Comment: Some time ago, I became interested in information theory partly due to my career and mostly because I began seeing elements of the theory popping up everywhere in movies, theological commentaries, war fighting etc... I studied the theory off and on purchasing books, watching movies, reading essays, and in general where ever I caught a wisp of the theory. The interesting thing about truth is that it is self-evident and reveals itself in nature. So I did not have to look far. Although, a curious thing about information is noise or that which is distracting, like a red herring and there is plenty of noise out there. Anyhow, the point in this post is an information theory overview. I would like to share basic information theory and relate it to the world around us. I will be coming back to this post updating and refining with more citations.
Information Theory
Information theory is relatively new and is part of probability theory. Like the core disciplines of mathematics and the sciences, information theory has a physical origin with broad spectrum applications. The theory has captured the attention of researchers spawning hundreds of research papers since its inception during the late 1940's. This new discovery has generated interest in deeper research that involves biological systems, the genome, warfare, and many other topical arenas. Claude E. Shannon PhD is the father of generalized information theory as developed during 1948 and theorized:
If the receiver is influenced by information from the transmitter then reproducing the influencing information at the receiver is limited to a probabilistic outcome based on entropy.
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| Figure 1: Mathematical Formulation of Entropy (H) in a system |
There are several terms in the thesis statement that may be difficult to grasp and the mathematical formulation, Figure 1, may be overwhelming to some people who wonder how is entropy and information linked. Entropy is an operative concept behind diminishing returns or the rate at which a system dies, decays, or falls apart. Entropy operates under order as formulated in figure 1. Thus, the phenomena is not random. Within the context of information theory, entropy is the minimum size of a message before a meaning or value is lost. The notion of a probabilistic outcomes involves multiple possible results in which each result has a degree of uncertainty or a possibility that the result may not occur. For example, a rolling of the dice is limited to only six possible outcomes or results. The probability of any one outcome occurring is 1 in 6. The uncertainty in rolling the dice is high being 5 to 6 that any specific outcome will not occur. As for the mathematical formulation, I will just leave that for general knowledge of what it looks like.
The thesis is pointing towards a 'lossy' system and promotes a simplistic communication model, Figure 2.
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| Figure 2: Simple Information Theory Model |
From the thesis, formula, and model more complex related theories and models spawn coupling information theory to biology, quantum physics, electronic communications, crowds, and many other topical subject matter. All fall back on entropy or the smallest message before it looses its meaning. The big question is so what? We will explore the 'so what' in the next section.
Information Theory Around Us
Most people fail to realize that information theory impacts us on an everyday basis. Aspects of the theory appear in movies, underpin all biological sensory capabilities, and appear in information networks in many ways. Many people philosophize that human and natural existence is purely information based. Let us explore information theory as it is exposed to many people. Most people have some familiarity with the sciences at some level, movies, and religion. Let us begin with a survey the sciences.
Atom smashing experiments during the 1970's lead to the discovery that the universe has boundary limits. According to physicist such as Richard Feynman, the father of quantum computing, matter ceases to exist at 10-32 meters. When matter ceases to exist so does space-time. Matter has dimensions and time's arrow spans dimensionality. When matter no longer exists neither does dimensionality and time is mutually inclusive. What remains are non-local waveforms or electromagnetic waves which are illustrated as strings that vibrate. The region where this occurs is the Planckian realm which is where matter is quantized or discrete having the qualities of a bit of information. Matter and energy are interchangeable based on the Theory of Relativity, Figure 3, and the wave-particle theory of light. Those vibrating waveforms in the Planckian realm slam together in a process of compactness that is not fully understood forming a particle having discrete size, weight, and possesses a positive (+), neutral (0), or negative (-) charge. These particles then begin to assemble in a computational algorithmic manner based on the charge and tri-state logic into more complex particles from the sub-atomic into the physical realm. In the physical realm, complex molecules form such as DNA from which biological life emerges.
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| Figure 3: Theory of Relativity Formula Energy = Mass x (Speed of Light)2 |
The DNA is somewhat unique according to Microbiologist Dr. Matt Ridley. This is because not only did an computational information process arrive at the DNA molecule but injected into the DNA molecule are 4 bits of information ( G, C, A, and T ) which is used by nanites to endow biological life. Nanites are intelligent molecular machines that perform work and made out of amino acids and proteins. These molecular machines have claws, impellers, and other instruments. They communicate, travel, and perform work based on DNA informational instructions. The information process continues as even more information is applied against the DNA strand such as variation of timing, sequencing, and duration under which a gene fires. By varying the timing, sequencing, and duration of a firing gene then specific features are managed on the life form under gestation. Dr. Ridley quips the genome is not a blueprint for life but instead a pattern makers template having some sort of Genome Operating Device, a G.O.D (Ridley, 2003). The point here is that there is some sort of intelligent communication ongoing during the endowment of life and development of the natural universe. All of which are the outcome of computational processes and information.
During the 1960's extensive research was conducted into the operation of human biological sensory processes in relation to information theory. The conclusion of this research determined that the sense of sight, sound, touch, smell, and taste undergoes an electro-chemical process in which information is encoded using Fourier Transforms into electrical waveforms. The base Fourier equations are somewhat ominous, Figure 4.
