Space is what time looks like

[michel123456]

 

So the ratio of a circle's circumference to its diameter isn't pi before we do a calculation?

Taking the ratio of something is a mathematical operation. The fact that in this specific case the ratio is constant is remarkable. But the operation of taking the ratio is time related.

[ajb]

Taking the ratio of something is a mathematical operation. The fact that in this specific case the ratio is constant is remarkable. But the operation of taking the ratio is time related.

Again, you seem to be mixing how we do mathematics with mathematics.

 

Do you agree that as a universal and timeless statement the ratio of any circle's circumference and its diameter is always the number pi? This is irrespective of if it took me time two write that?

[michel123456]

Again, this is how we do mathematics and is really tied to our notation.

 

 

I disagree.

 

There is a universal truth there that does not have anything to do with the physical notion of time.

 

The real numbers have an operation on them that we call addition - we use the notaion '+' for this. We have a specified number, that we denote as '1' and another we denote as '2'. It is a universal and unchanging truth that

 

1+1 =2

 

as we write it.

 

Nothing to do with time here in any deep way.

 

The only place where time comes into it is that I am subject to time as you are. Thus how we do mathematics is constrained by time - but not the mathematics itself. Time is not written into mathematics in any deep way.

I disagree. Mathematics cannot exist without time.

How would you make an operation? How can you get a result? How do you proceed in calculations? How do you make a reasoning? How do you make a proof? How do you state a theorem?

1+1 represents a change.

Again, you seem to be mixing how we do mathematics with mathematics.

 

Do you agree that as a universal and timeless statement the ratio of any circle's circumference and its diameter is always the number pi? This is irrespective of if it took me time two write that?

You used the word "always". That is not timeless, it is full of time.

Edited July 13, 2016 by michel123456

[Prometheus]

Taking the ratio of something is a mathematical operation. The fact that in this specific case the ratio is constant is remarkable. But the operation of taking the ratio is time related.

 

So before we perform the operation, pi isn't any specific number?

 

Or to use a quadratic: [latex] x^2 - 4 =0 [/latex] doesn't have roots of 2 or -2 until after we calculate it? Is it enough that some ancient Sumerian probably solved this one, or do we each have to solve it? Could it change with time: if it doesn't in what way is its existence dependent on time?

[ajb]

Mathematics cannot exist without time.

For sure we cannot do mathematics without time! But that is another issue.

 

How would you make an operation? How can you get a result? How do you proceed in calculations? How do you make a reasoning? How do you make a proof? How do you state a theorem?

Again, this is about doing mathematics - we are all subject to time.

 

1+1 represents a change.

Not really... it represents another number that we denote as 2.

 

You used the word "always". That is not timeless, it is full of time.

Again, we are not timeless.

 

 

-------------------------------

 

So how do we think of the example given earlier

 

[math]\frac{C}{d} = \pi[/math] ?

 

Where is the time in this?

 

The key point is that [math] \frac{C}{d}[/math] represents another number, which we know is [math]\pi[/math] for any given circle. Thats it... no time here. (and this would be true if we use some other notations)

 

Time comes into it when we calculate the left hand side or work on presenting some proof of this statement. But this is expected as we are in the Universe and subject to time.

Edited July 13, 2016 by ajb

[michel123456]

For sure we cannot do mathematics without time! But that is another issue.

 

 

Again, this is about doing mathematics - we are all subject to time.

 

 

Not really... it represents another number that we denote as 2.

 

 

Again, we are not timeless.

 

 

-------------------------------

 

So how do we think of the example given earlier

 

[math]\frac{C}{d} = \pi[/math] ?

 

Where is the time in this?

 

The key point is that [math] \frac{C}{d}[/math] represents another number, which we know is [math]\pi[/math] for any given circle. Thats it... no time here. (and this would be true if we use some other notations)

 

Time comes into it when we calculate the left hand side or work on presenting some proof of this statement. But this is expected as we are in the Universe and subject to time.

