing higher dimensions. Humans didn’t evolve to perform such mental tasks. So we just work through the equations, and that hope they’re not leading us astray.
Brian Green helped me to at least pack in a few more dimensions. The idea is that we humans can’t actually perceive them, but they do still exist. If you just think about a point in our 3 dimensional space, and then imagine that at that very point exists another 3 dimensions that are so infinitesimally small that you can’t perceive them, then you’ve taken the total to 7 dimensions. Now expand your thought and imagine a set of dimensions so large that you can’t perceive them either, essentially the system in which our 3 dimensions are constituent.
Okay, so it’s all BS, but it’s still fun to play with.
OT, but has anyone else seen this:
U.S. attorney, IRS and FBI investigating Florida GOP credit card use
Could this be a “game changer”
trying to catch up. are epicycles what you ride in those higher level dimensions? are they powered by strings instead of chains or do the strings just flop from the handlebars like the multicolored ones here? oh! and do they glow are are they dark because reflective strings would be really good if we have to go out riding at night.
@Jim, Once: Much better than the usual crazy we talk about.
@bystander: I tell non-mathematicians that mathematics is the only field which consists entirely of formalized similes. We don’t know what the natural numbers *are* (in a very deep sense, in fact, we *can’t*), yet we can say that they’re like small piles of sticks, which we can pick up and put down and rearrange into pretty patterns. Beyond that, though, they don’t exist, except as essentially poetic images. All of math is like that — it’s just more so.
we don’t even use the dimensions we have, why do we need more dimensions. /dad.
It was actually Hawking’s book that was the breakthrough for me, and the analogy of the orange. From a distance, the surface of a orange is 2D, right? It’s a smooth sphere. But if you look closer, it’s really 3D, because there’s pits and pores and such.
@scav: Well, you have to be careful at night; that’s when the zombies come out for the branes.
@demimondian: Snort. I’m glad I’m not the only one who thinks of zombie string theorists whenever someone brings up branes.
@dmsilev: ’tis true, we may find all sorts of things.
Evidence of supersymmetry or indeed, any sort of superparticle would be grand, but I personally would like to find strangelets.
<3 strange matter
I just want to point out that, despite what you might say about your own abilities, nearly everybody–Tunch included–can visualize in four dimensions (space + time). Otherwise, simple motor skills like walking or driving would be impossible.
On the other hand:
@Mumphrey: I don’t understand that shit at all.
Question: do we need a new theoretical construct to explain the anomalous expansion of Star Trek continuity blogs and disturbingly thorough articles on the World of Warcraft wiki? I propose “dork energy.”
LOL…He’s French. So along with chaos theory and good wine, there was a great appreciation for good food…..It was a difficult decision…
Nobody did a better job of explaining the psychosis of trying to grapple with the intensely abstract better than one D. F. Wallace.
We’ve all been there. You reach a point where toying with it in your head actually becomes physically uncomfortable. Imagine doing it for a living, or full time.
For me, it’s trying to imagine what “was there” before, say, the Big Bang. What is “nothing?” It’s got to be something, right?
So I just read blogs.
@demimondian: no…that is wrong….that is the opposite of Tegmark’s quote…..and…..of Pythagoras.
Virtually all the “commonsense” aspects of the world as we humans experience it — space, time, matter, light, movement, etc. — are human-scale approximations to the underlying reality. When we try to understand that underlying reality, we use these familiar aspects to assist our imaginations, but we have to remember that they don’t really apply. As several commenters have noted, the amazing thing is that math and science let us make symbolic representations of things we can’t really “understand” (or at any rate visualize) and test whether those representations are true or false.
I recently had occasion to show this excellent animation of DNA replication to some junior high students, and had the damnedest time trying to explain why atoms didn’t really have colors.
@Annie: oooo moi je parle tres bien le francais!
Didja ever read Dewdney’s tribute to it, The Planiverse? Excellent book.
Bullshit is a bit harsh. People have been working on designing experiments to falsify it. IIRC one of the early experiments at the LHC can falsify string theory but doesn’t go anywhere towards proving it.
It’s an interesting idea, but yeah, I’d like to see a transit of Venus moment.
Way I look at it, there’s a certain class of Math Brains that need concepts beyond the provable to keep themselves entertained. Our society has stopped rewarding royal astrologers and academic theologians with the best available perquisites, instead preferring to give the prize money and coveted fellowships to “rocket scientists” who, it is hoped, will allow us to
placate the godsblow up enough shit that our precarious position at the top of the food pyramid will not be called into question. Because having a sufficient grain surplus to feed a whole non-productive caste of Enablers-to-the-Throne proves (a) that we shouldn’t be fvcked with, because (b) obviously, God-or-the-Universe loves us more than those guys out beyond the reach of our firelight. I am thereby exempted from trying to visualize eight dimensions, just as the atheists among us are exempted from trying to “believe”.
Tim in SF
Hey John Cole,
There’s no way to actually picture it in your head – our brains just aren’t wired that way. But it’s not impossible to comprehend it implicitly. This youtube can help you understand the dimensions 1 through 10.
