I've come to the conclusion that the uncertainty principle should have been discovered by Zeno of Elea, nearly 500 years BC, since in my opinion the only satisfactory way of resolving Zeno's paradoxes is by recognising the incompatibility of the notions of momentum and position - something which is immediately self-evident in ordinary experience, and obvious after one abandons the dogmatic assumption that counterfactual experimental outcomes exists.

As for special relativity, it's scope was narrowly concerned with the logical consistency of theories such as maxwell's equations that employ temporal indexicals but otherwise lack explicit temporal frames of reference. So I think it's right to point out that special relativity isn't particularly relevant to phenomenological puzzlement and concerns about the nature of time, but at the same time SR cannot be criticised on that ground, for the nature of phenomenological time wasn't the theory's intended purpose and SR leaves the relationship between theoretical space-time and ordinary experience undefined.

What an odd thing to say, considering that you asserted physicists have been impaired by their ignorance of metaphysics, and your examples were a fail. — Relativist

I see you haven't addressed my examples, only contradicted yourself, saying metaphysicians are better trained to do metaphysics than physicists, yet physicists are decidedly better at some forms of metaphysics.

That is a novel view of an "uncertainty principle" That's interesting that you think that time can't be measured precisely. You're wrong, but it's interesting that you believe it. — Relativist

Are you familiar with the frequency-time uncertainty exposed by the Fourier transform? Once you familiarized yourself with this uncertainty principle, you'll see that what it says exactly is that time cannot be measured precisely.

Consider that to measure time precisely requires the ability to determine the shortest time possible. However, a time period is measured by means of some determinable frequency. How could we determine the number of cycles/time period (frequency) of the highest frequency, without having a higher frequency by which to compare it to, as a temporal measurement? To determine the frequency requires a measured period of time, and to determine the period of time requires a determined frequency. Hence uncertainty. So what the uncertainty principle says is that a precise moment in time cannot be determined because the frequency required to determine this, cannot be determined; and the frequency required to determine this, cannot be determined because the precise moment in time cannot be determined. Do you see the vicious circle which creates the uncertainty principle? Having a measured period of time is dependent on determining the frequency of something, and determining the frequency of something is dependent on having a measured period of time. Therefore as we move toward a shorter and shorter period of time (precise measurement of time), there is greater and greater uncertainty.

Out of idle curiosity, what exactly is your objection to quantum physics?
— fishfry

If you're interested, just go back and read the posts I made in this thread. They aren't large, and there isn't a lot.
— Metaphysician Undercover
Fishfry - don't waste your time. — Relativist

LOL.

Are you familiar with the frequency-time uncertainty exposed by the Fourier transform? Once you familiarized yourself with this uncertainty principle, you'll see that what it says exactly is that time cannot be measured precisely. — Metaphysician Undercover

Well this isn't so bad. I seem to recall that Heisenberg uncertainty comes ultimately from Fourier analysis or some such. The idea seems to be referenced here.

I'm not sure how this relates to your concerns regarding QM; but I will say that this particular remark of yours is quite a bit more sophisticated than your usual nihilistic denialism of basic symbolic reasoning whenever you attempt to discuss math with me. Odd that someone who denies that 2 + 2 and 4 represent the same thing, is willing to accept the Fourier transform.

I certainly agree with your point that Heisenberg and ultimately the theory of Fourier series imply that we can't measure time with absolute precision; and that measurement precision trades off between time and frequency. But we already knew this so I don't know the point you're making. Heisenberg's uncertainty principle is in any event an epistemological and NOT an ontological fact. It's a limitation on what we can know (with our current theories) and says nothing about what truly is.

Which is the same point I made to you in my previous post. Science isn't making any ontological claims. You're fighting a strawman of your own imagination.

A historical note that I find interesting. What was Cantor doing when he discovered set theory? He was studying the zeros of the trigonometric polynomials that arose from Fourier's study of heat transfer.

That is: If you apply a heat source to one end of an iron bar under laboratory conditions, and carefully observe how the rest of the bar warms up; you will inevitably discover transfinite ordinals and cardinals.

