Introduction
America: the land of the double cheeseburger, large fries, and a diet coke: that weirdly normal land of mini-trucks, working vacations, and negative income.
Everyone wants the thing that is not the thing. Because once you have A and not-A, then you can prove anything.
This post is going to be more of an experiment: an exploration of how one can start thinking upon mastering the generator functions of OM (or at least some of them). In other words, this is your brain on Ontological Mathematics (*1). I feel I've read enough of their books such that I can start "improvising", or "riffing" on some original ideas of my own i.e. not just a dialog, but a digalog.
*1 or perhaps I should say this is your mind on Ontological Mathematics.
Thus in that spirit, we introduce the concept of the controlled paradox.
A Controlled Paradox (CP) is not an official OM concept (*2), but there are lots of places in OM (as well as philosophy and nature in general) where they appear.
*2 At least the term "controlled paradox" isn't. They do have some sections on "the thing that is not the thing", but unfortunately, I can't locate any references in my "OM text database" so I can't list any specific locations.
Controlled Paradoxes
First off, let's start with what I mean by the term controlled paradox (CP). Basically, a CP is something that is one thing at one level, and another thing, esp. it's opposite at another level. It's the fact that the contradiction is spread across two levels that makes it "controlled" and saves it from being an ordinary "uncontrolled" paradox. It's interesting to note that the term "controlled paradox" is itself a form of controlled paradox i.e. how can a paradox be controlled?
A very obvious set of levels to spread the contradiction across is physical and logical. For example, in computer science you have virtual memory (logical level) and physical memory (physical level) -- a 32-bit virtual address space can be up to 4 GB, but you can run a 32-bit process on a machine with a much smaller physical memory (today, in order to get reasonable performance, you would need at least 1GB of physical memory, but back in the 70's, mainframes would run 32-bit processes on absurdly tiny physical memories like 2 megabytes).
Some other possible levels to split across are semantic and syntactic, actual and potential, and noumenal and phenomenal.
In effect, you're decoupling the two contradictions from each other, firewalling them so to speak, with one of the levels being the "sane" level -- the level that anchors the paradox to reality, and the other level being the opposite or "crazy" level.
Some other terms in the vein of controlled paradox are "amphibious" (a creature that is of the land and of the water), "the thing that is not the thing", oxymoron, ambiguously gay, syndiffeonesis from CTMU, or "inverse duals". However, as we explore the concept further, we'll try to distinguish what makes a CP different from these other forms.
Our final goal is to examine the fundamental Controlled Paradox that lie at the heart of the universe and reality itself.
Controlled Paradox Examples
First, let's look at some "fun" examples:
- Diet Coke
> All the taste, no calories. - Barack Obama
> The first non-black black president. Or is he the first black non-black president? - Mini trucks
> Is it a truck? is it a car? - Gerunds
> A verb that acts as a noun: "running is fun" - Green Screens
> a green screen, when active, is no longer a "green screen". - Bungee jumping
> You're committing suicide but you're not committing suicide. - Zentrepreneur
> A non-capitalistic capitalist.
My favorite from this group is green screen. The purpose of a green screen is to project onto its surface a (typicalllly) non-solid, non-green background. This leads to seemingly paradoxical expressions like "when a green screen is being a green screen it's not a green screen".
The prior group are mostly silly examples. In fact, they're really just plain old oxymorons -- a kind of fake CP. They're mostly just artifacts of the limited i.e. human-based languages used to describe them. For instance, if a green screen was instead called a "projection screen" then the fact that you're projecting a non-green image on it wouldn't make it lose it's definitional nature as "something that is projected upon", and the expression "it's no longer a projection screen" wouldn't even make sense, much less be paradoxical. Even with the label "green screen", if you happen to project a static green image on it, then it would still be a "green screen". So the "paradoxical" nature of "green screen" is only skin deep and mostly an artifact of it's literal name.
What we really want are CPs that are more paradoxical "to the bone" -- paradoxical by their very nature and not merely a side effect of the language used to name or describe them.
nomos-, co-, anti-, and un-
Before we can start talking about these more authentic types of CPs, we need to take a little excursion to increase the nuance of our vocabulary. Thus we'll talk about a quaternity of qualifiers to help us distinguish among "opposites".
First off, we posit that for every concept there are four flavors: nomos-, co-, anti-, and un-.
Note: throughout this explanation we'll use the light-hearted nomos concept of "cola" as the modifying example. This nomos concept should of course be called "nomos-cola" but we'll oftentimes simply refer to it as "cola".