Getting back to John’s original plaintive cry, there are stranger things in physics than imagining 9 dimensions. For instance, there are certain problems, relating to actual real world effects (such as phase transitions like water boiling into steam) which are most easily solved in four dimensions. Since the real world only has three “large” spatial dimensions, we solve these problems by saying “OK, we know how to solve them in 4D. So the solution in 3.9D will be a little bit different. The solution in 3.8D is a little bit different from that” and so forth until d=3 is reached.
We’ve established pretty solidly that there is an edge of the universe, right? It’s expanding, therefore has a limit somewhere way out there?
So, what’s on the other side? Nothing? What is that nothing? Space? Well, that doesn’t work now, does it?
Go to a beach in Rio to appreciate String Theory.
LOL…You are awesome….If I wasn’t married, I would ask you out — chaos theory and all….
@matoko_chan: Actually, that was Pythagoras, not Aristotle. My view is more closely aligned with Aristotelian ontology than it is with Pythagorean or (neo) Platonic ontology, which hold that number exists as form, extrinsic to its functional properties. Godel, Turing, Kleene, and Post, however, taught us otherwise a hundred years ago.
It’s also heating up in the sun, so throw in temperature and you’ve got six.
@John O: Well…actually, we haven’t. There’s a boundary beyond which we can’t see, to be sure, because it is receding from us at the speed of light. There’s also a finite radius of the matter which was created in the Big Bang. Those two things might, or might not, coincide; it’s possible that the first is larger than the second.
Here’s everything you need to know about Dark Energy.
That’s provably false. Higgs bosons are part of the Standard Model.
“The Higgs boson is the only Standard Model particle that has not yet been observed.
The Standard Model is the combination of quantum mechanics + quantum chromodynamics (quarks) that explains almost all the experimental data we have gotten to date from particle physics.
To date, string “theory” has not made a single prediction that can be tested. The existence of the Higgs boson is predicted by the Standard Model, so detecting a Higgs boson proves nothing about string “theory.”
If we were to detect superpartners of particles already observed, that could provide evidence for string string — but since these superpartners are so massive, the energy required to produce ’em in a collision is far higher than we can reach in the Large Hadron Collider, so no one expects to see any signs of superpartners like the photino in the LHC experiments.
To expand on what dmsilv explained about dark matter and dark energy, dark matter is mass we know must be present in other galaxies, but which we can’t detect. The dark matter might simply be dark (dust particles or burned-out stars), or it might be made of exotic particles that we can’t detect easily with our telescopes. At present we don’t know what dark matter really is.
How do we know dark matter exists? In the 1940s, the astronomer Vesto Slipher applied Kepler’s laws of motion to the rotation of distant galaxies. By observing periodic stars in distant galaxies and comparing their apparent brightness with their periodicity, we can tell how far away other galaxies must be, because these Cepheid variable stars have periodic fluctuations in their brightness which correspond precisely with their mass, and from their mass we can calculate their true brightness and then compare that with their apparent brightness to determine how far away these variable stars in other galaxies really are.
When Slipher compared the results of Kepler’s laws of motion to the actual observed rotation rates of other galaxies, he discovered that the galaxies were rotating much more slowly than they should be, based on their apparent mass. Slipher concluded that much of the mass of other galaxies must be invisible. Thus, the origins of “dark matter.” Subsequent astronomers have confirmed Slipher’s hpothesis that other galaxies are much more massive than we can account for from their visible mass by using other means. We still don’t know exactly what dark matter is, but we know it must be present in other galaxies (and almost certainly in our own galaxy too).
Dark energy is a form of energy which appears to be pushing the galaxies apart faster than they ought to be traveling. When the Big Bang erupted at the start of the universe, all the matter in the universe was created and flew apart. From this matter (mostly hydrogen, with some helium) stars formed and from those stars, all the heavy elements we observe today. Astronomers back in the late 1990s discovered that red shift measurements showed that distant galaxies appear to be picking up speed as they race away from us (every galaxy seems to be racing away from every other galaxy, so this does not indicate that our galaxy is the center of the universe).
This was unexpected. No one has yet explained why the expansion of the universe appears to be accelerating. There are a number of competing hypotheses, but none has yet accrued enough evidence for scientists to agree on what’s causing all the galaxies to fly apart at an increasingly faster rate. Whatever is causing it must involve some extra energy we can’t see, energy that the distant galaxies are picking up in addition to the original energy that flung them apart in the Big Bang. Some theoretical physicists have hypothesized that the additional energy might come from the structure of space itself — but no one really knows right now. As a result, this extra energy that seems to be pushing all the galaxies apart at an accelerating pace is known as “dark energy.”
Link to NASA site about dark energy & dark matter.
@gnomedad: And, if you have normal color vision, you can add three dimensions of reflectivity for the three optical pigments. Now you’re at nine.
i said pythagoras.
Let me introduce you to Max Tegmark.
so what you are saying is, seeing a woman in a mid-thigh skirt, and visualizing the various points that are, from your viewing point hidden, and imagining an angle that might allow you too see the points you are certain exist, but are obscured from your limited view, is something like other dimensions?
The LHC folks I met seemed confident they will find the Higgs. If they can cool 44K tons of equipment to absolute zero, there better be a Higgs in there.
While I’m sure all the physicists have heard some version of this story, I’ll relate something from my undergrad days when someone asked a prof at an open house if anyone understood quantum mechanics. I think it was Weinberg at UT, somebody pretty famous.
