Write4U
Valued Senior Member
That's all of the televangelists? What about their followers? Believers!
Definition of God - one thread to rule them all
- Thread starter James R
- Start date
Just had another brilliant brain fart idea
Now I know Lie Detectors are no such thing
So what would happen if gathered together a mixture of believers and run all of them through a Lie Detector?
Any bets on the % pass / fail a Do you believe in god? question?
I know the results of the test depend on the skill of the examiner at reading tells. The machine is for show and to provide a science looking trace the tester can make notes on
My problem with that is that mathematics seems to be a mental construct, not a physical construct. As far as I can tell, the universe contains things that have physical substance and not just mental substance. On the other hand, if we want to get all philosophical about it, we could certainly go down the rabbit hole of "What is real?" There's a whole major branch of philosophy devoted to trying to grapple with that question.
Nothing can, if you're talking about mathematical properties. You're begging the question. Nobody disputes that mathematical properties are mathematical. The question is whether there are any non-mathematical properties, separate from the mathematical ones.
In your worldview, if anything exists it must be a mathematical construct.
The opposing position would be that mathematics is merely one way of describing the unavoidable properties of every single atom, etc. Maybe not the only way, maybe not even a necessary way.
How do you know the universe could not exist without mathematics?
Hmm. If mathematics is viewed as a formal system - or perhaps as a collection of formal systems - then mathematical "discoveries" are just previously-unknown features of the constructed formal system. There's no way to know whether "new" mathematics represents an unveiling of "existing mathematics" or a newly constructed addition to the body of knowledge about the formal system. It's like adding a new room to an existing house. In adding an extension, one is constrained by what is already there.
You say that all physical objects have mathematical order, and you even give hydrogen wavefunctions as an example. But the thing is, we keep refining our mathematical model of the hydrogen atom (and all the other atoms). The non-relativistic model of the atom is good, but a relativistic treatment is better. Features like spin were added as afterthought ad hoc refinements to the original quantum model of the atom, at least initially.
Do you think we now have a "complete" mathematical model of the hydrogen atom, such that we'll never have to change the mathematics describing that again?
The thing is, the more you dig down into just about any physical system you care to examine, the more you find you need to add to the mathematical model you have of that system. Things that start of mathematically simple more often than not end up mathematically complicated - even "messy" in the aesthetic judgment of many mathematicians. It tends to buck the idea of a mathematically neat and tidy universe constructed according to some grand mathematical symmetry.
So far, we've teased out a Higgs boson. Nobody knows for sure if the one we found is the only kind, or just one of many kinds. Nobody is yet able to predict the mass of the Higgs boson accurately. We can't even do that for something as commonplace as the electron. That suggests to me that we're still building the maths. You, no doubt, would say there's still "existing maths" out there to be "discovered". But these are just philosophical beliefs, one way or the other.
How many advanced maths texts have you read and understood? From personal experience, I can assure you that there's a lot of maths out there that is neither simple, nor "orderly". Consistency, on the other hand, is something that we try our best to build into maths. Yet even that is frustrating elusive, as Godel proved.
How are you measuring simplicity? Arguably, a circle is just as "simple" as a triangle - maybe moreso.
There's more to constructing a fractal than just adding triangles at random. A triangle by itself does not a fractal make.
The process of cutting an apple in half is quite a bit different from the process of writing down "1/2", as far as I'm concerned.
Write4U
Valued Senior Member
I see mathematics as a metaphysical construct. A fortunate organizational ability (potential) of the spacetime.
(See Causal Dynamical Triangulation, Renate Loll)
What is a physical substance other than a dense but orderly arranged pattern of sub-atomic "values" ?
I agree, therein lies the crux of the matter, so to speak....
But any assumption of a prior physical existence to the BB is going down the "turtle hole", no?
I would rephrase the question to ask whether there exist non-mathematical patterns at all, separate from mathematical patterns. Even within chaos self-organizing mathematical patterns form and emerge as expressed physical reality.
