The Unreasonable Effectiveness Of Mathematics In The Natural Sciences - A Possible Explanation

TheMadFool

The Unreasonable Effectiveness Of Mathematics In The Natural Sciences [Eugene Wigner (b. 1902 d.1995)]

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. — Eugene Wigner

Wigner sums up his argument by saying that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it — wikpedia

It seems that scientists and mathematicians are puzzled by the "unreasonable effectiveness" of math in the natural sciences. In other words, they have no explanation why math has proved to be such a useful tool in science, allowing scientists to derive precise mathematical formulae that describe almost every conceivable phenomena except maybe women :grin:

Anyway, I will attempt to provide an explanation for why math is such a fine tool in describing our universe.

Imagine two universes A and B with two objects each and governed by two different laws. For simplicity the laws will be about motion only but the idea is applicable, mutatis mutandis, to all laws in any universe.

Universe A:
1. Two objects
2. Law of motion: if one object is struck by another object the struck object will move. This law is non-mathematical

Universe B:
1. Two objects
2. Law of motion: if one object travelling at velocity w, strikes another object at an angle x the, the struck object shall move with a velocity y at an angle z., This law is mathematical

As must already be obvious, universe A is chaotic as the struck object can assume any velocity and any path - the motion is completely random as the law fails to fully describe motion.

The situation is different in universe B as there is order - the struck object's velocity and path is fully determined by the object striking it. Motion is fully described in this universe and there can be no chaos in the sense that the struck object can assume any velocity or any trajectory.

As I mentioned before, this is true for any law, whether physical or chemical - the law governing such phenomena has to be mathematical for there to be order.

Can life arise in chaos, in universe A? Considering that life requires different sets of chemical and physical laws acting in concert and the formation and persistence of some pattern of matter and energy which is impossible in a chaotic universe that is completely random, it follows that life is not possible in universe A.

This isn't the case for universe B though; it has order and allows patterns in matter and energy to take hold and persist, thereby making life possible.

To make the long story short, math gives rise to order and order gives rise to life and life gives rise to Eugene Wigner. The reason why math is so effective in describing the universe we live in is that life can't exist in a nonmathematical universe of chaos. Every universe life exists must have order and where there's order there'll always be mathematics.

Comments...

ADDENDUM: As @Harry Hindu was kind enough to point out, there is a pattern in universe A viz. an object will move when struck. So, to call a system that has a law, a pattern, chaotic is a contradiction (or so it seems).

Indeed, chaos precludes any and all patterns and universe A has a pattern (if struck, move). So, then is universe A not chaotic? To answer "yes" amounts to saying universe A has order. If the law/pattern in universe A (if struck, move) is just that and nothing more then, struck objects can assume any velocity or trajectory in a random fashion, the net effect of which would be chaotic/patternless motion. What does this, this patternless motion, imply but that motion in universe A is chaotic?

It seems, prima facie, that we're faced with a contradiction. We agree that universe A has a pattern (if struck, move) and, at the same time, universe A doesn't have a pattern (struck objects take on random trajectories and velocities).

How do we make sense of this, if there's any sense at all in it?

In knowing that in universe A, a struck object will be in motion, we have a pattern, but in not knowing how that motion will occur, we have no pattern.

Perhaps if look at the usage of the word "pattern", we'll make some progress. A pattern is found in something - patterns don't exist without a thing it's a characteristic of. So, the pattern "if struck, move" is found in the physical interaction of objects in universe A and B. This pattern is labeled motion. The pattern "if an object with velocity w strikes an object at an angle x then the object struck shall move at a velocity y, at an angle z" is a pattern, a mathematical pattern, in motion in universe B and not in A. In other words we're looking at patterns in patterns.

As might be already obvious to you now, there is no contradiction in the universe A scenario because the chaos in it (random velocities and trajectories of struck objects) is the absence of a mathematical pattern in the nonmathematical pattern "if struck, move"; in simple words there is no pattern in the pattern. The chaos (mathematical) is at a different "level" than the pattern (nonmathematical). I believe I already mentioned this is one my comments.

