What qualifies as science?

Yes, this has been brought to my attention before. But, IMO. that's just sophistry.
The territory has to exist before you can map it, which is a symbolic representation of the territory and today through the use of fractals we can exactly replicate the territory in every detail.

Causal Dynamical Triangulation (CDT) hypothesized by Renate Loll (and others), is an attempt to explain (map) how the universe (the territory) itself unfolds .

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

I have read that there is an effort to create a mini universe, which geometrically and functionally conforms to the existing universe, except of course for size. But if we can actually create such a model, then IMO, the notion (hypothesis) of a multiverse would be strengthened considerably.

IMO, the same holds true for natural functions/mechanics, such as self-assembly. If we can physically duplicate some of the actual mechanics of how the universe functions and explicates itself, don't we call that proof that these functions/mechanics do exist in reality, prior to and independent of human observation?

This may be of interest:

http://www.education.mrsec.wisc.edu/cineplex/self/index.html

 

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You cannot exactly map "the territory" - any territory, much less a fractal one - in every detail. You can't even complete your fractal map of it.
You can't "replicate" it at all.

I'm sorry to hear that.

 

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And these "functions" would be this sort?:-

Mathematics; Function;

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What is the mathematical function for self-assembly?

See what I mean? You continually flip-flop between meanings of this term, one of which is mathematical and one of which isn't.

So it is not surprising that you end up blurring - and then overestimating - the extent to which things are mathematical in nature.

 

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This may again have been sloppy wording on my part, but if I may backtrack a little, this was in response to

which I believe was at least partially resolved earlier.

Probably a better answer would have been to say that human mathematics are symbolic representations of naturally occurring mathematical automorphisms?

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

Is symmetry not a mathematical property of some naturally occurring objects? Yazata mentioned triangles as true mathematical objects, as are circles, etc.

In answer to Iceaura's post, I also quoted

and my link to

http://www.education.mrsec.wisc.edu/cineplex/self/index.html

Self-assembly must have some mathematical implications, because self assembly follows certain specific rules of what is mathematically allowed or forbidden., IMO

In respect to your question of what would be the mathematical function of self-assembly, would mathematical mechanics be a better term in context of self-assembly? At this time, I cannot think of a better generality to convey an idea.

But as I understand it, self-assembly can be found in chirality?
[/quote]Chirality /kaɪˈrælɪti/ is a geometric property of some molecules and ions.[/quote] https://en.wikipedia.org/wiki/Chirality_(chemistry)#In_biology

Is a geometric not a mathematical term?

You may well be correct and that is what I am trying to sort out. Please bear with my ignorance of definitive scientific terms instead of the vague generalities which at this time I am prone to use (from ignorance).

But iceaura's argument that no natural mathematical anythings exist in nature by comparing it to looking at the symbolic scribbles on a white board, is IMO is a misleading and duplicitous perspective.

Of course those symbolic scribbles don't exist in nature, they are a manmade symbolic language, which attempt to explain quantitative and qualitative values of objects and their apparent relationships which become expressed/explicated in our reality.

No human language of any kind, except as translated by our mathematical language is used by nature, unless you are religious and God speaks to you in the specific language of the culture, which seems to have "confounded" those languages. Mathematical language is consistent throughout science and if put in proper terms....

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, are understandable to all scientists.

 

T

There is a perfect example in the measurement of the coast line of England used by Mandelbrot, which could in theory measure the coastline of England down to individual atomic scale and represent it graphically and even 3 dimensionally, using fractals. The problem is the enormous amount of numbers required, which even our most sophisticated computers would have trouble processing the vast amounts of mathematical data involved.
Tegmark compares the universe to a universal size computer, just processing data, numbers (quantities) and equations, the equatable relationships between those numbers and patterns.

p.s. fractals are fundamentally based on self iterating triangles. There seems to be no limit to the patterns they are able to create, even as the self similarity can be found at every level of reduction.

 

I'm inclined to think of physical functions as these kind of things that everyone is exposed to in beginning physics (along with their more arcane cousins that Rpenner loves so much):

http://www.dummies.com/education/science/physics/physics-equations-and-formulas/

One or more independent 'input' variables, plugged into a suitable equation (seemingly a mathematical function), determines (or perhaps defines, that needs exploration) a dependent 'output' variable. A great deal of the homework assigned in beginning physics classes consists of calculating various things, using these relationships between variables.

