I think we've established that there are (at least) two modalities or "channels" in our discourse: intra-model and extra-model. When we're talking about the model, we're no longer within the model and so are using the extra-model channel. In this modality we can use whatever words and concepts are necessary to communicate our thoughts.

Affirmative!

BTW, let's call a spade a spade: what you call ORKs are axioms. There's nothing wrong with axioms; you can't build a model without them because we have to start somewhere. So, we should probably start with defining a few axioms.

There was a method to my madness there.

Because we are dealing with a congenital, ontological framework, I think there's a small proviso here:

Given that the token axiom itself might in fact be the very principal of literally every axiom, I'm on-board with "calling a spade a spade" here, only if you're on board with using spade to define spade, and then subsequently use spade to define spade derivatives. The very reason I used ORK was for a virginal token apart from the existing utility of the term axiom itself that could encompass it.

In addition, rather than a table of axioms, this might actually be more like a general tree data structure, where the root node is token AXIOM, or even —OMG she did not — LIFE (I explain below).

It sets them off ontologically and from any potential noise in the definition of axiom.

However, I defer to you in this with respect to what you feel the largest bodies of science would agree to. If you think axiom is in the clear if it itself is an axiom, then I have no problem. In any case, it would be nice to label this tree as something — Ontological Axiomatic Congenital Architecture?

Almost as if we are defining a programming language, what is also your feeling in setting the terms off syntactically: e.g. uppercase with a prefix character, like _AXIOM, _INFINITY, etc. rather than having to constantly italicize, etc.?

[intra-model channel]

Axiom 1: Information is a measurable quantity.

Axiom 2: A state is a particular configuration or arrangement of measurable quantities.

Axiom 3: A process is a mapping between states. Some process P transforms state A to state B according to some rule.

As a measurable quantity, information can be processed. Examples of information processes are transferring and storage, wherein state is copied and saved. Let I represent some particular configuration of information. To transfer and store I, then, means to configure the storage state S to that of I: \[ S \to P(I) \to I \] Axiom 4: A bit is a discrete unit of information; we measure information by counting bits.

A convenient representation for bits is sequences of 1s and 0s; we call such sequences bit strings. There are precisely two possible 1-bit bit strings: "1" and "0".

The information capacity of a state is the amount of information that can be stored in the state. This is equivalent to the count of possible configurations of the state.

Lemma 1: There is a one-to-one correspondence between any state of n possible configurations and a bit string of log2(n) bits.

Proof: A string of n-bits can represent \( 2^n \) different configurations. Taking the base-2 logarithm of both sides gives us the lemma. QED.

Theorem 1: The information capacity of a state is given by the count of bits in its corresponding bit string.

Proof: Using Lemma 1, map the state to a k-bit bit string. Then, by axiom 4, the state has k bits of information. QED.

[/intra-model channel]

So far, this is a very small model -- with only 4 axioms, a single lemma, and a single theorem -- but it's already pretty powerful: we can quantify the information in any state.

What do you think about this approach?

100% — and bravo on the excellent work in systemizing that portion.

Because we are dealing with rendering this model as a direct reflection and extension of human ontology here, I think we need to zoom out some for establishing some starting axioms/ORKs/whatever and identify some ontological macro-level ones first.

This said, I'm going to once again pull a Valkyrie and affix an IED under someone's philosophical desk here, and argue from a non-philosophical, bare empirical, observational perspective — and this speaks to no religion or philosophy but life and consciousness itself:

The man who just got rolled into the coroner's office to be "tagged and embalmed" is no longer creating axioms, models, QED's, calculation, or otherwise doing any conscious science, deriving meaning, or any other such activities. Beyond asking where the cube is in the brain, or where the dog is in the light — he can't ask perhaps a more poignant question that speaks to the nature of consciousness itself: Where is his body in the space, the head on said body, and the brain in said head?

He's considered as unequivocally labeled "non-living" by any other human being.

Every other human effortlessly agrees with one minimal observation, using the ontological axiomatic lexicon: he's definitively keyword DEAD, or NONLIFE — definitely implying another base axiom here.

What justification does one brain-based ambulatory substrate have in defining (DEFINE being another token) the "state" of another brain-based ambulatory substrate (spade-a-spade here: T-800 with friendly [or maybe NOT!] programming) — this one, of course, now horizontal on a gurney.

If LIFE is NOT one of the base axiomatic tokens, then WHAT is on the gurney (WHAT axiom vs. using another axiom WHO) is simply a broken down machine with a face, hair, and body to begin with, pre- or post- gurney state.

Ergo, a human living "being" (vs. "machine") would altogether not be a being at all, since at what point does the logic-derived machine definition above equate to being? Positively never.

If his arms were propped up by more machinery, if we could make his eyes blink, lips move — nothing. We'd be puppeteering an axiomatic DEAD man.

There would be no "WHO" token (1 of the 6 interrogative axioms) ever. There would be no concept of science doing "observation" upon "space" or "time" which are also axioms, since all axioms relate to them somewhere.

This is where Siri Watson is different from John Smith when reading off the weather forecast, and intrinsic to what I would consider to be a novel observational starting supposition.

The man on gurney would simply be deemed, inarguably, no different than any other physical substrate capable of mechanical functioning. We'd (somewhat creepily) be only giving special semantic treatment in everyday parlance only to what in-reality would be a motorized, soft-CPU-controlled mannequin.

Indeed, if we told anyone we were dead, could not be qualified axiomatically as having LIFE and typing this, they would call the Zombie Acquisition hotline, and not believe whatsoever it was true (BELIEF being another token in my estimation, nothing more than a simple term for scientific hypothesis). This is how powerful and integral this starting axiom is and must be, in my estimation, for any "Theory for Everything" that wants to be honest and incorporate the living humans doing the very theorizing!

Since no other machine can be observed to define and employ an axiom such as LIFE, then:

The man on the gurney must be semantically distinguished from his state prior to being placed on the gurney when he was using his phone in the car, and then crashed, and must be defined with this elementary axiom which gives rise to the ability to define all other axioms.

The problem with why science does not have a definition for life is due to this very core axiomatic issue. It will magically co-opt INFINITY, TRUE, FALSE, ADDITION, VECTOR and other axioms into its sciences, but then ignore LIFE, which is just as "Hogwarts"-ready as any other.

