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
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
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? — jgill
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
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.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. — 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
Law of motion: if one object is struck by another object the struck object will move. — TheMadFool
Well, my contention is that a nonmathematical law leads to chaos but a mathematical law leads to order. — TheMadFool
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
No, that both universes are explainable. Like I said, you can use words or numbers to explain it, and numbers are just words.I believe you're describing what my first intuition was, that both universes are actuallymathematical, just at a different level of description and precision. — 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.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
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.The cell is defined and described in non-quantitative means, by empirical observation. — QuixoticAgnostic
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
I don't know. It's your imaginary universe. You tell me.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
Mathematical chaos theory is, to my reckoning, simply about unexpected complexity in fully deterministic systems. Nevertheless, there are patterns that can be discerned — TheMadFool
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
I don't know. It's your imaginary universe. You tell me. — Harry Hindu
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.
As a former meteorologist I disagree. Your approach is very Newtonian, which is not bad, but rather insufficient. — jgill
Your Universe A is a fairy tale and thus cannot be compared to our universe.
As a former meteorologist I disagree. — jgill
(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: )
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 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
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.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 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
As I have said many times already, there is no distinction between mathematical and nonmathematical laws. Mathematical explanations are worded explanations.Yes. Exactly. Nonmathematical laws are incomplete and also precludes order, a necessary ingredient for life. — 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?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
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
"I believe you're describing what my first intuition was, that both universes are actuallymathematical, 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
Both you and QuixoticAgnostic have used numbers in both of your "non-mathematical" laws! — Harry Hindu
This is the part I was referring to:Yeah, that certainly doesn't look like denial — QuixoticAgnostic
The part you are referring to was me translating "mathematical" to "explainable", as mathematics is a type of explanation - so no contradiction.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
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.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
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
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
As I have said many times already, there is no distinction between mathematical and nonmathematical laws — Harry Hindu
Chaos is a term than can refer to randomness or complexity. — Harry Hindu
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
, and not randomness.Mathematical chaos theory is, to my reckoning, simply about unexpected complexity in fully deterministic systems. — 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
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
It seems to me that chaos was prevented the moment you established any pattern in a universe — Harry Hindu
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
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
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