Cantor's work arose directly from physical considerations. This point should be better appreciated by those who dismiss transfinite set theory as merely a mathematical abstraction.

There can't be a potentiality infinite past. Unless it's a koan of sorts, it's a contradictory statement

Maybe potentiality is like an infinitesimal

I might have struck at something you guys will find interesting. If time goes back through descending fractions, as has been suggested here and by Hawking as well, than the limit of the segment of time is potentiality, an infinitesimal. It starts the beginning of time because the segment is on a slant and gravity pulls the potential into actuality. It's self contained. Potentiality will always remain some thing mystical or mythical for homo sapiens because we live in actuality. In an instant though of self creation the physical (gravity) would act on the vague (potentiality) and walla the start of casual motions, governed by uncertainty, would start to roll forward

Heisenberg's uncertainty principle is in any event an epistemological and NOT an ontological fact. It's a limitation on what we can know (with our current theories) and says nothing about what truly is. — fishfry

That view assumes counterfactual definiteness; the belief that the possibility of stopping a moving arrow to construct a definite position implies that the moving arrow must have a real and precise but unknown position when it isn't stopped or it's position otherwise measured.

Yet this unquestioned assumption of counterfactual definiteness is the reason why Zeno's paradox appears paradoxical. To my understanding, Zeno's arguments are perfectly sound, which means that i have no choice but to reject counterfactual definiteness in order to resolve the paradox, and is the reason why i believe that Zeno ought to have stumbled across the underlying logic of Heisenberg's principle (when it is interpreted ontologically).

Of course, the rejection of counterfactual definiteness is only one means of making sense of quantum entanglement and which is also the view of the Copenhagen interpretation, which means that Heisenberg uncertainty is interpreted as ontological ambiguity/incompatibility, rather than as epistemic uncertainty.

Objective idealists have no problem with the beginning of the universe. Neither has Hinduism or most non-theist religions. A materialist would say that everything is governed by uncertainty. But is there actuality at the beginning and potentiality at the end, or conversely?

When I say for example that 1+1=4, I mean it esoterically. When Hawking says time acts as a fifth direction of space, he is talking as a scientist. He says nothing was before this curve in spacetime, meaning I think that the free lunch is contingent. Quantum uncertainty may be the root of physics, the answer to Descartes's vortex of the universe. Any talk of the "necessary" is sitar music thinking, and if our brains control time we have access to the heart of contingency

I think we just need to distinguish serious chains from casual ones.

Cantor's work arose directly from physical considerations. This point should be better appreciated by those who dismiss transfinite set theory as merely a mathematical abstraction. — fishfry

Touché . . . Good point! :smile:

Touché . . . Good point! — jgill

But if objects are trans-finitely infinite, how can they remain finite as well

Well this isn't so bad. I seem to recall that Heisenberg uncertainty comes ultimately from Fourier analysis or some such. The idea seems to be referenced here. — fishfry

I had this in a signals processing/wavelets class a while back. There's a standard proof here.

The Fourier transform of the momentum operator applied to a wavefunction is the position operator applied to that wavefunction. There's a theorem in signal processing called the Gabor limit that applies to dispersions (variance) of signals; the product of the dispersion of a signal in its time domain representation and the dispersion of a signal in its frequency domain representation is at least (1/4pi)^2. Math doesn't care that time is time and frequency is frequency, it might as well be position and momentum. The Gabor limit applied to (position operator applied to wavefunction) turns into the Heisenberg uncertainty principle for position + momentum of wavefunctions.

It's illustrated in the link you provided, if you Fourier transform a Gaussian with variance $x$, you get a Gaussian with variance $1/x$; the product of the two variances is strictly positive. If you scale the original distribution by k, the Fourier transformed distribution will be contracted by 1/k. Contractions in transform space are dilations in original space. When dilations in time result in contractions in frequency, it isn't so surprising that the product of "overall scale"/(variance) of time and frequency has a constant associated with it.

It isn't an epistemological limit.