If we do not insist on this, we are entirely stuck — as science is — in a recursive loop, because no machine is able to create axioms, per the above QED that a machine is a bit-processing device.

You can't ever define a machine with the axiom LIFE, since LIFE is not a function of the quantity, complexity, or means by which it derives novel, discrete bit sequences, again per your QED's above.

As I said above, this may sound incensingly incisive, but I feel it is bare essence stuff:

It's simply a fact — no matter how ornate the fossil record becomes, or how closely one genome can be correlated to another over millennia — token LIFE is not scientifically defined, because it's precisely on the same axiomatic tree as INFINITY that it has not also bracketed into mind-space as such.

Science is woefully, and I'd say — eternally — devoid of a definition for life for this reason and this reason alone, if it does not embrace this axiom LIFE.

Side-note: The science of Biology to me is like a 4GL language for describing what we call "life" (funnily, talking about something it doesn't and can't define!).

It's like,

"Class, we're going to study life today — we don't have a definition for it yet, but bear with us as we show partiality to this dead frog vs. the living one for a magic under-rug-swept reason! The one that functions is "alive"."

Uh huh. You mean like the “functioning” photo-taking microscope we're using to observe it?

Call me crazy, but is this not like the used car salesman that sells cars in his lot, and the moment you ask him in the office, "Ok, so can you go show me one of them?" He's like, "Wellll — I can tell you ALLL about the V8 in our 2018 BMW M5!" "Ummm, but can you take me to it, bro?" And he just shrugs it off as something he’ll try to get to at some point.

What right does he have to talk about the components of a car if he can't point one out?

Precisely the case here — the guy on the gurney is scientifically at present considered EQUAL to his state PRIOR to the gurney, because no level of complexity of function divorces it from the definition of machine, since function of any level and rate still = machinery! Naturalism, the current foundation of mainstream science is therefore defaulted to labeling him a machine and thus can't define him as a life, because "dead" machinery is the very opposite of axiom LIFE. In fact, we'll universally and readily contrast this phenomenon everyday with phrases such as, "The song needs more life! It sounds like a quantized MIDI note-generating machine!"

Rather than using the lower-level info-theory framework we're using here, the science of biology is employing a higher level language lexicon for soft, carbon-based machinery elements and labeling them such as RNA, DNA, mitochondria, aminos, etc. without further cannibalization of these things under a legit foundational lower-level info science framework.

These are all just abstract terms for things like soft capacitor, transistor, transformer, RAM, ROM, cache, CPU, etc. In which case the complexity of those things, as you said before — if we turned them on — would NOT yield a conscious, alive state, as they don't with the dude on the gurney, because the man is not just "on" and bit processing, his existence involves the innate experiential component of token LIFE. To be alive means to feel and know (two other tokens).

With that logic, are you agreed on AXIOM and LIFE as axioms #1 and #2?

Then I'd like to move onto a model for SCIENTIFIC REASON and MEANING tokens as axiomatic supersets of WHO, WHAT, WHEN, HOW, AND WHERE in a LIVING human mind as they relate to tokens INFINITY, OBJECT, SPACE, and TIME, where some of your QEDs above and beyond will lead to principled means of interrelating them after they're defined in discussable new mind-space framework.

See you in the E-wing lobby once they come knockin'!

 

...it would be great if what I wrote above (and everything else) could be somehow formally systemized as how you did with the machine/bit portion above.

 

Axiom LIFE: Anima principium — a phenomenon endowing every human being with an innate capacity to define, know, and derive axioms.

 

Once the LIFE axiom is accepted as a model foundation contrasted to the machinery definition you crystallized, it would be great to start with a formal deductive BRAIN / MIND SPACE separation logic proof (which would be utterly superb if you could systemize such based on that info that would be recognized by mainstream science)... (as mentioned, the thought is that "mind" is a 5D phenomenon to have rational presumption to be further defined).

This would mean you fully ex-communicate yourself as the very holy pope from the church of exclusive-brain-based thinking and jump over to investigating a meta-landscape as a novel framework to exploring the mind as the basis of science.
So if you can QED that sh*t, we're green-lighted to do so!

From there, the mind space can be further investigated and delineated as a new starting framework where deterministic machinery models can be incorporated to yield a working novel bed for scientific reason, which can then be used as a vantage point for further reality inquiry that is yet untapped, and hopefully unknot some of the problems in science today that are based on models that may or may not have ontological relevance(!)

Once a mind space is accepted, we can begin hashing the following:

I see 6 fundamental ontological axioms which form the foundation of all scientific inquiry (clearly the below is NOT happening in the grey matter—it's quite simple, it just needs to be formalized):

WHY/REASON
WHO
WHAT
WHEN
HOW
WHERE

...These are predicated on the existence of these axioms:

ME/YOU/WE/HIM/HER
SELF/OBSERVER
SENSE (5 senses)

...in turn predicated on these axioms:

SOMETHING -> numerically represented as 1
NOTHING -> numerically represented as 0

...which are predicated on the existence of axioms (which I would say comprise axiom REALITY):

SPACE
TIME (a rolling observer axiom NOW)
INFINITY

... and which are emulsified by axiom:

MEAN


The 6 interrogative axioms permit a querent to acquire information upon which further inquiry can be made.

Interrogative axiom WHY is the parent nodal axiom of the other interrogative axioms, and is assumed to also be invoked upon every use of any of its child nodes, because it sets and reveals the contextual framework and experiential magnitude for storage of the pending question’s answer.

For example, the question “What is a point?” assumes a “reason” for asking. Axiom REASON is synonymous with token WHY and is often used redundantly in tandem (“What is the reason why you’re asking”).

The reason for asking the question is inextricably connected to the child node question, and is used to store the answer in direct connection with further potential child node inquiries.

"WHY are you asking the question 'WHAT is a point'" is indicative of the WHY token's superintendence, and if sufficient answer to the WHY component is not addressed, the child WHAT question is deemed worthless, moot, or of no experiential consequence.

In answer to WHY, one might answer:

1. Because I WANT to
2. Because I’m CURIOUS
3. Because I need to know, irrespective of desire, to answer other questions

Reasons 1 and 2 invoke the concept of experiential worth, or “pleasure of seeking.” The question was asked to feel an experience simply in knowing the answer. This is irrespective to the question's conscious or subconscious ramifications into the piquing of other child nodal questions, like “WHERE is the point," “HOW big is it,” “WHEN is it there,” etc.

