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

[Speakpigeon]

As I understand it, if space in all its configurations was infinitely divisible, each division would also be infinite, which would lead to infinite repetition, IMO. i.e. Ellis' # 3
A fractal ?

You're not making sense.
At best, it might be a non-sequitur, but I would need to understand what you say to decide.
EB

 

[Write4U]

You've given a list of definitions that you are using, said that you always check with that list, and then you used the word. Which of those definitions did you use? It's literally you just pointing to the correct one in the list. No need to think about it any deeper, no need to ask other questions first: which definition did you use?

I use the common denominator present in all of the definitions, applicable to all subjects that involve a process and a method of processing. Input---->Function---->Output

 

[NotEinstein]

So, you're treating words as if they were your private property. No wonder you have communication problems.

There can't be but one language, the one we share. I can't understand the the kind of private language you use. Your choice.
It's already difficult enough to understand each other when we discuss the sort of things we tend to talk about here without making it more difficult by using an arbitrary lingo.

Yeah, I some months ago had a long, long discussion with Write4U where I reached this conclusion too. Write4U just doesn't seem interested in clear communication; he's appears content with purposefully making people misinterpret him.

 

[Write4U]

You're not making sense.
At best, it might be a non-sequitur, but I would need to understand what you say to decide.
EB

So you disagree with Ellis also? ok.

 

[NotEinstein]

I use the common denominator present in all of the definitions, applicable to all subjects that involve a process and a method of processing. Input---->Function---->Output

So you were lying: you were not using any of the definitions on the list, you made up your own.

 

[Speakpigeon]

I purposely choose the word "value" as a generic substitute for all identified inherent "properties" of objects. The same with "function" which I choose as a generic identification of any kind of ''work" or "process".

To me these generic expressions seem suitable for use in most mathematical identifications and processes. I may be wrong, but I did try to be as informative as possible, while covering a large range of conditions.

That's where the confusion will inevitably happen. The different definitions of a word you'll find in a dictionary are always context-dependent. Each definition applies to a particular context. It appears you're frequently using some words with the wrong definition given the the context of the discussion. The idea of a function in maths isn't the same as the idea of a function in medicine or in everyday talk.
What you do could conceivably be justified. What isn't justified is that you should do it without warning. Hence the confusion. If you have good reasons to think that the word "function" should be used wherever we would use instead the word "work" or "process", you should explain yourself by providing a justification for you choice. But there's already a difficult here since obviously it wouldn't be practical at all to do that in the middle of a discussion. The only practical way to do it would be to start a thread about it. But you'd need to understand first what you're doing exactly and be prepared to argue your point. And you would also need to be able to use words in the normal way to argue your point. You should understand at least that you can't use a language that's foreign to the people you want to have a conversation with.
EB

 

[Speakpigeon]

So disagree with Ellis also? ok.

I didn't say that. I said you didn't make sense.
It seems you're also playing fast and loose with your interpretation of what people say. That can't help.
EB

 

[Write4U]

Yeah, I some months ago had a long, long discussion with Write4U where I reached this conclusion too. Write4U just doesn't seem interested in clear communication; he's appears content with purposefully making people misinterpret him.

Give me an example of a clear communication which describes a function. I am eager to learn, but critique without correction is not very useful is it?

So you were lying: you were not using any of the definitions on the list, you made up your own.

Lying? Why the need for ad hominem?

If you cannot find common denominators in the various definitions of a word, then indeed it may seem that I making things up, but I am not really. Seems to me that your problem is you cannot think in the abstract and that you need everything spelled out.

Sorry, but I can't spare the time to study physics. You need not read or respond to my posts. There are others who seem to be able to understand the gist of my posits and can respond to my propositions, which I always gratefully acknowledge and respond to in turn.

 

[Speakpigeon]

What about the concept of an infinite tape, for a Turing Machine?
Why, I ask myself at night sometimes, is it convenient to choose a starting place for the read-write thingy?

You don't have to choose anything. Pick a place at random and see what happens. Presumably, it will either do something and start to move or it won't do anything and stay put. The general principle doesn't change. The tape is infinite but the machine needs not move at all, or not much.

Why does a program then halt successfully if it returns to the start position and is in a terminal state?

I don't understand.

IOW, what difference is there between a tape which is infinite in one direction and a tape infinite in both directions, as long as you identify a start state and position--the beginning of the input string?

