I would like to clarify very emphatically something here, especially for anyone else reading:

True math and logic is the very underlayment of sanity. True balance, symmetry and fairness are mathematically described. I have the utmost of respect for those who study these fields, and with them, build technologies we can use every day. Only a blithering fool would question the mathematical sciences that allow him to type on a computer built by them, which is the empirical proof of their conceptual and applied veracity.

Though it seems as though I may be doing "just that" at times, I want to clarify specifically that this actually isn't true.

I am interested in the "substances behind" the math, and bare essences that allow us to potentially scientifically define things that "lie outside the numbers" by "using the numbers and logic to triangulate them." For example, the set ℝ is well defined, and in use every day. My intention is to not disprove the existence of it, but to probe the deep reasoning beyond number construction itself that led to defining all sets as they are, and the potential hidden connections between them, infinity, consciousness, and enumeration in general, that may lead certain experts to make sweeping intuitive claims, like Pythagoras and Kronecker — claims I feel I share.

In the same way alchemist Newton attempted to triangulate a strange thing he called "a force" in the 18th century using established concepts like mass and acceleration, I believe this "triangulation" approach can be had in delineating a better concept of the nature of consciousness, life, reason, form, feeling, meaning, order, disorder, and the intersection of the continuous and the discrete as it relates to a "theory of everything."

Though I myself am not a trained mathematician, I am akin to a person who was raised in a family that spoke another language for years, and though she can't conversely speak it herself, she understands it when she hears it. My strength is deep intuition that has never failed me, deep linguistic awareness, logic, and the gift of being able to plumb the core drivers and inconsistencies of any system as a kind of "ontolo-apologist," as well as in having years of exposure to computer hardware and software systems at every level.

It should be said and publicly recognized that Javier here is positively a consummate mathematician, and one can see his conversance across a variety of intersecting topics. It is at least in 50% part due to his rigid adherence to specificities, protocols and communicative conventions used by academia that we have any hope of writing any kind of respected white paper on the topic of a Theory of Everything.

 

My strength is deep intuition that has never failed me, deep linguistic awareness, logic, and the gift of being able to plumb the core drivers and inconsistencies of any system as a kind of "ontolo-apologist,"

Life is all about finding people who are your kind of crazy. You are out there...in the ether. I'm always in awe of people who are artists in their fields - people who understand that simply by taking ideas and translating them into reality, they've created value in the world.

 

A Tabula Rasa Observation upon Numbers

Way before there were any number sets of any kind, mankind groked the use of what we call a "number."

What is a number specifically?

To find out, we have to figure out how we all universally use it as part of the innate language within our universal psyche.

Let us assume we are early man, and have come across several rocks in a field. We have very simple language. We see rock, and we GRUNT. We go to next rock, and we GRUNT GRUNT. Then we go to next rock, and we GRUNT GRUNT GRUNT. Then we go to next rock, and we GRUNT GRUNT GRUNT GRUNT.

We now have rocks that are uniquely labeled, using GRUNT as the only token:

GRUNT ROCK
GRUNT GRUNT ROCK
GRUNT GRUNT GRUNT ROCK
GRUNT GRUNT GRUNT GRUNT ROCK

Today in English we may call that GRUNT 1 or one. Remember, we can't say we have 4 rocks. We don't know what 4 is. So let us rename our rocks using more familiar terminology:

ONE ROCK
ONE ONE ROCK
ONE ONE ONE ROCK
ONE ONE ONE ONE ROCK

The question is, how many rocks do we have? You may be tempted to say 4, but we don't have that luxury. The answer is, we have no idea how many we have, because we don't know the last rock has two roles:

1) it represents both the unique label of one particular rock and also
2) the totality of the number of rocks we are working with

Also, we don't know ONE ONE ONE ONE comes after ONE ONE ONE or is a larger number. We don't know one is the first rock 1 of 4. We haven't invented the concept "1 through 4."

Using one as our only number, we can attribute qualities like size and sequentiality only with a reference point to something else. That is, only if we associate one rock to another do we have any idea that any particular element is "later" or "before" in a series, or "bigger" or "smaller."

