The Universe Is Not Like a Computer by Lorraine Ford

Robert,

Please forgive me for starting a new internal thread here, but I really hate the layout of these topic forums. Re: Kahre ... and you are going to despise this absolutely, I just know it (from Hans C. von Baeyer's blurb or review)(quote):

In The Mathematical Theory of Information Jan Kahre presents a bold new approach to classical information theory. With profound erudition, refreshing iconoclasm, and an appealing sense of humor he leaps over half a century's received wisdom and starts afresh. From common sense observations such as "information is ABOUT something", "transmission tends to degrade information," and "noise can be beneficial", he constructs a rigorous framework that is general enough to encompass a great variety of conventional results in different fields, yet discriminating enough to prune the accumulation of dead wood. His most lasting accomplishment is the demonstration that Claude Shannon's measure of information, which has dominated the subject since 1948, is by no means the only candidate, and not always the most appropriate one. This remarkable book is sure to stretch the horizon and inspire the imagination of every physicist, computer scientist, mathematician, engineer, and philosopher interested in the theory and practice of information science.

(end quote)

In all fairness it's no fruitier than most blurbs. Anyway, here's Kahre himself, getting more or less technical (and I too tend to wince at "This would make the Second Law of Thermodynamics a special case of the Law of Diminishing Information"):

Toward an Axiomatic Information Theory

He says "Towards" but then his native languages and Finnish and Swedish.

nmann,

"Z gets all its information about X from Y." Not too many entities get all the knowledge they possess from a single source. Even if there is only a single input message source, the a priori knowledge built into the receiver, and being exploited to recover info from that source, probably did not come from that source.

"Shannon's famous entropy measure is not a general information measure, but a consequence of the statistical properties of long strings of symbols." This statement represents a profound misunderstanding. As I mentioned in a post under my essay, Shannon's Capacity measure is simply equal to the number of bits required to "digitize" a band-limited signal. His equality statement simply says that the number of recovered bits of information cannot exceed the number of bits required to digitize a band-limited signal, in the first place.

The entropy measure is probably the best known, but least significant aspect of Shannon's work. A much more significant aspect was the non-constructive proof he gave, which demonstrated that some coding scheme must exist, which would enable messages to be received error free, right up to the maximum limit. The proof gave no clues how to do it, but it inspired two generations of communications engineers to search for the answers. After fifty years of research, and for the first time ever, that research enabled dial-up telephone modems to operate, virtually error free, at rates over 90% of the maximum limit. When I started graduate school, forty years ago, dial-up modems operated at 110 bits per second. It was a BIG deal, a year or so later, when the Physics dept. bought the new, latest and greatest modems, that operated at 300 bits per second. By the beginning of the 21st century, discoveries in coding theory and signal processing algorithms had pushed it up over 30,000 bits bit second, aided by the recent development of integrated circuit technology, that was powerful enough to run the algorithms.

Lorraine,

You asked : "But what does this code represent?"

It represents how to behave towards future, similar experiences. We learn from experience, but there is no point in accumulating learning for its own sake. If you never actually "use" it, then it is a pointless waste of time, from a "survival of the fittest" point-of-view. What makes this so interesting to me, is that the system never has to learn "why" anything is useful. It merely has to treat it as though it is - and then it will be. In this sense, it becomes a self-fulfilling prophecy.

Robert,

The fact that a real X generally doesn't get all its information from any single Y is one of those obvious things a critical reader processes automatically. It's akin to the way thermodynamic entropy is sometimes introduced by discussing two hypothetical molecules, X and Y or A and B with different temperatures, and what occurs when you put them in isolated juxtaposition. Writ large you have what used to be called the heat-death of the Universe.

Here's the first chapter of the magnum opus with considerably more detail, including the original mention of the Chinese newspaper. Kahre stubbornly insists on calling its content Information.

1. About Information

Lorraine,

"I feel that the content of 'pure' information is necessarily categories and relationships, and that new information categories and even numbers can be built from existing categories and relationships. For example mass is a category of information that we humans can represent with a symbol; and our symbols ' - x /' etc. represent the only types of relationships that categories of information can have. Laws of nature are our representation of information category relationships."

Okay ... well over a decade ago the physicist David Mermin originated what's called the Ithaca Interpretation of Quantum Mechanics, named after Ithaca, NY where Cornell U is located. In a paper from the end of the last century called "What is Quantum Mechanics Trying to Tell Us?" he presents the concept of "correlations without correlata" (which Piet Hut, a FXQi member, popularized in a piece titled "There Are No Things"). I can supply links. "Correlations have physical reality; that which they correlate does not," Mermin says. Anyway, do you see this as at all analogous to "pure information"?

Got my X and Y juxtaposed.

