Ontological Math Snigglets

Introduction

One of the best things about the books from the Pythagorean Illuminati are the little "mini-articles", or "meme-breaks", between the chapters on the more substantial topics. Here they'll analyze more casual faire, and kind of riff on certain ideas. Oftentimes, they'll mostly ask questions and not try to reach any specific conclusions. They actually state this is an intentional literary device to help keep the interest high, especially among readers who might have attention spans conditioned by social media and the internet.

I call them snigglets (even though they actually read more like a series of tweets). Anyway, I keep a running series of notebooks containing my thoughts, and after having completed the most recent one, I decided to take some of the more interesting entries and turn them into something like the aforementioned "snigglets".

So here is the result. The goal is to entertain, and make you think, not so much to authoritatively answer questions. Some are more essay-like and some more question-like. Most are not directly about Ontological Mathematics at all. The entries have no special order, other than the basic chronological order that I originally recorded them.

I hope you enjoy them.

Monads, Zinfinity, and Arrays

Zinfinity is the combination of zero and infinity. It's the infinite inside a zero box. Interestingly, this is very close to what a (Leibnizian) monad is.

An Array, as used in programming languages, is just a lesser version of zinfinity: it's the finite inside a unitary box.

Zinfinity is physically zero, but logically infinite.

An array is physically one, but logically "n".

An array is an immanent projection of zinfinity. It's a projection from the coherent domain down to the correspondent domain.

Both are things that have a split personality: you can think of them as being many things, yet at another level they appear as zero or one.

The universe itself has all four aspects: infinity, n, one, and zero. The universe has infinite potential inside it, with finite realization. However, there is always by definition, only one universe. However still, on the outside, it appears as a zero because the universe must sum to zero at all times.

Skills of a programmer

There are three types of thinking a programmer needs to have:

• Abstract thinking
• Critical thinking
• Knowledge

The first two types are dynamic: the ability to come up with new insights. The third (knowledge) is static. It's basically digesting the learning (or more accurately, the critical and abstract thinking) acquired by other people.

The most important in practice are critical thinking and knowledge. Knowledge is simply knowing how to do things. Unfortunately (or fortunately depending on your perspective), the permutations of knowledge, plus the dynamically changing and evolving nature of IT systems, results in the amount of knowledge needed to master it unobtainable, thus causing the need for good critical thinking to deal with novel situations. This split can be likened to the difference between genetic information, stored in the biome, and memetic information, stored in the connectome (neural circuits in the brain). I would say early in my career in the 90's you needed about 75% knowledge and 25% critical thinking. Now, I would say it's about 50-50.

Of course, if you happen to excel at any one of these types of thinking you can compensate for the others. People who are unusually good at critical thinking, for instance, can oftentimes pull a rabbit out of the hat, and manage to work on a system they have relatively little knowledge about. Unfortunately, people who are good at this have a tendency to over-rely on it, and never really just "break down" and understand the system e.g. it's a bit of a mixed blessing.

The good thing about knowledge is it is the easiest to acquire through effort. If you make enough effort, you can always acquire more knowledge -- it's the great equalizer. Critical and abstract thinking can be developed to a degree, but largely are skills you either have or don't.

Very few people have all three in a balanced fashion. Most people have one main one, and a secondary one, and then are kind of weak in the other.

Abstract thinking is good for seeing common connections among diverse fields. It comes in handy in condensing information down to a few core concepts. It's a nicety, but probably the least useful of the three in actual practice (although probably very beneficial in academic Computer Science)

Coders vs. Programmers

What's the difference between a "coder" and a "programmer"?

Some cynics might say "about 50k/year", with "programmers" being considered more prestigious, thus better paid than mere "coders".

I would say one difference is a coder is a little more knowledge-based. That is to say, a little more practical and just knows how to do things because they're familiar with them. They are the workhorses of the IT industry, and are needed for a lot of the routine and boilerplate programming tasks.

Programmers are a little more critical and abstract thinking based. They are more useful for designing and implementing novel systems.

