Announcement: Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal Cosmos and History.
Cognitive-Theoretic Model of the Universe
The Cognitive-Theoretic Model of the Universe or CTMU (pronounced "cat-mew") is a philosophical theory of the relationship between mind and reality. Its author, Christopher Michael Langan, has been billed as "the smartest man in America", with an IQ reported by 20/20 and other media sources to have been measured at around 195. Langan created the CTMU in the mid-1980s while working as a bar bouncer on Long Island. Among his claims for the theory are that it constitutes absolute truth, provides the logical framework of a Theory of Everything, and proves the existence of God.
Of limited means and largely self-taught, Langan created the CTMU in the mid-1980s while working as a nightclub bouncer on Long Island, New York. His first published paper on the theory, "The Resolution of Newcomb's Paradox", appeared in the December 1989–January 1990 issue of Noesis, the journal of the Noetic Society, a high-IQ society to which Langan belonged. Over the next decade Langan refined his work, continuing to publish and discuss it in high-IQ journals.
Wider recognition for Langan and his theory came in 1999, when Esquire magazine published a profile of him and other members of the high-IQ community. Billing Langan as "the smartest man in America", the article's account of the weight-lifting bouncer and his Theory of Everything sparked a flurry of media interest. Articles and interviews highlighting Langan and the CTMU appeared in Popular Science, The Times, Newsday, Muscle & Fitness, and elsewhere. Langan was featured on 20/20 and interviewed on Errol Morris' First Person. In 2008, Langan was profiled in Malcolm Gladwell's book Outliers.
By 2002 the CTMU had drawn the attention of the International Society for Complexity, Information, and Design (ISCID), a professional society founded by intelligent-design proponent William Dembski. Langan was made a fellow of the society and in September 2002 published in its online journal a 56-page paper, "The Cognitive-Theoretic Model of the Universe: A New Kind of Reality Theory". Langan's paper "Cheating the Millennium: The Mounting Explanatory Debts of Scientific Naturalism", relating the CTMU to existing theories of causality, appeared in the 2004 anthology Uncommon Dissent, edited by Dembski.
Langan has also posted articles about the CTMU on his Web site and debated his theory on Internet discussion boards. His essay collection The Art of Knowing, published by Mega Press, has some CTMU content, and he has reportedly written an unpublished book about the CTMU called Design for a Universe.
Prominent among the tools of epistemology are the axiomatic method (associated with rationalism, deduction, and mathematics), and the scientific method (associated with empiricism, induction, and the physical sciences). The axiomatic method derives theorems from axioms, but which theorems can be derived depends on which axioms are started with. (For example, consider Euclidean vs. non-Euclidean geometry.) The scientific method infers laws from observations, but future observations can break these laws (creating the problem of induction). Such methodological limitations have led some theorists to conclude that all knowledge is relative: to arbitrary axioms or to restricted observations.
The CTMU is an attempt to circumvent these limitations and achieve absolute knowledge. Langan writes:
"What I mean by 'absolute' is precisely this: (1) you can't relativize your way out of it by changing the context; (2) finding it in error equates to destroying your own basis for inference. These criteria are built into the theory from the ground up using some very effective, that is to say ironclad, techniques. Logically, there is no way out."
The CTMU, Langan says, is based on logical tautologies. In 2-valued logic, a tautology is a statement that is true under every assignment of "true" and "false" to the variables within it. For example, "A or not-A" (the law of the excluded middle) is a tautology because it is true regardless of whether A is true or false. Langan argues that all meaningful theories conform to 2-valued logic, and that because the axioms and theorems of 2-valued logic are tautological, tautologies "define the truth concept for all of the sciences. From mathematics and physics to biology and psychology, logical tautologies reign supreme and inviolable".
Langan further holds that logical tautologies constitute absolute knowledge in the sense of his criteria above. That is, where "changing the context" amounts to changing truth assignments to contextual variables, tautologies are true in every context. And where "your own basis for inference" includes 2-valued logic, logically disproving a tautology requires use of the tautology itself, destroying the inference. Accordingly Langan calls tautologies self-evident or "self-proving".
