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

[Write4U]

You would need a more general definition, unless you want to exclude the possibility of anyone talking about the essence of God or some such. See?

I do.
Of all possible inherent universal potentials and causalities a sentient and motivated God is the absolute least probable in my book.
Bohm speaks of a hierarchy of orders. To me that clearly indicates a form of patterned mathematical values and functions. I know of no other ordering system which can be defined by mathematics that is not mathematical in essence.......

Well, I am not about to change my writing style and if you can't follow the gist and logic of my posts, I'm sorry about that. Try harder or not. It's your choice.

 

[Write4U]

Now, if space was infinitely divisible, i.e. continuous, then even a quantified physics wouldn't necessarily lead to repetition.

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 ?

 

[NotEinstein]

That's funny...and I agree...

Just for the record, as I fear you may have read something into what I said that I didn't mean: I just took Chinese and English as examples. I considered adding a disclaimer to my original post, but I thought it would be clear. I do not advocate for English-only speech; no western chauvinism was intended!

But if you agree, then why don't you learn what the traditional meaning of all the words you are using are, and actually communicate that way, instead of causing confusion and frustration? It'd be a heck of a lot more productive, for sure!

 

[Write4U]

Just for the record, as I fear you may have read something into what I said that I didn't mean: I just took Chinese and English as examples. I considered adding a disclaimer to my original post, but I thought it would be clear. I do not advocate for English-only speech; no western chauvinism was intended!

I know how you meant it, and my retort was an attempt at a little lighthearted humor....

But if you agree, then why don't you learn what the traditional meaning of all the words you are using are, and actually communicate that way, instead of causing confusion and frustration? It'd be a heck of a lot more productive, for sure!

I may not always use traditional words, but if you check the dictionary as I do often, you will find that at least one definition in my choice of words is actually precisely what I mean to say and that may not always be mainstream. I recognize that Bohm, Tegmark, Loll, Hameroff, are all scientists at the cutting edge of their respective disciplines and present new perspectives on mainstream science.

I just see common denominators in their hypotheses which I have never seen proposed in mainstream science before. So I put them forward best I can, admittedly from fairly limited knowledge.

 

[NotEinstein]

I know how you meant it, and my retort was an attempt at a little lighthearted humor....

No worries!

I may not always use traditional words, but if you check the dictionary as I do often, you will find that at least one definition in my choice of words is actually precisely what I mean to say and that may not always be mainstream.

And don't you think that if one has to go hunting through a dictionary for just about every term you use, and try to deduce from context which exact definition you are using, this is just a miscommunication waiting to happen? If clear communication isn't your goal on a public discussion forum, then what it?

I recognize that Bohm, Tegmark, Loll, Hameroff, are all scientists at the cutting edge of their respective disciplines and present new perspectives on mainstream science.

(Irrelevant to what I was saying.)

I just see common denominators in their hypotheses.

(Irrelevant to what I was saying.)

 

[Write4U]

And don't you think that if one has to go hunting through a dictionary for just about every term you use, and try to deduce from context which exact definition you are using, this is just a miscommunication waiting to happen? If clear communication isn't your goal on a public discussion forum, then what it?

What I am trying to say is that I have to go hunting for words with the definition of what I am trying to say. After all, English is my second language......

 

[NotEinstein]

What I am trying to say is that I have to go hunting for words with the definition of what I am trying to say. After all, English is my second language......

Ah, I misunderstood, sorry.

Do you do the same hunting for mathematical definitions, such as for terms like "value" and "function"?

 

[Write4U]

Ah, I misunderstood, sorry.

Do you do the same hunting for mathematical definitions, such as for terms like "value" and "function"?

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".

Value;

• Value (mathematics), a property such as number assigned to or calculated for a variable, constant or expression
• Value (semiotics), the significance, purpose and/or meaning of a symbol as determined or affected by other symbols
• Note value, the relative duration of a musical note

Function;

1. Mathmatics.
2. 1. Also called correspondence, map, mapping, transformation, a relation between two sets in which one element of the second set is assigned to each element of the first set, as the expression y = x2; operator.
   2. Also called multiple-value function.a relation between two sets in which two or more elements of the second set are assigned to each element of the first set, as y2 = x2, which assigns to every x the two values y = +x and y = −x.
   3. a set of ordered pairs in which none of the first elements of the pairs appears twice.
3. Geometry.
   1. a formula expressing a relation between the angles of a triangle and its sides, as sine or cosine.
   2. hyperbolic function.

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.

 

[arfa brane]

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

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?

 

[Write4U]

What about the concept of an infinite tape, for a Turing Machine?

If it does not halt it has no answer for an infinte length of time (never). If it halts it is not infinite.
The Turing machine creates an infinity paradox.

 

[someguy1]

If it does not halt it has no answer for an infinte length of time (never). If it halts it is not infinite.
The Turing machine creates an infinity paradox.

That is an interesting point.