So the question arises, is physics just a mathematical game played on chalkboards? Is it just a matter of the mathematical symbolism and how that symbolism is defined? (That's what many people imagine when they hear the word 'mathematics'.)

Or do the calculations in physics class actually tell us something about physical reality, enabling us to predict how physical reality will behave in particular conditions (when the independent variables are as described)?

If we agree that the symbolic chalk-board mathematical apparatus in physics classes does tell us something about the behavior of physical reality, the question arises: why and how?

One way of addressing that is to say that physical reality possesses an abstract structure to which physical behavior (always?) conforms. (That's exceedingly mysterious too.) The idea then would be that the formal logical structure of the mathematical symbolism on the physics chalkboard shares the same form (is isomorphic with) the abstract structure of how physical reality itself behaves and how various properties of physical reality are related to each other (the so-called "laws of physics").

It seems to me that this is the underlying controversy in the latter part of this thread. Some people seem to be using the word 'mathematics' to refer only to the mathematical symbolism written on the chalkboard. That's entirely mankind's creation so it sounds outrageous to say that physical reality is mathematical at its core. Others are using 'mathematics' to refer to the abstract structures and relationships that are captured by that symbolism, the thing that makes mathematics objective rather than subjective, and that in the case of physics, seemingly correspond to how physical reality behaves.

At the moment (it's tentative and provisional) I personally lean towards mathematical Platonism in the philosophy of mathematics.

http://www.iep.utm.edu/mathplat/

 

Question: Is the concept of symmetry and symmetry breaking relevant to this discussion?

https://plato.stanford.edu/entries/symmetry-breaking/#4.1

 

No, it couldn't. At "individual atomic scale" the entire abstraction breaks down, and no longer corresponds to physical reality.

Meanwhile, your fractal representation remains an approximation at all the scales at which it makes sense, and making it exact is theoretically impossible in finite time.

That's not my comparison. I'm comparing the abstractions symbolized with the non-abstract physical reality they are intended to explain or describe.

Some are. Most aren't. Mandelbrot's most famous one, the one on the T-shirts, is not. https://en.wikipedia.org/wiki/Mandelbrot_set
There are no triangles in physical reality, btw. That's a mathematical abstraction, invented by people. So is the function and algorithm that generates the Mandelbrot set.

That "correspondence" is the issue causing trouble. "Seemingly" is not good enough by a long shot, and it's a correspondence - not an identity. It's between two different things. The math and the physical reality are not the same thing.

 

Ok, can you describe by what rules reality becomes expressed?

p.s. what do you think about the "symmetry breaking" paper above? post #447

 

Perhaps, but I don't know enough about 'symmetry breaking' in physics to comment.

I wrote "Others are using 'mathematics' to refer to the abstract structures and relationships that are captured by that symbolism, the thing that makes mathematics objective rather than subjective, and that in the case of physics, seemingly correspond to how physical reality behaves.

At the moment (it's tentative and provisional) I personally lean towards mathematical Platonism in the philosophy of mathematics.

http://www.iep.utm.edu/mathplat/ "

I agree. There's a tremendous problem in the philosophy of science lurking there, namely the nature of the relationship between the mathematical theories of theoretical physics on one hand, and the nature of physical reality on the other.

I used 'seemingly' on purpose, as a way to make room both for the possibility of error and for the fact that mathematical models of physical events are usually simplifications of more complex states of affairs.

But A and B might be two separate things that display the same structure and form. That's how I'm inclined to look at it. Not unlike two equilateral triangles or a photograph and the scene that it's a photograph of.

A (the squiggles on the physics chalkboard) somehow symbolize the same (or a suitably similar) abstract form that's also seemingly (as far as we can tell) exemplified in the behavior of B (whatever physical reality we are talking about).

If that wasn't true, then it would be hard to see how all the scratching on physics chalkboards would have any relevance to physical reality. Theoretical physics would have as little relevance to the physical world as Sodoku puzzles.

 

The unexplained , has always been the foundation of science . For thousands of years .