More degrees of freedom. If it's infinite in one direction only, then the thing can't go in the other direction. If it tries to go beyond the limit then it will move out of the tape and probably stop doing any much. At least it won't be able to come back to read the tape, presumably, although a human being could do just that.
I would have thought all that fairly obvious myself. Maybe I misunderstand your question.
EB

 

[Write4U]

I didn't say that. I said you didn't make sense.
It seems you're also playing fast and loose with your interpretation of what people say. That can't help.
EB

Listen to Ellis! See Q-reeus post # 4. He specifically mentions that divisions of infinity leads to exact copies of each division, because they all are infinite and contain all the information of the original infinity.
In addition , Bohm speaks of a Holonomy.

The law of the holomovement: Holonomy[edit]
The starting point for Bohm's articulation of what he means by a "new order in physics" is his notion of wholeness. Thus crucial for understanding the holomovement is his notion of how interconnected phenomena are woven together in an underlying unified fabric of physical law. In the following section, called "Law in the Holomovement", he takes up the question of order, and the laws of organization which relate the parts to each other and to the whole. This is what he calls the "law of the whole", or holonomy.

Rather than starting with the parts and explaining the whole in terms of the parts, Bohm's point of view is just the opposite: he starts with a notion of undivided wholeness and derives the parts as abstractions from the whole.

The essential point is that the implicate order and the holomovement imply a way of looking at reality not merely in terms of external interactions between things, but in terms of the internal (enfolded) relationships among things: "The relationships constituting the fundamental law are between the enfolded structures that interweave and inter-penetrate each other, through the whole of space, rather than between the abstracted and separated forms that are manifest to the senses (and to our instruments)"

https://en.wikipedia.org/wiki/Holomovement#The_law_of_the_holomovement:_Holonomy

Hence my question if this indicates some kind of self-similar fractal function.

 

[Speakpigeon]

But that is not an accurate quote of what Tegmark actually says.
Verbatim Tegmark's words are; "our physical world does not just have some mathematical properties, it has only mathematical properties."

He also said:

I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure.

Do you think our physical world is an abstract mathematical structure?

Mario Livio recalls how Einstein wondered why mathematics worked so well in explaining the universe as we see it.
Thus the first question is; does the universe have indeed any (some) mathematical properties and what constitutes mathematical properties?
Obviously it does not recognize our mathematical symbolisms, but we are able to recognize universal mathematical patterns and are able to unlock its mysteries by means of our symbolic mathematics. So it would seem that the assumption of some mathematical properties is not unreasonable.

Yes it is literally unreasonable if taken literally. Given that we can only use words to talk about the physical world, you may just as well ask whether the physical world may have word-like properties. Or given that we see the physical world as patterns of colours, you may just as well ask whether the physical world may have colour-like properties.
There's no possible answer to this sort of questions. You can go on all your life wondering about these without ever getting any definitive and sensible answer.
Seems more like a let's-waste-our-time strategy.

If so, is it reasonable and logical to propose that the universe might indeed have only (pervasive) mathematical properties, which eventually can lead us to unlocking the remaining mysteries?

You would need to be able to explain why that would help. Given the remarkable progress already made by science, it's really unclear why that would help at all.

If it is not reasonable and logical to propose that the universe functions in a mathematical fashion, then what is the alternative?
Can anyone imagine a different set of universal laws more informative than our human perception of reality and ability to translate that perception with our symbolic mathematical language?
I can't, but I am wide open to suggestions.

That's irrelevant.
You seem unable to stick to the point. You can't refrain from making irrelevant remarks. That also doesn't help.
EB

 

[Speakpigeon]

Listen to Ellis!

No, I'm not going to be able to have any conversation with Ellis so I'm not interested just listening to what he says.
My position may well be contrary and even contradictory with that of Ellis but I didn't say that I disagreed with him as you claimed. You keep playing fast and loose with what people say and that creates confusion. You need to tidy up your language.

See Q-reeus post # 4.

That's irrelevant. You claimed I had said I disagreed with Ellis. I didn't. Try to concentrate.

He specifically mentions that divisions of infinity leads to exact copies of each division, because they all are infinite and contain all the information of the original infinity.

There's no logical reason that continuously dividing a continuous space leads necessarily to repetition. It's only if you make very specific assumptions that you'll end up inevitably with repetition. So, you would need first to prove that these assumptions are all true. And that's a very tall order.
EB

 

[Speakpigeon]

I read post #4 and was impressed with logic why infinity cannot exist in reality.