Before we invent any other numbers, we must take note:

Our number is therefore a generic, unique name only. Indeed, many might say, "Don't call me a number, I'm a name." But in reality, if you were named 4842, people could refer to you by that as a name.

So a number is first simply a generic assignment of unique nomenclature or label for an item. What does one mean? Nothing. Nor does grunt, uno, or une.

The term "meaning" here is somewhat self-evidentiary in the attribution of value mapped from a unique word token like one to an observed element in physical or mind space. We have token rock. Now we have one rock. Or rock one. A new token such as one does not have meaning until it is associated with something else to create a base observation of something.

One or rock are both NOUNS alone. But when one is attributed to rock (either before or after it), it becomes a modifier, or adjective to ascribe a uniqueness, or referentiality — that is, the ability to reference THAT SPECIFIC rock — by a certain, unique name, and the rock starts to have an elementary sense of contextual significance to thought or discourse.

Therefore, a number is FIRST a unique name. We "number" (verb) or "count" using unique names.

When we use the same name in succession, like one one, we are now creating a new unique name using the one number we have. We could technically label the rock we "first" encounter (note, we don't have "first" as an understanding, because first implies sequentiality that we don't know) as ROCK, then the next as ROCK ROCK, then ROCK ROCK ROCK, then ROCK ROCK ROCK ROCK. But because the word rock speaks to the object and not of any specific one, we can now add a word to it to make it special. We can use any word. It doesn't matter what it is.

With that one word, we are able to create the unique labelings for the token ROCK that is used to describe that object in space.

Rock one
Rock one one
Rock one one one
Rock one one one one

If someone asks us, “to which rock are we referring?” We can point to it in space, and say rock one one one. But that doesn't mean rock one one one follows rock one one or is before rock one one one one.

Not until we define the relationship between rocks can we say one comes "after" or "before". We can do that spatially using built in tokens AFTER and BEFORE, but not until we correlate AFTER and BEFORE to our number "one"'s arbitrary use can the words have any value to the token "one" itself.

Further, there is no concept of after or before without appending an inner space or time concept to give it meaning, or worth in discussing.

"Meaning" here is tied to what we are referencing. What does "one" mean until it is defined with respect to something else? Nothing. Token one gets its meaning here in relationship to token rock. Token one is employed more than once to describe another rock. One vs. one one vs. one one one has NO defined meaning or partiality of relevance to us until we treat one one as a separate element from one vs. one one one, etc.

How many rocks do we have?

The concept of how many gets its meaning from the last thing we attributed value to. To say we have one one one one rocks isn't correct until we define one one one one in relation to the other rocks, or the use of one in relation to the multiple use of one. How do we know that one one one one is bigger or greater than one one for example? We don't.

Notice it's tempting for us to say, "Well what if we have n ones then we simply know". We do not have n here to do such a thing or question such a thing with it! We only have one thus far!

If we want to use "one" as a token to describe another object in space, we have the same issue.

Chair One
Chair One one
Chair One one one
Chair One one one one

Using the token one again, we have the same issue. Which chairs are "before, after, bigger or smaller?" No idea. We haven't defined it.

So if we want to use the same token "one" to number different objects in different sets, we must delineate the relationship between the use of one vs. one one vs. one one one vs. one one one one one irrespective of the object these tokens are describing.

We must create the concept of "sequentiality" or "ordinality."

We may say:

Example 1:
One, then one one, then one one one, then one one one one.

Note that there is absolutely nothing that prohibits us from doing:

Example 2:
One one, then one, then one one one one, then one one one.

The thought that one one one one is bigger or "more than" does not conceptually exist in any example as of yet.

Now, the innate concept of sense might say, or perhaps feel to all human beings, that the first order shown above is more rational, as possessing more innate order in that we are building upon the former sequence to create higher quantity. There are more one's, so we should start from a smaller number of one's and work our way up to having more.

But what is higher value when all the rocks are the same? When there is no bigger rock in size, and there is no partiality to the order that we are naming them in, why is it important?