IMO, non-mathematical properties cannot contain mathematical potentials, and could not be causal to any self-ordering, except for chaos, as an intial stae of unimaginable violent and chaotic inflationary processes.
Yes, it is the mathematical rabbit "pattern" (relational values contained in it's DNA), in the rabbit hole.
I agree. The universe doesn't need any symbolic language, it doesn't need to describe anything, we do!
p.s. is "unavoidable properties of every single atom" a naturally self-forming mathematical pattern?
It would be forever chaotic, without any self-ordering imperatives?
Moreover we can observe the mathematically consistent evolutionary self-organization as it presents in everyday reality.
I agree, but knowledge of universal mathematics is only true for human interpretive mathematics, not in nature itself. The Universe is capable of performing mathematically driven actions which are impossible to duplicate in a lab. But we are improving our observational abilities constantly.
continued....
Write4U
Valued Senior Member
.......continued
Inaugural Laboratory Astrophysics Prize Goes to Louis Allamandola
Adapted from a press release from the AAS Laboratory
Richard FienbergAmerican Astronomical Society (AAS)Astrophysics Division:
This is precisely why Tegmark points to mathematics as ultimately being able to explain the universe in terms of relational values interacting via mathematical (algebraic ) functions. Mathematics IS what physics also uses, no? Thus if we ever devise a TOE in physics, it would need ALL the mathematics to explain those physics also, no?
The word physics is just as descriptive as the word mathematics in identifying Natural phenomena, but physics is descriptive of physical behavior, whereas mathematics is descriptive of the Logic in the physical behaviors.
CERN experiments announce first indications of a rare Higgs boson process, 3 AUGUST, 2020
The ATLAS and CMS experiments at CERN have announced new results which show that the Higgs boson decays into two muons.
("God doesn't play dice", A.E .) is a statement of a mathematical nature.
The wonderful world of fractals is based iterations of a single triangle. It is truly amazing. Mathematical Art. "Natura Artis Magistra"
Iterated function system
It is not the cutting that is described by the maths, it is the division (an algebraic function) of the single whole into two equal parts.
That equation is a Universal constant, AFAIK and applicable to everything that is potentially divisible into ever smaller parts, until we reach an indivisible singularity, a purely metaphysical dimensionless mathematical object.
Inaugural Laboratory Astrophysics Prize Goes to Louis Allamandola
Adapted from a press release from the AAS Laboratory
Richard FienbergAmerican Astronomical Society (AAS)Astrophysics Division:
https://aas.org/posts/news/2014/12/inaugural-laboratory-astrophysics-prize-goes-louis-allamandola
I accept that, but spin is a relational mathematical pattern, no?
I don't have the knowledge to make such a statement, but Tegmark himself admits to incompleteness of our knowledge of universal mathematical properties and functions. But so do the physical sciences, no?
But then, is it scientific to accept "messy" physics, when it has been proven that all things can be explained by their relational values and algebraic mathematical interactions.
This is precisely why Tegmark points to mathematics as ultimately being able to explain the universe in terms of relational values interacting via mathematical (algebraic ) functions. Mathematics IS what physics also uses, no? Thus if we ever devise a TOE in physics, it would need ALL the mathematics to explain those physics also, no?
The word physics is just as descriptive as the word mathematics in identifying Natural phenomena, but physics is descriptive of physical behavior, whereas mathematics is descriptive of the Logic in the physical behaviors.
AFAIK, several kinds of bosons have been observed (i.e. different mathematical arrangements and potentials). They may all be teased from the field under specific mathematical conditions, but they have no existence of themselves and decay immediately into simpler patterns, which can show the differences in the bosons and their functional potetials.