There's no logical reason that infinity could not possibly exist in reality. People make assumptions and from those they deduce that infinity couldn't exist. That's very different. They would need to prove first that these assumptions are true of the real world.
EB

 

[Seattle]

Why are you guys badgering Write4U about his use of language? I have little problem understanding him and he has already said that English isn't his first language.

Speakpidgeon, you would be easier to comprehend if you would use a few paragraphs from time to time rather than one large run-on paragraph.

NotEinstein, you seem intent only on baiting Write4U rather than actually contributing to the (any) discussion.

 

[Write4U]

I will keep this in mind as I read. I would like to understand exactly what it is that Tegmark is actually asserting.

Yes, I have listened to several of his lectures and to be honest I am a little confused by some of his assertions, but so far I haven't seen or heard anything that I would find disqualifying of his general proposition.

I've often wondered why hammers work so well in building houses. But houses are not hammers. Again you'd say I'm mischaracterizing Tegmark. You're probably right.

Well, not necessarily. But I would say that you could not build a house without the use of a hammer.

Well first, are the properties inherent in the universe? Or is our math the way our mind understands the world, no different in principle than the way a bat uses sound to experience the world?

But think about how a bat uses his sound to locate insects. Its is a mathematical function, using sonar pings to accurately create an internal picture of the insect's location and movement. Similar to whales and dolphins.

On the contrary, it's an entirely unreasonable metaphysical speculation. When you have a hammer everything looks like a nail. When you have a brain wired for binary logic it perceives the world in terms of binary logic. Bumblebees have an understanding of the world too.

Bumblebees navigate and find blooming flowers with a mathematical use of infra-red vision. They don't know they do this, they just do it.

It just doesn't happen to involve the historically contingent subject of human physics.

I agree. But consider that Lemurs (a distant ancestor) already have a rudimentary sense of quantity. They know the difference between more and less, and make choices based on that cognition.

The claim that the mathematics is "literally" true about the world is a gross conceit. Tegmark acknowledges this point (in the paper) and admits that when he says the world obeys the laws of physics, he doesn't mean to imply that we know all those laws yet!

I agree and moreover the universe does not need to know our mathematical system. It merely has to function by some form of mathematics (a human term) which creates specific repeating patterns, which we are able to symbolize. "Natura artis magistra" (nature is the teacher of the arts)
The same as many flowers grow petals in accordance to the Fibonacci Sequence (a human term) . Do they know the grow that way? Actually they don't need to know, they just have an evolved growth pattern which forms the Fibonacci Sequence, also known as the Golden Mean and which shows up in spiral Galaxies. IMO, a clear example that the Golden Mean is a cosmic imperative. We have recognized this mathematical imperative and named it after Fibonacci, the scientist who codified it into human maths.

The assumption that our models PERFECTLY represent some aspect of reality has no support. Every physical theory is an approximate. How do you know there is ANY "ultimate" law?

I agree, but we also must acknowledge that our mathematics can be astoundingly accurate in predicting certain events. The Higgs boson was mathematically predicted and the mathematics used in the collider function actually resulted in the appearance of the Higgs particle that had heretofore never been seen or created. Pretty neat trick, if you ask me.

The premise is absurd on its face and as false as false can be. Math is the toolkit we use to deal with the world. It's not the world itself nor necessarily any part of it. But if for sake of discussion I grant you your false premise, then I suppose your conclusion holds vacuously. That's the best I can do in granting a tiny degree of agreement. Since your premise MIGHT be true but you have no proof, and I have plenty of evidence it's false.

I disagree. On the contrary we have plenty of evidence that our mathematics, the symbolic representations of values and functions, can be astoundingly accurate, as witnessed and expressed by Einstein himself.

Ah that's the fallacy that says, "If you're so smart, what would YOU do?" I haven't got the answer here. I just note that the claim that there even ARE any ultimate laws of the universe is a metaphysical speculation. All known physical laws are historically contingent approximations that are breakthroughs one century then refined and seen in a larger context the next. It's a game of successive approximation. Any speculation past that is not science. Science is descriptive and not explanatory, that's the great lesson of Newton's "I frame no hypotheses."