Within each person is the concept of "addition". This is an innate order structure in the being. If we have rock one, we can add it to rock one one and we get rock one one one. We can actually establish the additive rules without the need for a rock, so that if we are dealing with a chair, a table, or anything else, the same rules apply.

One + one = one one
(One one) + (one one) = one one one one
(One one one) + one = one one one one


Same with subtraction:

(one one) - one = one
(one one one) - (one one) = one
(one one one one) - (one) = one one one

But then something strange happens when we do this:

one - one = ?

One - one we have not defined, because we have nothing other than one yet! We can't use one to label the absence of all rocks.

In every case above, when we used token one singly or multiply, we were labeling something we could observe.

In the set of rocks we were dealing with, we did not have more than one rock labeled "one", so there was no way to subtract any specific rock from another and yield the absence of all rocks as a number unto itself!

This problem only arises when we are dealing with 2 different sets of rocks, but each are named using token "one" in some way. If we have a bunch of other rocks that we are labeled identically with the same naming scheme, and we want to subtract rock one from one set to rock one from another set, we must create another label for the absence of rocks. We can call that zero.

So now we have the fundamental flexibility, with two numbers, one and zero, to create more unique labels for more rocks.

But before we do that, we still do not know "how many" rocks we have in any one set, because we have not established partiality to any one element of the sequence. We must establish rules to do this by attributing a quality one might call "feel" to this to be able to make sense of this difference. It simply "feels right." Otherwise there is no intellectual justification to show partiality to one particular element in the set with any other. The uniqueness of each set's name is a separate metric from its comparative relationship to any other.

Even using addition and subtraction, "one one one" rock is no more than "one one" unless we define token more to mean greater comparative quantity to something else. OTherwise it's just a different name. And "one" is no less than "one one" unless we do the same. By creating a relationship between "ones," we can then tell "how many we have in the set":

Rock one
Rock one one
Rock one one one
Rock one one one one

How many do we have in the set of rocks? We have established the final element to be the name of the final rock AND the name of the "total number of rocks" we have in a given set.

The meaning of this difference one could call FEELING. In the same way a heavier rock ways "more" than another, we determine the values we attribute to it based on experiential feel. Every person picks up a rock and can label it one value. If the next rock weighs differently, we will attribute the word more or less to the weight. If it weighs heavier, we will say it weighs "more." For the next rock, we will say the same.

Thus, if we attribute an observational and experiential difference between rocks, we can justify an order to the rocks based in an observable experiential thing.

But what if the rocks are all identical? What if we still want to have a concept of sequence without a property difference to the rocks?

We can again invoke the sense of "more" by saying one one is greater than one. And one one one is greater than one one, and one one one one is greater than one one one. We are now attributing successive feeling of moreness to a greater presence of "ones" and "lessness" to a lesser presence of ones.

From rock one to rock one one, we have increased in size of the number of rocks we are working with. Size here is a term we are using to compare the quantity of total rocks we have vs. another quantity. Without the comparison, we do not know we have size. Size can also be called "cardinality."

And thus, through universal feel, we have created the concept of ordinality and cardinality using just one number.

But what about 0 — the other number we have made?

(to be continued)

 

Life is all about finding people who are your kind of crazy.

Good t-shirt! Cheers

 

A smile is something you can’t give away; it always comes back to you.
I also do a whole lot of grunting believe it or not that's why I prefer
GRUNT ROCK
GRUNT GRUNT ROCK
GRUNT GRUNT GRUNT ROCK
GRUNT GRUNT GRUNT GRUNT ROCK

 

A smile is something you can’t give away; it always comes back to you.
I also do a whole lot of grunting believe it or not that's why I prefer
GRUNT ROCK
GRUNT GRUNT ROCK
GRUNT GRUNT GRUNT ROCK
GRUNT GRUNT GRUNT GRUNT ROCK

After a monumental leap in time, they reappeared here.

 

After a monumental leap in time, they reappeared

The irreversibility of leaping in time,they reappeared both grunting.

 

You CANNOT represent any number in your PC. Just like the decimal system, some numbers can only be represented by an infinite length of bits. And there are some solutions to a function which do not exist. Just like fractals in the decimal system.