Tautologies are sometimes dismissed as "empty", "vacuous", and "uninformative" on the grounds that they tell us nothing about the world. Disagreeing, Langan adjoins to logic three metalogical principles (described below), themselves analytically tautological, intended to relate logic to reality. The resulting theory (the CTMU) Langan calls a "supertautology": the reality-theoretic counterpart of a tautology. A supertautology is semantically tautological with respect to its universe; that is, "(a) the theory is intrinsically tautological, and (b) its tautological structure is modeled by its universe".
Unlike scientific theories, which rely on observation to establish their correspondence with reality, the CTMU is intended through its tautological construction to correspond with reality necessarily, in all possible worlds. In fact, claims Langan, "any other valid theory of reality will necessarily equate to the CTMU up to isomorphism; whatever it adds will come by way of specificity, not generality". Verification of the CTMU is made "largely rationalistic" by its tautological nature, so that "much of the theory has to be proven like a math theorem rather than confirmed on a lab bench".
In the CTMU, reality takes the form of an algebraic structure Langan calls a "Self-Configuring Self-Processing Language" or SCSPL. The CTMU blends elements of various branches of advanced mathematics, including category theory, model theory, computation theory, abstract algebra, and the logic of formalized theories. Langan's public writings are meant to be relatively accessible, and for that reason, he says, tend to avoid heavy use of symbolic notation in favor of informal characterization. Nonetheless, he claims, the CTMU is axiomatizable and formalizable, SCSPL is well-defined, and he "can reduce that entire 56 page paper to variables and functional, operational and relational symbols".
Langan defines reality as "the perceptual aggregate including (1) all scientific observations that ever were and ever will be, and (2) the entire abstract and/or cognitive explanatory infrastructure of perception". That is, reality is defined on relevance to perception. Associated with this definition is a tautological containment principle Langan calls the Reality Principle: "reality contains all and only that which is real". That is, reality is self-contained.
The three metalogical principles used in the CTMU to relate logic to reality are:
- Metaphysical Autology Principle (associated with closure), or MAP
- Mind Equals Reality Principle (associated with comprehensiveness), or M=R
- Multiplex Unity Principle (associated with consistency), or MU
Langan calls these principles and properties the Three Ms and Three Cs. They can be viewed as axioms of the CTMU, with the caveat that they are not meant to be assumptions, but rather to be analytic truths necessarily modeled by reality as a condition of its existence.
MAP says that reality is closed with respect to all internally relevant operations. In other words, everything essential to reality, including everything needed to describe it, is contained in reality itself. MAP is implied, Langan argues, by the definition of reality: were anything outside of reality relevant to it, it would be included by the definition and therefore inside reality.
M=R says that reality is comprehensive enough to describe itself. That is, reality conforms to the categories of the minds describing it from within. Whereas MAP gives reality what it needs to describe itself, M=R empowers it to actually do the describing. M=R follows, argues Langan, from the definition of reality. On one hand, mind itself is included in reality by perceptual relevance. On the other hand, mind acts as a filter: that which does not conform to mental categories is irrelevant to perception, and therefore not real. Langan here breaks with Kant, who posited a noumenal reality of "things-in-themselves", independent of the phenomenal reality we perceive. Discarding this "Kantian fallacy", Langan rejects noumena as oxymoronic "inconceivable concepts" and holds that phenomenal reality, as the only reality we can know, is the only reality there is. Accordingly, reality relates to our minds as a sort of "distributed solipsism".
MU says that reality is consistent by virtue of the mutually inclusive relationship between itself (unity) and its contents (multiplicity). That is, reality topologically includes its contents, while its contents descriptively include it. Reality is here analogous to the set of all sets; SCSPL extends set theory with the above two senses of inclusion so that sets, now "syntactic operators", can consistently contain themselves. The consistency of reality is implied, Langan argues, by the stability of perception: a single irresolvable paradox of the form "A = not-A" would destroy the information content of reality, making it impossible to perceive.
The question of why reality exists is sometimes taken to be unanswerable or meaningless: reality "just exists", it is held, and no further explanation can be given. Alternatively, it is sometimes held that reality exists because it was created by something outside of it, an external creator. Langan opposes both views, arguing that were reality to lack an explanation, it would be acausal and could not sustain itself, whereas for an external creator to create reality, the creator itself would have to be real, and therefore inside reality by definition, contradicting the premise.