Which was Newton's correct assesment of the limitations of his theory, as was later proven.
I agree, all theory starts as a hypothesis and often needs considerable refinement to account for all the enfolded potential values and function in play. But I believe that our mathematics of geometry is pretty accurate.

The caterpillar on a leaf on a tree in a forest has a theory of his own world too. What makes anyone think we're nature's final product? If intelligence evolves past us (either elsewhere in the universe or ourselves in the future) perhaps our own contemporary physics will seem as quaint and wrong as the phlogiston theory of heat and the geocentric universe.

If a mathematical equation is fundamentally wrong it is usually discovered and usually corrected later by greater knowledge of the scientific community.

I'm only questioning Tegmark's metaphysical assumptions. I can still grant him his IF this THEN that, which is all he's really claiming in fact. He doesn't assert his premises, he only examines their logical consequences. I can live with that.

Yes, I agree. Tegmark is not claiming truth, he is making a proposition, which prima facie may well have merit and is indirectly supported by other recent hypotheses such as; Causal Dynamical Triangulation (CDT) by Renate Loll., which proposes that the universal fabric itself unfolds in a fractal manner.

Causal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent.

This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves.

https://en.wikipedia.org/wiki/Causal_dynamical_triangulation

I'm going to go read some more.

As will I, these things stir my imagination..

 

[Write4U]

It's only if you make very specific assumptions that you'll end up inevitably with repetition.

If you assume that each division itself is infinite, you will inevitable end up with repetition, IMO

 

[iceaura]

You've proved my point with your comment about the impossibility of having an infinite series.

I asked, not declared.

The number 2 appears, to me, to exist. It is also that infinite series - that infinite series is the number 2. They are equal to each other, two different ways of writing down the same thing. So if the one exists, so does the other.

I was asking whether the one existed, in the sense of this thread - i.e. as more than a mathematical abstraction.

We haven't found infinite space, energy, density, etc. in the real world.

Have we found the number two in the real world?

 

[NotEinstein]

Give me an example of a clear communication which describes a function. I am eager to learn, but critique without correction is not very useful is it?

Take any of the definitions you gave. Those are pretty good examples of clear communication which describes a function.

Lying? Why the need for ad hominem?

Please learn what an ad hominem is; this isn't one.

You said that you look up the definition of words. Turn out, you don't: you look at definitions and then make up your own based on those.

If you cannot find common denominators in the various definitions of a word,

It's not about me being able to find common denominators: it's about using words in the way they are intended/expected to be used.

then indeed it may seem that I making things up, but I am not really.

You literally admitted to making up the definition yourself, so yes, you really are.

Seems to me that your problem is you cannot think in the abstract and that you need everything spelled out.

No, the problem is that you are making up definitions (without explicitly telling anybody), and are thus unable to communicate what you mean.

Sorry, but I can't spare the time to study physics.

If you can't be bothered to invest the effort to learn even the most basics of physics, then why should we take anything you say about physics seriously?

You need not read or respond to my posts.

True, but sometimes I want to, so I do.

There are others who seem to be able to understand the gist of my posits

No, they think they understand them. But since you are using private definitions, they probably don't; they understand something different than what you do.

and can respond to my propositions,

I'm responding to your propositions just fine, thank you.

which I always gratefully acknowledge and respond to in turn.

And when I point out a serious problem with the way you communicate, you don't? That's a very strange way of trying to learn and grow...

 

[NotEinstein]

Why are you guys badgering Write4U about his use of language? I have little problem understanding him

Okay then, you explain to me what definition of "function" Write4U is using in post #94, so that it is possible to equate it to "process".

and he has already said that English isn't his first language.

English isn't my first language either, but Write4U never responded to my suggestion to write a couple of things out in his native language.

NotEinstein, you seem intent only on baiting Write4U rather than actually contributing to the (any) discussion.

I'm merely trying to understand what Write4U means when he uses the word “function”. I've tried to understand his usage of the word for many months (in a different thread), but he was never able to provide a definition he is actually using. And I'm not even talking about a strict definition; just an encompassing description would be fine. If you want to call my insistent attempts to actually understand him “baiting”, then I guess, under that definition of the word, I am.

 

[Speakpigeon]

If you assume that each division itself is infinite, you will inevitable end up with repetition, IMO

Opinions are rather irrelevant here.
What you'd need to do is to provide some logical reason based on some known fact.
But, I understand you won't do that.
So, instead, all you can do is express your opinion.
But opinions are irrelevant here.
EB