Two For One: Crackpot Physics and Crackpot Set Theory

I was asked by a reader to take a look at yet another crackpot theory of everything. This time, it’s the Cognitive Theoretic Model of the Universe. This one is as cranky as any, but it’s actually got some interestingly silly math to it.

Stripped down to its basics, the CTMU is just yet another postmodern
“perception defines the universe” idea. Nothing unusual about it on that
level. What makes it interesting is that it tries to take a set-theoretic
approach to doing it.

The real universe has always been theoretically treated as an object, and specifically as the composite type of object known as a set. But an object or set exists in space and time, and reality does not. Because the real universe by definition contains all that is real, there is no “external reality” (or space, or time) in which it can exist or have been “created”. We can talk about lesser regions of the real universe in such a light, but not about the real universe as a whole. Nor, for identical reasons, can we think of the universe as the sum of its parts, for these parts exist solely within a spacetime manifold identified with the whole and cannot explain the manifold itself. This rules out pluralistic explanations of reality, forcing us to seek an explanation at once monic (because nonpluralistic) and holistic (because the basic conditions for existence are embodied in the manifold, which equals the whole). Obviously, the first step towards such an explanation is to bring monism and holism into coincidence.

Right from the start, we can see the beginnings of how he’s going
to use a supposedly set-theoretic notion. And also, right from
the beginning, we can see exactly the kind of semantic games
he’s going to play. He manages to say pretty much nothing about
the universe – all he’s doing is playing with the semantics
of the words “Universe”, “real”, “holistic”, etc.

I particularly love this next bit.

When theorizing about an all-inclusive reality, the first and most important principle is containment, which simply tells us what we should and should not be considering. Containment principles, already well known in cosmology, generally take the form of tautologies; e.g., “The physical universe contains all and only that which is physical.” The predicate “physical”, like all predicates, here corresponds to a structured set, “the physical universe” (because the universe has structure and contains objects, it is a structured set). But this usage of tautology is somewhat loose, for it technically amounts to a predicate-logical equivalent of propositional tautology called autology, meaning self-description. Specifically, the predicate physical is being defined on topological containment in the physical universe, which is tacitly defined on and descriptively contained in the predicate physical, so that the self-definition of “physical” is a two-step operation involving both topological and descriptive containment. While this principle, which we might regard as a statement of “physicalism”, is often confused with materialism on the grounds that “physical” equals “material”, the material may in fact be only a part of what makes up the physical. Similarly, the physical may only be a part of what makes up the real. Because the content of reality is a matter of science as opposed to mere semantics, this issue can be resolved only by rational or empirical evidence, not by assumption alone.

After a particularly egregious exercise in english semantics, in which
he does nothing but play with word meanings, coming nowhere near
actually saying anything, but using lots of impressive-looking
words, he concludes that it “is a matter of science as opposed to mere semantics”. Rich!

He spends some more time rambling about semantics of words like “physicalism”, “materialism”, and “containment”, before finally getting to
the part that’s got any math content at all.

Now for a brief word on sets. Mathematicians view set theory as fundamental. Anything can be considered an object, even a space or a process, and wherever there are objects, there is a set to contain them. This “something” may be a relation, a space or an algebraic system, but it is also a set; its relational, spatial or algebraic structure simply makes it a structured set. So mathematicians view sets, broadly including null, singleton, finite and infinite sets, as fundamental objects basic to meaningful descriptions of reality. It follows that reality itself should be a set…in fact, the largest set of all. But every set, even the largest one, has a powerset which contains it, and that which contains it must be larger (a contradiction). The obvious solution: define an extension of set theory incorporating two senses of “containment” which work together in such a way that the largest set can be defined as “containing” its powerset in one sense while being contained by its powerset in the other. Thus, it topologically includes itself in the act of descriptively including itself in the act of topologically including itself…, and so on, in the course of which it obviously becomes more than just a set.

First – he gets the definition of set wrong. He’s talking about naive
set theory
, which we know is unsound. And in fact, he’s talking
about exactly the kinds of inclusion issues that lead to the unsoundness
of naive set theory!

Then he uses semantic word-games to argue that the universe can’t be a set according to set theory, because the universe is the largest thing there is, but set theory says that you can always create something larger by taking a powerset. What does he conclude from this pointless exercise? That playing
word-games doesn’t tell you anything about the universe? No, that makes
too much sense. That naive set theory perhaps isn’t a great model for the
physical universe? No, still too much sense. No, he concludes that this
problem of word-games means that set theory is wrong, and must be
expanded to include the contradiction of the largest thing being both smaller
than its powerset and larger than its powerset.

Yes, the solution is to take an unsound mathematical theory, and make it
doubly unsound.

