Paradox?

[Philosophy Explorer]

Wrong on both counts.Actual solid objects are made up of points, but the size of the object has no relationship to the size of the set of the points within the object. Who are these people who think this? Mathematicians such as Cantor for one. Have you checked Wikipedia?

Why yes Phil, I did check Wikipedia's article on Cantor. There I found:

Cantor's philosophy on the nature of numbers led him to affirm a belief in the freedom of mathematics to posit and prove concepts apart from the realm of physical phenomena, as expressions within an internal reality.

Again: ... concepts apart from the realm of physical phenomena ...

If you know of any specific work of Cantor's in which he claims that mathematical points have anything to do with the physical universe, please feel free to supply that citation.

To the contrary, as Arising_uk repeatedly notes, dimensionless points are purely mathematical abstractions. In physics, nothing smaller than the Plank length can be sensibly spoken about or measured. Physicists build particle colliders to look for quarks, bosons, neutrinos, and the like. But there has never in the history of physics ever been a grant proposal or research program to find dimensionless points. That's because there are no dimensionless points in the physical world. Dimensionless points are mathematical abstractions. Dimensionless points are useful for doing physics but they are not themselves physical.

I'll add that I'm disappointed but not surprised that you never replied to my post in which I debunked your erroneous notions regarding the cardinality of the real numbers. You seem to read snippets of text on Wikipedia, extrapolate false conclusions, and then close your mind to reason.

Certain articles I read did not specify if they pertained to math or physical reality, therefore I presume both. Just because you can't see it or imagine it doesn't mean it can't exist, therefore I'm within my rights to demand an article specifying it can't exist in physical reality (along with some proof).

PhilX

[wtf]

Certain articles I read did not specify if they pertained to math or physical reality, therefore I presume both. Just because you can't see it or imagine it doesn't mean it can't exist, therefore I'm within my rights to demand an article specifying it can't exist in physical reality (along with some proof).

You made the explicit claim that Cantor believed points had physical reality, and challenging us to check Wikipedia. I did, and found evidence directly contradicting your claim. So back up your claim about what Cantor believed, or retract it.

For reference, here is your original quote.

Wrong on both counts.Actual solid objects are made up of points, but the size of the object has no relationship to the size of the set of the points within the object. Who are these people who think this? Mathematicians such as Cantor for one. Have you checked Wikipedia? [my emphasis]

So yes, I checked Wikipedia, and it says the DIRECT OPPOSITE of what you claimed.

Are you capable of responding directly to this point?

[Philosophy Explorer]

Wrong on both counts.Actual solid objects are made up of points, but the size of the object has no relationship to the size of the set of the points within the object. Who are these people who think this? Mathematicians such as Cantor for one. Have you checked Wikipedia?

Why yes Phil, I did check Wikipedia's article on Cantor. There I found:

Cantor's philosophy on the nature of numbers led him to affirm a belief in the freedom of mathematics to posit and prove concepts apart from the realm of physical phenomena, as expressions within an internal reality.

Again: ... concepts apart from the realm of physical phenomena ...

If you know of any specific work of Cantor's in which he claims that mathematical points have anything to do with the physical universe, please feel free to supply that citation.

To the contrary, as Arising_uk repeatedly notes, dimensionless points are purely mathematical abstractions. In physics, nothing smaller than the Plank length can be sensibly spoken about or measured. Physicists build particle colliders to look for quarks, bosons, neutrinos, and the like. But there has never in the history of physics ever been a grant proposal or research program to find dimensionless points. That's because there are no dimensionless points in the physical world. Dimensionless points are mathematical abstractions. Dimensionless points are useful for doing physics but they are not themselves physical.

I'll add that I'm disappointed but not surprised that you never replied to my post in which I debunked your erroneous notions regarding the cardinality of the real numbers. You seem to read snippets of text on Wikipedia, extrapolate false conclusions, and then close your mind to reason.

Certain articles I read did not specify if they pertained to math or physical reality, therefore I presume both. Just because you can't see it or imagine it doesn't mean it can't exist, therefore I'm within my rights to demand an article specifying it can't exist in physical reality (along with some proof).

