[HN Gopher] What is the Fourth Dimension? (1884)
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What is the Fourth Dimension? (1884)
Author : drdee
Score : 25 points
Date : 2024-04-02 12:57 UTC (3 days ago)
(HTM) web link (en.wikisource.org)
(TXT) w3m dump (en.wikisource.org)
| dang wrote:
| Related:
|
| _What is the Fourth Dimension? (1884)_ -
| https://news.ycombinator.com/item?id=27329211 - May 2021 (45
| comments)
| NomDePlum wrote:
| Time: https://www.amnh.org/explore/ology/physics/space-and-time2
| nomel wrote:
| This is discussing a euclidian fourth dimension, not time.
| NomDePlum wrote:
| The cited article is speculating on what the Fourth Dimension
| is. I'm just pointing out that there is already an accepted
| answer to that.
|
| Nothing to stop others discussing the alternatives.
| qorrect wrote:
| That's Lorentzian geometry and Minkowski space from the
| 1900's and created for Relativity.
|
| This is Euclidian geometry, much older and more 'accepted'.
| r14c wrote:
| I imagine there would still be a relationship with `c` in
| a fourth spatial dimension, but it might be useful for
| taking shortcuts around 3d space without having to
| violate causality.
| NomDePlum wrote:
| I'm sure you are right on that.
|
| I'm going to have to plead ignorance on this. Which will
| likely not surprise you.
|
| I'll have more than the cursory read through the article
| in an attempt to educate myself.
| anthk wrote:
| https://www.sciencealert.com/light-speed-electrons-discovere...
| Synaesthesia wrote:
| I highly recommend a book called "Spaceland" by Rudy Rucker. It's
| like a modern take on "Flatland". In it a Silicon Valley hotshot
| gets visited by a 4th dimensional entity called Momo.
|
| He also wrote a book called "The 4th dimension" which explores
| the concept historically and in various ways.
| shagie wrote:
| For another take at trying to understand the 4th dimension -
| https://4dtoys.com ( 4D toys -
| https://news.ycombinator.com/item?id=17685858 592 points | 110
| comments)
| zen_of_prog wrote:
| Even better, 4D Golf was released a couple weeks ago [1]
|
| [1] https://store.steampowered.com/app/2147950/4D_Golf/
| roywiggins wrote:
| a personal pet peeve (brace yourselves, it's pedantry):
|
| Technically speaking, we're talking about _four dimensional
| space_. It doesn 't really make sense to call such a space "The
| Fourth Dimension", any more than real life space is "The Third
| Dimension", or a tabletop is "The Second Dimension". This
| sometimes trips people up into arguing over whether The Fourth
| Dimension "is" time, or whatever. For that matter, maybe the
| first dimension is time, and the second, third, and fourth
| dimensions are space. These things aren't ordered, and in fact
| you can't really distinguish between the three familiar spatial
| dimensions: imagine trying to point along _dimension one_ ,
| whatever that means.
|
| The familiar three-dimensional space as we know it is three
| dimensional because you can put three straight lines to meet at
| right angles to each other, and no more. And you can label those
| lines x, y, and z if you like and pick their orientation. Four
| dimensional space allows you to cram another in. Two dimensional
| space only allows two, and one dimensional space is just a single
| line.
| felipeccastro wrote:
| That's not pedantry, that's clarifying, haven't thought like
| that before. Thank you.
| munchler wrote:
| Meh. If a circle was able to escape Flatland by rising into the
| third dimension, how would you prefer to describe it?
|
| Similarly, if we were able to escape 3-space by moving into a
| 4th spatial dimension, what would you call it? If this
| hypothetical 4-space is Euclidean, then it contains exactly one
| dimension that is perpendicular to our familiar 3-space, so we
| would be perfectly justified in calling it The Fourth
| Dimension.
| roywiggins wrote:
| Fair, but two perpendicular Flatlands embedded in the same 3D
| space won't be able to agree on which is the fourth
| dimension. It's fine as a shorthand when Flatlanders talk to
| each other, but "the fourth dimension" still won't be an
| unambiguous direction, for Flatland A it's actually one of
| Flatland B's two dimensions, and vice versa. For us any
| dimensions perpendicular to the entire universe will be
| "special", but only for us. Native four dimensional critters
| won't see what's so different about the ana/kata axis, unless
| our universe happens to be their tabletop RPG.
