Noesis - The Online Journal of the Mega Society

Catch-22, the Circle Jerk, or “Yes, Academia,

There is a Good Will Hunting…”

by Gina Lynne LoSasso

It is impossible for a cube to be written as a sum of two cubes, or a fourth power to be written as a sum of two fourth powers or, in general, for any number which is a power greater than the second to be written as a sum of two like powers... I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.

- Fermat, a marginal note in his copy of Bachet's translation of Diophantus' Arithmetika, 1637

HEADLINE: Big Money For Math's Unsolved Mysteries; Institute Offers 7 $1 Million Prizes Washington Post; May 24, 2000

Anyone who wants to be a millionaire, and happens to be a genius at mathematics, now has seven chances to become one.

The Clay Mathematics Institute, a nonprofit foundation based in Cambridge, Mass., unveiled seven brain-bending problems here today and a corresponding number of $1 million "Millennium Prizes" to anyone who can provide an "approved" solution.

"We are convinced that the resolution of these problems will open up a whole new world that we cannot yet imagine," said Andrew Wiles, a Princeton University math professor known for cracking a 350-year-old problem called "Fermat's Last Theorem" in 1995. Experts say solving the problems could lead to breakthroughs in encryption and other fields.

The contest pays homage to a list of 23 math problems announced in Paris 100 years ago by mathematician David Hilbert. These problems taxed the greatest minds in the field for decades, and three remain unsolved.

The seven new problems, which can be found on the Internet at http://www.claymath.org, defy easy description for a lay audience. Some go by names that sound like Robert Ludlum novels: "The Poincare Conjecture," "The Riemann Hypothesis" and "The Yang-Mills Theory."

However, the Clay Institute did offer some analogies to try to describe the problems to novices. Take "The P vs. NP Problem," first formulated by mathematician Stephen Cook in 1971:

"It is Saturday evening and you arrive at a big party. Feeling shy, you wonder whether you already know anyone in the room. Your host proposes that you must certainly know Rose, the lady in the corner next to the dessert tray. In a fraction of a second you are able to cast a glance and verify that your host is correct. However, in the absence of such a suggestion, you are obliged to make a tour of the whole room, checking out each person one by one, to see if there is anyone you recognize."

This kind of problem--"deciding whether an answer that can be quickly checked with insider knowledge may without such help require much longer to solve"--is considered "one of the outstanding problems in logic and computer science," according to institute officials.

The founder and benefactor of the institute, retired business executive Landon T. Clay, said he was inspired as a schoolboy by a Greek quotation that translates loosely as "Wherever there is mathematics, there is comeliness," or beauty. "The appeal of mathematics is universal, not cultural," he said. "There is no country that will dominate mathematics."

To qualify for the prizes, the proposed solutions must appear in a recognized mathematics journal and then be scrutinized for at least two years, said Arthur M. Jaffe, the Harvard mathematician who heads the institute's scientific advisory board. He acknowledged that this means no prize is likely to be given before 2004. There is no time limit, officials said.

Asked if a non-mathematician might stumble upon a solution, Wiles said with a smile, "We do not believe these will be solved by someone untrained. I'm afraid 'Good Will Hunting' is for the movies."

In response to Mr. Wiles, I offer the following paraphrase of the famous editorial response to a little girl named Virginia O'Hanlon regarding the existence of Santa Claus (Yes, Virginia, There is a Santa Claus, written by Francis B. Church, appeared on the Editorial Page of the New York Sun in 1897).

We take pleasure in answering thus prominently the communication above, expressing at the same time our lack of surprise that its author is numbered among the members of Academia.

Academia, you and your little friends are wrong. They have been affected by the skepticism of a skeptical age. They do not believe except what they see. They think that nothing can be which is not comprehensible by their little minds. Many minds in Academia, whether they be tenured or not, are little. In this great universe of ours, the Academic is a mere insect, an ant, in his intellect as compared with the boundless world about him, as measured by the intelligence capable of grasping the whole of truth and knowledge.

Yes, Academia, there is a Good Will Hunting.

He exists as certainly as unfettered brilliance and beauty exist, and you would know that they abound if you would brush away the cobwebs festooning your ivory towers. Alas! How dreary would be the world if there were no Good Will Huntings! It would be as dreary as if there were no dreams. There would then be no free thought, no creativity, no passion to make tolerable this existence. We should have no enjoyment, except in sense and sight. The external light with which imagination fills the world would be extinguished.