He related a story from his graduate student days, something like a quantum chromodynamics course, and his prof had filled the white board with equations. Looking at the grad students, he realized none of them got it. So he erased the board and started from a different approach. 30 minutes later, the best and brightest had their eyes rolled back into their heads. So he said, OK, OK, lets go back to the original approach, erases the board and gets 15 minutes into it.
At some point, he stops, and steps back from the board, arms splayed, hands trembling. The students perk up, thinking some major breakthrough has just been made. The prof turns around to them and exclaims “Oh my God, for the first time I think I actually understand this stuff!”
This movie on visualizing ten dimensions is the best I’ve come across.
The basic idea (which I’ve had to use in some of the math I do), is that you sort of collapse a set of dimensions down into a point, so that what you usually think of as a point is actually a multidimensional object.
Kevin Phillips Bong
String theory, like climate change and really all other science, is just a community-wide conspiracy to keep the grant money flowing. Amirite?
@mclaren: pardon, i think the relevence to string theory was supersymmetry….it was when tonnes of laymen articles were describing higgs bosons as “the god particle”.
Your explanation is quite correct.
I apolo if I have unintentionally misled anyone.
I’ve long since given up on trying to understand string theory. I figure if only a hundred or so people in the world have actually mastered the concept, why should I expect to be one? What I haven’t given up on is understanding realitivity. I feel I should be able to understand that one, but like others in this thread my brain actually feels like its hit a brick wall right before I think I’ve got it. The other thing I don’t get and think I should is Schroedinger’s G’damned Cat. Different subject, same brick wall.
Fools! Meddling idiots! As though our ape brains could contain the secrets of the Krell!
Thanks. I can actually grasp that.
Seriously. Dark Energy and possibly Dark Matter can realistically be described as Fudge Factors to make the maths come out right. I so love that. Forget happy and beauty and charm and whatever those 7 quarks are, let alone the higgs boson, we’re looking for Dark Chocolate.
@beltane: This summary of Dark Matter written by someone who understands and explains dark matter well at GOS might be of interest to you…
It’s not important to comprehend what the universe is doing in all those dimensions; the important part is that you can derive testable predictions from the equations. I think that’s the most we can expect from these primitive meat-based antelope hunting computers in our heads.
I hear that some OB/GYN’s are hyping the use of 5D imaging in lieu of typical sonograms. 3D I can accept, but how can something be shown in 5D??? The fourth dimension is time. And the Fifth Dimension is that group from the 60’s that sang about going up in beautiful balloons and the Age of Aquarius. I think these doctors are dropping acid.
A smell of petroleum prevails throughout.
Visualizing up to ten dimensions
This is about as good as it gets, really. It doesn’t REALLY help you visualize higher dimensions, but it’s a good explanation of how, in principle, they can exist.
(nods in approval)
This is a joke (based on a true incident?), but I can’t resist:
@Kevin Phillips Bong:
String “theory” appears to be a sincere effort in good faith to unite quantum mechanics with gravity. Alas, it doesn’t seem to be going anywhere. The word “theory” keeps appearing in quotes because string “theory” hasn’t yet made any predictions we can test in a lab yet, and that’s a bad sign in the hard sciences. Physicists are reluctant to abandon string “theory” because some of ’em have put their entire careers into it and done some amazingly beautiful mathematical work related to string theory. There’s no evidence that string “theory” is any kind of scam — instead, it seems to be one of many theories in the hard sciences that just didn’t work out.
Most hypotheses in the hard sciences don’t work out. That’s how science works. It doesn’t mean scientists are running a scam or wasting our tax dollars. It just means that science progresses slowly, by fits and starts, and as fallible humans we make many many mistakes in the process of coming up with mathematical models that accurately predict the universe around us.
@Matoko_Chan: I probably made mistakes in my explanation too. It’s almost impossible to talk about things on the cutting edge of science in words, sans math, without creating a few mistaken impressions.
Right now we have two separate entirely different theories that explain two different aspects of the universe: gravity, and elementary particles. Unfortunately these two different theories use entirely different kinds of math and two different sets of assumptions about the universe. Quantum theory assumes that particles don’t even exist until we observe them so quantum theory is probabilistic, while Einstein’s gravitational theory is deterministic and has nothing to do with probabilities. These two theories can’t be combined in any obvious way. This causes a problem when we try to explain the origin of the universe, because during the Big Bang the universe was compressed into a tiny volume with immense gravitational forces (so we need Einsteins theory of gravity to model it) and the Big Bang also seethed with highly energetic particles (so we need quantum mechanics to model it).
So far no one has found a way to combine gravity with quantum mechanics in a way that doesn’t blow up and create impossible mathematical difficulties. This leaves us at a loss to understand the early conditions of the universe…at least, so far.
Perhaps the best way to “visualize” 11 dimensions is to think of a spreadsheet with 11 cells associated with a particular point in space. Those 11 cells interact with other cells in the spreadsheet that represent other points in space (this is a highly simplified explanation).
Basically, if you are comfortable with spreadsheets (especially formulas that involve multiple cells) then you have a feel – sort of – for matrices, which are often used in physics to calculate outcomes.
@mclaren: I’m going to politely defend the string theorists here.
They’re doing quite lovely mathematics, and, as such, yes, they’re entitled to call what they are doing a “theory”. After all, we have “model theory”, “group theory”, “graph theory”, and the like. They’d just be another cool theory in the menagerie.