CERN experiments announce first indications of a rare Higgs boson process, 3 AUGUST, 2020
The ATLAS and CMS experiments at CERN have announced new results which show that the Higgs boson decays into two muons.
https://home.cern/news/press-releas...ce-first-indications-rare-higgs-boson-process
Yet, we use mathematics to prove any deviation from normal physically consistent relational interactions. Without the maths how would we know there is something unusual going on? Moreover, if something appears not to fit the maths, it is always due to the incompleteness of the human symbolic mathematics, not to any unsolvable chaotic behavior of the physics.
("God doesn't play dice", A.E .) is a statement of a mathematical nature.
I agee. IMO, all the Platonic solids are examples of fundamental self-organizing mathematical patterns.
The wonderful world of fractals is based iterations of a single triangle. It is truly amazing. Mathematical Art. "Natura Artis Magistra"
But is that not the argument for mathematically self-ordering patterns? It needs a mathematical function in order to execute a self-referential equation and make a copy of itself. This mathematical equations are also a fundamental requirement for living systems and organizational patterns, such as "mitosis". Is that not an iterative process?
Iterated function system
https://en.wikipedia.org/wiki/Iterated_function_system
I agree of course. But that's comparing "apples with mathematics".
It is not the cutting that is described by the maths, it is the division (an algebraic function) of the single whole into two equal parts.
That equation is a Universal constant, AFAIK and applicable to everything that is potentially divisible into ever smaller parts, until we reach an indivisible singularity, a purely metaphysical dimensionless mathematical object.
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I don't know what that even means. Tossing words like "organizational potential of the spacetime" around doesn't actually generate meaning.
Values are not substances. But I already said that.
That's setting yourself up for a win. Mathematics is, more than anything else, the study of patterns. You're begging the question again.
You're failing to distinguish chaotic mathematical systems from chaotic physical systems. One is a description; the other you can touch.
What is a "mathematical potential"? (Did I ask you that before? Apologies, if so.)
Does that mean you're agreeing with me that mathematics is descriptive rather than constructive, now?
How do you know that mathematics is driving anything? How could it do that?
It's great that somebody won a prize, but I'm not sure why that is relevant to our discussion.
Spin is a physical property. It can be described mathematically.
I don't know of anybody who has claimed that our knowledge of mathematics is complete.
Who has proven that all things can be explained by their relational values and algebraic mathematical interactions? Can you please link me to the relevant proof, or tell me where to find it? What's a "relational value"?
I understand that you're a Tegmark fan. I disagree with his position that the universe is nothing but maths, and I disagree with your agreement with him.
Maybe I should talk to him about this rather than you. I don't think you're presenting his argument in its best possible light.
As a tool, yes.
"Explaining the physics" can be done in a lot of different ways. We usually turn to mathematics when we want quantitative predictions from a physical theory. Mathematics does numbers pretty efficiently.
It almost sounds like you're agreeing with me again.
Only one Higgs boson has been observed. There are lots of bosons. A lot of atoms are bosons, for instance. Photons are bosons.
Again, interesting news, but what is the relevance?
What you really mean by "normal relational interactions" is just those interactions that conform to some existing mathematical model. Of course we need to know what that model is before we can know if something deviates from it. The point is, though, you're assuming a mathematical model from the start. Begging the question again.
How do you know that? Is there another proof I haven't heard of?
No. It's just A.E.'s personal opinion, based on his personal preference for a certain kind of order in physical theory. He spent many years trying to prove (using maths!) that his opinion was correct, and utterly failed. In fact, physical experiments proved that his intuition was completely off on this.
Self-organising? How does the maths self-organise? How does it do anything, by itself?
I'm aware of fractals. I was around when the initial fractal craze first hit and every 8-bit computer hobbyist was coding up BASIC programs to generate the Mandelbrot set (which typically took those machines hours).
No. I can't see any self-ordering there. If I write $z=z^2 + c$ into a computer, that's me doing the mathematical ordering, not mathematics itself. The resulting pattern has many interesting mathematical features, but as I said previously, in writing that equation and calculating we're building an extension onto a pre-existing house.
Last time I checked, cells didn't need a mathematics text book in order to manage mitosis.