In statistical modelling, there's a distinction between epistemic and aleatoric randomness. Epistemic randomness is like measurement error, aleatoric randomness is like perturbing a process by white noise. One property of epistemic randomness is that it must be arbitrarily reducible by sampling. Sample as much as you like, the uncertainty of that product is not going to go below the Gabor limit. That makes it aleatoric; IE, this uncertainty is a feature of signals that constrains possible measurements of them, rather than a feature of measurements of signals. There is no "sufficient knowledge" that could remove it (given that the principle is correct as a model).

Cantor's work arose directly from physical considerations. This point should be better appreciated by those who dismiss transfinite set theory as merely a mathematical abstraction. — fishfry

Do you have a source for this? I'd love to see the connection.

I'm reading Hegels lesser logic and just got his greater logic in the mail. The latter has the smallest print I've ever seen and there aren't even page numbers. In the next few.months a i want to have some type of answer to Zeno. The mathematical community does not recognize that we have a contradiction with the core of matter. Matter is inherently finite and infinite in the same respect

It isn't an epistemological limit.

In statistical modelling, there's a distinction between epistemic and aleatoric randomness. Epistemic randomness is like measurement error, aleatoric randomness is like perturbing a process by white noise. One property of epistemic randomness is that it must be arbitrarily reducible by sampling. Sample as much as you like, the uncertainty of that product is not going to go below the Gabor limit. That makes it aleatoric; IE, this uncertainty is a feature of signals that constrains possible measurements of them, rather than a feature of measurements of signals. There is no "sufficient knowledge" that could remove it (given that the principle is correct as a model). — fdrake

:100:

Maximum clarity and simplicity, maximal appreciation.

Do you have a source for this? I'd love to see the connection. — fdrake

I don't have any references saved but I Googled around and found these. No warranty is expressed or implied as they say. I found these links but did not read them. Some are behind academic paywalls, a practice I will abolish under pain of death when I am made Emperor. There were many more links out there if you Google "Cantor trigonometric series."

https://www.researchgate.net/publication/274008538_About_Cantor_Works_on_Trigonometric_Series

https://www.jstor.org/stable/41133323?seq=1

https://arxiv.org/abs/1503.06845

https://www.maa.org/press/periodicals/convergence/mathematical-treasure-cantors-on-trigonometric-series

The long and short of it is that by the mid 1850's, people were interested in trigonometric series because Fourier had shown that these highly abstract series were vitally important in understanding heat flow. So mathematicians got interested in them.

Now remember this is a little before the time that analysis finally got completely rigorized. And trigonometric series posed challenges to the handwavy calculus of the day. Questions of convergence weren't well understood. The efforts to formalize analysis were in part driven by these kinds of issues.

Fourier showed that a given function could be decomposed into a trigonometric series; by analogy, in the same way a musical note is composed of tones and subtones. A natural question is, given a series, how do you know whether it converges to some function: And given two series, how do you know if they might happen to converge to the same function?

That latter is equivalent to saying that the difference of the two functions converges to zero. We are naturally lead to be curious about the structure of the zeros of a trigonometric series.

My understanding is that the zeroes might be distributed in many different ways. There might be one at every integer, say. Or what if there was a zero at each of 1/2, 1/4, 1/8, etc. But now what if there were those zeros, and you threw in at 1/4, a nearby sequence that converges to it: $\frac{1}{4} + \frac{1}{n}$. So the main sequence 1/2, 1/4, 1/8, ... could have little tendrils coming off it. And each tendril could have tendrils. Each tendril would be countable, but there would be a graph of unimaginable complexity to keep track of.

In order to notate and keep track of the tendril graph, one would inevitably discover the transfinite ordinal numbers. The transfinite ordinals arise more or less directly (by way of abstract math) from purely physical considerations.

As I say, this last bit is my own personal understanding of how trigonometric series must have led Cantor to the ordinals. I could be wrong. It's a belief looking for the written evidence, which is probably behind a paywall somewhere. (Note -- The Wiki page on trig series that I linked seems to confirm my theory in a general way).

Now at this point, Cantor, who was very religious, decided that after all the infinities he'd just discovered, the ultimate infinite must be God. So he dropped his work in real analysis and gave himself over to set theory. Today set theory has become the standard conceptual framework for mathematics; but Cantor's theology is long forgotten. I wonder if he'd be more happy or more sad at those two outcomes.