In the Cognitive-Theoretic Model of the Universe or CTMU, the set of all sets, and the real universe to which it corresponds, take the name (SCSPL) of the required extension of set theory. SCSPL, which stands for Self-Configuring Self-Processing Language, is just a totally intrinsic, i.e. completely self-contained, language that is comprehensively and coherently (self-distributively) self-descriptive, and can thus be model-theoretically identified as its own universe or referent domain. Theory and object go by the same name because unlike conventional ZF or NBG set theory, SCSPL hologically infuses sets and their elements with the distributed (syntactic, metalogical) component of the theoretical framework containing and governing them, namely SCSPL syntax itself, replacing ordinary set-theoretic objects with SCSPL syntactic operators. The CTMU is so-named because the SCSPL universe, like the set of all sets, distributively embodies the logical syntax of its own descriptive mathematical language. It is thus not only self-descriptive in nature; where logic denotes the rules of cognition (reasoning, inference), it is self-cognitive as well. (The terms “SCSPL” and “hology” are explained further below; to skip immediately to the explanations, just click on the above links.)

(His text refers to “the above links”, but in fact, the document doesn’t
contain any links.)

This is pure muddle. It’s hard to figure out what he even thinks he’s doing. It’s clear that he believes he’s inventing a new kind of set theory, which he calls a “self-processing language”, and he goes
on to get very muddled about the differences between syntax and semantics,
and between a model and what it models. I have no idea what he means by
“replacing set-theoretic objects with syntactic operators” – but I do know
that what he wrote makes no sense – it’s sort of like
saying “I’m going to fix the sink in my bathroom by replacing the
leaky washer with the color blue”, or “I’m going to
fly to the moon by correctly spelling my left leg.”

From there who moves to adding a notion of time, which he
seems to believe can be done using nothing but set theory. Unfortunately, that makes no sense at all: he wants to somehow say that sets have
time properties, without modifying the sets, modeling the time property,
or in fact anything at all – once again, he just throws around lots of
terminology in meaningless ways:

An act is a temporal process, and self-inclusion is a spatial relation. The act of self-inclusion is thus “where time becomes space”; for the set of all sets, there can be no more fundamental process. No matter what else happens in the evolving universe, it must be temporally embedded in this dualistic self-inclusion operation. In the CTMU, the self-inclusion process is known as conspansion and occurs at the distributed, Lorentz-invariant conspansion rate c, a time-space conversion factor already familiar as the speed of light in vacuo (conspansion consists of two alternative phases accounting for the wave and particle properties of matter and affording a logical explanation for accelerating cosmic expansion). When we imagine a dynamic self-including set, we think of a set growing larger and larger in order to engulf itself from without. But since there is no “without” relative to the real universe, external growth or reference is not an option; there can be no external set or external descriptor. Instead, self-inclusion and self-description must occur inwardly as the universe stratifies into a temporal sequence of states, each state topologically and computationally contained in the one preceding it (where the conventionally limited term computation is understood to refer to a more powerful SCSPL-based concept, protocomputation, involving spatiotemporal parallelism). On the present level of discourse, this inward self-inclusion is the conspansive basis of what we call spacetime.

I can’t make head or tails out of this. It’s just word-games, trying to
throw in as many fancy-sounding terms as possible. What on earth does Lorentz invariance have to do with this muddle? LI means something quite specific,
and he’s done nothing to connect any of this rubbish to it. He’s just
throwing around words: “conspansion”, “lorentz invariance”,

But it gets worse. We get yet more of his confusion about just what “syntax” means:

Every object in spacetime includes the entirety of spacetime as a state-transition syntax according to which its next state is created. This guarantees the mutual consistency of states and the overall unity of the dynamic entity the real universe. And because the sole real interpretation of the set-theoretic entity “the set of all sets” is the entire real universe, the associated foundational paradoxes are resolved in kind (by attributing mathematical structure like that of the universe to the pure, uninterpreted set-theoretic version of the set of all sets). Concisely, resolving the set-of-all-sets paradox requires that (1) an endomorphism or self-similarity mapping D:S–>rÎS be defined for the set of all sets S and its internal points r; (2) there exist two complementary senses of inclusion, one topological [S Ét D(S)] and one predicative [D(S) Éd S], that allow the set to descriptively “include itself” from within, i.e. from a state of topological self-inclusion (where Ét denotes topological or set-theoretic inclusion and Éd denotes descriptive inclusion, e.g. the inclusion in a language of its referents); and (3) the input S of D be global and structural, while the output D(S) = (r Éd S) be internal to S and play a syntactic role. In short, the set-theoretic and cosmological embodiments of the self-inclusion paradox are resolved by properly relating the self-inclusive object to the descriptive syntax in terms of which it is necessarily expressed, thus effecting true self-containment: “the universe (set of all sets) is that which topologically contains that which descriptively contains the universe (set of all sets).”

