Ontological Math Snigglets # 4

Quotes

Knowledge is knowing that a tomato is a fruit. Wisdom is knowing not to put it in a fruit salad.
- Brian O'Driscoll

We've been tricked, we've been backstabbed, and we've been, quite possibly, bamboozled.
- Super Colonel Sarge of Red

A civilization or individual who cannot burst through its current abstractions is doomed to sterility after a limited period of progress.
-Alfred North Whitehead

One of the greatest pains to human nature is the pain of a new idea.
-Walter Bagehot

The MAGA Left

You've probably heard of the MAGA right, but what about the MAGA left: Microsoft, Apple, Google, and Amazon?

Infinity

Infinity is just something that converges on some sort of behavior and then doesn't change once you add to that. You never reach infinity, but you effectively do once you reach this emergent behavior.

A circle is a polygon with an infinite number of sides. However, you don't really have to get to an infinite number of sides before a polygon starts to act like a circle. The number at which it starts essentially acting like a circle can be considered a form of zenith number.

Bill Gates is another example. He basically has an infinite amount of money. If you give him another billion dollars is it really going to make a difference? Is he going to live his life differently? Is he going to even notice? I remember an interview where they asked him how much money he has on him. The answer was zero -- he said he stopped carrying a wallet a long time ago.

In effect this definition is a correspondent interpretation (or epistemological truth) of infinity. The coherent interpretation (or ontological reality) of infinity is that infinity is only "true" at infinity, and thus can never be reached. This coherent truth interpretation of infinity is the more traditional understanding of infinity.

Languages and Paradoxes

The proper language can transform paradoxes into tautologies (self-evident truths). Conversely, an improper language can transform tautologies into accidental paradoxes (sleight of word).

For example, in English the following statement is paradoxical: "nothing is something". However, in mathematical language this becomes "0 = 1 - 1": a tautology. This identify has nothing (zero) on the left side and two somethings (1 and -1) on the right side, and the equals signs indicates they are at the very least equivalent (although not identical -- remember an equal sign can denote from weak to strong: equivalence, equality, or identity relationship).

A woo language (example quantum woo) can even transform a paradox into a transrational or a superrational statement. A woo language is preferred by Meyers-Briggs NF types. Buddhism is full of this type of language.

Nature uses the most pure and rational language, one that is compatible with the PSR, to avoid as many paradoxes as possible. Ontological Math is an attempt to model this language.

The Zenith Number and Frequency

Actual reality is based on a smallest possible number (the size of any flowing point of energy – all flowing points have exactly the same size) – and the highest possible number (the Zenith number), for which the next number in the sequence is zero.

Another critical point to bear in mind is the double-sided coin relationship of zero and infinity. Zero is always a portal to infinity, and infinity always a portal to zero. If we think of zero as the beginning (origin; alpha point) of a process, and infinity as the end (terminus; omega point) then, when we reach infinity, the next step will be zero, i.e. we finish the present process and begin the next. This is the basis of the eternally oscillating, Cyclical Universe. The instant before the Big Bang of a new universe was the Big Death (or Crunch) of the previous universe.

Also, any dimensionless infinite-energy process must be made dimensional to enter physical reality and this involves the “collapse” of infinity to the Zenith Number.

Hockney, Mike. The Mathematical Universe (The God Series Book 14) . Hyperreality Books. Kindle Edition.

The notion of a Zenith Number is one of my favorite ideas from the God Series. Basically, it's saying that the number system is circular (as opposed to linear) and that as you approach the zenith number, the next number in sequence will be zero, or more accurately, the nadir number. This actually occurs in the case of a circle. Remember, a circle is a polygon that has an infinite number of sides. However, once a polygon actually gets to an infinite number of sides, it actually has zero sides since all the edges are now points. So you can see how infinity wraps to zero in something that is "real".

But as suggested by the prior quotes, it's a little more nuanced than that. They seem to be distinguishing between logical numbers (dimensionless numbers), such as zero and infinity, which can exist potentially, and physical numbers (dimensioned numbers), which can exist in actuality. Then, the logical numbers zero and infinity, necessarily "collapse" to the Nadir and Zenith numbers respectively when transitioning towards actualization.

