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Related: Editorials & Other Articles, Issue Forums, Alliance Forums, Region ForumsDU math whizzes, I have a question for you, if you can help this nongeometrical thinker
understand something that I know is being studied extensively and not agreed upon. I just can't find a way to wrap my mind around the concept of 4D space. Someone referenced it in a chat yesterday and I went googling and got immediately sucked into math jargon and notations. Is there a way to explain the idea in nonmath language? I thought it was the space-time continuum thing of Star Trek fame but apparently, in one article, those are not the same. Then I was looking a fractals on a site sent by a friend and thought those might be visual representations of 4D only to learn that they are considered 3D. And the Wiki rotating version of a "simple" 4D whatchamacallit confused me more. I don't understand what property is being sought to describe 4D space. Can you describe it or name it for me? Perhaps I just need something to occupy my mind beyond political BS today, but I pulled this thread out of the stuff that flows through my space and would like to know what is sticking to it.
Thanks.
longship
(40,416 posts)In math one uses things like vectors to express multidimensional concepts where there is a value for each dimension. For instance, to represent a location one needs three numbers. One for east-west, one for north-south, and one for height above or below sea level. Now let's say you have an appointment to meet somebody, you would need a location (the three values just mentioned) and a fourth value, the time of the appointment. That would be four dimensions.
A mathematician would represent that as a four vector (x, y, z, t) where x, y, and z are the location coordinates and t is the time.
Hope that helps.
DetlefK
(16,423 posts)That's why space-time isn't considered 4-dimensional but (3+1)-dimensional.:
If you are looking at an object, you can lay the spatial axes in any direction you want: You can transform them, rotate them, mix them.
You can exchange length and height, by changing your point of view.
But no matter what you do, you can't for example tilt the length-axis and the time-axis to define a new length-axis and a new time-axis.
longship
(40,416 posts)I was merely looking for a simple example as an illustration. I was not trying to be rigorous.
Actually, physicists resolve the units by expressing time as ct, the speed of light multiplied by time. That at least makes all the units the same. But I did not wish to confuse the OPer with such details.
Thanks anyway, my friend.
Cirque du So-What
(25,812 posts)...seeing all time as you might see a stretch of the Rocky Mountains. All time is all time. It does not change. It does not lend itself to warnings or explanations. It simply is.
-Kurt Vonnegut, Jr., Slaughterhouse-Five
Savannahmann
(3,891 posts)It is understood that two things can not occupy the same point is space, and time. In other words, if you are standing at a particular corner, at a particular time, no one else can stand right at that same spot, at the same time you do. But, two people can occupy the same point, at different times. You can stand on the corner, walk away, and then someone else can come and stand at the exact same point in space, but not time.
Imagine a race where cars are tearing around a track. They are in a line, each a few inches behind the one in front. Racing forward at two hundred miles an hour. At each moment in time, they occupy different spaces, but a moment later, a fraction of a second later, the one behind occupies the same point in space, but time has shifted to allow that. When one wishes to pass, he must get out of line, because his car will not occupy the same point without a horrific crash. That is 4D. Where a change in time allows objects to occupy the same point.
Skidmore
(37,364 posts)Is there a math concept for the crash? I remember that when my son was in one of his courses for engineering he wrote a paper on the forces at play when an object was not in motion, something I had never considered. Just thinking about that paper and how it represented that state, it would seem logical that there would be some way of notating the "crash." Or that may just be a stupid question. Every once in a while, I try to revisit math. It has never been something that came intuitively to me in life.
Savannahmann
(3,891 posts)But they are mutally exclusive to the specific question. Tracking asteroids for example. Each moment, there are minute changes to the trajectory of the asteroid. So the calculations for that are exclusive, planetary bodies in motion, effected by gravity, proximity to other bodies, thermal shifting due to solar radiation which causes minute bits of thrust to be experienced.
Remember Voyager? We came up with the trajectory for Voyager back when the Beetles were the best band ever. We worked it out with slide rules, and computers the size of office buildings.
