## A Critique of “Imagining the Tenth Dimension”

Recently I saw a video called *Imagining the Tenth Dimension* (there is also a part 2). I suggest that you watch the video before reading this post. If you can get past the annoying sound effects, it’s actually pretty entertaining.

The beginning of the video is perfectly acceptable; it discusses some widely-known ideas popularized by Edwin Abbott’s Flatland.

The first problem is that this video assumes that time is the fourth dimension. Well… not really. Space and time are not actually dimensions, but rather are constructs that can be represented as dimensions. A dimension is simply a range through which something can change. In a square, you can either move up and down or you can move left and right; hence, two dimensions. Time is one-dimensional, as you can only move forward or backward (in practice you cannot move backward, but that’s irrelevant in this case). Dimensions can also be represented in other ways. Images of the Mandelbrot Set, for instance, often represent a third dimension using color rather than depth, because color is more convenient in that case. But it could just as easily be represented using depth, or time, or even something else.

A dimension is a mathematical construct. Space is not three dimensions. Space *has* three dimensions; that is, it’s three-dimensional. To say that time is the fourth dimension can be useful sometimes, but it is not inherently true. The only reason time is the fourth dimension is because we say it is. The fourth dimension could be saltiness, for instance. That may seem counter-intuitive, but think of it this way. A dimension is something that you can change though. Your geographical location can change, and we call this a dimension (actually, three dimensions). But your saltiness can also change. You can become more salty or less salty. If you place saltiness values on a line, you can even represent saltiness using a spatial dimension. In fact, we often represent other dimensions in two spatial dimensions by using graphs.

There is nothing wrong with representing the fourth dimension with time; but there *is* something wrong with assuming that time is the *only* way to represent the fourth dimension, which is exactly what this video does.

The next problem is a good deal more serious. After five minutes, the narrator states,

The long undulating snake that is us will feel like it is moving in a straight line in the fourth dimension, but there will actually be in the fifth dimension a multitude of paths that we could branch to at any given moment.

Wait, hold on. How did the fifth dimension get in there?

To be able to have a multitude of paths through time, we do not need five dimensions; we still only need four. Think about Flatland. A Flatlander can get a sense of us when we pass through the second dimension. But it can get a different sense of us if we pass through while walking sideways rather than forward. It can get a completely different sense if our friend passes through the Flatlander’s space. The Flatlander can see a multitude of paths branching out, but only needs three dimensions to do so. Similarly, we would not need five dimensions to see all the branching paths of time — only four.

At five minutes and thirty seconds, there is a reference to quantum physics which is used as some sort of completely unnecessary metaphor which only seems to serve to make the video seem more strange and interesting.

At 6:40, the narrator proposes yet another unnecessary dimension. For this one, remember the analogy of the Möbius strip. Your own timeline is like a two-dimensional strip of paper, except that it is in four dimensions. To visit your own past, you can wrap the paper around itself through the third dimension, forming a Möbius strip. To visit an alternate timeline, you do not need another dimension; you only need to attach your current strip of paper to a different strip, one that contains the timeline of preference. This means that we do not need six dimensions, nor do we even need five; we still are good enough at four.

If you are following along on YouTube right now, please go to the next video.

As soon as the second video starts, it attempts to compress three dimensions into a single point. You’re not allowed to do that. The fourth dimension does not join the Big Bang to one of the possible endings of our universe; rather, that is what our particular cross-section of the fourth dimension does. The fourth dimension is capable of containing all possible timelines; but we are not able to simultaneously perceive them all.

Now, as we enter the seventh dimension, we are about to imagine a line which treats the entire sixth dimension as if it were a single point. To do that, we have to imagine all the possible timelines which could have started from our Big Bang joined to all the possible endings for our universe (a concept which we often refer to as infinity) and treat them all as a single point. So for us, a point in the seventh dimension would be infinity.

All right, now the author of this video clearly has no idea what infinity is. Infinity “is an unbounded quantity that is greater than every real number.” The number of possible points along one dimension is not even infinity, but is aleph one. The number of points in two dimensions is also aleph one — they have the same cardinality. In fact, the number of points in any number of dimensions (greater than zero) will always be aleph one.

What the author is calling “infinity” really refers to everything that can possibly be perceived by humans. And, if I may point out, we’re still not in seven dimensions. We’re only in four.

