forcing everything metal to shine
September 10, 2018 6:57 PM Subscribe
Can you help me think through my misinformed idea/question re: how the 4th dimension would manifest in 3d/ours, and what implications that has for being alive?
(I'm like 80% sure there are some huge glaring holes in my logic. Also, upon reread, I may just be paraphrasing the plot of Interstellar.)
First off, I came across a video this weekend about extrapolating what we know about perceptions of three-dimensional objects in 2D planes to imagining how four-dimensional objects might manifest in ours. First question: is this person's basic reasoning sound?
I had a strong reaction when I watched this. I guess I've been thinking about death and temporality a lot lately (not in a bad way). And I wondered, if the span of a living creature's life - both in terms of time, and also in terms of the growth and death of physical embodiment - be in itself the trace of a 4D object passing through a three-dimensional space (our universe)? I was thinking about his various ways in which a 2D-plane-bound witness would be unable to comprehend aspects of the structure and nature of a 3D object, and it seemed, transposed to our dimension, such an apt and lovely way to think about how we are limited by space and time in our experience of each other/the world/our lives. I suppose what this might imply, for me, is that the concept of "a larger existence beyond the constraints of space and time" which we often think of in metaphorical/religious terms could be in a sense a property of living within one mode of dimensionality, and at least reasoned towards/imagined about even if we lack the tools to perceive it.
I suppose my question is, presumably some of these ideas I'm sort of invoking have a longer history within math/philosophy/etc. Are there any concepts I could research or learn more about that might sort of follow this tangent? Are there any sort of hard fallacies that it would come up against at once? And also, the video focused on a few experiments that would reveal the limitations of perspective on the 2d plane. Of course these experience hinged on having that additional dimension that was inaccessible to plane-dwellers. But are there any known or theorized experiments that could get at glimpses of what might exist in four dimensions, from our vantage point in the third?
(I'm like 80% sure there are some huge glaring holes in my logic. Also, upon reread, I may just be paraphrasing the plot of Interstellar.)
First off, I came across a video this weekend about extrapolating what we know about perceptions of three-dimensional objects in 2D planes to imagining how four-dimensional objects might manifest in ours. First question: is this person's basic reasoning sound?
I had a strong reaction when I watched this. I guess I've been thinking about death and temporality a lot lately (not in a bad way). And I wondered, if the span of a living creature's life - both in terms of time, and also in terms of the growth and death of physical embodiment - be in itself the trace of a 4D object passing through a three-dimensional space (our universe)? I was thinking about his various ways in which a 2D-plane-bound witness would be unable to comprehend aspects of the structure and nature of a 3D object, and it seemed, transposed to our dimension, such an apt and lovely way to think about how we are limited by space and time in our experience of each other/the world/our lives. I suppose what this might imply, for me, is that the concept of "a larger existence beyond the constraints of space and time" which we often think of in metaphorical/religious terms could be in a sense a property of living within one mode of dimensionality, and at least reasoned towards/imagined about even if we lack the tools to perceive it.
I suppose my question is, presumably some of these ideas I'm sort of invoking have a longer history within math/philosophy/etc. Are there any concepts I could research or learn more about that might sort of follow this tangent? Are there any sort of hard fallacies that it would come up against at once? And also, the video focused on a few experiments that would reveal the limitations of perspective on the 2d plane. Of course these experience hinged on having that additional dimension that was inaccessible to plane-dwellers. But are there any known or theorized experiments that could get at glimpses of what might exist in four dimensions, from our vantage point in the third?
From a brief glance at the video it seems reasonable, yes.
One thing worth realizing is that space dimensions and time dimensions are fundamentally different from each other in physics (in fact, special relativity says that a time dimension is like multiplying a space dimension by the square root of -1!), so any attempt to swap them with each other (e.g., "time is really just a fourth spatial dimension and we're seeing a 3D cross section") is going to run into mathematical problems fast.
You might be interested in Flatland, which I assume inspired the video (he may have said so at some point - I just took a few peeks).
posted by dfan at 7:20 PM on September 10, 2018 [2 favorites]
One thing worth realizing is that space dimensions and time dimensions are fundamentally different from each other in physics (in fact, special relativity says that a time dimension is like multiplying a space dimension by the square root of -1!), so any attempt to swap them with each other (e.g., "time is really just a fourth spatial dimension and we're seeing a 3D cross section") is going to run into mathematical problems fast.
You might be interested in Flatland, which I assume inspired the video (he may have said so at some point - I just took a few peeks).
posted by dfan at 7:20 PM on September 10, 2018 [2 favorites]
Charles Jencks has had a good go at the 4th dimension in his Garden of Cosmic Speculation. There are other things there besides time but the Cosmos and deep time is the focus - here's another look at the garden on someone's blog.
the trace of a 4D object passing through a three-dimensional space - I think Turing may have explored this area but in terms of animal form - link to my reply to a mefi post a while back re self organized systems - has a Turing book link.
Forgive me if I've taken an odd tangent away from your question
posted by unearthed at 11:07 PM on September 10, 2018
the trace of a 4D object passing through a three-dimensional space - I think Turing may have explored this area but in terms of animal form - link to my reply to a mefi post a while back re self organized systems - has a Turing book link.