One might default to think WHAT has supersedence to WHY, because one might ask “WHAT does WHY mean.” But then one might reply, “WHY” are you asking, implicitly bracketing WHY as the parent node irrespectively.

In all cases, in order for a question to have meaning, or MEAN something, the question must have contextual reason to ask and/or ultimate experiential worth, or deemed MEANingless.

Therefore, token MEAN is the emulsifier of all 6 interrogative axioms, because only those questions that MEAN something, or have ultimate experiential worth through contextualization and thus variable experiential magnitude based on said contextualization, is a question considered meaningful to axioms SELF or OBSERVER that asked them (ASK being another axiom itself). Depending on the WHY context, the same exact question may modulate higher or lower dopamine or related pleasure chemical releases to the SELF.

When one uses any of the interrogatives, axioms SOMETHING and NOTHING are implicitly or explicitly invoked in axiom MEAN.

"WHAT is a POINT" assumes POINT is something prospectively “in” something else, like SPACE. Even the question itself might be deemed as something. The question itself might alternatively be dismissed as NOTHING if it has no meaning.

SOMETHING implies observable form via token SENSE (and one of them, either internally or externally!) — of an internal or external FORM. The form must logically exist as a first order continuous or indivisible phenomenon.

It is comprised of a starting axiom POINT in axiom SPACE, another POINT in said space, and a continuous Euclidean REAL line between them, defined as having infinitely “un”countable points. The combination of such continuous lines can create addressable objects that can be assigned names within this SPACE, where SOMETHING can be invoked vs. a default state of NOTHING, both of which are special phenomena of the 5D mind. The SOMETHING is imbued the properties the SPACE gives it from its NOTHING state, which is an infinite energy potential state, a kind of supra-meta-substance from which all things derive....

(The 5D space definitions would then be further hashed out... like objects having intention, native affinities for other objects, vibratory phenomena which produces uniquely ID'd waves and their wavelings, etc., and all of which are the basis of interfacing to our "matrix" derivative material world).

 

Given that the token axiom itself might in fact be the very principal of literally every axiom, I'm on-board with "calling a spade a spade" here, only if you're on board with using spade to define spade, and then subsequently use spade to define spade derivatives. The very reason I used ORK was for a virginal token apart from the existing utility of the term axiom itself that could encompass it.

I don't have a problem with neology when it makes good sense, but -- just as in programming -- we should prefer familiar, conventional variable names (i, count, password) to novel ones (p, runningEnumeration, hideyWords). This saves brain cycles and, most importantly, expensive context-switches while reading.

Taking spade as a given (axiom), and using it to define and derive other terms is precisely the goal.

In addition, rather than a table of axioms, this might actually be more like a general tree data structure, where the root node is token AXIOM, or even —OMG she did not — LIFE (I explain below).

Whatever data structure we use, we should respect its, erm, structure. The advantage of a table of axioms is that it imposes little structure, making it versatile. Trees, on the other hand, impose a lot of structure. Trees enforce a hierarchical relationship, can't have cycles (which may want), and require us to define the rules for assigning child nodes to parents. A tree may be appropriate, but caveat structor, as it were.

It sets them off ontologically and from any potential noise in the definition of axiom.

However, I defer to you in this with respect to what you feel the largest bodies of science would agree to. If you think axiom is in the clear if it itself is an axiom, then I have no problem.

The word or concept of axiom doesn't belong to the model; it belongs to the space (the higher-order model) in which we embed our model when we talk about it. In other words, we don't need to axiomize axiom within the model. Nor do we need an ontology for axioms; they're the givens, the things that exist as they are. Demanding anything more from our axioms would we throw us into infinite recursion.

Almost as if we are defining a programming language, what is also your feeling in setting the terms off syntactically: e.g. uppercase with a prefix character, like _AXIOM, _INFINITY, etc. rather than having to constantly italicize, etc.?

I'm fine with that, though -- in the spirit of compilers-- let's reserve the underscore prefix for identifiers associated with concepts outside our language. We may define INFINITY within our model, yet find occasion to contrast it with some extra-model notion of infinity, which we can designate with _INFINITY.

100% — and bravo on the excellent work in systemizing that portion.

Thanks!

The man who just got rolled into the coroner's office . . . . He's considered as unequivocally labeled "non-living" by any other human being.

Every other human effortlessly agrees with one minimal observation, using the ontological axiomatic lexicon: he's definitively keyword DEAD, or NONLIFE — definitely implying another base axiom here.

If we're going to make LIFE an axiom, we need to give it some defining properties. DEAD would then just be the absence of these properties where they once existed. Here's a template of the idea:

Let L be a set of states associated with LIFE. We say that an object has LIFE when all of its state transitions are closed under L. That is, an object in state \( S \in L \) has LIFE if, for any processes P on S, it is the case that \[ P(S) \in L \] Death, then, is the (non-unique) process P such that \[ P(S) \notin L \] Of course, we'd like to be able qualify what exactly distinguishes sets in \( L \) from sets in its complement \( \bar{L} \), but this is the basic skeleton of model, as I see it.

What justification does one brain-based ambulatory substrate have in defining (DEFINE being another token) the "state" of another brain-based ambulatory substrate (spade-a-spade here: T-800 with friendly [or maybe NOT!] programming) — this one, of course, now horizontal on a gurney.

Is define a token of the model? It feels like a regular English word to me, and so part of the background model. Unless we're trying to model psychology -- and, for the love of everything unholy, let's not go there -- whatever brain-based objects declare about other brain-based objects within the model is kind of irrelevant, isn't it? The model itself is omniscient of everything in its universe, so we don't have to worry about Gilligan's island shenanigans where a voodoo poison can make someone temporarily appear dead when they're not.

If LIFE is NOT one of the base axiomatic tokens, then WHAT is on the gurney (WHAT axiom vs. using another axiom WHO) is simply a broken down machine with a face, hair, and body to begin with, pre- or post- gurney state.

Again, I don't see "what" or "who" as axioms within the model. A foundational precept of any model is that not everything is the same (otherwise you have a trivial model). Anyway, the only salient difference between the hunk of meat lying on the gurney and the gurney itself is that hunk of meat used to have LIFE.

We can look at this in the other direction, too. An object with LIFE is composed of various _ELEMENTS that have existed long before the object became associated with LIFE states. More still, the living object and the gurney are comprised of mostly the same types of _ELEMENTS -- we can, in fact, replace all _ELEMENTS of the same type in one with the other and not affect the LIFE status of either.