What I don’t think that they’re entitled to do any more is call what they do “physics”.
To the math as similie person: Combine that view with a deep semantic understanding of parsing and utterances. *pop*
I was a physics student once also. I had trouble visualizing 3 dimensions sometimes (rotating things in my imagination, for example) and never even tried for 4. I don’t believe it can really be done, except by a very fuzzy analogy. I’ve known quite a few physicists and none of them could either. So its not an intellectual disability!
The use of the word “dimension” is a historical accident (like “imaginary” number). Take anything, a system, an object, a process you want to describe with mathematically. The number of independent quantities (things that you can conceptually vary one at a time without affecting the others) is called the dimension. That’s all there is to it. To describe the position of a fly in a room at some instant you need 3 independent numbers….ergo, 3 dimensions. If you want to track it through time, you need 4. And so on.
As far as imaginary numbers go, i to the ith, is in fact exp(-pi/2) and that is a real number. It goes like this:
i = i*sin(pi/2) = exp(I*pi/2). Multiplying by i follows the laws of exponents. You multiply the two i’s together and get -1 (that is the definition of i). so the result is exp(-pi/2), as above. (Ignore the strike-through; I don’t know how I did that and didn’t want to.)
Entropy in our macroscopic world just expresses (and finds a way to measure) the simple fact that energy tends to dissipate in natural processes (particularly involving heat): If you put a cold object next to a hot one, the first warms up and the second cools until they are the same temperature. If you use heat to run an engine, a certain amount of it will always be wasted, not converted into useful work…it is like a tax on an energy transaction. The definition of entropy is such that in an isolated system the entropy change for any spontaneous process is an increase. The picture of white and black balls lining up is how you account for this always observed effect from the level of atomic processes. In fact, it might happen that the balls line up…but it is very improbable.
The entropy is a number that measures this probability…the lower the entropy, the less likely the arrangement.
We are not facing an energy crisis…the 1st Law says that energy is always conserved, although it may take varied forms. We are having an entropy crisis, the entropy of a gallon of gas is lower than the products of its combustion…heat, motion, CO2, etc.
The three Laws of Thermodynamics in a nutshell:
(1) There’s no free lunch (energy can’t be created or destroyed)
(2) You can’t even break even (some energy must always be dissipated, i. e., thrown away in every process), except at absolute 0
(3) You can never get there, except with an infinite amount of work.
I have to get some sleep before the increasing entropy destroys the organization of my brain.
@Tattoosydney: This whole thread reminds me of the fact that I was doing very well in my college physics class until the more advanced math hit us. Then my head went flat and I had to drop it.
There’s an old Richard Feynman quote saying “anybody who tells you that they understand quantum Mechanics is a liar.” I think fewer folk undertand superstring theory.
YES – the sort of folks who grasp 9-dimensional string theory are the sort who can do differential equations involving complex (imaginary) numbers and matrix manipulation in their head, and find working math proof problems to be a form of interesting recreation.
> didn’t help me conceptualize nine dimensions at all.
Read “Flatland” by Edwin Abbott Abbott, an old book but a nice primer to understanding dimensions and it can be read in an afternoon.
Entropy means the whole system tends toward disorder. Your monkeys may produce the Mona Lisa, but the world around them got more disordered in doing so.
Best way to think about entropy is to use energy instead of disorder. Entropy is a measure of the difference in energy of two states. A rock at the top of a hill is low entropy — it has all the potential from gravity to roll down and mash a lot of stuff. At the bottom, it’s high entropy. It’s at the same state as the bottom of the hill, it’s not going anywhere, and the energy difference is gone.
So, for your monkeys — the marbles can move from a disordered state to an ordered one, but they needed the energy differential of the monkeys to accomplish it.
Talk to Kant bitch
Not at all. Leonard Susskind, a prominent physicist from Stanford who wrote “The Black Hole War,” often ridicules students who think they can perceive more than 3 spacial dimensions. Physicists tend to imagine extra dimensions wholly on a mathematical level, not visually.
Just to say that the commentary community on this blog is the most interesting and intelligent of all my regular ones. But I do miss BOB from time to time. He helps to get my juices flowing. It’s like a small dose of what in a larger quantity would be poison. If I want that, I can go to the comments at WaPo.
Of course “i” is a real number. Any electrical engineer will tell you that. Except they call it “j”. You can’t do alternating current without it.
“The treatment of resistors, capacitors, and inductors can then be unified by introducing imaginary, frequency-dependent resistances for the latter two and combining all three in a single complex number called the impedance. ” (Wikipedia)
as this originally started with a program, from those who know this stuff, how dated is this BBC show Horizon on Parallel Universes? I remember having vague glimmers of possibly understanding at least the context / outlines of the theories when I watched it but it could be ferociously old / outdated or dumbed down.
Reminds me — back in the day I used to like to get stoned and read “Scientific American”. Especially cosmology. That was the best, although Herman Kahn’s nuclear war gaming wasn’t bad either.
@demimondian: Excellent point. I stand corrected.
Surprisingly easily. Many companies today build and sell high-end computer workstations that display 3D images using polarized glasses of the kind people used to watch a 3D movie like AVATAR. That gives you 3 dimensions.
