Information in analog wave

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
756
Whatever helps you sleep at night. :cool:


You said that "mind-space" is distinct from "physical-space", so is mind physical or not?
Yes, it is. But it can only be perceived internally. I can “grok” by “sense” and conceptualize an infinite line whereby I can “pull points” off it, but the line remains undivided. The line is in a “space” and I can “feel” it and do literally anything with it, like bend it into a dog form, and put a light on it, attribute apple flavor to it, then eat it. The whole space is an environmental “state” of some kind.
 

bogosort

Joined Sep 24, 2011
1,037
Do me a favor if you will, as part of tabula rasa. Consider for a moment there might be something more than your brain. You don't know this is a fact or not, especially with such unidentified words like "feel" and "meaning" and "life." So be open to it instead of just shooing it at the rip so we can have a tabula-rasa starting point.
What do you mean by "there might something more than your brain"? I already believe this -- there are far more things than my brain in the universe.

To answer the question, intuition could also be seen as "imagination" or "conjecture." Feynman talks all about conjecture as the basis of science. Einstein declared imagination is most important. We do not CONCLUDE the theories based on intuition, but we can start it as a reasonable proposition. Where do you think most scientific postulates come from? Some inner sense that is often deeply hunched and then hashed out and pursued in a formal way.
Huh? Intuition is not a synonym for imagination. Intuition is closer to the opposite of imagination, as intuition effectively tells us that we don't need further explanation. Please re-examine your concepts of intuition and imagination.

I would say a minimal degree, yes. Because I link "consciousness" with feeling, which you've asked me about before.
Great! So, a cell is alive and has some degree of consciousness. Now, recognizing that a cell is just a molecular machine, what stops a computer -- an electrical machine -- from being alive and having consciousness?

Take a deeply felt performance of EVH (or whomever — pick another person so we can reference someone else, lol), versus a quantized version, where all the notes are "100% identical" but with 127-level MIDI velocity.

Which one is music to you?
I'd recognize both as music, though the heavily quantized version will sound stupid and shallow to me.

The one that you "feel" employs variable force application upon each note using different velocities and articulations that convey a thing called "meaning" to you.
An expressive guitar solo doesn't convey "meaning" to me, it conveys "musicality", which is difficult to define. Roughly, musicality for me is a combination of creativity and technical ability. The creative aspect is probably the more interesting one, and I think it relates to how "surprising" I find a musical passage. That is, due to my cultural upbringing and technical proficiency, I have a vocabulary of well-known melodic, harmonic, and rhythmic progressions. A song that is entirely a I-IV-V progression will probably bore me as "uncreative". An expressive guitar solo over harmonically interesting chords will tend to surprise my musical expectations, which have been developed over a lifetime of listening and playing.

I'd note that a performance need not be "expressive" to capture my interest. I dig minimalist composers such as Philip Glass and Steve Reich, who manage to have high musicality while sounding almost computer-quantized.

The feeling of the piece can invoke other "feelings" that are tied to imagery. This imagery does NOT seem like 1D data in the being, especially when you can close your eyes and enter perceived 3D worlds. These are NOT just 1D states.

Where are these "3D" worlds in your living being and in your dreams where such music is playing?
My optical states are almost never affected by a musical performance, i.e., I don't "visualize stuff" while playing or listening to music. There are no "3D worlds" in my musical experience.
 

bogosort

Joined Sep 24, 2011
1,037
I quote them both because they are established names that have legitimate lines of thinking and have established pillars in science, so I'm not just a "renegade cowgirl alone in the desert" on X topic. I only quote them (or anyone else) when I feel there is parity of thought there. I disagree with Einstein's presumptions about space. Math has no worth to me unless it has ontological significance. For the record, I don't disagree with Newton on anything.
Personally, I don't give a sh!t what Newton or Einstein or any other celebrity did or said outside of their formal work. You can tell me that Newton raped children and that Einstein was a nazi -- iit wouldn't matter to me, because none of it has any effect on the math and science they passed along.

Any bit string, even if infinitely long, is countable up to a point that a living human, and only a conscious, living (whatever THAT is) human made out of a finite amount of dirt, can come the f*ck up with "unique names" for them, because that's the origin point of the thinking on the matter.
A computer can count, so why the insistence on humans? Even if we restrict counting to humans, we don't know the upper bound on human lifetimes. Even if we knew the upper bound on a single life, we can continue a single count over multiple human lifetimes.

