Thanks for the link. How's the weather? :smile: :wink:

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? — TheMadFool

Again, you aren't using a consistent definition of chaos. Is chaos a lack of patterns or a lack of mathematical explanations? As and I have pointed out, one doesn't necessarily entail the other.

Even then, in your Universe A, you have both patterns and mathematical explanations.

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

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

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

Seems quantitative to me.

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. — TheMadFool

In Universe A, why does an object move when struck?

To say that there is a pattern of objects moving when struck, yet no pattern in how the struck object moves, seems to be an incomplete explanation. When explaining why an object moves when struck, you'd be explaining the nature of the objects themselves. Is there something in the nature of the objects that would inform us how they would move when struck? Again, what kinds of questions can we ask about the objects in Universe A? It seems to me that we can ask both non-mathematical and mathematical questions about the objects in Universe A, as in how many objects exist, and how many objects it takes to move another.

Again, you aren't using a consistent definition of chaos. Is chaos a lack of patterns or a lack of mathematical explanations? — Harry Hindu

I agree completely with you that chaos is the absence/lack of patterns. We'll begin from there.

Let's take an example of our universe: look at the physics of falling bodies. Observation informs us that when an object is let go in the air, they fall to the earth. This is the nonmathematical pattern we see in our universe and is called free fall. The next step is, as any science history buff will tell you, to find out if this nonmathematical pattern (free fall) has, within it, a mathematical/quantitative pattern. In other words, we're looking for a pattern (a mathematical one) in a pattern (a nonmathematical one). This is the story of Galileo that every science student knows.

As you know, Galileo discovered that, for falling objects, the distance travelled by a falling object is directly proportional to the square of the time spent falling.

Can you see here that a pattern can appear in two places? This should be obvious to you since you did mention in a previous post that one of my imagined universes lacks a description of "how" motion takes place. Anyway, here's what the situation regarding patterns vs chaos with Galileo is:

1. There is a pattern, a nonmathematical one, in the way the earth interacts with objects that are let go in the air - they always fall. This pattern is called free fall. Call this pattern X.

2. There is another pattern, a mathematical one, in free fall as discovered by Galileo: the distance an object falls is directly proportional to the square of the time spent in falling. Call this pattern Y.

You can see, quite clearly, pattern Y is a pattern in pattern X and pattern X is NOT pattern Y. Keep this in mind.

Now, since pattern X is not pattern Y, it is completely possible for pattern X to be present (no chaos = free fall ) and pattern Y to be absent (chaos = there is no mathematical relationship between the distance an object falls and the time it takes to fall) without contradiction for one is a pattern and the other is the pattern in that pattern - two entirely different things . This is exactly what's the case with universe A which has the nonmathematical pattern, "if struck, move", which you were so kind to point out to me (thanks), but lacks the mathematical pattern "if one object moving at velocity w, at an angle x, strikes another object, the struck object will move at a velocity y at an angle z." Let's call the pattern "if struck, move", pattern/law S. In universe A, pattern/law S exists but what's missing is a mathematical pattern in the pattern/law S. I'm using the term "chaos" consistently and without contradiction.

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

2. the lowest cardinal number; half of two; 1
— TheMadFool
Seems quantitative to me. — Harry Hindu

So, a lexicographer was so intent on causing confusion that he repeated the same meaning twice and even numbered them differently as 1 and 2?

Another thing I wanted to mention. Here's another law you're familiar with: if "one" object of mass m (kg) has an acceleration of a (m/s^2) then, the force acting on it is F = m * a. Does the "one" in the sentence that states the law make the law quantitative? By your logic "yes" but as a matter of fact the correct answer is "no". Similarly the "one" in the universe A's law, "if one object is struck by another object, the struck object will move" doesn't make the law quantitative.

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

I like thought experiments a lot. But your Universe A is too much to wrap my mind around. Sorry.

I like thought experiments a lot. But your Universe A is too much to wrap my mind around. Sorry. — jgill

Thought experiments can't get simpler than the one I came up with in this thread. I know I'm not right, at least not completely right; if it were this simple, Eugene Wigner, a proven genius, would've been onto it before I could've said Jack Robinson.

I agree completely with you that chaos is the absence/lack of patterns. We'll begin from there. — TheMadFool

Ok.

1. There is a pattern, a nonmathematical one, in the way the earth interacts with objects that are let go in the air - they always fall. This pattern is called free fall. Call this pattern X.

2. There is another pattern, a mathematical one, in free fall as discovered by Galileo: the distance an object falls is directly proportional to the square of the time spent in falling. Call this pattern Y.