Yes, lucky us, more wordplay!

The thing to notice here is right in the first sentence: “Every object in spacetime includes the entirety of spacetime as a state-transition syntax“. Spacetime isn’t a syntax. Like I said before,
it’s like talking about spelling your leg. An object can’t be a syntax. A syntax is a method of writing down a sequence of symbols that expresses some
logical statement. An object in spacetime can’t “include the universe as a state transition syntax”.

What I think he’s trying to say here is that we can describe objects in
the universe as state transition systems, in which the state of an
object plus the state of the universe can be used to compute the next state of
the object. But he doesn’t understand that a syntax and a system are different
things. And he seems to think that the idea of describing the universe as a
state transition system is somehow profound and original. It’s not. I’ve read papers proposing state-transition semantics for the universe dating back to
the 1950s, and I’d be surprised if people like von Neumann hadn’t though of it
even earlier than that.

The rest of that paragraph is yet more of his silly word-games, trying
to cope with the self-created paradox of inclusion and size in his
mangled set theory.

At this point, I’m going to stop bothering to quote any more of his
stuff. The basic point of his argument, and the basic problems that pervade it are all abundantly clear after this much, and you’ve already
experienced as much fun as your going to by laughing at his foolishness.

To recap: this “theory” of his has three problems, each of which is
individually enough to discard it; with the three of them together, it’s
a virtual masterpiece of crap.

  1. The “theory” consists mostly of word-games – arguing about
    the meanings of words like “universe” and “inclusion”, withou
    actually explaining anything about how the universe
    works. It’s a theory with no predictive or descriptive value.
  2. The “theory” is defined by creating a new version of set theory,
    whose axioms are never stated, and whose specific goal guarantees
    that it will be an unsound theory. Unsound mathematical theories
    are useless: every possible statement is provable in an unsound theory.
  3. The author doesn’t understand the difference between syntax
    and semantics, between objects and models, or between statements
    and facts – and because of that, the basic statements in his
    theory are utterly meaningless.

42 thoughts on “Two For One: Crackpot Physics and Crackpot Set Theory

  1. Frederick Ross

    “The predicate “physical”, like all predicates, here corresponds to a structured set.”
    Och, let’s see you get that one to fly in an arbitrary topos, laddy! And I suppose those guys who are attempting to construct a quantum mechanics in topos theory are just chopped liver who don’t count as a non-set based model of the universe?
    I admire your sense of public service for even addressing this rubbish, but feel that it may be better directed towards, say, picking up litter on the street.

  2. Benoit Essiambre

    Laplace proposed something like a state-transition system as a presumption to probability theory in 1814!
    “We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.”'s_demon

  3. Blake Stacey

    For a while, there was a Wikipedia article on the CTMU; once it got noticed, it was quickly re-filed under “Bad Jokes and Other Deleted Nonsense”. Highlights included the following:

    The universe can also be thought of as the “set of all information”. The CTMU brings together all the fields of science in the sense that it blurs all the lines between all the fields to a point where they become indistinguishable. Hence the reason it can be called the “unified field theory”.

    And this:

    Since the CTMU cannot be proven under the traditional scientific method (involving an observer and that which is observed because in the CTMU observer = observed) it proposes to prove itself. Hence the CTMU can be thought of as supertautological; an axiom of choice; or self-proving.

    My Wikipedian friends tell me that things got a little nasty when the creator of this, ahem, theory showed up under an alias to defend his, ahem, work. I told the story (Google, Google, aha!) at Pharyngula last year. Incidentally, the person in question — Christopher Michael Langan, self-described autodidact — is a member of ISCID, the moribund Intelligent Design society.

  4. Torbjörn Larsson, OM

    An act is a temporal process, and self-inclusion is a spatial relation. The act of self-inclusion is thus “where time becomes space”; for the set of all sets, there can be no more fundamental process.

    I will give him credits for reinventing the block universe.
    But it’s still an “F”.

  5. Cye Stoner

    This sort of thing always brings one interesting thought to my head.
    Is time continuous or discrete?
    It has interesting statistical implications regarding our ability to make claims of truth sort of like Laplace’s ethical writings on probabilities. A countable vs uncountable sample makes a HUGE difference in the ‘prediction accuracy’ of most claim we make as thoughtful beings.