The only "end" to counting is if the universe ends. And since we don't know if that will happen, we can assume counting will go on forever. Therefore, ℕ is countable.

Good luck on coming up with unique nomenclature for grunt googolplex^99999, though.
You just did! We'll never run out of symbols to count ℕ.

I couldn't make sense out of the rest of your "proof".
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
756
What do you mean by "there might something more than your brain"? I already believe this -- there are far more things than my brain in the universe.
I mean to your being (and more than your body).

Huh? Intuition is not a synonym for imagination. Intuition is closer to the opposite of imagination, as intuition effectively tells us that we don't need further explanation. Please re-examine your concepts of intuition and imagination.
Technically, yes. However, to me, intuition is not unilaterally VALID typically until corroborated by reason, so that’s why I see both intuition and reason synergistically as “another way of saying imagination.” “I intuit that there’s a 5D space in the being.” “You’re just imagining things.” “Correct, not until I can substantiate it via logic

Great! So, a cell is alive and has some degree of consciousness. Now, recognizing that a cell is just a molecular machine, what stops a computer -- an electrical machine -- from being alive and having consciousness?
No, because I intuit “continuum” is part of first order definition of “know and feel” and a discretizing machine isn’t doing. It matches and computes, not feels and means.

I'd recognize both as music, though the heavily quantized version will sound stupid and shallow to me.
Hella interesting use of term there: shallow invokes serious sense of 3D dimension. No dimension to the music, no worthwhile meaning.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
756
Personally, I don't give a sh!t what Newton or Einstein or any other celebrity did or said outside of their formal work. You can tell me that Newton raped children and that Einstein was a nazi -- iit wouldn't matter to me, because none of it has any effect on the math and science they passed along.
Attention readers: By saying he doesn’t care, Javier is not implicitly sanctioning any such behavior. Lol.


A computer can count, so why the insistence on humans? Even if we restrict counting to humans, we don't know the upper bound on human lifetimes. Even if we knew the upper bound on a single life, we can continue a single count over multiple human lifetimes.

The only "end" to counting is if the universe ends. And since we don't know if that will happen, we can assume counting will go on forever. Therefore, ℕ is countable.
Nah, “Countable” here is semantic hell. I don’t care what the upper bound is: it’s not infinite, because infinity is DEFINED as the absence of an up an upper bound, Georg.


You just did! We'll never run out of symbols to count ℕ.

Oh, so you’re saying your n-size brain or brains can generate symbols beyond n? Wow! “I can’t believe it’s not fecal butter!” is a lower calorie option. ;)


I couldn't make sense out of the rest of your "proof".

Not buying it. It was Crayola simple. Try reading it again in Safe Mode without Academix 4.9 installed that needs it written in Hilbertonics. :—)
 

bogosort

Joined Sep 24, 2011
1,037
What reasoning can be done if every QED is true regardless of its ACTUAL truth value? If you refuse to call every statement TRUE, then there's no such thing as "true unary" from this perspective, just urinary only. QED on that?
Again with the logic system confusion. In a unary language there is only a single symbol. You can call it "TRUE", but you will undoubtedly confuse it with the "TRUE" symbol in binary logic. So, let's call the unary symbol "@".

Let's make a simple unary system. Here is the single axiom: the string "@" is a theorem. Here is the single rule: in any string, the substring "@@" can be replaced by "@".

Is "@@@@@" a theorem of our system? We can prove that it is:

By our single rule, replace the last two "@@" with "@", giving us "@@@@".
Again, replace the last two "@@" with "@", giving us "@@@".
Again, replace the last two "@@" with "@", giving us "@@".
Again, replace the last two "@@" with "@", giving us "@", which is a theorem. Therefore, "@@@@@" is a theorem.

Note that this proof is entirely mechanical, i.e., a computer (or a system of pulleys) could verify the proof.

Is everything a theorem in this system? No: the empty string is not a theorem. Neither is the string "@@x@", as it is not well-formed.