So any argument based on the assumption that ANY number can be represented by a fixed length of binary is wrong.

 

Question about how you define and reckon an undeniable, as-demonstrated statement, a “QED”:

Would you say the statement (and I have to make it personal, and humorous, so the point has relevance):

“I am a human, my name is Javier” is a QED?
“I am married with a daughter” is a QED?

Any news on this question, because I'm curious how you handle the whole "others believe in objectivity thing" from the Cantoral Temple of Set —

"Do you have cajones to answer" is a QED?
"Are you sitting at your desk right now laughing" is a QED?

 

You CANNOT represent any number in your PC. Just like the decimal system, some numbers can only be represented by an infinite length of bits. And there are some solutions to a function which do not exist. Just like fractals in the decimal system.

So any argument based on the assumption that ANY number can be represented by a fixed length of binary is wrong.

Correct. Any finite physical medium can store a finite 2ⁿ bits. It is the source of my very contention that a finite bit processor such as the brain has no “business“ trafficking in such “supra-numeric” elements, and that there is a theoretical storage medium that is 5D, storing infinite, continuous geometric thought forms and waves in a “different state” than what is observed in physical reality. AKA the mind-brain duality shared by Newton and dozens of others.

It dawned on me: in a unary framework, you can’t even tell how many bits you can store using math, because math is based on outputs having a TRUE/FALSE XOR nature.

So... 1ⁿ ? AKA— 1 big massive bit?

 

Writing decades after Cantor's death, Wittgenstein lamented that mathematics is "ridden through and through with the pernicious idioms of set theory", which he dismissed as "utter nonsense" that is "laughable" and "wrong".

A counter proof to transfinities:

https://arxiv.org/pdf/math/0408089.pdf

Thinking infinity is essentially “finished” which effectively renders it a discretized quantity, is to nullify its own definition, calling a cat a dog, and vice versa. Nope!

Unfortunately, this blurs mathematical truth and falsehood and is the very sanitarium Cantor died in.

 

But as a physical device, you have no “right” separating the math from the physical. You are the physical. You are the math.

Have my Conceptual Constitutional privileges been revoked?

I can grab a few rocks from the ground and count them. Suppose I count three rocks. The concept of 3 and the rocks in my hand are entirely different states. How do I know? Because I can grab a few sticks, count them, and arrive at the same concept of number 3. I doubt you would disagree that the rock states and the stick states are different from each other. Therefore, the states associated with the number 3 must also be different from each of these. Therefore, the physical and the math can indeed be separate.

Conceptual Constitutional privileges restored!

Our terms need to be precise, but also not presumptive. “Concepts” are bits of highs and lows. You’re a brain made out of dirt. Math is literally neurons. Abstractions are groups of highs and lows. Must see from the most granular or conclusions and “proofs” can be made that do not reflect the physicality.

Above I gave the high-level view; here's the low-level view.

It's all just states, but if all the states were identical, then the universe would be an indistinct homogeneous goo in which nothing happens (this is one possible way the universe "ends"). Since the universe is not this way -- there are stars and planets and such -- there must be differences in state.

An information processor acts on these differences -- these differences are information.

Consider that each air molecule in a room has an associated state. The state of the air in the room, then, is the set of air molecule states. This "air state" is a very large state that, by virtue of its degrees of freedom (how much it can change), can hold some amount of information. If I yell "Hey!" into the room, I modulate the air, arranging it in such a way that another information processor can receive the information. This is how information gets "moved around".

Once received by an information processor, what happens to the information depends on how the processor was designed. Generally speaking, the information is stored and then acted upon. In the case of humans, we tend to use information to make associations with other bits of information that we've stored (i.e., we tend to look for connections between events). Part of this process often includes building, organizing, and using a set of states (CONCEPTS) that are not the direct result of external events. These internal states include things such as love, jealousy, fear, math, and political affiliations.

So, yes, one might say that "math is literally neurons", but that doesn't reflect the characteristic differences between, say, hearing a sound (which is also literally neurons) and pondering the nature of infinity.