But if you think about it, the first sentence of my last paragraph is actually not true. We are capable (in theory) of perceiving infinitely many degrees of saltiness; these cannot all be represented in four dimensions. It would require adding a fifth. The same logic applies to the other four tastes, as well as to the three colors of light, every volume and pitch of sound, and every other thing that we are capable of perceiving. By the time you’ve added these all up, there are more than a dozen major dimensions, as well as at least a hundred less noticeable ones.

The video goes on to propose that the set of possibilities stemming from our Big Bang is only one infinity. There are other infinities resulting from other initial conditions. The problem with this, though is that having these two infinities does not necessitate another dimension because adding two infinities results in the same infinity.

At this point, you should watch up to 2:00.

If we’re really talking about adding other initial conditions, though, then we’d end up with a lot more than eight dimensions. We would need one axis to cover all the universes with different speeds of light; an axis for all the universes with different gravitational constants; all the universes with different fundamental forces, different types of particles, the list goes on and on. So either we are in four dimensions, or way too many to count, depending on how you look at it. But we are certainly not in eight.

The tenth dimension, which is introduced at around 3:30, is just absolutely ridiculous. The author keeps extending dimensions further and further when all we really need is four. He claims that there is “no place left to go” after 10 dimensions; hmm, according to this author’s perverse logic, wasn’t that true after seven?

The reference to string theory near the end is essentially the same as the reference to quantum mechanics: only in there to sound cool, and without any relation to the actual content of the video.

Before I wrap up, allow me to get in one final point. Mathematics has no problem with defining *however many dimensions it wants*. These dimensions are not spatial; space is merely a way to represent these dimensions, albeit only three of them. There is absolutely no reason to be limited to ten dimensions (or rather, four, as I have demonstrated). But remember, no matter how many dimensions you are using, you can’t cover any more ground. You’re still looking at aleph one points.

Maybe you watched that video and thought it was amazingly cool, and I have just crushed your dreams. But there are plenty of mind-blowingly cool things out there that *don’t* rely on lies and pseudoscience. If your mind is blown by a lie, is it really worth it?

Have you ever heard of a movie called What the Bleep Do We Know? Man… If you htink this youtube vid is bad, just watch that video.

So just to make sure I got this right, time is not actually a form of space? Cause that’s what I always thought they were saying…

They were sort of equivocating time with space. What I’m saying is that they are not the same; rather, they are both ways to represent dimensions.

One more thing: they were trying to expand time to more dimensions by bending it, but you can only do that with space.

Dear All,

If that author says time is like a 2 dimensional strip and we can fold it to get back

to our past……….. its stupidity…. as we are in between time and as there is no

end strip of time…. because time will continue forever… we should think another way

may be the answer lies in anti-matter to be used to open worm hole in another time space..

what do you say…. ?

But it is still possible to fold and attach a part of the string to the other without using the end point of the sting or if that string has no end points at all.

Than you for writing this. I just watched his video, and was greatly annoyed by it. Especially by the bogus representation of string theory, which he obviously doesn’t understand. But it’s pretty hard to write a good rebuttal confined by youtube’s character limitation. I trust you won’t mind if i leave a comment linking to this in the video.

I don’t mind at all. Quite the contrary: I appreciate the attention. I’m glad you found my essay valuable.

I also wrote two additional posts on the same subject, in case you haven’t seen them already: https://mathematicalmulticore.wordpress.com/2010/04/23/four-dimensions-a-simple-proof/ https://mathematicalmulticore.wordpress.com/2010/04/24/four-dimensions-objection-refutation-objection-refutation-confusion/

At first I tought that saltiness, temperature, pressure etc. are another dimensions, but they are not. They are something else, because for each point in temperature dimension there is many unique points but not all, that exist in the 3+1 dimensional space.

Such like temperature, wind velocity are fields – scalar or vector fields. They are some values that are defined for all points in spatial and/or temporal space.

In other words, temperature or saltines may be a function of 3D, 4D or whatever-D space (for each point in space there is exactly one value) but the inverse relationship does not hold : space is not a function of temperature ( because for a given temperature ther may be many areas of space).

I agree that we can think of as many dimensions as we want, and also, that the video cited looks like a pseudoscience to me too. But please do consider distinguishing between dimensions and fields.

