The Measure Problem

[Strange]

8 minutes ago, DannyTR said:

What is natural about a quantity larger than any other possible quantity?

It follows naturally from the definition of the natural numbers

[DannyTR]

- Assume a natural number X such that X >  all Naturals

- But X+1>X

- Reductio ad absurdum, no such number exists 

- Actual Infinity does not exist 

[studiot]

Strange/quiet

I think there is a language difficulty here I often have to think several times because of quiet's the unusual (in English) sentence constructionn which doesn't always result in what he means.

I'm sure though that there is no 'ill intent aforethought'.

Quiet's last post was urging the OP (in a roundabout way) to do some proper research of his own; we all do this from time to time.

Although the OP seems suddenly able to pull out very technical words, that are not taught until University full mathematics courses, and (purposely?) misuse them, instead of engaging in the discussion.

I have reported this behaviour.

[Strange]

1 hour ago, DannyTR said:

Assume a natural number X such that X >  all Naturals

- But X+1>X

- Reductio ad absurdum, no such number exists 

We know that. If the point you are trying to make is that you cannot treat infinity as a number (in combination with the natural numbers, for example) then obviously this is correct. As pointed out in the article linked in your OP. 

Of course, there is arithmetic defined on the trans-finite numbers. 

Properties of the natural number system don't define the nature of the universe. 

Edited September 23, 2018 by Strange

[druS]

Before this discussion may be shut down, I just wanted to say just how much I have enjoyed the responses to OP, especially to the "long termers" here.

I'm nothing but a novice but increasingly intrigued by math, for once a discussion I could largely follow. Cheers people.

[DannyTR]

1 hour ago, Strange said:

Properties of the natural number system don't define the nature of the universe. 

But we use math to model the universe. Actual Infinity:

 - does not exist mathematically

 - does not (provably) exist in nature 

 - yet it is in our cosmological models

Actual Infinity is akin to magic... the universe is not magic it’s material...

[Strange]

1 hour ago, DannyTR said:

But we use math to model the universe.

Any maybe our math is not able to fully describe the universe. Who knows.

1 hour ago, DannyTR said:

 - does not (provably) exist in nature 

But you can't prove it doesn't exist. So you are still just repeating the same claim without evidence. This is just reaching your personal (religious?) beliefs. Stop it. 

1 hour ago, DannyTR said:

- yet it is in our cosmological models

Not all of them. The universe may be finite or infinite. No one knows and it makes no difference to cosmology.

1 hour ago, DannyTR said:

Actual Infinity is akin to magic...

And unsubstantiated beliefs are akin to religion. Your belief that the universe is finite is basically a religious belief.

[MigL]

I think this has been mentioned before by other members...

We use complex and imaginary numbers to model physical processes also.
Does that mean these observed processes don't actually happen ???

( must be magic then )

Edited September 24, 2018 by MigL

[DannyTR]

3 hours ago, MigL said:

I think this has been mentioned before by other members...

We use complex and imaginary numbers to model physical processes also.
Does that mean these observed processes don't actually happen ???

( must be magic then )

The observed processes happen, but they are processes that don’t involve the infinite.

There are no examples of actual infinity in the physical world.

The world is discrete but the only sensible way to model it is continuous... catch 22

[Strange]

33 minutes ago, DannyTR said:

There are no examples of actual infinity in the physical world.

Evidence please. 

34 minutes ago, DannyTR said:

The world is discrete

Evidence?

This is a new baseless claim. 

[DannyTR]

No it does not work that way:

- You are asserting the existence of an irrational and spiritual concept (Absolute Infinity)

- There are no provable instances of it in nature 

- It does not exist mathematically 

- The burden of proof is on you to show that Absolute Infinity exists 

[Strange]

7 minutes ago, DannyTR said:

You are asserting the existence of an irrational and spiritual concept (Absolute Infinity)

No. I am asking YOU to support YOUR claim that there is no such thing.

8 minutes ago, DannyTR said:

The burden of proof is on you to show that Absolute Infinity exists 

It would do, if I claimed it does. I am not making any such claim. The burden of proof is on the one making the claim.

If you do not provide evidence in the next post I will report you for soapboxing (and trolling).

[DannyTR]

9 minutes ago, Strange said:

No. I am asking YOU to support YOUR claim that there is no such thing.

It would do, if I claimed it does. I am not making any such claim. The burden of proof is on the one making the claim.

If you do not provide evidence in the next post I will report you for soapboxing (and trolling).

Evidence for my claim that Actual Infinity does not exist above:

 

Materialistic Argument:

 - Actual Infinity and the materialistic world view do not mix.

