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

Discussion in 'Physics & Math' started by Seattle, Jun 24, 2018.

1. Write4UValued Senior Member

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How about Implied Potential Order ?

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3. someguy1Registered Senior Member

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5. Write4UValued Senior Member

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Just made it up by scrambling some of David Bohm's ideas on "Wholeness and Implicate Order".

rolls right off the tongue...

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.. and it is mathematically useable under certain circumstances other than the stock market...

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Last edited: Aug 5, 2018

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7. someguy1Registered Senior Member

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That's the name of his book. https://www.amazon.com/Wholeness-Implicate-Order-David-Bohm/dp/0415289793

Can you summarize his ideas and put them in the context of this discussion?

Can you give an example of one of these circumstances? I haven't that much imagination.

Last edited: Aug 5, 2018
8. Write4UValued Senior Member

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Ok, take a spring fed mountain lake. It's very location implies that the water can be used for generating power further down the hill. There is a narrow gulch which is perfectly suited for routing the water down hill. At the bottom of the hill is a plateau which is perfectly useable for building a generator and there are no natural obstructions to lay powerlines to the nearest town.

What we have here is an ordered set of evironmental circumstances (conditions) which imply a perfectly suited model with potential for generating and providing power to the nearest town.

Civil planners deal a lot with implied potential orders.....

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(as do scientists)

9. someguy1Registered Senior Member

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Jeez man. Give me something to work with. What the hell does that have to do with anything? You failed to make your own point. You failed to even refer to your own point.

10. Write4UValued Senior Member

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Well, I told you that I made it up!

But as far as relevance to my point, if you are familiar with BM (Bohmian Mechanics) you can see that I am perfectly within the scope of his philosophy of "potential" and "potential implications".
You may need a paradigm shift to fully understand the implications of the word "potential" (that which may become reality), a common denominator of all things real.

11. someguy1Registered Senior Member

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So you can't explain it in your own words. Can't help you here.

12. Write4UValued Senior Member

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I just did explain it in "my own words". I gave you an entire scenario explaining the concept of an "implied potential order". That you don't take the time to try and understand what I'm saying is not my responsibility.

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Whateva.

14. iceauraValued Senior Member

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It means I was tired and didn't catch a typo for OP = Original Post, or thread topic.
But all Cauchy sequences that we need to model physical phenomena converge. And that's all we need.
Excluding one of the roots when calculating a distance via Pythagoras is not a philosophical error.
And the wording of that is odd - we weren't talking about the existence or nonexistence of functions, or the computability vs noncomputability of functions.
The subtleties of the math are not directly relevant.

15. someguy1Registered Senior Member

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LOL. Too late! Write4U already provided a much more interesting example. And even though I gave him a hard time about it, I learned something from looking up Bohm's interesting book. It's all good.

Aha!!!!!!!!!!! Then you admit that physics has no need for the mathematical notion of continuity. You can choose to call your system continuous, but it isn't.

And besides, QM is based on mathematical continuity. A Hilbert space is a topologically complete complex inner product space. Now we don't know whether reality itself is discrete or continuous; but we do know that the QM model is built on the assumption of mathematical continuity.

D0 you mean to reject the contemporary mathematical model of quantum mechanics?

Perhaps we can agree to disagree on this point. I don't see the connection between ignoring the negative root of a quadratic if the physical model requires that the answer is nonnegative; and saying you can take an incomplete mathematical space and call it continuous. In one case you're tossing out a physically meaningless answer because you're trying to solve a physically meaningful problem. In the other case you're changing the technical definition of a word. Like saying an orange is yellow because you say so.

But again, if you are a mathematical constructivist and you hope to reframe physics in terms of constructive mathematics; you won't get an objection from me. It's a perfectly legitimate pursuit. It's a lonely one though, there are only a handful of people trying to do it. And I don't think you mean to go that far. Rather, I think you are just not holding yourself to a high enough standard of intellectual rigor. If you model your physics on mathematical models that are not continuous, then your physics is not continuous. You can't change that just by changing the meaning of the word.

As I understand you, you are trying to claim that physics based on noncomputable numbers may still be called "continuous." This is simply a falsehood, not a "subtlety."

I wonder if there's a name for the rhetorical trick of labeling a fact that's inconvenient to your argument as a subtlety. Usage: "Oh, we don't need to worry about such subtleties," when presented with an actual, universally agreed-on fact that destroys your argument.

As I say, perhaps you are a constructive physicist and don't realize it. That's perfectly ok, but it's a distinct minority position and you have a ton of technical work in front of you to make your case. I don't think you really mean to imply all that. Rather you are indulging in lazy thinking. Pardon my directness. I said it more tactfully in my earlier paragraph. You are not holding yourself to a high enough standard of intellectual rigor.