When I say for example that 1+1=4, I mean it esoterically. When Hawking says time acts as a fifth direction of space, he is talking as a scientist. He says nothing was before this curve in spacetime, meaning I think that the free lunch is contingent. Quantum uncertainty may be the root of physics, the answer to Descartes's vortex of the universe. Any talk of the "necessary" is sitar music thinking, and if our brains control time we have access to the heart of contingency — Gregory

That's a very interesting post. I don't know if it's specifically aimed at something I wrote. It doesn't sound like it offhand. If you say that 1 + 1 = 4, what do you mean? Esoteric as in woo? Crystal healing and Rosicrucians? Better narrow this down for me else I don't know what you mean at all. I used to know of many esoteric practices.

What does Hawking have to do with this? I wonder if you mis-tagged me perhaps? None of this convo sounds familiar. Free lunch is contingent? What am I supposed to make of that? I apologize if I was at one point having the other side of this conversation and no longer remember. Descartes's vortex theory is a discredited and discarded theory of gravity that lost to Newton's. It has absolutely nothing to do with quantum uncertainty.

Quantum uncertainty may be the root of physics. Ok. What's that mean? Sitar music thinking? What is that? Like dropping acid listening to the Beatles? I am really lost here.

"... if our brains control time we have access to the heart of contingency"

Ok. I can't argue with you there! Is the heart of contingency near the root of physics?

Definitely style points, this was a great post. I don't understand it though.

But if objects are trans-finitely infinite, how can they remain finite as well — Gregory

The point here would be that transfinite numbers are an abstraction but not an isolated one. They're an abstraction that arose naturally from the study of heat; just as the infinity of natural numbers is an abstraction that arises from everyday counting.

Odd that someone who denies that 2 + 2 and 4 represent the same thing, is willing to accept the Fourier transform. — fishfry

You clearly do not understand, if you think that I accept the Fourier transform. I accept it as an example of an unresolved problem. And when that unresolved problem is united with the bad metaphysics of special relativity, the result is the uncertainty principle of quantum mechanics.

Relativist seemed to be arguing that a metaphysician is better trained to do metaphysics than a physicist, yet there is some metaphysics, such as the metaphysics of time, which a physicist is better trained to do. However, the uncertainty principle is clear evidence that physicists should leave the metaphysics of time in the hands of metaphysicians.

My understanding is that the zeroes might be distributed in many different ways. There might be one at every integer, say. Or what if there was a zero at each of 1/2, 1/4, 1/8, etc. But now what if there were those zeros, and you threw in at 1/4, a nearby sequence that converges to it: 14+1n14+1n. So the main sequence 1/2, 1/4, 1/8, ... could have little tendrils coming off it. And each tendril could have tendrils. Each tendril would be countable, but there would be a graph of unimaginable complexity to keep track of. — fishfry

Thanks for offering your take on this. I think this is exactly where the unresolved problem lies. It appears like the size of a chosen base unit might be completely arbitrarily decided upon. Yet the possible divisions are not arbitrary because divisibility is dependent on the size of the proposed base unit. Take 440 HZ as the baseline, for example. From this baseline, one octave (as a unit) upward brings us to 880HZ, and one octave downward brings us to 220HZ. So the higher octave consists of 440 HZ, and has different divisibility properties from the lower octave which consists of 220 HZ. This results in a complexity of problems in music.

If you say that 1 + 1 = 4, what do you mean? Esoteric as in woo? — fishfry

Well I had a thread a few days ago that got closed because I claimed math maps out the impossible and that the opposite flip side is true of every mathematical statement. So perhaps the negative numbers are positive and vice versa, e.g. I was trying to start a conversation but people got upset. I don't deny math's usefulness and it's beauty, but math might not be the last statement about math itself.