Ok, so we have a formal language. Can a binary computer recognize this language? Of course. But so can a unary computer! We can model such a computer as a state machine with a single output state: "@". Feed the state machine a string and if it halts on the output state, the string is a member of the language.
 

bogosort

Joined Sep 24, 2011
1,037
I can FEEL the dog exists as 3D, dog exists in my mind as 3D. I am not going to pretend there's "more observable, macro-level geometry to the dog that isn't there." I'm not going to ignore the "knowing element of the term FEEL" which is inextricably connected to my sight of the dog as well.
Your brain assimilates a bunch of sensations and that's enough for you to say "Yep, that's all there is." Sorry, but that's ignorant as sh!t. That's the opposite of rational analysis.

Human perspective is a tiny, distorted peephole to the universe.
 

bogosort

Joined Sep 24, 2011
1,037
Said the brain talking about a function that generates such values that have meaning to it!! Call 1-800-WTF-NOWW for more information!
Is this a trend? I ask a question and, instead of answering the question, you give a snarky response?

A function is an object in OOP programming, no? It means you can relate to it not just as a process but as an addressable object in your mind. Draw a sine-wave on a white board. It's some "thing" you can relate to in time and space, not just sine() generator, and "feel" the "meaning" of the wave on the board vs. the one inside you that you can further distinguish as discrete or continuous.
A mathematical function is an abstract mathematical object. A function in code is an abstract collection of abstract computer instructions. We can't "touch" either type of function. They are both CONCEPTs.

Whatever squiggly line you draw on a whiteboard, it is not a sine. Broken record time: the representation of a thing isn't the thing itself.
 

bogosort

Joined Sep 24, 2011
1,037
Question:

INFINITY not as a process, but as the description for the continuous VALUES (plural) of a Euclidean line or a sine wave:

“Values” = uits to you? If not, why do you call these “values” plural? And are these values also “states?”

(For the record, the “infinite dimension” I was referring to in a Hilbert space was the same concept and question)
INFINITY is the concept of an unbounded counting process. INFINITY does not apply to the points on a Euclidean line or the values of sine, because neither can be counted. For those, we need _INFINITY from ℝ (which I've wanted to avoid since the beginning, because it is far too technical to not get bogged down with in difficult details).

Sine is a function from ℝ to ℝ. Real numbers cannot in general be represented by uits (or bits or trits, etc.), and so the values of sine are not "uits". We can use uits (or bits or trits) to quantize some values of sine, but the resulting values are in ℚ.

I use plural "values" because sine has more than one value.
 

bogosort

Joined Sep 24, 2011
1,037
Huh? And you know what the true infinite nature of ℝ is? A set of values/bits/uits but you can’t know them? How do you know they’re not discrete and continuous at the same time? Funny how you can address elements of R, but then it’s also uncountable and infinite and nebulous AF!
I have a pretty good idea of the nature of ℝ. In particular, almost all values in ℝ cannot be expressed as uits or bits. How do I know that they're not discrete and continuous at the same time? Because that's a logical contradiction, and ℝ is consistent. That ℝ is uncountable does not mean that all of its elements are conceptually invisible. I know a bunch of elements in ℝ. Just not most of them (by any stretch).
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
756
Is this a trend? I ask a question and, instead of answering the question, you give a snarky response?


A mathematical function is an abstract mathematical object. A function in code is an abstract collection of abstract computer instructions. We can't "touch" either type of function. They are both CONCEPTs.

Whatever squiggly line you draw on a whiteboard, it is not a sine. Broken record time: the representation of a thing isn't the thing itself.
I give snarky responses to bring levity only.

When you insist you’re a state machine, but then insist there’s a distinction between the states, the hardware, the software, the representation, and then insist consciousness and _LIFE have something to do with it but don’t know what, you insist you exist in physical space but essentially “can’t see yourself as 3D” because real and reality aren’t defined.... etc. etc. you have no logical right as a dirt-derived machine to insist there’s a distinction between the “info” and “its representation.” Is any computer doing that?? No. I do not believe you have any right to call any group of disparate bits a “concept,” truly.

And again, you keep referencing number sets and other invented elements.

Sadly, I might have to give up. You don’t ever stop seeing through immense abstractions. I’m in safe mode, and you touch on it for one message and then revert back.
 
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bogosort

Joined Sep 24, 2011
1,037
Because you, as a discrete dirt-based digital system, and most likely Von Neumann-sanctioned discrete state processor from Utah, truly have no business(!) drawing partiality between anything of the kind other than binary or unary grunts without a full-on magical abstraction continuum device. Claude Shannon just stuck his thumbs up through the grave dirt to corroborate.
What do you mean by "have no business drawing partiality"? Speak to the problem you're seeing precisely, otherwise I have to try to guess what you mean.