Forgive me if I've taken an odd tangent away from your question
posted by unearthed at 11:07 PM on September 10, 2018
I wondered, if the span of a living creature's life - both in terms of time, and also in terms of the growth and death of physical embodiment - be in itself the trace of a 4D object passing through a three-dimensional space (our universe)?
You could certainly conceive of it that way.
Having done so, though, you're pretty much forced to conceive of the universe itself in the same way, because you need somewhere for your proposed 4D object to be. Then comes the thorny issue of working out the relationship between your proposed conceptual 4D universe, your perceived 3D universe, and the notion of time.
Personally I'm least uncomfortable with a 4D model of the universe where time is one of the dimensions, and the rules for measuring distances between points in that universe mean that you have to multiply any distance measured along your local time axis by the speed of light times the square root of -1 in order to get meaningful results.
The obvious advantage of this model is that it actually yields useful, verifiable predictions. The obvious objection is that multiplying any real number, like a distance or time measurement, by the square root of -1 yields a result that's impossible to visualise; but this is not a strong objection, since 4D models are in and of themselves impossible to visualise in the first place. All we can ever actually visualize is samples of their behaviour.
The way I figure, if I'm going to go through the mental gymnastics required to posit a 4D model of any kind, I'd rather work with one that's useful than one that's intuitively appealing, on the basis that any 4D model that is intuitively appealing is probably being thought about wrong from the get-go.
I also find it important to maintain the distinction between this conceptual 4D model and the observational 3D + time model that my brain constructs for me automatically. Failing to do that leads down an unproductive spiral of speculation into the "real" nature of time, involving endless talking-past arguments about causality and the apparent failure of the conceptual block universe to support the concepts of time, movement and change in any appealing fashion.
That said, if you forced me to nominate a personal position on the philosophy of space and time I'd be more likely to identify as an eternalist than anything else; I'm more comfortable with the apparent paradoxes inherent in that view than with those inherent in others.
posted by flabdablet at 3:00 AM on September 11, 2018
You could certainly conceive of it that way.
Having done so, though, you're pretty much forced to conceive of the universe itself in the same way, because you need somewhere for your proposed 4D object to be. Then comes the thorny issue of working out the relationship between your proposed conceptual 4D universe, your perceived 3D universe, and the notion of time.
Personally I'm least uncomfortable with a 4D model of the universe where time is one of the dimensions, and the rules for measuring distances between points in that universe mean that you have to multiply any distance measured along your local time axis by the speed of light times the square root of -1 in order to get meaningful results.
The obvious advantage of this model is that it actually yields useful, verifiable predictions. The obvious objection is that multiplying any real number, like a distance or time measurement, by the square root of -1 yields a result that's impossible to visualise; but this is not a strong objection, since 4D models are in and of themselves impossible to visualise in the first place. All we can ever actually visualize is samples of their behaviour.
The way I figure, if I'm going to go through the mental gymnastics required to posit a 4D model of any kind, I'd rather work with one that's useful than one that's intuitively appealing, on the basis that any 4D model that is intuitively appealing is probably being thought about wrong from the get-go.
I also find it important to maintain the distinction between this conceptual 4D model and the observational 3D + time model that my brain constructs for me automatically. Failing to do that leads down an unproductive spiral of speculation into the "real" nature of time, involving endless talking-past arguments about causality and the apparent failure of the conceptual block universe to support the concepts of time, movement and change in any appealing fashion.
That said, if you forced me to nominate a personal position on the philosophy of space and time I'd be more likely to identify as an eternalist than anything else; I'm more comfortable with the apparent paradoxes inherent in that view than with those inherent in others.
posted by flabdablet at 3:00 AM on September 11, 2018
Also vitally important to armour one's thinkamus with a prophylactic dose of The Tyranny Of Words before launching into any of these areas of speculation. It doesn't do to take them more seriously than they deserve.
posted by flabdablet at 3:06 AM on September 11, 2018
posted by flabdablet at 3:06 AM on September 11, 2018
There's a famous quote from Einstein, which he wrote in a letter of condolence to the family of a deceased friend:
You can read a bit more about this idea in this article on Forbes (originally from Quora.)
posted by Johnny Assay at 4:39 AM on September 11, 2018
Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.What he's saying here is that in a 4D view of the cosmos, the "past" is no more or less "real" than the present or the future, just as the bottom of a tower is no more or less real than the top.
You can read a bit more about this idea in this article on Forbes (originally from Quora.)
posted by Johnny Assay at 4:39 AM on September 11, 2018
Flatland might be a fun read for you, although it's physics (and metaphysics) come with a heavy dose of Victorian social satire
posted by parm at 5:52 AM on September 11, 2018
posted by parm at 5:52 AM on September 11, 2018
You might consider the Rudy Rucker book Spaceland, which involves 4-dimensional beings that manifest in 3-dimensional space.
posted by slkinsey at 7:26 AM on September 11, 2018
posted by slkinsey at 7:26 AM on September 11, 2018
Oddly enough, there's a lot about this in James Gleick's Time Travel: A History. A good read in general. Also, if you're thinking about death and consciousness, I would highly recommend Douglas Hofstadter's I Am a Strange Loop.
posted by rikschell at 9:04 AM on September 12, 2018
posted by rikschell at 9:04 AM on September 12, 2018
This thread is closed to new comments.
posted by bonobothegreat at 7:06 PM on September 10, 2018 [1 favorite]