Also, I want to say again, please ignore my capital letters, bolds, exclamation points as anything other than an attempt to inject passion into the arguable dispassionate machinery. Anything sounding like an ass is toward the frustration of communication and wanting to see my intuition proven alone, and not at all toward you. I very much appreciate your taking the time to delineate stuff with such detail. It’s a pleasure discussing these things with you, even though I want to uninstall 35% of certain software you came through time with.

100%! I totally get that and totally agree! This is a long, involved conversation. I know personally I've responded when I was having a bad day, which no doubt influenced the tone of my response. And there's always an undercurrent of the hard problem of communication, which can be frustrating. But I truly enjoy this and look forward to it daily (even though you make batsh!t crazy claims about ℝ).

 

Writing decades after Cantor's death, Wittgenstein lamented that mathematics is "ridden through and through with the pernicious idioms of set theory", which he dismissed as "utter nonsense" that is "laughable" and "wrong".

A counter proof to transfinities:

https://arxiv.org/pdf/math/0408089.pdf

Thinking infinity is essentially “finished” which effectively renders it a discretized quantity, is to nullify its own definitiom, calling a cat a dog, and vice versa. Nope!

Unfortunately, this blurs mathematical truth and falsehood and is the very sanitarium Cantor died in.

Apparently, the author is considered a crackpot by professional mathematicians. Anyway, in his "proof" there is at least one glaring flaw: he assumes en enumeration of ℚ that preserves the order of ℚ, which cannot be.

It's not hard to show a bijection from the rationals to ℕ, but any such algorithm is necessarily un-ordered: it is impossible to list the rationals "in order".

To see this, suppose that p and q are two rational numbers, with p < q, and let [p, q) be an interval of ℚ. What number follows p? We might guess p/2, but p/4 is smaller. If we try p/4, we see that p/8 is smaller. For any n we can think of, there will always be a rational number closer to p than p/n.

 

Have my Conceptual Constitutional privileges been revoked?

I can grab a few rocks from the ground and count them. Suppose I count three rocks. The concept of 3 and the rocks in my hand are entirely different states. How do I know? Because I can grab a few sticks, count them, and arrive at the same concept of number 3. I doubt you would disagree that the rock states and the stick states are different from each other. Therefore, the states associated with the number 3 must also be different from each of these. Therefore, the physical and the math can indeed be separate.

Conceptual Constitutional privileges restored!

Agreed to the first part. Hopefully my little "rock-grunt" story illustrates that well, because they are, indeed fundamentally different. "Concept 3" can apply to sticks or stones.

As always, we can look at "Concept 3" at a 7GL or a ZOFP abstraction level. We need to get ridiculously specific, as you said.

We must see any machine as being programmed and relating to its environment as the basis of what it's "doing to that environment."

This is essential, because no human "machine" exists in a vacuum. It's working on external stimulus, and it has built-in reference points to work with it.

Problem I'm having is how "you" (which is some undefined group of states) will "point" to 45,000 other discrete states and say "concept 3," when any machine must be programmed at any given moment in time to react to stimulus in physical space and "know 3 even applies" with respect to what it's referencing (and we haven't even defined "what"... because remember, they're just photons hitting your CCD). You're saying at that very moment, "nature" programmed you to use "those 45,000 states" to "flick high" in relation to that particular string of states, and not the 87,000 neighboring states that may reflect 13.493 to describe said stones, sticks, or TV sets, that you might even be envisioning as imaginary sheep in your mind(!). How do you know the states reflect 3 countable things in reality — THOSe specific things having "more meaning" to you at that moment vs. not (again, meaning not defined) — and not, for example, a picture, a dream, or even another concept of those things? Further, you only have digital classification essentially (because the said dog, cat, stones, sheep etc. are not geometrically in the space as described).

Where is the "partiality" and "predilection" coming from? Nature? Where's hers?

You would agree there's a distinction between geometric form and informatic "form"... where is this "differentiator" intelligence?

 

Apparently, the author is considered a crackpot by professional mathematicians. Anyway, in his "proof" there is at least one glaring flaw: he assumes en enumeration of ℚ that preserves the order of ℚ, which cannot be.