The only thing is though ya can’t just criticize without offering better (in terms of understandability), many many people are often in many many states of misery and ignorance “understanding” causes typically good sensations which are highly valuable, thus if yer going to criticise then it’s necessary to offer a better-explained alternative or else you’re just talking to people who already understand. If you want to be a scientist and not a humanist fair enough just don’t expect that those you see in front of you in Univ. lectures represent a typical demographic (which includes the majority), because it doesn’t and alas, as cumbersome as it might be, that’s where the real change in understanding needs to occur. I see how Bryanton’s videos are wrong — now — yet it caused me to start a good journey of discovery which wasn’t caused by you for example, in this subject specifically. Indeed you may not have had the time and calling, fair enough, but someone needs to cause just moaning about it won’t get far at all.

My understanding is that he used the word “imagine” as his title and repeated over and over again, this is an “idea.” – He wanted to summarize what physicists have postulated as food for thought. Some of these physicists I’m a fan of and some were knew to me and excited me to read their books.

I disagreed strongly with the duality in the mind idea, because I don’t believe in metaphysics. Because, metaphysics falls under the superstition umbrella. You can’t measure fiction. Therefore, if I were the author of this project, I would have left metaphysics out of it. Otherwise, I found his ability to visualize what may or may not be real, rather entertaining.

You don’t seem to have any idea what metaphysics is. It has nothing to do with superstition, and it does not involve “belief” at all. It’s simply the word we use to describe discussion about what it means to exist. Probably every human ponders this at some point in some way or another, and people come up with lousy answers and lousy support for them, but that isn’t relevant. In its academic form, metaphysics is made up of rigorous arguments, not superstition or belief, and these arguments are regularly scoured in peer review for any errors in logic, and viciously torn apart if they are found. This is not a field of study you can merely handwave away.

Hi. I’m a physicist. I would love to agree with you, but no. It does have a lot to do with belief. If nobody agrees with you, you’re crazy until people do. This is why when you give your thesis for a doctorate, you try to give analogies and examples that the audience can relate to. The reason behind this is simply because the audience, no matter what university you’re in, is probably not studying what you are. A visualization, even if a little skewed, is a wonderful thing to help others know what you mean. We don’t just look at equations and automatically think that it deserves an award. Take for example Einstein with this Theory of Relativity. Nobody believed him for the first decade or so that it was published even though it was correct. We live in a world where correct is not always what’s best, and the fact that you believe that the science community is untainted by this is wonderful and all, but it implies you’re not so deeply connected to this.

Well Michael, how wonderful. Your dry and curmudgeonly academic breath is so welcome and needed. We who do not perceive mathematics easily still have the desire to pursue the unknown in ways that we can see. Your academic usage of the word “perverse” to describe a limit of perception must be a sort of antagonist argumentation tactic? You are jealous. How petty. Bryanton has struck a chord with many of us ignoramuses and it is your job to challenge the suppositions. You will find that your valid input is properly respected when you do so with a sense of the joy of discovery. Your pouting tone reminds me of Marvin the manic-depressive robot: “…well, ok, but you won’t like it.” I do truly thank you, but do try to bring the nose up.

Oh shut up, stop being such a pretentious douche.

And therein the circle of irony is complete.

Haha, yes it is. I agree this critique is nothing more than the same dry, antagonistic jargon that I’m sure the Wright brothers, Einstein and Newton have all had to deal with in their times. Bryanton very clearly and repeatedly notes that this is a method of visualizing and idea and in that, you don’t really have much credibility to criticize so matter-of-factly.

I have a degree in music from Berklee. If I heard someone playing a song they wrote at an open mic I would equate this critique to me approaching them and giving them an objective list of why their song is wrong (i.e. “because the subdominant V7 of ii that they used in their second verse does not resolve to a bIIImaj7”, or “there is no resolution to the tonic at the end of your phrasing in the verse”, etc.)

Just like mathematics, there are actual tangible rules to music. Regardless of the syntax you may be using as your medium: western, atonal, textural, microtonal or rhythmic, etc. or in mathematics: calculus, trigonometry and algebra, these rules may take a backseat to creative manipulation once the initial rules are understood. This is what makes good musicians. This is also what makes good mathematicians. Although you do seem intelligent, you obviously aren’t very fluent in the language of creativity. I would encourage you to put more energy into seeing what can be done rather than speculating than what cannot. Typically nay sayers are later in time redefined as “those who were’t intelligent enough to understand what was possible”. Don’t join them.