Not believe in Good Will Hunting! You might as well not believe in humanity or its future. You might get your department chairs to have academics keep watch in all the journals to catch Good Will Hunting, but even if you manage to keep Good Will Hunting out, what would that prove? Nobody reads the work of Good Will Hunting, but that is no sign that there is no Good Will Hunting. The most real things in the world are those that neither you nor I can fathom. Did you ever see an electron dancing with a proton? Of course not, but that's no proof that they are not there. Nobody can conceive of or imagine all the wonders there are unseen and unseeable in the world.

You tear apart the baby's rattle and see what makes the noise inside, but there is a veil covering the unseen world which not the most powerful academic, nor even the united credentials of all the most powerful academics who ever lived could tear apart. Only unfettered brilliance and originality can push aside that curtain and view and picture the supernal beauty and glory beyond. Is it all real? Ah, Academia, in all this world there is nothing else real and abiding.

No Good Will Hunting? Thank God he lives, and lives forever. A thousand years from now, Academia, nay 10 times 10,000 years from now, he will continue to edify the mind and gladden the heart of humanity.

Unlike little Virginia's original letter to the Sun, and unlike the concise proof claimed by the author of the arithmetical conjecture long known as Fermat's Last Theorem, Andrew Wiles’ proof could scarcely be contained in the margin of even the most epic of tomes. The proof is 150 pages long and about as elegant as forklift full of crated primes. Still, it satisfies the demonstrative criteria of Fermat’s Last Theorem:

The equation xⁿ + yⁿ = zⁿ has no non-zero integer solutions for x, y and z when n > 2.

Regardless of his departures from elegance and his heavy reliance on circuitous proofs in new branches of mathematics, Wiles was able to connect the dots and come away with the prize. This achievement was, of course, lauded as a major coup. But when one considers that this professional academic had secluded himself for a full decade in order to slave uninterruptedly away on his demonstration, anything less than complete success would have seemed little more than a testimony to his intellectual limitations.

It is more than a little insulting to non-academics that Wiles and his smug, plodding and self-congratulatory ilk are so ready to voice doubts that an academically untrained mind could possibly solve a truly "important" problem and thereby take one of the million-dollar Millennium Prizes. In fact, given "Wiley's" Wile E. Coyote-like re-call of his original proof attempt, his unkind remark would be downright laughable were it not very likely (and very sadly) true. For its truth is due not to any inherent deficiency of the academically untrained mind, but because academic outsiders lack the “keys to the club”: access to publication in a soi-disant "reputable" and "peer-reviewed" academic journal. Unfortunately, possession of these keys is a Rule of the Game in the Clay Institute’s openly biased competition. And the circle jerks on…

So, fellow members of the superHIQ community, it is left entirely to us to share and support our own fresh ideas. We, of all people, should understand that great ideas are often difficult to grasp and sometimes even more difficult to convey, particularly where one needs to be concerned with proprietary issues in light of academic self-interest in the assignment of intellectual credit. The self-imposed bonds of academic orthodoxy are chains that bind the well-trained mind, allowing such minds to take only baby steps off the beaten track. We, on the other hand, can take giant steps if only we support each other's efforts despite the unfair constraints imposed on independent researchers by the academic machine.

When someone in our community, one of us, comes forward and puts his or her work out there, it is our sacred responsibility to support him or her to the utmost. This means doing our best to understand that work, acknowledging its strengths as well as its weaknesses; open-mindedly evaluating, critiquing, and exploring it; and yes, personally encouraging its author. For if *we* don't do this, then who will?

One thing's for sure, my dear Good Will Hunting: it won't be Academia.

Discussion with a member of the HIQ community on the CTMU (January, 2001):

Part I -

In the HIQ&A section Chris writes: "In other words, the real universe timelessly emerges from a background of logically unquantified potential to which the concepts of space and time simply do not apply." Chris, this sort of reminds me of a thought experiment I once did: Imagine that we made up laws for a (computable) universe, which we then ran on a computer. How would this universe be different from one "actually existing" with the same laws?