What does Hawking have to do with this? I wonder if you mis-tagged me perhaps? None of this convo sounds familiar. Free lunch is contingent? What am I supposed to make of that? I apologize if I was at one point having the other side of this conversation and no longer remember. — fishfry

Well I tagged you because other people weren't responding to posts I was making here. I started out ny explaining what I meant about the math thing so you don't think I'm a nut. The OP here, however, was talking about Aquinas, who said that the world was contingent and needed a necessary God. Physicist are now saying nothingness was before the big bang, making the world contingent without the need for "the necessary". Sean Carroll explicitly says this. He says the world is a brute fact of quantum fluctuation, using Russell's old phrase btw

Descartes's vortex theory is a discredited and discarded theory of gravity that lost to Newton's. It has absolutely nothing to do with quantum uncertainty. — fishfry

I think any mechanical theory can be resurrected in the search for a "theory of everything". I said quantum physics is answer to Descartes, but perhaps Descartes is the answer to QM. Newton replaced Cartesianism with a lot of forces. God was the ultimate one that Descartes had wanted one force to control everything and thought God could be found only in the mind. Perhaps that "one force" is pure leverage, as he thought. It's a thought that needs to be worked out for sure, but the Stanford Encyclopedia says there is growing interest into Cartesian physics again

Ok. I can't argue with you there! Is the heart of contingency near the root of physics? — fishfry

Probably. There are studies that literally argue our brains control time. There are lots of Youtube videos that run with this and say we are in almost complete control of our "free lunch", given us by the universe. There might be some truth in these videos that the universe gives itself to us freely. And then there are Napoleon Hill types (the forerunner of The Secret), that say our thoughts are in complete control of everything. These ideas may have a kernel of truth still

The point here would be that transfinite numbers are an abstraction but not an isolated one. They're an abstraction that arose naturally from the study of heat; just as the infinity of natural numbers is an abstraction that arises from everyday counting. — fishfry

Well I think my point was that objects are finite on one side, but flip the coin and it's infinite was well. There no end to the descent into an object. Imagine taking a spaceship (one that forever shrinks) into a banana. Only infinity is in there. This seems to be a contradiction of logic. I have had enough trouble trying to explain the problem to people, let alone getting a satisfactory explanation. Think about it: objects are finite and infinite in the same respect

Thanks for your response man :)

https://plato.stanford.edu/entries/descartes-physics/

And the man who directly tried to refute his whole philosophy:

https://plato.stanford.edu/entries/leibniz-physics/

The model I use to conceptualize time is cyclical. The two types of singularity in the Cosmos are interconnected, and movement from one to another creates what I call Cosmic Time. The universe in this model is a perpetual motion machine, self-causing, self-creating, self-contained. I admire the working analogy for time as a single line of dominoes, but this analogy doesn't fit in with the Cyclical Model. it doesn't apply. Its more like the inflating and deflating of a balloon. The fundamental physics of Cyclical Time at as of yet very basic, at least mine are. They will improve their explanation power with time.

Imagine taking a spaceship (one that forever shrinks) into a banana — Gregory

A+ for original thinking, Greg! :cool:

The model I use to conceptualize time is cyclical. The two types of singularity in the Cosmos are interconnected, and movement from one to another creates what I call Cosmic Time. The universe in this model is a perpetual motion machine, self-causing, self-creating, self-contained. I admire the working analogy for time as a single line of dominoes, but this analogy doesn't fit in with the Cyclical Model. it doesn't apply. Its more like the inflating and deflating of a balloon. The fundamental physics of Cyclical Time at as of yet very basic, at least mine are. They will improve their explanation power with time. — Josh Alfred

Tonight I've been reading about Nagarjuna on the Internet Encyclopedia of Philosophy. I feel like most of us on this forum are Westerners. Modern physics is getting into more Eastern ideas even since Borh, and our philosophical culture is resistant, and maybe it should be. I read the Tao of Physics book and felt it was purely a philosophical work. Modern physicists speak of pure nothing, while even the Eastern idea of sunyata-nihsvabhava doesn't mean “non-existence”. The word for that is actually Abhava. But when the world's existence was granted, Indian thinkers still thought the answer was the interconnection of all within one motion, within which is allowed infinite regress (Anavastha in Indian thought) and circularity (karanasya asiddhi). Some Vedic philosophers did believe in what they called svabhava, which can be compared to the modalities of Liebniz, so there is division within Eastern thought as well