Of course, they're not mutually excusive. Any software developer can be expected to wear coding and programming hats as necessary depending on the project. But most people will have a preference for one mode over the other.

A similar distinction can be made between the terms "Administrator" and "Analyst". An Administrator is someone who is more knowledge based, being familiar with workaday situations that are likely to arise on a daily basis, like adding users, maintaining databases etc.

An analyst is someone who is better at dissecting novel use cases.

Usually, the pairs match up. That is to say most people are either one of "coder/administrator" or "programmer/analyst".

The Gay Voice

Is the "gay voice" genetic, an accent, or a mere affectation?

Why do some gay men talk in a higher-pitched more melodious "feminine" style AKA the "gay voice", while some do not? Gay women typically do not speak with any vocal distinctions over heterosexual women. Some men who identify as heterosexual may also talk this way. Does that mean they are latently gay?

Most people seem to think it's literally genetic, as if there's some "gay gene", that in addition to making you gay, also affects your accent. If this is true, then why do some gay men not speak like this?

The answer is that the "gay voice" is an affectation. Nurses report that when people wake up from anesthesia, for several minutes they are unaware of "who" they are i.e. not in touch with their persona. They say gay men speak "normal", as well as some British people who have been living in the U.S. for a long time, who start speaking with an American accent. After a few minutes they regain full awareness, and then the accent, or more accurately the affectation, magically returns.

Is it a conscious or unconscious affectation? There are videos of Michael Jackson talking with a deep voice. It certainly would be a lot easier to pull off if it was indeed unconscious. I doubt if anyone would admit it's conscious.

Posh British accents presumably started off as an affectation to distinguish class. Is the gay voice then used to distinguish identify?

What's the difference between an affectation and an accent? Accents are just affectations that have penetrated so deeply into one's psyche that even the unconscious mind is no longer aware of them.

Genetic level means an "accent" that has penetrated further still, into your biology, so deeply it's forgotten (or remembered?) by even your future offspring.

Do Gay men from foreign countries speak in the gay voice? I knew a co-worker from Taiwan who was unable to notice a distinctly gay voice in a native-born U.S. co-worker. If gay men in other countries speak in the gay voice, it might be difficult for non-native speakers to detect it.

Is the "black voice" an accent or an affectation? It's almost certainly an accent since everyone from some predominantly black neighborhoods typically speak with one common accent, while blacks from predominantly white neighborhoods typically don't speak "black". Of course, now we venture into the politically incorrect as some people say it's racist to even suggest that there's even such thing as a "black voice".

Theories of Anything

You can have a:

TOA: Theory of Anything
TOE: Theory of Everything
TON: Theory of Nothing

Some (all?) Theories of Anything (TOA) are actually Theories of Nothing (TON). If you can explain everything cheaply, or you just assume everything is true, you in fact have a Theory of Nothing: if everybody is a star, then nobody is a star.

God is the biggest, archetypal TON. So is, arguably, the Many World Interpretations of Quantum Mechanics.

Set theory, which up until about fifteen years ago was regarded as the foundation for all of mathematics, is considered to be a model of a TOE. Category theory, being considered highly abstract even among mathematicians, has supplanted Set theory and is sometimes referred to as a meta-model of a TOA. Does this make it in fact a meta-TON? Or simply a TOA on steroids?

Interestingly, Set theory, which up until about 15 years ago was considered to be the ultimate foundation for all of mathematics, until Category theory replaced it, is considered to be "merely" a model of a TOE.

Category theory needs to be a TOA because it is not only restricted to modeling reality: it can be used to model unreality as well.

You have to thread the needle just right on a TOE. If you make it too narrow, it's no longer a TOE. But if you make it too general, it runs the risk of turning into a TOA, and thus into a TON.

On the Meaning of FI

"FI" nominally stands for "Financial Independence". I say it stands for "Fuck It".