You’re obviously some kind of idiot. This video is only a VISUALIZATION of ten dimensions, not what they actually are. You also use analogies like “infinity” and the “Mobius strip” against him. THEY’RE JUST ANALOGIES. I own a copy of the book and this video opened my eyes to science and is the sole reason why I am so interested in modern science today.

So…it’s nothing?

If it’s only a ‘visualization’ without stating what they are, then they have no scientific or rational bound to them and are therefore random speculation.

Meaning, dropping words like quantum physics and string theory is a patently false thing to do, as they would have no correlation to the content being discussed.

I think you have an incomplete understanding.

None of what you’ve said delegitimizes these videos.

Provide counter evidence and support for it. Bryanton is a lot smarter than you… Sorry.

Could you explain in more detail why you don’t think my arguments properly address the flaws with the video?

you wrote:

|”There is nothing wrong with representing the fourth dimension with time; but there is something wrong with assuming that time is the only way to represent the fourth dimension, which is exactly what this video does.”

I disagree. Unsupported assertion. Please show your work.

you wrote:

” The Flatlander can see a multitude of paths branching out, but only needs three dimensions to do so. Similarly, we would not need five dimensions to see all the branching paths of time — only four.”

First, I don’t see how discreet instances of proposed individual 4D beings equate to multiple potentialities of each being. Your construct collapses into mixed metaphors.

Second, does string theory say that there is no need for a fifth dimension? It seems you take issue with the bigger theory. Please explain your position regarding string/’brane theories.

you wrote:

“To visit your own past, you can wrap the paper around itself through the third dimension, forming a Möbius strip. To visit an alternate timeline, you do not need another dimension; you only need to attach your current strip of paper to a different strip, one that contains the timeline of preference. This means that we do not need six dimensions, nor do we even need five; we still are good enough at four.”

What does the ‘different strip’ in your analogy signify? Please explain.

i could go on.

“I disagree. Unsupported assertion. Please show your work.”

From my understanding (correct me if I’m wrong), the problem with assuming that time is the fourth comes from the logical problem that assuming length, width, and height are the first, second, and third respectively and that there is an absolute order in which dimensions follow.

This can be easily shown by the simple question: which is the second dimension? Is it width, or is it height, or is it depth?

“First, I don’t see how discreet instances of proposed individual 4D beings equate to multiple potentialities of each being. Your construct collapses into mixed metaphors.”

Following the video’s logic, a 1D being can see left to right, and does not need an extra dimension to do so. From here on the logic follows that any extra dimension that a being perceives can be perceived fully while still in that dimension. The logic breaks down once you hit the 4th dimension because up until then, logic dictates that time being a dimension means that we can see past and future equally just as we can see length equally, depth equally, and height equally. He therefore needs to make a 5th dimension to compensate for the obvious fact that we cannot do this, and all subsequent dimensions need additional dimensions just to even completely perceive them.

You do realize each dimension has 2 directions, right? A 1D being can see left to right, but not in the directions perpendicular to that.

I’m might be wrong about this. I liked the video and also liked your critique, but I’m not an expert on any of this, just a Mathematics undergrad. I kind of get your point, but I have to ask about this part: “The problem with this, though is that having these two infinities does not necessitate another dimension because adding two infinities results in the same infinity.” How does adding two different infinities can result in the same infinity? I mean, if we are talking about numbers I’m pretty sure you know it won’t be the same infinity. It’s like saying all infinities are equal while you also say there are different infinities. If you add A + B it won’t necessarily result in A or B, it’s probably gonna be something else.

As I said before, I’m know nothing at all.

Some infinite sets are the same size as other infinite sets (e.g. the set of all integers and the set of all even numbers). See here for some basic information about infinite sets.

The video is titled ‘imagining’ 10 dimension, not ‘knowing’ 10 dimensions

Why do humans insist on confusing innate human comprehension with reality. Psycho-physics have very little relevance beyond human experience. We see three colors because of the way our rod/cone eye-brain system developed. The ‘color wheel’ and primary colors exist in our comprehension solely because of how we perceive and have no basis in reality.

