Fractal - The Way of Universe

Two Envelope Paradox

If I place two envelopes in front of you and tell you that both envelopes have some amount of money while one of them has twice as much as another. You have a choice to pick either one. Once you picked, you are given another chance to either keep the picked one or switch to another. There are two ways of reasoning you could employ. One way to think is that both envelopes has equal opportunity of having larger amount of money so that the one has been picked is as good as another. This way, either keeping or switching would make no difference to you. Another way is to argue that the opportunity of the second envelope having either twice as much or half of the first envelope is 50%. Assuming the amount of money inside the first envelope is $100, then the expected total value inside the second envelope is 50%*($200) + 50%*($50) = $125 which is greater than what you have on hand. Therefore, you should switch.

The problem now becomes which way of reasoning is correct one. It seems that both make sense while one or both of them must be wrong. To me, as an outsider of your reasoning/decision making process, the outcome is the same, i.e. you picked one at the end regardless which way of thinking you employed. Either one you picked is no better or worse than another. In other words, your decision/will has no meaning or your decision/will is equivalent to no decision/will.

Somehow I feel that the Two Envelope Paradox is related to Bell’s inequality which may lead to an insufficient prove. 

Name-calling

All animals have evolved the ability to discover patterns in the barrage of visual and aural stimulus. In humans this ability is particularly well-tuned. Just look at a cloud or that random pattern of cracks on the wall of the bathroom. Pretty soon you begin to see a face or an animal or some other form. You know that the face you see is not really there, but your mind, trained to find patterns, identifies one there. The night sky is nothing more than a random sprinkling of stars, yet even these have been ordered into constellations.

We cannot help but name things, and group what we see into categories and classes, all with names of their own. Without a name, a thing simply doesn't exist. It is indistinguishable from the chaotic universe of things we have not yet named. Given a name, it belongs to a group. Given a group, it shares properties with other members of that group. Science is our best attempt to exhaustively enumerate and relate those names and properties.

I suspect that the difficulties we have with free-will, determinism, quantum reality, and ordering rest of the named universe is simply that we are confusing the named, and perceived reality for the true reality that surges like a current beyong the limits, beyond the very nature, of our perception.

What You See Is What You Get

Keep going further on previous post, even though the earlier “conclusion” says that the behaviors of all balls on the pool table is determined right after the cue ball is hit, we still can not predict the outcomes since the nature says that we can’t even look at (observe) the table as well as the balls. For our nature, “watching” is considered as a disturbance to the system. If we insist on looking at the table that needs some light, the disturbance from the lighting would alter the outcomes that would be different from the outcome if we don’t look at the table. In other words, the nature says “don’t look at (observe) me, if you do, then you would only see what you saw and you would never know where what you saw comes from”

However, if human has no freewill and the act of observation is also pre-determined by the big ban, then the outcome of the pool table is unique even though we still can’t predict it.

Pool Table

Imagine a pool table with 9 balls either scattered around or racked at their original place while the cue ball is ready to be hit by a player. If the theories based on classical physics are true and complete, then the future courses of all balls on the table is determined right after the cue ball is hit (The Big Bang). The only condition required to support the statement above is that neither the table nor the balls would be disturbed during the event. Efforts have been made in the past to develop computer programs and robots to compete with humans based on classical physics.

If we expand this thought to the entire universe including human brains which are made by various elementary particles, the development of our universe should follow its determined course after the big ban happened years ago. Keeping in mind that the universe we are living in is an enclosed one (limited space-time) and no evidences have been found that our universe is interacting with or disturbed by other universes at this moment. How about parallel-universe theory? I have to think about it.

Duality and Uncertainty Principles

If we have a perfect cube in our hand, we could only see maximum three of the six surfaces. Any one of the visible surfaces is not perfect square unless we turn the cube till only one of the surface is facing us. By then, the rest of the surfaces are not visible. In other words, to have a complete picture of one surface, we are no longer able to see the rest. The main reason of this is that we can only see two dimensional image of a three dimensional object.

The same analogy could be applied to the wave-particle duality principle. To have complete knowledge of wave properties of a particle, we then would lose the particle side of properties of the same particle. Of cause, if we pay all the attentions to particle properties of a particle, the we would lose the insight of wave aspect of the same thing. However, neither particle properties nor wave properties are complete for describing a given particle. Both wave and particle properties are similar to surfaces of a cube. i.e. different aspects of a whole truth.

Again, the same principle could be used to explain why the uncertainty principle exists. By paying all attentions to velocity, then we are no longer able to determine the position. Of course, any particle has many other attributes such as mass, dimensions, electrical charges etc. representing different surfaces of a whole.

Freewill

Do we human beings really have freewill? If we do, what are the things could possibly make it happen? Also, does any other life form such as a dog have freewill? If not, then what is the key difference between the two making a such profound distinction? By now we know for fact that all living things on earth are governed by DNAs which has only 4 different chemical compounds arranged in different sequences. The differences are merely the length and order of the DNA.

To answer the question, we need first to define what FREEWILL really mean. To me, if we do have freewill, then the future of our universe is at mercy of our decisions. If classical physics is good enough to explain all things in our universe, then to have freewill, some laws of classical physics we known today have to be broken since classical physics tends to say that the future could be predicted. If everything in the future could be predicted by using the laws of physics, then we should not have freewill since the matter made up our human beings also follows laws of physics. That is the determinism point of view.

Today, due to the discovery of quantum theory, the claim of future predicability is no longer accepted. However, does this un-predicability (uncertainty) gives us the ability of freewill? If it does, then why does it not give a dog the same ability?

Based on the quantum theory, as mentioned in earlier post, everything in this universe could be described by using the concept of probability. Only when a observation effort is made, the reality as we know is realized. However, human beings is not above or separated from the nature, but is part of it. All laws of physics we know today or not known yet can be applied to both studied nature as well as studying humans. Therefore, a effort of observation is merely a interaction between one part of nature against another.

Fractal theory comes in my mind. Life is a fractal system of DNA. Laws of physics describe fractal aspect of universe. Two hundred some elements make up such a complicated world.

Reality

Based on the modern quantum mechanics, without any observation, questions such as "what has really happened" do not mean anything. We only know what has happened when we observe. In other words, observation tunes the possibilities into reality or reality only exists when observations occur.

Then the question becomes "what does observation really mean". Does human beings have the freewill to decide where, when and how to observe or so called observations are merely predetermined events between two or more groups of matters interact with each other.

Another question is what "really has happened" mean to us. We know that we can't tell what is going to happen in the future since we are part of the universe. However, if we were not part of the universe, then we can't even tell anything about it at all.

The first time

The first post to verify the quality