The Importance of Ontology

Gaining an independent ontology is important because it disavows you of the notion that epistemology is all you need to model reality: it deconstructs you. Thus gaining an ontology involves creative destruction.

Epistemology models the correspondent side of life, while ontology models the coherent. The force needs to be balanced, so use the epistemological perspective when that's best, and the ontological view when that's best.

One point is an observation. Two points is a trend. Thus, gaining an ontology opens you up to the idea of possible perspectives beyond ontology: an essence of the ontology. One possibility for the essence of Ontological Mathematics is "idealism". Unfortunately, by the time we get up to the "essence of the ontology" we're talking about a third derivative, which corresponds to jerk in physics. This level is getting so abstract, it doesn't yield much tangible information. The first two derivatives of the thing in itself (epistemology and ontology) corresponds to velocity and acceleration. They are first class peers of the thing in itself. However, jerk is rarely used in physics. To the extent that it is used at all it would be modeled as the velocity of acceleration.

Category Theory and Orthogonalizing Types

Category theory is good for dealing with an explosion of invented ad-hoc types. You need some standard Orthogonalizing types to give you a common language across multiple systems. You can think of these as discovered types instead of invented types.

Math has the power to maximally reduce and thus gives a minimum of possible types.

Physics dealt with particle hell by resorting to group theory, in a similar fashion to the way Computer Science resorted to category theory.

Having a common language to compare and contrast other systems is also a stated goal of the CTMU.

One could also consider that this is a secondary goal of OM, it's primary goal being to simply model reality itself.

UFOs 1.0, 2.0, and 3.0

UFOs 1.0: people seeing fairies, goblins, leprechauns, ghosts, sea monsters, gnomes, sprites and pixies.
UFOs 2.0: people seeing flying saucers and aliens.
UFOs 3.0: machines (radar) seeing unknown aerial phenomenon.

UFOs exist at the boundary between what is known and what is unknown. You might think as we learn more this boundary gets smaller. However, as your "island of awareness increases so increases your shore of ignorance". That is to say, there will always be a grey region of things that are just on the fringe of your understanding. As a matter of fact, it will get exponentially bigger as you become more aware. This is the zone where orphans and phantoms can appear. Orphans are things that are there but we don't see. Phantoms are things that aren't there but we think we see.

You can consider this unknown zone to be the impedance mismatch between epistemology (what is true) and ontology (what is real). Casinos know all about this mismatch: it's the house edge that gives an essentially guaranteed 1-5% return on all bets. People's epistemology (subjective belief in luck) is generally more optimistic than what ontology (reality) dictates. So real is this illusion however, that it's the house that has to keep reminding itself of the underlying reality and to ignore the siren song of luck.

Another popular term for this zone would be the "Twilight zone".

Starting in 1947, when Kenneth Arnold reported seeing flying saucers (most likely a flock of geese), the modern UFO 2.0 era began. This worked as sort of a grand unifying theory for the twilight zone. Instead of the menagerie of assorted beasts, they were all unified into flying saucers and "greys".

Still, all we ever seem to get is blurry images and anecdotal encounters involving a single witness. To me, one of the most convincing "meta-arguments" against UFO's is that with the rise of smartphones, there are literally thousands of times more cameras available yet the number of photographed incidents is only up maybe 50% at most. If the aliens are out there, given that we have orders of magnitude more recording devices readily available, why are we not seeing a corresponding increase in the amount of documentation?

UFO's: from deep space or the deep state?

Starting in the 1990's, we began what I call the UFO 3.0 era. First of all, they're no longer called UFOs but UAPs. I think the main impetus for this era has been drones and radars. First off drone technology got good enough that drones became prevalent. Some drones are the size of small planes, but now they can be the size of a model airplane. This necessitated an increase in radar capability. However, there are a lot of weather balloons and other terrestrial, man-made objects out there that subsequently started getting picked up by radar. Also a lot of military subterfuge can exploit radar: submarines that float balloons with a radar-deflecting panel up in the air, can be quickly rotated to prevent detection. Meanwhile, another radar detection balloon above can be rotated to be detectable by radar. A radar operator would then see a radar blip vanish and then reappear far away. If incorrectly interpretted as a single object, you will think it's moving very fast and instantaneously. The military probably knows the correct interpretation (that it's two separate objects) but is in no mood to reveal this act of military misdirection to its enemies.