So you accept that we live in the universe and that we are subject to time but for mathematics no.

 

[math]\frac{C}{d} = \pi[/math] ?

 

Where is the time in this?

 

You have a fraction, which is a mathematical operation. You are transforming something into something else. It is a change. Something before, other thing after. Time.

Time is even in the way you read the equation. Like music. If we were talking about language or music would you be so reluctant to admit there is time in it?

Edited July 13, 2016 by michel123456

[ajb]

So you accept that we live in the universe and that we are subject to time but for mathematics no.

It seems that the mathematical world is not subject to time in any meaningful sense.

 

 

You have a fraction, which is a mathematical operation. You are transforming something into something else. It is a change. Something before, other thing after. Time.

No - I have a fraction which is really just notation for 'some' real number.

 

Again, doing maths takes time. But thats as deep as it gets here.

 

 

If we were talking about language or music would you be so reluctant to admit there is time in it?

But we are not.

[michel123456]

Mathematics is a language.

[ajb]

Mathematics is a language.

Not in the simple way you mean it - also I think it is more than that.

 

Still, this does not convince me that time is part of mathematics - in the way you mean anyway...

[cladking]

It is a universal and unchanging truth that

 

1+1 =2

 

 

 

As an abstraction this is true and quite timeless. One car plus one train equals two things. It would even be true that a car in the here and now plus a train in the 1860's equal two things. The problem comes if we try to apply such truths to the real world. c / D = Pi. This is true and the entire statement is true independently of how it is read, the order it is comprehended, or the numbers applied to test it. If we say one bridge plus one bridge can carry us to our destination we are obviously invoking time. The same applies if you are computing the number of bolts needed to build a bridge; twenty girders and ten bolts per girder equals 200 bolts. 20 / (1/ 10) = 200 (or 10 x 20 = 200). As abstractions equations are necessarily correct and timeless; the entire statement stands at once.

 

The problem I see is that our math assumes that space is three dimensional with time as a fourth dimension. If this isn't reflective of reality I believe that equations would have to be rewritten to deal with space as a property of time. How can you define "circumference" or "diameter" if there's no such thing as space as we know it? This equation would have to be rewritten to reflect the reality even though the answer is going to be just about the same thing. This would apply to even purely abstract equations that involve space or time would it not?

[CarbonBasedOverlord]

My point is that you cannot have the slightest notion of mathematics without time.

 

I work in metaphor, not math, but I know change requires time. "5-2=3" is the expression of a change occurring over time. "The character 5 suffered a loss of two of itself and was transformed into 3."

 

I like the way this conversation is going.

[ajb]

I work in metaphor, not math...

That will be ypur first problem.

 

"5-2=3" is the expression of a change occurring over time. "The character 5 suffered a loss of two of itself and was transformed into 3."

How poetic... but you (and others) are reading to much into this as regards to time.

[michel123456]

I wonder if the difference between our understandings is about the meaning of "without time" and "timeless".

 

From what I understand from AJB posts is that he believes that some mathematical truth is timeless, meaning by that it it was true yesterday, today, tomorrow, whenever it will always be true. I agree with that except that this statement uses time, so it is not "timeless", it is "timefull". Or one could say that it is time-independent. IOW in a world where time exists, the statement is true and does not depend on time.

 

OTOH what I try to make clear is that without time such a statement cannot stand, because you need time to make this statement, either writing it down, either reading it, either explaining it, either proving it, either conceptualizing it. The fact that 2 things are compared means time. Any mathematical operation need time as a prerequisite. It is change, transformation. You have something before and something else after. An equation is to be read from left to right, or right to left. It just not stands there, it is a process.

 

And it is a good thing, I wonder why anyone would find it bizarre or difficult to accept.

Edited July 14, 2016 by michel123456

[ajb]

Again, you are mixing mathematics and how one does mathematics...