Ergo, a human living "being" (vs. "machine") would altogether not be a being at all, since at what point does the logic-derived machine definition above equate to being? Positively never.

But LIFE applies to more than just humans, yes? What about the "low end" of bacteria and such -- are they not "beings" that seem more like purely mechanical processors than humans?

There would be no concept of science doing "observation" upon "space" or "time" which are also axioms, since all axioms relate to them somewhere.

So LIFE is associated with _CONSCIOUSNESS? I really think we need to set down some properties for LIFE.

 

Points noted, and will return to that.

But lest too many windows end up open on the desktop here (which I take full responsibility for, since my "sneak-peek" of my future thoughts shouldn't be any basis of how we should preceptively lay this out), what's say we siphon the scope down to the opening shot of a game-changing whitepaper:

Can we QED a bulletproof proof that gets science to cease and desist with brain-based approach as its inception-point?

Given that no living bit-processing human brain substrate can be involved with:

• Invocation of non-numeric axioms
• Cognizing the concept of actual continuous geometric forms
• Storing untold waves, wavelings, digitizing and interrelating them in relation to said forms
• Differentiation between itself and observer of itself
• Infinity of any kind — infinite points not about to be represented on a discrete n bit-processing medium
• Capacity to DEFINE something vs. nothing in relation to other somethings
• Distinction between random and non-random events
• Distinction between signal and noise (meaning)
• Hypothesizing there may be more to itself by invoking axioms like MIND to do so
• Caring about "music" or having any structure within itself to make "sense" of untold musical note combinations over time
• Only does the above when it's considered "alive" by other "brains"

If we cannot do this, it's game over for any additional 5D mind-space exploration (which we need to take one term at a time).

 

(i.e., parlay the hard machinery proofs you began into a full differentiation proof — maybe the first of its kind)

 

Can we QED a bulletproof proof that gets science to cease and desist with brain-based approach as its inception-point?

The only bulletproof assertion of truth that humanity has figured out how to achieve is logical/mathematical proof. So, if you want bulletproof, we'll have to try to make this entirely mathematical. I'm guessing you'd prefer to include non-math, even if it means only a spitball-proof result.

That said, I'm not sure what "brain-based approach" to science means. I think your bullet points below speak to that, so I'll address those.

Given that no living bit-processing human brain substrate can be involved with:
Invocation of non-numeric axioms

I don't get the distinction between numeric and non-numeric axioms. Here are two possible axioms, the first with a numeric flavor, the second with a non-numeric flavor:

1. The successor to a number is also a number.
2. An operation \( \star \) is called commutative if \( A \star B = B \star A \).

You seem to claim that human brains "can be involved with" the first, but not the second. I don't see the distinction.

Cognizing the concept of actual continuous geometric forms

This isn't a given. I suspect your argument rests on the continuum aspect, the notion of _INFINITY. But you have to "prove" that continuous is incompatible with brain before you can make this statement.

Storing untold waves, wavelings, digitizing and interrelating them in relation to said forms

Again, not a given. I don't see any problem with the concept of information being transferred by waves and being stored in a neural net of voltage potentials.

Differentiation between itself and observer of itself

This needs work, too. I can design a circuit that "observes" and reacts to its own battery level. What's the difference between this form of "self-awareness" and ours?

Infinity of any kind — infinite points not about to be represented on a discrete n bit-processing medium

Very much disputable. The fundamental idea in the human notion of infinity is very simple to state:

Pick any number n. Then, n + 1 is also a number.

This little seed of an idea captures the essence of infinite: there is no largest number. It's such a simple idea that we can mechanize it. Indeed, programs such as Wolfram Alpha (and MATLAB, Microsoft Math, et al) happily accept \( \pm \infty \) as parameters, allowing us to mechanically calculate limits, sums, and integrals using infinity. If a 64-bit CPU with finite memory can hold the notion of infinity, why can't a brain?

Capacity to DEFINE something vs. nothing in relation to other somethings

This ability goes hand in hand with the discrete aspect of our neural circuitry. A sensor neuron fires if there was a stimulus (something), or it doesn' if there was no stimulus (nothing).

Distinction between random and non-random events

This one's actually trickier. The heart of the issue is that "random event" isn't a well-defined notion. What we actually mean when we say "random event" is that the event was generated by a random process, and random process is a well-defined concept. The short of it is that we call a process random if its output appears to follow a random probability distribution. These distributions (e.g., Gaussian, uniform, binomial, etc.) are perfectly understood and characterized. Thus, distinguishing between random and non-random processes -- though probabilistic -- is entirely straightforward.

Distinction between signal and noise (meaning)

The main difference between signal and noise is perspective: the part we care about is the signal, the rest is noise. The universe doesn't care, either way. If we want a less human-centric distinction, we can say that in any energy transfer, signal is the correlated components, while noise is the uncorrelated components. Correlation is a precise mathematical notion, and we've built innumerable machines to pick out signal from noise. Your phone certainly distinguishes between signal and noise, so I don't see why it would be a problem for human brains.

Hypothesizing there may be more to itself by invoking axioms like MIND to do so

Hypothesizing is the important point here, as it's one of the surest signs of intelligence. There's no doubt that we do it, but we have good evidence that other animals do it, too. Researchers tested birds and found that crows will hide their food for future consumption, but only if they know they aren't being watched. The experiment accounted for a lot of variables, and ultimately the researchers were confident that crows have the ability to imagine possible future scenarios.

Caring about "music" or having any structure within itself to make "sense" of untold musical note combinations over time

Humans (and other animals) have the physiological capability to hear multiple simultaneous sounds as being related. Our particular capability is almost certainly linked with our ability to vocalize, and the extreme evolutionary advantage language gave us as a species. Humans speak by modulating their vocal chords and mouth shape as they blow air through them. The resulting acoustic energy has a particular harmonic and temporal structure (that we recognize as human speech). It stands to reason that our brains have evolved to integrate sounds that follow a similar harmonic and temporal structure (treating them as a single cohesive sound), while separating sounds that do not follow the template.

It also stands to reason that music, as we know it, takes advantage of these harmonic and temporal patterns to make cohesive sounds. Musical instruments are designed to sound cohesive to human ears. An alien that evolved with a different harmonic/temporal template would not hear music like we do. Depending on their particular integration/separation parameters, they'd likely hear a piano chord as several distinct, dissonant ringing tones.