To get the fourth dimension you change the pictures over time.
To get a fifth dimension, you change the color of the images over time. (In a medical image, the changing color might represent the density of plaque in an artery, or the number of cancer cells in a tumor, or the amount of a virus in the bloodstream, etc.)
If you want a sixth dimension, you can change the texture of the surfaces in the 3D computer images over time.
If you want a seventh dimension, you can accompany the 3D computer images with a sound and change the sound over time.
This is not just “pie in the sky” theoretical stuff, it’s part of an area of science known as scientific visualization, and it’s expanding with explosive rapidity right now. Scientists and engineers are using this kind of technology to visualize everything from the inner structure of the earth, to the assembly of proteins inside living cells, to the formation of galaxies in distant parts of the universe. This new visualization technology works, and it’s giving practical results, and doctors are now working with engineers and physicists to apply scientific visualization to medicine, where it promises all sort of breakthroughs, from earlier and better diagnosis of illnesses, to faster and much cheaper methods of surgery.
I miss the Gibbs free energy equation and deriving the Schrödinger wave equation and integral calculus.
Here is an elegant animation depicting one way to visualize 10 dimensions… it actually is pretty easy to understand. I doubt this is the way mathematicians see it, but for us laypeople it works fine.
Visualizing up to ten dimensions.
What’s before the Big Bang? What’s on the other side of the expanding universe? Piece of cake: the Tao.
“The way that can not be named is The Way.”
Well, just for the record, you’re not supposed to be able to visualize anything in nine dimensions. That is actually the point (and also strangely related to why wingnuts only see things in two). Nine dimensions exist in equations and National Geographic / Discovery Channel specials. Still important, none the less. We visualize ideas in the dimensions that are familiar to us. Nine dimensions, familiar are not. That said, string theory (especially in its current incarnation) is a pretty fascinating conduit for understanding the universe. Just don’t try to visualize it. That’s when things get hairy.
@beltane: Dark matter is matter that does not interact with most matter and is not luminous for one or more of several reasons, though my understanding is that the main reason would be being a neutral lepton (since it’s not made of charged quarks nor has net charge itself, it cannot really interact with matter except by gravity, and light is essentially the dropping of electrons from a higher energy level to a lower one, although with the caveat that nuclear reactions or radioactive decay can also release electromagnetic waves [light] from atomic nuclei). Unlikely to be “exotic” forms of hadrons since they would consist of unstable quarks that would annihilate in contact with “normal matter” (e.g. anti-particles).
Dark energy I am less clear on but it’s apparently repulsive in nature (as opposed to attractive) and only really interacts on a universal scale.
For a slight explanation of some vocabulary: Matter is made up of two types of particles : hadrons and leptons. Protons and neutrons make up hadrons, or things that are made of smaller things known as quarks, and electrons are an example of leptons (basically don’t divide any further). Neutrinos also are in the latter category, and a possible component of “dark matter”.
I have issues with Baltimore
This is a long-ass thread, but let me put something out there: the act of doing physics and mathematics are as much a human endeavor as anything else. I never did string theory myself, but back at Columbia I ran with a crew who do/did. At this point it’s more cult and avenue for research dollars than it is anything substantial and relevant to reality. String theory as “real” science definitively died back in the early naughts with “the landscape.” Now some of these string theory guys, like Michio Kaku, have revealed themselves to be what they truly are: pure snake-oil conmen. Some of them, like Lubos Motl, are vindictive or insufferable assholes who’d make great popes. Others, like Brian Greene, well, they had good intentions….
@kommrade reproductive vigor:
Concidering the # of physicists floating around the Juice Pool, I’m surprised this comment went unanswered, because it addresses visualizing the “unvisualiable”. How does gravity warp space to make planets revolve around suns? Get a rubber sheet, a weight (the gravity of the sun), and some marbles to roll around the indentation (the planets).
Most of you probably jumped right past the “rubber” and “weights” thinking “yeah, and don’t forget the KY…”
Thinking in multiple dimensions isn’t something you picture; it’s something you imagine. Thinking in one dimension is linear; locations on a string; How many places you can stop along I-80 between New York and San Francisco. Each new dimension adds richness; two dimensions is how many places on the surface of the earth you could visit; an infinite number of strings. Three dimensions gets you off the planet; it’s the number of places you could visit in our universe right now. Four dimensions is how many places in our universe you could visit at any time since the big bang. Five dimensions is how many alternative universes exist at the point in space and at the time when my finger hit the period key at the end of this sentence. Six dimensions is all the places I could visit in each of them since the big bang.
Seven through eleven? You’re on your own. Don’t hurt your head.
It’s weirder than that. Time doesn’t slow as you approach the speed of light; time slows when you move — period. At relatively low speeds, it’s imperceptible to humans, but that doesn’t mean it isn’t observed — GPS satellites’ time is different from ours because they’re in a different part of the Earth’s gravity well, and if we didn’t account for relativistic temporal effects in the satellites, they’d be off significantly.
As for getting it, there are times I can almost get it, but then it slips away. The human brain didn’t evolve to picture 13-dimensional space. That said, I find cosmology fascinating, despite my human limitations.
To clarify, the dimensions I describe are most assuredly not the dimensions string theorists think about. I’m just trying to help move people past the “visualize” roadblock.