Coming back to what I really want to demonstrate here, the fact that there is chaos in a universe like A with nonmathematical laws, and that life is about patterns (order) in matter-energy, it follows that a nonmathematical universe wouldn't be able to support life. A universe with life has to be mathematical.

Shawn

Giftetedness is a burden.

TheMadFool

Yes, math is a burden, burdened. A burden to learn and burdened with the task of explaining the universe.

jgill

Universe A:
1. Two objects
2. Law of motion: if one object is struck by another object the struck object will move. This law is non-mathematical — TheMadFool

I can see Tegmark's Mathematical Universe as an outlandish, but somewhat plausible argument, but I don't see a reasonable path to a conclusion here.

Every universe life exists must have order and where there's order there'll always be mathematics. — TheMadFool

Huh. Is that true? Does order always imply mathematics? A Pharaoh decrees orders that govern the treatment of slaves - does this orderliness imply mathematics?

Does chaos imply no mathematics? I think it possible to envision a chaotic universe that is entirely mathematical since mathematics underlies chaos theory in our own universe. I can easily produce a chaotic structure by simple iteration. Sensitive dependence on initial conditions (Butterfly Effect) does the trick.

TheMadFool

Huh. Is that true? Does order always imply mathematics? A Pharaoh decrees orders that govern the treatment of slaves - does this orderliness imply mathematics? — jgill

Order¹: the arrangement or disposition of people or things in relation to each other according to a particular sequence, pattern, or method.

Order²: A command

Does chaos imply no mathematics? I think it possible to envision a chaotic universe that is entirely mathematical since mathematics underlies chaos theory in our own universe. I can easily produce a chaotic structure by simple iteration. Sensitive dependence on initial conditions (Butterfly Effect) does the trick. — jgill

Mathematical chaos theory is, to my reckoning, simply about unexpected complexity in fully deterministic systems. Nevertheless, there are patterns that can be discerned. The chaos I'm reffering to is completely devoid of any pattern and is also wholly random and undeterministic except perhaps in a qualitative sense.

QuixoticAgnostic

I've been busting my brain over this question for the past several hours now: what makes something mathematical? Is it a level of rigor? Must you reason from fundamental concepts? What makes physics so mathematical as opposed to the "higher-level" sciences? Is it the quantitative nature over qualitative? Maybe I'm just having a bad night but I can't figure it out for the life of me.

Harry Hindu

Universe A:
1. Two objects
2. Law of motion: if one object is struck by another object the struck object will move. This law is non-mathematical

Universe B:
1. Two objects
2. Law of motion: if one object travelling at velocity w, strikes another object at an angle x the, the struck object shall move with a velocity y at an angle z., This law is mathematical — TheMadFool

Mathematics is simply a method of symbolizing relationships. F=m*a. We can use words or numbers to represent the relationship, which is what you did here. Neither one is chaotic if the both contain LAWS. You said the same thing, one with words and the other, with more symbolic details about the relationship. The extra detail allows me to use the representation to make predictions about other instances of where objects bump into each other and what the results will be.

TheMadFool

Mathematics is simply a method of symbolizing relationships. F=m*a. We can use words or numbers to represent the relationship, which is what you did here. Neither one is chaotic if the both contain LAWS. You said the same thing, one with words and the other, with more symbolic details about the relationship. The extra detail allows me to use the representation to make predictions about other instances of where objects bump into each other and what the results will be. — Harry Hindu

Well, my contention is that a nonmathematical law leads to chaos but a mathematical law leads to order. Your comment reveals a not unexpected bias engendered by (over)exposure to the laws of this universe in which we live where all known phenomena are non-chaotic. You've been conditioned to associate "law" with "no chaos" as there are no known exceptions that could've made you think otherwise.

The fact of the matter is a ~~qualitative~~ nonquantitative/nonmathematical law can exist such as the one I described in my OP that can only lead to chaos; on the other hand, a quantitative/mathematical will always lead to order.

