5 ms·

I didn't understand the article at all, but it did make think about about how many dimensions are required for humans to understand how objects in life relate t

I didn't understand the article at all, but it did make think about about how many dimensions are required for humans to understand how objects in life relate to each other. I counted: a point, a line, a plane, a solid, a solid at a point in time, a solid that might exist in some possible future, and a solid at a point in time that might have existed if our past had been different. That's all I could come up with (and I'm not even sure if the last one is a dimension). It's probably a coincidence (there's nothing crankier than numerology), but it did make me happy that it adds up to seven.

echelon 6y ago
> I counted: a point, a line, a plane, a solid, a solid at a point in time, a solid that might exist in some possible future, and a solid at a point in time that might have existed if our past had been different. A solid in some parallel universe. A solid in some fictitious parallel universe. A solid in some non-cannon fictitious universe. A solid thinking of another solid in some parallel universe derived by combining one of more non-cannon offshoots of a particular fictitious universe combined with our own but also exploring and deconstructing revisionist history themes. All of that, but also the main character is revising her schema to be in fifth normal from. That's kind of arbitrary, but I'm sure it regularly happens on fanfictiction.net Just because picturing geometry in more than three dimensions is hard, doesn't mean we can't grapple with dimensionality or abstraction. We're pretty good at it.
- kohtatsu 6y ago
  I think we limited "Math" to the wrong things in school.
- jerf 6y ago
  In the sense being used by the original article, those are not dimensions. That is a very scify type of dimension, which has no known real-world referent. The original list goes wrong at "a solid that might exist in some possible future"; that is not a dimension. That is simply a solid with a time value in the future, which is the same four dimensions as the preceding example. A dimension is an additional necessary number to characterize a system. Beyond the location inside a point (0 numbers required), a line (1 number required), a plane (2 numbers required), and a full 3D space (3 numbers required), examples of real world entities that require more than three dimensions are: A RGBA color value, which is four-dimensional. The location and orientation of a rigid object; 6 dimensional. Three for the location, three additional for the rotation. The location, velocity, orientation, and spin rate of a rigid object: 12 dimensional. In addition to the previous six, three new ones needed for the translational vector and three new ones needed for each spin axis rate. Any arbitrary multiple of three: Any RGB image, where each pixel is three dimensions each, one for R, G, and B. Images get to be high-dimensional spaces very quickly. High numbers of dimensions are hard to visualize, but they are completely bereft of any "woo woo" value or any of the sort of mystery one might be inclined to ponder on illegal substances. Bog-standard examples of such things are encountered on a daily basis; the state of the display you are reading this on is characterized by a several-million-component vector. That's how "boring" and "normal" such things are. If you've got any of the woowoo in your concept of "dimension", you don't understand dimensionality. The bad news is that this may take away the vague fuzzy fun of pondering the meaningless concept; the good news is that this opens you to much more concrete and real, and still quite mysterious, fun of pondering real high dimensionality spaces, which is a much richer and more interesting space that has enough stuff to explore for the rest of your life, were you so inclined. The "woo woo" scify concept is exhausted in five minutes, or perhaps a drug-fueled trip. It may feel fun for a moment but it doesn't go anywhere.
  - uniqueid 6y ago
    > That is simply a solid with a time value in > the future, which is the same four dimensions > as the preceding example. My train of thought (not to say it's original) is: You can't move a solid without another (a fifth) dimension (ie: time). You can't move the trail of solids that exist in time without a second dimension of time (the sixth, if we're counting all the way up from a 1D point). If you have two sequences of events that are slightly different (side by side, ignoring that a "side" is a 4D side, I guess), that "timeline" which differs from the original is a "possible universe".
    - uniqueid 6y ago
      My numbering was off. 4th is time. 5th adds the direction going between one universe and a variation of it, both at the same point on the time axis. I also notice in my example I start with zero dimensions. All in all, a reminder that I should exercise more self-restraint and not comment on Physics articles :D
    - jerf 6y ago
      The problem here is that you've got a subset/superset relationship reversed. "Dimension" is simply the need to add a number to fully describe a system, as I gave in the several examples. It is true that if there was some system of parallel universes that a number identifying the universe could be necessary to fully identify the location of an object. (Depending on the nature of the multiple universes, it could even require more than one.) But "identifying which universe something is in" is not the definition of "the fifth dimension". It is simply a particular instance/subset of the general concept of dimension, which happens to also be currently meaningless and without referent. But even so, it manages to screw people up and provide significant cognitive interference for the real concept of dimensionality, which is, as I said, much less "woo woo", which may be sort of disappointing, but also a much richer concept that provides much more to explore, because it actually has content to it. You can also see the confusion in the miscounting of dimensions, because they are not being thought of as simply numbers that identify a place/thing, but some sort of ordered list of "concepts", where "things that don't exist yet" are somehow in another "dimension". But as I said, you don't need another "dimension" for that; it's just a time coordinate, which we already have, in the future. This is the sort of thing that drives me to post this point. It's a surprisingly popular viewpoint. There's a YouTube video that does this sort of thing, which got very popular, and I don't even want to link to, because it's a steaming pile of garbage, leaving viewers who watch it feeling like they understand better when in fact they understand far worse. It's not necessarily in the top ten list of "ideas that will prevent you from understanding the world better" or anything, but it's certainly on that list.
polishdude20 6y ago
Yeah but when you imagine a point, you're not really imagining a true point. You most likely think of it as a tiny sphere. Even if you are imagining a true point in a mathematical sense, you can't imagine the point without imaging what is around the point. So it has to have a location in x and y at least. You could even say the z dimension is there since when imagining this point, you are imaging it in your mind's eye as an observer would. We are completely trapped in our viewpoint of the world of it being at the least in three dimensions probably even four because of time.
- uniqueid 6y ago
  I think a point, in the sense I was thinking about, maps to a boolean: it either exists, or does not exist. It's not even a line which can have a distance, so there's nothing else for itself to relate to.
  - polishdude20 6y ago
    Oh that's a good way of thinking about it.

