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Probability theory can be interpreted as an extension to logic where variables can take fractional values (rather than just be 0/false or 1/true). E.g., ((A

Probability theory can be interpreted as an extension to logic where variables can take fractional values (rather than just be 0/false or 1/true). E.g., ((A or B) and C) = (A and C) or (B and C) => P[(A or B) and C] = P[(A and C) or (B and C)] = P[(A and C)] + P[(B and C)] - P[(A and B) and (A and C)] = P[(A and C)] + P[(B and C)] - P[A and B and C] = P[A|C] P[C] + P[B|C] P[C] - P[A and B and C] Notice the last couple lines -- this is the way in which probability extends logic. In you take the limit where P[A], P[B], P[C] = 0, 1, then the probability statement reduces to the logic statement at the top.

deltasevennine 4y ago
I already mentioned that logic can be defined in terms of probability above. Here's the strange part. Let's say we make those probabilities to be 100% thus we have ordinary logic without probability. Then let's create a physical closed Newtonian system: The interior of a cube with no gravity and a bunch of identical bouncing balls which obey Newtonian physics and therefore logic. Let's say those balls all have a random initial velocity at a random direction but all those balls are initially positioned near one corner in the cube. Thus the balls from a position stand point start with low entropy. I use the term random, but it's not really random as you have perfect knowledge of these numbers, you know what they all are. As time increases, entropy increases. The balls as a system begin to increase in entropy. Entropy continues to rise towards an equilibrium. That is the question. Entropy is a probabilistic phenomenon. It occurs because ball configurations that are spread out have higher probabilities of occurring then balls that are concentrated in a corner. Thus given enough time the balls occupy the higher entropy state. My question is, WHY does this occur. Probability (aka Entropy) is ARISING out of a perfect Newtonian system following perfect logic without any probabilistic extensions. Can entropy be derived from Newtonian physics? The better question is, can probability be derived from Newtonian physics because entropy is in actuality a phenomenon of probability? Any system that uses pure logic (and completely avoids probability in any part of its definition) exhibits this sort of rule as long as you introduce a sort of randomness into initial parameters above. Probability permeates everything.
- kgwgk 4y ago
  > As time increases, entropy increases. The balls as a system begin to increase in entropy. Entropy continues to rise towards an equilibrium. If you know the positions and velocities of the balls at all times arguably the entropy is always zero. What defintion of entropy are you using?
  - deltasevennine 4y ago
    The statistical version. The equation is independent of knowledge. Your logic is flawed. Think about it. Knowing more or less about a system does not change it's entropy. If I knew the position and velocity of every particle in a gas chamber does that somehow lower it's temperature? No. Macro-states summarize perfect information. But with knowledge of perfect information, you still have the ability to summarize it. Or in other words, probability still exists even when you have perfect knowledge of everything and the future.
    - kgwgk 4y ago
      If you mean Boltzmann's formula it will be valid for systems in thermodynamical equilibrium. Is your system in thermodynamical equilibrium? You talk about macrostates. How do you define a macrostate for your initial configuration? Why this one and not another? Does it change over time? Think of it from another angle. You have a box with some of these balls inside - all you know is that they all have the same energy. Do you agree that the macrostate won't change over time and the entropy will remain constant? However, if you knew the positions they will be concentrated in some regions more than in others. That's what you called lower entropy in your example. So what is it, does knowing more about a system change it's entropy or not?
      - deltasevennine 4y ago
        > If you mean Boltzmann's formula it will be valid for systems in thermodynamical equilibrium. Is your system in thermodynamical equilibrium? Gibbs >You talk about macrostates. How do you define a macrostate for your initial configuration? Why this one and not another? Does it change over time? I'll choose something arbitrary. Temperature as measured by a thermometer is the macrostate. Every possible configuration of particles (microstates) that causes mercury to rise to a certain degree represents a different macrostate. And yes it changes with time; even at equilibrium. >Think of it from another angle. You have a box with some of these balls inside - all you know is that they all have the same energy. Do you agree that the macrostate won't change over time and the entropy will remain constant? No don't agree. If balls are located on one side of the box and the thermometer is on the other side of the box. The thermometer reads nothing. When the balls increase in entropy they collide with the thermometer producing a reading. >However, if you knew the positions they will be concentrated in some regions more than in others. That's what you called lower entropy in your example. Yeah I already don't agree with you, so the rest of your argument is gone. If you define macrostate as total energy in a system then yeah it never changes. But that's not the definition of macrostate. It's just one arbitrary choice you have chosen.