What I wanted to say though was that we are culturally Westerners (most of us) and unless we want to be like Pyrrho, we want a satisfying explanation of how this world came about. Pyrrho said he doubted and doubted that he doubted. Stephen Hawking had a paper trying to argue that this type of paradox (i guess introduced into math by Godel?) could be in matter (in the universe) itself as well. That's a little too loopy for me.
It's been a good day

"Nagarjuna reminds his readers, all change in the world, including the transformations which lead to enlightenment, are only possible because of interdependent causality (pratityasamutpada)"

The Indian words for physical Pratityasamutpada are anitya, anepikrita, nihsvabhava, or shunyata. The last is the most used word. Just because I don't like infinite regress (A cause B, because B cause C which cause A because A causes C), that alone doesn't mean it's not true. But I like ideas about the world to be clear: "A literally cause B". However, Zeno seems to have prove Heraclitus true instead of Parmenides. If the world is pure fluidity, what kind of mathematics would even apply anymore to the world? I thought that might be an interesting question for those schooled in mathematics

Addition: The finite seems to contain the infinite. But how the infinite got contained in the finite is a physical, mathematical, and philosophical puzzle.

My only answer is philosophical (and maybe even esoteric), because I don't know enough non-Euclidean geometry to deal with that question. I imagine the universe started from gravity and quantum uncertainty, as I suggested already, but I don't read up on modern physics so I can't really take an authoritative stance.

This guy thinks an infinite regress which does not reside in a divine mind is impossible:
https://www.youtube.com/watch?v=ZJDYPZYMt0Q

I just say simply that potentiality (infinite vagueness) turns into actuality (finite objects). I think Heidegger already answered that Youtuber in the 20's. The thread on Heidegger going on right now is great for anyone out there wanted to know more about this

I had this in a signals processing/wavelets class a while back. There's a standard proof here.

The Fourier transform of the momentum operator applied to a wavefunction is the position operator applied to that wavefunction. There's a theorem in signal processing called the Gabor limit that applies to dispersions (variance) of signals; the product of the dispersion of a signal in its time domain representation and the dispersion of a signal in its frequency domain representation is at least (1/4pi)^2. Math doesn't care that time is time and frequency is frequency, it might as well be position and momentum. The Gabor limit applied to (position operator applied to wavefunction) turns into the Heisenberg uncertainty principle for position + momentum of wavefunctions. — fdrake

Great stuff!

It's illustrated in the link you provided, if you Fourier transform a Gaussian with variance xx, you get a Gaussian with variance 1/x1/x; the product of the two variances is strictly positive. If you scale the original distribution by k, the Fourier transformed distribution will be contracted by 1/k. Contractions in transform space are dilations in original space. When dilations in time result in contractions in frequency, it isn't so surprising that the product of "overall scale"/(variance) of time and frequency has a constant associated with it. — fdrake

Ok. I will take another look at that.

It isn't an epistemological limit. — fdrake

Uh oh I'm in trouble. This is the opposite of what I thought was true.

So first, I did not follow all the technical details you presented yet. My general understanding is that first, there are two things going on. One, the mathematical formalisms of convergent series, Fourier series, etc.; and two, whatever it is that nature itself is doing. Mathematical model versus reality.

My understanding is that, for example, the Planck length is the length at which our current theories of physics break down and may no longer be applied. So that we can't sensibly speak of what might be happening below that scale. We can't say that reality is continuous or discrete; only that our current theories only allow us to measure to a discrete limit.

So the Planck scales (space and time) are epistemological and not necessarily ontological. That is my understanding. Why are you saying that uncertainty is true of nature, not just a limitation of what we can know?

In statistical modelling, there's a distinction between epistemic and aleatoric randomness. Epistemic randomness is like measurement error, aleatoric randomness is like perturbing a process by white noise. One property of epistemic randomness is that it must be arbitrarily reducible by sampling. Sample as much as you like, the uncertainty of that product is not going to go below the Gabor limit. That makes it aleatoric; IE, this uncertainty is a feature of signals that constrains possible measurements of them, rather than a feature of measurements of signals. There is no "sufficient knowledge" that could remove it (given that the principle is correct as a model). — fdrake

More good stuff. I found an article that said that the outcome of a coin toss is aleatoricaly random before it's flipped; but once it's flipped, it's epistemically random. Someone who can see the coin has a different rational belief in the probability than one who hasn't.