Last edited: Aug 5, 2018
16. iceauraValued Senior Member

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I'm saying that the mathematical notion of continuity - like the mathematical notion of a square root - is quite useful in abstracting and modeling physical phenomena. But like all such abstractions, it is not the thing itself.
Not at all. I just think that it's a model, not the thing itself.
We aren't talking about a physical model, but a mathematical model, in both cases.
The mathematical model requires editing, pruning, restriction, etc, because otherwise it hands us stuff that has no physical correspondent - negative distances via Pythagorous, noncomputable quantities via naive use of the real line, etc.
No, I'm claiming that as far as we know a physically continuous physical universe can be modeled perfectly without involving single noncomputable number in actual calculations. The fuzz covers the holes.
Again, the wording there is odd. Do we call physics "continuous"?

17. someguy1Registered Senior Member

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I have been strenuously arguing this point as long as I've been in this thread. We're in perfect agreement.

Right.

Is that particular analogy that important to you? I'd prefer to agree to disagree.

The more important point (IMO) is that you say the mathematical model needs to be trimmed. First, what is your proof that the real world DOESN'T instantiate noncomputable numbers? Secondly, even if it doesn't, your complaint is not with me. It's with the entire physics community. All of modern physics, from Newton through Einstein and all of the QM geniuses, modeled the world using continuous mathematical structures.

If you have a problem with this, take it up with them. It's a model that works very very well. I might for sake of discussion perfectly well agree with you that a better model would have some tweaks or whatever. But it's the physicists who have NOT done this tweaking. I was not consulted one way or another. You are arguing against the modern formulation of every branch of physics. Why are you trying to convince me of anything?

I don't think your claim is supported by the science. The SchrÃ¶dinger equation inputs a real-valued parameter called t, for time, and outputs a particle's probability wave. The input is NOT restricted to computable values. Why on earth should it be? What makes anyone think computability is important to how the universe works? It's a serious issue for people trying to claim the world's a computer, but nobody else.

Tell it to the physicists. You're wrong on the science. Perhaps there SHOULD be "trimming" of the theory, but there ISN'T. The physicists DON'T DO THAT. You agree or not? Look up Hilbert space and then please STOP claiming that physics uses a modified, incomplete model of mathematical completeness. You're just wrong about that.

Now I AGREE with you that something is fishy. Continuity assumptions are built into our models of physics, but we don't actually know whether the world is continuous. Philosophers care about this. I personally care about this, that's why I'm in this thread. But the claim that physicists restrict their theories to computable numbers is just factually wrong. This is not a matter of opinion. It's how they do physics. If you think they SHOULD do physics differently, please address your concerns to them. Not me

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Usually we do. Certainly in daily life we do. When we're doing philosophy we can argue the point. Is your question "is the world continuous?" Or "Is physics based on the model of continuity?" Or, "Do we call physics continuous?" Is your question about what we call things, or how we model things, or how things actually are?

Last edited: Aug 6, 2018
18. keith prosserRegistered Member

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Re Pythagorean distance between two points... the negative solution does have a physical interpreation as distance measured in the opposite direction. Consider 3 co-linear points a -> b -> c. To get the distance from a to b we could take the positive root of a ->c and the negative root of b -> c.

In genreal, we don't 'throw away' the negative solution as physically meaningless - it is rather that we are often only interested in the absolute value.

19. Write4UValued Senior Member

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I don't think so. Quantum mechanics forbids smooth change and presents sudden change from one energetic state into another. This can only be achieved by quantum "packets", where limits are exceeded, resulting in a quantum event, a little skip in time where the quantum state is in suspension between reality 1 and reality 2

If expression in reality depends on QM then it cannot be smooth and continuous....no....

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20. iceauraValued Senior Member

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That's not a distance. That's a distance plus a specified direction of measurement, which is not a physical entity.
Taking the absolute value "throws away" the negative solution.
There is no such thing as proof of such claims - any of them.
There is evidence, and I have posted some above, clearly labeled as such.
We can agree, I hope, that however the noncomputables might eventually be interpreted as aspects of the physical world, it's not as holes. They don't mark physical gaps or absences of any kind.
That is of course among the evidence I presented, labeled above, in support of my argument.
If you think I'm wrong on the science, it's odd that you switch to talking about the mathematics instead.
I made no claims whatsoever about which models physicists use - except to point out that they often use the Pythagorean theorem to calculate distances, and that they never do calculations using or yielding noncomputable numbers, and that they apparently don't need to - they can achieve sufficient precision and accuracy to account for all measurements ever made, so far, without them.

Meanwhile, I have no objection to the use of any models, including the use of the Pythagorean theorem and the real numbers for calculating distances. Notice that the noncomputable reals are discarded in the use of that formula as well - along with the negative numbers.

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21. Write4UValued Senior Member

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Is our physical world not modeled after QM? Are photons not discreet packets of energy or do they seamlessly integrate?

Are all particles discreet packets travelling or manifesting through/from a continuous field?

Seems to me that we can make distinctions if viewed from different perspectives.

The wave function is continuous, the physical constituents are discreet, no?

Last edited: Aug 6, 2018
22. someguy1Registered Senior Member

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You're right, they don't gossip much.

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23. Write4UValued Senior Member

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But they each tell a different story.