However, the occurrence of the zenith number can occur an infinite number of times, so even the Zenith number is ultimately unbounded:

Even though, ontologically, we can’t get below a certain number (the Nadir number), or above a certain number (the Zenith number), this doesn’t mean that we can escape “abstract” zero or infinity. We can still generate infinite loops from which we can never escape. Even the Zenith number itself can be infinitely repeated! This is why the universe can never end.

Hockney, Mike. The Mathematical Universe (The God Series Book 14) . Hyperreality Books. Kindle Edition.

But what is the actual value of the Zenith number? No one really knows of course. Is it even possible to know? One empirical suggestion would be that it would have to be bigger than 10^80, since that's the estimate of the number of particles in the universe. But could it be a stupendously large number like 10^googol^googol...(a googol number of times)? I think a good gauge, like all fundamental units are the planck numbers. For instance, the planck length is 1.6 x 10^-35 meters, and the planck time is 10^-44 seconds. These are believed, with reason, to sort of be the digital "bits" of the physical world just like their counterparts in the digital world. Almost all the planck numbers are appropriately small or large enough to seem intuitively "reasonable" as a limit, at least to humans (except for the plank mass with which is about 2 x 10-5 grams, about the mass of a grain of pollen, that while small to us is absurdly large as a fundamental minimum for mass).

There's a planck number for just about every measurement, including frequency. And since, in OM, everything derives from a flowing point: a rotating vector on a unit circle in the complex number plane, it seems a maximum frequency, if one exists, might be an appropriate proxy for the Zenith number. The value for the Planck frequency is 1.855 x 10^43 hz, that is to say 10^43 rotations per second. Basically, it's one rotation every Planck unit of time. At this frequency, light (photons) becomes little black holes.

Unfortunately, the absolute value for the Planck frequency is based on an arbitrary unit of time, namely one second. If your unit of time was a minute, then the number of rotations would necessarily be 60x greater (the rate of rotation would be the same, but the absolute number would be bigger). And the value of one second is very much a human level interval, it basically being a value that balances the tension of two forces: one for the duration of a heart beat, and one for having a "reasonable", and easily divisible, number of seconds in a day: 60 x 60 x 24. However, I think it's reasonable to assume that other alien civilizations would have a "second" that is within 3 orders a magnitude of our second. Thus we have a value for Planck frequency anywhere between 10^40 and 10^46. However, while the Planck frequency is certainly large, like the Planck mass it's scaled absurdly wrong (absurdly small in this case). Still, maybe it can kind of give us a ballpark as a reasonable minimum for the Zenith number.

Interestingly, there's the concept of Schelling points from Game Theory. These are "natural" numbers that some unknown third-party might "randomly" decide on as well. Examples are either "3" or "7" for "pick a number between 1 and 10". People will select 3 and 7 much more frequently than random (it would be 8 in Asian countries). Thus if you had to guess what number the other person picked you should pick these. Another example would be "noon at Grand Central Terminal" for "Where should we meet in New York City?".

Can the Planck frequency, or some multiple thereof, serve as a Schelling point as a carrier wave frequency for extraterrestrial search programs like SETI? Then we would have the concept of Planck Schelling points, where Schelling points meets Planck units. Currently, the preferred Schelling point for SETI is 1420 MHz, the hydrogen 21 cm line from spectroscopy.

Returning to the value of the Planck frequency, perhaps a more intuitive unit of time for humans would be the smallest unit of time we can consciously perceive. There is something called the Critical flicker fusion frequency, which denotes the temporal resolution of the brain for various animals. For humans it's 1/60 of a second, since any sequence of 60 frames per seconds (fps) will appear as continuos to us. Interestingly, per this video, the fusion frequency for dogs is 75 fps (so we appear slow to dogs), but only 50 fps for cats (so we appear fast to cats). Unfortunately, this makes the Planck frequency even smaller, which is not what we are looking for. The most natural fundamental time of all would be the Planck time, but as previously mentioned, by definition, the Planck frequency for this interval of time would be 1 (cycle/plank time).