What has happened is the , unexplained has become defined , therefore a restriction , on science , rather than an open minded attitude toward the unexplained , therefore science is not about the unexplained but more about what is accepted . In the mainstream science attitude towards knowledge .

But Knowledge - Science - Science - Knowledge are synonymous , inextricably woven together as they should be and have always been . With philosophy . To explain the unexplained .

What qualifies as science is anything that is unexplained .

 

Again I ask; if it is not a form of mathematical imperatives, what then governs the physical reality?

https://spec2000.net/06-basicphysics.htm

This link lists the majority of the laws of physics, as we know them to exist in reality. But no one seems to be able to explain why and how these laws came to be in the first place.

What is that ordering imperative that transformed a state of complete chaos into a very specific hierarchy of orders/patterns and predictable physical behaviors. IMO, Symmetry and symmetry breaking is a powerful argument in favor of natural mathematical functions.

Just saying "the laws of physics" isn't very satisfactory, IMO. A law is not a physical thing, but an abstraction, derived from observation and experimental confirmation of physical behaviors, IOW, the how.

But IMO, the unpacking the physical how by means of symbolic mathematics begins to explain the why.

Leibniz was only able to symbolically represent that bodies fall and Galileo was able to demonstrate that all bodies fall at the same specific rate. Newton explained how bodies fall at all, i.e. gravity. Einstein finally translated all these physical phenomena as a result of the geometry of space around a massive physical object , a metric configuration, and here we seem to enter the domain of universal metaphysics (abstract mathematics), the law of gravity.

Thus, working backward from the physical mechanics of falling bodies, we arrive at the geometry of space and things become more and more abstract in terms of physical expression and begin to cross over into the metaphysical domain of geometric forms and their mathematical imperatives, i.e. functional permissions and restrictions?

If I used incorrect terms, please forgive, but try to look at the logic of the argument. If the logic fails, I would appreciate a correction.

My main question is ; are the laws of physics physical objects in and of themselves, or are they forms of mathematical imperatives which science has been able to translate into a symbolic language?

 

I agree on that point.
But what are your thoughts on Causal Dynamical Triangulation (CDT). Just a flight of fancy?

 

I am probably missing an important aspect, but here is one definition from Wiki:
Fractal

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and

 

In the relevant aspects of interest, sure. As the branching patterns of trees and blood vessels might, in certain significant respects.

Two "equilateral triangles" are identical in relevant structure and form by the human definition that created them, but models of them in chalk or pixels or popsicle sticks are apt to vary. As far as a photograph having the same structure and form as the scene - There's that famous story of Picasso accosted by a stranger, who produced a lovely photograph of his wife and presented it to the painter, saying: "See this? This is my wife, this is how she really is, not like your ugly distortions". Picasso took the photo and examined it, and said diffidently: "She is small, is she not? And rather flat?"

They are created by people, whatever they are.

Mathematical imperatives are a created form of it. What governs mathematical imperatives?

 

We can include neural networks in that group also. Are they not identified as fractal forms?

What difference does that make? As Livio explained, our drawings of circles and triangles are approximations of that which already exists "out there".

and

and

https://www.goodreads.com/author/quotes/13550.Mario_Livio
https://en.wikipedia.org/wiki/Mario_Livio

Did people create the natural laws of physics or (to turn a phrase) did we discover the existing "territory" before we could "map" it?

IMO, they are part of the essence/properties/potentials of spacetime itself. Bohm's Implicate Order.

But I do agree that evolution and natural selection played a major part in the emergence of certain natural imperatives. Is there not a philosophical analogy that even in nature "things tend to move in the direction of greatest satisfaction", which seems to apply universally, including humans?

Note that the human term spacetime itself is a subjective symbolic term describing the existence of an objective permittive and restrictive geometric spatial construct with an abstract temporal chronology.

Did we create the condition we linguistically (English) symbolized as "spacetime" or did it create us?

"A rose is a rose by any other name" or "as painted by a child or in fractal form".

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The laws are a mapping. Whatever we "discovered", it wasn't a map - we made all the maps we know. (Likely, all minds and sufficiently complex reacting systems map and model - but we do not "know" them).

Our geometric concepts and definitions are (we hope) abstractions from what is "out there" - part of the mapping or modeling. As such they are simplifications of a kind.