Innate human comprehension is a rudimentary paradigm of reality.

Saltiness in a sensation that comes from how taste buds evolved and can only remotely be considered a dimension in the puny realm of human consciousness.

Learn to think beyond psycho-physics then we might figure out dimensions.

I did watch the video and I found numerous places where it makes ridiculous assumptions and oversimplifications but overall I think it is very thought provoking and I have a whole lot of areas to mull over in my mind both mathematically and philosophically. I think you are being a bit to harsh in your treatment of this video simply because it is a truly difficult topic to visualize and conceptualize and as an armchair physicist, I enjoy pondering the fundamental nature our universe and our role within it as sentient beings. The curvature of spacetime and time dilation and other bizarre relativistic predictions have all been verified by experimentation and observation and it takes a new perspective sometimes to see things in a new way to allow us to progress. Even college textbooks from a few years ago are full of half truths and simpflications due to our more limited understanding of string theory etc and so no matter what you read it should be taken with a proverbial grain of salt as another view of the great mystery.

Not totally wrong, but still wonky. Time actually is a spatial dimension. This is the essence of relativity. The part about other types of dimensions can be true still, but if width and height and depth are spatial dimensions with a special meaning, so is time. Not simply because we say it is like we might about saltiness, but because relativity shows that time is space in exactly the same way width is depth when rotated.

Thing is a dimension is indeed a construct. A variable in a system constitutes a dimension on its own within the system. For the rest you can play around, using simple ideas. Bryanston’s reasoning holds interest for me in the sense that it gives an interesting path to follow because it does give a simple (simplistic?) perspective on complex ideas (adding/folding/orthogonal dimensions), and as a physicist I wouldn’t dismiss it so trivially as I consider I can learn and imagine from it. I thank him for his efforts and will think about it in my own research endeavours, if/when need be.

I watched the video and as a physicist and lover of mathematics, I couldn’t believe such nonsense. I searched for “critics to n-th dimensions” and I found this video. The following points, I wrote them BEFORE reading this article.

—————————————

I’ve been there. But after years, I find these are pure manipulations of concepts. This is not as “deep and profound” it might look at first sight. Let’s look closer to this:

1. We never “imagined” 10th dimension, only discussed the theoretical consequences of it, based on rules of the first two dimensions. But n-th dimensions is an abstract concept perhaps born in descriptions such as linear algebra and set theory, only for combining sets. These guys are getting lost in such descriptions, giving the representation more power than it should have. I’ve been there.

2. Imagining time like this has some contradictions. For example, if you were to travel in time and afterwards then realize you are watching yourself with another age, that would mean being on two different coordinates of one dimension simultaneously, something that wasn’t a concept of the first three dimensions.

3. Time has been supposed “coexistent” for every “imaginary creature of 1st and 2nd dimensions”, it is present with them, so they can “walk”. And the inventors of this absurde speech of n-th dimensions suddenly take time apart, but in the prior sceneries no dimension was simultaneously involved with the other.

4. Let’s don’t forget history. Cartesian dimensions were invented as a representation in order to DESCRIBE a position in plane and then in space. For making a better description, the REPRESENTATION was built such that time could be a 4th coordinate. There are other ways to build the first three coordinates, for example cilindrical and spherical coordinates, which wouldn’t fit in this artificial description. All descripcions coincide in one point: there are needed 3 coordinates to locate a point in space as we currently know it. The 4th coordinate (time) adds a description to be more precise. But we could add another coordinate to make our description more precise, so we can know something more about our object, and then invent some mathematics to fit with this new coordinate.

These are CONSTRUCTIONS, let’s don’t forget that when listening to these stuff.

Those are very interesting points to explore. The only quibble is that you seem to dismiss the very notion of imagining the concept you discuss more formally.

I believe a certain amount of meaning is allowed-for, dictated, and limited-by form. Artist have been imaging implications of theory forever-ish

Enjoyed reading your reply Pedro. Interested pop-sci reader.

On Mon, Sep 10, 2018 at 9:15 AM Mathematical Multicore wrote:

> Pedro Montaño commented: “I watched the video and as a physicist and lover > of mathematics, I couldn’t believe such nonsense. I searched for “critics > to n-th dimensions” and I found this video. The following points, I wrote > them BEFORE reading this article. ———————-” >