Maybe the opposite approach of picking a larger interval for the "natural" time interval is a better way to go. How about the entire duration of the universe as our interval? The current age of the universe is 13.7 billion years. If you assume that we are an average civilization, it seems likely that we would exist at the halfway point of the universe, thus we could expect the universe to last for 27.4 billion years. Lets round that to 30 billion years, so at 31.5 x 10^6 seconds per year, we get approx 10^18 seconds in the life of the universe, thus upping the number of rotations in this time to 1.855 x 10^61. Unfortunately, this is still an absurdly tiny value, much less than even the number of particles in the universe, so unless you can justify something like squaring the Planck freq (yielding 3.42 x 10^86) it's hard to nominate the Planck frequency in its various time intervals as being a viable candidate for the Zenith number.

In conclusion, in this snigglet we examined the Planck Frequency and tried to determine if it could somehow give us a ballpark estimate for the Zenith number. Unfortunately, we have to conclude that it's simply way to small to serve as a reasonable proxy for the Zenith number. However, the planck frequency could serve as a potential Schelling point for SETI.

On Truth *1

Materialism: the correspondent theory of truth.
Idealism: the coherent theory of truth.

Materialic truth is when you make a link between a physical state and a mental state e.g. it's phenomenal. Idealistic truth is just the actual ontological reality e.g. it noumenal.

*1 Paraphrased from Bernardo Kastrup

Theory-free Physics

Big Data gives us the concept of theory-free physics. Via data mining we can detect patterns in the training data that are certain enough for us to make actionable decisions on, while not providing us with any deeper understanding as to the how or why for this conclusion. While this may seem like a new dilemma of the modern age, it has actually happened many times before in the past. For instance, we knew how to fly planes for twenty years before we could adequately explain the aerodynamics of flight (e.g. how lift comes from the pressure differential across an asymmetric teardrop shaped wing). In short, for twenty years we had no idea of "what holds the plane up", yet were able to fly and even begin perfecting air travel. Still, it's kind of scary to have to take something on faith especially if it involves life and death. With theory-free physics, no one can predict under what circumstances the model may begin to fail, for instance.

A related principle is evidence-free physics. This is a theory that has no evidence to back it up. If theory-free physics is a naked conclusion, with no theory, then evidence-free physics is a naked theory with no conclusion, or confirming testimony. This may seem like a technical edge-case, but once again, it's actually quite common. Many current preferred physical theories such as string theory and supersymmetry can arguably be considered as "evidence-free". Physicists have a tendency to fall in love with "beautiful" theories and cling on to them well beyond their expiration date, thus shepherding them into the zombie graveyard of evidence-free theories.

Technically speaking, OM considers any scientific theory to be "theory-free". This is because Science does not have an independent, well-worked out, intentional ontology (it's ontology is basically an accidental echo of its epistemology). In short, OM says Science is basically epistemology only. A theory is the realm of ontology, and a model is the realm of epistemology. I'm always reminded of the CTMU: the Cognitive Theoretic Model of the Universe. This name is essentially saying the CTMU is idealistic (cognitive), has an independent ontology (theoretic), an independent epistemology (model) and describes everything (the universe) i.e. the phrase "CTMU" very precisely describes what it is: an idealist ontology and epistemology that describes the universe.

Note: the CTMU is not part of OM, and while I think it's similar to OM, it certainly has nothing to do with it, and I suspect the Pythagorean Illuminati probably wouldn't appreciate the comparison.

Algebras and Calculi

This one is going to be kind of technical. But since it's a snigglet, I'll try to keep it short and sweet.

Most people are familiar with Algebra and Calculus from school. However, there isn't just one of each, there are several: Algebras and Calculi (or Calculuses). The Algebra taught in school can be considered real number algebra. Some other algebras are Linear algebra (AKA matrix algieba), Group Algebra, and Lie Algebra. Calculus taught in school are differential and integral calculus. Some other calculi are Differential Geometry and Multivariate Calculus.

What's the relationship between algebras and calculi? Intuitively, an algebra is like being. It just makes statements of brute fact that are either true or false. A calculus is like becoming: it's a connected series of statements in order to establish a proposition: a composition of "algebras" with a specific order. An algebra is space like, calculus time-like. A calculus is a dimensioned algebra. In a general sense, a computer program is closest to a calculus, since it involves a time sequence of steps to reach a goal. Addition is the patron saint of algebras as it represents parallelization. Multiplication is the patron saint of calculus as it represents sequence.