In any case, I don't find it unusual that human brains can hear and care about music.

Only does the above when it's considered "alive" by other "brains"

What do the considerations of other brains have to do with whether or not one brain can do all of the above? If everyone in a room thinks that Bob is dead, does that mean Bob stops hearing music?

 

I had some initial apprehension to employing the term "math" before we (a) hashed out consensual agreement to the term and (b) you identified this extra-intra element of the discourse nomenclature. INFINITY vs. _INFINITY being the best case-in-point. I thought we we might have a MATH vs _MATH issue here potentially, but in the end that feels as bizarre as Carol-Anne Freeling getting sucked into Poltergeist's TV.

So no matter what, we are employing mathematics, which at this point I would say is essentially the "backbone to mental reasoning" (that it would be nice to prove has 5D origin!). Essentially we're dealing with logic and logical reasoning, sets, groups, etc. as the "moteur de définition."

Since clearly crystallizing using math is your long-term wheel-house — while I do understand everything you have written thus far mathematically — I will leave to you what further combination of logic calculus you feel is best to employ here.

I don't feel something extremely complex like the existing ZF "axiom of infinity" is necessary here, because the goal is to simply "get the camera to stop thinking it can use itself to take a picture without defining a mirror to do so" and this is not some sort of 900-term, 18-level beast to prove logically. I want to keep as spatial and straight-forward as possible.

If INFINITY is mathematically defined (everywhere) as:

A number greater than any assignable quantity or countable number (n + 1).

Well, then, what we are doing here is calling it just another number. This allows us to represent it in calculations with discretized bits. But this ain't _INFINITY (which INFINITY needs to subsume).

In the case of using a digital computer on a physical substrate, INFINITY would essentially be the nth bit of any n-bit system.

A 32-bit system, for example, is representing INFINITY using its maximal string length of discrete bits maximized at 4,294,967,295.

We can do "calculations involving infinity" within this system that can represent strings of bits (numbers!) up to this, which means this final n number logically has to also double as a definition for infinity since we have no more room to represent or calculate with n+1 on the physical substrate.

But technically in this case, INFINITY scientifically defined as the (n+1) here is 4,294,967,296. We have a paradoxical duality here (a "bug" you mentioned before). In essence, "n+1" is incongruous to a finite n-bit system that knows of nothing beyond it (as is the case with the brain)!

So calling INFINITY just another number with respect to defining _INFINITY is entirely inadequate and I'd say incongruous. It's because, in an n-bit system, n is not only the final number in the set, it's also doubling as the n+1 bit definition due to the finitude of the physical matter.

And this is what we have to get back to, how is all of this relating to the ontological limits of the medium we're dealing with here— from the naturalist premise, just another earth-derived, discrete-bit-processing physical substrate "brain."

Roughly speaking, if hypothetically the brain is processing 10^11 neurons at 10^3 bits per second = 10^14 bits per second.

This is 100,000,000,000,000 bits throughput. I don't care how many zeroes we tack onto that number, we are STILL dealing with n-bits, and INFINITY would being reckoned as an n+1 definition all the same here too. But it's not really "n+1" as its full axiomatic definition, and despite it being conveniently discretized into a number, _INFINITY is the token referencing in part the very ability of the mind to generate and delineate n+1 as all that is indivisibly continuous and supra-numeric. A discrete system doesn't even know or CARE about n+1!

If the largest known number is googolplex, and we call this n, what if we were to come up with a name for googolplex + 1? And we called it Appleplex (I'll take "I see what you did there" for $800). Two seconds before we did that, (googlplex +1) would have been INFINITY as represented in a digital computer (a quantum one from the future). But it's not infinity anymore, it's Appleplex!

The very concept is supra-numeric AXIOM, and AXIOMS themselves are not numbers, and it's taught that way for a reason.

There is no point in having a word "infinity" which to the mind means "endless." In summary, if we had another token for n+1, we'd simply call it "yet another number." This "number" is NOT infinity, because infinity is the axiom that describes the very ENDLESS CAPACITY to have n+1, not the n+1 token itself.

The capacity to always create and discretize the n+1 as yet another number is incompatible with infinity also being n+1. Infinity is NOT n+1 in that sentence.

So 3 things:

1) There is still no dog or light in these bits irrespective of the number of bits.

2) The brain itself may equate the nth bit in its n-bit system as infinity, but INFINITY ITSELF is describing the n+1 bit it cannot represent, cognize, define, or even define to exist anywhere.

3) In order to define where the dog or light is, we must call upon axioms that are in the same domain as an extra-bit domain, the same domain _INFINITY lies.

_INFINITY is therefore about genuine indivisibility, or TRUELY continuous phenomena, which I will postulate is required for 5D axiom KNOW to work in a living human, to differentiate between n, n+1, or label it anything as something other than a string of bits, or have those bits represent a truly continuous form called "dog" or "light" which are supra-numeric axiom-space tokens that are a property of 5D LIFE (since no non-living brain could a sh*t give).

This is completely lock-solid inarguable to me at this point, and you said this was kind of "bug" before — and barring some kind of up-sleeve Harry Potter thing you got, anything that counteracts it is entirely a naturalist strawman, so let's get this thing represented in hard logic symbology dammit!

 

In summary, if we had another token for n+1, we'd simply call it "yet another number." This "number" is NOT infinity, because infinity is the axiom that describes the very ENDLESS CAPACITY to have n+1, not the n+1 token itself.

Ding, ding. You nailed it here. The token "n + 1" stands for a number, which is not infinity. All that's left to do is follow this to its logical conclusion: infinity is not a number.

Though there are a few weird and cool areas of math that do treat infinity as a number, the vast majority of mathematical fields do not recognize \( \infty \) as a number. Rather, infinity simply means unbounded. This is the notion that "n + 1" expresses, i.e., not that "n + 1" is infinity, but that the process of counting is unbounded: whatever number you stop at, you can always add 1 and get another. When we see an expression over the reals such as \[ \int_0^\infty e^{-x} \, dx \] we're not suggesting that x take on every value, including infinity (which is not a real number). What the expression is telling us is to let x's value grow without bound. And if we do that, we find that the entire expression has a very finite, very pedestrian answer: 1.

Can we agree that INFINITY, regardless of the various possible flavors of _INFINITY, is restricted to this notion of unbounded processes?

