I’m putting this here because I’m not convinced there is a factual answer.
So, what got me thinking about this was a documentary I watched some time ago about a group of people who could count to 3 or 4 and then it was just “many”. They had no concept of any distinct numbers above that in their culture.
Could humanity as a whole, be in a similar situation, at least superficially, regarding the 3D+time universe we live in? Meaning we are aware there is another dimension, we percieve it as time, but not as a distinct thing, we call it spacetime.
I just picked up Hawkins’ A Brief History of Time for a reread. I wanted to backtrace my sense that he had pushed away from the Big Bang.
That’s still the sense that I have. He seems to be saying that as you backtrack in time, the gravitational centrality of the universe makes quantum physics inescapable and (for reaons i did not follow) that means that instead of linear time we should think of time in two dimensions, real time and imaginary time, and as you go farther back there is more imaginary time in the equation and you never get back to a true singularity.
Meanwhile, I can’t mentally visualize a universe that is somehow shaped like a saddle and is infinite yet if you go far enough you get back to where you started. Sounds quite groovy but over my head.
There is more than one language that works like this. John McWhorter addressed this is one of his Lexicon Valley podcasts. It is not that the people do not have the ability to conceptualize larger numbers, it’s just that they have no use for it. Their lives do not involve large numbers of things that must be counted. IMHO you could teach them this idea in a few minutes and have them counting things.
Humans as a whole, OTOH, seem to have a common experience of how space and time work, which may be a little different than what mathematicians and theoretical physicists are able to describe abstractly. Sure you could teach an intelligent person the math, but it would change the day-to-day perception. (I have heard at least one person claim that he can mentally visualize 4D space but I have my doubts.)
Spacetime isn’t a cultural phenomenon. It’s math. There are many good reasons why a fourth spatial dimension doesn’t exist, except as one of a number of “hidden” dimensions in string theory. Orbits are not stable in four dimensions, for a start. Both mathematicians and theoretical physicists have worked intensively in analyzing higher dimensions for a couple of centuries. It’s not likely that anything comparable to the fourth dimension bandied about in sf and comic books can possibly exist.
For some reason, your post reminded me of this bit from Carr’s Uller Uprising:
Tense is applied to words used as nouns, not words used as verbs; there are four tenses—spatial-temporal present, things here-and-now; spatial present and temporal remote, things which were here at some other time; spatial remote and temporal present, things existing now somewhere else, and spatial-temporal remote, things
somewhere else some other time.
At the risk of hijacking, I think something like this happens when we count down:
2 things, 1 thing, nothing
Where because “nothing” is itself a noun in English, we get notions like “nothing is still something” and “demonstrate that nothing can exist” as well as the general idea of nothing existing being self-contradictory.
It’s all a bit of a misconception though, because “no-thing” is something of a special noun, that does not refer to a discrete entity in most contexts.
I’ve seen a few variants of this argument, and I wonder if you’re saying the right thing. These kind of arguments don’t convince me that a universe of four (or more) spatial dimensions could not exist. It only tells me that it’s probably a good thing that the universe we inhabit isn’t like that, or else we probably wouldn’t inhabit it.
I’ve seen arguments to the effect that if certain fundamental parameters or charges at the quantum level were just a little bit different, then life could never have evolved. In fact, quarks could never have stuck together to form protons or neutrons, and matter could not exist.
Imagine an entire universe full of pulsing quantum-level complex probability wave functions that can’t even form protons or neutrons let alone whole atoms. (Prof. Matt Strassler discusses stuff like that on his web site.) What a waste of a universe that would be.
And yet, for all we know, if there are multiple universes, ones anything like ours are quite probably the rare exception rather than the rule.
Hasn’t it been historically just the opposite? People have always perceived three distinct Euclidean spatial dimensions, and time was always seen as something entirely separate and distinct from space, and not as a “dimension” at all. Anything like a unified “spacetime” was unthinkable and unthought.
Only in recent history, since the time of Einstein, has there been the notion of something like a unified space+time, and even so it’s largely abstract and not the way most people typically “perceive” anything.
Even Einstein himself didn’t come up with the idea of unified spacetime. His 1905 paper of Special Relativity was not written in those terms. It was one of his professors, Hermann Minkowski, who first came up with the idea of a mathematical model that unified space and time, in 1908. Einstein didn’t accept that until some years later. From Wikipedia:
George Gamow tells this story at the very beginning of his book One, Two, Three, . . . Infinity (originally published in 1940-something, not 1988), Chapter 1, Page 1.
He tells the story of two uneducated Hungarians who could not count past three (Hungarians, apparently, being the butt of “stupid people” jokes in those days?) then tells of African tribes whose entire number system consists of One, Two, Three, Many. (IIRC, he names Hottentots specifically.)
He describes how these Hottentots could be taught to compare the sizes of larger sets (e.g., to determine who had the most cattle or wives) by placing the object in the sets in one-to-one correspondence until you run out of items in one set. Then the other set is the larger, even if both are “Many”. He then leads into Georg Cantor’s discovery of multiple “sizes” of infinity, as determined by attempting to put various infinite sets into one-to-one correspondence, likewise.
Well, in Russian, 2, 3, and 4 take the genitive singular, while 5–10 take the genitive plural, so clearly >4 is thought of as “many”. This is not something special Khoe thing (and such languages have plenty of numerals past 3, as far as I know(?), so what lexical point was he trying to make?). e.g. you may naturally think of pairs or triples of things, less often of 34-tuples.
This is interesting because I know that extra spatial dimensions are often proposed as one explanation for why gravity is so weak.
But this doesn’t seem to make sense on analysis; if gravity projecting into the 4th spatial dimension would not lead to stable orbits, then we can rule that out. Alternatively, if the 4th dimension is “wrapped up small”, my understanding is that gravity waves and gravitons would wrap around too, so it wouldn’t help explain the weakness of gravity.
So I guess either I’ve misunderstood something (most likely) or perhaps orbits are stable (or at least not ruled out as unstable), with >4 dimensions.
There seems to be a universal ability (called subitising) in humans to instantly judge the number of objects in a set, but it only works up to about 4 items. Beyond that you have to count. This probably explains the commonality in different languages of using ‘many’ for numbers beyond three or four.
All makes sense, but does that mean we can rule out additional dimensions where gravity propagates?
I guess one solution is if gravity propagates in the other dimension(s) (thus helping to explain the weakness of gravity) but matter is confined to the familiar 3 spatial dimensions. Thus all those gravitons and gravity waves are shooting off to never affect anything ever.