Bohm's Implicate Order didn't exist until 1980. As of right now, nobody really knows if it's useful or not. If it is found to be too different in significant ways from what it purports to model, it will be discarded; if it proves its worth, it will be treasured and added to the canon. Either way, what is "out there" will remain unaffected.

 

Obviously you ignored my qualification; (to turn a phrase)

Of course, they were quick excerpts to give you a taste of the expanded narratives.

Well, rather than confusing the issue with my ignorance of universal mathematical imperatives, I'll defer to Mario Livio who has spent a lifetime studying them and does know about what is "out there"

If you have not read the two embedded links in my quoted excerpts of this renowned Astrophysicist's papers on the subject, I would really recommend it. For your convenience I'll repost them here:

Mario Livio, The Golden Ratio: The Story of Phi, the World's Most Astonishing Number

Mario Livio, The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry

Be sure to read the [open preview] of the entire books, on both sites.

I spent several hours in fascination reading these narrative papers (with a minimum of formal maths) and found a wealth of knowledge about the subject of the size and scope of what's "out there". I plan to reread them several times, because he covers an enormous range of knowledge about the science of astrophysics and its history. This guy is an expert, as well as a great and easy to understand narrator. Just read the list of eminent scientists which contributed to these books.

IMHO, these are scientific narrative gems, worthy of any scientist's library. Please trust me on this.

p.s Yazata, you professed limited knowledge of symmetry . I recommend reading especially the second link, which deals specifically with that subject.

 

Universal mathematical imperatives are human concepts - created, arranged, worked out and checked out over hundreds of years, and recorded in some suitable notation for others to learn and explore, by human beings.

"Discovered" as human concepts, that is.

Bohm's Implicate Order is a new one, still being checked out. It may, or may not, prove useful and enlightening about the world - depending on whether it proves to be a good model or map. It is definitely an interesting concept, a deep and inspiring contribution to human thought and comprehension, whether or not it proves useful as a model of what's out there in the world.

I have absolutely no doubt of that. I take that for granted.

 

From a human perspective I fully agree.

I fully agree.

I fully agree, those type of all-encompassing hypotheses have so many variables that warrant deep study by many different scientific disciplines and from many perspectives. But as I understand it, some Bohmian mechanics are already being functionally applied in several ways.

One great advantage is the development of computers and the internet, which allow for processing of large volumes of data and the ability to transmit the results almost instantaneously which may speed things up a little. What used to take weeks or months to deliver a letter or an important paper, can now be done in minutes. Very encouraging.

What intrigues me most is those common denominators which hold true universally, i.e. Gravity, which has been observed everywhere we look.

The curious thing is that gravity can be observed, not only as a cosmological physical phenomenon, but also in sociological and psychological sciences. People with like beliefs tend to gravitate into groups, two individuals may gravitate to each other, also known as compatibility and love. There is an expression that "each individual fills the emotional or intellectual gaps of the other".
In physics, gravitational behavior can be physically measured and explained with great exactness as a universal constant.

From a sociological or personal perspective this becomes much more variable (unpredictable), but still, there seems to be natural abstract tendency to being drawn to or being repulsed by something or someone or a group. I wonder if these expressions are abstractly related to the concept of "movement in the direction of greatest satisfaction".

When I think of Bohm's "wholeness and implicate order", I can see a certain parallels with the abstract
concepts of a stable "symmetry" and the dynamical results of "symmetry breaking", such as a stable balanced economy and the unstable chaos of war.

These phenomena may seem completely unrelated to physics, and I may be reaching too far into woo, but
in an abstract sense, these behavioral effects seem to have some fundamental abstract relationships. That's why I feel so "attracted" to Bohm's scientific and philosophical perspectives.

btw, Bohm was also involved in neurology of the brain, and even into more exotic concepts such as holography and the Eastern philosophies. And I believe that the De Broglie-Bohm Theory is at least in part used in mainstream science.
De Broglie–Bohm theory

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Re: Mario Livio's contribution to science;

Thank you for your confidence in me, in that respect. I really appreciate all exchanges with people more knowledgeable than me. It helps me navigate through the overwhelming amount of real science and pseudo science.....

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......

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