A while ago I was writing a sequence of articles — interrupted for some weeks by all the hullabaloo over Higgs particles and all the noise about neutrinos — concerning the possibility that the world has more than the three spatial dimensions that are obvious to us. These “extra” dimensions seem to be very confusing to non-experts, so I’ve been trying to find a way to make them seem a little less strange. We’ll see if I’ve succeeded. Building on my articles describing some types of worlds of 1 spatial dimension and of 2 spatial dimensions, I’ve now written an article giving one type of example of an “extra” dimension. Other articles to follow over coming weeks will provide other examples of extra dimensions, as well as an attempt to explain how scientists can potentially look for evidence of an extra dimension.
A Bit More About “Extra Dimensions”
POSTED BY Matt Strassler
ON 01/06/2012
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13 Responses
Sergei Petrov, sorry for offending you with my comments. I did know that my second comment is a bit over the line as a comment. Thanks for Matt’s tolerance.
To Tienzen (Jeh-Tween) Gong:
If you strongly believe in your ideas, perhaps you should start your own blog. Otherwise, please, take pity on those of us who come to this site to hear what Matt has to say.
And Id like to throw my 2c on this:
Quoting Tienzen (Jeh-Tween) Gong
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“However, your example of boat/canal has hinted that consciousness could be a necessary gateway for the manifestation of an extra dimension”
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My interpretation of Matt’s example with the quasi 1D is totally different then yours. No “consciousness” is needed for the extra dimension to manifest itself. It is intrinsically manifest in the region where it’s physics is relevant. It doesnt need superior mammals to manifest itself, no more than gravity needed us to keep Earth in orbit around the sun. If it’s there, it’s there, regardless if the universe is populated by amoebas or by animals with a sufficiently developed frontal cortex to build a particle accelerator, which may one day allow then to infer it;s existence.
Ok,ok — let’s keep on the narrow path here. Consciousness is ONLY necessary here in illustrating that in developing a picture of the world it is possible to make a mistake, in which one’s brain is led to think that the world has fewer dimensions than in actually has.
But consciousness has NOTHING to do with the geometry of the world itself!!!
I’m just trying to explain why you might think the world has three dimensions whereas in fact it might have four or five or ten or twenty-six.
I’m now sorry I introduced consciousness so cavalierly into the article. Clearly I did it poorly and I’m going to have to rewrite it.
Matt, in my opinion your article is very well written and it doesn’t need a rewrite. It is perfectly readable and it is not ambiguous. I see that I made a mistake not quoting Tienzen (Jeh-Tween) Gong in my first reply. My query to define consciousness and intelligence and how can be “dimensions” where addressed to him not to you.
Hi Tienzen,
it`s the first time I read about such “life dimensions” here from You, so this concept seems a bit strange or “esoteric” to me …
Is it right that the total of 11 dimensions with 7 extra “life dimensions” has nothing to do with M-theory and the corresponding 7 extra “space dimensions” and the agreement of the numbers is just a coincidence?
Umm — all I can say is that I have no idea what Tienzen is talking about. I have never heard of any of these concepts in any scientific context.
Ok, so I`m not the only one …
Ok, you throw away terms like “consciousness” and “intelligence” without carefully defining them. What the heck are “consciousness” and intelligence ? What do you understand them to be ? And how could them be “dimensions” of anything ?
Read carefully: neither consciousness nor intelligence are defined, in the text, to be “dimensions”. Indeed they are NOT dimensions. The directions across, along, and down into the canal are the dimensions.
Consciousness and intelligence are important, however, in discussing extra dimensions, because extra dimensions are intuitively confusing to most people. Through our experience, we all grow up believing the world has three spatial dimensions, the ones we can see in, move around in, and conceive of in our minds. If in fact the world has four or even more dimensions, it is important to understand WHY we believe something about nature that is actually wrong.
If we were not conscious and intelligent, we would have no picture of the world and there would be nothing to discuss. All science is done by conscious intelligent creatures, and much of science is about learning how and why our brains’ view of the world is mistaken.
This dimension issue is the rock bottom foundation for physics. When how many dimensions this universe has is known, the physics will be complete.
Of course, what is dimension? And, what are its attributes? What those attributes got to do with the universe?
First, we should look what are already known.
1. In 1870s, Georg Cantor proved that every n-dimensional space can always be brought into a one-to-one correspondence with the one dimensional line, that is, one dimensional line can give rise to n-dimensional space.
2. This dimensionality issue can also be understood with fractal geometry. In fractal geometry, there are many space-filling curves, an infinite number of them to be exact. With the Hilbert space-filling curve, it crosses every point on a plane without crossing itself, that is, a two dimensional plane is reduced to a one dimensional line.
From two facts above, all high-dimensions can always be reduced to one-dimension.
Your explanation about dimension is truly inspirational, especially for the spatial dimension in terms of physics. However, we should look the definition of dimension in a bigger scope, in general term.
New definition: If “all” information of system B can be “wholly” described with n codes, then system B has n dimensions.
The above definition is a linguistics definition. Yet, it is similar to the base-dimension of a vector space, and it is in line with your saying, Matt: “A location inside a two-dimensional space is specified by two pieces of information.”
With this new definition, the entire world must change.
1. Regardless of how many physical dimensions it has, the entire computable world has only two-dimensions, as it can be wholly described with two codes (such as, [0, 1]). This is guaranteed with the Two-code theorem of mathematics.
2. The outer surface of a ball has 4 dimensions, guaranteed with the four-color theorem.
3. The outer surface of a torus has 7 dimensions, calculated by the edge-equations or the Heawood Conjecture.
Then, how many dimensions does the non-computable world have? If we know how many dimensions the infinity has, then the physics will be complete.
With this new definition, the consciousness and the intelligence could be dimensions, even the dimensions for the non-computable world. Of course, this statement will make a wonderful day for the crackpot callers, and they will reach their ecstasy on this.
However, your example of boat/canal has hinted that consciousness could be a necessary gateway for the manifestation of an extra dimension although the consciousness itself might not be a dimension.
I wrote a blogpost about this some time back. Maybe you find something useful in it, e.g. figures or links etc.
Indeed this is a nice post, though it is oriented toward aspiring physics undergrad and grad students more than for the general public.