Is it possible to bridge the gap between algebra and calculus? This is essentially like asking how you can get becoming from being. The answer is yes. Of course, you have to take a rather abstract and highly intuitive perspective to appreciate this.

Let's look at two examples.

1. In OM (Ont. Math), a monad is basically mind, and a brain is matter. Mind is associated with being, since it's eternal and outside of space-time. Space-time and matter is associated with becoming. Thus the inverse Fourier transform which converts between the frequency domain (the domain of mind and being) into the time domain (the domain of matter, space-time, and becoming) is what converts the algebra into a calculus. This can be considered taking dimensionless numbers (algebras, mind, aligned light) and making them dimensional (matter, or broken light)

2. In Computer Science (CS), the pure function is basically algebra. Pure functions take an input and return a value only and cannot be sequenced. Imperative statements are like traditional programming statements that can be chained into a sequence. They represent calculus. In CS an algebraic data type, ironically also called a monad (different than the Leibnizian monad of OM), is used to "fatten up" a pure function turning it into an imperative statement. Thus we can see how a CS monad serves essentially the same purpose as an inverse fourier transform in OM.

There's actually a lot of parallels between Functional programming and OM monadology. I never really started to appreciate the OM side of things until I studied Functional programming, esp. with regard to the question "what is a monad" in the programming language Haskell.

Can we extend this further to other types of being? From Continental philosophy we get the (epistemological) concept of levels of being: pure, process, hyper, wild, and ultra, with pure = being, and process = becoming. What type of math is represented by hyper being? This is an interesting question, beyond the scope of a snigglet. I might suggest, since hyper is more about potential becoming than actual becoming, any math that is really out there, and perhaps represents non-reality such as non-euclidean geometries (although the universe is actually more non-euclidean than euclidean), or weird math systems that yield "truths" such as 2 + 2 = 5 as candidates. If being=position, and becoming = velocity, then hyper= acceleration. Analogously, there has to be "hyper" math because we know we have acceleration in physics.

Lightspeed and Dreaming

You're always moving through spacetime at the speed of light. Even when you're stationary, you're moving through time at the speed of light. This is why time slows down when you start moving through space at a significant fraction of c -- since more of your speed is now directed in the space direction, you necessarily move slower through time. Thus your clock slows down.

Likewise, you're always dreaming even when you're awake. When you're awake you're an unwitting participant in the collective dream. All that exists is mind. All the matter in the universe is a creation of the universal mind. You create your own private matter when you dream at night. So you're always either in a private dream or a public dream.

Your mind is also always thinking, at least when you're "awake" (less true when sleeping or esp. in, say, a coma). We only have a finite number of thoughts before we die so why not make them good ones? Twenty years of good productive thoughts is much better than forty years of banal, boring, or agonizing thoughts. Fill your brain with healthy, rational ideas as much as possible. You can't think about nothing. Try it (although the mediators might disagree). Read the God Series and the Truth Series. Listen to me now, thank me later.

Aristotelian Logic and Multiple Truths

Imagine a locality that spent one billion dollars per year on highway infrastructure. The citizens, being unhappy with the current state of the highways and the amount of traffic congestion, passed a special sales tax to raise extra money for road repair. It was very important to the people that the additional revenue only be used on road repair and not go into the general fund where it could be spent on things they didn't approve. So the law passes and after one year there is now one billion dollars in a special account created for this new tax. Then, as promised, the government puts this money into the highway account. That is to say they literally take the money from the bucket labeled "road tax" and put it into the bucket labeled "highway repair".

So at this point there should now be two billion dollars allocated to road repair, and everyone is happy, right? However, the government decides to take the one billion that was previously allocated to road repair and put it back into the general fund, saying that since the one billion dollars from the special fund is now covering road repair costs it's best to spend the previous billion on other items in the general fund they consider more worthwhile.

So one billion in new revenue was raised, with the expectation that two billion dollars per year would be spent on road repair, but in the end there's still only one billion being spent annually, while the general fund received a one billion dollar increase.