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| Figure 4: Fourier Transforms Equations |
The equations are shown to see what they look like. Extensive mathematic philosophy and practical understanding of how these equation perform is necessary to appreciate these equations. In lay jargon, Fourier transforms encode and extract information embedded in a waveform. These waveforms are constructed from the biological sensory devices; eyes, ears, nose, tongue, and skin. Once the information is encoded into a waveform the human brain stores information holographically. Consider the operation of the eyes attached as part of the brain. The reason for two eyes is that they act symbiotically. One eye is a data source while the other eye acts as a reference source. When the waveforms from these two sources collide then information is encoded in the constructive and destructive patterns that result. These patterns are then imprinted into the brain material to be recalled on demand as human's think in terms of images and not attributes. The human brain is capable of storing up to 6 terabytes of information. The eye has a curious tie to the quantum realm detecting a photon of light coincidental with the smallest instance of time, Planck's Time, which is of the order of 10-43 second. This leads to the concept of quantum reality or that human perception is limited to the boundaries of the natural universe.
The human experience is said to be a digital simulation and the universe is computationally organized. This lends credence to the creative license of writers and authors who imagine story lines such as The Matrix, Timeline, The Lawn Mower Man and countless others. But the concept of information in the human experience goes even further into theologies.
Information Theory and The Theological Argument
Theologies are belief systems and inclusive of godless belief systems such as atheism and agnosticism to mono-theistic and polytheistic systems. Theologies are also inclusive of belief systems that deify idols and objects such as Pantheism which deifies the mother Earth. Cosmologies and philosophies are generally treated as a theology as well since the adherent's behavior is the same as any theological adherent. Religion is the practice of theological doctrines. All theologies and related religions are information based. That is all theologies possess defining information effecting actions among the believers and/or reactions among non-believers. Some theologies are well organized and others are left to individual expression but all are based on some sort of information or lack of information. Adherents of any specific theology or religion gather, learn, and discuss the merits of their theological doctrines by communicating in order to increase membership or believers.
Under information theory the Judeo-Christian Bible demonstrates many interesting qualities. The Judeo-Christian Theology advances one of the most comprehensive of all the theologies detailing a narrative from before-the-foundations-of-time to the end-of-time. The narrative begins not with the creation of the universe but a war between good and evil. Michael, the ArchAngel, defeats the rebelling forces lead by Satan. In the meantime, the Judeo-Christian God was busy creating the natural universe and gathered the defeated rebels casting them into the universe like a bolt of lightning effectively trapping evil in the universe or world. The Judeo-Christian God then turned his attention to the souls, the believers, whom he knew before the creation of time and breathed their souls into human embodiments on Earth. Those human embodiments were architected with an image as well. The purpose of this was to test their loyalty through trials and tribulations having had the war break out in heaven. Evil, trapped in the world, causes the fall of humans into rebellion and the Judeo-Christian God declares war on evil as an outcome. Christ shows the believers the way by communicating the narrow path home. This epic war between good and evil in the world is actually an information war.
Information warfare, IW, is a broad field of warfare that leverages ambiguity, deceit, innuendo, doubt, and truth in order to dominate the battle space or more correctly space-time. IW tactics often involve hostile jamming, man-in-the-middle attacks, psychological operations, in order to diminish, deter, deflect, or degrade the will of the opposition to fight.
In response to noise, the Bible has been designed to pre-empt hostile jamming by delivering the messages multiple ways and times. Thus, by having a high signal-to-noise ratio jamming attempts can be defeated. The more important the message the more ways and times the message is repeated. The Bible tactically uses parables to encrypt messages that humans who have the Holy Spirit, the decryption key, in them can understand. The Bible also tactically makes use of language being written originally in Greek and Hebrew. Greek is very concise and cannot have mistaken translations. Hebrew makes use of the highest language compression ratio communicating messages both phonetically and pictographically. Hence, the use of many ways and means of getting the message through is an IW tactic.
Under the auspices of information warfare, the war can be fought and won solely on the basis of information without committing conventional ground forces to battle. However, the final epic battle in Christian Eschatology is fought and personally won by Christ who is the victor over all evil. This becomes necessary because those human hearts are hardened and many humans become demonically possessed such that their ears do not hear and eyes do not see. Thus, all communications have failed.
Additional support for the information perspective is the Judeo-Christian God spoke the universe into existence or communicated information; Gen 1:3. This act of speaking a universe into existence was built perhaps in the informational manner discovered by science and is ongoing today. Perhaps the Genome Operating Device varying the information of timing, sequencing, and duration of firing genes is the Judeo-Christian God's hand in the universe. What ever the theology, the underlying premise is informational. Humans then decide to act based on the information they have or understand.
In conclusion, information theory affects us everyday in our world views, sciences, and personal beliefs leading to actions. Information theory hovers around the notion of a lossy system in which meaning is lost due to noise, interference, natural decay, and provocative measures. Creative works have leveraged information theory to advance ideological movements. Even the human life form may very well be the result of pure information causing humans to rethink theologies and established beliefs in a new light.
In conclusion, information theory affects us everyday in our world views, sciences, and personal beliefs leading to actions. Information theory hovers around the notion of a lossy system in which meaning is lost due to noise, interference, natural decay, and provocative measures. Creative works have leveraged information theory to advance ideological movements. Even the human life form may very well be the result of pure information causing humans to rethink theologies and established beliefs in a new light.
References:
Knuth, D. (2001). Things a computer scientist rarely talks about. CSLI Publications: Stanford.
Moser, S. and Chen, P. (2012). A student's guide to coding and information theory. Cambridge University Press: United Kingdom.
Reza, F. (1994). Introduction to information theory. Dover Books: New York.
Moser, S. and Chen, P. (2012). A student's guide to coding and information theory. Cambridge University Press: United Kingdom.
Reza, F. (1994). Introduction to information theory. Dover Books: New York.
Ridley, M. (2003). Nature via Nurture. New York: Harper Collins Publishers.
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