It's not hard to show a bijection from the rationals to ℕ, but any such algorithm is necessarily un-ordered: it is impossible to list the rationals "in order".

My entire contention is that at some point prior to Cantor, we didn't have "sets." We had numbers, and we decided to "group them into sets" having "set properties." By making "infinity" a natural physical thing, we have simultaneously bastardized its definition and created another thing. I'm sorry, but I side with Aristotle, Leibniz, Gauß, Cauchy, Kronecker, Konig, Wittgenstein, and others.

His "indirect proof" *exists* as a sole function of the existence of man-made abstractive sets. That's my entire contention. Who is to say the phenomena of "numbers" belong in any set? The numbers are built-in to us, the sets are something we "made" and now we're forced to try to make sense of what we made.

The complete state of the matter in empirical existence is that every single set can be represented by 0's and 1's, and we're essentially grouping the 0's and 1's into abstract "concepts" for our own purposes. It's really ZOFP vs. Visual Basic again.

We innately know infinity exists outside of n. What business do we have as n-discretizers to "look outside of n" and pull it into itself? To "boundarize" infinity is self-negate its own definition and create another n with a different name!

 

"Cantor's continuum 'is mostly made of gaping holes'" said the modern noted metamathematician, Gregory Chaitin, at IBM's T. J. Watson Research Center in Yorktown Heights, New York, "shattered mathematics with a single number" [Chaitin 2001]. Chaitin named this number Omega ['ÍT] (not to be confused with Cantor's patent transfinite ordinal 'omega' ['w']!). Chaitin's Omega is "an unending, random string of 0s and Is" where the value of nth binary digit is defined by the condition of whether a certain Diophantine equation ("that was 200 pages long and had 17,000 variables") has a finite or infinite number of solutions for each value of some parameter n = 1, 2, 3, Chaitin states that each digit of such a binary sequence "is as unrelated to its predecessor as one coin toss is from the next," and therefore the number Omega is "the outstanding example of something which is unknowable in mathematics." According to Chaitin, his "Omega infects the whole of mathematics, placing fundamental limits on what we can know." He has found that "the core of mathematics is riddled with holes." Chaitin has also shown that "there are an infinite number of mathematical facts but, for the most part, they are unrelated to each other and impossible to tie together with unifying theorems. If mathematicians find any connections between these facts, they do so by luck."


The brain is a discrete counting machine that works on binary principles (per John Von Neumann), and we create binary computers as a reflection of our own logic centers. All of our "man made" sets can be represented with 2 logic states. (QED)

For the record, while I think existence can be considered unary, I believe REASON must be binary, for the simple reason that in order to determine the truth value of whether or not you have a "4, 9, or 5", you must distinguish between 2 logic states:

@@@@
@@@@@@@@@
@@@@@

"Is it TRUE" that @@@@ == @@@? NO, therefore {execute...}
"Is it TRUE" that @@@@ == @@@@? YES, therefore {execute...}

There is no computational reasoning without binary foundation, because you can't create conditionals and logic branchings without at least 2 fundamental states.

My entire contention is that those base logic states are the building blocks of all numbers, and man-made sets. It's utterly irrefutable that we are able to represent all numbers, systems, and calculations with these 2 fundamental states. Empirically proven all day long on the very computers we are using to communicate. These logic states 1 and 0 I believe double as 2 different "flavors" of infinity (as in positive and negative, polar "attraction or repulsion"). We then discretize these infinities into integer 1 and 0, and then we create even further abstractions from those foundations.

 

Problem I'm having is how "you" (which is some undefined group of states) will "point" to 45,000 other discrete states and say "concept 3," when any machine must be programmed at any given moment in time to react to stimulus in physical space and "know 3 even applies" with respect to what it's referencing (and we haven't even defined "what"... because remember, they're just photons hitting your CCD).

The states associated with "concept 3" are internal states that were derived from external states. I didn't start out with "concept 3" in my brain -- those states developed as I experienced the world and formed internal associations.

