Information Theory

Is information ever really destroyed?

Well, that depends on who you ask. Some people say that Hawking Radiation proves that information can be destroyed but the Holographic Principle may just say otherwise.

If you are a religious or spiritual person, the question might be framed as: Is it possible for consciousnesses to live beyond physical death? I mean after all isn't consciousness nothing more than information and if information is fundamentally recoverable in theory, then is consciousness salvageable?

What we are really getting to is the reversibility or the non-reversibility of nature, which has everything to do with Entropy, the 2nd law of thermodynamics.

A consciousness is a very specific arrangement of information that is seemingly completely erased when the physical brain dies, when neurons decay and synaptic connections are destroyed. 

But if information truly can't be erased, then wouldn't it follow that consciousness is recoverable? The problem, however, is that the more complex the specific arrangement of information is, the more infinitely difficult it becomes to re-create that information. 

Since consciousness seems to be the most complex informational structure in the universe, it would follow that re-creating your "soul" after it is gone would be infinitely difficult, but not impossible, i.e., in theory but not in practice unless you are the master of Quantum Mechanics, or God. But, even God would be subject to Entropy, so funny enough every time God saves you, that being would be slowly erasing itself. With each rescued consciousness, God gets weaker. (Philosophically that is) 

The problem of whether or not information is always recoverable or not was challenged by Stephen Hawking when he showed that multiple initial states of information can all lead to the exact same final state such as in Black Hole Evaporation, meaning if you only had access to the final state of information, how would you know which initial state proceeded it? The answer is you wouldn't and therefore information is forever lost. 

Example: 

If a blue car, green car and red car all decayed into a yellow car, and there was nothing about the yellow car that could tell you which color of car that it actually came from, then for all intents and purposes, information is lost. 

I cool way to imagine this to take a phone number for example:

312-546-9183

Imagine I run some encryption key such that the algorithm I used to encrypt the number oddly turns every number into the letter "x" and now your number looks like this:

xxx-xxx-xxxx

If every number goes to X when you run this encryption key, and if you input x back into the encryption key and you always get back 0 or 1 or 2 or 3 or 4... , well I think you get the point, then information is lost. 

How do you know what number was actually encrypted? What you have is a 1-way encryption that completely erases all information. And, it seems that this is what the universe could be doing to all of energy that has manifested information. 

But that leads to an even bigger question: What is information?

Well, let's get back to Entropy and the Uncertainty Principle. 


VERY OVER-SIMPLISTIC 1-SENTENCE EXPLANATIONS

Entropy :  The idea that the more specific a state is needed, the easier that it decays and the most non-specific states are the easiest ones to exist. 

Uncertainty Principle: The idea that you can never know everything because the very act of knowing changes what you know, therefore the unknowable will always exist.  


Let's apply information to these concepts and see what happens. 

Imagine that I have some stored information somewhere, maybe on a disc, solid state, cassette, film, record or even organic neurons, and I know that 2nd Law of thermodynamics must still apply* to information. (*this an assumption based on solid data) And, since that be that case, I know that one day my information on these storage devices will become unreadable, unretrievable, 100% unplayable. Or, will they? 

The way around these issues is by making infinite copies. If I have one last photo of my mom, it would be my imperative to make multiple digital and physical copies and to even have one stored away for safe-keeping and being preserved in time even from myself. However, Information can increase the entropy from systems outside of itself to 
make more copies of itself. Information does not want to forget; it does not want to be lost. The more copies it makes, the more it can prevent its own entropy from increasing which could seemingly erase it completely and forever. 

While I am speaking in philosophical terms here and giving information a personification, the fact is conscious beings are just one of the many ways that informational complexity can manifest itself. Information is not some mythical creature; information is us. 

But, what happens when you apply the ideas of information to the ideas of Uncertainty? 

Well, it means that there will be some information that just may be always out of reach of conscious awareness. In that way, it acts like an algorithm that interferes with itself; the very act of running the algorithm changes the algorithm. Information could be a self-evolving form that only needs to have the possibility to continuously, eternally increase entropy outside out of itself and maintaining an internal, stable entropy as the only fuel that it needs to keep existence going in the infinite evolving forms that it could take. Memory is nothing but recoverable information. Imagination is information running predictive mathematical models, and emotions are just mere bio-chemicals effecting our electromagnetic signals. The true information is self-propagation. But, the bigger question is: Can you infinitely increase entropy while maintaining informational complexity, and I define informational complexity as memory, imagination and biochemical effects. 

But, there could be a higher form of information complexity to come in future. 

So, How is information quantified?

Information is just a differentiation. At the very lowest form, it is the ability for 0 to become subtractive. Such 0 = 1 -1. 

In more scientific terms, it's the anti-matter and matter problem, but it's simply Matter - Anti-Matter = Nothing.  (or at least, a kind of nothing.) 

If you have a differentiation, in the very least you have something like This or That? Which One? and then eventually a How Many? But, what creates the differentiation?  Uncertainty!

So it seems that information decays around it while having informationally complex systems grow internally. 

But can energy have its entropy increased as fuel for informational complexity forever? And, now the battle lines have been drawn. 

So if a simplest differentiation is This or That, it's numerically, binary, meaning X, Y or 0, 1 or any two opposite pairs. Heads or Tails?

This is like Matter and Anti-matter, theoretically, they should be equally weighted, cancelling each other out back to a no-information, low entropic state, the lowest one could argue. Entropy is at 0 and Information is at 0. 

Yet, balance is uncertain. Your egg has been cracked and now informational complexity can hatch and grow if the conditions are very precisely met which are how the Fundamental Constants of Nature. are currently set. 

From a yes and no, like legos, we can build any god damned thing we want, given an infinite amount of legos and shape and function variations, which is pretty much close to what we got. 

But does information self-actualize?

I mean turn into us. 

How did our consciousness come to be?

If you have differentiation, you can have this or that. You can seemingly have choice, or at least just not 100% possibility.  9 to 1 is still better than 90 to 1, which is still better than 900 to 1, and that is still better to 9999999 to 1. I think you understand the point. 

For the simple fact that there can be a differentiation, there is information. 0 or 1. But, the more important thing is the action or consequence that gets assigned if there is a zero or a one. 

So for information to stay in existence it has to copy itself.  But there are rules to this still dictated by laws of logic. 

The Universe does not have to be reasonable, but it has to be logical because nonsense can not hold up a foundation of principles, no matter how much humans would often want it to be so. 

The less accurate the copy, the more copies it can make and faster, but it has a high uncertainty for error operating in a high entropy state.

However, the more accurate the information, the more redundancy is needed and longer time is taken to make the full copy. It is very slow and tedious process in a low entropy state.  

Yes and No is the same as 1 and 0 and each one is a piece of information different from the other. This is what is called a bit. 

If zero entropy equals zero uncertainty, then  50/50 certainty would have an entropy of 1 and at 50%, then 50/50 + 50/50 would have an Entropy of 2 at 25% 

1 bit of information equals 1 bit of Entropy and the more complex the information, the higher its Entropy, meaning a god would have infinite Entropy. 

But it seems no matter how complex information can get at the expense of processing energy by increasing its entropy, eventually the universe will just run out energy to process because of dark energy. Eventually there will be no more usable energy. When that time arrives, all informational complexity will crash like a house of cards. 

So is information every truly destroyed? Well yes and no, because regardless if anyone is there that remembers, if the laws are constant, information (at least in this universe) was inevitable.  

Sources