CML: Unlike an actual universe, its existence would be programmed by an already-existing entity in the internal artificial reality of a computer that *itself* exists in true (external) reality. Thus, it would differ from an actual universe in being (1) artificial, (2) a non-reflexive construct, and (3) subject to all of the implicit constraints applying to mechanical devices *within* an actual universe. In addition, it would lack teleological integrity...the ability to explain and justify its own existence.

DE: Would it exist even though we didn't carry out the computations on the computer? Would its existence be dependent on us writing down the formulas for its laws? If not, then it would exist simply because it is logically possible for it to exist. Not minding computability, our universe and every other logically consistent universe would exist as long as its laws could be formulated with logic.

CML: You're leaping to conclusions regarding the sufficiency of logical consistency to guarantee full existence. As conventionally defined, logical consistency alone is insufficient for this purpose. A universe also needs teleological consistency, something that is not an explicit component of any conventional system of logic. This is why every mainstream cosmologist has been forced to either adjoin to reality a quasi-teleological stopgap like the Anthropic Principle, or violate some necessary property of reality like self-containment. To some extent, the CTMU can be characterized as a logical theory of teleology which fills this breach, and thereby extends the self-referential capacity of logic to include self-justification and self-explanation.

Bear in mind that the existence of that which is neither self-explanatory nor embedded in a self-explanatory medium can be neither scientifically nor theologically explained in any depth. On the other hand, pronouncing it "random" amounts to saying that it is forever inexplicable. Needless to say, declining to explain reality in depth, let alone dismissing it as "forever inexplicable", is not what science and theology are about. In fact, this is antithetical to their existence and is belied by the truths they contain.

DE: (referring, as always, to his own last entry): Now, this is very fuzzy, and extremely speculative, in the same way CTMU seems to be to me. I'm not that up-to-date regarding philosophy, particularly its jargon, so this is obviously one reason it seems to be that way to me. I was wondering if the theory is also formulated in a more mathematical or exact way.

CML: Yes, it is. In order to recursively define the signature and relations of the symbolic version of the theory in terms of its general structure in a self-contained, self-consistent way, it suffices to describe its mathematical structure at its highest (most general) level of discourse. On this level, the CTMU describes reality, including the CTMU itself, in terms of metalogical axioms corresponding to internal consistency, universal quantification (including self-quantification), and algebraic closure on the objective and operational levels. These are all mathematical properties with definite mathematical formulations.

Rather than encumber you and others with strings of math symbols that you might not be able to decipher, I have chosen to convert these strings to verbal explanations in more or less plain language. It would be a mistake to suppose that the mathematical integrity of the CTMU has somehow been compromised in the process. After all, every mathematical theory you have ever been taught is embedded in natural language, at least on the applicative or interpretational level. Otherwise, you couldn't understand or apply it.

DE: It is difficult to understand your texts when things like SCSPL are never defined, only hinted at. One gets as much as that you *may* be on to something, but not enough material to validate the reasoning. I also wonder which philosophy texts would be, so to say, preliminary.

CML: "SCSPL": Self-Configuring Self-Processing Language. Like groups, rings and fields, languages have algebraic structure. Up to a certain level, this structure is already well-understood, relieving me of the obligation to rehash what any high school student or undergrad can find in any reasonably comprehensive algebra text (evidently the preliminary material to which you refer). If we take a language that contains logic and mathematics, adjoin to its syntax certain metalogical axioms like those just mentioned, semantically inject subjective and empirical verities like ourselves and our perceptions in the appropriate places, and then deduce the structure of this language according to the rules of its own logical and mathematical syntax, then it becomes precisely the kind of self-explicating construct that I've been describing in relatively plain English for over a decade. While this is admittedly short on detail, it is quite pithy and contains more than enough information to let you formulate specific questions to which meaningful answers can be given.

For example, why language as opposed to some other algebraic structure? Because language is sufficiently general that any conceivable mathematical structure can be defined in terms of it; because like reality, it has spatial and temporal aspects associated with the structural and grammatical components of its syntax; and because it describes the nature of our minds (through linguistic constructs like psychology, the Chomsky hierarchy, and the theory of cognition) as well as our objective environment (as described in chemistry, physics, and astronomy). All I needed to do was build into the already-known algebraic structure of language enough extra power to make it self-configuring and self-processing. Regarding the question of whether I've already succeeded in doing that, I'd advise you to believe it.