Not to be combative, but for some reason you don’t see yourself as different than “information itself,” . . .
I'm made of states, just like everything else in the universe. These states convey information. So, yeah.

And then call upon utterly undefined Darwinian magical 18th century terms like “evolved” that say you “evolved” to do this, but you literally have zero definition for life or consciousness, or what capabilities these things impart, and your iPhone doesn’t qualify equally as being “an iPhone” cremated over the Atlantic.
Evolution over time is recognition of change. Nothing magical about that, unless you believe either change or time are magical. The theory of evolution through natural selection is not magical thinking, either. It's a rational and cogent explanation for the enormous variety of life.

I believe the theory of evolution can be expanded to non-biological processes. I believe that life is a consequence of the universe evolving with a utility function to maximize entropy. Life is an entropy-maximizing strategy, whereby entropy is increased globally by reducing it locally. I believe that consciousness is an emergent phenomenon of sufficiently complex forms of life.

And just because we can’t represent the data as “bits” *ourselves* doesn’t mean it doesn’t exist as such.
So, your logic is to conclude that quantum data "exist as bits", we just can't "see" them? Insanity.

We can represent portions of it as bits, in the case of ℝ; in fact trillions of bits of tasty apple “pi.”
Yup, Pi is computable. So are a bunch of other numbers in ℝ, like 42. But these computable numbers represent precisely 0% of all the numbers in ℝ.

Incidentally, we only need a couple hundred bits to fully represent Pi. That you'd think we'd need "trillions" belies your confusion on the subject.
 

bogosort

Joined Sep 24, 2011
1,037
Time is part and parcel of the information, or it does not exist! So why can’t time be part of the info? Why is info different than time to you?

Why not {0, 1, t} and {@, t} ?
Because "t" is not a symbol of a binary language with alphabet {0, 1}. An alphabet of {0, 1, t} describes a ternary language.

Again, information has nothing to do with the symbols in the language we use to represent it. Whether we use {0,1} or {a,b,c,d}, the information expressed is still the same. I really want you to grok this.

"I can say a sentence in conversational English that contains some amount of information that we can measure in bits."

Consider the sentence above. We can convert it to Spanish (alphabet {[A-Z]}), or we can convert it to Morse code (alphabet {., -}) or ASCII bit strings (alphabet {0, 1}), or some unary encoding (alphabet {@}). In all cases, the information conveyed by the resulting string is the same, whether in English, Spanish, Morse, ASCII, or unary.

Can you see that?

As this information is measurable, we can express the amount of information conveyed in terms of bits. Note that this representation -- bits of raw information -- is different than the representation of the sentence as a string of bits in the ASCII language. Superficially, they look similar -- they both use the same alphabet -- but they represent different levels of conceptual zoom. For example, the symbol 'A' as an ASCII bit string looks like "01000001", an 8-bit sequence. On the other hand, the amount of information conveyed by 'A' in the English language is not much more than a single bit. In a language that only consists of single strings of 'A', each 'A' conveys zero bits of information. In a language of 26 symbols where 'A' is uniformly distributed, each 'A' represents a little more than 3 bits of information.

Finally, just as we can represent the information contained in the sentence in multiple forms (languages), we can represent the measurement of the information in multiple forms (number bases). So, we can count information in a binary language using unary representations, or vice versa and every which way.

I say all of this to highlight the very confusing notations and ideas that can easily be mixed together in such discussion. The key thing to remember is that information (and its measurement) is distinct from its representations (and symbols).
 

bogosort

Joined Sep 24, 2011
1,037
Yes, it is. But it can only be perceived internally. I can “grok” by “sense” and conceptualize an infinite line whereby I can “pull points” off it, but the line remains undivided. The line is in a “space” and I can “feel” it and do literally anything with it, like bend it into a dog form, and put a light on it, attribute apple flavor to it, then eat it. The whole space is an environmental “state” of some kind.
Mind is physical. Can we measure it? Where is it located? Where does mind go when we die? Does a person who died 5 seconds ago weigh less than he did when he was living?
 

bogosort

Joined Sep 24, 2011
1,037
No, because I intuit “continuum” is part of first order definition of “know and feel” and a discretizing machine isn’t doing. It matches and computes, not feels and means.
Even if "feeling the continuum" is somehow a criterion of consciousness, what prevents a computer from feeling the continuum? Specifically, what mechanism do we have that they cannot, even in principle, have?
 

bogosort

Joined Sep 24, 2011
1,037
Attention readers: By saying he doesn’t care, Javier is not implicitly sanctioning any such behavior. Lol.
Indeed! I do not condone the raping of anyone, especially children or nazis.