I’m never gonna get it either (I don’t think), but I’ve come to think about this stuff the way that Evan suggests. I try to think of a “dimension” as being more of a concept than a property. In the same way I think about the “fabric” of space-time. My problem has always been that I try to take these things too literally. Like when I see graphics depicting these things in a book or documentary, I try to imagine their referents in real life. What exactly they would look like, how they would behave, etc. My imagination fails. So, I’ve fallen back on seeing a “dimension” as just a way to explain an idea rather than as a physical attribute of something. I’ve probably got it all wrong, but it helps me, at least.
Edit: To be more concrete, I think I prefer to “conceptualize” rather than “visualize” these subjects.
Lots of very clever people providing mucho detail so there’s not much I can add.
However as the token philosophy grad (and yes, one of my interests was “What do the interpretations of quantum mechanics actually mean?”) I’d just like to throw out one additional point that can get lost in the mix sometimes.
A lot of the theories, entities, terms, etc discussed in physics aren’t quite what they first appear, they’re just functional terms we use to describe something that does a specific required job that fits in with our current observations and theories. That “something” isn’t necessarily what its name suggests, or even one specific thing at all-it could be multiple events or properties that all combine to produce the effect we observe. “Dark matter” for example, is just a term for something that seems to need to exist given all our current observations and theories, but hasn’t been observed yet. (Note that these “somethings” need to be as parsimonious as possible to be more reliable than fantastical storytelling-whatever we eventually find on the other side of these explanations will eventually look a lot like what we’ve described, but won’t necessarily be identical.)
Generally, it’s useful to think about “extra” dimensions and so on the same way-rather than trying to see them as actual “things” you could look at, they are simply the way we have of talking about certain aspects of our observations and theories that can’t be explained otherwise.
daniel thomas macinnes
If you want to comprehend 9-dimensional spacetime, that’s easy. Just take what Terence McKenna called a “heroic dose” of psilocybin mushrooms. Five dried grams should throw you into the lap of God, hehe hehe.
John, John, John: just drop a tab of acid, relax, and let your mind float downstream. Taste the colors, baby!
Will it? I thought Higgs was predicted by the standard model.
That’s a risky choice, too. Sardony is still illegal in many cultures.
Help me! All this physics I don’t understand at all.
My two cents.
I don’t think the unease Cole has is not being able to visualize or imagine lower dimensional representations. I think the unease is comes from the lack of intuition about what happens if you want to manipulate high dimensional objects or estimate relationships. Many of our 2 and 3 dimensional intuitions turn out to be wrong in higher dimensions.
Close one eye and navigate across the room, or try to interpret a 2-dimensional drawing of three dimensional scene. Because of practice at learning correct ‘intuitions’ we know what happens when we manipulate objects or relationships in 2 and 3 dimensions and can even translate what happens when we move from two to three dimensional representations and back again, and vice versa.
Most people have little intuition about properties of objects and relationships in higher dimensional settings. So even if we can visualize and imagine, we cannot do or predict anything or evaluate relationships we are used to in 2 and 3 dimensions.
Not sure I have a good example. Maybe, what happens to the surface area and volume of a 1 inch circle/ball/sphere as you increase the number of dimensinons.
So you got a circle. then a ball, then the three dimensional generalization of a ball.
What happens to the volume and surface area as the number of dimensions increases? What is the relationship of the surface area and volume of the 1 inch n dimensional hypersphere to a 1 inch n dimensional hypercube?
Check it out.
Edit: final advice is quit worrying about it or Tunch will punch you in the neck again.
Wile E. Quixote
Try getting one of those new 9-D TVs that are coming out. They work by projecting a succession of separate 8-D images to your left and right eyes and you wear a special pair of glasses that only shows one image at a time, so your brain is then able to combine the two 8D images into a single 9D image.
If you can’t get a 9D TV Make magazine has a hack where you can build one with four 2D TV sets, two bottles of Nyquil, a copy of Going Rogue and a chicken.
@Wile E. Quixote: I heard you can poke your eye out with one of those things if you’re not careful.
Back in my MIT days, I had a professor who probably did drop too much acid, though what he said did make a lot of sense (maybe I dropped too much acid?).
His position was that the human mind has evolved to tackle three dimensions and while it is built to tackle more than that (hence our capacity for mathemeatics and metamathematics), because three dimensions so throughly define our reality, we would not recognize other dimensions if and when we were ever exposed to them.
Instead, the human mind would use the inputs it was used to in a three-dimensional world to translate those other dimensions as some sort of anomaly within our three dimensions.
Four or more dimensions would appear so damned bizarre (since it would turn our everyday three-dimensional physics inside out), that you simply would not know what to make of it. It would be tantamount to suddenly perceiving reality shimmer or ripple like a stone dropping into a pond or bend in simply impossible directions.
In short, a wild acid trip. As I recall, the book “Godel, Escher, Bach” helped me to conceptualize higher dimensions (without the acid).
Wile E. Quixote
Only if you get the ones that are imported from Fragile. Stay safe, buy American!
Exactly. Just to expand on it a bit, saying that something has “9 dimensions” just means that there are 9 measurable properties of that thing that are completely independent of each other. The real-world example could be something like a table — if you look at tables in general, the length of the table doesn’t constrain what the width or the height of the table will be. You need to know what all three measurements are to say how much space it will take up in a room.