Nomos-
nomos (Greek for "law") is the baseline concept itself. Because it's the baseline and assumed, it's typically not explicitly stated e.g. not prefixed with "nomos-".
Co-
Next up is "co-". This is the opposite of the nomos concept but in a "partner", or "complementary" way ("complementary" is presumably where the prefix "co" comes from). Think of a dancing couple: the lead's (or nomos-dancer's) partner would be the co-dancer. Co-dancers are typically of the opposite sex, and do the opposite steps, but at the same time they follow the lead, in a mirror image sort of way: they're coordinated peers. So the co- is the opposite in a way yet still compatible, thus nomos/co pairs are naturals for forming CPs, and probably the easiest to actually physically achieve.
In keeping with the "cola" example, I would nominate diet cola as the co-cola.
Note: by our definition, in order to be a physical and realizable "cola", a substance has to semantically taste like cola. Diet-cola, or co-cola, achieves this by substituting aspartame, for sugar at the syntactic level. Nomos-cola's syntactic layer is the same as the semantic layer: cola. Nomos-cola is not a CP, thus the syntactic and semantic layer can be the same substance. The co-cola is a CP, in fact it's a co-CP (it's the version of CP that is coupling the nomos- semantically with the co-opposite syntactically).
Anti-
Next up is "anti-". This is the closest to being the "true" opposite -- the opposite that is not complementary. For cola, it becomes a little problematic to identify what the anti-cola is. This dilemma happens quite often as there isn't typically one "archetypal" or canonical breakdown for all opposites that everyone will agree on. Indeed, one candidate for "anti-cola" would be a light-colored soft drink like 7-up or Sprite (although the marketers seem to think 7-up is the "un-cola" and not the "anti-cola"). Another perhaps more over-wrought candidate for "anti-cola" would be meso soup with bitter melon per this quora answer , since meso soup is umami flavored which is considered the opposite of sweet in taste, and it's also light in color.
Un-
And finally, we have "-un". un- is for the thing that isn't the thing at all. Usually, it's a different class of thing or another thing transcendent of the original. The un-thing is often a zero or a null or an imaginary number. For cola, I would say the un-cola is water.
It can be an insightful exercise trying to come up with co-, anti-, and un- "opposites" for a given nomos-. This is a quaternity, not a simple duality. For instance, what is the "opposite" of infinity? Two obvious answers would be "zero" and "negative infinity". A duality model is not sufficiently nuanced to accommodate these two opposites, thus we need a triality of opposites (which forms a quaternity when you include the nomos-). Of course, now you have the opposite problem of having three slots to fill instead of one.
Anyway, for infinity I would answer as follows:
nomos-infinity: infinity
co-infinity: zero
anti-infinity: negative infinity
un-infinity: an imaginary number (or better imaginary infinity)
A quaternity is a more nuanced and richer model than a duality, and in the case of nomos-infinity, it can convey a very subtle distinction when you assign zero the co- vs. as the anti-, for example. Of course, as previously stated, there's typically no "right" answer, and it's kind of intuitive.
Context
There is a third thing that can also participate in a controlled paradox, and that is the context. Every experience is a syntax in a context, which is perceived semantically as an interpretation.
You can either think of the syntax and semantic in a context
or think of the syntax in a context yielding a semantic interpretation.
I'm not going to really talk about contexts much in this post, other than to note it can serve as a modifier to the syntax, or act as an substitute for syntax itself.
Note, there is one exception to this rule: at the level of the fundamental universal controlled paradox of zinfinity (which we'll talk about later), there is no external context. That is to say the universe has no external context with which it can compare itself (because if there were an external context, you would have to say that is then part of the universe and not external to it). Thus the universe can't say what it is, or how big it is by looking to some external reference, and has to split itself up into a self and alienated self, that is to say create an internal context, from which to try to understand itself.
Notice how any nomos concept has three "opposites". Thus there are three flavors of controlled paradoxes for a given nomos: co-, anti-, and un-. Co-controlled paradoxes are the easiest to achieve since the "opposite" is actually compatible with the nomos. Anti- and un- controlled paradoxes are typically harder to achieve. It doesn't necessarily follow that you actually can achieve a "real" CP for each flavor of opposite -- i.e. it may not be physically obtainable.
For instance, in the case of cola, the goal is to have the semantic of "cola taste". The un-cola of nomos-cola is water, but the only way I can see to make it semantically taste like cola is to apply a hypnotic suggestion as a context:
You can thus use the context as a way to change the interpretation (the semantic), sort of as a second syntax. We're really not going to exploit the context for now, as it will just make things too complicated, so we'll just stick with syntax and semantics.
