The Measure Problem

[studiot]

I am guessing that you have read a populist maths book about 'infinity' and found the Ancient Greek ideas which they used to avoid their difficulties with the subject.

I am trying to help you see the next two and a half thousand years of development of mathematical and logical thinking where many great men have considered this problem.

 

When you are categorizing things into a binary (two way) choice it is important to choose the correct one to define.

Everything else in then defined as being 'not the basis of definition'.

 

In this case infinite is a very difficult thing to define since it is open ended.

So the correct way is to define finite first.

The you define everything that does not meet this definition as not finite or 'infinite'

That avoids the wooly words.

 

The only problem with this approach is when you have tried to divide up a subject hat naturally has more that 2 distinct categories.

 

Does this help move forward?

[DannyTR]

The integers are purely a concept; in no way are they fully defined. You have to iterate all of the members to fully define a set else you are missing the cardinality (and making up ‘numbers’ for cardinality is not sensible).

[studiot]

?

2 minutes ago, DannyTR said:

The integers are purely a concept; in no way are they fully defined. You have to iterate all of the members to fully define a set else you are missing the cardinality (and making up ‘numbers’ for cardinality is not sensible).

?

[DannyTR]

6 minutes ago, studiot said:

I am guessing that you have read a populist maths book about 'infinity' and found the Ancient Greek ideas which they used to avoid their difficulties with the subject.

I am trying to help you see the next two and a half thousand years of development of mathematical and logical thinking where many great men have considered this problem.

 

When you are categorizing things into a binary (two way) choice it is important to choose the correct one to define.

Everything else in then defined as being 'not the basis of definition'.

 

In this case infinite is a very difficult thing to define since it is open ended.

So the correct way is to define finite first.

The you define everything that does not meet this definition as not finite or 'infinite'

That avoids the wooly words.

 

The only problem with this approach is when you have tried to divide up a subject hat naturally has more that 2 distinct categories.

 

Does this help move forward?

 - Ok everything that is not finite is infinite 

- We note from nature the complete lack of anything non-finite 

- We conclude empirically that the non-finate does not exist 

[Strange]

3 minutes ago, DannyTR said:

We note from nature the complete lack of anything non-finite 

How do you know that?

[DannyTR]

Give me one example of Actual Infinity (https://en.m.wikipedia.org/wiki/Actual_infinity) from nature.

There are no such examples.

 

 

[Strange]

Just now, DannyTR said:

Give me one example of Actual Infinity (https://en.m.wikipedia.org/wiki/Actual_infinity) from nature.

There are no such examples.

The universe may be infinite.

[DannyTR]

One example that you can prove.

[studiot]

So will you please answer my question about the term bounded?

You did introduce it.

Edited September 22, 2018 by studiot

[Strange]

Just now, DannyTR said:

One example that you can prove.

Don't be silly. The universe might not be infinite. We don't have enough information to "prove" it either way. (And science doesn't really prove anything.)

But you are the one making a definitive claim, so it is up to you to provide evidence. Can you do that?

[DannyTR]

I think the universe is finite because:

 - Actual Infinity does not exist mathematically 

- There is no proof of Actual Infinity in nature 

- The concept of the material world and Actual Infinity do not stack up. You buy one or the other. I buy the material world.

[Strange]

 

Quote

- There is no proof of Actual Infinity in nature 

There is no proof against it either.

What evidence do you have for your claim?

If you don't provide some evidence in the next post then I will report this thread to the moderators.

Edited September 22, 2018 by Strange

[studiot]

57 minutes ago, studiot said:

1 hour ago, DannyTR said:

- finite is within bound, IE fully defined 

- Infinite is without bound, IE not fully defined IE undefined.

 

Thank you.

 

So by within bound do you mean has a boundary?

If so, is that boundary part of whatever is finite or not part of it?

What is beyond that boundary?

If not what does within bound mean?

You can't cherry pick what parts of a discussion suits you and what doesn't.

[DannyTR]

11 minutes ago, studiot said:

You can't cherry pick what parts of a discussion suits you and what doesn't.

Yes the bounded has boundaries of the same nature as the bounded itself.

I guess nothing is beyond that boundary there is no time or space there.

 

[Strange]

2 minutes ago, DannyTR said:

Yes the bounded has boundaries of the same nature as the bounded itself.

I guess nothing is beyond that boundary there is no time or space there.

 

You do know that in modern cosmology, even if the universe is finite it has no boundary ... don’t you?

[DannyTR]

14 minutes ago, Strange said:

 

There is no proof against it either.

What evidence do you have for your claim?

If you don't provide some evidence in the next post then I will report this thread to the moderators.

The complete lack of existence of Absolute Infinity in nature ***IS*** evidence that it does not exist. 

The impossibility of consistency defining such a term is evident from the many paradoxes that stem from it:

https://en.m.wikipedia.org/wiki/Paradoxes_of_infinity

These paradoxes go away in a finite discrete universe.

 

3 minutes ago, Strange said:

You do know that in modern cosmology, even if the universe is finite it has no boundary ... don’t you?