The complication of these other dimensions comes when you try and figure out a set of mathematical rules that takes them all into account at the same time. Things like string theory need that mathematical gumbo in order to come up with predictions that can be tested — a starting point (“state”) with 9 numbers for the 9 different things you measure (a.k.a. “dimensions”), some kind of action that describes a change (this is where the nuts and bolts of the theory itself come into play), and an ending point with 9 other numbers for the dimensions, where the values of those numbers follow the mathematical rules set out by the theory.
The action is a testable scenario that scientists with time on their hands and grant money in their pockets can carry out. If they can get the thing they’re using to test the theory into the starting state, perform the action described in the prediction, and measure the final dimensions in the end state, then they’re in a position to say whether the theory predicted right or if it was just blowing smoke out of its mathematical ass.
The problems with string theory in particular (and cosmology in general) are that no one knows how many dimensions they need mix into the gumbo and how the action really works.
We’re kinda sure that there was this Big Bang Thingy billions of years ago (start state), and what we see now (end state) was a consequence of some action that started after the Big Bang Thingy. Even the idea of this Big Bang Thingy is subject to debate — check into the truly groovy set of assumptions that went into the underpinnings of that concept (a.k.a. the “Cosmic Distance Ladder”).
Ultimately, thinking about this this stuff is great for passing the time, but no one (even Hawking) has been able to think it through to the point where you could do what we think of as science with it.
Wile E. Quixote
A-ha! Now we know the truth. Gary Aldridge wasn’t a disgusting perv with a wetsuit fetish. He was conducting investigations into string theory. That’s what all of the leather straps and plastic cords, including the one tied around his neck, were for.
Methinks this video about Imagining the Tenth Dimension will be helpful.
Forget string theory. Do not listen to the high priests of physics and their esoteric mumbo-jumbo. String theory is the exact equivalent of “How many angels can dance on the head of a pin?”. Same shit, different day, or, same bullshit, different religion. They’re pretty close to rediscovering homunculi, I hear.
Didn’t he end up in a land rover with Laura Dern in Jurassic Park?
so you could be said to observe an orange in multiple dimensions simultaneously:
the 2-dimensional shape (circle)
the 3-dimensional shape (sphere)
the 3-dimensional texture of the surface
the reflection of light off the surface
also like the soccer ball analogy, changing in 5 dimensions. very useful.
Someone (my bad, lost you) mentioned that trying to wrap one’s head around advanced physics is uncomfortable, even painful. And that may be true. But the moment when you do see, the moment of understanding… That’s something else. An almost physical sense of …not pleasure, but something else. Perhaps this is how the religious feel when they have a religious experience.
Understanding = good. :)
Then there is this old joke:
A Mathemetician (M) and an Engineer (E) attend a lecture by a Physicist.
The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The M is sitting, clearly enjoying the lecture, while the E is frowning and looking generally confused and puzzled. By the end the E has a terrible headache. At the end, the M comments about the wonderful lecture. The E says “How do you understand this stuff?”
M: “I just visualize the process”
E: “How can you POSSIBLY visualize something that occurs in
M: “Easy, first visualize it in N-dimensional space, then let N go to 9”
and if the orange was simultaneously falling from shadow into light, and aging as it fell, and producing a “swooshing” noise….
fuck it. i’ll just have grapefruit for breakfast. grapefruit resists abstraction through the intensity of its souring effect on the taste buds.
About Schroedinger’s Cat (and mind that I’m neither a physicist nor native English speaker, so the following will be garbled in two dimensions): try going back to when you were a kid, and dreaming of all that you could become later in life. An astronaut, captain, doctor, engineer, vet, whatever your dreams were – they all still seemed possible. Later, of course, the road would narrow, and now you’re only one of those, or something else entirely – but back when you were seven they were all still possible, kinda like a cloud of possibilities in your future, and only time resolved that cloud to one single state only. That’s pretty much what Schroedinger’s poor cat is about in my understanding: there’s this cloud of possibilities hanging in that box, and only by opening it will you change the superposition into one outcome only.
Now if you want someone to explain parallel universes, please ask the pros here – the above is pretty much the end of my understanding’s rope. :)
Because they need grants and they dont understand string theory?
BTW, if you really want to visualize 11 dimensions, first you need to acquire a Tardus…
(sorry, I missed the edit window for above post)
@Mjaum: Yup, I remember when I finally understood what was the sound of one hand clapping after my years of schooling, er meditation.
I thought Pavlov’s dog ate Schroedinger’s cat. Kind of like the Prometheus myth. Each day conditioned behavior eliminates possibilities altogether. Speaking of cats,
Tunch is in ur dimension, eaten ur grapefruit.
Nihil in intellectu quod non fuit prius in sensu.
“Aristotle holds that thought is dependent on imagination, and hence on perception: phantasms are, or represent, or accompany, the objects of thought, and we cannot think without phantasms. Since phantasms are the traces of perceptions, it follows that we cannot think without having perceived, and that the scope of our thought is determined by the extent of our perceptual experience.” See Aristotelis De Anima.
@demimondian: Max Tegmark is a theoretical physiscist that thinks the metaverse is made of math.