Languages and Anti-Languages
Per OM, language is the true description of reality, that which highlights its true nature. An anti-language then is one that obscures the true nature. Most anti-languages are unintentional, a side effect of human languages with their emphasis on perception and emotions, but some are intentional. I would suggest that the language of identity politics and cancel culture is an example of an intentional anti-language, with the intent of hiding, obfuscating, and shutting down real discussion.
For the nomos-language of OM, I would say the co-language is science, the anti-language is religion, and the un-language is intuition.
Controlled Paradoxes and anti-language
So now that we've established the concept of anti-languages, the first question you have to ask of a CP is if the 'paradoxical' nature is simply a result of using an anti-language. If it is, then it's not really a "true" CP, but a "fake" CP: a side effect of a bad language. Most of the examples given thus far (e.g "mini truck") are really just artifacts of "bad" or anti language.
Computronium vs Unobtainium
Our goal now is to start categorizing CP's so we can separate the wheat from the chaff. One analogy I like is Computronium, which is basically any arche that can act as a universal substrate (*3). For our purposes we can simply consider computronium to be "good". Unobtainium, however, is the opposite. It means the concept is unobtainable. For our purposes we simply consider it to be "bad".
(*3) Another good analogy is a "holon"
So the computronium vs unobtainium question distinguishes between an uncontrolled paradox (unobtainium) and a controlled paradox (computronium), or alternatively "false" CPs (unobtainium) and "true" CPs (computronium).
Classes of Computronium CP's
Now that we have identified something as being computronium at the language level, we can now start to classify the "strength" or validity of the controlled paradox itself.
Anti-Fragility
A CP is basically something that has (at least) two levels. And if it's a language-independent CP of computronium, one of the levels has to be "sane" or "rational" or "real" (this is usually the syntactic level). However, the quality of the CP can vary depending on the "strength" of this real component. I think an interesting way to categorize this rational level is using Nicholas Taleb's concept of fragility, robustness, and anti-fragility.
A quick summary of the levels of anti-fragility: things that are anti-fragile are the "strongest" and the best. They are things that are strong but flexible. Robustness would be the second best. It's things that are strong, but metaphorically speaking, rigid and inflexible. Worst of all is fragile. It's weak and inflexible. The opposite of fragile is not robust as most people think. Taleb created a new category "anti-fragile" to denote the true opposite of fragile, for things that are robust, yet flexible. A tea cup is fragile, an oak tree is robust, and an elm is anti-fragile (because it can bend with the wind).
So once you have identified something as a language-independent computronium CP, next we look at the quality of it's "sane" (syntactic) tier. The weakest CPs are ones where this tier is fragile, the next best is where it is robust, and CPs that have an anti-fragile rational basis are the strongest. We can then talk about the half-life of the computronium. This is how "stable" the computronium is -- the amount of "time" (metaphorically if not literally) it takes for it "decompose" into unobtainium.
Nootropics and Anti-Fragility
Let's look at the utility of modeling CPs using these anti-fragile categories with the specific example of nootropics. Nootropics is an umbrella term for "smart drugs". For instance, Provigil (or Modafinil in Europe) is a smart drug that is said to be similar to the drug in the movie Limitless. Funnily enough, Provigil itself is kind of a controlled paradox in that it increases your focus by narrowing your focus. It is said to give you "tunnel vision" so you can concentrate on one thing for long periods of time without any distractions.
I think smart drugs pass the first test as a language-independent computronium (it's not a result of wordplay due to a bad anti-language). The "paradox" in this case is the tension between the assertion that a smart drug is good thing -- it's a "smart" thing to use, even in the long run (not to be confused with the "smart" that using the drug gives you), whereas we typically know from experience that drugs are bad things in the long run. Thus the paradox of nootropics is that you can take them, get all the benefits and avoid all the side effects, esp. if you're "smart" about it and don't abuse it, and have proper dosing etc.
I think the promoters of nootropics would say their base or sane tier is robust (I don't think even they would go as far as saying it's anti-fragile).
But I say this base level is actually fragile. I would say this for several reasons. First, I would say it's a dangerous game to alter your brain chemistry for a long period of time. Look at Jordan Peterson -- he suffered seizures, and other painful side effects after withdrawing from benzodiazepines. Second, to the extent that they actually do work, at least in the short term, I think there's a real danger of succeeding yourself into a corner -- you'll soon find yourself in a position where you need to take it just to run in place, and you'll quickly normalize on the amped-up version of you as your baseline, so that when you're off them you'll literally feel stupid and unproductive instead of "normal". Third, is more of a cultural level issue where we regard smart drugs as a form of mental doping. Is it ethical if you take a smart drug, when others either don't or can't?