Most people use Turing machines to define the limits of what they think is real. Whatever can be computed. So Tegmark goes from the MUH to the CUH. So the metaphysical claim is that not only is the world a mathematical structure; it is also a computable one, in the sense that the world is described (or maybe "is" in Tegmarkian metaphysics) by a TM.

Now the halting problem shows that there exists a question that we are easily able to formulate in our minds -- namely, "Can we write a program to examine the code of an arbitrary program and determine whether that program will halt on a given input?" And the answer is no. So we have a problem that we can conceive and state; and that lies beyond the reach of computation (as we currently understand the term).

Now I think that's important. If you believe the CUH then you must believe the Halting program is irrelevant to your ontology somehow. On the contrary. I think the Halting problem falsifies the CUH.


In other news I'm a quarter of the way through my first skim of Tegmark's paper (not his book). So far he hasn't said anything to make me change my opinion that he's confusing the map with the territory. "Math seems to describe the world therefore the world IS math." That doesn't even make logical sense. Tegmark's having us on.

 

[NotEinstein]

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.

If you are so aware of the different definitions of these words, why do you often mix them up?

 

[Write4U]

"Math seems to describe the world therefore the world IS math."

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."

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.

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?

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.

 

[Write4U]

If you are so aware of the different definitions of these words, why do you often mix them up?

I was not aware that I did, I usually cite them in tandem as being fundamental to universal functional properties.
Imo, you cannot have a function or process, without having values or properties of things to process .

Hence Tegmark's 33 numbers (processable values) and a handfull of equations (functional processes) and by his own admission a few unknowns, which he believes will be mathematical in nature.

 

[NotEinstein]

I was not aware that I did, I usually cite them in tandem as being fundamental to universal functional properties.

I see you have forgotten about our previous long discussion. Such a bad memory would explain why you don't seem to grow intellectually...

Imo, you cannot have a function or process, without having values or properties of things to process .

Good, now explain to me what definition of "function" you are using here from the ones you just quoted, so that you can equate it to "process".

Hence Tegmark's 33 numbers (processable values) and a handfull of equations (functional processes) and by his own admission a few unknowns, which he believes will be mathematical in nature.

(Irrelevant.)

 

[Write4U]

Most people use Turing machines to define the limits of what they think is real. Whatever can be computed. So Tegmark goes from the MUH to the CUH. So the metaphysical claim is that not only is the world a mathematical structure; it is also a computable one, in the sense that the world is described (or maybe "is" in Tegmarkian metaphysics) by a TM.

That is the impression I get. He specifically cites an instance that if we could enter a computer created virtual reality as a virtual intelligence, we would not be able to tell the difference, because in a virtual reality all things happen in the same way as they do in physical reality. e.g. the universal mathematical laws of how things work remain the same.

 

[Write4U]

Good, now explain to me what definition of "function" you are using here from the ones you just quoted, so that you can equate it to "process".

Allow me to ask if you can point me to a physical process or function which is independent of any physical or even abstract value or values.

If we are talking about processing abstract literary values, we do have the expression; "his words carry weight", or; "that information has great value in understanding and solving the apparent problem".

IMO, you cannot have one without the other. The processing of information requires value(s) and function(s). I believe I have demonstrated this clearly by the illustration above.

 

[someguy1]

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."

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

Mario Livio recalls how Einstein wondered why mathematics worked so well in explaining the universe as we see it.

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.

Thus the first question is; does the universe have indeed any (some) mathematical properties and what constitutes mathematical properties?

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?

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.

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

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?

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?

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.

If it is not reasonable and logical to propose that the universe functions in a mathematical fashion, then what is the alternative?

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."

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?

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.

I can't, but I am wide open to suggestions.

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.

I'm going to go read some more.

 

[NotEinstein]

Allow me to ask if you can point me to a physical process or function which is independent of any physical or even abstract value or values.

I will answer the question if you first point me to the definition of the word "function" that you are using; I literally cannot interpret your question as you meant to ask it if you don't.

If we are talking about processing abstract literary values, we do have the expression; "his words carry weight", or; "that information has great value in understanding and solving the apparent problem".

I'm not "talking about processing abstract literary values" specifically, so this is all irrelevant.

IMO, you cannot have one without the other. The processing of information requires value(s) and function(s). I believe I have demonstrated this clearly by the ilustration above.

Also irrelevant.

Are you going to answer my question? You've completely dodged it. 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?

 

[Speakpigeon]

I do.
Of all possible inherent universal potentials and causalities a sentient and motivated God is the absolute least probable in my book.

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

Bohm speaks of a hierarchy of orders. To me that clearly indicates a form of patterned mathematical values and functions. I know of no other ordering system which can be defined by mathematics that is not mathematical in essence.......

Sorry, you're not making sense.

Well, I am not about to change my writing style and if you can't follow the gist and logic of my posts, I'm sorry about that. Try harder or not. It's your choice.

My choice is already made. 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.
EB