ONE of the most elusive goals in modern physics has turned out to be the creation of a grand unified theory combining general relativity and quantum mechanics, the two pillars of 20th-century physics. General relativity deals with gravity and time and space; quantum mechanics with the microscopic workings of matter. Both are incredibly successful in their own domains, but they are inconsistent with one another.
For decades physicists have tried to put the two together. At the heart of the quest lies the question, of what is the universe made? Is it atoms of matter, as most people learned in school? Or some sort of energy? String theory, currently a popular idea, holds that the universe is made up of tiny vibrating strings. Other equally esoteric candidates abound. Indeed, cynics claim that there are as many grand unified theories as there are theoretical physicists attempting unification.
Now Vlatko Vedral, an Oxford physicist, examines the claim that bits of information are the universe’s basic units, and the universe as a whole is a giant quantum computer. He argues that all of reality can be explained if readers accept that information is at the root of everything.
So what is information? Mr Vedral’s notion of information is not the somewhat fuzzy concept most people have of it, but a precise mathematical definition that owes itself to Claude Shannon, an American mathematician considered to be the father of “information theory”. Shannon worked at Bell Labs, at the time the research arm of AT&T, a telephone giant, and in the 1940s became interested in how much information could be sent over a noisy telephone connection. This led him to calculate that the information content of any event was proportional to the logarithm of its inverse probability of occurrence. (Unlike many popular-science books that eschew equations, Mr Vedral includes a couple and tries his best to explain them to the reader.) What does the equation mean? As Mr Vedral points out, it says that an unexpected, infrequent event contains much more information than a more regular happening.
Once he has defined information, Mr Vedral proceeds to show how information theory can be applied to biology, physics, economics, sociology and philosophy. These are the most interesting parts of the book. Of particular note is the chapter on placing bets. Mr Vedral gives a good description of how Shannon’s information theory can be applied to winning at blackjack or in buying shares (Shannon and his friends made fortunes in Las Vegas as well as on the stockmarket). And his exposition of climate change and how to outwit the CIA make entertaining reading. One quibble: Mr Vedral often digresses from the point at hand, so the overall effect tends to be a bit meandering.
Mr Vedral’s professional interests lie in quantum computing and quantum information science, which use the laws of quantum mechanics respectively to build powerful computers and render codes unbreakable. There is a lot of discussion of both, which is very welcome because there are not many popular science books that cover these relatively young fields. Quantum computers, as Mr Vedral points out, “are not a distant dream”. Though still rudimentary, “they can solve some important problems for us that conventional computers cannot.”
Unusually for a physicist, Mr Vedral spends a fair bit of time talking about religious views, such as how God created the universe. He asks whether something can come out of nothing. Throughout the ages philosophers and theologians have debated this question with respect to Judeo-Christian faiths, in which dogma holds that the world was created from the void, creation ex nihilo. Others side with King Lear who tells Cordelia that “Nothing can come of nothing.” Mr Vedral makes a persuasive argument for a third option: information can be created out of nothing.
Read until you have something to write...Write until you have nothing to write...when you have nothing to write, read...read until you have something to write...Jeremiah
This article is from The Economist
I was just reading C.E. Shannon's paper on two-internal-state Universal Turing machines, actually, yesterday.
Among other people to make the information claim is a great physicist David Deutsch, who basically got the idea of quantum computers.
Anyway, it is true that an infrequent event has much more information than a regular event. For instance, from one paper I read sometime back,
a stochastic noise + information carried in a positive signal > a chaotic information-carrying encoding of timing between signals (which is a constant stream of data).
However, it is also clear that the way people think, use logic, and mathematics is not computable (as argued by John Lucas way back when). Probabalistic logic from neural networks, which is an outgrowth of all this stuff, is not useful in economics, since it is entirely deterministic. For instance, see the various automata inspired by Von Neumann.
Furthermore, probalistic logic, such as that developed by Keynes and Von Neumann already assumes the concept of cardinal number, prior to proving the concept of difference. So its at best a sort of programmer's code, rather than machine code; the surface order rather than the underlying process.
Indeed, my thoughts on the matter somewhat echo those of the lion. When first encountering information theory as a student last year, just as I had got into Austrian theory, I was very enthusiastic about the possible incorporation of Hayek's insights into prices as information "signals" within the context of classical information theory. My enthusiasm soon faded however, as I came to realise that the subject matter of information theory is really about "raw data", which is differentiated from knowledge which refers to how the data are cognitively organised and given a contextual meaning. The former can be treated with the methods of information theory, the latter I am not aware has been.
Also, quantum information entropy is really a nascent rearch program in the study of the entropic properties of many particle QM systems and their transitions.
"When the King is far the people are happy." Chinese proverb
For Alexander Zinoviev and the free market there is a shared delight:
"Where there are problems there is life."
"My enthusiasm soon faded however, as I came to realise that the subject matter of information theory is really about "raw data", which is differentiated from knowledge which refers to how the data are cognitively organised and given a contextual meaning."
Wouldn't a price signal be considered raw data in that strands of information within it are boundless?
"a stochastic noise + information carried in a positive signal > a chaotic information-carrying encoding of timing between signals (which is a constant stream of data)."
This is an interesting concept and i can only remember studying stochastic & determinstic processes vaguely in my undergrad. What is the difference between random information and chaotic information?
Basically, chaotic process is determined by inputs and predictable. However, since it depends very much on the initial conditions, we can only predict it only in the short-run unless we know the function.
However, stochastic process is random. Law of failure of gambling systems applies to it, so expected mean of the process is 0. We cannot put in inputs to get out predictable outputs.
Suppose, now, we add in a signal. The stochastic process acts as a threshold, so errors are filtered out (by being mixed with random noise and ignored), while the signal of sufficient intensity without errors remains.
We can assign a 0 to the threshold, so signal 1 when it occurs can sharply indicate something.
"Wouldn't a price signal be considered raw data in that strands of information within it are boundless?"
This was along the lines of what I was thinking, but I don't think one can progress beyond simply describing this characteristic qualitatively. The arrival at a price is dependent upon valuation and appraisement based on future expectations between buyers and sellers, and can take into a whole host of considerations about present trends and where they may continue. However, there does not seem to be a clear cut way in which one could identify all the separate inputs that go into determining a price, and adequately assign a numerical probabillity to each for generating this or that particular outcome, and hence predict the way in which the system will equilibrate deterministically.
What I mean by raw information is, for example: On this page there are 26 letters and 10 numbers used to "communicate" a message. if I want to define a transfer channel to relay this "information", then this will mean that I need to know the relative likelihood of each letter appearing in order to efficiently allocate bits for the transfer of the message, and to help reduce errors. This is simply the information to transfer the actual array of symbols however, it is not the message or information itself.
It is rather the meaning of the raw data, in the minds of human actors, rather than the raw data itself which is the main causative agent in price determination, and hence these are my reasons for estimating classical information theory's abillity to describe this situation adequately. This is not to say, a future form of information theory may be ingeneiously developed to help tackle this problem, yet much more needs to be considered in order to tackle the problem than the analytical apparatus offered by Shannon's information theory, IMO.