Harry Hindu

Well, my contention is that a nonmathematical law leads to chaos but a mathematical law leads to order. Your comment reveals a not unexpected bias engendered by (over)exposure to the laws of this universe in which we live where all known phenomena are non-chaotic. You've been conditioned to associate "law" with "no chaos" as there are no known exceptions that could've made you think otherwise.

The fact of the matter is a qualitative nonquantitative/nonmathematical law can exist such as the one I described in my OP that can only lead to chaos; on the other hand, a quantitative/mathematical will always lead to order. — TheMadFool

You are wrong in your assessment of my worldview. It seems like you didn't really bother reading what I said. You are the one that labeled each statement in each universe as a LAW, not me, and then you went on about explaining what is the case:

Law of motion: if one object is struck by another object the struck object will move. — TheMadFool

If it were a universe of chaos, then it wouldn't always be the case that if one object is struck by another object the struck object will move. Maybe the objects would pass right through each other. Maybe the struck object doesn't move, and you wouldn't be able to make statements like this, which means that there aren't any laws.

A law is a statement, or a representation, of some state-of-affairs. You can represent things with words or with numbers and numbers are just words. (7 is seven, 8 is eight, f=m*a is force equals mass times acceleration).

How did you learn to pronounce, or even say, "7" if not for "seven"? Just as Dr. is an abbreviation of doctor, 7 is an abbreviation of seven.

So all you have done is provide the same explanation in both universes, just with different symbols. Both statements allow you to make predictions - that struck objects will move. How can you make predictions in a chaotic universe?

Pantagruel

Well, my contention is that a nonmathematical law leads to chaos but a mathematical law leads to order. — TheMadFool

But chaos has an inherent order, as non-linear dynamics clearly establishes through the use of attractors.

QuixoticAgnostic

↪Harry Hindu

I believe you're describing what my first intuition was, that both universes are actually mathematical, just at a different level of description and precision. But this seems to run into problems, which I think you may or may not be addressing by specifying the symbolizing of relationships.

If we speak about a universe where there exist 3 masses that follow the classical laws of gravitation, you have the 3-body Problem which is mathematical. But if you imagine the universe of a cell (I'm not going to pretend I understand how the cell works at even a high school level), you can define all the parts and describe how all those parts interrelate, and even though this may be a consistent and determinable system of relationships, we wouldn't generally consider that mathematical. Yet, we can go on to consider something like Conway's Game of Life, which is similar to a cell in the sense that you describe the parts (the grid of cells, "live" and "dead" states, neighborhood, tick) and how those parts interrelate (the rules by which cells are born and die according to their neighborhood and their propagation through ticks), but this is mathematical in nature. Which brings me back to my initial question: what makes one thing mathematical and the other not?

I suspect the devil's in the details. The cell is defined and described in non-quantitative means, by empirical observation. Something about this is different from how we define and describe the Game of Life, which is a priori, in a sense. I don't think it's merely quantitative though, as plenty of mathematics isn't quantitative, in the sense that not all mathematics is about numbers and measurement. But if it's not quantitative, what is it?

TheMadFool

↪Harry Hindu

Remember that I had to find an explanation for why the laws of the universe are mathematical. Thus the necessity for a scenario with two different universes, one operating under a mathematical law and the other under a nonmathematical one. Only then could I demonstrate why s universe with life has to be mathematical.

As far as I'm concerned, regarding your claim that the imagined universe A with the nonquantitative law is not chaotic, all I ask from you is to describe the pattern (since you deny this is chaos) in the motion of objects with the law: if one object is struck by another object the struck object will move. The pattern you might claim exists is simply that the struck object will move but how this motion occurs will be totally chaotic, no? It is this chaos I'm referring to. All other physical and chemical laws too will result in chaos if the laws that govern them are nonmathematical for the same reason. This chaos, I hope we're clear on what I mean, is sufficient to prevent any kind of order in universe A. Without order, life, which is simply patterns (order) of energy and matter, is impossible.

That said, you're not entirely wrong in saying that the existence of a law implies there is no chaos; all I can say about that is this chaos is at a different level than the chaos I'm referring to.