  6. Uncle Al

    Contemporary physical theory justifies near anything. If the math stinks go with perturbation (e.g., string theory) or a Yukawa potential (e.g., compactified dimensions). Avoid falsification with a log-log chart (e.g., proton decay half-life and Super-Kamiokande).
    Talk is crap. Stop screwing around under the bright corner streetlight. Take a flashlight to the dark middle of the block where the answer sits.
    Predictions are lubricated to avoid seizure, postulates cannot escape. If your classical (Einstein) or quantized (string theory and BRST invariance) gravitation postulates isotropic vacuum and the Equivalence Principle, affine and teleparallel gravitations don’t. The disjoint non-overlap is falsfiable. A vast acreage of journal fillings is empirically wrong. The tests are explicit… though predicted divergent amplitudes are well below detectability, with three exceptions:
    1) 15 years observation of binary pulsar PSR J0737-3039A/B for relativistic spin-orbit coupling,
    2) 90 days of parity Eotvos experiment opposing space group P3(1)21 (right-handed screw axes) and P3(2)21 (left-handed screw axes) quartz. Affine and teleparallel vacua have anisotropic chiral backgrounds. Left and right shoes fit upon a left foot with different energies. Try walking a straight line (eyes closed!) wearing two left shoes.
    3) A week of parity calorimetry experiments opposing single crystals of space group P3(1)21 and P3(2)21 organic chemical benzil. An undergrad lab could falsify both General Relativity and string theory for chump change over Christmas break.
    Stop whining. Somebody should look.

  7. Torbjörn Larsson, OM

    Is time continuous or discrete?

    AFAIU Lorentz invariance predicts a continuous spacetime, as otherwise you would have a preferential frame. The continuing failure of loop quantum gravity (which seems to build on discretization of spacetime in an attempt to quantize it) to beat that very problem seems to support this.

  8. Coin

    Methinks you have way too much free time on your hands.

    Technically, MarkCC is being paid to spend his free time on this blog. What’s your excuse? 😛

    Neither — time is a statistical artefact.

    Hm, what do you mean by this?
    I can think of a couple interesting ways in which one could make a statement like that make sense, but I don’t see how it answers the question. If it’s a statistical artifact, doesn’t that imply there’s some sample space or somesuch that you’re doing statistics on? Doesn’t the question just become, is that sample space [or whatever] continuous or discrete?

  9. Aaron

    Well, not knowing anything about higher level theories or crap, for that matter, as this is called, I do have some to say. first, I have often been interested in learning much physics and math to help come to a unified theory of everything, but I don’t, purely because it seems obvious and intuitive that the universe can never be described by its parts and must therefore be its own self descriptive theory. This would mean that all it really is is syntax, not a system, as would all its parts be. the ultimate syntax is the universe and all in it, to infinitely deeper levels, as pure physicists and mathmaticians seem to enjoy complicating things in order to ‘better’ explain the universe. They really muddle everything by trying to use objects and set theories to describe that which is self descriptive by definition. the universe and all in it is pure syntax – its own syntax which cannot be defined from within. An object IS syntax, it equals syntax; that “method” which is the universe. matter, wave particle duality and all theories are just a limited attempt at DESCRIBING properties of that whole. A state transition syntax would be the universe as a whole at the same time as being fully embodied in each of its parts in its syntax. This is all word games because we are attempting to best describe, not define. Therefore we define the universe by existing and it defines us by existing. My question then is what does it mean to exist? it is to be a part of this “syntax”. this undefineable yet fully ordered method that is the universe. One philosopher once said, “god is that which no greater can be defined. I believe in “god”. “god” is that “syntax”, that order which is seen through the “universe”. In my opinion we spend way too much effort try ing to “unblur” the lines which are by nature blurred; there are no lines between fields.

  10. Jeff

    God is the Universe and the Universe is God
    Mankind is Gods ATTEMPT to understand the Universe
    It gets no clearer than this…

  11. Old Bogus

    Actually, all this makes perfect sense . . . if your stoned. But afterward, WTF? Get back to you, uh, later.