The CTMU treats the origin of reality in the context of freedom and constraint. Concepts are defined by constraints specifying their structure, and structure requires explanation. Consequently, Langan argues, the only concept not in need of structural explanation is the "terminal concept" with no constraints, and no structure to explain. In the CTMU, this "ontological groundstate" is called "unbound telesis" or UBT.
Because, Langan argues, UBT is a medium of pure potential, everything is possible within it, and this means that what can exist, does exist. However, the requirements for existence are, asserts Langan, more stringent than is normally supposed. Because UBT is unstructured, the only possibilities which can actualize from it are those with sufficient internal structure to create and configure themselves. So in the CTMU, reality, rather than being uncaused or externally caused, is self-caused, and constrained by the structure it needs to create and configure itself, that of SCSPL.
The above reasoning, holds Langan, resolves the ex nihilo or "something-from-nothing" paradox. The paradox arises when "nothing" is taken to exclude not just "something", but the potential for "something". Because exclusion of potential is a constraint, "nothing" in this sense requires its own explanation, and cannot serve as an ontological groundstate. But when "nothing" is viewed as unconstrained potential or UBT, asserts Langan, reality arises inevitably from it.
Reality, Langan argues, requires as a condition of its existence not merely logical consistency, but also "teleological consistency". To arise from UBT, he says, reality needs a function to distinguish what it is from what it is not—to "select itself" for existence. This requirement, the "Telic Principle", generalizes the well-known anthropic principle: whereas the anthropic principle addresses the degree to which human existence constrains reality, the Telic Principle addresses the way in which reality tautologically constrains itself.
Because reality is self-contained, it serves as its own selection function. That is, the function, that which it selects, and the act of selection itself are identical; "existence is everywhere the choice to exist" and "reality triples as choice, chooser and chosen". Langan explores the logic of this arrangement: "[a] large part of the CTMU is about what happens when functions, including choice, generative and causal functions, are looped so that input coincides with output coincides with functional syntax".
The requirement that reality serve as its own selection function gives it a reflexive form whose goal is to self-actualize. This "MU form" is the starting configuration of SCSPL grammar. With "existence and its amplification" as its sole imperative, reality selects its "future" by maximizing a parameter Langan calls "generalized utility". The CTMU is therefore a teleological theory in which the purpose of reality is to optimally self-actualize.
Because reality inherits distributive freedom from UBT, parts of reality can deviate from the teleology of reality as a whole. Unable therefore to maximize utility directly, reality instead maximizes potential utility, "setting things up" for maximum benefits should teleology be pursued. Langan takes generalized utility as the basis of a system of ethics, defining goodness as that which furthers teleology and extending the Golden Rule to fit the stratified structure of SCSPL.
In the CTMU, reality evolves by "telic recursion", a metacausal generalization of ordinary recursion suited to pre-informational contexts. Telic recursion occurs in two stages, one primary and global, the other secondary and local. The primary stage creates the distributed laws, including the laws of physics, which reality obeys, while the secondary stage creates nondistributed, ad hoc supplements to those laws as reality transitions from state to state.
Guided by the Telic Principle, telic recursion seeks to maximize generalized utility through "telic feedback" between past and future states. This potential for reverse causality extends back to the very origin of reality, so that in effect, "the system brings itself into existence as a means of atemporal communication between its past and future whereby law and state, syntax and informational content, generate and refine each other across time to maximize total systemic self-utility."
The CTMU relates space, time, and matter through a process Langan calls "conspansion"—"material contraction qua spatial expansion". Because reality is self-contained, argues Langan, its external size and duration are undefined, and it cannot expand in an external sense: it has nothing to expand into, and nothing to expand during. Mainstream cosmologists hold that expansion need not occur externally, invoking results from differential geometry to show that the spacetime metric can change without reference to an embedding space. Langan asserts that mainstream models nonetheless fall short of full self-containment, arguing that they fail to "conserve spacetime", employ a non-endomorphic concept of motion, and cannot intrinsically explain the creation of the spacetime manifold itself.