In short, I don't think nootropics avoid the basic problem with all drugs, which is that they fall prey to the inverse stoic curve: "feel good now, pay later", with all its known negative consequences vs. the much healthier stoic curve "pay now, feel good later". I think most nootropics are the equivalent of a vitamin-enriched twinkie e.g. they're just speed with some "vitamins" mixed in to make you feel better about it.
However, my point here is not to argue that nootropics are a bust (something probably worthy of an entire post), but merely to show how two groups may differentially classify a CP. It shows how a controlled paradox can be presented as good and powerful, using an improper classification, when in fact it's bad and dangerous. Here, I'm going to also apply "computronium" and "unobtainium" at the classification level. While smart drugs are computronium at the language level, I say it's unobtainium at the classification level: it's an unsustainable illusion.
Perhaps a better way to say this is that if the syntax of nootropics is fragile, as I assert, then it will decay into unobtainium relatively rapidly, but if the syntax is robust, as its supporters say, then it will decay into unobtainium much more slowly. I would say the half-life of nootropics computronium is on the order of six months to a year. That is to say 50% of people using it for that amount of time would either recognize it as being an illusion (unobtainium), or have some sort of negative side effect as a result of using them. On the other hand, I would say the promoters of nootropics, saying the syntax is robust, would estimate the half-life as something like 10-15 years e.g. you can safely use them for at least 10-15 years before experiencing problems.
Conflation
This highlights the desirability of not only being able to properly classify a CP, but also having a proper language that can at the very least distinguish between the two tiers rather than a restricted language that conflates them to one. If you can properly see the two tiers, and see that the syntax tier is in fact fragile, then you can deduce that it's overall bad (even if the semantic tier is "good", that is to say one "bad" tier taints the entire CP). If you conflate the two levels on a CP to one tier (say to just see the semantic tier) and if said semantic tier is robust or anti-fragile, then you're misled into thinking lead is in fact gold (i.e. you ignore or can't see the fragile syntactic level, and only see the "good" semantic level). This is a trick that manipulators and marketers (anti-language experts) exploit to deceive you into thinking something is good when it isn't, or vice-versa.
There are many things in the world where the syntax and semantics are not properly distinguished. These are what I call "canonically conflated variables.
Some examples:
health and health insurance
> People confuse having good health insurance with having good health. In order to actually get health insurance, they will work 40 hours a week, inducing stress, poor eating habits, and lack of exercise as result. Thus they actually damage their actual health in order to maintain their perceived health. Would it not be preferable to have no health insurance, but be relaxed, eat properly and exercise? Of course, having both is the best, certainly as some health events are not related to being healthy e.g. being hit by a bus, but there is still a danger in conflating these two concepts.Beauty and familiarity
> People think the things they work with routinely e.g. are familiar with are the most "beautiful". In fact, it most likely is only beautiful to you because you know it. People have a tendency to learn things for arbitrary reasons, so the reasons you learned something initially are probably not good ones. A thing that is actually beautiful but unfamiliar will be avoided by most people, because then they would to make an effort to learn it.Topology vs geometry
> Topology is different than geometry. A coffee cup and a donut have the same topology (one hole) but vastly different geometry. The geometry of a pretzel (3 holes) is similar to a donut (one hole), but topologically it's complete different (as a result of having a different number of holes.)Art vs. Fine Art
> The essence of "art" is manifestation: making an abstract idea in your head actual. Thus, by this definition creating a business, or writing a computer program is a form of art. Most people only assume the "fine arts", writing, painting, music, dance etc. qualify as art.
These are all just examples of confusing the correlates for the essence, the correspondent for the coherent, the syntax for the semantics, or the correlation for the causation.
Zinfinity
This brings us to our final concern: is there a CP that is in fact anti-fragile at the syntactic level? That is to say a controlled paradox computronium that has an infinite half-life: a form of computronium that will never decay to unobtainium, in fact is impossible for it to do so.
The answer is yes: the amalgamation of zero and infinity or zinfinity has this property.
Note: zero is always the "sane" syntactic tier. You cannot have infinity as the sane syntactic tier because physical infinities are never realizable or can be actual.
This is the mother of all controlled paradoxes: when something is infinite at the same time it's zero. Nature is this. Inside it's a seething mass of energy, waves, and numbers. Externally, it always adds to zero. This is an (and the only?) anti-fragile computronium.