3017amen

Wigner sums up his argument by saying that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it — wikpedia

Agreed! Particularly since mathematics confers no Darwinian biological advantages!

Harry Hindu

I believe you're describing what my first intuition was, that both universes are actually ~~mathematical~~, just at a different level of description and precision. — QuixoticAgnostic

No, that both universes are explainable. Like I said, you can use words or numbers to explain it, and numbers are just words.

But if you imagine the universe of a cell (I'm not going to pretend I understand how the cell works at even a high school level), you can define all the parts and describe how all those parts interrelate, and even though this may be a consistent and determinable system of relationships, we wouldn't generally consider that mathematical. — QuixoticAgnostic

As I said, mathematics describes the relationship between things. If things are interrelated then they are explainable in mathematical terms (which are just words). F=m*a is the symbolic representation of how force, mass and acceleration are interrelated.

The cell is defined and described in non-quantitative means, by empirical observation. — QuixoticAgnostic

It seems to me that it is all quantitative. Look at TheMadFool's Laws, they both include the concept of one, and another which is quantitative.

Universe A:
1. Two objects
2. Law of motion: if one object is struck by another object the struck object will move. This law is non-mathematical

Universe B:
1. Two objects
2. Law of motion: if one object travelling at velocity w, strikes another object at an angle x the, the struck object shall move with a velocity y at an angle z., This law is mathematical — TheMadFool

Objects of perception are bounded and quantitative by their very nature. It is how the mind conceives of the world that isn't made up of objects, but of relationships.

Harry Hindu

Remember that I had to find an explanation for why the laws of the universe are mathematical. Thus the necessity for a scenario with two different universes, one operating under a mathematical law and the other under a nonmathematical one. Only then could I demonstrate why s universe with life has to be mathematical.

As far as I'm concerned, regarding your claim that the imagined universe A with the nonquantitative law is not chaotic, all I ask from you is to describe the pattern (since you deny this is chaos) in the motion of objects with the law: if one object is struck by another object the struck object will move. The pattern you might claim exists is simply that the struck object will move but how this motion occurs will be totally chaotic, no? It is this chaos I'm referring to. All other physical and chemical laws too will result in chaos if the laws that govern them are nonmathematical for the same reason. This chaos, I hope we're clear on what I mean, is sufficient to prevent any kind of order in universe A. Without order, life, which is simply patterns (order) of energy and matter, is impossible.

That said, you're not entirely wrong in saying that the existence of a law implies there is no chaos; all I can say about that is this chaos is at a different level than the chaos I'm referring to. — TheMadFool

I don't know. It's your imaginary universe. You tell me.

If one object strikes another and the other will move is a law, it seems to be an incomplete law because it doesn't tell how the struck object will move after being struck, or anything about the nature of the objects themselves. If there isn't a pattern then it can be said that the universe is chaotic. It wouldn't be chaotic because one pattern is explained by mathematics and the other is explained by words, which I pointed out isn't a difference because numbers are just words. It would be chaotic because you couldn't establish a pattern of like causes leading to similar effects.

QuixoticAgnostic

↪Harry Hindu

I can't tell if we're disagreeing or not lol. I'm happy to accept that mathematics describes the relationship between things. In fact, that is the basis to most of my philosophy. However, I would qualify that mathematics isn't just about relationships, but interrelationships or, better put, interactivity.

The distinction is in relationships that don't merely describe, but define. For example, in Conway's Game of Life, you can say there is a dead cell with 3 live cells in its neighborhood. I just described a relationship between a cell and its neighbors, but this isn't a mathematical description because it doesn't tell me about how these things interact with one another. If I say, however, that cells are initially either "live" or "dead" and transition states according to rules X, Y, Z, then I am making a mathematical statement because it is defining the behavior and interactivity of things.