This is a good distinction to make.

But I am still confused about your conclusion. You're saying that a situation is ontological if there's no knowledge I could have that would settle the matter. Whereas I seem to mean something different. There's what we can know, and there's what really is. Two different things.

Can you help me understand why you think uncertainty is ontological? What does it mean that reality itself is uncertain? Isn't it just our measurements that are?

Heisenberg's uncertainty principle is in any event an epistemological and NOT an ontological fact. It's a limitation on what we can know (with our current theories) and says nothing about what truly is.
— fishfry

That view assumes counterfactual definiteness; the belief that the possibility of stopping a moving arrow to construct a definite position implies that the moving arrow must have a real and precise but unknown position when it isn't stopped or it's position otherwise measured. — sime

I have not been talking about Zeno's paradoxes of motion at all. I don't understand why you're mentioning it.

Yet this unquestioned assumption of counterfactual definiteness is the reason why Zeno's paradox appears paradoxical. To my understanding, Zeno's arguments are perfectly sound, which means that i have no choice but to reject counterfactual definiteness in order to resolve the paradox, and is the reason why i believe that Zeno ought to have stumbled across the underlying logic of Heisenberg's principle (when it is interpreted ontologically). — sime

Oh I see the connection you're making. Perhaps Zeno was getting at the fact that the universe CAN'T be continuous, hence the Planck length. Something like that. Is that what you mean?

Of course, the rejection of counterfactual definiteness is only one means of making sense of quantum entanglement and which is also the view of the Copenhagen interpretation, which means that Heisenberg uncertainty is interpreted as ontological ambiguity/incompatibility, rather than as epistemic uncertainty. — sime

I don't know what counterfactual definiteness is.

I'll stipulate that uncertainty is part of nature in the Copenhagen interpretation. That's a good point to keep in mind, thanks. But interpretations are metaphysics and not physics. Nobody knows what's "really" going on. For all we know it's all been determined at the moment of the Big Bang; or, everything that can happen does happen in some branch of the multiverse. In those interpretations, there is no ontological randomness or uncertainty. Fair enough?

Well I had a thread a few days ago that got closed because I claimed math maps out the impossible and that the opposite flip side is true of every mathematical statement. — Gregory

Oh I see. I don't generally read every post, just the ones that tag me, unless it's a topic I'm especially interested in. So I may have missed your other posts. I am not a moderator and have no influence on what posts get closed, or why.

So perhaps the negative numbers are positive and vice versa, e.g. I was trying to start a conversation but people got upset. I don't deny math's usefulness and it's beauty, but math might not be the last statement about math itself. — Gregory

I myself am very openminded and pluralistic about math. In fact mathematical pluralism is a philosophical idea that's coming into vogue through the idea of the set-theoretic multiverse. That there's not one right set of rules for math; but rather, there's a whole universe of different axiom systems, related in some overarching superstructure of some sort. It's all pretty far out there. But I'm perfectly ok with alternative math thinking.

That said, however, negative numbers can NOT be positive. The positive numbers can be defined as a particular set of real numbers that satisfy a formal property. If you called them the negative numbers you could do that, but they'd still be the positive numbers. The negative numbers are logically different.

By contrast, in the complex numbers you can't define positive and negative numbers. You literally can't distinguish between $i$ and $- i$ using any logical formula.

So yes, we are free to imagine; but our imaginings must still meet certain standards of logic and mathematical interest.

Well I tagged you because other people weren't responding to posts I was making here. — Gregory

LOL. I'm the rhetorical foil of last resort? I'm not sure how to take that ... :-)

But do bear in mind that I have not seen any of your prior comments on this topic so feel free to loop me in from the beginning and don't assume I have any idea what we're talking about.

I started out ny explaining what I meant about the math thing so you don't think I'm a nut. — Gregory

"They closed my last thread and nobody else will talk to me so I'll try my ideas out on you," may not be how to accomplish that. [Just joking, hoping you have a sense of humor].