 

And if we do that, we find that the entire expression has a very finite, very pedestrian answer: 1.

Ahhhhhhhhhhh.... [cue Doc Brown's voice] what did you just say? Ding to the ding ^ ding power! That old .9 repeating = 1 situation. Pan to Boole's 1 = "[unbounded] universe of thinkable thoughts" ??

When we are referencing an INFINITY as a "provisionally bounded element" that is a set of all boundless quantities within it, we have created a unique set of unbounded phenomena that can thus be utilized in discrete calculations. Also known as a "number."

When we use infinity as a number and bound it, we are creating a number. Pi anyone? The only difference between 1 and base-2 numbers 01101 and 01010100 is each's quantifiable uniqueness with respect to delineating bounded infinities. Size and magnitude are separate attributions to them which requires arbitrary comparison to other bounded infinities.

Hearkening to what I postulated before: A wave is an INFINITY of uncountable points containing n number of wavelings that compose it. The wave itself cannot be divided or it loses its identity, in the same way a unique bounded INFINITE element would.

Because of science's facility and partiality in making INFINITY an axiom, I say COUNTING or HOWMANY is one as well, because why the partiality to one over the other? One can number multiple sets of bounded infinities, so both are axiomatic.

Yes, I would agree both INFINITY and _INFINITY are the tokens that denote a boundless set, and is the cornerstone of what we deem as an identifiable object such as a line. Pan to Euclid's use of REAL line as composed of dimensionless, infinite points. No infinity, no cognizance of ”line!”

But I would also say _HOWMANY is as well, which is the ability to instantiate bounded infinities and call them "numbers."

 

(The difference between the _REAL (and heck, REAL according to Euclid) Euclidean plane and your Euclid-space mathematical simulation/derivation is that the former has, as its axiomatic construction, the integral use of INFINITY to describe form, and the latter is using implied infinity digitization/discretization to simulate it with discretely countable phenomena and functions to model it. The x and y axes of the Cartesian plane are themselves infinite lines in order to plot discrete floating-point points with theoretically boundless significant digits to them!)

 

Ahhhhhhhhhhh.... [cue Doc Brown's voice] what did you just say? Ding to the ding ^ ding power! That old .9 repeating = 1 situation. Pan to Boole's 1 = "[unbounded] universe of thinkable thoughts" ??

Erm, not really? I mean, we can equally say \[ \int_0^\infty 2e^{-x} dx = 2 \] Do we then insist that 2 = "[unbounded] universe of thinkable thoughts"? We can produce any real number whatsoever using this "infinity machine", so what's so special about 1?

When we are referencing an INFINITY as a "provisionally bounded element" that is a set of all boundless quantities within it, we have created a unique set of unbounded phenomena that can thus be utilized in discrete calculations. Also known as a "number."

No, no, no. INFINITY encapsulates the notion of "unbounded process". We can cogently apply this to sets, if you want: if the process of counting the elements in a set is boundless, then we say that the cardinality of the set is INFINITY. Cardinality is only superficially related to size or magnitude. To wit, it's trivially provable that the set of all natural numbers has the same cardinality of the set of all even natural numbers, even though the former is intuitively twice the size of the latter.

There are notions of _INFINITY where the elements of an INFINITE set are themselves infinite sets, but thar be dragons. Believe me, we don't want to get tangled in the second-order logic of set theory.

When we use infinity as a number and bound it, we are creating a number. Pi anyone?

I'm going to have to insist that we not use infinity as a number, as that's a highly technical subject. So, unless you're an expert in hyperreals and transfinite ordinals (I'm not), we should stick with the "mundane" use of infinity as an unbounded process.

By the way, the number Pi has nothing to do with infinity. It is a finite number (a little bigger than 3!) that, like the vast majority of finite numbers, requires an unbounded count of digits to write down in any number base.

Hearkening to what I postulated before: A wave is an INFINITY of uncountable points containing n number of wavelings that compose it.

That's not at all how I would descirbe a wave. The air in your room and the water in your nearest ocean have a large, but assuredly finite number of particles.

 

(The difference between the _REAL (and heck, REAL according to Euclid) Euclidean plane and your Euclid-space mathematical simulation/derivation is that the former has, as its axiomatic construction, the integral use of INFINITY to describe form, and the latter is using implied infinity digitization/discretization to simulate it with discretely countable phenomena and functions to model it. The x and y axes of the Cartesian plane are themselves infinite lines in order to plot discrete floating-point points with theoretically boundless significant digits to them!)

Euclid had no idea what a Euclidean plane is, or what the real number line is, or, for that matter, what a real number is. More to the point (as it were), Euclid made no pretense of associating infinity with a number. When he describes parallel lines, he describes them as extending "indefinitely", meaning an unbounded process (INFINITE), not as having some magnitude that equals \( \infty \) (_INFINITE).

BTW, there is only one Euclidean plane, whether one describes it with words (as Euclid did) or with linear algebra or topology or whatever. They all describe the same mathematical object, and no particular representation has any kind of privilege over the other (except in so far as some might be judged to be more elegant than others). It's the same idea as "9", "IX", "1001", "nine", "nueve", etc. all describing the same mathematical object. We don't say that "9" is the REAL representation.

 

Erm, not really? I mean, we can equally say \[ \int_0^\infty 2e^{-x} dx = 2 \] Do we then insist that 2 = "[unbounded] universe of thinkable thoughts"? We can produce any real number whatsoever using this "infinity machine", so what's so special about 1?

Correct! "1" just means any unique "number" in reality! Boole's identity as a foundation for the Laws of Thought (and is empirically proven in daily use) is simply marrying the concept of boundedness on the left of it to unboundedness on the right. This identity undergirds all practical comp. sci. that came after. Everyone's subsequent work is based on it. On the left side is simply a unique identifier for the right side's unbounded implication. It is doubling as a truth state and cardinality for the presence of the unbounded phenomenon on the right side.

Because he's using 1 as an elemental contrasting "something" — one can put n-length byte to the left of the identity, and whether 1, 01011, 1101010, 11000110 — these are all existential placeholder tokens for unique infinite universes (within a parent metaverse of universes). Any of them can be on the left side of the equation, irrespective of cardinality. It's simply a uniquely labeled TRUTH state + cardinality overlap. If there wasn't one, bits could NOT be used for computation purposes. It will take a lot to convince me otherwise—beware the potential DEBKAC (Dragon Existing Between Keyboard and Chair here).