No I don’t understand how anything in the material world cannot have boundaries. 

Could you explain?

[Strange]

5 minutes ago, DannyTR said:

The complete lack of existence of Absolute Infinity in nature ***IS*** evidence that it does not exist. 

But you can’t say there is a lack of “absolute infinity” without evidence that the universe is finite. You have not yet provided that evidence. 

7 minutes ago, DannyTR said:

No I don’t understand how anything in the material world cannot have boundaries. 

Could you explain?

Well, it is good that you admit your Ignorance of the subject you are discussing. And hopefully you are willing to learn.

I would suggest you start a thread on the subject. In part because I am going to suggest this thread is closed as you are unable to follow the rules. 

[geordief]

9 minutes ago, Strange said:

You do know that in modern cosmology, even if the universe is finite it has no boundary ... don’t you?

Is that simply because nothing that is dynamic can have a definite boundary? 

[Strange]

2 minutes ago, geordief said:

Is that simply because nothing that is dynamic can have a definite boundary? 

No. The best analogy is the surface of the Earth; the 2D surface has a finite area but no edges. Extend that to three dimensions (not easy to visualise!) and you have a finite but unbounded volume. You can also think of it as a "Pacman universe": if you go far enough in one direction you end up coming in from the there side. 

[DannyTR]

2 minutes ago, Strange said:

No. The best analogy is the surface of the Earth; the 2D surface has a finite area but no edges. Extend that to three dimensions (not easy to visualise!) and you have a finite but unbounded volume. You can also think of it as a "Pacman universe": if you go far enough in one direction you end up coming in from the there side. 

But the surface of the earth is bounded by the earth and sky, don’t they count as boundaries?

[geordief]

4 minutes ago, Strange said:

No. The best analogy is the surface of the Earth; the 2D surface has a finite area but no edges. Extend that to three dimensions (not easy to visualise!) and you have a finite but unbounded volume. You can also think of it as a "Pacman universe": if you go far enough in one direction you end up coming in from the there side. 

Is the curvature of spacetime responsible for this ?(if galaxies are not bound together  by gravity does this change the model?)

1 minute ago, DannyTR said:

But the surface of the earth is bounded by the earth and sky, don’t they count as boundaries?

I think that was just meant to be an analogy, and not to be taken literally.

Edited September 22, 2018 by geordief

[Strange]

Just now, DannyTR said:

But the surface of the earth is bounded by the earth and sky, don’t they count as boundaries?

Not of a 2D surface, no.

For someone who appears to be almost completely ignorant of mathematics, it probably isn't a good idea to try using mathematics to argue that the universe must be finite. Let's stick to the science, instead.

2 minutes ago, geordief said:

Is the curvature of spacetime responsible for this ?

It depends on the topology. For example, measurements of the overall curvature of the universe show that it is flat, within the limits of measurement. That would imply that the universe is infinite (sorry, Danny!). 

But, it might not for at least two reasons:

1. The curvature might just be smaller than we can measure (for example, draw a triangle on the surface of the Earth; if you make the triangle big enough the sum of the angles will be more than 180º. Now imagine being on the surface of planet that is so huge that however big a triangle you can practically make, the angles still add up to 180º as near as you can measure. It's not flat but you can't detect the curvature.)
2. The topology could be such that it is flat but still finite. For example, the surface of a torus (donut shape) is geometrically flat even though it is finite. What this means is that if you draw a triangle on the surface of a torus, the angles will add to 180º - unintuitive, I know.

[DannyTR]

11 minutes ago, Strange said:

Not of a 2D surface, no.

For someone who appears to be almost completely ignorant of mathematics, it probably isn't a good idea to try using mathematics to argue that the universe must be finite. Let's stick to the science, instead.

It depends on the topology. For example, measurements of the overall curvature of the universe show that it is flat, within the limits of measurement. That would imply that the universe is infinite (sorry, Danny!). 

But, it might not for at least two reasons:

1. The curvature might just be smaller than we can measure (for example, draw a triangle on the surface of the Earth; if you make the triangle big enough the sum of the angles will be more than 180º. Now imagine being on the surface of planet that is so huge that however big a triangle you can practically make, the angles still add up to 180º as near as you can measure. It's not flat but you can't detect the curvature.)
2. The topology could be such that it is flat but still finite. For example, the surface of a torus (donut shape) is geometrically flat even though it is finite. What this means is that if you draw a triangle on the surface of a torus, the angles will add to 180º - unintuitive, I know.

You are making things too complicated:

 - You have a paradox; the measure problem

 - It’s resolved with a finite universe 

[Strange]

4 minutes ago, DannyTR said:

- You have a paradox; the measure problem

 - It’s resolved with a finite universe 

The measure problem is, as you said, a mathematical problem. It tells us nothing about the nature of the universe. That isn't how science (or reality) works.

As you are unable to provide any evidence for your claims I will report the thread for closure.

[DannyTR]

The measure problem tells us that our models of the universe must be finite; that is the nature of a paradox - it means an error in the underlying assumptions - IE the error of assuming an infinite universe.