What is really needed is what UFO skeptic Mick West calls "triangulation". We need at least three independent sources of information to confirm an actual UAP. For instance, a high-resolution photograph, showing that it's not a balloon, drone, or plane, then a radar image, proving it's not an optical illusion, and then two independent observations by groups of people from two angles, and who are not "ufo nuts" with an obvious motivation to see UFO's.

Still, there are enough cases out there that are hard to explain (although "ball lightning" is potentially a good explanation for a lot of these case IMO, even though we still know very little about it). To the point where I, as a skeptic, find myself unable to put the final nail in this coffin.

Smart money among the true UFO cognoscenti is that UAPs are not advanced terrestrial aircraft, or aliens, but rather some form of higher consciousness. Perhaps we really are in an idealistic universe (colloquially understood as "being in a simulation") and this is "interference" or side effects of some kind produced by a form of higher consciousness on the other side of the universe.

Basically, the higher consciousness model is saying UAPs live in the ontology, not in the epistemology: that they are more noumenal than phenomenal.

This is right up the alley of Ontological Mathematics. Ironically, they only at best, briefly mention UFO's or aliens in any of their books. Maybe they're worried about getting lumped in with traditional UFO crackpots.

Supposedly, the military has high-resolution photographs of the vehicles, some where you can clearly see beings inside. It only takes one clear case to prove that ETs exist. All I know is I'm keeping an open mind, but waiting -- endlessly waiting, for some acutal "triangulated" proof.

Theory-free, evidence-free, and zero-knowledge

Theory-free simply means you know something in practice before you know the principles behind it. I first heard this term in data analytics: modern AI algorithms can make accurate predictions, yet at the same time no one, not even the creators of the system, can explain the logic behind it.

This makes it sound like a modern phenomenon only. However, if you think about it, theory-free physics has been around for a long time. Take airplanes. We could fly airplanes for twenty years before physics was able to actually explain how they worked.

Randomness is also considered to be the absence of explanation, that is to say it is theory-free as well.

The opposite of theory-free is evidence-free. This means that we have a theory worked out but no actual evidence to back it up. You might think this would be rare, but it's very common in physics. Theoretical physicists create a very well-worked out, "rational" theory, that no one seems to be able to find any actual evidence for. Supersymmetry is an example of an "oh so beautiful" theory that decade after decade seems unable to find any of the predicted super particles.

Even proofs can be "knowledge-free".

Wikipedia says a zero-knowledge proof "is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true while the prover avoids conveying any additional information apart from the fact that the statement is indeed true". It's a way of determining if someone holds a particular card, without knowing the value of that particular card.

Everything has two aspects: a syntax and a semantic. Isn't it interesting how you really only need to know one of the aspects to understand something in a practical sense? A Double-book auditing model is nice, but minimalistically, all you really need is a single-book accounting model.

Rockstars and Programmers

In an interview with Wolfgang Van Halen, son of rockstar Edward Van Halen, he was asked if he always wanted to be a musician. He said no, that actually he originally wanted to be a games programmer. However, after going to a coding camp one summer, he realized it was way too hard and thus "settled" on being a musician.

As a professional programmer, my dream has always been to be musician (nay, "metal god"). I only "settled" on programming after realizing how hard music is and how good you have to actually be in order to be a professional musician.

It seems like everyone always wants what they don't have. Women with naturally curly hair wish it was straight, and women with straight hair wish they had curly hair, oftentimes resorting to costly and messy perms in order to achieve it.