Although what I'm confused about is you say both universes are explainable, but deny that the first universe is mathematical? You say "if things are interrelated, then they are explainable in mathematical terms", so in universe A the two objects are interrelated, so they are explainable in mathematical terms, which means the universe is mathematical, no? Regardless, we're both in agreement that there is no fundamental difference between universe A and B.

jgill

Mathematical chaos theory is, to my reckoning, simply about unexpected complexity in fully deterministic systems. Nevertheless, there are patterns that can be discerned — TheMadFool

Well, if I could upload imagery of a dynamical system I devised I would challenge you to find a pattern.

Your comment reveals a not unexpected bias engendered by (over)exposure to the laws of this universe in which we live where all known phenomena are non-chaotic. — TheMadFool

As a former meteorologist I disagree. Your approach is very Newtonian, which is not bad, but rather insufficient.

Your Universe A is a fairy tale and thus cannot be compared to our universe. (My late Hungarian ex-father-in-law carried on a lengthy correspondence with Wigner. I'm surprised the Nobel Laureate did not formulate and advance your argument. :roll: )

TheMadFool

I don't know. It's your imaginary universe. You tell me. — Harry Hindu

What's wrong with imagined scenarios? They're legit philosophical devices, no? Isolate the key variable and do something to it and see what follows and so on...

If one object strikes another and the other will move is a law, it seems to be an incomplete law because it doesn't tell how the struck object will move after being struck, or anything about the nature of the objects themselves.

Yes. Exactly. Nonmathematical laws are incomplete and also precludes order, a necessary ingredient for life.

If there isn't a pattern then it can be said that the universe is chaotic. It wouldn't be chaotic because one pattern is explained by mathematics and the other is explained by words, which I pointed out isn't a difference because numbers are just words. It would be chaotic because you couldn't establish a pattern of like causes leading to similar effects.

This last paragraph is irrelevant so long as you agree that nonmathematical laws come off as incomplete. In this incompleteness is the seed for chaos and where there is chaos, life, but a pattern (order) in matter-energy, becomes impossible.

As a former meteorologist I disagree. Your approach is very Newtonian, which is not bad, but rather insufficient. — jgill

I used motion as a jumping board because it's conveniently simple and still to the point. Also, I mentioned quite clearly that the basic idea - that nonmathematical laws lead to chaos - applies to all the laws of science.

By the wat what would be a non-Newtonian approach? How would that affect my argument?

Your Universe A is a fairy tale and thus cannot be compared to our universe.

Albert Einstein used thought experiments (a lot). That should allay your concerns, hopefully.

As a former meteorologist I disagree. — jgill

Hi, Mr. Meteorologist. Wonderful to have you on the forum. Chaos must be familiar to you; after all Edward Lorenz who discovered The Butterfly Effect was a meteorlogist too.

I agree that Chaos Theory is a legitimate field of study in mathematics. I don't contest that. However, correct me if I'm wrong, mathematical chaos is deterministic chaos i.e. chaotic systems of Chaos Theory are technically not chaotic - they are simply extremely complex but completely deterministic systems. Wittgenstein may have an issue with the use of the term "chaos" here.

The chaos I'm referring to is a different kind of chaos - one that is non-deterministic due to the complete lack of mathematics in the laws of a universe; such a universe would be chaotic too and this particular type of chaos would preclude life, if life is construed as patterns (order) in matter-energy.

(My late Hungarian ex-father-in-law carried on a lengthy correspondence with Wigner. I'm surprised the Nobel Laureate did not formulate and advance your argument. :roll: )

I'm surprised too. :chin: My argument is very simple. Nonmathematical laws lead to chaos and chaos doesn't allow life. Ergo, a universe that has life will always have mathematical laws.

Harry Hindu

The distinction is in relationships that don't merely describe, but define. For example, in Conway's Game of Life, you can say there is a dead cell with 3 live cells in its neighborhood. I just described a relationship between a cell and its neighbors, but this isn't a mathematical description because it doesn't tell me about how these things interact with one another. If I say, however, that cells are initially either "live" or "dead" and transition states according to rules X, Y, Z, then I am making a mathematical statement because it is defining the behavior and interactivity of things. — QuixoticAgnostic

Sure it's a mathematical description. You just described the number of dead cells relative to live cells. TheMadFool did the same thing in his OP, that I pointed out in my previous post to you, but you seem to have missed it.