I remember a story, some years ago, where NASA was going to study the math involved. There was a slight deviation, over fourty years, of a small fraction of a degree for the flight plan. NASA ran into a problem, the original calculations were done with magnetic tape machines, and punch cards. There weren't any machines that could read it, even if they ever found all the original data, which was unlikely.
That deviation, microscopic in comparison to the time and distance covered, was the effect of thousands of things we just didn't know about. Asteroids that gave a small gratational tug to the probe. Solar heating that gave it a small thermal push. Solar wind that gave it a microsopic nudge. A tiny misestimation on the mass of some object it was going to pass by. All of those tiny timy mistakes added up to an even more miniscule deviatin of the expected course of Voyager.
The math is out there for this kind of thing, but it's beyond me. It is a combination of so many theories, that I would not insult the truth by trying to list them all here.
As for the crash, you have kinetic energy, objects in motion, energy absorbing design, energy resistant design, mass in motion, and I don't know how many other physical laws in play in a handful of seconds. In the end, it comes down to the truth. Two things may not occupy the same point in space time.
Skidmore
(37,364 posts)I really appreciate the effort and the immensity of the task of quantifying our universe.
Laura PourMeADrink
(42,770 posts)Savannahmann
(3,891 posts)And I like reading books, especially books on science. If you want a good series, the BBC did one called Hyperspace. Six or seven thirty minute shows with some of the best special effects I'd seen at that time. The Universe Series is excellent as well. Understanding the math is for those few who are studying it for the next great discoveries. Hoping to understand our world, our universe as much as we can, is the purview of the rest of us.
ChairmanAgnostic
(28,017 posts)Figures.
srican69
(1,426 posts)Image in our 3d world as obama negotiaties his pieces through a maze of n-dimensional hyper-cuboids...
Hope that helps. :-D
Savannahmann
(3,891 posts)Those higher dimensions was where they played Ultra Cricket, and they would be destroyed for that as soon as someone figured out how to fire a missile at right angles to reality.
Kolesar
(31,182 posts)Maybe it is part of quantum physics, where we don't use Newton's laws.
Savannahmann
(3,891 posts)Just add the time component to them. An object in motion will remain in motion, but if it strikes another object, by attempting to occupy the same point in space at the same time, then the motion, in compliance with Newtonian laws, has changed. It has been acted upon by an outside force.
chervilant
(8,267 posts)our puny brains have *SUCH* a tough time with math!
(Yeah, I know it's a bad pun...I can hear you groaning from here!)
RadiationTherapy
(5,818 posts)4D is a solid existing in/over time (length x width x height x time).
pinboy3niner
(53,339 posts)ljm2002
(10,751 posts)...on a graph. They are drawn perpendicular to each other. An x, y coordinate represents a point within this flat area. The area represented by x and y has no depth; it is 2-dimensional. Now if you want to represent depth, you add a z axis going up and down, perpendicular to both the x and y axes. So now an x, y, z coordinate represents a particular point in a volume; it is 3-dimensional.
Now if you want to represent a 4th dimension, you need to think of another axis, call it t, that is perpendicular to each of the x, y, and z axes. It is hard to visualize directly without chemical aids, but it can be done. Just build on what we've done before. Once you think about what it would mean for a 4th dimension to be perpendicular to the others, it is easier to see what they're getting at when you look at figures trying to represent that idea. Assuming this 4th dimension is time, you now have a representation of space-time: any point represents a particular place in the 3-dimensional volume, at a particular time.
Time is different from the three spatial dimensions in that (as far as we know) it only goes in one direction. But putting that aside (*), time is often used as a 4th dimension in calculations, and it can be thought of as perpendicular to the rest of the dimensions -- its value is independent of the x, y and z values. Mathematicians call this property being "orthogonal" to the others.
Once you have worked out the mathematical relationships between orthogonal values, the same techniques can be employed for 4, 5, and n-dimensional problems. It's a matter of extending the basic building blocks used to explore the more familiar world of 3 dimensions.