Nah, “Countable” here is semantic hell. I don’t care what the upper bound is: it’s not infinite, because infinity is DEFINED as the absence of an up an upper bound, Georg.
There is no upper bound. Remember n + 1?

Oh, so you’re saying your n-size brain or brains can generate symbols beyond n?
Truly an amazing notion to behold. Let me make it more concrete.

We can easily label numbers that are too big to fit in the universe. For example, 10^(10^10) represents a number that is -- by far -- greater than the number of particles in the universe. Take every single particle in the universe, split each of them into a trillion new particles, and we still wouldn't come close to having 10^(10^10) particles.

That's a lot of particles. But powers of powers is child's play when it comes to naming big numbers! People have come up with all kinds of compact notation for labeling unimaginably big numbers, numbers so big that they make 10^(10^10) seem like zero. The point is, we'll never run out of symbols to express numbers in ℕ. This goes hand in hand with the fact that both ℕ and the set of all possible symbols are countable.

Not buying it. It was Crayola simple. Try reading it again in Safe Mode without Academix 4.9 installed that needs it written in Hilbertonics. :—)
Seriously, I have no idea what you were trying to say.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
756
Because "t" is not a symbol of a binary language with alphabet {0, 1}. An alphabet of {0, 1, t} describes a ternary language.

Again, information has nothing to do with the symbols in the language we use to represent it. Whether we use {0,1} or {a,b,c,d}, the information expressed is still the same. I really want you to grok this.

"I can say a sentence in conversational English that contains some amount of information that we can measure in bits."

Consider the sentence above. We can convert it to Spanish (alphabet {[A-Z]}), or we can convert it to Morse code (alphabet {., -}) or ASCII bit strings (alphabet {0, 1}), or some unary encoding (alphabet {@}). In all cases, the information conveyed by the resulting string is the same, whether in English, Spanish, Morse, ASCII, or unary.

Can you see that?

As this information is measurable, we can express the amount of information conveyed in terms of bits. Note that this representation -- bits of raw information -- is different than the representation of the sentence as a string of bits in the ASCII language. Superficially, they look similar -- they both use the same alphabet -- but they represent different levels of conceptual zoom. For example, the symbol 'A' as an ASCII bit string looks like "01000001", an 8-bit sequence. On the other hand, the amount of information conveyed by 'A' in the English language is not much more than a single bit. In a language that only consists of single strings of 'A', each 'A' conveys zero bits of information. In a language of 26 symbols where 'A' is uniformly distributed, each 'A' represents a little more than 3 bits of information.

Finally, just as we can represent the information contained in the sentence in multiple forms (languages), we can represent the measurement of the information in multiple forms (number bases). So, we can count information in a binary language using unary representations, or vice versa and every which way.

I say all of this to highlight the very confusing notations and ideas that can easily be mixed together in such discussion. The key thing to remember is that information (and its measurement) is distinct from its representations (and symbols).
I’m not sure why it seems I don’t grok that, but I have known that... perhaps I’m not communicating the zoom level properly. (Although very nice explanation... you totally need to make tutorials!)

What I was doing was making the unary into binary, and the binary into ternary.

I was intimating that there is no real unary, because you can use “time” as another bit in a sense.

So {0, 1}, which I originally proposed, would become {0, 1, t}. And your unary proposition of {@} is actually now binary {@, t}. And there “effectively” is rendered no such thing as pure {@} because some kind of contrasting element is necessary to convey info.
 
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Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
756
Indeed! I do not condone the raping of anyone, especially children or nazis.


There is no upper bound. Remember n + 1?


Truly an amazing notion to behold. Let me make it more concrete.

We can easily label numbers that are too big to fit in the universe. For example, 10^(10^10) represents a number that is -- by far -- greater than the number of particles in the universe. Take every single particle in the universe, split each of them into a trillion new particles, and we still wouldn't come close to having 10^(10^10) particles.