Thanks for the comments!

Chris Langan

Part II -

(Disclaimer: Daniel's philosophical curiosity = 100 * Daniel's philosophical knowledge ;-)

CML (rpt): Unlike an actual universe, its existence would be programmed by an already-existing entity in the internal artificial reality of a computer that *itself* exists in true (external) reality.

DE: However, an isomorphism is assumed. (Btw, I don't use the words universe and reality interchangeably. It is for example logically possible for several universes to exist, but there is only one reality, by definition.)

CML: Whether or not something is an isomorphism as opposed to a homomorphism depends on your vantage. If you recognize, in the computational sense, a metalanguage with sufficient expressive power to describe a mapping which carries a group into a proper subgroup thereof, and a nonempty kernel into the subgroup's identity, then you can speak of it as a group homomorphism (an injective structure-preserving morphism from group to subgroup). If, on the other hand, you recognize only a language expressive enough to describe the subgroup, then you recognize this same mapping as an isomorphism because you can discern no kernel and no many-to-one mapping into the identity. But in that case, you hedge your bets by qualifying your statements with the phrase "up to isomorphism" (with your own possibly inadequate accepting syntax)...e.g., when trying to compare the reality you have programmed in your device to the reality in which you and your device exist, to crucial parts of which you may, for all you know, be blind or merely ignorant. That is, you are not free to equate these two levels of reality, but only to define an isomorphism "up to which" you (think you) can no longer distinguish between them in point of structure. At the same time, someone who has investigated this mapping in more detail may be able to recognize certain differences after all. I sometimes find myself in this position. ;-)

>Thus, it would differ from an actual universe in being (1) artificial

DE: The proposed universe is supposed to be characterizeable using a few simple rules, that may be carried out on the computer. These rules form a function which describes the position of various particles, their velocities and so on, whatever the universe is composed of, i e the information implicitly contained in the rules will be a complete description of the state of the universe at each point in time. The keyword here is description: an isomorphism does not guarantee identity.

CML: Quite so.

DE: However, the success we have had so far at describing our universe using formalized systems, logic, mathematics and so on, hints at that the universe may exist in this form or a similar one at its most fundamental level. At least, that is the thought I wanted to explore.

CML: This applies only to the kinds of relation we have been successful in explicating. There are other kinds of relation that science has not been so good at revealing - witness all those centuries-old cosmological paradoxes - and these relations may be also be relevant to the problem of existence. One such set of relations is called "teleological" and pertains to the deepest and most general levels of explanation and justification. We've already touched on the cosmological significance of teleology.

DE: If I don't misread you, your CTMU deals with reality as a set, more precisely the set containing everything, which no doubt is a theoretical construct. You proceed to derive properties of this set, which you assume must be properties of reality. Is the all-inclusive set treated as a description of reality or reality itself?

CML: Actually, I've been careful not to describe reality as a mere set. There's a paper linked to the Mega Foundation and UltraHIQ sites that explains some of the differences between a set and an SCSPL.

DE: Which are the necessary and sufficient conditions for existence?

CML: For present purposes, we could cite several: e.g., logical and teleological closure and consistency. If you're talking specifically about the physical stage of existence, we would add physical consistency.

>(2) a non-reflexive construct, and (3) subject to all of the implicit constraints applying to mechanical devices *within* an actual universe.

DE: Such as...? It seems to me that these constraints could be part of the rules defining the proposed universe.

CML: The point, of course, is that a real universe, as opposed to a simulated universe, autologously (self-descriptively) defines its own constraints, whereas the constraints on a simulated universe are defined "from above". Because these external constraints depend on the structure of the primary reality in which the simulating device is embedded, no programmer can enumerate them without first describing primary reality. Trying to get away with less is putting the cart before the horse...or in the language of group theory, putting the image of a homomorphism ahead of its argument.

>In addition, it would lack teleological integrity...the ability to explain and justify its own existence.

DE: I understand this to mean that it would not contain the information needed to explain why it exists. This seems to be a necessary condition for a Theory Of Everything, rather than a universe itself. (Same goes for point number 2 maybe.) If it is necessarily a property of the latter, it is far from trivial.

