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# Can be that the Natural Numbers are Finite?

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If I give every point of space, every electron and atom a natural number(by the time of existence)  I got a huge number, inexpressible, but still finite. Now.

For every physical entity, even for the points of space, time will pass with every upcoming moment in the future, which again an add to the set of natural numbers I will not be able to count but countable.

I know that with every moment of time there is more information in the system.

But how could it be infinite, if the Future numbers and the possibility to account them, not yet happened?

Where are the physical signs of infinity?

Why are we counting infinite?

Why don’t we count finite?

Edited by Conscious Energy
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• Conscious Energy changed the title to Can be that the Natural Numbers are Finite?
52 minutes ago, Conscious Energy said:

If I give every point of space, every electron and atom a natural number(by the time of existence)  I got a huge number, inexpressible, but still finite

You have an infinite number of points in any finite, one-dimensional line segment. So this is incorrect.

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Where are the physical signs of infinity?

Why are we counting infinite?

Why don’t we count finite?

Infinities are useful in analysis

We absolutely count finite things.

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8 hours ago, swansont said:

any finite, one-dimensional line segment

The line is time and the one dimensional segment is a point of space.

The shortest time we take the smallest space and we call it plank unit.

If I record this smallest unit of space in a moment of time how is it possible that there are an infinite number of plank units to be count?

If you try to count, you count on a 2D line of Time because of your physical reality related capabilities to measure.

Time pass. Linearly forward pointing to the future within every point of space.

0D —> 1D —->4D (Space)Time.

0D = moment of time

1D= point of space

2D= line of space or Time within Space(Time) we can measure

4D= 3D volume by 1D Time. The size of Natural Reality, Now.

Edited by Conscious Energy
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2 hours ago, Conscious Energy said:

The line is time and the one dimensional segment is a point of space.

No, the line is not time. You said space, and I meant space.

There are an infinite number of points in any volume of space.

2 hours ago, Conscious Energy said:

The shortest time we take the smallest space and we call it plank unit.

If I record this smallest unit of space in a moment of time how is it possible that there are an infinite number of plank units to be count?

You previously said points, not planck lengths. A point has no length. Don’t change the argument

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As Swansont states,

A point is not a Planck length.

A Planck length is the smallest possible measurable distance of space, a point has no physical dimension.

Edited by Intoscience
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7 hours ago, swansont said:

No, the line is not time. You said space, and I meant space.

If there is space, there is time.

There is the timeline of Time (t0—>Tnow).

It is a linear vector pointing to the Future. It is true in every point of space, independent a black hole or interstellar space exist in it.

Of course the perception of current time in the local space is depending from: is it a black hole there or almost emptiness.

The shifting black hole does not change the age of the space it is pathing through or alter the age of the galaxy it is existing in by being heavy. Or? How?

What physical property space has which can be impacted by gravity?

Isn’t gravity is the result of mass? —> the heavier object has bigger gravitational pull? Maybe big enough to pull even a photon or it’s wave distribution.

How could we realise that photons and waves also has some minimal mass?

What proves that a photon is absolutely mass less?

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7 minutes ago, Conscious Energy said:

If there is space there is time.

There is the timeline of Time (t0—>Tnow).

It is a linear vector, true in every point of space independent a black hole or interstellar space exist in it.

Of course the perception of current time in the local space is depending from: is it a black hole there or almost emptiness.

The shifting black hole does not change the age of the space it is pathing through or alter the age of the galaxy it is existing in by being heavy. Or?

What does this have to do with anything?

You mentioned points in space, not time. I specified a line segment in space, and noted that there are an infinite number of points in it. No mention of time at all.

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What physical property space has which can be impacted by gravity?

None.

Space is not impacted by gravity. The curvature of space is gravity. A little more specifically, mass (really, energy-momentum) causes space to curve, which we perceive as gravity.

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Isn’t gravity is the result of mass? —> the heavier object has bigger gravitational pull? Maybe big enough to pull even a photon or it’s wave distribution.

Yes.

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How could we realise that photons and waves also has some minimal mass?

What proves that a photon is absolutely mass less?

Because if the photon had mass then it wouldn't behave the way it does. Note that this is physics and not philosophy, and seems to be OT for this thread. There have been other discussions about this, and you are free to start a new one (in an appropriate subforum) if you actually want to discuss the physics of it.

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19 minutes ago, swansont said:

line segment in space, and noted that there are an infinite number of points in it

How you prove, that segment of space has infinite points?

A point has a minimal space (extent), not? What proves a point has absolutely no space?

You need time to determine the segment.

You need time to count the points.

19 minutes ago, swansont said:

What does this have to do with anything?

Space does not exist without time.

Thought experiments to prove it.

Edited by Conscious Energy
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2 hours ago, Conscious Energy said:

How you prove, that segment of space has infinite points?

A point has a minimal space (extent), not? What proves a point has absolutely no space?

It's settled math. You can pick any two points and always find a point in between them.

2 hours ago, Conscious Energy said:

You need time to determine the segment.

You need time to count the points.

But not an infinite amount of time. Math is a labor-saving device.