That's a lot of particles. But powers of powers is child's play when it comes to naming big numbers! People have come up with all kinds of compact notation for labeling unimaginably big numbers, numbers so big that they make 10^(10^10) seem like zero. The point is, we'll never run out of symbols to express numbers in ℕ. This goes hand in hand with the fact that both ℕ and the set of all possible symbols are countable.


Seriously, I have no idea what you were trying to say.
We agreed infinity is not a number. n+1 is still a number. There is no counting the elements of infinity.

You don’t like the word “real” and I don’t like the word “countable” without qualification. If one disabuses themselves of Cantor’s theories, and pretend it’s 1860, what are number sets again? There are only numbers. They are countable to a point. But there are always more.
 

bogosort

Joined Sep 24, 2011
1,037
I give snarky responses to bring levity only.
I'm a big fan of levity, but not at the expense of communication. Ask me a question and I try to answer it sincerely.

When you insist you’re a state machine, but then insist there’s a distinction between the states, the hardware, the software, the representation, and then insist consciousness and _LIFE have something to do with it but don’t know what . . .
No, I've never said life or consciousness has anything to do with the fact that there are different states. Long before humans showed up, the universe was a state machine. Consciousness is what we call the phenomenon in certain state machines that have memory and a feedback loop. As part of the feedback loop, these conscious state machines form CONCEPTs and argue about them on internet forums.

. . . you insist you exist in physical space but essentially “can’t see yourself as 3D” because real and reality aren’t defined....
I don't believe physical space is 3D because of science, i.e., empirical investigation. You believe it's 3D because of intuition. So, whose opinion has more weight behind it?

you have no logical right as a dirt-derived machine to insist there’s a distinction between the “info” and “its representation.”
I have "no logical right", meaning that I am speaking in contradictions? Please point them out.

Information and representations are human abstractions, i.e., they were created by humans to help us organize our experiences. When we explore these abstractions -- and when I say "we", I mean humanity for the past 100 or so years -- we find that information is independent of representation. They are distinct concepts. You're free to disagree, but it won't get you very far.

Is any computer doing that??
I mean, every computer does that implicitly. If I double-click on the file labeled JAV_IS_AWESOME.JPG, my computer loads an image file from the hard drive, writes it to RAM, and then displays it on my screen. On the hard drive, the information is represented as a sequence of magnetic polarities; in RAM, the information is represented as a sequence of HIGH and LOW voltage levels; on my display, the information is represented as a matrix of color and brightness gradients.

All different representations, all representing the same information.

So, yes, computers know the difference between information and representation. And since you seem to dispute the distinction, please explain how JAV_IS_AWESOME.JPG is able to be displayed at all? If information depends on representation, then the information must change when I email the picture or store it on a CD?

And again, you keep referencing number sets and other invented elements.
I remind you that you brought up the various number sets. I was happy to stick with COUNTING.

Sadly, I might have to give up. You don’t ever stop seeing through immense abstractions. I’m in safe mode, and you touch on it for one message and then revert back.
What frustrates me most is that you actually believe that your "safe mode" is tabula rasa. You think I'm coming from "7G" level abstractions, while you're at the true ground floor. But that's not at all what I see.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
756
I believe science is empirical and observational concerning things in space and time, and that physical space isn’t information. Correct me if I’m wrong, but for you, it’s all just information and equations only, or “99% + mystery component” and don’t “really” differentiate anything from information?

I know the dog is 3D because I can measure it and know and feel it. This is original, Newtonian-level science. You don’t believe in such basic things. Yet you will say your house and car exist and can take 3D measurements? You want to throw the senses away as any form of arbitration or empirical plumb line. We will never get anywhere if (with me anyway) that is your stance.

You’re content with counting? My “grunt” beginning thesis (named in obvious humor for unary “counting”) was about as basic as it got and discussed cardinality and ordinality and led to the creation of 0. It also made very clear that information is separate from how it’s represented! You didn’t really comment on it?

I can literally prove using grunts that all numbers are composed of them. But that is “Kronecker and Poincare,” and you won’t show any partiality to an elemental anything like that. That’s why you see all 16 logic states as equal and not derivative of one or 2, and probably don’t believe all 4 principal arithmetic operations are just addition in disguise. I simply can’t budge you there, even if I found 15 Ph.D’s to back me, and Claude Shannon resurrected in the flesh to thumbs up. Sadly, because of these things, I see no hope in getting anywhere, despite 1000 posts to that end. :(
 
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