On the subject of progamming, in the latest Matrix movie, Neo is a "lead game developer". This is the only programming job that is considered worthy by Hollywood writers. They normally look down on programmers as autistic nerds. Why is it socially acceptable to demean engineers and programmers, areas that requires years of discipline, hard work, study, and sacrifice, as geeks and nerds? They never call Lawyers or doctors this. Being an Engineer or Programmers is on par with the intellect and training needed in these other professions.

The Balance of the Force

The message of Star Wars is not "Jedi good, Sith bad". The message is about the balance between the force. Most people assume this means 50-50. However, it's quite clear the Jedi is a little bit "better" than the Sith. George Lucas is mum about what the proper balance is.

Is it 70-30? Is it dynamic, varying by time and context?

In general, how can you tell what the proper balance is between any two opposing forces?

One possible answer is "where essence and existence are the same thing":

Only at the Omega Point do Essence and Existence, Form and Content, rationalism and empiricism, align. That’s when we all become Gods!

Hockney, Mike. Psychophysics (The God Series Book 27) . Hyperreality Books. Kindle Edition.

IQ and Standard Deviation

One standard deviation in IQ is about 15 IQ points. To put that into perspective, one standard deviation in height is about 4 inches (10 cm).

Imagine if your parents were average height: 5'4 for women, 5'9 for men. Let's say you, as an offspring of a mother and father of average height, were yourself average height: 5'9. What if you had a brother that was 6'1, one standard deviation taller? Would you consider that odd? Most people would not: that would be within normal variation.

Let's say you had another brother that was 6'5, and another 5'1: two standard deviations taller and shorter respectively. Would you consider this to be odd? Would you consider that one or even both of them to have some sort of underlying medical condition: a tumor on the pituitary gland in the first case, or a mild form of dwarfism in the second?

What about three standard deviations taller: A normal height couple producing a son who is 6'9?

The average Asian IQ is said to be 105. The average IQ of the Ashkenazic Jews is said to be 110. Both are under one standard deviation from an IQ of 100.

What would the world be like if everyone's IQ was one standard deviation higher? Would it have the same relative effect as if everyone was 4 inches taller?

My guess is that mothers who smoke or drink while pregnant, perhaps during the first month when they are unaware, drop the IQ of their babies by something on the order of five IQ points. Lead, mostly from (now banned) leaded gasoline, still has a negative effect on global IQ to this day.

What would it feel like to have a drug that lifted your IQ four standard deviations (60 IQ points)? Would you even be the same person? Could you ever return back to your original IQ even it was already considered relatively high at 130 say, or would you become addicted like in the movie "Limitless"?

Some people say IQ only make sense for measuring IQs lower than 100 i.e. mental disability, which was it's original charter, and that anything beyond that usage is "Daft speculation".

Position, Velocity, and Acceleration

Imagine if you could only ever measure the position of a particle, but never know it's velocity or acceleration. You would then only be certain about the particle's current position, but never about its past or future. In short, you could only react and never respond.

Now let's say you know the particle's velocity. If it was a constant velocity, you would now be able to determine it's past and future positions from its current position. In short, you would be able to fully characterize the particles behavior, and be able to respond not merely react. However, if the velocity was not constant, your predictions would be less accurate the further you went out. To rectify that, you would need to know the particles acceleration too.

On the earth, where gravity is essentially constant, knowing a particle's position, velocity, and acceleration allows you to fully characterize a particle: you can describe (position), explain (velocity), and predict (acceleration). In other words you can react, respond, and predict.

Now let's compare these with the real world. The state of the current world gives you its "position".

In order to understand the universe's "velocity" you need a model of the universe -- an epistemology. Likewise, in order to understand the universe's "acceleration" you need a model of the model -- an ontology.

So having direct sensory awareness of the universe (position), and an epistemology (velocity), and an ontology (acceleration) allows you to fully characterize the universe in a very real, practical sense.

Most people have no intentional model for the universe: they only know the position and thus can only react to events in life. If you're educated properly, you may be lucky enough to have an intentional epistemology (velocity). Now you can respond.