The tax supporters cry foul, but the government says it kept its promise in that they literally did put the new money into road repair.

So aside from this being an all too common bait and switch used by "special tax" advocates, what is the truth? We have two possible scenarios:

A. The new money was indeed added to the highway fund as promised.
B. The new money was actually transferred into the general fund.

With traditional Aristotelian logic, something is either true or false. And if A and are B are coupled and mutually exclusive (that is to say B is actually "not A"), then you can know that if A is true then B (or not A) must be false. For instance, let's consider human height. If I say a person is either five foot nine or six foot nine, and then I tell you the person is not six foot nine, then you know he must be five foot nine. Because one thing that is true with height is you cannot be both five foot nine and six foot nine -- there's only one truth.

However, in the special tax case it's pretty obvious that both A and B are true. As previously stated, the one billion from the tax is literally put into the highway fund. So A is true. However, due the fungibility of money, B is also true. If you only saw the end effect, you literally couldn't tell if the new billion in the general fund was taken from the previous highway fund allocation, or from the new tax fund. So B is literally true too -- and the fact that there is now one billion more in the general fund is physical evidence this "interpretation" is true.

This example illustrates a common, non-abstract situation where Aristotelian logic breaks down. In effect, this is like a human being that is simultaneously five foot nine and six foot nine. And this isn't some weird artificial mathematical edge case. This literally happens all the time (although most governments aren't so brazen to to take away all of the previous funding).

If you want to get really technical you could nuance your language by distinguishing between an "identical" fund transfer (where we limit the fungible nature of money) and an "equivalent" fund transfer (where we exploit the fungible nature of money). But can you really do this when the "money" is literally numbers on a hard disk?

We can use analogies like talking about superimposed and entangle truths (from quantum mechanics), or distinguish between coherent truth vs. correspondent truths, or talk about epistemological truths vs. ontological reality. As far as "truth" goes, I say there's at least three types: reality (ontology), objective truth (epistemology), and subjective truth (hermeneutics [?]). Usually, there's either just one truth, or alternatively all three truths align, so you don't have to distinguish between the "levels" of truth.

The point is your "language" can really affect what you see. And by "language" we mean this very broadly: the model, the context, the assumptions you make all fold into a "language". Your language can literally cause you to see paradoxes where none exist, or inversely, make a paradox invisible. With a strict Aristotelian "common-sense" of logic it's not possible for both A and B to be true.

Here are some other examples of things with multiple truths that I've mentioned previously in other snigglets: dice, which are both deterministic and probabilistic; credits scrolling at the end of a movie -- are the credits scrolling past the camera or is the camera panning down on a fixed list; a circle: it has an infinite number of edges yet at the same time has zero edges (the "edges" on a circle are effectively points, and a circle is "smooth" not edgy at all).

OM is more about unlearning than learning. You have to broaden your horizons and let go of things that may have been really successful for your world view over time. You have to open your mind to new ideas, while resisting the temptation to veer into woo. To quote the old adage, open your mind but not so much that your brains fall out.

So to bring it back to the tax example, what are some language distinctions we can add to clarify the situation. When there's multiple "truths", you want to ask if one truth is "deeper" or more fundamental than an another. In the tax case, I happen to think B is the more fundamental case, but honestly that's not as natural an interpretation as it is in the case of dice, where the "deterministic" interpretation is the ontological reality. I think we can say that case A is the coherent truth (theoretical, mind interpretation) and B is the correspondent truth (practical, material interpretation).

Alternatively, and perhaps more simply we can distinguish between semantic truth and syntactic truth. Thus you can say it was syntactically true that the billion went into the special fund, but semantically true that it went into the general fund. This is akin to a situation where someone is saying something they believe to be true that is not true. If you place a key in a box and then, unbeknownst to you, someone removes it, when you then state that there *is* a key in the box are you in fact lying? Here I think we can say that semantically you're not lying since you believe it to be true, but syntactically you are lying, since the key *really* is not in the box. Then the two layers of truth are superimposed upon each other, and the proper question becomes not "are you lying", but are the telling the semantic truth or telling the syntactic truth -- using the proper languange and nuance eliminates the paradox of simulataneously lying and not lying. Incidentally, this is the situation I think a lot of the recent UFO whistleblower to congress are in. They might have read some disinformation claiming to have recovered UFO's, so they say what the believe to be semantically true, while at the same time it's syntactically true that we have in fact not been visited by extraterrestials.