  12. Jonathan Vos Post

    Re: #14: “God is the Universe and the Universe is God”
    Not a bad one sentence condensation of a more sophisticated argument by Spinoza [24 November 1632 – 21 February 1677].
    As the Stanford Encyclopedia of Philosophy begins its article on this genius:
    “Baruch (or Benedictus) Spinoza is one of the most important philosophers — and certainly the most radical — of the early modern period. His thought combines a commitment to Cartesian metaphysical and epistemological principles with elements from ancient Stoicism and medieval Jewish rationalism into a nonetheless highly original system. His extremely naturalistic views on God, the world, the human being and knowledge serve to ground a moral philosophy centered on the control of the passions leading to virtue and happiness. They also lay the foundations for a strongly democratic political thought and a deep critique of the pretensions of Scripture and sectarian religion. Of all the philosophers of the seventeenth- century, perhaps none have more relevance today than Spinoza.”
    Near the end of the wikipedia article on Spinoza (as of today) we have this:
    “Spinoza has had influence beyond the confines of philosophy. The nineteenth century novelist, George Eliot, produced her own translation of the Ethics, the first known English translation thereof. The twentieth century novelist, W. Somerset Maugham, alluded to one of Spinoza’s central concepts with the title of his novel, Of Human Bondage. Albert Einstein named Spinoza as the philosopher who exerted the most influence on his world view (Weltanschauung). Spinoza equated God (infinite substance) with Nature, consistent with Einstein’s belief in an impersonal deity. In 1929, Einstein was asked in a telegram by Rabbi Herbert S. Goldstein whether he believed in God. Einstein responded by telegram: “I believe in Spinoza’s God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with the fates and actions of human beings.” Spinoza’s pantheism has also influenced the environmental theory. Arne Næss, the father of the deep ecology movement, acknowledged Spinoza as an important inspiration. Moreover, Argentinian writer Jorge Luis Borges was greatly influenced by Spinoza’s world view. In many poems and short stories, he makes constant allusion to the philosopher’s work, not as a partisan of his doctrines, but merely in order to use these for aesthetical purposes.”
    Unfortunately, I cannot accept the 2nd sentence in #14: “Mankind is Gods ATTEMPT to understand the Universe.”
    Even after inserting the the apostrophe — “Mankind is God’s ATTEMPT to understand the Universe” — we have an incoherent muddle, which falsely elevates human beings to the “crown of creation” and degrades the theological dogma of omniscience.
    To give this the benefit of the doubt, it could be a half-hearted summary, through a glass darkly, of the “Omega Point” notion of Pierre Teilhard de Chardin [1 May 1881 – 10 April 1955] and/or “Star Maker” — the great cosmological science fiction novel by Olaf Stapledon, written in 1937.

  13. Jeff

    The inteligent human endeavers in the pursuit of knowledge.
    This is a fact.
    Universe=God (missing third line[Exactly equal])
    Given this equivelance lets reset the second sentance.
    Mankind is the universe’s attempt to define itself.

  14. Jeff

    Let me be a little more specific since my last comment did not post.The Universe is God and God is the Universe OR Universe is exactly equal to God. Pantheism may descibe this on the surface but fails when the history of man is introduced. Mankind has historicaly assigned “God” to facets of his reality that was not well understood by the populace. Goddess of love,God of war…ect.Modern religion teaches us societal lessons. Religion is therfore a tool,just as science is a tool. These tools are to be used in the advancement of humanity and his thought process.
    Since we do not fully understand the Universe, then by the process that has proven fruitful in the past we must posulate the Universe..God.
    I suppose since this blog is titled set theory we should attempt to speak in sets. Therfore…
    all subsets=Universe
    I did not mean to elevate humanity to the crown of creation as Jonathan may have alluded,Mankind is a subset,A subset amongst many subsets.In religion we are created in Gods image.In science we are created from a specific portion of material from the Universe.We cannot exist without the particle preciptation from space.It is not concievable and we will not achieve the ability to leave this planet until the knowledge is gained to fix what our forefathers understandably screwed up. Granted we would not have spiritualy and technicaly advanced to this point if our forefathers did not produce,However the knowledge required for ascention,space travel must be developed on earth or at least within the spheres that are accessable. It is only through constant correction of past environmental flaws that this knowledge will be attained. By environment I mean all aspects,transportation,communication,energy,trees,water,air,ect.As we spiritualy and technically evolve we are driven by the same goals……Knowledge. Knowledge to what end? Who will answer ? Thank you for the oppertunity to express my thoughts, I will go away now, Back to what Nasa calls the Heliophysics.

  15. Kiriel

    Thank you very much Mark. I referenced to the introduction that was lacking maths. Here is the ‘entire’ paper that Mr. Langan always seems to refere in his discussion that contain lots of details and elaborations of the introductory remarks you made:
    Which I found from:
    I have had this looming feeling that if he is not able to communicate clearly his ideas then he does, with high probability, not really understand them himself, and there is followingly a high probability that their use will lead to lots of wrongful conclusions.
    Thanks again Mark for taking your time to clear confusions and illustrate to us Mr. Langans understanding about what he is talking about.

  16. Escuerd

    I’ve tried reading this thing before, and the writing was too opaque for me to get anything coherent out of it. A lot of the same bizarre, and evidently out of place jargon usage like what you mention was a bit troubling.
    Langan is a minor media darling because he has scored high on IQ tests, but works or has worked a relatively menial job (bouncer for a bar).
    When I looked at this paper and noticed his fawning over “intelligent design” and that William Dembski is one of his references, a few things started to make sense.

  17. Blake Stacey


    Langan is a minor media darling because he has scored high on IQ tests, but works or has worked a relatively menial job (bouncer for a bar).