Otherwise this doesn't seem to be pertinent.

2 hours ago, Conscious Energy said:

Space does not exist without time.

Thought experiments to prove it.

Again, not pertinent to the OP.

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15 minutes ago, swansont said:
2 hours ago, Conscious Energy said:

Space does not exist without time.

Thought experiments to prove it.

Again, not pertinent to the OP.

It has a link I think.

Because if SpaceTime is a finite entity there is no way that any point of it would be absolutely infinite. Physically for sure.

If something is physically finite, I do not see how that something could be mathematically infinite.?

Edited by Conscious Energy
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56 minutes ago, Conscious Energy said:

I do not see how that something could be mathematically infinite.?

You need more precise mathematics for that.

In particular you need to understand what is meant by finite and infinite.

Every (individual) Natural number is finite.

But the collection of all natural numbers is infinite.

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21 hours ago, Conscious Energy said:

I know that with every moment of time there is more information in the system.

It depends on what you mean by "information", and on what you mean by "the system".

For example:

If you mean accessible (macroscopic) information, and the system is the whole universe, it's never true.

If you mean all information (the negative of so-called fine-grained entropy), and the system is the whole universe; it's also never true (fine-grained entropy is always constant for the whole system+environment).

...

Only very rarely it's true (example: living organisms). Living organisms can organize (the information stored in them grows) at the expense of "disorganizing" the environment.

So you see, you must be a lot more careful when making sweeping statements like that.

I also agree with what you've been told by other users on numbers and the infinite.

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35 minutes ago, studiot said:

Every (individual) Natural number is finite.

But the collection of all natural numbers is infinite.

How can the collection of all natural numbers be infinite if the numbers of physically recognisable entities are finite?

Reality sure has a limit by Time Now —> the future not yet happened.

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40 minutes ago, Conscious Energy said:

How can the collection of all natural numbers be infinite if the numbers of physically recognisable entities are finite?

Numbers don’t physically exist.

2 hours ago, Conscious Energy said:

It has a link I think.

Because if SpaceTime is a finite entity there is no way that any point of it would be absolutely infinite. Physically for sure.

If something is physically finite, I do not see how that something could be mathematically infinite.?

But these aren’t the same thing. A volume of spacetime is not the same as the points inside it.

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42 minutes ago, Conscious Energy said:

How can the collection of all natural numbers be infinite if the numbers of physically recognisable entities are finite?

Reality sure has a limit by Time Now —> the future not yet happened.

I asked you to be mathematically precise.

So please avoid mixing up mathematics and other topics, particularly physics.

This thread is claimed to be about the 'Natural numbers', which is a precisely defined mathematical description.

Do you know what the natural numbers are ?

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9 hours ago, studiot said:

I asked you to be mathematically precise.

I try to be. There is a big difference between finite and infinite natural numbers.

9 hours ago, studiot said:

So please avoid mixing up mathematics and other topics, particularly physics.

It is in the philosophy section.

I avoid other topics. I think I am allowed to think with any parts of reality (space, time, energy, matter) and try to express them with math to answer such a difficult question.

You could express where from you could have the energy matter and time to account every natural value of space, time, energy and matter. I understand it seems infinite.

Since time is a natural physical limit, theoretically math can not be absolutely infinite. We have no chance to count every natural number because it’s overall number to account is more with every upcoming moment of time.  Sadly we do not know the exact age of time and the exact rate of empty space expansion by time. st0 —-> st1 ca 9 billion km/s (c2) to all direction, to know everything exactly. If the system is finite we can call its overall value 1.

You always measure under gravity in a local space and a relative time, what is impacting your measurement but not impacting the age of SpaceTime you measure within!

Or galaxy moves within the extragalactic frame of reference with 660km/s.

There is space before and after on the path of a black hole, where in a 1 000 years time difference in the extragalactic frame of reference a photon path with a different path.

Or do you think that a black hole put an extra spin in the space it path?

Can you help me with a physical example undeniably proves infinity?

Edited by Conscious Energy
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12 hours ago, joigus said:

It depends on what you mean by "information", and on what you mean by "the system".

Time is information

The system is the Universe

Every macroscopic physical entity has an age since when it exist and the age is increasing by time.

Time is countable by natural numbers. Time is not infinite. It has a physical limit by the present, now.

11 hours ago, swansont said:

Numbers don’t physically exist.

True, but we count the members of the physical reality with math (natural numbers)

Can I try to recognise and understand anything physical without math?

Edited by Conscious Energy
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17 hours ago, Conscious Energy said:

What proves that a photon is absolutely massless?

Being "massless" in physics mean "having no rest-mass" (aka "invariant mass").

Did you see photon at rest?

Particles, molecules or objects, with mass ("rest mass", "invariant mass"), can be accelerated and decelerated i.e. their frame of reference can be changed.

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1 hour ago, Sensei said:

Did you see photon at rest?

Did you see anything at rest?

An atom for example without our galaxies 660km/S  motion in the extragalactic frame of reference and the gravity it provides?

Isn’t the volume of SpaceTime is the fundamental frame of reference? How this frame could be infinite if we have a present and not yet happened Future.