CML: Due to the necessity of closure, reality must everywhere embody its own syntax. Where this syntax is viewed as a theory, reality and reality theory are one and the same. Of course, this only applies to a *correct* theory. But much of the CTMU comes from assuming that a correct theory exists, and deducing its properties from the requirement that it in fact be "correct". Because reality is a valid model of itself corresponding to a correct object-level theory of itself, we can always use this kind of reasoning.

DE: If logic and mathematics exist independent of human perception (the old question, was mathematics discovered or invented?), and if the mathematical/logical characterization of a universe is equivalent to the universe itself, then every possible universe exists. I don't believe this to be the case, but I'm interested in which other criteria must met for a universe to exist.

CML: Logic and mathematics do not exist apart from perception, human or otherwise. In fact, there is a sense, first enunciated by Berkeley, in which perception is the primary ingredient of reality. But any act of perception can be noncommutatively factored into a (cognitive) perceiver and an (informational) percept. Where reality accordingly consists of "infocognition", a monic blend of information and cognition, and mathematics is real, mathematics too is "infocognitive" and therefore perceptual in a generalized way.

Note that where perception is understood to have a cognitive aspect, this is not the same as saying that mathematics is "empirical" in the conventional sense and therefore "discovered"; neither is it equivalent to saying that mathematics is "invented". Rather, mathematics is self-explanatory in the sense that it is a part of the syntax, or set of structural and dynamical rules, of the universe from which it derives its justification. The self-explanatory nature of mathematics is a function of teleology.

>A universe also needs *teleological* consistency, something that is not an explicit component of any conventional system of logic. This is why >every mainstream cosmologist has been forced to either adjoin to reality a quasi-teleological stopgap like the Anthropic Principle, or violate some necessary property of reality like self-containment.

DE: Again, this teleological consistency seems to be more a necessary component of a theory that fully explains the universe (or more precisely reality), rather than the universe itself.

CML: Again, one gets the same answer: where the syntax of reality is viewed as a theory of reality, reality and reality theory are one and the same. This may seem counterintuitive, but the CTMU takes the equivalence quite seriously. It is analogous to saying that a correct theory of physics would consist of "the laws of physics" themselves (and indeed it would, with respect to both form and content).

<snip>

(What follows is mostly a justification of why a theory like CTMU is needed to fully explain reality. I agree with this.)

>Rather than encumber you and others with strings of math symbols that you might not be able to decipher, I have chosen to convert these strings to verbal explanations in more or less plain language. It would be a mistake to suppose that the mathematical integrity of the CTMU has somehow been compromised in the process.

DE: I would be interested in reading both versions, so to say.

CML: You'll probably get your chance.

<snip>

>For example, why language as opposed to some other algebraic structure? Because language is sufficiently general that any conceivable mathematical structure can be defined in terms of it; because like reality, it has spatial and temporal aspects associated with the structural and grammatical components of its syntax; and because it describes the nature of our minds (through linguistic constructs like psychology, the Chomsky hierarchy, and the theory of cognition) as well as our objective environment (chemistry, physics, astronomy). All I needed to do was build into the already-known algebraic structure of language enough extra power to make it self-configuring and self-processing.

DE: Do you think that when we understand how the mind works that a more "basic" structure will be more successful? Language would be a consequence of this structure (namely how our minds work) and at a "higher level."

CML: On the physical level, we already possess a general understanding of how the mind works: it is a biological neural network. Neural nets are PDP systems in which neurons (or in the simplified mathematical model, neurodes) speak to each other a "language" consisting of 2-valued logic; that is, they have just two interactive states, ON or OFF, by which they do (or do not) affect each other's behavior. So to some extent, we are assured that everything we can think, no matter how complex, can be comprehensively formulated in the more basic language of 2VL.

But "comprehensive" does not mean "complete"; interpretation enters on the semantic level of predication, making mere propositional logic inadequate to formulate SCSPL in full (this amounts to saying that in addition to 2VL and a few other things, the brain needs complexity of wiring and synaptic weighting in order to function well enough to perceive and describe its reality). Equivalently, language arises from infocognition only by way of semantic extensionality in a metric capable of sustaining its structural and behavioral complexity and richness of thought and perception. Since this (SCSPL) metric contains more information than conventional 2VL alone, SCSPL can never be wholly reduced to 2VL...or for that matter, to any other simpler structure.