@RadioOne: In the Black Hole War, Susskind (the father of cosmic landscape theory) talks about rewiring ones brain to accept non-intuitive mathematics….q-mathematics if you like. A good book for Cole to read, even it is dated by being written before Hawking recanted on the persistance of information in black holes. ( I can’t imagine Dr. Susskind mocking students.)
It is easier for some people to do this, and impossible for others.
A lot of literature described higgs boson as the “god particle” last year. Validating the standard model simply opens the door for the next step… for proving the existence of theoretical superparticles and exotic matter, things that are currently only described as mathematical theory.
Here’s one way to visualize 11 dimensions.
im so happy to be alive right now.
opening up physis review section D is like christmas morning.
damn good mr. jam
Perhaps the world’s a cube, or a tunnel, or a tube.
Darn it, someone already posted the “set n to 9″ joke.
John, if you want to stretch your mind out, you might want to try Eliezer Yudkowsky’s sequence of posts, once on Overcoming Bias, and now (since Robin Hanson has gone Full Choad) at his own place called Less Wrong. He describes rationality as a mental martial art in that traditionally, martial arts are not contests of strength but rather in proficient use of that strength, so rationality is not simply about high intelligence, but about the trained use of whatever intelligence you have.
It’s an interesting read; it’s difficult and long, but it’s broken into bite-sized pieces that follow each other. Plus, at one point he writes about visualizing n-dimensional spaces.
@John O: When cosmologists talk about the observable edge of the universe, it’s generally understood that this is very likely to be a tiny portion of the universe as a whole. There’s no direct way of knowing how big the entire universe is, since by definition we can’t observe it.
So far as I can tell from a cursory bit of reading, if you were to keep going in one direction (assuming an imaginary universe which wasn’t expanding or contracting, and a very good set of running shoes), you’d come back to where you started–like walking on the surface of a sphere, in that it has a finite surface area, but no actual edges. The only reason we don’t see repeating patterns in the backround radiation is because the section of the universe we’re causally connected to (i.e., that we can in any way affect or be affected by, a sphere 93 billion light years in diameter) is, in the scheme of things, a tiny part of the whole.
I think it’s been said – nobody really intuitively understands (post-classical) modern physics. They are just better or worse at working through the math and making predictions, and this can be a convincing simulation of understanding.
jake the snake
FTW. I think you win the thread.
@JBerardi: Not like trying to imagine new colors. A bit more like trying to imagine HEARING colors that have never been seen.
I had a similar “does it make sense to have to prove that something is ‘obvious'” moment in college. I was v. stoned at the time, so it struck me as a profound insight. As usual.
Re color, reflectivity,etc.–Surely those aren’t dimensions. They’re properties.
BTW, for a good sound thrashing vis a vis entropy, check out From Eternity to Here, by Sean Carroll, just being published. Beautifully and amusingly written, about the arrow of time, grounding its irreversibility in entropy.
Strange as it sounds, the process of learning these things re-wire your brain to the point where slowly but surely, the most dense and impenetrable concepts CAN be grasped by the human brain.
Trust me – I got a B in Differential Equations as a final grade when I had a 22 on my mid-term. And if I can grasp DiffEQs…ANYONE can grasp ANYTHING.
…not sayin it ain’t painful as all hell…
And by the way, speaking of Susskind:
Thanks to all for not (yet) invoking the Holographic Principle, or Model, or whatever the hell it is. Ie, that our entire universe is a holographic projection from a higher-dimension. I read his The Cosmic Landscape and deeply, deeply do not understand this notion.
Just read this comment – we are approaching a nearly Wonkette Level of snark here. We need to tone it down. If Lord Murdoch makes John “an offer he can’t refuse.” (funny I originally typed “reduced”) – Where will we go then? Sometimes you just want to stay under the radar. Of course then you hit a tree and crash and burn, but nobody said being a Liberal, Socialist, Kenyan Muslim was going to be easy, did they?
I’m not a physicist either.
The 4th dimension, time, would be hard to show on a blackboard. Maybe as series of snapshots?
For #5 I picture mass, how each body of mass warps space / time around itself, like the images I’ve seen of a ball pushing down on a trampoline net.
So #1-5 I can do pretty well. #6-8 anyone?
@Tom: Time dilation (the fancy physicist way of saying it) is a direct consequence of light always moving at the same speed in every reference frame. There’s also time dilation due to gravity, but that’s not as easy to understand.
Picture a clock that is made of two mirrors and a ray of light. Every time the ray goes from one mirror to the other and back, that’s one second (and we know the speed of light, c, pretty well, so we could tell you how far apart to set the mirrors). Now put one of these clocks in motion, while keeping another one in place. If you’re traveling with the moving clock, it looks like its standing still, and dutifully counting off the seconds. However, if you’re standing still, the clock moves some distance laterally while the ray is in motion, so it covers a larger distance than the original, stationary clock. Since light moves at the same speed, a “second” for the moving clock is slower than a second for the stationary one (and vice versa, since an observer moving with the clock sees the other clock in motion). If you work out the math, which isn’t any more complicated than the Pythagorean theorem, you even get the right factors.
@ Howard Y
Thank you. That mirror illustration may not be original, but it’s the first time I have finally understood time dilation, and how it is predicated on the fact that the speed of light is a constant.
Now if only I can start to grasp how mass increases toward infinity as velocity approaches c, I’ll know everything.