If Kahre wishes to allow the unintelligible text on the newspaper (input, rather than output), to be "information" then he must also allow for the fact, that unbeknownst to him, I secretly genetically engineered the newspaper fibers. To decode my message, he must recover every DNA molecule, from every cell, from every fiber, string them all end-to-end and read my preamble, which then informs him he must acquire every newspaper on earth and do the same in order to read my complete message. Preventing such absurdities is why information is defined on the output of the recovery process, not the input.

Hi Lorraine,

I hope that I'm making some progress in understanding this problem that you pose.

I ran into some theorems by Tarski and Godel about the limitations of self-referential languages. They are interesting, but I'm not sure how these may or may not apply to what you are trying here. In any case, these theorems indirectly lead me to the thought that the only representation of the Universe that is not self-referential is the Universe itself. The problem I am seeing is that in order to have such a representation would be for us to create a Universe. This is pretty much where my thought process implodes and my ears begin to emit a little smoke. Have your thoughts about this essay ever traveled down this path? If so, did you make it further than I did?

- Shawn

Lorraine,

I never said anything at all about "the foundations of reality." It is you, not I, that speaks of such things. I merely spoke about an observer's perception of that reality. And like it or not, all of our perceptions of reality are indeed being filtered through, as you put it, "a block of code", residing in our brains. And, like it or not, that is our reality.

I am basing my definition of information on the Khinchin-Shannon measure

S = -k sum_n P(n) log(P(n))

For P(n) the probability of the occurrence of the n-th bit. Entropy is the basic measure of information. If there is a process which changes the distribution of probabilities and thus this entropy measure, then information has been lost or erased. If you have a bit stream that enters a channel and at the output side the entropy measure is the same you conclude your information has been conserved. The largest probability occurs when you have the equipartition of probabilities so P(n) = P for all n. and the minimal entropy for P(m) = 1 for a unique m and P(n) = 0 for all n =! M.

It might be of course you don't understand how it is conserved. Suppose you have bit stream, or a quantum bit stream, with probabilities P(n). You have a code for this bit stream; for example the bit steam is an image and the code is a gif or jpeg algorithm. You then run this into a channel to communicate it to the output. The output is corrupted in some way, the image algorithm gives no picture or only part of it. This means there has been a scrambling of your information with other information. If all that other stuff is given by some density of probabilities ρ for random bits, the total entropy is

S' = -k sum_n P(n) log(P(n)) - k sum_aρ_a log(ρ_a)

= S S(channel),

where you have a problem with mixing your signal with the channel noise. What you want is some error correction system which unscrambles this so you can trace out the channel noise. This can be accomplished by various means of computing Hamming distances or the application of a Steiner system.

So this I think connects to the different definitions of information used here. The distinction is between information with bit probabilities on a channel

The entropy of a black hole is given by the Bekenstein formula S = kA/4L_p^2. Here L_p = sqrt{Għ/c^3} is the Planck length, and L_p^2 is a unit of Planck area. A is the area of a black hole event horizon. The entropy is equal to the number of Planck units of area that comprises the event horizon S = Nk/4. This is given by the total density matrix of the black hole, where ρ is the quantum density matrix ρ_{op} = sum_n|ψ_n)(ψ_n|. A trace over the density matrix in the Khinchin-Shannon formula determines entropy. If you threw a bunch of quantum states into a black hole entropy of the black hole is

S = k sum_nρ_a log(ρ_n) S_{BH}

The black hole entropy increases. You are not able to disentangle entropy of your signal from the black hole by performing the proper partial trace necessary. However, if you kept an accounting of all states in the black hole and the joint entropy of the states you put into the black hole, which are negative, then you could in principle extract the information you put into the black hole. How joint entropy can be negative is a consequence of quantum entanglement, and by putting a quantum bit stream into a black hole is to entangle it with the black hole.

A detailed understanding of this requires the use of error correction codes. The most general one is the Leech lattice Λ_{24}, which is constructed from a triplet of E_8 heterotic groups. string theory has a heterotic sector with E_8 ~ SO(32). The so called sporadic groups, such as the Leech lattice, are a system of automorphisms and normalizers which define something called the Fischer Griess (or monster) group.

At any rate the idea of the universe as a computer is really just a mathematical gadget. It is not as if the universe is identical to the Matrix computer in the movies of that title.

Cheers LC

Lorraine,

No need to apologize. You are in good company. Most of the world's physicists have their wires crossed in exactly the same way. Imagine a "Skyscraper of Perception", built on "The Foundations of Reality." As one journeys upwards, bottom to top, one passes through realms of increasing levels of perception; Physical behaviors, chemical behaviors, biological behaviors, and at the top, conscious behaviors.

You and the physicists are on the roof, looking downwards, through the mists, trying to "See", "The Foundations of Reality". I went to graduate school, in physics, expecting to spend my career doing the same thing. But before I had even finished school, I had noticed all the communication antennae on the roof, and began to wonder what all that was about. That was much nearer, and not surrounded by mists, and thus more readily discerned. Then, after having satisfied my curiosity about information and communications systems, I once again took note of all my former colleagues, the physicists, still peering intently down into the mists. But now, rather than joining them, I began to peer at them. I wondered if they were really doing anything all the different than the other antennae on the roof. They certainly believed that they were. But I had my doubts. They believe that they are "seeing", but like all the other antennae on the roof, they are only "perceiving". And when they set up their instruments, to enhance their "seeing", they merely perceive the perceptions of the instruments, in addition to their own.