| munchler wrote:
| I think you're making my point. The Fourth Dimension is
| still uniquely defined for our 3-space (which is the entire
| universe, as far as we know). I think that's pretty solid
| justification for giving it a distinct name.
|
| Hypothetically, if there are other (infinite) 3-spaces
| embedded in our 4D metaverse, then we either intersect them
| (which would cause all sorts of problems), or they are
| parallel and agree with our definition of The Fourth
| Dimension.
| roywiggins wrote:
| Our universe might be a much more complicated manifold
| than a plane in the space it's embedded in. Of course, we
| experience it as a flattish 3D space, but maybe gravity
| makes it _four dimensionally lumpy_. Or something else,
| who knows. Maybe it 's actually closed and is the surface
| of a very, very large 4D sphere.
|
| This would make the ana/kata vectors pointing outwards
| away from the universe where I am and the ana/kata
| vectors where you are not line up, and there wouldn't be
| any way to decide which ana/kata vector is the special
| one, even between different points inside our universe.
|
| But really, my objection is mostly that "The Fourth
| Dimension" makes it sound like a "Dimension" is a kind of
| _place_ , which is confusing.
| mistermann wrote:
| > Fair, but two perpendicular Flatlands embedded in the
| same 3D space won't be able to agree on which is the fourth
| dimension.
|
| A lot of religious/spiritual people will say that God or
| the metaphysical realm (some people agree, some
| disagree...just like certain ideas in physics) is where
| many higher dimensions can be found. Say what you want, but
| people's incorrect models of reality having more influence
| than "reality itself" _isn 't nothing_ (if it kills people,
| _it 's at least something_[1]). Besides, almost everyone
| complains about it, they just don't _consider it_ (thus it
| is not) dimensional, it 's "just reality", kind of like how
| a lot of phenomena now understood due to science were(!)
| formerly "just reality".
|
| [1] https://en.wikipedia.org/wiki/Popper%27s_three_worlds
| roywiggins wrote:
| Well that's where I think the Flatland analogy is
| helpful, there's nothing inherently mystical about a
| fourth spacial dimension any more than Flatlanders ought
| to be worshiping us because we have one more dimension
| than they do.
| bbor wrote:
| I'm just an amateur but it seems like the argument above
| yours is pretty airtight, just based on the difference
| between the mathematic definition of Dimension ("...is
| informally defined as the minimum number of coordinates
| needed to specify any point within [a space]") and the
| colloquial definition ("a space") which your last sentence
| seems to rely on.
|
| If I'm reading the first paragraph of Wikipedia right (surely
| an airtight source for a pedantic argument about advanced
| mathematics!) "dimensionality" is an adjective describing a
| space (a set?), so saying that we moved to "the fourth
| dimension" is about as meaningful as saying we moved to "The
| Euclidean" or "the big". Rather than "a euclidean space" or
| "a big space".
|
| That said you're colloquially absolutely correct, of course.
| If I was giving advice to fiction writers or journalists I'd
| definitely endorse your common-sense argument.
| staplers wrote:
| if we were able to escape 3-space by moving into a 4th
| spatial dimension
|
| We are perpetually suspended in this '4th dimension' given
| that we are orbiting a galaxy and star. Find a way out of the
| observable universe which doesn't move and you might escape
| this fourth dimension.
| tshaddox wrote:
| > It doesn't really make sense to call such a space "The Fourth
| Dimension", any more than real life space is "The Third
| Dimension",
|
| It makes _a lot more_ sense to refer to time as "the fourth
| dimension" than to refer to all three spatial dimensions
| together as "the third dimension." Time is indeed one of the
| four dimensions that we're discussing here!
|
| Of course you can quibble that the four dimensions are not in
| some _fixed_ order, but in this context we 're clearly
| referring to time as the fourth dimension because _it 's the
| one being introduced_ as an addition to the other three.