The former and the latter are simply answering, or explaining, two different things. They each answer two different questions, yet they both use mathematics in their explanation. They also use words, and I have said that numbers are words, so essentially you explain everything with words, which mathematics consists of.

Although what I'm confused about is you say both universes are explainable, but deny that the first universe is mathematical? You say "if things are interrelated, then they are explainable in mathematical terms", so in universe A the two objects are interrelated, so they are explainable in mathematical terms, which means the universe is mathematical, no? Regardless, we're both in agreement that there is no fundamental difference between universe A and B. — QuixoticAgnostic

I never denied that the first universe was mathematical. I specifically said that it was, and even bolded the text to make it easy for you to see, but you still missed for some reason. I also said that both universes are explainable and by explainable I mean that you use words to represent some state-of-affairs, and mathematical explanations consist of words.

So, if numbers are words, and you explain things with words, then there is no distinction between a universe that you can explain with mathematics and one you can explain with words.

Harry Hindu

I don't know. It's your imaginary universe. You tell me.
— Harry Hindu

What's wrong with imagined scenarios? They're legit philosophical devices, no? Isolate the key variable and do something to it and see what follows and so on... — TheMadFool

You asked me a question about the state of your imaginary universe. If it is imaginary, then that means we can make up whatever we want, so you could imagine that your Universe A actually does have more information than what some statement (law) about it exhibits.

We don't live in an imaginary universe. We live in a universe that is a certain way and that we come into, being ignorant of. We make stuff up in our minds, but the universe has a different story that contradicts our story about it, so we have to adjust our story from time to time to fit our observations of it. The universe fine tunes our explanations via our observations of it. To keep making stuff up about the state of the universe without using our observations to filter the stuff we make up would be a symptom of delusional disorder.

Yes. Exactly. Nonmathematical laws are incomplete and also precludes order, a necessary ingredient for life. — TheMadFool

As I have said many times already, there is no distinction between mathematical and nonmathematical laws. Mathematical explanations are worded explanations.

Both you and QuixoticAgnostic have used numbers in both of your "non-mathematical" laws!

This last paragraph is irrelevant so long as you agree that nonmathematical laws come off as incomplete. In this incompleteness is the seed for chaos and where there is chaos, life, but a pattern (order) in matter-energy, becomes impossible. — TheMadFool

No, explanations are incomplete or complete depending on the question being asked. What kinds of questions can we ask about both universes? Can we ask the same questions about both? If so, would we receive the same answers? Why or why not?

QuixoticAgnostic

I never denied that the first universe was mathematical. I specifically said that it was, and even bolded the text to make it easy for you to see, but you still missed for some reason. — Harry Hindu

Hmm. . .

"I believe you're describing what my first intuition was, that both universes are actually ~~mathematical~~, just at a different level of description and precision."
— QuixoticAgnostic
No, that both universes are explainable. Like I said, you can use words or numbers to explain it, and numbers are just words. — Harry Hindu

Yeah, that certainly doesn't look like denial :roll:

Also, reducing mathematics to numbers and numbers to words (not even descriptive words, but literally just the denotation "one", "two", "three", etc.) doesn't make a whole lot of sense. Mathematics encompasses much more than just quantity and words don't always describe mathematical relationships. Your "numbers are words" argument is confused: just because numbers are words doesn't mean all words are numbers, which means it isn't necessarily the case that words describe mathematical relationships.

QuixoticAgnostic

Both you and QuixoticAgnostic have used numbers in both of your "non-mathematical" laws! — Harry Hindu

"You can say there is a dead cell with 3 live cells in its neighborhood" is a description of a state, but not a mathematical law because it doesn't describe the behavior of the system or how things interact, which was the point of me bringing that up. "However, I would qualify that mathematics isn't just about relationships, but interrelationships or, better put, interactivity. The distinction is in relationships that don't merely describe, but define."