The difference between "seeing" and "perceiving" is important. As noted elsewhere, in these posts, you can "see" "data", but "information" can only be "perceived." Data is what exists "out there", but perceptions and "information" only reside at the output, not the input, of an information recovery process. By confusing the two, you confuse everything you can ever know about what actually resides within the mists. Physicists have assumed that they were "seeing" "The Foundations of Reality", But they merely perceive "Our Reality", the false-colored, coded information, generated by our entire collection of perceptual apparatus.

By failing to take into account the "instrumental effects" produced by their own perceptual apparatus, they have convinced themselves that "Our Reality" must be necessarily identical to "The Foundations of Reality." But that is not in fact necessary, and as I attempted to demonstrate in my essay, it is in fact not the case. At present they are still quite different. The subject of this essay contest, is ultimately about why they no longer seem to be growing any closer together. My reply is "Because you have failed to clearly perceive perception itself", because you do not clearly understand what information even is.

Thus, while the physicists continue to debate if information is lost, when a book is dropped into a black-hole, I respond "NO!" Information only exists at the output of a recovery process, a perception. For information to be lost, all the observers capable of reading the book must be dropped into the black-hole.

Hi Lorraine,

Ok, thank you for laying out some more constraints for the conversation. :)

The following is what had ran through my head when I made my last comment, and I believe that it kind of relates to what nmann and Lawrence are saying too. Forgive me if none of this is new to anyone. I just want to eliminate the dead end paths in my understanding.

I think that symbols exist in order to defer (or outright eliminate) the gathering of materials and expenditure of effort (heat generation) required to fully re-

present some physical system.

A lateral case would be the symbols that we have for the word "blue". Ancient people couldn't generally shoot out blue photons at will, and so the spoken/written word

was created in order to defer the gathering of materials / expenditure of effort required to make blue light. In the end, neither the word "blue" written on paper or

the brain cell/chemical/electrical pattern are very similar to a blue photon in terms of spatial or temporal physical configuration.

A vertical case is the modeling of the Solar system.

We can partially defer our re-presentation of this system by making a wood and metal model that runs by a small electrical motor. The spatial configuration is much

different from the real thing, and so the dynamics must be driven manually by the motor.

An even more deferred approach for modeling the Solar system is to write down on paper the equation F = GMm/r^2 alongside a list of real vectors that correspond to the

current locations and velocities of some planets. The ink on the page looks absolutely nothing like a Solar system in terms of either spatial or temporal physical

configuration -- the dynamics are entirely deferred (F = ... doesn't even move around the page). If we use a computer simulation to calculate and drive the dynamics

of the system, we take up some of that slack caused by our previous deferral, but not all of the slack since it still would take much more material and effort to

create an actual copy of the Solar system.

As for what Lawrence and nmann are saying, I think that it's fair to say that we have deferred our re-presentation of the actual physical configuration of some thing

over space and time by writing down the density matrix, which encodes the physical states, and by writing down some equations that encode the dynamics. Like in the F= ... case, we can then do a computer simulation to drive the dynamics and take up a bit of the slack from our deferral.

This is the point in my line of thought where I had come to the conclusion that the most faithful representation of the Universe is the one where we defer no gathering of materials or expenditure of effort. One `simply' puts the materials in the right places and the dynamics take care of themselves from then on. In effect, spacetime and the interactions take over the place of our computer that was required to re-present the dynamics. However, it's clear to me now that this isn't the end of the symbolism spectrum that you were looking for.

I think that the `Universe is a digital computer' idea got a real boost when the papers on the holographic principle came out in the early-mid 90s. One of the most literal interpretations of the holographic principle is that those microstates states which are represented by the density matrix actually map directly to a set of oscillators (that flip up or down). If the black hole's event horizon is in any one of n microscopic states (and the states are all of the same probability of occurring), then this oscillator paradigm says there must be log_2(n) oscillators. It's like how an 8-bit integer can be in any one of 2^8 = 256 different microscopic states. The dynamics are still another matter altogether though. For instance, the original holographic principle paper (Dimensional Reduction in Quantum Gravity) does not just lay out this idea of mapping the states to binary oscillators, but also starts to lay out a kind of cellular automaton rule that would govern how exactly the black hole evolves from one specific microstate to the next as time proceeds.

In the end, I think that these people who take the holographic principle literally are just looking for something that can be subsequently framed as an object-oriented cellular automaton (just slap it into some classes, compile and run in order to re-present the dynamics). How different is this from what you are looking for, besides the fact that they take the existence of binary "bits" literally?