The OP here, however, was talking about Aquinas, who said that the world was contingent and needed a necessary God. Physicist are now saying nothingness was before the big bang, making the world contingent without the need for "the necessary". — Gregory

I am ignorant of classical philosophy and can not comment on Aquinas or any of his contemporaries.

Sean Carroll explicitly says this. He says the world is a brute fact of quantum fluctuation, using Russell's old phrase btw — Gregory

I love Sean Carroll. I've watched a lot of his videos. I love his vocal delivery, I find it very soothing. His mathematical and physical clarity of exposition are wonderful. He is a lot like Feynman in that he's a great physicist and a great teacher.

Now, when Sean Carroll is doing physics, he's doing physics. And when he's doing metaphysics, he's doing metaphysics. I'm aware he advocates the multiverse interpretation. But that's a metaphysical stance.

So when I say I love Sean Carroll, I would add that when he's doing physics I believe him; and when he is advocating for his favorite interpretation of QM, that's just his opinion.

The entire business of interpretations is nonsense. Newton didn't have an interpretation or an explanation of why gravity worked. He only knew that his theory predicted the results of observations and experiments. The same can be said, and that's ALL that can be said, for quantum mechanics.

I think any mechanical theory can be resurrected in the search for a "theory of everything". I said quantum physics is answer to Descartes, but perhaps Descartes is the answer to QM. Newton replaced Cartesianism with a lot of forces. God was the ultimate one that Descartes had wanted one force to control everything and thought God could be found only in the mind. Perhaps that "one force" is pure leverage, as he thought. It's a thought that needs to be worked out for sure, but the Stanford Encyclopedia says there is growing interest into Cartesian physics again — Gregory

That's very interesting. The difference between Descartes's approach and Newton's was that Descartes gave a mechanism for gravity; and Newton only described how it behaved. I frame no hypotheses, a very famous instance of Newton's tremendous insight into the very nature of science. Sean Carroll and all other celebrity physicists by day and metaphysicians by night, should study it.

If Descartes's vortices are coming back that would be great news. Have you a specific link please?

Probably. There are studies that literally argue our brains control time. There are lots of Youtube videos that run with this and say we are in almost complete control of our "free lunch", given us by the universe. There might be some truth in these videos that the universe gives itself to us freely. And then there are Napoleon Hill types (the forerunner of The Secret), that say our thoughts are in complete control of everything. These ideas may have a kernel of truth still — Gregory

I like to read widely too, but I try to be selective in what I believe. Perhaps you might tune your filter a bit. Newton himself was a mystic; but when he wrote about science, he stayed with science. He was a mystic when he was doing alchemy or looking for coded messages in the Bible. In his science papers he's very straight up hard core math and science. You might find it helpful to make that distinction for yourself.

Well I think my point was that objects are finite on one side, but flip the coin and it's infinite was well. — Gregory

Sorry don't know which coin that is. You know Gabriel's horn? It's a cone that has infinite surface area but finite volume. It's a famous calculus puzzler.

There no end to the descent into an object. Imagine taking a spaceship (one that forever shrinks) into a banana. Only infinity is in there. This seems to be a contradiction of logic. I have had enough trouble trying to explain the problem to people, let alone getting a satisfactory explanation. Think about it: objects are finite and infinite in the same respect — Gregory

No I don't follow that example. Why would "only infinity" be in there? Say a guy has a blood clot in his brain and you want to fix it before it bursts and kills him. So you take a team of neurosurgeons, put them in a submarine type of contraption, shrink them down to tiny size, inject them into the body into a blood vessel, and have them navigate to the brain to repair the clot.

This was the plot of the 1966 science fiction movie Fanstastic Voyage. I mention it only because it's an example where you shrink a spaceship to the size of a banana, to the size of a tiny spec of dust, even, and all the people and equipment inside it would just shrink proportionally. Of course this may be physically nonsense; but it's at least conceptually feasible if only in a science fiction sense. We can imagine it. In particular, there's no infinity in there. Just tiny little people. And why not?

Thanks for your response man — Gregory

You're very welcome. I hope you got your money's worth. And thank you! There are some on here who won't speak to me at all.