PhilX

You brought up Planck's length or constant. I've always heard it claimed that it's the smallest length in our universe (maybe due to your postings). I've decided to check the internet to see what it had to say. I found this article:

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

Here's an excerpt from that article:

"When it is expressed in SI units, it is one of the smallest constants used in physics."

IOW Planck's constant is NOT the smallest unit or length in physics, otherwise there would be no need for smaller units. So if you want to peddle your baloney, feel free to do so, but I no longer accept it.

Once again, prove your assertion.

PhilX

[wtf]

You brought up Planck's length or constant. I've always heard it claimed that it's the smallest length in our universe (maybe due to your postings). I've decided to check the internet to see what it had to say. I found this article:

Good job of changing the subject again. I refuted your claim about the cardinality of the reals, you ignored me. Three years ago, and again two weeks ago. You post the same crap year after year in multiple forums and never show the slightest sign of intellectual growth.

I refuted your claim that Cantor was talking about physics, and you changed the subject twice in the last ten minutes.

Regarding the Planck length, it is the length below which we can't sensibly reason or measure. I said nothing about what's true of the universe; only what's true about the state of contemporary physics.

But hey, feel free to bring up a completely different topic so as to avoid ever engaging with what I'm saying to you or actually thinking about anything.

[Philosophy Explorer]

You brought up Planck's length or constant. I've always heard it claimed that it's the smallest length in our universe (maybe due to your postings). I've decided to check the internet to see what it had to say. I found this article:

Good job of changing the subject again. I refuted your claim about the cardinality of the reals, you ignored me. Three years ago, and again two weeks ago. You post the same crap year after year in multiple forums and never show the slightest sign of intellectual growth.

I refuted your claim that Cantor was talking about physics, and you changed the subject twice in the last ten minutes.

Regarding the Planck length, it is the length below which we can't sensibly reason or measure. I said nothing about what's true of the universe; only what's true about the state of contemporary physics.

But hey, feel free to bring up a completely different topic so as to avoid ever engaging with what I'm saying to you or actually thinking about anything.

I didn't change the subject. You did when you brought up Planck's length or constant so stop your whining. Physics is about what's true about the universe which you can't deny.

I know you can't prove me wrong. And I won't bring up anything else as I'm faithful to the OP. And you haven't refuted my claim.

PhilX

[wtf]

Physics is about what's true about the universe which you can't deny.

Actually I do deny that. Physics is about our best theoretical models of what's true about the universe. Any claim beyond that is metaphysics. In other words, Newtonian physics was once our best theory of the universe, and now relativity and quantum theory, which cannot yet be mutually reconciled, are our best theories of what's true in the universe.

But to claim that any physical theory is literally what's true about the universe itself, is a metaphysical assumption. No experiment could determine its absolute truth or falsity.

To illustrate this, suppose you said, "Physics is about what's true about the universe" in 1700, shortly after the publication of Newton's Principia. Your statement would have been wrong, since we now know that Newtonian physics fails for objects moving at sufficiently high speeds or possessing sufficiently high energy.

So now if you looked at relativity, or at quantum physics, and said, "Physics is about what's true about the universe," you'd still be wrong. And the proof is that nobody knows how to reconcile those two theories.

So there are two distinct things:

* The universe itself; and

* Our best historically contingent ideas about how the universe works.

It's a metaphysical assumption to imagine that there even are any laws of the universe; let alone that our latest atom smasher has discovered them. I really hope you can see this, it's an important point.


Now to the matter at hand. I pointed you to a quote in the Wiki article on Georg Cantor to the effect that Cantor well understood that mathematical abstraction is independent of physical reality.

This is manifestly true in the context of modern physics. In math, the real numbers can be subdivided endlessly, to arbitrarily small intervals. We have intervals of length 1/2, 1/3, 1/4, 1/5, and in general 1/n for any natural number n.

But in contemporary physics, we know that we can not sensibly reason about any length below the Planck length, around 1.616229 10^(-35) meters.

NOTE WELL that this is not an ontological fact, but rather an epistemological one. That is, nobody is saying that there is nothing meaningful below the Planck length. On the contrary: There might be interesting things going on down there, or there might not. We have no way of knowing.