echelon 6y ago

> I counted: a point, a line, a plane, a solid, a solid at a point in time, a solid that might exist in some possible future, and a solid at a point in time that might have existed if our past had been different. A solid in some parallel universe. A solid in some fictitious parallel universe. A solid in some non-cannon fictitious universe. A solid thinking of another solid in some parallel universe derived by combining one of more non-cannon offshoots of a particular fictitious universe combined with our own but also exploring and deconstructing revisionist history themes. All of that, but also the main character is revising her schema to be in fifth normal from. That's kind of arbitrary, but I'm sure it regularly happens on fanfictiction.net Just because picturing geometry in more than three dimensions is hard, doesn't mean we can't grapple with dimensionality or abstraction. We're pretty good at it.

kohtatsu 6y ago
I think we limited "Math" to the wrong things in school.
jerf 6y ago
In the sense being used by the original article, those are not dimensions. That is a very scify type of dimension, which has no known real-world referent. The original list goes wrong at "a solid that might exist in some possible future"; that is not a dimension. That is simply a solid with a time value in the future, which is the same four dimensions as the preceding example. A dimension is an additional necessary number to characterize a system. Beyond the location inside a point (0 numbers required), a line (1 number required), a plane (2 numbers required), and a full 3D space (3 numbers required), examples of real world entities that require more than three dimensions are: A RGBA color value, which is four-dimensional. The location and orientation of a rigid object; 6 dimensional. Three for the location, three additional for the rotation. The location, velocity, orientation, and spin rate of a rigid object: 12 dimensional. In addition to the previous six, three new ones needed for the translational vector and three new ones needed for each spin axis rate. Any arbitrary multiple of three: Any RGB image, where each pixel is three dimensions each, one for R, G, and B. Images get to be high-dimensional spaces very quickly. High numbers of dimensions are hard to visualize, but they are completely bereft of any "woo woo" value or any of the sort of mystery one might be inclined to ponder on illegal substances. Bog-standard examples of such things are encountered on a daily basis; the state of the display you are reading this on is characterized by a several-million-component vector. That's how "boring" and "normal" such things are. If you've got any of the woowoo in your concept of "dimension", you don't understand dimensionality. The bad news is that this may take away the vague fuzzy fun of pondering the meaningless concept; the good news is that this opens you to much more concrete and real, and still quite mysterious, fun of pondering real high dimensionality spaces, which is a much richer and more interesting space that has enough stuff to explore for the rest of your life, were you so inclined. The "woo woo" scify concept is exhausted in five minutes, or perhaps a drug-fueled trip. It may feel fun for a moment but it doesn't go anywhere.
- uniqueid 6y ago
  > That is simply a solid with a time value in > the future, which is the same four dimensions > as the preceding example. My train of thought (not to say it's original) is: You can't move a solid without another (a fifth) dimension (ie: time). You can't move the trail of solids that exist in time without a second dimension of time (the sixth, if we're counting all the way up from a 1D point). If you have two sequences of events that are slightly different (side by side, ignoring that a "side" is a 4D side, I guess), that "timeline" which differs from the original is a "possible universe".
  - uniqueid 6y ago
    My numbering was off. 4th is time. 5th adds the direction going between one universe and a variation of it, both at the same point on the time axis. I also notice in my example I start with zero dimensions. All in all, a reminder that I should exercise more self-restraint and not comment on Physics articles :D
  - jerf 6y ago
    The problem here is that you've got a subset/superset relationship reversed. "Dimension" is simply the need to add a number to fully describe a system, as I gave in the several examples. It is true that if there was some system of parallel universes that a number identifying the universe could be necessary to fully identify the location of an object. (Depending on the nature of the multiple universes, it could even require more than one.) But "identifying which universe something is in" is not the definition of "the fifth dimension". It is simply a particular instance/subset of the general concept of dimension, which happens to also be currently meaningless and without referent. But even so, it manages to screw people up and provide significant cognitive interference for the real concept of dimensionality, which is, as I said, much less "woo woo", which may be sort of disappointing, but also a much richer concept that provides much more to explore, because it actually has content to it. You can also see the confusion in the miscounting of dimensions, because they are not being thought of as simply numbers that identify a place/thing, but some sort of ordered list of "concepts", where "things that don't exist yet" are somehow in another "dimension". But as I said, you don't need another "dimension" for that; it's just a time coordinate, which we already have, in the future. This is the sort of thing that drives me to post this point. It's a surprisingly popular viewpoint. There's a YouTube video that does this sort of thing, which got very popular, and I don't even want to link to, because it's a steaming pile of garbage, leaving viewers who watch it feeling like they understand better when in fact they understand far worse. It's not necessarily in the top ten list of "ideas that will prevent you from understanding the world better" or anything, but it's certainly on that list.

polishdude20 6y ago

Yeah but when you imagine a point, you're not really imagining a true point. You most likely think of it as a tiny sphere. Even if you are imagining a true point in a mathematical sense, you can't imagine the point without imaging what is around the point. So it has to have a location in x and y at least. You could even say the z dimension is there since when imagining this point, you are imaging it in your mind's eye as an observer would. We are completely trapped in our viewpoint of the world of it being at the least in three dimensions probably even four because of time.

uniqueid 6y ago
I think a point, in the sense I was thinking about, maps to a boolean: it either exists, or does not exist. It's not even a line which can have a distance, so there's nothing else for itself to relate to.
- polishdude20 6y ago
  Oh that's a good way of thinking about it.