(*) Since you can represent both the past and the present in a timeline, for some purposes it can be treated just like the line of real numbers, extending forward and backward from an origin point given the value of 0. But for many calculations you must account for the fact that time goes only forward.
caraher
(6,276 posts)There's nothing remotely controversial about "spacetime" consisting of 3 spatial dimensions plus time. Einstein's special theory of relativity pretty much demands that, and it's more of a bedrock principle for physicists today than F=ma.
Usually this come up in the context of string theory, which generally calls for the existence of more than 3 spatial dimensions. The question then becomes why we only experience three. One possibility is that some are "compact." A classic example of this is to consider an ant walking on a power line.
From a distance, you can describe the ant's progress in just one dimension - its distance x along the wire from one pole, for instance. But if you look close, you see that the ant, walking on the outer surface of the wire, is moving on a two-dimensional surface. To fully track its motion you also need a second coordinate - its location on the circular slice of constant x. (Is it on the top of the wire, bottom, the side facing me as I look or the side facing away - I can characterize any arbitrary location on this circle by some angle, or a circumferential distance from some reference line.)
So the idea is that these extra dimensions are kind of like the angular dimension in the example - you can't go indefinitely far without "wrapping around" and thus the dimension is "confined."
The Straight Story
(48,121 posts)In 2d plane (like a piece of paper) think of how a ball looks on the paper if it passed through it.
First a dot, then a circle that got bigger and bigger, then smaller and smaller.
In 3d plane imagine a 4d sphere coming through our plane, a tiny sphere, then bigger, etc
Skidmore
(37,364 posts)Phillip McCleod
(1,837 posts)that's always been my favorite way to visualize it. mathematically useful to.. it's looking at the contours .. from N space to N-1 space.
they're called 'hyper-spheres', 'hyper-cubes', etc. when they have more than 3 dims. as you said the contour lines of a 4D hypersphere (called a 3-sphere) may be represented by an infinite series of concentric 2-spheres.
the whole 4D/3-sphere thing confuses some. basically the sphere is named after the dimensionality of its manifold (surface). flatten out a globe and into a map and that's why we call a sphere existing in 3D space a '2-sphere'.. it's surface is 2-dimensional. similarly the 'surface' of a 3-sphere is 3-dimensional and it exists in 4D space.
riemannian geometry is the good shit.
RC
(25,592 posts)You'd never expect to find anything close to the information and patients of explanations posted here, on a right-wing site, even if they could grasp the concepts.
Festivito
(13,452 posts)Dimension Description
0 A dot
1 A line, you choose the length.
2 A plane, like a sheet of paper. You choose the two dimensions.
3 A box. You chose the length, width and height.
4 A series of boxes, you choose each length, width, height and number of boxes.
Also, for the fourth, I think of a hexagon on poles. That is for me a cube extending from one position on the left through an infinite number of positions until the other side of the box reaches the right hand side of the hexagon. That's my personal symbol for time.
Recursion
(56,582 posts)That's probably the best introduction to it.
Skidmore
(37,364 posts)Skidmore
(37,364 posts)I hate sounding so stupid but I've never had an easy time with math. Some health problems I had a few years ago also left me with some soft neurological symptoms as well. That didn't help me in this area. I really appreciate the sincerity of the responses and the absence of snark.
gateley
(62,683 posts)s-cubed
(1,385 posts)In engineering we often deal with multidimensional spaces. The key notion is that each dimension is independent of the others, ie perpendicular. If I want to control such p a system I have to control each of the dimensions.
A military plane would be an example of a multidimensional system. We might think of it as moving in 3D but in terms of controlling it you have to control the dimensions that are translated into 3D movement. To use another example, a chemical plant or refinery might depend on a number of independent variables which interact to produce the desired outcome.
If you just think of it in terms of our familiar 3D world, your head starts to hurt. So try to think instead of variables that are independent in a large complex system.
Hope this helps.
lastlib
(22,981 posts)tesseract--the generalization of a cube to four dimensions of space.
Mariana
(14,849 posts)be right angles, in the same manner that all of the angles in a cube are right angles? It was explained to me that way. Do I understand correctly?
lastlib
(22,981 posts)...essentially a 'shadow' of an actual tesseract--a 3-D representation of a four-dimensional object.