Chris Langan

Part III -

DE wrote:

CML (rpt): But in that case, you hedge your bets by qualifying your statements with the phrase "up to isomorphism" (with your own possibly inadequate accepting syntax)...e.g., when trying to compare the reality you have programmed in your device to the reality in which you and your device exist, to crucial parts of which you may, for all you know, be blind or merely ignorant. That is, you are not free to equate these two levels of reality, but only to define an isomorphism "up to which" you (think you) can no longer distinguish between them in point of structure. At the same time, someone who has investigated this mapping in more detail may be able to recognize certain differences after all. I sometimes find myself in this position. ;-)

DE: Of course it is a matter of isolating a particular part of our reality, namely those particular rules programmed on the computer, and then mapping these isomorphically to the artificial computer reality - since it is not assumed there is a isomorphism between the *entirety* of our reality and the other one (that would be the homomorphism instead). Then we ask, could a reality isomorphic to this isolated part of our reality, namely the rules in the computer, exist?

CML: No. The computer is a local construct that varies from point to point in space, yet coheres and persists over time. If all we had were the rules visibly coinciding with the material components and physical behaviors of the machine, we couldn't explain the machine's coherence and persistence. We wouldn't be able to explain how its laws act on matter, or why they are coherent in space and time. Where physical reality is assumed to coincide with the computer, this implies that these deeper explanations are "more than physical", or to put it more formally, that they can only be formulated in a metalanguage of physics called "metaphysics". Now, either the simulation (the program running on the physical machine) is capable of expressing this higher level of explanation, in which case the simulation is indeed self-explanatory and the physical machine a function of it (rather than vice versa), or it is incapable of expressing this higher level of explanation and is therefore a secondary construct. In the first case, the simulated reality is in effect self-simulated and depends on nothing external, in which case it is an SCSPL. In the second case, its existence depends on embedment in an SCSPL and is therefore ontologically secondary. Either way, the CTMU holds true.

DE: Let me turn this around a bit. Suppose such a reality as the one (completely) described by the computer could exist. The rules in the computer would be the physical laws of this reality, i e by definition be a complete description of its physical part. Since the description is assumed complete, I come to the conclusion that if you say this reality cannot exist, then you are saying that (computable) realities which are only physical cannot exist. (I assume you say this about non-computable ones as well.) We must add a non-physical part and so, the homomorphism is now so to say the other way around: A complete description of the alternative hypothetical reality (now including non-physical parts) could be a homomorphism to the computer rules (only descriptions of the physical), but not the other way around.

CML: This makes no obvious sense. The "reality" simulated inside a computer depends on (1) the physical existence of the computer, and (2) the medium which sustains the physical existence of the computer. Take away (2), and you can forget about (1). On the other hand, you can take away (1) without affecting (2) at all. Since (1) depends on (2) but not vice versa, they are not equivalent and cannot be interchanged; there is no "turning the homomorphism around". The morphism is injective from metalanguage to language, not vice versa.

DE: To make this clearer - and less hypothetical! - you seem to be saying that a description which only describes reality on the physical level, is necessarily incomplete. I understand that what you add to make the description complete is among other things something to account for teleological closure, which then seems to be concerned with non-physical parts of reality. (Right? I hope I am not misreading you.) This is what I have trouble understanding (partly because I'm not sure exactly what you mean by "teleological closure" I guess) - again this "reality must be able to account for its own existence"! The crux of the biscuit.

CML: A system possessing telological closure is one that is self-contained with respect to justification. That is, it provides its own reason to exist. Since the physical aspect of reality exists right along with the *rest* of reality, teleological closure applies to physical existence as well as nonphysical existence.

CML: This applies only to the kinds of relation we have been successful in explicating. There are other kinds of relation that science has not been so good at revealing witness all those centuries-old cosmological paradoxes and these relations may be also be relevant to the problem of existence. One such set of relations is called "teleological" and pertains to the deepest and most general levels of explanation and justification. We've already touched on the cosmological significance of teleology.

DE: Right. Where do I learn more about teleology?