deltasevennine 4y ago

I already mentioned that logic can be defined in terms of probability above. Here's the strange part. Let's say we make those probabilities to be 100% thus we have ordinary logic without probability. Then let's create a physical closed Newtonian system: The interior of a cube with no gravity and a bunch of identical bouncing balls which obey Newtonian physics and therefore logic. Let's say those balls all have a random initial velocity at a random direction but all those balls are initially positioned near one corner in the cube. Thus the balls from a position stand point start with low entropy. I use the term random, but it's not really random as you have perfect knowledge of these numbers, you know what they all are. As time increases, entropy increases. The balls as a system begin to increase in entropy. Entropy continues to rise towards an equilibrium. That is the question. Entropy is a probabilistic phenomenon. It occurs because ball configurations that are spread out have higher probabilities of occurring then balls that are concentrated in a corner. Thus given enough time the balls occupy the higher entropy state. My question is, WHY does this occur. Probability (aka Entropy) is ARISING out of a perfect Newtonian system following perfect logic without any probabilistic extensions. Can entropy be derived from Newtonian physics? The better question is, can probability be derived from Newtonian physics because entropy is in actuality a phenomenon of probability? Any system that uses pure logic (and completely avoids probability in any part of its definition) exhibits this sort of rule as long as you introduce a sort of randomness into initial parameters above. Probability permeates everything.

kgwgk 4y ago
> As time increases, entropy increases. The balls as a system begin to increase in entropy. Entropy continues to rise towards an equilibrium. If you know the positions and velocities of the balls at all times arguably the entropy is always zero. What defintion of entropy are you using?
- deltasevennine 4y ago
  The statistical version. The equation is independent of knowledge. Your logic is flawed. Think about it. Knowing more or less about a system does not change it's entropy. If I knew the position and velocity of every particle in a gas chamber does that somehow lower it's temperature? No. Macro-states summarize perfect information. But with knowledge of perfect information, you still have the ability to summarize it. Or in other words, probability still exists even when you have perfect knowledge of everything and the future.
  - kgwgk 4y ago
    If you mean Boltzmann's formula it will be valid for systems in thermodynamical equilibrium. Is your system in thermodynamical equilibrium? You talk about macrostates. How do you define a macrostate for your initial configuration? Why this one and not another? Does it change over time? Think of it from another angle. You have a box with some of these balls inside - all you know is that they all have the same energy. Do you agree that the macrostate won't change over time and the entropy will remain constant? However, if you knew the positions they will be concentrated in some regions more than in others. That's what you called lower entropy in your example. So what is it, does knowing more about a system change it's entropy or not?
    - deltasevennine 4y ago
      > If you mean Boltzmann's formula it will be valid for systems in thermodynamical equilibrium. Is your system in thermodynamical equilibrium? Gibbs >You talk about macrostates. How do you define a macrostate for your initial configuration? Why this one and not another? Does it change over time? I'll choose something arbitrary. Temperature as measured by a thermometer is the macrostate. Every possible configuration of particles (microstates) that causes mercury to rise to a certain degree represents a different macrostate. And yes it changes with time; even at equilibrium. >Think of it from another angle. You have a box with some of these balls inside - all you know is that they all have the same energy. Do you agree that the macrostate won't change over time and the entropy will remain constant? No don't agree. If balls are located on one side of the box and the thermometer is on the other side of the box. The thermometer reads nothing. When the balls increase in entropy they collide with the thermometer producing a reading. >However, if you knew the positions they will be concentrated in some regions more than in others. That's what you called lower entropy in your example. Yeah I already don't agree with you, so the rest of your argument is gone. If you define macrostate as total energy in a system then yeah it never changes. But that's not the definition of macrostate. It's just one arbitrary choice you have chosen.