    When my Wikipedian friends started having trouble with Langan’s #1 fan (whose IP address resolved to Langan’s home town, strangely enough), my first reaction upon hearing the story was, “Hey, he’s that guy from TV! You know, the super-genius bar bouncer, the real-life Will Hunting. He’s that guy!
    Read more widely.

  18. Blake Stacey

    This is too priceless. I was looking up Errol Morris documentary clips online, and I found that he’d done a show on Christopher Langan. YouTube has it in three parts; in the second, he reveals himself ignorant of the brain/body ratio concept, but it’s not until the third that he (a) brings up the CTMU and (b) turns into a raving eugenicist.
    “Every human being is an endomorphic image of the Mind of God.”
    I’m not sure how you can claim that all humans share the same unified, divine essence while in the next breath advocating a priesthood of intellect and, to put it bluntly, stating that stupid people shouldn’t breed, but hey, I’m not the Smartest Man in the World.

  19. eddie

    I don’t know about this ‘god’ thing but;
    Yes. Time is discrete or continuous.
    It’s basic QM. Bound states have discrete energy levels and limited transitions between them, while free systems don’t have such limits.
    Of course, you need to have an idea about what’s free and what’s bound. I think you can only ever get locally free systems so isn’t time only locally continuous?
    Just a thought.

  20. isotelesis

    His work has more to do with philosophy than math/physics, so while I understand why you consider it cranky and uses awkward language, much of filawzafy is generally unnecessarily verbose and rarely explains ‘how’ reality works deeply.
    You are missing an opportunity for inspiration, while his writing is of little consequence, it is related to ideas (such as hyperincursion, n-dimensional quantum holographic computing, metacybernetics, plectics, self-dual ontology) which may at the very least give a better context for his concept…which is in dire need of good math…there are some basic terms which one might find useful for such emerging fields.
    His goal of dealing which the problem of cartesian duality for example is similar to what Chu Space theory attempts to resolve.
    I would like to know whether you consider the following ‘good math’ or ‘bad math’, a perhaps a comment or two on filawzafy.

  21. isotelesis

    More Filawzafy applied to Computer Science:
    *Protocomputing* and ontologic observation written by Yukio-Pegio Gunji
    “Biologically motivated computing presents us with a measurement process in science. It triggers an epistemological shift from state-oriented physics to measurement-oriented physics, in which we can find a parallelism with Wittgenstein’s shift from rule following to a language game. We argue here that an approximation or computing process can be viewed as a language game and propose an idea of proto-computing which is metaphorically formalized through disequilibration between tree- and loop-program, as a model for measurement-oriented computing.” (1996)

  22. holodeck

    What if you take the objects of the universe to be information? Then you can talk about them in terms of syntax.

  23. Doug

    Mark writes: “Unsound mathematical theories are useless: every possible statement is provable in an unsound theory.”
    This assumes that either a mathematical theory works with axioms as sound (true) or unsound (false) with no other truth value possible for the axioms. It also assumes that the notion of soundness (truth) actually applies to axioms. Both come as problematic. Compare something like ZFC and non-well founded set theory. One has the axiom of foundation, and one has the axiom of anti-foundation. If axioms have to work out as either True or False, then one of the theories logically works out as wrong and useless. If you want to select ZFC as correct, then interval arithmetic and its applications works out as wrong and useless, as does any use of a fuzzy number (since the concepts of a fuzzy number and an interval number rely on statements like there exists an number n such that n={n}, which can’t happen in ZFC if it’s consistent… and if it’s not consistent, it’s wrong by it’s own logic) and that implies fuzzy process controllers and other applications of fuzzy numbers work out as wrong also, even though they exist. Go figure.