How do you deny it is Finite?

How you prove SpaceTime is infinite and there is infinite amount of natural numbers to account every point of information of it? How can you have more (infinite) numbers than the information the universe provides? We can not account 0,000…01% of the universe. Why do you suppose it is infinite?

Numbers are a human invention we need energy invested to be able to account! There are no signs of infinite Energy or Matter. No signs of infinite Time or Space.

If I use every existing energy and matter to feed a device counts natural numbers, when the Universe is out of energy and matter my device stops and gives a limit to the counted natural numbers (worst case scenario). Our lack of accounting further the natural numbers won’t stop the Universe to provide more and more information.

Edited by Conscious Energy
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3 hours ago, Conscious Energy said:

Time is countable by natural numbers. Time is not infinite. It has a physical limit by the present, now.

True, but we count the members of the physical reality with math (natural numbers)

But that doesn't limit the math. You seem to be insisting that it does.

3 hours ago, Conscious Energy said:

Can I try to recognise and understand anything physical without math?

Your thread title is all about math and nothing about physical things.

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Do you see Time at rest?

Is there any physical circumstances time absolutely do not pass?

A black hole gets older, time (differently) pass in it, not?

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6 hours ago, Conscious Energy said:

It is in the philosophy section.

Yes and I have several books on the philosophy of the Natural Numbers, along with large sections in many more maths books.

You are using a different version of the Natural Numbers from the rest of us.

You have not answered my question:

15 hours ago, studiot said:

Do you know what the natural numbers are ?

Further, just because this is the philosophy section, it does not entitle you make make unsupported claims such as  "youcannot have space without time", most especially not in support of other wild musings.

6 hours ago, Conscious Energy said:

Can you help me with a physical example undeniably proves infinity?

You have asked several such questions and been answered before.

Even though, just like with the Natural Numbers I do not know what you mean by the much more difficult notion to tie down, that of infinity.

Be all that as it may, I will offer you some hopefully useful thoughts on these questions.

But they will only be useful if you take some note of them, instead of immediately trying to challenge them with unconventional interpretations of conventional definitions.

OK so space, with or without time and Infinity for a physical object.

Using zero and the positive integers we can propose temporal and spatial dimensions  as follows:

Let  S1, S2, S3, S4..........   denote spatial dimensions.

Let T1, T2, T3, T4..........   denote temporal dimensions.

Then for each of 0, S1, S2, S3, S4..........  spatial dimensions we can propose 0, T1, T2, T3, T4.......... temporal dimensions

Now we can do the maths of how each of these situations would operate, ie what our universe would be like if there were  eg say only two spatial and one temporal dimensions, two spatial and zero temporal, two temporal and zero spatial and so on.

Then we can do the physics and compare our observations on our universe to see which one matches our maths the best.

Again there are many books and meaty subsections of books and papers doing exactly this.

The results of this is why we believe our ordinary sense impression that there are three spatial and one time dimensions.

For any other combination we can derive mathematical results we do not observe.

OK so to consider an physical object existing in this 3 + 1 universe and the relationship to infinity.

Let us say a building stone in a dry stone wall.

Say we move this brick 1 metre to the left, so that instead of being the fourthe stone from the left hand corner of the wall it is now a cornerstone.

What have we done ?

Well we have changed its spatial position and in doing so did the stone disappear at any point in the move and reappear anywhere else or did it at some instant occupy every

point lying between its initial and final position ?

I would say we have no evidence that any stone has ever done the former but has only ever passed through every point on its way.

So what links the initial and final points ?

Mathematically the word is continuity.

And continuity requires infinite division.

Now you have mentioned Planck lengths.

Swansont has told you that we cannot measure within a PL.

But he did not say that the points in the space within do not exist, just that we can't measure there.

And continuity requires the existence of these points.

So by the mathematics of continuity (infinite division) we have a physical infinite.

The interesting thing to learn from all this is that an infinite sum can add up to a finite total, which is the principal underlying 'limits', another specialist term that you are so loosely bandying about.

Note the importance of recognising and taking note of what others say.

Edited by studiot
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42 minutes ago, swansont said:

But that doesn't limit the math. You seem to be insisting that it does.

You can not have more natural number then the information about them in Nature. I think the present Time = Now provides a limit to information available.

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The problem is that you say  you are talking about mathematics but you are actually talking about physics. You do not know what mathematics is and you do not know what physics is!  There is "infinity" in mathematics but there is no "infinity" in physics.

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24 minutes ago, Country Boy said:

The problem is that you say  you are talking about mathematics but you are actually talking about physics.

I think they are interconnected.

24 minutes ago, Country Boy said:

You do not know what mathematics is and you do not know what physics is!

I don’t know imaginary math and physics.

I am relative good with the math and physics of Natural Reality.

24 minutes ago, Country Boy said:

There is "infinity" in mathematics

This what I doubt if:

24 minutes ago, Country Boy said:

there is no "infinity" in physics.

53 minutes ago, studiot said:

Do you know what the natural numbers are ?

Yes.
0 1 2 3 4 5 ….

the ones in Nature I can count with.

Edited by Conscious Energy
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