To tie this back to OM, never forget that your language dictates what you see. When dealing with the fundamentals of our universe, you want a language that aligns with reality as closely as possible. You want a coherent ontological language to complement your correspondent epistemological language.

The Answer

The material world is the answer. The (meta) question is: what question does this answer? You have to go to the noumena for the answer. This is your quest (ion), and the universe's quest (ion): the quest (ion) of the holy grail.

When you find the question, then you can integrate and complete yourself.

The question for the universe is "Who am I?", which is the answer to our previous meta-question.

The material world is the alienated self. It gives the universe some reference and context. How can you know who/what you are until you can compare yourself against some outside metric?

As above so below. The question for an individual is "What is my true self?"

110 Bits/ Second

You can only consciously perceive 110 bits per second. Talking to someone requires 60 bits per second. That's why you can't listen to two people speak at the same time.

If you can find something that uses up almost all that bandwidth, then the background bits like "I'm hungry", "why is it so hot in here?", and "what am I going to do tomorrow?" are all dropped, and you experience ecstasy. In this state, more prosaically called "flow", your body and identify disappears. That's why you feel "at one" with whatever it is you're doing at the time.

Ecstasy means "standing next to something". That is to say you're outside of your normal state or normal spacetime. You're literally outside your 110 bits of consciousness. The great pyramids are an ecstasy of the Egyptian culture. A moment of a new reality is an ecstasy. This is in contrast to "euphoria", which means "no place".

Mind altering drugs can alter this limit -- by reducing it. If a psychedelic drug lowers your conscious bits per second down to 65 bits, then a normal conversation would seem "ecstatic", and things like listening to music will completely absorb you. You think you're expanding your consciousness, but you're literally diminishing your consciousness by reducing your bit rate.

While taking mind altering drugs may give you the sensation of enlightenment, it seems highly unlikely that reducing your bit rate is the way to do it. Some even say that you can't truly create anything new without 10 years of immersions in that field.

All of our reasoning takes places in the mind. That’s why sticking electrodes into the brain absolutely never results in reasoning. Epileptic fits do not cause “reasoning storms”. When people take alcohol and drugs, they don’t then engage in complex reasoning. Things that affect the brain cause sensory distortion, tiredness, lack of concentration, degraded memory, and so on.

Knox, Harry. Consciousness: The Real Neuro-Linguistic Programming (p. 263). Kindle Edition.

Nothing, Something, and Anything

Nothing is something. But Nothing is not anything. A "7" by itself is an anything (and a something), and certainly it's not a nothing. In order for a "bare naked" seven to be a nothing it needs to be counterbalanced by it's opposite, a -7 or -3 and a -4, for instance.

And while nothing is something, it doesn't follow that something is nothing. Nothing is a very particular subset of something, and an even smaller subset of anything. A nothing has to be composed of somethings that add to zero. The most you can say is that something is a nothing some of the time.

If something goes up, some thing, or some things, must go down. The universe must add to zero at all times (or perhaps to the nadir number which leaves room for a flowing point). This is why you have conservation laws like conservation of energy and momentum. Nothing guides and restricts the universe at every point and at every time. Nothing can prevent nothing from manifesting, and nothing lasts forever: nothing is eternal. The nothing that is the universe is in fact a totality.

Nothing is all there is, all there ever was, and all there ever will be.

All of this sounds very paradoxical, or enigmatic, or even "cypherpunk zen"-ish when expressed in an everyday human language, but it's all trivial, obvious, and non-paradoxical when expressed with numbers and basic arithmetic.

Once again, the proper language will enlighten and save the day.

History

-> Internal Note: Snigglets 4 primarily based on notebooks 29 and 30.

-> Update History:
2022-12-30: first publishing.

2023-03-04: Change snigglet order. Fix minor typos

2023-10-05: Add discussion about semantic and syntacic truth