Can "Infinity" ever be more than a mathematical abstraction?

I wouldn't be quite so assertive but I do believe we have something we can broadly regard as the equivalent of an organ to perceive mathematical relations in the world, something like a mathematical sense. It's interesting for example that we should have a sort intuitive notion of a continuum and it seems very plausible that mathematicians would have drawn on their own intuitive sense of the continuum to work out their theories on the infinite, if only to some extent.
It's definitely an interesting fact that needs to be explained. Yet, it's not because we have an intuition of a continuum that infinities necessarily exist in the physical world. This may just be a sort of conceptual by-product of evolution, something that happens to work but without that there be any actual infinity in the world. Somewhat like the colour red. It works to some extent but there is presumably no actual red colour in the physical world.
Also, the fate of 2 and infinity are not necessarily linked. There may be 2's in the world but not necessarily infinities. And 2 may be something that works most of the time but not necessarily all the time.
EB

 

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Nice deflection.

I say again: If you use the word "infinity" on a math/physics discussion forum, but you ignore the actual technical meaning of the word in favor of some vague touchy-feely nonsense about how infinity is a "timeless uncountable physical state, which apparently resulted in the emergence of the universe" -- your exact words -- are you not engaging in late night stoner philosophy? It's not even metaphysics, since you have no sensible argument or point of view at all.

What say you to this charge?

My remarks apply equally to everyone else using the word "infinity" while completely ignoring the last 140 years of mathematical formalization of infinity in favor of vague metaphysical/theological speculations.

 

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The subject does not lend itself to sensible argument at all. It's more mental masturbation and it is fun.........

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Isn't everybody speculating or just regurgitating what is already (not) known about infinity?

Yes, my remarks do also....

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, and it would be hubris to say otherwise when it comes to a unfathomable concept such as infinity.

Especially in view that our current understanding leads to a bounded and finite universe, nestled in what, infinity?

 

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So you admit you're completely ignorant about the past 140 years of mathematical research into infinity.

They're making a mockery of a math/physics discussion forum.

You call it unfathomable, but mathematicians have been fathoming it for 140 years.

Since you don't know the meaning of the word (even after I told you the meaning!) your remark is devoid of content.

 

What matters in the end is not what scientists believe, or even assert, but the scientific theories they produce and whether they are predictive. Different scientists will believe different things but they have to come to a consensus at some point as to what works and that will put what they believe into perspective.

The universe might be computable and yet contains some infinite elements, like space perhaps. Energy is quantified per QM but I don't think anyone has managed to measure what would be the smallest quantity of energy that would be physically possible if quantities of energy were effectively finite.
And I also already pointed out that an infinite universe would anyway be computable using an infinite computing power. So, this issue is similar to the issue computable/non-computable numbers in that the so-called non-computable numbers are only so if you try to express them in terms of rational numbers. In reality, they are expressible in terms of each other, so they are effectively computable. So, I think you need to be careful in drawing conclusions from mathematical theorems. They usually are true within a very restrictive set of conditions.
Further, scientists are at liberty to express beliefs that go beyond what scientific theories can support. So, here again, you need to take what these guys say with a pinch of salt, not least because they quickly tend to disagree with each other on these issues.

No, I'm perfectly in line with the scientific outlook. Perhaps just a little bit ahead.

I definitely didn't say or suggest that the notion of rational or integer numbers doesn't apply to the real world. You seem to have a tendency to interpret what people say in terms of black and white. What I said is much more nuanced than that. You'd need to watch yourself.

I don't need to quarrel with anyone. You should read again my first posts in this thread. I said something to the effect that we should let scientists to decide how best to represent the physical world, if need be using the notion of infinity, and let experience be the judge. Plus, personally, I really don't care if scientists wrongly claim infinities exist as long as this doesn't affect the predictive power of their theories. Newton also made metaphysical assumptions. He was wrong and experience proved him wrong. So, what matters is science, not individual scientists.

You should pay more attention to what people say. My criticism of Tegmark started way back in this thread. I tried to discuss this with Write4U for a while but had to give up since he doesn't seem able to explain himself.

My criticism of Tegmark is that his view doesn't make sense.
That being said, I already said I am perfectly comfortable with the idea that the evolution of the universe could be entirely and exactly represented using a mathematical model. Might never happen but I'm fine with this idea in principle.

I don't think you should assert that. The question seems more complicated that what you make it out to be.

That's certainly a relief.
EB

 

Energy is quantised but there's no known lower limit to EM frequencies and so no known lower limit to the size of quanta. There's also no known limit to the size of the universe and no known smallest distance between two points or time interval.
Whether this might come to matter, time will tell and I wouldn't myself prejudge.
EB

 

No, I'm not completely ignorant about the past 140 years of mathematical research into infinity.
Didn't get us very far, did it?.......

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That's about where we're at.

Infinity is a timeless permittive condition to which there is no beginning nor end, no smallest, nor biggest.
You can't measure something which is unmeasurable. You can only measure finite things.

p.s. fathoming is performing a measurement.

Happy fathoming infinity....

