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arichards

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I've been trying to find a way to incorporate the 4th dimension in particular into a short talk in which I can relate this to everyone's life as it is today with specific examples. Does anyone have any ideas?

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- #1

arichards

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I've been trying to find a way to incorporate the 4th dimension in particular into a short talk in which I can relate this to everyone's life as it is today with specific examples. Does anyone have any ideas?

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marcus

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The use of a time coordinate is very useful and goes back, I think, to Galileo and Newton---to the 1600s.... Does anyone have any ideas?

It is useful to plot motion and study trajectories, and in many many other ways that you learn about already in highschool and freshman college physics and engineering courses.

But I don't know of any solid scientific evidence that a 4th dimension exists in the same way that our 3 spatial dimensions do.

At present I don't think there is any (scientific) reason to believe in the actual geometric existence of higher dimensions---beyond the 3 space dimensions that we experience.

So I would suggest that you try not to lead your listeners into believing that a fourth dimension actually exists. So far it is a convenience in constructing useful mathematical models, but to some extent an arbitrary mental construct.

For example take General Relativity (GR) which is the most widely accepted theory of geometry. It has been our theory of geometry for almost 100 years (published in 1915)! It does NOT have a unique physically meaningful time coordinate. It does NOT specify a fixed 4D block universe. Different observers experience time differently. The time coordinate in GR is not physically observable. You have to make an arbitrary choice of some particular clock, and Nature does not tell you the "right" one. So Einstein's GR does not make a 4th dimension "real". It probably seemed more real to Newton, back in the 1600s than it does to us today.

I would not suggest mentioning the String research program since it has not, so far, resulted in a definite testable theory and seems to have lost credibility in recent years. Instead of a single unique theory, there are various string theories (plural) and still some hope of putting them together, but less optimism now, about the enterprise, than there was some years back.

The theme you raise about

- #3

arichards

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The mathematical time-coordinate or "4th dimension" has been an indispensable tool in the study of motion (essentially in all of physics and much of engineering) for several hundred years. It isenormouslypractical and has been so for centuries, in spite of being (as far as we know) an artificial mental construct.

I like how you bring up the "mathematical time-coordinate" as our idea of the "4th dimension." If I can focus on the idea that the "4th dimension" is essentially "time", physics applications (e.g. something as simple as graphing position, velocity, or acceleration of an object in motion against time) could potentially be used as practical applications of this "4th dimension." From here, perhaps I could expand on the idea that if we can prove a 4th dimension exists, what sorts of physics problems could we perform with a 5th dimension?

Another friend of mine mentioned transistors - 3D objects that essentially use 4-dimensional equations (functions of x, y, z, and time). I may be able to use this as a nice "For example" in my discussion.

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