 - For example, can a physical quantity larger than any other possible physical quantity exist?

 

Numerical Argument:

- There is an number X such that X > all N

- But X+1 > X

- There is no such number

- Hence Actual Infinity is not a number.

 

Geometrically:

 - It is impossible to construct a line segment with the property that it is longer than all other line segments 

 

Temporally:

 - Assume infinite time

- so anything than can possibly happen will eventually happen

- If it happens once it will eventually happen again

- So it will eventually happen an infinite number of times 

- no matter how unlikely it was in the first place

 

 Paradoxes are solved

 

  - Zeno’s paradoxes. It’s impossible to travel any distance as movement requires an infinite number of steps. We can move. Reductio ad absurdum. Space must be discrete

 

 - Galileo's paradox is solved:

 - There are less squares than numbers because not all numbers are squares. Yet each number has a square so the number of numbers and squares must be the same. 

- He is trying to compare two actually infinite sets, IE comparing two undefined things. A set definition is not complete until all its members are iterated. 

 

- Hilbert’s infinite hotel paradox is solved; such a hotel cannot exist.

 

 - Cantor's Paradox:

‘The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.’

The set of all sets is an ACTUAL INFINITY so not a completly described set. You cannot soundly reason with it. Leads to the paradox.

 

Common sense View:

The Actually Infinite exists. Reductio ad absurdum. No it doesn’t.

 

 

 

[Strange]

13 minutes ago, DannyTR said:

For example, can a physical quantity larger than any other possible physical quantity exist?

Do you have any EVIDENCE that it doesn't?

13 minutes ago, DannyTR said:

Numerical Argument:

Not evidence.

14 minutes ago, DannyTR said:

Geometrically:

Not evidence.

14 minutes ago, DannyTR said:

Temporally

Not evidence. 

14 minutes ago, DannyTR said:

Paradoxes are solved

Not evidence.

15 minutes ago, DannyTR said:

Cantor's Paradox:

Not evidence.

15 minutes ago, DannyTR said:

Common sense View

Definitely not evidence.

OK. So you have no evidence, just your faith. Reported.

I have to assume you don't know what the word "evidence" means.

[swansont]

1 hour ago, DannyTR said:

 Paradoxes are solved

 

  - Zeno’s paradoxes. It’s impossible to travel any distance as movement requires an infinite number of steps. We can move. Reductio ad absurdum. Space must be discrete

 

No, the conclusion is the opposite. You can't move an infinite number of steps, yet we can move, thus space must be continuous.

[Phi for All]

5 hours ago, DannyTR said:

Evidence for my claim that Actual Infinity does not exist above:

 

Materialistic Argument:

 - Actual Infinity and the materialistic world view do not mix.

 - For example, can a physical quantity larger than any other possible physical quantity exist?

 

Numerical Argument:

- There is an number X such that X > all N

- But X+1 > X

- There is no such number

- Hence Actual Infinity is not a number.

 

Geometrically:

 - It is impossible to construct a line segment with the property that it is longer than all other line segments 

 

Temporally:

 - Assume infinite time

- so anything than can possibly happen will eventually happen

- If it happens once it will eventually happen again

- So it will eventually happen an infinite number of times 

- no matter how unlikely it was in the first place

 

 Paradoxes are solved

 

  - Zeno’s paradoxes. It’s impossible to travel any distance as movement requires an infinite number of steps. We can move. Reductio ad absurdum. Space must be discrete

 

 - Galileo's paradox is solved:

 - There are less squares than numbers because not all numbers are squares. Yet each number has a square so the number of numbers and squares must be the same. 

- He is trying to compare two actually infinite sets, IE comparing two undefined things. A set definition is not complete until all its members are iterated. 

 

- Hilbert’s infinite hotel paradox is solved; such a hotel cannot exist.

 

 - Cantor's Paradox:

‘The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.’

The set of all sets is an ACTUAL INFINITY so not a completly described set. You cannot soundly reason with it. Leads to the paradox.

 

Common sense View:

The Actually Infinite exists. Reductio ad absurdum. No it doesn’t.

 

!

Moderator Note

The attempt at producing evidence is very much appreciated, but your examples are mostly more unsubstantiated claims based on your assumptions and incredulity. Please take the corrections being offered to you and adjust your arguments. And please present actual objective evidence, not hand-waving and "common sense".

 

[studiot]

6 minutes ago, Phi for All said:

Please take the corrections being offered to you and adjust your arguments.

@DannyTR

 

And please reply to the question I asked you about 35 posts back in the middle of page3.

None of the succeeding posts have addressed this question.

