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
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
Seems quantitative to me.Definition:
one:
1. denoting a particular item of a pair or number of items
2. the lowest cardinal number; half of two; 1 — TheMadFool
In Universe A, why does an object move when struck?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
Again, you aren't using a consistent definition of chaos. Is chaos a lack of patterns or a lack of mathematical explanations? — 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
— TheMadFool
Seems quantitative to me. — Harry Hindu
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. — jgill
Ok.I agree completely with you that chaos is the absence/lack of patterns. We'll begin from there. — TheMadFool
Yes, but is the fact that a pattern exists at all in Universe A indicative that Universe A is not chaotic?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
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
So now you are using the kind of chaos that you said you aren't using - complexity.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
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
Yes, but is the fact that a pattern exists at all in Universe A indicative that Universe A is not chaotic? — Harry Hindu
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 now you are using the kind of chaos that you said you aren't using - complexity — Harry Hindu
Thought experiments can't get simpler than the one I came up with in this thread. — 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.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
Sure, because it's not two or three, etc. It's basically saying: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
I thought we agreed to use this definition:I'm using your definition of "chaos". Does that include complexity? — 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 agree completely with you that chaos is the absence/lack of patterns. We'll begin from there. — 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. — 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
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
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
I don't see what's so funny, unless it's your silly imaginary universe you're laughing at. Is your imaginary universe funny?: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
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.