Harry Hindu

Yeah, that certainly doesn't look like denial — QuixoticAgnostic

This is the part I was referring to:

It seems to me that it is all quantitative. Look at TheMadFool's Laws, they both include the concept of one, and another which is quantitative. — Harry Hindu

The part you are referring to was me translating "mathematical" to "explainable", as mathematics is a type of explanation - so no contradiction.

↪QuixoticAgnostic

The type of explanation depends on what type of question is being asked.

Harry Hindu

↪QuixoticAgnostic

As must already be obvious, universe A is chaotic as the struck object can assume any velocity and any path - the motion is completely random as the law fails to fully describe motion.

The situation is different in universe B as there is order - the struck object's velocity and path is fully determined by the object striking it. Motion is fully described in this universe and there can be no chaos in the sense that the struck object can assume any velocity or any trajectory. — TheMadFool

TheMadFool's assertion was that Universe A is chaotic because the Law isn't a mathematical explanation, while Universe B is orderly because the Law is a mathematical explanation.

But each explanation is about, or answers, very different questions about each Universe.

Order and chaos are not dependent on what type of questions we ask. They are dependent on whether or not a patterns can be found and then used to make predictions in each Universe.

Mathematical chaos theory is, to my reckoning, simply about unexpected complexity in fully deterministic systems. Nevertheless, there are patterns that can be discerned. The chaos I'm reffering to is completely devoid of any pattern and is also wholly random and undeterministic except perhaps in a qualitative sense. — TheMadFool

Chaos is a term than can refer to randomness or complexity. Randomness can be a result of our ignorance. Once we are able to establish a predictable pattern in the Universe, randomness disappears and becomes order.

In Universe A, you established that a pattern exists - that a struck object moves when struck. If you want to say that the way in which it moves is random, that's fine, but Universe A is still not completely random, as you were still able to establish a pattern within it, and that pattern answers a different question than what your pattern within Universe B does.

If you're saying that the question we are asking about Universe B is unanswerable in Universe A, why is it unanswerable - because we just haven't established a pattern yet, or that there is no pattern to establish? How would you know which is the case in Universe A, unless you imagined it because after all, it is an imagined Universe, and you are its god. Unfortunately, we aren't god in this Universe.

The fact is that, in this universe we have established patterns - a great many of them, and each of them answers different types of questions - mathematical and non-mathematical.

TheMadFool

You asked me a question about the state of your imaginary universe. If it is imaginary, then that means we can make up whatever we want, so you could imagine that your Universe A actually does have more information than what some statement (law) about it exhibits.

We don't live in an imaginary universe. We live in a universe that is a certain way and that we come into, being ignorant of. We make stuff up in our minds, but the universe has a different story that contradicts our story about it, so we have to adjust our story from time to time to fit our observations of it. The universe fine tunes our explanations via our observations of it. To keep making stuff up about the state of the universe without using our observations to filter the stuff we make up would be a symptom of delusional disorder. — Harry Hindu

Once upon a time, to think humans could fly was delusional. Imagination, which you seem to have a dim view of, is what has made heavier-than-air flight possible.

As I have said many times already, there is no distinction between mathematical and nonmathematical laws — Harry Hindu

I'm curious about this statement. How so?

This amounts to the contradiction that:

mathematical is nonmathematical

Perhaps, being exposed to only mathematical laws of our universe, you find it difficult to conceive of a world with nonmathematical laws.

If I maybe so bold as to give you a glimpse of nonmathematical laws in this/our universe and how it leads to chaos, consider social laws. One good example is the law: a good turn deserves another. You wouldn't dispute the fact of this law being nonmathematical would you? If you do, set it aside for the moment and just go with me on this. If there's no math involved at all in this law then the interaction among people following this law would be erratic [chaotic], no? There would be no pattern, i.e. no order, in the behavior of people following this law. No predictions would be possible.

However, the moment quantification/math enters the fray, patterns will begin to emerge on the basis of who did more/less/equal (math) good to whom. The law I spoke of becomes: a (more/less/equal) turn deserves another (more/less/equal turn). Of course, the quantification/math involved is not precise but all that's important for you to note is this: even a crude and imperfect quantification generates patterns (order) and so you can imagine what a completely mathematical version of a simple nonmathematical law can achieve.