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My contention is that we construct - via math - means of perceiving the world, analogous to sensory organs. (Evidence: the incrementally increasing reliance on such virtual perception as we incrementally leave the realm in which our biologically given senses function. Image: a blind man analyzing a rainbow via wavelengths etc)
And that these perceptions share whatever reality other sensory perceptions possess.
So that "length 2" and "infinite sum of denumerated lengths equalling 2" have the same status with regard to reality, whatever we may decide that status to be.
That being an address of the thread topic.

 

Nevermind most of this. You're either agreeing with me about things we agree on or arguing with me about things we agree on, interspersed with snide personal remarks. Knock that part off. Nobody likes it.

Re your misunderstanding that all noncomputables are related by a rational multiplier, that's not true. Sometimes the quotient of noncomputables is rational. In fact you can put the noncomputables into buckets, putting two numbers into the same bucket if their quotient is rational. You'll still have uncountably many buckets. So "factoring out" the rationals doesn't help your argument.

I also wanted to mention for anyone interested that if you Google "noncomputable numbers and physics" you will find many interesting stackexchange threads and papers where knowledgeable people do indeed discuss the topic. Roger Penrose himself has discussed how noncomputable numbers related to physics. It's not a huge area of research but there is a body of literature out there.

 

I don't know what you mean. Can you elaborate? I'd like to see evidence, based on some actual familiarity with the subject, to back up your claim.

Or just admit you typed in some stuff you can't back up and let's talk about something else.

You're just doubling down on nonsense. You haven't given a workable definition of infinity and you haven't given any sign you understand the actual one, or why you think it wouldn't apply in physics.

Really?

https://en.wikipedia.org/wiki/Measure_(mathematics)

Measure theory is the foundation of functional analysis and the math of QM. You could not get QM off the ground without the ability to measure infinite things. For example the unit interval has uncountably many points but has a length of 1. You learned about the length of infinite intervals of points in high school. Did you forget

So you agree that we can measure infinity.

 

ps -- Here is Sir Roger himself making the speculative claim that consciousness involves noncomputable ingredients.

https://www.edge.org/conversation/r...sciousness-involves-noncomputable-ingredients

 

That's what I had understood of your previous post.
I think our problem is that while we can take the human mind as an operationally effective system for navigating the physical world, it's nonetheless very difficult to sort out exactly was is absolutely necessary in our mind for it to be so effective. We've understood for quite a while that the particular quality of the colours we experience, the qualia, are not essential. Any other palette of colours would have been just as effective. There's even no good reason to assume that we experience the same qualia as each other. Yet, our mind relies essentially on colours to represent the world around us and does so in an operationally effective way. We can take this as an indication that our mind's representation of the world is certainly exact about something in the world. Yet, we understand that the quality of our colours are not true of the world. I would expect same situation to prevail as to our mathematical intuitions. Some must be true of the world, others may just be artefacts, short-cuts, by-products, metaphysical padding. How do we decide which is which?
I feel confortable with the notion that in practice a particular infinite sum of infinitesimals is exactly 2 but I also accept that I don't see how I could even get to know that it's true. Also, I don't see why we would need to be too affirmative in this respect. Let's pretend it's true, work on this basis and be aware that we're working on this basis, and then wait to see if this ever leads to a contradiction in terms of observables.
EB

 

Not with "fathoms".

https://www.iep.utm.edu/infinite/

 

Sorry but contrary to what you asserted, I didn't say or suggest that the notion of rational or integer numbers doesn't apply to the real world.
If you can't quote people when you assert something about what they have said there's no possible conversation. It's up to you to clean up your act.

Sorry, but I don't know what you're talking about. If you can't quote people when you assert something about what they have said there's no possible conversation. It's up to you to clean up your acts.
EB

 

No they don't, in reality an infinitely small point does not have a length of 1, which is a measurement of a finite value. We just made it up for convenience. Infinite intervals is a different concept than Infinity.

QM deals with discrete quanta, which are a universe as compared to infinitely small.
The finite (expanding) universe is a quantum particle as compared to infinitely large.
It's existence is a single interval as compared to infinite duration.

One can theorize about infinity and make up all kinds of perspectives, but in the end "infinity" is "unmeasurable" .

https://www.iep.utm.edu/infinite/#H5

 

Why?
From the link you yourself provided:

The term actual infinity is now very different. There are actual infinities in the technical, post-1880s sense, which are neither endless, unlimited, nor immeasurable. A line segment one meter long is a good example. It is not endless because it is finitely long, and it is not a process because it is timeless. It is not unlimited because it is limited by both zero and one. It is not immeasurable because its length measure is one meter. Nevertheless, the one meter line is infinite in the technical sense because it has an actual infinity of sub-segments, and it has an actual infinity of distinct points. So, there definitely has been a conceptual revolution.​

Don't you read stuff?
EB

 

Yes , I addressed that in my post #433 and quoted links. I'll repeat if for your convenience.

 

Sorry, but you're not making sense, once again.
You should try it while you can.
EB

 

Naaah, if you don't get the gist of my reasoning, you never will. I'm not going to waste any more time on this.
Hint: Actual infinity as opposed to theoretical Potential infinity or philosophical Transcendental infinity.

 

Don't you see the inherent contradiction in; 1 meter = infinity, and; infinity = 1 meter?
Get Real!