Even fewer people still have an intentional and independent ontology. This is what Ontological Mathematics gives you. It gives you the missing "acceleration" perspective. Now you can describe, explain, and predict: the holy triumvirate.

Can Ambiguity Be Fundamental?

Next time you watch the credits scrolling at the end of a movie, ask yourself if it's the credits that are scrolling upward past a fixed camera, or if it's a fixed set of credits (etched on a plate for instance) with the camera scrolling downward. Technically speaking, it can also be some combination of these two, but for purposes of analysis we'll just assume it's one or the other.

Most people assume it's the first option: upward scrolling credits past a fixed camera.

But how can you tell which one it "really" is?

Back in the very early days of film, it probably was literally a roll of credits scrolling past a camera. You could tell which one it really was by seeing the external context in which the system exists. But if all you have is the film itself, and not the filming environment, you cannot actually disambiguate between the two. However, you would assume there is some sort of ultimate reality, so this ambiguity doesn't feel like it's really fundamental. In other words, you need a context to disambiguate the ambiguity, but even if you can't get to it, you feel that you could somehow.

But let's look at a modern film. The credits are done as a computer animation. Now, there is no external physical context that can disambiguate the situation -- in principle even. The closest you could get might be that the programmer who coded up the scrolling had a mental model of names scrolling past a fixed camera, and programmed it that way e.g. the camera's position variable in the computer doesn't change but the text's position variable does.

But there is no physical camera, or list of names. Thus there is no context that will be able to explicitly "prove" which model is occurring -- ever, for all time.

Isn't it amazing how such a simple situation can manifest the concept of fundamental ambiguity? Quantum mechanics also talks about fundamental ambiguity: a particle can literally be in two places at same time, and it takes a collapse of the wave to force the universe to pick one. It seems appropriate that something as "weird" as quantum mechanics might have built-in ambiguity, but the credit scrolling scenario shows there's nothing really mysterious about it, and can arise naturally in simple situations.

There is another thing that always lacks an external context: the universe itself. How can the universe then disambiguate certain questions? How can universe say if a distance of a googol light-years across is large? How can the universe know who or what it is, if it has nothing or nobody else to compare to?

The solution is the universe divides itself up into two and creates an alienated self. Now it has something to compare itself against, even if ultimately it's only comparing against itself. Another more sophisticated way to phrase this is to ask how can "God" experience non-existence? If God knows everything, then he must know about non-existence as well and have experienced it. But if you experience non-existence, it would no longer be non-existence. But if an alienated self -- an other, were to experience existence, this can potentially be interpreted as God experiencing non-existence.

-> update 2022-06-02
A deeper analysis vis a vis the computer generated scrolling credits yields the following. There are two interpretations you can make about this situation. One is to say that since there really is no camera, or credits, or even scrolling for that matter, due to the fact that everything is in fact pixels on a screen controlled by a program, it's a meaningless question to ask if the credits are scrolling or the camera is. That is to say the question is a false paradox, and there is not any ambiguity, fundamental or otherwise. This is kind of the hard-nosed reductionist, utilitarian response.

Another, perhaps more inclusive interpretation, is to say that both cases are true: the credits are scrolling and the camera is scrolling. Since both are equally valid, they both have to be true. That is to say they are superimposed truths just like in quantum mechanics. This gives an interesting insight into how the collapse of quantum waves works. A quantum observation in effect is providing a context, and then the universe has to decide at that point which of the multiple "truths" become real.

In fact, I say that both these interpretations are correct at the appropriate level of analysis. Epistemology is what is true, and ontology is what is real. I would say that epistemologically the second interpretation is true, but ontologically, the first holds. So its epistemologically true that both the camera and credits are scrolling, but at the same time it's either ontologically false, null, or unreal. In other words, it's just like a pair of dice that are epistemologically probabilistic, but ontologically deterministic: two different properties at two different levels of interpretation.

This once again illustrates out the power of having an ontology complementing your epistemology

Article Update History:
2022-05-09: Minor typo fixes.
2022-06-02: Add analysis to scrolling camera snigglet.