| datascienced wrote:
| I think time is special in Einsteins equations. It therefore
| should be considered special. Been a while since I read about
| it.
| kang wrote:
| Its not that simple. Time it seems IS the first (0th?)
| dimension. A point is space denotes existence in time of the
| object & observation by the subject. In other words, rate of
| change of existence is observed as time. Rate of change of a
| point is observed as a line. A moving point accepts line as its
| track, moving interval accepts square as its track and moving
| square accepts cube as its track. 2-eyed observer has 3D vision
| & 1-eyed observer as 2D vision (try touching your fingers with
| one-eyes closed exercise) has some role about role of
| observation as well.
|
| Further, dimensions being relative vs absolute makes more
| sense. In absolute sense, time is its own dimension T & point
| line cube are L, L^2 & L^3. A 3D object, a cube, has 2D object,
| plane, as its boundary & 1D object, lines, as its dimensional
| denotion. A square has 1D object as its boundary & n-2=0D
| objects, points, as its dimensions, relatively speaking. This
| is important because of the number of eyes? So basically, those
| 2D hypothetical characters in your physics are 1-eyed
| creatures, lol.
| mentos wrote:
| If a 3D object casts a 2D shadow, then as 3D objects what are we
| the shadow of?
|
| What dimension is thought in?
|
| I propose that thought is the fourth dimension and we are the
| shadows of our thoughts.
| roywiggins wrote:
| 3D objects _cast_ shadows, but not all 2D objects _are_
| shadows. A flat piece of paper is (an approximation of) a 2D
| object, but it 's not a shadow of anything 3D.
|
| Shadows behave really differently to real objects. They
| disappear into nothing, they can move _faster than light_ ,
| they can fully overlap each other and then separate again.
| dgfitz wrote:
| How can a shadow move faster than the thing that causes it?
| This is new to me.
| itishappy wrote:
| Projection. If your shadow is further away than your object
| then the dimensions of the shadow will be exaggerated and
| so will it's motion. The light itself travels at light
| speed (duh?), but the image moves faster. Think how your
| monitor makes moving images without moving pixels.
|
| Here's a Vsauce video about it:
|
| https://www.youtube.com/watch?v=JTvcpdfGUtQ
| rekado wrote:
| Think of a sunset just before the sun appears to fall below
| the horizon as the length of the shadows approaches
| infinity.
|
| Not only shadows can move faster than light. Any projection
| can. Take a laser pointer and aim for the moon, then flick
| your wrist back and forth. The point appears to move faster
| than light across the surface of the moon. The photons
| still travel in a straight line, at the speed of light; but
| you are sending new photons in a different direction. There
| really is no single photon actually moving across the
| surface of the moon; it is merely an image.
| samatman wrote:
| They can't.
|
| Imagine an enormous black-body plane appears out of nowhere
| twenty light-seconds from the Sun, large enough to blot it
| out completely from Earth.
|
| We would see that shadow eight minutes later.
| roywiggins wrote:
| If you build a arbitrarily large Dyson sphere, the
| shadows cast by planets orbiting the sun inside the Dyson
| sphere onto the inner surface of the Dyson sphere will
| appear to "move" arbitrarily fast.
|
| If a planet orbits in, say, a day, its shadow will make a
| full circuit of the Dyson sphere in a day. Make the
| circumference of the Dyson sphere _larger than a light-
| day_ , and now the shadow is "moving" faster than light.
| verisimi wrote:
| I think this - thought/'inner life' being the fourth dimension.
| But the problem is that there are several senses of the term
| dimension - there is the mathematical/topological sense and the
| philosophical sense, and possibly others. Confusing contexts
| doesn't help in talking about this stuff.
| karaterobot wrote:
| Weird synchronicity, I just had a long conversation about this
| book a couple days ago, because the subject of jungle gyms came
| up. I was also wondering wondering whether Hinton had any
| freemason connections, since I learned about him from _From Hell_
| , and a lot of that book seems to draw on masonic references.
| vowelless wrote:
| Yes, he is related to Geoffrey Hinton
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