TheMadFool

Chaos is a term than can refer to randomness or complexity. — Harry Hindu

Agreed.

In Universe A, you established that a pattern exists - that a struck object moves when struck. If you want to say that the way in which it moves is random, that's fine, but Universe A is still not completely random, as you were still able to establish a pattern within it, and that pattern answers a different question than what your pattern within Universe B does — Harry Hindu

Agreed but the pattern is not sufficient to prevent chaos or more accurately the pattern is not sufficient to generate the order necessary for life.

Harry Hindu

↪TheMadFool

You keep moving the goal posts.

So you seem to be contradicting yourself in using two different qualifiers for chaos - one that the universe has unpredictable patterns and the other being the universe can't be explained in mathematical terms.

Now you are saying that chaos something that can't be prevented. How does it follow that because you can answer a mathematical question with a mathematical answer that that prevents chaos?

It seems to me that chaos was prevented the moment you established any pattern in a universe. From that point you would just be talking about

Mathematical chaos theory is, to my reckoning, simply about unexpected complexity in fully deterministic systems. — TheMadFool

, and not randomness.

TheMadFool

You keep moving the goal posts.

So you seem to be contradicting yourself in using two different qualifiers for chaos - one that the universe has unpredictable patterns and the other being the universe can't be explained in mathematical terms. — Harry Hindu

Compare the following three:

1. Universe with no laws. There would be absolutely no pattern. This is the chaos you're talking about. I agree with you here.

2. Universe with a nonmathematical law. As you rightly pointed out, there is a pattern that the law describes but does this pattern preclude chaos?

If one object strikes another and the other will move is a law, it seems to be an incomplete law because it doesn't tell how the struck object will move after being struck, or anything about the nature of the objects themselves. If — Harry Hindu

Why did you say "an incomplete law" and use the word "how"? For the simple reason that the nomathematical law "if an object strikes another object, the object struck should move" is not sufficient to predict the behavior of objects in a universe that has such a nonmathematical law. Why can't you predict? That would be because there is no pattern in the motion of objects in such a universe. Where there is no pattern, there is chaos no? Basically, there is a pattern in that struck objects will move but there is no pattern in how the struck object will behave/move.

In the scenarios I put for consideration the pattern you see is nonmathematical but the chaos is mathematical. I'm not contradicting myself. Why is the pattern nonmathematical? Why, numbers don't figure in it. Why is the chaos mathematical? There's no pattern in the trajectory or speed, both mathematical entities, of objects.

3. Universe with mathematical laws. These laws, you will agree, are both "complete" and permits us to know "how" matter-energy interact. There's no room for chaos in such a universe because everthing that happens to matter-energy will evince a pattern.

So life, being patterns of matter-energy, isn't possible in a universe with either absolutely no laws or nonmathematical laws as these are chaotic universes.

It seems to me that chaos was prevented the moment you established any pattern in a universe — Harry Hindu

Please read the above.

Syamsu

There is also mathematics of randomness / decisionmaking processes.

Actually if mathematics is the theory of everything, then objects consist of the laws of nature. Then as laws unto themselves objects exhibit freedom. Objects anticipate their alternative future states for some parameters.

And without randomness / decisionmaking then it is impossible to generate information.

TheMadFool

t seems to me that it is all quantitative. Look at TheMadFool's Laws, they both include the concept of one, and another which is quantitative — Harry Hindu

Definition:
one:
1. denoting a particular item of a pair or number of items

2. the lowest cardinal number; half of two; 1

jgill

3. Universe with mathematical laws. These laws, you will agree, are both "complete" and permits us to know "how" matter-energy interact. There's no room for chaos in such a universe because everthing that happens to matter-energy will evince a pattern. — TheMadFool

https://www.researchgate.net/publication/287422786_The_myth_of_the_clockwork_universe_Newton_newtonianism_and_the_enlightenment

:nerd:

The Unreasonable Effectiveness Of Mathematics In The Natural Sciences - A Possible Explanation

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