CML: Any decent philosophy text containing a history of Western philosophy will do, with one caveat. Most philosophy texts state, imply or otherwise suggest that teleology went out with the Dark Ages...that as a philosophical hypothesis, it has been permanently discredited by modern arguments like the theory of evolution. This is an unfortunate bit of disinformation that academic philosophers have been feeding their students for many years now...*too* many years. But that's academia for you. ;-)

DE: If the simulated universe actually exists, then it doesn't care whether or not we have happened to accurately describe it on our computer. I don't mean that the universe would exist *because* of the computer. It's a hypothetical investigation: "Suppose such a universe exists - now, is it logically(/teleologically?) consistent?"

CML: Not unless it has created, with no external help, the machine on which it is running.

CML: Due to the necessity of closure, reality must everywhere embody its own syntax. Where this syntax is viewed as a theory, reality and reality theory are one and the same. Of course, this only applies to a correct theory. But much of the CTMU comes from assuming that a correct theory exists, and deducing its properties from the requirement that it in fact be "correct". Because reality is a valid model of itself corresponding to a correct object-level theory of itself, we can always use this kind of reasoning.

DE: That reality may be seen as a valid model of itself, does not mean that this model contains the answer to the question of why reality exists, or (the better question) why reality is this way and not another way. The CTMU seems to assume that there exists a theory which can answer these questions, and then derives certain properties of such a theory. This, of course, is very interesting in and of itself. However, does the CTMU have anything to say about reality, if these questions are unanswerable, and/or even meaningless?

CML: First, to deny that something has an explanation is to say that it is "random" in a sense that doesn't even fly in pure mathematics, where von Mises' traditional definition of randomness led to numerous difficulties. Conversely, to say that something is "random" in the sense often encountered in the physical sciences amounts to saying that it is without cause, or in slightly more colorful terms, that it is a magical production of something from nothing. In quantum theory, we are so inured to the idea that wavefunction collapse is "random" that it almost seems to make sense...but not quite, for the measurement problem is still regarded as a paradox. So it is important to understand that once you start talking about not having to answer the question of why something happens or exists, you no longer occupy the logical high ground. Your refusal to explain requires an explanation of its own.

Now that you understand the weakness of your position, the question of why reality exists is in fact amenable to logical analysis. Consider the generic question "why does X exist?" This question is really a statement of causality; it says that X, rather than being a magical production of something from nothing, must have a cause, and asks that this cause be identified. In other words, it requests a label for the origin of the cause-to-effect arrow pointing at X. But where there is no external causality (because there is nothing real outside of reality), the arrow becomes a loop; point and tail, question and answer, now coincide. In mathematics, this looping arrow is called a "reflexive relation", and because the shape of the arrow has changed, the associated "why?" question changes its meaning accordingly. Now the question becomes "why is X identical to X?", which amounts to a demand that the observable coherence and persistence of X be described in terms of X itself. To deny this demand is to deny the existence of the reflexive relation in question, which (because it is an identity relation) is to deny the existence of X. Since X exists, this is a contradiction. Ergo, the question must be answered. The answer is what we have been calling "teleology".

CML (rpt): Note that where perception is understood to have a cognitive aspect, this is not the same as saying that mathematics is "empirical" in the conventional sense and therefore "discovered"; neither is it equivalent to saying that mathematics is "invented". Rather, mathematics is self-explanatory in the sense that it is a part of the syntax, or set of structural and dynamical rules, of the universe from which it derives its justification.

DE: It only needs justification when it is applied to reality. For example, it would be misleading to say that axioms are "self-evident truths," as you often hear people say. They only become self-evident (whatever that means anyway!) in a context that includes more than mathematics itself, for example physics, or, well, meta-mathematics. In this sense "true" and "false" are meta-constructs.

CML: Yes. The concepts "true" and "false" are expressible only in a metalanguage of the object language and object universe to which they are applied.

CML (rpt): Again, one gets the same answer: where the syntax of reality is viewed as a theory of reality, reality and reality theory are one and the same. This may seem counterintuitive, but the CTMU takes the equivalence quite seriously. It is analogous to saying that a correct theory of physics would consist of "the laws of physics" themselves (and indeed it would, with respect to both form and content).

DE: It is not so counterintuitive. What is beyond me, though, is why necessarily a correct theory of reality must include answers to questions such as "why does reality exist?". Ideally, this is the case, I agree, but we can't just assume that is a question that is answerable/meaningful. You assume a true TOE exists (in which case it follows that reality can justify itself), but maybe such a theory is an impossibility due to the very nature of reality.