In Langan's model, reality stratifies inwardly into a superposition of sequentially related states, each state topologically contained by, but descriptively containing, the one preceding it, and parallelized with respect to its successors. In the resulting "conspansive spacetime", rather than reality expanding relative to its contents, its contents contract relative to it, and time speeds up to preserve the laws of physics—an idea adumbrated in 1933 by Arthur Eddington. The point, says Langan, is to retain the valid relationships of conventional spacetime while changing their interpretations so as to resolve paradoxes of cosmology and physics.
Conspansion alternates between two phases: a generative phase in which events produce new possibilities, and a selective phase in which possibilities collapse into new events. The alternation occurs at a fixed conspansion rate c, understood as the rate at which reality creates itself and identified by Langan with the speed of light in a vacuum. Langan associates conspansive alternation with wave-particle duality, and asserts that the CTMU constitutes a new interpretation of quantum mechanics called "sum over futures".
The fundamental entity of SCSPL reality is the "syntactic operator", or unit of self-processing information. Because, argues Langan, cognition is just the specific form of information processing that occurs in a mind, information processing can be described as "generalized cognition" and self-processing information as "infocognition". So in the CTMU, reality is a dual-aspect monism consisting of one substance (infocognition) with two aspects (information and cognition); space is a configuration of syntactic operators, and time is the activity of these operators as they process themselves and each other.
The CTMU therefore supports a kind of panpsychism. Although every part of SCSPL has a cognitive aspect, the mental capabilities of a given subsystem depend on its structure. Langan distinguishes three "levels of self-cognition": subordinate, agentive, and global. The lowest of these levels, subordinate, encompasses low-complexity objects such as rocks. In the CTMU, rocks are cognitive in the generalized sense—their molecules interact, thereby processing information—but they do not possess independent volition or any intrinisic ability to optimize their environment.
The next level of self-cognition, which includes humans, is that of agents or "telors": observer-participants in the ongoing creation of reality. Telors possess independent volition and constructive, creative intelligence or "sentience". In the CTMU, the distributed laws of physics do not fully determine reality; they are supplemented by "meta-laws" created by telors as reality evolves. This ability of telors is constrained by factors including locality, interference, and the fact that it must occur within the probabilistic limits of the laws of physics.
The third and highest level of self-cognition, the global level, is that of reality itself. This level possesses three formal properties of SCSPL: "syntactic self-distribution" (analogous to omnipresence), "perfect autotransductive reflexivity" (analogous to omniscience), and "self-configuration up to freedom" (analogous to omnipotence). Because these are theological attributes, Langan describes reality as "the mind of God". So, claims Langan, because the CTMU constitutes absolute truth—because it is founded on tautology and supported by logical and mathematical reasoning—it proves the existence of God.
In short, the CTMU construes physical interaction as information processing, regards information processing as a generalization of human cognition, and assigns cognitive classifications to information processors—from rocks, to humans, to reality itself—based on their structure.
Outside of the popular media and the high-IQ community, assessment of the CTMU has occurred largely on the Internet. Online discussion-board participants range from supporters hailing the CTMU as a major breakthrough and praising its author for his brilliance, to critics hurling scorn and invectives at Langan and pronouncing his theory incomprehensible or utterly incorrect, to neutral bystanders preferring to reserve judgement until the publication of Design for a Universe.
Critics of the CTMU maintain that because it has been published in venues associated with ideas that are currently unpopular within the academic community, particularly intelligent design, it is suspect by association. They assert that since the CTMU has not been submitted to and properly criticized in what they consider to be reputable academic journals, it can be neither notable nor correct. They evidently believe that if it were correct, academia would already know all about it; on the other hand, if academia has not yet actively discussed it, then notability and correctness are out of the question. That is, they believe that academia is the sole arbiter of correctness and notability.
It is not clear whether the critics regard the correlation between academia and important new ideas as a logical implication, the outcome of empirical induction, or a definitional premise. In any case, the academic community has on many occasions discussed and developed a favorable consensus on theories that were ultimately found to be erroneous or incomplete (for example, the luminiferous aether of classical physics). Similarly, academia has sometimes failed, for considerable periods of time, to properly note and discuss correct theories which were duly submitted to it (e.g., group theory, which was introduced by Evariste Galois but long neglected due to various unfortunate circumstances and snafus).