I also explained in that post why I had broken my discussion down into small pieces

and

Why you were totally wrong to introduce the 'number line' as an explanation of your contention.

[substitutematerials]

To push this question back towards cosmology, can we ask what would fill a infinite universe? 

The possibilities I can think of are:

a.) we live within a finite section of an infinite volume which contains matter, which is surrounded by infinite emptiness.

b.) We live within one of a finite number of such finite sections in an infinite volume.

c.) the universe is homogenous and isotropic on an infinite scale, and all configurations of matter exist in it, including a bizarro Earth where invisible unicorns live on the moon

d.) the universe is homogenous and isotropic on an infinite scale, filled with an infinitely repeating pattern of precisely the same configurations of matter we observe in our observable universe

 

Is this list of possibilities exhaustive?

[Strange]

6 hours ago, substitutematerials said:

To push this question back towards cosmology, can we ask what would fill a infinite universe? 

As far as we know, the entire universe is full of matter just like the observable universe.

6 hours ago, substitutematerials said:

Is this list of possibilities exhaustive?

I assume it could also be uniformly filled but not repeating like your (d). 

 

[substitutematerials]

2 hours ago, Strange said:

As far as we know, the entire universe is full of matter just like the observable universe.

I assume it could also be uniformly filled but not repeating like your (d). 

 

So if it is infinite and uniformly filled, but not repeating (c), there is definitely a moon with invisible unicorns right?

[Strange]

8 minutes ago, substitutematerials said:

So if it is infinite and uniformly filled, but not repeating (c), there is definitely a moon with invisible unicorns right?

Who knows. But bear in mind that only things that are possible can occur. However, there are animals with one horn. And there are animals that are (almost) invisible. So maybe v

[DannyTR]

Another example of the non-existence of actual infinity.

Consider the numbers on the real number line. EG between 0 and 1. Does the interval contain an actual infinity of numbers?

 - No. 

 - Numbers have length zero

 - they are just logical labels on a line

 - So the length of the interval 1 divided by the length of a number zero equals UNDEFINED.

 

So it’s correct to say that the number of real numbers between 0 and 1 is undefined (rather than Actual Infinity).

Actual Infinity does not exist and it should not be used in cosmology.

Can anyone give me a counter-example of Actual Infinity from maths or nature?

[Strange]

1 hour ago, DannyTR said:

So it’s correct to say that the number of real numbers between 0 and 1 is undefined (rather than Actual Infinity).

No. It is well defined. And it is also infinite. 

1 hour ago, DannyTR said:

Can anyone give me a counter-example of Actual Infinity from maths or nature?

Well, if the universe is infinite ...

Look, no one cares if you want believe that the universe is finite. After all, it might be. Just stop trying to justify your faith with spurious logic. You are as bad as a creationist. 

Edited September 29, 2018 by Strange

[Airbrush]

On ‎9‎/‎21‎/‎2018 at 7:43 AM, Sensei said:

"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."... Albert Einstein

Now that we have the concepts of big bang and multiverse, I wonder what Einstein would say about whether or not our big bang is infinite?   Could there be more than one big bang in an infinite multiverse?  Assuming that our big bang is not all there is.  It seems hard to believe that an event such as the big bang could extend to infinity.  It would have to be infinite already at the moment of the big bang because something finite in size cannot ever grow to an infinite size, no matter how fast the rate of expansion.  I've never heard any mention of a rate of expansion that is infinite in speed.

Edited September 29, 2018 by Airbrush

[Strange]

19 minutes ago, Airbrush said:

Now that we have the concepts of big bang and multiverse, I wonder what Einstein would say about whether or not our big bang is infinite?

Einstein was aware of the Big Bang model. Before that, he preferred the idea of a static (ie. temporally infinite) but spatially finite universe. After the Big Bang model was developed, he dropped the idea of the static universe (it is unstable) but I don't know if he changed his view about whether it was spatially finite or not.

19 minutes ago, Airbrush said:

Could there be more than one big bang in an infinite multiverse?

The eternal inflation model does assume that each "bubble universe" is finite. 

Because of the odd nature of infinity, it is (I think) possible to have a multiverse of infinite universes. Whether it is physically realistic or not, is something else.

19 minutes ago, Airbrush said:

Assuming that our big bang is not all there is.  It seems hard to believe that an event such as the big bang could extend to infinity.  It would have to be infinite already at the moment of the big bang because something finite in size cannot ever grow to an infinite size, no matter how fast the rate of expansion. 

It is probably better not to think of it as an "event" (or at least, not a "creation" event from nothing). Otherwise you end up with problems like this.

 

Edited September 29, 2018 by Strange