You're saying at that very moment, "nature" programmed you to use "those 45,000 states" to "flick high" in relation to that particular string of states, and not the 87,000 neighboring states that may reflect 13.493 to describe said stones, sticks, or TV sets, that you might even be envisioning as imaginary sheep in your mind(!).

What do you mean "at that very moment"? At the moment I saw a group of rocks? When I see a group of rocks, it takes some time for the visual information to be transferred and stored, and then a bit more time for the pattern matching on my internal associations. Once the appropriate patterns are matched -- I'm looking at a group of rocks, and each rock is a distinct thing -- the association with "concept 3" is formed. I don't associate "concept 13.493" with groups of distinct things, so that connection wouldn't be made.

How do you know the states reflect 3 countable things in reality — THOSe specific things having "more meaning" to you at that moment vs. not (again, meaning not defined) — and not, for example, a picture, a dream, or even another concept of those things? Further, you only have digital classification essentially (because the said dog, cat, stones, sheep etc. are not geometrically in the space as described).

I don't understand your point. "How do you know"? I don't know with 100% certainty, but -- given the various states before and the various states after -- I surmise that I am not dreaming or whatever. On the other hand, I may be engrossed in a movie and a scene with three rocks comes on the screen. I may "forget" that there aren't actually three rocks in front of me because, to my fairly autonomous visual processing system, there are three rocks in front of me.

What's the big deal?

Where is the "partiality" and "predilection" coming from? Nature? Where's hers?

You've used these two words before and I still don't understand what you mean by them.

You would agree there's a distinction between geometric form and informatic "form"... where is this "differentiator" intelligence?

I'm in a room with a rock and a chair. What's the difference between them? At the abstract, information-processing level, their properties are different -- chairs have chair-like properties, e.g., crafted structures that are used for sitting, and rocks have rock-like properties, e.g., natural structures that are hard. Crafted, natural, sitting, and hard are all concepts in my brain, each derived over years of experience with the external world. When I see the rock and the chair, I associate the corresponding concepts with them. I, the information processor, is the differentiator at the abstract, property level of differentiation.

At the low-level, sensory data level, the differences between the chair and rock are the differences in their states. The rock reflects light differently than the chair, and that state-level information is captured by the photoreceptors in my eyes. That their is a difference is noted by my processing, which kicks in the various higher-level associations. But at the state level, the universe is the differentiator.

 

My entire contention is that at some point prior to Cantor, we didn't have "sets." We had numbers, and we decided to "group them into sets" having "set properties."

It's not like one day humanity decided to see what would happen if we treated numbers as sets. Rather, when humanity sat down to say, "Ok, wtf are these number things, anyway", and tried to answer in a rigorous way, set theory popped out.

Set theory is our attempt to describe what's happening under the hood of numbers. Set theory speaks to the foundations, not the practice. You're free to ignore set theory -- most mathematicians do -- but if you want to speak foundationally about numbers, then you're going to need a formal system that doesn't already assume numbers. Hence, set theory.

By making "infinity" a natural physical thing, we have simultaneously bastardized its definition and created another thing.

Huh? Who suggested that infinity is a physical thing?

I'm sorry, but I side with Aristotle, Leibniz, Gauß, Cauchy, Kronecker, Konig, Wittgenstein, and others.

Side with them on what? Leibniz believed in infinitesimals, which are way[/] outside the realm of integers. Gauss, the greatest of them all, invented non-Euclidean geometry. Cauchy formalized the notion of a limiting process; it is because of Cauchy sequences that we can define ℝ. Kronecker needed to get laid. I don't know Konig is. I don't think Wittgenstein knew much about math.

His "indirect proof" *exists* as a sole function of the existence of man-made abstractive sets. That's my entire contention. Who is to say the phenomena of "numbers" belong in any set? The numbers are built-in to us, the sets are something we "made" and now we're forced to try to make sense of what we made.

It seems pretty arbitrary to suggest that sets are "man-made" and numbers are "built-in". They're both abstractions. Moreso, we can define numbers in terms of sets, but we can't go the other way. It seems cogent to say that sets are more fundamental in some way. Indeed, math is built on top of logic, and logic and sets go hand in hand.