The most comprehensive paper on the CTMU is the 56-page "A New Kind of Reality Theory". A shorter explication is the "Introduction to the CTMU". As a gentler introduction, there are questions and answers.
- Related work - work related to the CTMU
- Brabham, Dennis. (August 21, 2001). "The Smart Guy". Newsday.
- Eddington, Arthur. (1933). The Expanding Universe: Astronomy's 'Great Debate', 1900-1931. Cambridge University Press.
- Langan, Christopher M. (December 1989–January 1990). "The Resolution of Newcomb's Paradox. Noesis No. 44.
- Langan, Christopher M. (1999). "Introduction to the CTMU". Ubiquity Vol. 1, No. 1.
- Langan, Christopher M. (2002). "The Cognitive-Theoretic Model of the Universe: A New Kind of Reality Theory". Progress in Complexity, Information, and Design 1.2–1.3.
- Langan, Christopher M. (2004). "Cheating the Millennium: The Mounting Explanatory Debts of Scientific Naturalism". In Uncommon Dissent: Intellectuals Who Find Darwinism Unconvincing, edited by William Dembski. ISI Books.
- McFadden, Cynthia. (December 9, 1999). "The Smart Guy". 20/20.
- Morris, Errol. (August 14, 2001). "The Smartest Man in the World". First Person.
- O'Connell, Jeff. (May 2001). "Mister Universe". Muscle & Fitness.
- Quain, John R. (October 14, 2001). "Wise Guy". Popular Science.
- Sager, Mike. (November 1999). "The Smartest Man in America". Esquire.
- Wigmore, Barry. (February 7, 2000). "Einstein's brain, King Kong's body". The Times.
- This pronunciation appears in Sager 1999. The acronym can also be spelled out (C-T-M-U) for clarity.
- McFadden 1999. 20/20 gave Langan an IQ test and reported that "his score was off the charts, too high to be measured. Neuropsychologist Dr. Bob Novelly was astounded", saying, "Chris is the highest individual that I have ever measured in 25 years of doing this." Sager 1999, Wigmore 2000, and Brabham 2001 also make much of Langan's IQ.
- Sager 1999.
- Quain 2001.
- Wigmore 2000.
- Brabham 2001.
- O'Connell 2001.
- McFadden 1999.
- Morris 2001.
- Langan 2002.
- Langan 2004.
- Langan 2002, p. 13. Langan argues that 'even so-called "nonstandard" logics, e.g. modal, fuzzy, and many-valued logics, must be expressed in terms of fundamental two-valued logic to make sense.'
- Langan 2002, p. 13.
- Langan 2002, p. 50.
- Langan 2002, pp. 15, 31–32.
- Langan 2002, p. 53, n. 6.
- Langan 2002, pp. 42–47.
- Langan 2002, p. 16.
- Langan 2002, pp. 20–22.
- Langan 2002, pp. 15, 22–23. Langan calls comprehensiveness "less thorough but also less undecidable" than the completeness prohibited by Gödel's first incompleteness theorem.
- Langan 2002, p. 12.
- Langan 2002, pp. 23–24.
- Langan 2002, p. 21.
- Langan 2004, p. 252.
- Langan 2002, p. 27.
- Langan 2002, p. 42.
- Langan 2002, pp. 37–38.
- Langan 2002, p. 37; Langan 2004, p. 253.
- Langan 2002, pp. 35–37.
- Langan 2002, pp. 6–7.
- Langan 2002, pp. 27–30.
- Frequently Asked Questions in Cosmology: What is the Universe expanding into?.
- Eddington 1933, pp. 90–92; Langan 2002, p. 27. In Eddington's words: "Smaller and smaller. Faster and faster." Though Eddington does not accept what he calls the theory of the "shrinking atom", he plays with the implications.
- Langan 2002, p. 28, diagram caption.
- Langan 2002, p. 20.
- Langan 2002, pp. 19, 33.
- Langan 2002, p. 33.
- Langan 2002, p. 36.
- Langan 1999.
- Cognitive-Theoretic Model of the Universe official site