As I understand it, you and Tegmark are both saying that apples are mathematics. I disagree.
Yazata
Valued Senior Member
It seems to me that if one can use mathematics to successfully describe something, a physical system let's say, then that physical system must incorporate or somehow display a structure that's isomorphic to the mathematical structure that's being used to describe it. I sense that's what W4U is struggling to say.
I hesitate to post this, fearing that I'll create a monster. W4U seems to have a tendency to read something, not really understand it, and then rush off on a stream-of-consciousness rush of conjecture regarding it. We've seen it with his approach to cell biology. Microtubules! The secret that supposedly explains everything!
But taking the chance that I'll regret it, W4U seems to be stumbling towards the idea of Structural Realism, without having ever heard of it. Given that structural realism is one of the hot topics in contemporary philosophy of science, that's kind of impressive in its way.
Wikipedia has a relatively comprehensible introduction. Pay particular attention to the distinction between epistemic structural realism and ontic structural realism.
Epistemic structural realism originally argued that what is preserved through theory-change in physics are certain mathematical structures (between observables generally). So that despite modern cosmology having seemingly overthrown the spheres and epicycles of geocentric cosmology, the ability to predict the positions of the planets in the sky is preserved through the change. This allows scientific progress to be conceptualized in the face of Kuhnian style challenges. (Which is a big part of what's motivated the recent resurgence in structural realism.)
Some of the later expressions of epistemic structural realism take a stronger line, arguing that all that science can possibly know are mathematical style structures linking observables. Which is a much stronger claim than the idea that what is preserved through theory change is the structure displayed by observables.
Ontic structural realism argues that all that exists to be known is the mathematical structure. It's basically the transformation of all the hieroglyphic squiggles on theoretical physicists' chalkboards into a metaphysics.
Some of the arguments for this one appeal to quantum mechanics and the idea that while physics is very good at predicting the observable outcomes of quantum processes, it is far less successful in telling us how reality is such that those outcomes occur. There's obviously a plethora of quantum interpretations, each of which seems to be consistent with observations. So ontic structural realism just kind of sweeps the interpretations off the game board with a sweep of its arm, insisting that the mathematical relationships between observables (the prediction generators) are all there is.
https://en.wikipedia.org/wiki/Structuralism_(philosophy_of_science)
A more technical discussion is here. It's written by James Ladyman who is one of the big names in structural realism, so the article naturally emphasizes Ladyman's own positions on the subject, positions that aren't without controversy.
https://plato.stanford.edu/entries/structural-realism/
Tegmark is kind of a pop ontic structural realist of the most extreme sort. And I agree with you in not buying it. I don't totally dismiss it but don't entirely accept it either. I'm much more favorable towards the less extreme sorts of epistemic structural realism (I think that it's a promising approach to scientific theory change) than I am towards stronger epistemic structuralism which tries to dictate what can and can't be known. And I'm inclined to be even more skeptical of hard-core Tegmarkian-style ontic structural realism.
But my thinking is very much a work-in-progress and might change tomorrow.
For one thing, if reality is nothing but mathematics, then why is some mathematics actualized in what we take to be physical reality while other mathematical structures are seemingly just conceptual or theoretical in the musings of mathematicians? There's an actualization event that hypostasizes mathematics in this account that really needs explanation. Why is some mathematics physical while other mathematics isn't?
And for another, my own background is in biology and structural realism seems entirely motivated by the desire to turn theoretical physics into a metaphysics. It's less applicable to biology. This kind of mathematical mysticism doesn't seem to have very much to tell us about molecular genetics or proteomics. I don't expect that it's very persuasive to geologists or to astronomers either (except maybe the cosmologists).
The explanatory schemas in biology are less often conformity to the mathematical formulae so beloved by theoretical physicists, than they are mechanical models of some sort. One probably can argue that biology is reducible to chemistry, which in turn is reducible to physics, but reducibility isn't necessarily the same thing as derivability.
So do I. Very strongly.
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