CML: See my above comments on the inevitability of teleology. To deny any explanation of the existence of reality (here to be read "TOE") is effectively to deny the existence of reality, period. Since reality does in fact exist, its explanation cannot be denied.

CML: But "comprehensive" does not mean "complete"; interpretation enters on the semantic level of predication, making mere propositional logic inadequate to formulate SCSPL in full (this amounts to saying that in addition to 2VL and a few other things, the brain needs complexity of wiring and synaptic weighting in order to function well enough to perceive and describe its reality).

DE: Interesting. How, then, is SCSPL formulated? What apart from propositional logic is needed?

CML: In addition to teleology, you mean? Higher-order predicate calculus, for one thing. Without that, there would be no perceptual or semantic correspondences, and thus no possibility of explaining anything whatsoever. There are other necessary ingredients as well, but I'm getting writer's cramp.

I hope this exchange has been helpful to you. Take it easy!

Chris Langan

Part IV -

DE wrote:

CML (rpt): Now that you understand the weakness of your position, the question of why reality exists is in fact amenable to logical analysis. Consider the generic question "why does X exist?" This question is really a statement of causality; it says that X, rather than being a magical production of something from nothing, must have a cause, and asks that this cause be identified. In other words, it requests a label for the origin of the cause-to-effect arrow pointing at X. But where there is no external causality (because there is nothing real outside of reality), the arrow becomes a loop; point and tail, question and answer, now coincide. In mathematics, this looping arrow is called a "reflexive relation", and because the shape of the arrow has changed, the associated "why?" question changes its meaning accordingly. Now the question becomes "why is X identical to X?", which amounts to a demand that the observable coherence and persistence of X be described in terms of X itself. To deny this demand is to deny the existence of the reflexive relation in question, which (because it is an identity relation) is to deny the existence of X. Since X exists, this is a contradiction. Ergo, the question must be answered. The answer is what we have been calling "teleology".

DE: This section addresses the core of that I've been wondering about, I think. My problem here is that if we take "A causes B" to mean "if A exists then B exists", then given B, if we find a cause of it, A, then we have found a reason why B exists (given that A is not B!). However, it is obvious that for any B "if B exists, then B exists" holds true. In other words, saying that the statement "Reality causes Reality to exist" provides a *reason* as to why Reality exists, sounds like the philosophical equivalent of "Why? Just because!" to me.

CML: Here's a postscript designed to help you avoid a waste of time. First, "reality causes reality to exist" gives rise to a further question, namely "how?", to which there is a nontrivial answer. Second, you're not merely asking "Why does reality exist?"; you're asking "Why is the self-evident existence of reality coherent and stable in space and time?", the answer to which also gives rise to a "how?" question. The answer to this "how?" question is this: "By reflexive self-action". So what we're really talking about is the degree and method of reflexivity of reality, considered as a relation. A true reality, analogized to software, is sufficiently reflexive to serve as the "hardware" on which it runs. A mechanically simulated reality is not; you must provide it with hardware, and when you do, you are its "god" in a supra-mechanistic sense. Now, since the reflexive structure of true reality is mathematically complex, explicating it is by no means equivalent to saying "just because!".

Let's take a slightly closer look. The "why?" question is really two questions in one: "what causes reality?" and "why is reality coherent and stable in space and time?" With each of these questions is associated a "how?" question, the answer to which requires the explanation of some facet of the reflexive structure of reality (considered as a relation). It is important to realize that this structure is mathematically complex and therefore nontrivial... as opposed, for example, to a philosophical equivalent of "just because!". On the other hand, if this structure does not exist, then what we have is a nonreflexive relation like the computer-simulated reality of your gendankenexperiments. By dint of its nonreflexivity, such a simulation cannot provide itself with hardware on which to run; you provide the hardware and thus assume the role of facilitator with respect to it. In contrast, if we consider true reality as a self-simulation written in a protean "programming language" called SCSPL, then it is sufficiently reflexive to write itself (self-configure) and execute itself (self-process), thereby serving as its own developer, programmer, hardware designer and hardware builder. Obviously, this takes self-containment to a whole new level. Since answering the "why?" question requires an explanation of this entire process, "just because!" won't cut it. So you'd be well advised not to let yourself think about it that way.

Good luck in your investigations!

Chris Langan