  24. P. George Stewart

    I dunno, it doesn’t seem all that nonsensical to me, and he seems to be doing quite the opposite of mystifying – he seems to me to be trying to take great pains to make what he’s saying clear, only it’s still extraordinarily condensed, and I think you’ve got to have a fairly broad education to catch the subtle allusions he’s making, and read it several times. Bear in mind, IQ is strongly related to analogical thinking. We tend to think “clever=fast reasoning”, but actually being intelligent means GETTING IT RIGHT. By hook or by crook, somehow, the genius is the person who notices _real patterns_, real similarities and real differences. (To be more precise, somehow they are able to consistently dream up possible patterns that actually do fit reality.)
    So that being said, it seems to me that what he’s doing is asking us to notice what he’s noticing, some deep structural properties of this whateveritis we see around us.
    I think the basic thing you have to start off with is the old philosophical question of how is it that the mind can conform itself to reality, how can it _know_? On the face of it, there seems no reason why knowledge should be possible at all! That it is possible, means there’s some kind of deep structural self-similarity between our thinking processes and the “laws” of the universe, the syntax of matter, so to speak (the manner in which it arranges itself, the patterns). So: the experienced Universe is a kind of language, the patterns matter shifts in follow laws that are deeply similar to the laws of thought.
    The ultimate upshot is that we are little chips of God (putting it poetically). And ultimately, there’s nothing wrong with anything.
    The Eugenics, though, does make me uncomfortable, and I’m not sure how he would derive it from the above philosophy. But OTOH, it’s not as if many very intelligent people haven’t thought along eugenicist lines in the past (going right back to Plato, even). We moderns prefer freedom – which is to say, we prefer to allow people to “seek happiness” – i.e. find that combination of activities that satisfies them. We trust that this “blind” (therefore highly randomised) process yields us a maximum of possible problem-solving algorithms (as housed in the various brains, as played out in the memes they generate). Eugenics seems to miss the unforeseen; unlike freedom, which works somewhat like the immune system – it throws out possibilities, and some of them may well be the right counters to unforeseen invaders.

  25. Ken Myers

    I thought Hegel laid the metaphysical enterprise to rest. I must agree with Mark, that the problems are not that the guy is trying to
    create anything new, it is that he is not creating thing new(no self-ref intended). He is simply creating empty sets, i.e. creating “observational terms” devoid of meaning …
    My Theory
    There exist purple santa wrappers that describe a self-similar quotidian map, such that the map is the territory, and as the map
    is the territory, there must exists a “term” in the map that contains the entire universe in a squirrellian “NUT”-shell …

  26. Chris Langan

    Hello, Mark. Your blog was just belatedly called to my attention. Having gone over some of it, I have a little friendly advice for you.

    First, when it comes to philosophy, particularly metaphysical theorization about reality at large, one doesn’t want to get too carried away with one’s supposed ability to distinguish “good math” from “bad math”. Beyond the structural and inferential rules of a given formal (uninterpreted) mathematical theory, the difference is obviously a matter of interpretation: can the theory be consistently interpreted in a given domain of discourse, in this case reality at large? If so, and if the theory in question is regarded as fundamental or foundational (as in “the foundations of mathematics”), then what are the implications for the domain – is the theory “fundamental” with respect to the entire domain under the operative (semantic or interpretative) mapping(s)? If not, then can it be extended and/or qualified in such a way that it does apply to the domain, i.e., so that it “explains” the entire domain? Although one would never know it from reading your remarks, these questions are central to the essay you’re criticizing.

    One of the things that I’m actually saying in this little essay is that while any version of set theory can be at least partially interpreted in the physical universe – specifically, in the set of material objects, the direct observations that can be made of them, and the logical implications of those observations, considered as basic elements of empirical science – no mere set theory qualifies as “fundamental” in the sense of accommodating a full explanation of reality at large (I trust you understand how and why physical objects form a “set”, at least in classical theories). Why not? To put it in a nutshell, it’s because set theories, unlike category theory – which “packages together” objects and morphisms and effectively reduces one to the other – make a hard distinction between elements and mappings. This problem has long been a central theme in my work, a fact apparently lost on you and several of your more idiotic commentators.

    Given the issue of self-duality, can category theory, and particularly topos theory, pick up where set theory leaves off? Almost but not quite, at least as it currently exists. The reasons are rather technical, and if I had to guess, I’d have to say that I probably know more about them than do you or any of your commentators. That’s because I have the ability to interpret (or model) arbitrary mathematical theories in my own, identify any ingredients missing from the resulting model, and analyze their explanatory functions. Needless to say, this takes more than rote familiarity with various mathematical structures and algorithms, and for that matter, the ability to write boilerplate code for a company like Google. It takes real insight, and a far better understanding of reality (and my work in particular) than you’ve troubled yourself to display here.

    I understand that despite my best efforts to be clear in my writing, it’s hard for some people to follow. I’ll be improving on that. But no amount of petulant incomprehension can provide you with an excuse for the wild hatchet job we see above. Suffice it to say that having scanned your blog, I’m quite certain that you lack the currency to cover the check your mouth has written on this particular topic, and possibly on other topics as well. This is something you’d be very wise to bear in mind the next time you decide to mislead your readers in so excessive and shameful a manner, at least regarding me and my writings. While I don’t necessarily want to make you look bad, I’m not incapable of doing so. You can test this if you like, but only with a certain amount of risk.