When we are referencing an INFINITY as a "provisionally bounded element" that is a set of all boundless quantities within it, we have created a unique set of unbounded phenomena that can thus be utilized in discrete calculations. Also known as a "number."

No, no, no. INFINITY encapsulates the notion of "unbounded process".

Ummm... If ℝ is the set of all real numbers and ℝ = {x | -∞ < x <∞} and INFINITY is NOT a componental element of the set, then ℝ is simply INFINITY #59108-B, no? Again, no preconceived notion here.

Heck, one could make an infinite alphabet, after Z, ZA, ZB, etc. It would be simply INFINITY #54919918-C, no?

The cardinality, magnitude, etc. of them are separate beasts.

I have a little issue with the word "process" here. As if "machinery" is required to negotiate what appears to be an uncalculated phenomenon?

I'm going to have to insist that we not use infinity as a number, as that's a highly technical subject. So, unless you're an expert in hyperreals and transfinite ordinals (I'm not), we should stick with the "mundane" use of infinity as an unbounded process.

Agreed, so long as it doesn't impact the capacity to make a proof in applying Boole's identity/law and applying further.

By the way, the number Pi has nothing to do with infinity. It is a finite number (a little bigger than 3!) that, like the vast majority of finite numbers, requires an unbounded count of digits to write down in any number base.

I haven't referenced The Elements in a long time, but I could have sworn Euclid's axioms were about essentially defining _REAL as having infinite points between 2 points, in contrast to ones we see in the natural world that are composed of discrete number of points (interpolated to infinity in my mind)? You have no reference point without invoking infinity to describe the form.

Assuming that, Pi's first-order definition is in reference to a _REAL Euclidean-space circle whose circumference is ∞ and whose diameter is also ∞. Pi in that context is one seriously bizarre number when dealing with that — seems 3.14... is its irrational manifestation in a discrete space, but what's its true nature in that case? There's no arithmetic for ∞/∞, but intuition tells me it's just "1" in that case — again hearkening back to infinity manifested as a number = 1 (or other numbers) when it is discretized for calculation.

That's not at all how I would describe a wave. The air in your room and the water in your nearest ocean have a large, but assuredly finite number of particles.

But the wave is separate from the particles. The wave is moving the discrete particles, and is considered a periodic disturbance OF the particles. The wave itself is a blast of periodic energy. A sine-wave can be plotted and subdivided by infinite floating-points. Truly continuous phenomenon is continuous only because of this property, in contrast to discrete phenomena.

 

Euclid had no idea what a Euclidean plane is, or what the real number line is, or, for that matter, what a real number is. More to the point (as it were), Euclid made no pretense of associating infinity with a number. When he describes parallel lines, he describes them as extending "indefinitely", meaning an unbounded process (INFINITE), not as having some magnitude that equals \( \infty \) (_INFINITE).

BTW, there is only one Euclidean plane, whether one describes it with words (as Euclid did) or with linear algebra or topology or whatever. They all describe the same mathematical object, and no particular representation has any kind of privilege over the other (except in so far as some might be judged to be more elegant than others). It's the same idea as "9", "IX", "1001", "nine", "nueve", etc. all describing the same mathematical object. We don't say that "9" is the REAL representation.

Hmmm... I know they teach in high and undergraduate the concept of using "REAL" when describing a theoretical line (as referenced in the prior post). We're plumbing depths of the very congenital linguistic engine, so INFINITE and _INFINITE here are potentially united in a 5D REAL definition that unifies bits, logic states, numbers, and geometric form to create a model for _REASON.

There is one _REAL Euclidean plane (we have not defined _REAL), but the one that is on a computer screen that you can plot things into is not _INFINITE, if unboundedness is all that is _INFINITE. Everything other than the one in the 5D mind would not be considered _REAL, and any computed version that isn't invoking infinity specifically is a piece of discretized simulative software for the _INFINITE / _REAL version.

 

Boole's work stems directly from trying to delineate the Laws of Thought upon which mathematics is made, and it informs the work of Shannon, et. al. and the entire information age is built on that book and Boolean Algebra, and unless I can truly see practical application otherwise beyond that book, everything else is just Boolesh*t. Nothing more is needed than that, and to me is just convoluting the matter...

I consider my investigations (and this conversation and paper, by extension) a direct extension of his Laws of Thought. He was trying to "get at" the very fabric of human reason, which ANY model of the universe and "theory for everything" has to hearken back to. We don't understand reason, so how can we think we will understand what reason is identifying?

Probing the "right side" of his seminal 1 = ∞ (and by extension 0 = its complement) identity is my angle here... THAT is where the 5D engine exists and where a model is going to be birthed from, once we can use _INFINITY as the 5D geometric computation device in the _CONSCIOUS and _LIVING being.

 

Correct! "1" just means any unique "number" in reality!

That's like saying "red" means any color in reality. At best, it's just plain confusing. And then there's the whole can of worms when we allow theorems such as "1 = 2".

Boole's identity as a foundation for the Laws of Thought (and is empirically proven in daily use) is simply marrying the concept of boundedness on the left of it to unboundedness on the right.

If the thing on the right of an equals sign is unbounded, then -- at minimum -- the thing on the left better be unbounded, too. Otherwise, the proper relation is less than "<" or greater than ">", depending on which side the unbounded thing sits.

Because he's using 1 as an elemental contrasting "something" — one can put n-length byte to the left of the identity, and whether 1, 01011, 1101010, 11000110 — these are all existential placeholder tokens for unique infinite universes (within a parent metaverse of universes). Any of them can be on the left side of the equation, irrespective of cardinality. It's simply a uniquely labeled TRUTH state + cardinality overlap. If there wasn't one, bits could NOT be used for computation purposes.

"Unique infinite universes"? What unique universe, pray tell, is 101 a placeholder for?

. . . beware the potential DEBKAC (Dragon Existing Between Keyboard and Chair here).

Hah! I love this warning! Yes, yes, we must always beware the DEBKAC!

Ummm... If ℝ is the set of all real numbers and ℝ = {x | -∞ < x <∞} and INFINITY is NOT a componental element of the set, then ℝ is simply INFINITY #59108-B, no?

