neilwilkes wrote:...the whole point of trying to turn time into a geometric to me is not so much spectacularly intuitive as spectacularly wrong...
CharlesChandler wrote:A "dimension" represents a quantity plotted in a coordinate system, and you get a total of 3 of them (X, Y, and Z). Of course, thanks to Descartes, we can use geometry to analyze non-spatial entities, by replacing one or more physical dimensions with abstract quantities. For example, we can use X and Y to represent a (flattened) surface of the Earth, and then we can use the Z axis to represent average income of the inhabitants of that part of the Earth. Stuff like this can be very useful. But you get a maximum of 3 dimensions when playing with coordinate systems.
Throwing in a 4th dimension doesn't make it a fancier concept -- it's simply a broken metaphor, and now you don't have a tangible concept of how to represent any quantity relative to some other quantity.
If somebody makes a mistake when doing calculations in 4 dimensions, how do you know? What are the rules?
Where are the axioms, postulates, and theorems of hyperdimensionality?
Your assumption is that geometry is limited to three dimensions, but you are wrong. Any mathematics can be used to describe physical phenomena, and whether or not the description is accurate depends on whether the predictions made by the theory are actually observed in practice.When people elaborate on such concepts, the issue doesn't get clearer -- it gets more abstract, more complex, and more non-physical. Such musings are not bounded by the characteristics of the reality they pretend to represent -- the only limit is the benefit of the doubt you grant to the speaker.
Yep, youi missed out on the whole Riemannian geometry thing. How do you know that space has the properties of R3 - 3 dimensional Euclidean space?As others have noted, this is similar to the idea that space can be warped, or that it can expand or contract. As Tesla said, if space is defined as nothingness, it has no attributes -- there is nothing in there that can get warped. The only thing getting warped is your mind. A coordinate system is a mental construct used to measure & analyze relationships among quantities. The matter doesn't know that it's in a coordinate system, or that it could simultaneously be in any number of them, depending on how many people had established how many frames of reference for however many different purposes. The matter simply is what it is. And then, if there isn't even any matter there, because it's empty space, there is nothing left to get warped. Hence the only warping is quite entirely within the mind of the GR proponent.
Higgsy wrote:The geometry of hyperdimensional spaces is standard undergraduate stuff.
Content free reply to a content-rich post. Charles basically says "Charles doesn't understand it, so no-one else should be able to either". How silly of Charles.CharlesChandler wrote:Higgsy wrote:The geometry of hyperdimensional spaces is standard undergraduate stuff.
Sometimes the standard is gibberish.
Higgsy wrote:
How do you know that space has the properties of R3 - 3 dimensional Euclidean space?
How do you know it's Euclidean? And we were talking about spacetime. Do keep up.seasmith wrote:`Higgsy wrote:
How do you know that space has the properties of R3 - 3 dimensional Euclidean space?
Because we are talking about SPACE.
What on earth are you bleating about?You may be thinking of something referred to as "counter-space", which is regularly used in electronic calculations to explain how electric and magnetic fields exist in the same space.
Cargo wrote:What dimension is space-time from? The 8th! lol..
Higgsy wrote:How do you know that space has the properties of R3 - 3 dimensional Euclidean space?
seasmith wrote:Because we are talking about SPACE.
Higgsy wrote:How do you know it's Euclidean? And we were talking about spacetime. Do keep up.
CharlesChandler wrote:Higgsy wrote:How do you know that space has the properties of R3 - 3 dimensional Euclidean space?seasmith wrote:Because we are talking about SPACE.Higgsy wrote:How do you know it's Euclidean? And we were talking about spacetime. Do keep up.
How do you know that space is non-Euclidean?
Here I side with Tesla in that empty space is ...
... that all perceptible matter comes from a primary substance, of a tenuity beyond conception and filling all space - the Akasha or luminiferous ether - which is acted upon by the life-giving Prana or creative force, calling into existence, in never ending cycles, all things and phenomena.
The primary substance, thrown into infinitesimal whirls of prodigious velocity, becomes gross matter; the force subsiding, the motion ceases and matter disappears, reverting to the primary substance.
The general geometry of the manifold is non-Euclidean. A Euclidean is a specific instance of the general.CharlesChandler wrote:How do you know that space is non-Euclidean?
And yet, despite this claim, you treat space as though it were Euclidean. So while explicitly claiming that it is neither, you make a strong implicit claim that it is universally Euclidean.Here I side with Tesla in that empty space is nothingness, which has no properties. It doesn't know that somebody has established an origin for a coordinate system, much less in how many dimensions. The coordinate system is in our minds. If it helps framing problems in solvable ways, we use it. We shift around the point of origin, and set the orientation of the axes, to reduce the complexity of whatever problem we're trying to solve -- without affecting space, or any matter it might contain. Space is not Euclidean, nor is it non-Euclidean -- space is nothingness. The math is in our minds.
Of course, one can argue that if a given mathematical system works in the real world, there must be something to it, beyond our own imaginations. But for that to support your position, you'd have to demonstrate that hyperdimensional math can solve real world problems that cannot be solved more easily with simpler constructs. Good luck on that.
Higgsy wrote:GR, which explains dynamic observations of free falling bodies better than any other theory, is explicitly hyper dimensional and non-Euclidean.
Higgsy wrote:But there are a vast array of practical problems which use hyperdimensions. If you want to solve a problem about the variation over time and space of an electric field (or any vector field) you are already solving an eight dimensional problem.
the variation over time and space of an electric field..[is] an eight dimensional problem
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