This guy has written a series of books, all 99p on Kindle, on various scientific issues. Tony recommended this one.
Not really about three dimensions, but I liked this as a working definition of art:
According to Frank Wilczek, Nature's "artistic style" has two obsessions: Symmetry - a love of harmony, balance and proportion, and Economy - satisfaction in producing an abundance of effects from very limited means
He talks about how useful theories are, and that if a theory takes as long to express as the sequence of observations that it explains, it's not much use. A theory is good to the extent that it compresses the data into a much smaller set of theoretical assumptions. The greater the compression, the better!
He criticises the anthropic principle ("we happen to be in a universe with three dimensions because that is the kind of universe which supports our existence - there might well be lots of other types of universe with different physical laws which would not be amenable to our type of existence, but we wouldn't be there to see them") and says that I get the impression that anthropic theories .. are invoked when a problem seems so difficult.. that it's hard to conceive of any conventional analytical solution. Anthropic theories could then be thought of as "theories of last resort". However, I would suggest it is best never to resort to such theories.
I'm very much with him on this, but I can't quite get my
head round his attack on it (I wish I could):
For example, I could ask why the Cuban missile crisis did not
end in mutual assured destruction, with a nuclear conflagration that
desroyed the workd. If I felt sufficiently brazen, I could respond
that the answer is the anthropic priniciple. If a nuclear war had
occurred in 1962, my parents are unlikely to have met a decade later,
and I would never have been born in 1981. However, many would feel
that the fact that I am right now contemplating the marvel of my own
existence is not a satisfactory explanation for why Kennedy and
Khruschchev managed to avoid taking their respective nations to war.
Having said that, he goes giving some information on various topics before he actually explains why we must have three dimensions.
He talks about general relativity, which he gives explanations of, but which I found hard to follow. He works through several pages of equations that I didn't really grasp, and ends up saying And that's it! That is Einstein's equation for general relativity. And I don't think he's being ironic when he says it's simple. Maybe it's not phenomenally difficult, but I had trouble.
He mentioned the experiments to detect gravitational waves - I went to a talk in the library about this with Tony, so probably I'd heard this before, but it's still a pretty amazing statistic: As the gravitational wave passed through the Earth, it changed the length of the four-kilometre LIGO tube by just ten thousandth of the width of a proton, equivalent to detecting a change in the distance to the nearest star by the width of a hair.
There was a bit where he talks about the fact that we might be able to measure the difference in electromagnetic potential between two points even though we can't ever know the absolute electromagnetic potential of either of them, and this leads on to the idea that it may be there, but in a dimension that's hidden to us, where I thought "I almost understand that!"
He talks about string theory, which proposes 25 dimensions of space, and one of time. In introducing this, he demonstrates that the sum of the series 1+2+3+4...(forever) is minus one twelfth. You might find this hard to believe, but I can assure you that this is an established an accepted result in mathematics, and it was rigorously proved by.. Euler in 1749". Here is a link to a youtube video which explains it. Not sure I could follow this - it feels like one of those tricks where you "prove" that 1=2.
But he then ends sort of dismissing string theory: as a result, string theory has been criticised as being untestable. I thought "hang on, I've just spent quite a lot of time trying to follow all the arguments and maths here, and you're now saying I shouldn't have bothered?"
At the end, he explains how he's going to demonstrate that there are three dimensions, using a simple theory. So by this time, we've done some relativity and some string theory and have the basis laid for understanding his explanation.
I think, at the end, I sort of followed most of what he was saying, but I don't think I could now give a defence of the central thesis. Probably I need to read it again (knowing better now which bits I need to pay attention to).
The overall style was good - it was quite readable and enaging and he's an enthusiastic teacher. So I think I'd be prepared to try some of his other books.
Completed : 23-Dec-2018