You can see, quite clearly, pattern Y is a pattern in pattern X and pattern X is NOT pattern Y. Keep this in mind. — TheMadFool

Yes, but is the fact that a pattern exists at all in Universe A indicative that Universe A is not chaotic?

How much chaos vs. order has to exist for a Universe to qualify as chaotic?

Another thing I wanted to mention. Here's another law you're familiar with: if "one" object of mass m (kg) has an acceleration of a (m/s^2) then, the force acting on it is F = m * a. Does the "one" in the sentence that states the law make the law quantitative? By your logic "yes" but as a matter of fact the correct answer is "no". Similarly the "one" in the universe A's law, "if one object is struck by another object, the struck object will move" doesn't make the law quantitative. — TheMadFool

Yes, but is the fact that you can refer to a number of objects in Universe A and how many are part of the process that we are talking about (falling bodies, and a falling body has to be falling relative to something else) indicative that Universe A is quantitative?

How much non-math vs. math has to exist for a Universe to qualify as non-mathematical?

Now, since pattern X is not pattern Y, it is completely possible for pattern X to be present (no chaos = free fall ) and pattern Y to be absent (chaos = there is no mathematical relationship between the distance an object falls and the time it takes to fall) without contradiction for one is a pattern and the other is the pattern in that pattern - two entirely different things . This is exactly what's the case with universe A which has the nonmathematical pattern, "if struck, move", which you were so kind to point out to me (thanks), but lacks the mathematical pattern "if one object moving at velocity w, at an angle x, strikes another object, the struck object will move at a velocity y at an angle z." Let's call the pattern "if struck, move", pattern/law S. In universe A, pattern/law S exists but what's missing is a mathematical pattern in the pattern/law S. I'm using the term "chaos" consistently and without contradiction. — TheMadFool

So now you are using the kind of chaos that you said you aren't using - complexity.

Chaos theory

states of dynamical systems whose apparently-random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions. — wikipedia

The initial condition is free fall. Can an object fall at a different rate if the initial condition of free fall wasn't met?

Yes, but is the fact that a pattern exists at all in Universe A indicative that Universe A is not chaotic? — Harry Hindu

People talk to each other - this is a pattern. However they maybe talking gibberish - this is chaos. I can't explain this any better. You'll have to reread my post and come back with better points.

Yes, but is the fact that you can refer to a number of objects in Universe A and how many are part of the process that we are talking about (falling bodies, and a falling body has to be falling relative to something else) indicative that Universe A is quantitative? — Harry Hindu

So, "one" in if "one" object of mass m (kg) has an acceleration of a (m/s^2) then the force acting on it F = m * a is central to the quantitative nature of the statement?

So now you are using the kind of chaos that you said you aren't using - complexity — Harry Hindu

I'm using your definition of "chaos". Does that include complexity?

Thought experiments can't get simpler than the one I came up with in this thread. — TheMadFool

Well, it is simple. Too simple. Not enough information to begin an intelligent discussion, IMO. Underlying any approach is an agreement of just what math is. Is there mathematics without symbols, words, or figures? In Universe A, Motion=F(Impact), a qualitative mathematical statement. Impact produces motion. Sorry, it all seems a little flaky.

I am not knowledgeable about mathematics or the philosophy of mathematics. What I have to say here may be totally wrong but reading the discussion stimulated me to consider some other ideas on the subject and, what the heck, I'll offer them and see what people think.

First, I'd like to call attention to the law of the conservation of energy. I'll argue that the law implies that the physical world is describable mathematically and I'll also argue that violation of the law requires that something can come from nothing and also that something can vanish into nothing - features of the universe that, for thousands of years have been considered illogical, though I understand that some of our quantum mechanics experts now have reason to believe that the ex nihilo fit principle is not exactly what we took it to be.

When an object strikes another object, if chaos results, that is to say, if the two objects can bounce off in any directions at any speeds, then there must be a net gain or loss of energy in the interaction. If that is so, then if we give up the rule that mathematics must be observed in physics, we also must give up the rule that energy is conserved. That seems to me to be a lot to give up. One wonders if there could even be a universe in which that is possible.

I can't prove it but I'm inclined to believe that "our" universe is mathematically describable, not because of the anthropomorphic principle, but because any universe - even any universe in an "expanding multiverse" in which physical constants may be different, must be so describable. It is the nature of existence that that be so. If it's not, then I suspect that logic and reason will go out the window along with mathematics. Or perhaps I should say, there couldn't even be a window for anything to go out.