    Look, here’s a general rule of thumb that any decent blogger should keep in mind: read what you criticize very carefully, and even if you find it hard to follow, avoid working yourself up into such a resentful faux-authoritative frenzy that you unwittingly dig a hole for yourself. In particular, don’t simply assume that your target is a dummy who doesn’t know any math, and therefore can’t possibly make you look stupid. Trust me, there are people out there who can make you, Mark Chu-Carroll, look quite stupid indeed, even on mathematical topics, and you don’t want to aggravate them too severely if you can possibly avoid it. Be controversial if that’s what floats your boat, but don’t pee down any rabbit hole that might turn out to contain a grizzly bear. In the long run, it just isn’t good for your reputation.

    Thanks for your attention, and have a nice day.

    1. MarkCC Post author

      In other words:

      “Nya, nya, I’m smarter than you, so you shouldn’t insult me for being stupid”.

      You completely ignore all of the actual substantial criticism of your “theory”, and instead go into a long rant about how brilliant you are. If you’re so damned brilliant, why don’t you bother to actually pick a real criticism of your “theory”, and show how I got it wrong?

      But cranks like you never do that. They just go on ranting about how brilliant they are, and how all of us inferior folks are just incapable of understanding their magnificent brilliance.

      1. Chris Langan

        Well, what a marvelously uninhibited little person you are!

        But just to give you the benefit of a doubt, where’s this “real criticism” of yours actually located?

  27. Chris Langan

    That’s fine, I’m relaxed.

    It’s just that we seem to have an ongoing problem with confusion here. The problem is, I’ve been accused of taking a “set-theoretic approach” to my subject matter when in fact, I was writing about the futility of doing that (a fact which has been duly understood by numerous people who have actually read the essay, and who actually understand English).

    Obviously, this precludes legitimate criticism. In fact, if we didn’t know that Mark here was an expert on “good math”, it would look more like the discombobulated carping of somebody who hasn’t bothered to read or understand what he’s criticizing, and who then compounds the problem with various nebulous gripes, ad hominem zingers, and deferred semantic hairsplitting about, ironically enough, the syntax-semantics distinction.

    I was just a bit concerned lest people think they’re reading about my work when in reality, this thread immediately wanders across the line separating “good math” from “personality disorder”.

    Not necessarily a big deal, mind you, but probably something worth keeping an eye on in the future.

  28. Composer99

    don’t pee down any rabbit hole that might turn out to contain a grizzly bear.

    And here was me thinking no one could ever mangle metaphors the way Ben Stiller’s character “Mr Furious” did in Mystery Men.

  29. Pingback: Big Bang Bogosity | Good Math/Bad Math

  30. debaterspock

    Salutations Mark. Let me try to speak what Chris Langan has to say on your own level. There is a super simple proof of the CTMU. And that is the fact that it contains itself in its own proof. What is self-containment containing, what is the thing that contains itself? Self-containment. So self-containment contains itself in the act of self-containment. This formulation of reality then proves itself. Is there “another” cause capable of causing reality? No, because that non-self-containing cause can’t serve as its own cause, and there is no ultimate cause in an infinite regress. Please forgive Chris Langan. He’s used to speaking at higher levels. By the way, if reality were to reduce to paradox, reasonlessness, then it couldn’t formulate itself, so reality must be self-contained for the purpose of consistency.

    1. markcc Post author

      That is, like most of Langan’s stuff, utter bullshit.

      It’s a way of taking vagueness, and pretending that it’s profound, when in fact, it’s absolutely content free.

      THe thing is, you can take exactly the argument that you just presented – and turn it into an argument for pretty much any Gödel-esque “theory”. There’s nothing in the “proof” which is actually specific to CTMU. It can be applied to a thousand different mutually contradictory theories.

      It’s the classic problem that I’ve talked about on this blog many times. A “proof” is a mathematical construct. A mathematical proof isn’t just a string of words. In fact, a good mathematical proof isn’t a string of words at all.

      A proof is a sequence of precisely defined logical statements, connected by the application of precisely defined rules of inference. One of the beautiful things about a proof is that you can view a proof and check it for correctness in symbolic form, without even knowing what any of the symbols mean.

      If you think about it, that’s a pretty radical concept. And it’s absolutely critical to the mathematical concept of “proof”. A proof is pure reasoning, abstracted away from anything that could bias the reader.

      Stuff like CTMU doesn’t have to have a mathematical proof. I’m Jewish, and I certainly don’t have any kind of mathematical proof of the correctness or validity of Judaism. But then, I don’t go around and say that Judaism is a proven mathematical theory.

      The problem with CTMU is that it’s presented as a mathematical/scientific theory that’s been proven. But in fact, nothing about it is well-defined. It’s all vague words that always contain enough weasel space to allow its proponents to “refute” any argument against it by saying that the arguers just don’t understand it.

      In short, it’s a gigantic fraud. It’s a content free pile of words pieced together in profound-sounding ways, whose meanings can never be pinned down enough to actually say anything that can be conclusively confirmed or refuted.


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