Is R real?

[Speakpigeon]

As I understand it, we have an intuitive notion of the continuity of space and time. Unfortunately, it seems there's no way we could even in principle prove space and time are continuous in this sense. However, mathematicians, well, Descartes as it turns out, invented the mathematical concept of the set of Real numbers, which seems now accepted as a very good representation of the continuity of space and time. But I have a problem with that.

Before I go into my beef about Reals, I would like to know what you think of this idea that the set of Real numbers would be a good model for the continuity of space and time.

Thanks.
EB

Nota. I think it's mostly not a mathematical question but mathematicians pros and amateurs are welcome to contribute.

 

[Bronzeage]

Whenever someone proposes that X has some property Y, my first response is always, "What would the world look like, if X had no Y. In other words, "What difference does it make?"

For myself, I have yet to find anything within reach which can't be measured by any of the instruments in my collection. For practical purposes, every point along my tape measure has a real number to mark it's place and there are no gaps between any two points.

It's difficult to argue against an idea which works, unless you can provide one which works better.

 

[Worldtraveller]

Whenever someone proposes that X has some property Y, my first response is always, "What would the world look like, if X had no Y. In other words, "What difference does it make?"

For myself, I have yet to find anything within reach which can't be measured by any of the instruments in my collection. For practical purposes, every point along my tape measure has a real number to mark it's place and there are no gaps between any two points.

It's difficult to argue against an idea which works, unless you can provide one which works better.

This is a big difference between engineering and science. Your comment is more the way engineers (I'm one too) look at the world.

There's nothing wrong with trying to continually drill down to the 'nature of reality' though, using science. Time/space may be discontinuous, and I've seen some hypotheses (usually mislabeled theories) that demonstrate that it is discontinuous. It won't affect most of us, but it may turn out to be the launch point for some technology in the future that allows interstellar travel (to assume a wild and probably unrealistic hope).

 

[Bronzeage]

Whenever someone proposes that X has some property Y, my first response is always, "What would the world look like, if X had no Y. In other words, "What difference does it make?"

For myself, I have yet to find anything within reach which can't be measured by any of the instruments in my collection. For practical purposes, every point along my tape measure has a real number to mark it's place and there are no gaps between any two points.

It's difficult to argue against an idea which works, unless you can provide one which works better.

This is a big difference between engineering and science. Your comment is more the way engineers (I'm one too) look at the world.

There's nothing wrong with trying to continually drill down to the 'nature of reality' though, using science. Time/space may be discontinuous, and I've seen some hypotheses (usually mislabeled theories) that demonstrate that it is discontinuous. It won't affect most of us, but it may turn out to be the launch point for some technology in the future that allows interstellar travel (to assume a wild and probably unrealistic hope).

If time/space were continuous, we could never have created the hyperimprobability drive, much less create Bistromath.

Even so, field effect transistors would not work, if there were no field, so although we can't see the field, it must be there. I read a commentary on string theory which said the whole idea is very clever, but so far no one has devised an experiment which would fail if strings did exist. This means that right or wrong, we can't take advantage of strings to change anything, in the same way we happily effect our FETs.

The core of the concept of real numbers is the idea that a straight line exists between any two points in the universe. Until the invention of powered flight, it was technically impossible to travel in a straight line, even when falling straight down. However, for the thousands of years in which humans have worried about this sort of thing, we thought we were doing just that, simply because it looked like we were traveling in a straight line. As we gained the ability to travel faster, the first thing we discovered was our straight lines were not straight and we had to change all calculations to account for living on a curved surface.

To rephrase my earlier post, if it doesn't make a difference, it doesn't matter if it's real or not.

 

[Cheerful Charlie]

Relativity. C is the constant that all other variables have at their core. The speed you travel at changes your dimension, mass and time. This has been demonstrated a number of times to be true. two atomic locks, on is at rest the other travels a long distance in a jet aircraft at 550 MPH. Their times compared show the difference, time does slow down when your speed increases. Time and space are strongly dependent as a whole, not separable. Lorentz-Fitzgerald contraction..

 

[untermensche]

There are no real infinities.

There could not possibly be one.

Infinity is not a real world concept.

Any apparent continuity is due to imperfect observation.

 

[Tigers!]

Perhaps the thread should be called "R U Real?"

 

[untermensche]

The movie on the screen.

It is continuous.

It has no breaks.

It must consist of infinite frames.

 

[bigfield]

If real numbers are imaginary, are imaginary numbers real?

 

[fast]

If real numbers are imaginary, are imaginary numbers real?

Wouldn’t the truth of whether or not imaginary numbers are real be independent of whether real numbers are imaginary?

 

[Testy Calibrate]

There is a huge difference between reality and models describing reality. Models are either useful or not. They are not "true" or "false" in any other sense than that. Newton's physics are true except when they aren't. The reals and maths themselves are human constructs and they are unreasonably effective as modeling techniques as wigner pointed out. But they only "exist" in brains. As far as we know, only in human brains. The question seems malformed.

 

[Morgan]

If all the reals are really real, what is the first real greater than 1(or any other integer)?

 

[Speakpigeon]

If all the reals are really real, what is the first real greater than 1(or any other integer)?

So just because you can't tell what is on my desk here it means these things are not real?!
EB

 

[Speakpigeon]

There is a huge difference between reality and models describing reality. Models are either useful or not. They are not "true" or "false" in any other sense than that. Newton's physics are true except when they aren't. The reals and maths themselves are human constructs and they are unreasonably effective as modeling techniques as wigner pointed out. But they only "exist" in brains. As far as we know, only in human brains.

Models are true or false.

And not because they may be useful or useless.

Stop taking human beings for complete idiots.

The question seems malformed.

Like what?
EB

 

[untermensche]

There is a huge difference between reality and models describing reality. Models are either useful or not. They are not "true" or "false" in any other sense than that. Newton's physics are true except when they aren't. The reals and maths themselves are human constructs and they are unreasonably effective as modeling techniques as wigner pointed out. But they only "exist" in brains. As far as we know, only in human brains.

Models are true or false.

And not because they may be useful or useless.

We simply label a model as "true" when it can be used to make any prediction. Most models only make very limited predictions. None can predict very much.

When the model is useful in other words it is kept and labeled by some as "true". Even though the label is not necessary or adding anything to the model or what the model can do.

You think giving something a label, adding the useless label "true" to a useful model, means you have some added knowledge.

Very strange.

 

[fast]

If I put oversized tires on my truck, the speedometer is no longer true (accurate), but it remains useful because the speed it registers remains close to my actual speed.

 

[fast]

Last nights long post disappeared TWICE, but to recap with much brevity: we should remain mindful of the distinction between the following four groups:

A) Real Numbers
B) Imaginary Numbers
C) real numbers
D) imaginary numbers

The first 3 exist.

 

[Testy Calibrate]

I do not think you understood my point but no, models are not true or false in some reality aligned way. They are either useful or not. Their truth or falsehood is only meaningful wrt their ability to align with experience. Not sure how that makes any sort of claim about a subjective quality of humans as a species.

 

[untermensche]

I do not think you understood my point but no, models are not true or false in some reality aligned way. They are either useful or not. Their truth or falsehood is only meaningful wrt their ability to align with experience. Not sure how that makes any sort of claim about a subjective quality of humans as a species.

The behavior is called raging at the moon.

Lunacy.

 

[Testy Calibrate]

I do not think you understood my point but no, models are not true or false in some reality aligned way. They are either useful or not. Their truth or falsehood is only meaningful wrt their ability to align with experience. Not sure how that makes any sort of claim about a subjective quality of humans as a species.

The behavior is called raging at the moon.

Lunacy.

What?