So, \( \mathbb{R} \) is tricky to define. Your definition doesn't work because it assumes \( \mathbb{R} \) in its definition (to see this, note that you could have defined \( \mathbb{N} \) precisely the same way). Historically, it was a long time between when humans first started using real numbers and when we finally figured out how to cogently define the reals. But we needn't bother defining it. I think it's sufficient to say that there is no INFINITY within \( \mathbb{R} \).

Where INFINITY pops up is when we try to write down examples of \( \mathbb{R} \) in some base, as the vast majority of real numbers are irrational. There's also the cardinality issue, when taken as a set: \[ |\mathbb{R}| = 2^{|\mathbb{N}|} \] In other words, the cardinality of the reals is exponential in the cardinality of the natural numbers, but this is an _INFINITY that we need not concern ourselves with now.

Heck, one could make an infinite alphabet, after Z, ZA, ZB, etc. It would be simply INFINITY #54919918-C, no?

The cardinality, magnitude, etc. of them are separate beasts.

Indeed, there is a mind-blowing bestiary of transfinite cardinals and ordinals, carefully collected and displayed by stern set theorists. But all of them belong to _INFINITY.

I have a little issue with the word "process" here. As if "machinery" is required to negotiate what appears to be an uncalculated phenomenon?

Tying one's show is a process. Counting is a process. Transferring energy is a process. A chemical reaction is a process. An INFINITE process is one that's repeated, as Euclid would say, "indefinitely". What's the issue?

I haven't referenced The Elements in a long time, but I could have sworn Euclid's axioms were about essentially defining _REAL as having infinite points between 2 points, in contrast to ones we see in the natural world that are composed of discrete number of points (interpolated to infinity in my mind)? You have no reference point without invoking infinity to describe the form.

I'm not familiar with the token _REAL. I'm also pretty sure Euclid never used the word "real" or "infinite" in his Elements. He defines a point as an indivisible unit ("that which has no part"), which is certainly discrete. He used points to define a line as a "breathless length between two points".

Assuming that, Pi's first-order definition is in reference to a _REAL Euclidean-space circle whose circumference is ∞ and whose diameter is also ∞.

The association between Pi and Euclidean-space circles is certainly the most familiar, but it's not the definitive aspect of Pi. Indeed, circles in non-Euclidean geometries (which are the vast majority of geometries) have different values for the ratio of circumference to diameter, i.e., what we'd normally call Pi.

Pi is just an ordinary real number. It has the property of being a transcendental (non-algebraic) number, but most real numbers have this property, so Pi isn't special in this regard. It's purely coincidental that the scale factor between a circle's circumference and its radius is Pi in \( \mathbb{R}^2 \). In other geometries, the scale factor is some other number. Note that our universe is demonstrably not Euclidean, so Euclidean geometry has no privilege or exalted status over other geometries.

In contrast, \( \sqrt{-1} \) is a special number, as it's the unique number that forms the algebraic closure of the reals. Of the unimaginably enormous set of real numbers, it's missing precisely one single number to make it algebraically complete. By including that single number, suddenly every polynomial has a solution. That's rather special, I'd say. In comparison, Pi seems quite pedestrian.

But the wave is separate from the particles. The wave is moving the discrete particles, and is considered a periodic disturbance OF the particles. The wave itself is a blast of periodic energy. A sine-wave can be plotted and subdivided by infinite floating-points. Truly continuous phenomenon is continuous only because of this property, in contrast to discrete phenomena.

The wave is the motion of the particles. Mechanically, a source provides the energy to set the medium (the particles) in periodic motion, but without the particles there's no wave! The fact that we often model waves as continuous is merely a mathematical convenience -- it's much, much simpler mathematically to treat a wave as a continuous system of a single equation, than as a discrete system of a trillion equations. Treating the wave as a continuum allows us to use all the mathematical machinery of real numbers and calculus, which makes the equations way easier to solve.

All of physics is like this. We don't know what that smallest units are (maybe everything becomes discrete at the Planck scale), but we know that it's far easier to model physical phenomena as continuous functions. When we calculate heat transfer, or fluid dynamics, or whatever, we treat the heat/fluid/etc. as a continuum, because the more accurate alternative is trying to write discrete equations for every molecule in the system, and that would very quickly become an impossible mess.

It's important we note the implicit as well as explicit models in use. And when we talk about continua, we're almost always implicitly assuming a mathematical simplification.

 

1) Original axiom — any material substrate, including the human brain is a bit-processing substrate of n bits.

2) How does the substrate define a number if not by bits?

3) What is _INFINITY to the substrate in terms of those bits?

 

Hmmm... I know they teach in high and undergraduate the concept of using "REAL" when describing a theoretical line (as referenced in the prior post). We're plumbing depths of the very congenital linguistic engine, so INFINITE and _INFINITE here are potentially united in a 5D REAL definition that unifies bits, logic states, numbers, and geometric form to create a model for _REASON.

The real line is a mathematical object, wherein every point is a unique real number. Euclid had no understanding of \( \mathbb{R} \) (it hadn't been invented/discovered yet), and so his lines are not real lines, as we understand them today.

This calls out an important distinction of context in mathematics. A line, as a geometric object, need not be comprised of real numbers -- any field of numbers will do. The real line can be considered as a geometric object, but we rarely do so, as the real qualifier is redundant (a line of one type is isomorphic to every other as a geometrical object). The real quantifier typically implies an algebraic or number theoretic context, in which case the real line is usually not a geometric object. For example, in an algebraic sense, the real line is isomorphic to the real cube, as we can uniquely map every point on the cube with a point on the line. Obviously, we don't think of lines and cubes as being in any sense geometrically equivalent, but they can be considered algebraically equivalent. Hence, the importance of denoting the background context. (Much, much confusion occurs when the context is not made clear.)

There is one _REAL Euclidean plane (we have not defined _REAL), but the one that is on a computer screen that you can plot things into is not _INFINITE, if unboundedness is all that is _INFINITE. Everything other than the one in the 5D mind would not be considered _REAL, and any computed version that isn't invoking infinity specifically is a piece of discretized simulative software for the _INFINITE / _REAL version.

Unboundedness is the essential aspect of INFINITE, the version of infinity that we've cogently introduced into our model. (The various, wacky aspects of _INFINITE are extra-model affairs.) Until we define _REAL, it's a parse error. As a mathematical object, there is one Euclidean plane, full stop. As for drawings on computer screens, they are shadows on the cave wall (back to Plato).