Alan

Well, it is simple. Too simple. Not enough information to begin an intelligent discussion, IMO. — jgill

I like thought experiments a lot. But your Universe A is too much to wrap my mind around. Sorry — jgill

:chin:

You're as fickle as the weather, Mr. Meteorologist.

People talk to each other - this is a pattern. However they maybe talking gibberish - this is chaos. I can't explain this any better. You'll have to reread my post and come back with better points. — TheMadFool

I don't see how you could be saying that people are talking to each other if they are "talking" gibberish. This is a contradiction. You need to come back with better arguments.

So, "one" in if "one" object of mass m (kg) has an acceleration of a (m/s^2) then the force acting on it F = m * a is central to the quantitative nature of the statement? — TheMadFool

Sure, because it's not two or three, etc. It's basically saying:

(n * mass) * a = F

where n = the number of objects.

I'm using your definition of "chaos". Does that include complexity? — TheMadFool

I thought we agreed to use this definition:

I agree completely with you that chaos is the absence/lack of patterns. We'll begin from there. — TheMadFool

but then you went about using a different definition - the one that refers to complexity, which I showed. Maybe you should be the one that re-reads posts, not me.

I don't see how you could be saying that people are talking to each other if they are "talking" gibberish. This is a contradiction. You need to come back with better arguments. — Harry Hindu

I was so nervous, I just started talking gibberish. — Cambridge Dictionary

Sure, because it's not two or three, etc. It's basically saying:

(n * mass) * a = F

where n = the number of objects. — Harry Hindu

:rofl: So, had I said, "if two objects strike each other and then the one, identified as p, having a mass m moves at an acceleration a" then the force acting on p is F = 2 * m * a?

but then you went about using a different definition - the one that refers to complexity, which I showed. Maybe you should be the one that re-reads posts, not me — Harry Hindu

You made a good point and I responded to it.

I like thought experiments a lot. But your Universe A is too much to wrap my mind around. Sorry — jgill


:chin:

You're as fickle as the weather, Mr. Meteorologist. — TheMadFool

Too much of a stretch. But nice rejoinder! :cool:

:rofl: So, had I said, "if two objects strike each other and then the one, identified as p, having a mass m moves at an acceleration a" then the force acting on p is F = 2 * m * a? — TheMadFool

I don't see what's so funny, unless it's your silly imaginary universe you're laughing at. Is your imaginary universe funny?

If two objects strike one object, what happens?

Do all the objects involved have mass?

Are any objects moving? If so, at what velocity. Remember that velocity is relative.

Are these not all mathematical questions that I'm asking you about the objects in your universe that you claim is non-mathematical? And these questions need to be answered before you even get to F=m*a

It's ok. Thank you.

You say there is an object in universe A. But if an object is to exist space must exist and space must be coherent/mathematical. A non mathematical universe would be chaos. It would not be possible to move from a to b firstly because there would be no coherent space between a and b and secondly, there would be no space for an object to occupy. Chaos is chaotic beyond imagining

If the objects you are talking about are coherent objects the space within and around them must be coherent and laws would simply be a description of the shape of this space. Once you have space you have law/mathematics.

@EnPassant,

I think your argument is right. As far as I can see, there is no possible alternative reality in which mathematics cannot describe the physical characteristics of the universe. Any such alternative would be unstable and beyond description. The effectiveness of mathematics in the natural sciences isn't "unreasonable". It is ineffectiveness of mathematics that would be unreasonable.

Is it true that "Chaos is chaotic beyond imagining"? I think it is though we might wish to rephrase the argument to avoid the criticism that it's only because we lack imagination. What I'd like to say is that the laws of mathematics aren't as separate from the laws of physics as some of us might imagine. To say that one apple plus one apple = two apples isn't just about numbers. It's true of apples, and also oranges, houses, words, and all other discrete objects. Apples are countable. Their masses and velocities are measurable. They don't wink in and out of existence. Their mathematical properties are as much a part of their being as their mass, their extension (i.e. occupation of space), their color, their taste, and everything else about them.

If countability, addition of velocities, and other descriptions of apples did not follow mathematical laws, then the very most basic principles of our physics, and the most fundamental descriptions of our universe, would not obtain - including the law of conservation of energy. We would not exist either since we too are countable and subject to gravity, additions of velocity, and so on. Your statement about this that "... Once you have space you have law/mathematics." seems to me to be right on target.

I think the argument that you and I (if I understand you correctly) are propounding is intuitive but it probably needs a real philosopher/mathematician/physicist beyond my limited knowledge to properly flesh it out.

Alan