Note: since I assert that zero is the co-opposite of infinity, this is a nomos/co controlled paradox or a co-controlled paradox. It's interesting question as to if there is an anti-fragile CP of the nomos/anti kind or the nomos/un kind, eg infinity and neg. infinity. I don't think there is. One argument for this would be how would nature "know" which zinfinity CP to select? How would it know to use the nomos/co zinfinity CP, over the nomos/anti zinfinty CP, for example? Might these be a violation of the PSR?
I was originally going to go into great depth about zinfinity here. However, in the interest of space, and in recognition of the fact that most people who know OM are probably already familiar with the concept (even though "zinfinity" is not the official word used by OM, but a "monad"), I'll just briefly talk about one of the best of examples of zinfinty I can think of: a circle. A circle is a polygon with an infinite number of sides. However, as a result each "side" is in fact a point -- it's no longer a line segment. Thus if you were to rest a circle on a plane it would have a tendency to roll because it has no sides (line segments) to rest on. So you can see how a circle simultaneously has an infinite number of sides and yet no sides at all, that is to say it has a zinfinite number of sides.
This is really cool idea, and I think about it when running sometimes. It has zero and infinites sides at the same time -- a superposition relationship, not merely one or the other in an entanglement relationship. This is like the difference between a bit and a qbit. An ordinary bit is an entanglement of 0 and 1: it's either zero or one. A qbit is a superposition of 0 and 1: it's both zero and one at the same time. That may seem like a small distinction, but it makes for a huge qualitative difference.
Renormalization
If the universe in fact has the CP of zinfinity at it's very core, and everything derives from this, why don't we see more CP's in everyday life? It seems like most thing agree syntactically and semantically i.e. things that are syntactically "hot", are usually semantically regarded as being "hot" too. So by what mechanism do we lose the CP nature of the universe?
One possibility is the concept of renormalization. This concept come from quantum mechanics. This is the mechanism where physics eliminates zeroes and infinities from physics -- for instance, you can never have an infinite amount of physical stuff in the universe, but sometimes the math has infinities. However, if you do things right you can have another infinity cancel out the first, thus eliminating them both.
Richard Feynman considered this a trick -- a "shell game" as he called it. Ontological Mathematics is also critical of renormalization, saying that physics should be more comfortable and accepting of true infinities and zeroes. But others say it's actually a natural and intuitive concept per this response on quora
The first example is something that everyone is familiar with: microphone-loudspeaker audio feedback. You place a microphone close enough to a loudspeaker, and it will produce a high-pitched sound. What is happening here? All sounds are made of waves of different frequencies. But when there is self-interaction (audio feedback in this case), one single frequency becomes dominant, and all other frequencies die off. That’s the essence of renormalization. When there are interactions, especially run-away interactions, the final situation simplifies, and is largely independent of how it was triggered. That independence is known as “universality.” The annoying pitch in audio feedback will be the same, regardless of the initial music note or voice tone that has triggered the audio feedback.
So maybe renormalization is the mechanism whereby down at our level, several steps removed from the source, we don't see many controlled paradoxes.
Conclusion
In this post we explored the concept of Controlled Paradoxes. We distinguished between true CP's and ones merely based on language artifacts. Then we categorized the remaining CP's as fragile, robust, or anti-fragile. We then used the analogy of computronium and unobtainium and half-lives to give an intuitive feeling for how stable these CP's are. We then tried to give a concrete example by breaking down the merits or non-merits of nootropics. We then explored the (only?) CP that is anti-fragile: zinfinity. We then briefly considered the idea of renormalization, borrowed from physics, as a mechanism for why CPs are relativity rare in our everyday world.
We basically had some fun riffing on ideas and concepts from OM (and other areas too). At the very least this hopefully shows the utility of learning OM. If some of my ideas aren't very clear, at least I hoped I inspired some new ideas or perspectives in you. While I've have had ideas like these before I learned OM, I certainly didn't have the vocabulary necessary to actually express them or take them to the next level. Concepts such as semantics vs syntax, coherent vs correspondent, necessary vs contingent, percept vs concept, which I learned from OM, all are incredibly helpful in me reifying and expressing my speculative musings.
And just by the mere act of me creating this post, I came up with a few nuances that I never fully appreciated before. So put me down in favor of the Sapir-Whorf hypotheses: that language actually increases understanding, and three cheers to OM for helping me get there.
Update History:
2020-08-06: Minor edits.
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