We innately know infinity exists outside of n. What business do we have as n-discretizers to "look outside of n" and pull it into itself? To "boundarize" infinity is self-negate its own definition and create another n with a different name!

Who is "boundarizing" infinity?

 

The states associated with "concept 3" are internal states that were derived from external states. I didn't start out with "concept 3" in my brain -- those states developed as I experienced the world and formed internal associations.

What do you mean "at that very moment"? At the moment I saw a group of rocks? When I see a group of rocks, it takes some time for the visual information to be transferred and stored, and then a bit more time for the pattern matching on my internal associations. Once the appropriate patterns are matched -- I'm looking at a group of rocks, and each rock is a distinct thing -- the association with "concept 3" is formed. I don't associate "concept 13.493" with groups of distinct things, so that connection wouldn't be made.

I don't understand your point. "How do you know"? I don't know with 100% certainty, but -- given the various states before and the various states after -- I surmise that I am not dreaming or whatever. On the other hand, I may be engrossed in a movie and a scene with three rocks comes on the screen. I may "forget" that there aren't actually three rocks in front of me because, to my fairly autonomous visual processing system, there are three rocks in front of me.

What's the big deal?

Because of the unreal level of abstraction. ;--) This is like a 938GL language. Like that statement is 300% zoom, and I need like minimally 1200% just to understand what you're talking about. You want to talk about rigorous??

A machine is based on some kind of instructive, sequential calculation schema utilizing a highly tuned ratio of external stimulus and stored stimulus that an agent programs. Concepts like "it was formed" over time is to me like saying, "Well, over time, my camera on my laptop just began developing circuitry that started doing face recognition, and the code appeared in the stack that is able to organize all of the stimulus into just the right neuronal flip flops. And then one day I found it video-conferencing on its own with another computer in Bejing. What's the big deal?"

At the low-level, sensory data level, the differences between the chair and rock are the differences in their states. The rock reflects light differently than the chair, and that state-level information is captured by the photoreceptors in my eyes. That their is a difference is noted by my processing, which kicks in the various higher-level associations. But at the state level, the universe is the differentiator.

"The universe is the differentiator!" Can we talk about the differentiator without invoking incredibly abstract terms like "evolve" or "chance" for a moment? It is this very Differenza® SDK that I'm interested in understanding. Like all of that code that's in the 6 interrogatives that is parsing an unreal amount of multimedia stimulus, knowing which waves to keep "discrete" and which to parse to create "meaning"?

 

There is no computational reasoning without binary foundation, because you can't create conditionals and logic branchings without at least 2 fundamental states.

You're confusing concepts. What makes binary logic binary is that there are only (not "at least") two different logic states. Conditional branching is an entirely different notion. To wit, you can have three or seven or however many conditional branches you want, irrespective of the number of acceptable logic states. This is so because we can use relation operators, such as "equals to" or "greater than", that evaluate to one of the logical states.

Remember, any single if/else conditional statement has an equivalent form as two if statements:

if ( x == a ) then doA();
else doB();

is equivalent to

if ( x == a ) then doA();
if ( x != a ) then doB();

What would conditional branching look like in a unary computer? A bunch of if statements:

if ( x == a ) then doA();
if ( x == b ) then doB();
if ( x == c ) then doC();

My entire contention is that those base logic states are the building blocks of all numbers, and man-made sets. It's utterly irrefutable that we are able to represent all numbers, systems, and calculations with these 2 fundamental states.

You're right, it's utterly irrefutable that we can represent any number or calculation in base-2. But the gigantic, blinking-neon point that you're missing is that it is utterly irrefutably true for any base. There is nothing special about base-2.

These logic states 1 and 0 I believe double as 2 different "flavors" of infinity (as in positive and negative, polar "attraction or repulsion"). We then discretize these infinities into integer 1 and 0, and then we create even further abstractions from those foundations.

What does infinity have to do with positive/negative or attraction/repulsion? It's crazy-talk to suggest that 1 and 0, pillars of finitude, are flavors of infinity.