What Planck showed is that we can not sensibly reason about distances below the Planck length. We can speculate ("The universe is ultimately continuous," or, "The universe is ultimately discrete"), but we cannot know using contemporary physics.

Whether future physics will give better insight, we can't say. But again, that fact emphasizes that physics is a historically contingent activity of human beings (*). Claims about the ultimate nature of the universe are metaphysics, and not physics. Physics is only about our latest theories and ideas.

(*) And cats. See Space-Time for Springers

[Philosophy Explorer]

Consider this:

"https://www.mathplanet.com/education/ge ... o-geometry

It reads in part:

:A space extends infinitely in all directions and is a set of all points in three dimensions. You can think of a space as the inside of a box.' "

This doesn't differentiate between theoretical and physical space (from a math website). While Cantor worked in math, there's nothing prohibiting his work from being applied to physical space.

PhilX

[wtf]

Consider this:

"https://www.mathplanet.com/education/ge ... o-geometry

It reads in part:

:A space extends infinitely in all directions and is a set of all points in three dimensions. You can think of a space as the inside of a box.' "

This doesn't differentiate between theoretical and physical space (from a math website). While Cantor worked in math, there's nothing prohibiting his work from being applied to physical space.

PhilX

1) Bad link.

2) Your misunderstanding of some misleading wording on some website does not constitute scientific evidence.

3) When you reply to me can you please quote a tiny bit of one of my posts, so that I'll get a big red Notification at the top of the page when I click on the site. Else I have no way of knowing that you are addressing me. Thanks.

[Philosophy Explorer]

Briefly let me talk about the natural numbers (a countable number). If one only considers the natural numbers, say along a ruler, then you can move along the ruler inch-by-inch with each unit (the inch) marked off by endpoints, one inch apart.

Let's now consider the real numbers. First the real numbers are uncountable because it can't be put into one-to-one correspondence with the natural numbers (the diagonal proof). But the real numbers contain the natural numbers so the ruler can be broken up into the real numbers as you can have a one-to-one correspondence between the real numbers not part of the ruler and the real numbers that are part of the ruler so there are an infinite number of points along the ruler (regardless of what birdbrain says).

By considering the three axes, this extends to space. The article on Cantor shows the controversy that arose due to the paradoxes.

PhilX

Note about the natural numbers: there are an infinite number of them, but it doesn't bother birdbrain that the ruler can be broken down into thirteen points containing the units, but it does bother him when we talk about the real numbers. What a contradiction.

[Philosophy Explorer]

Consider this:

"https://www.mathplanet.com/education/ge ... o-geometry

It reads in part:

:A space extends infinitely in all directions and is a set of all points in three dimensions. You can think of a space as the inside of a box.' "

This doesn't differentiate between theoretical and physical space (from a math website). While Cantor worked in math, there's nothing prohibiting his work from being applied to physical space.

PhilX

1) Bad link.

2) Your misunderstanding of some misleading wording on some website does not constitute scientific evidence.

3) When you reply to me can you please quote a tiny bit of one of my posts, so that I'll get a big red Notification at the top of the page when I click on the site. Else I have no way of knowing that you are addressing me. Thanks.

I don't know what you mean by bad link.

PhilX

[wtf]

I don't know what you mean by bad link.

Click on the link in your post.

[Philosophy Explorer]

I don't know what you mean by bad link.

Click on the link in your post.

Try this link:

https://www.mathplanet.com/education/ge ... o-geometry

[wtf]

https://www.mathplanet.com/education/ge ... o-geometry

Yes, it says a point in geometry. Not in physics. Geometry is a branch of abstract math.

[Philosophy Explorer]

https://www.mathplanet.com/education/ge ... o-geometry

Yes, it says a point in geometry. Not in physics. Geometry is a branch of abstract math.

It doesn't say that. And geometry isn't a branch of abstract math. It has a number of interpretations as Wikipedia explains:

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

PhilX

[Philosophy Explorer]

Based on this article, I don't see why there's such a strong desire to separate math from physics:

https://en.m.wikipedia.org/wiki/Relatio ... nd_physics

PhilX