 

There is nothing in inherent in mathematics that tells us anything about time and itself does not need the physical notion of time. And again, mathematicans are of course subject to time - I am not sure how many more times I can say this.

 

Anyway, none of this has anything to do with time being a non-fundamental concept in physics.

[cladking]

Again, you are mixing mathematics and how one does mathematics...

 

There is nothing in inherent in mathematics that tells us anything about time and itself does not need the physical notion of time. And again, mathematicans are of course subject to time - I am not sure how many more times I can say this.

 

Anyway, none of this has anything to do with time being a non-fundamental concept in physics.

 

How about V = d/ t?

 

Of course the statement is "timeless" but how can it be applied to anything timelessly?

[ajb]

How about V = d/ t?

What about it?

 

You may model time using mathematics - if that is what you mean by 't' in the above. So what? This does not tell me anything like 'mathematics needs time'.

[Strange]

And it is a good thing, I wonder why anyone would find it bizarre or difficult to accept.

 

 

Because it is complete nonsense.

 

The fact that you believe such things explains why you sometimes post such bizarre "theories".

[michel123456]

 

 

Because it is complete nonsense.

 

The fact that you believe such things explains why you sometimes post such bizarre "theories".

Ok, you are Strange, I am bizarre.

[cladking]

What about it?

 

You may model time using mathematics - if that is what you mean by 't' in the above. So what? This does not tell me anything like 'mathematics needs time'.

 

That a cirlce is related to its diameter is a concept that is independent of time. However, concepts like velocity have no meaning outside of time. Indeed, if space is really an emergent property of time than even the relationship of a circle to it diameter is changed. You would say that it's pi times longer around a circle than across it. These measurements would be a function of time rather than distance. From current perspective pi is 3.14 and this remains "true" even though it is not the most realistic way to depict it. Math is certainly adaptable enough to arrive at the same answer in many different ways.

[ajb]

That a cirlce is related to its diameter is a concept that is independent of time.

Okay

 

 

However, concepts like velocity have no meaning outside of time.

Okay... in the sense that we use mathematics to describe the rate of change of poistion. I think we all are okay with this. (Not quite seeing your point yet)

 

Indeed, if space is really an emergent property of time than even the relationship of a circle to it diameter is changed.

???? why ????

 

 

You would say that it's pi times longer around a circle than across it.

???? why ????

 

These measurements would be a function of time rather than distance.

???? why ????

 

From current perspective pi is 3.14 and this remains "true" even though it is not the most realistic way to depict it.

Yes, pi is pi ... ?

 

Math is certainly adaptable enough to arrive at the same answer in many different ways.

At last a reasonable statement.

 

cladking - I really have no idea what you are trying to say to me.

[cladking]

If "space" or "distance" is a property of time then there's not really such a thing as "diameter" for a circle. The earth would be about .05 seconds (light) across rather than 8,000 miles. Expressing it in "miles" isn't necessarily wrong but it would be less appropriate. It could be misleading.

[ajb]

If "space" or "distance" is a property of time then there's not really such a thing as "diameter" for a circle.

Sorry for the late reply...

 

 

You are confusing the physical world with the mathematical world. There is no problem with the notion of the diameter or a circle.

[Strange]

If "space" or "distance" is a property of time then there's not really such a thing as "diameter" for a circle. The earth would be about .05 seconds (light) across rather than 8,000 miles. Expressing it in "miles" isn't necessarily wrong but it would be less appropriate. It could be misleading.

Even if you were silly enough to express the distances as times, the ratio would still be pi.

[cladking]

You are confusing the physical world with the mathematical world. There is no problem with the notion of the diameter or a circle.

 

You can model things that don't exist in the real world. You can explain the motions of the planets in terms of a flat earth but they'll get incrediby complex.

[ajb]

You can model things that don't exist in the real world.

It depends exactly what you mean by model - we can construct theories that do not match nature well. Anyway, I still don't see how this relates to time being an intrinstic part of mathematics.