If you mention the likes of Galois, ℤ or similar one more time, I’m coming to your house and will sit Indian-style on your lawn chanting “REALITY, REALITY, REALITY” over and over while wearing a custom $2000 silicon Kronecker mask.


Rasa. Remember what we agreed to earlier. You’re in safe mode, it’s the year 1200 AD. You’ve never heard of any of these things!

If you can use "integer", I can use "GF(2)". Fair's fair!

 

If you can use "integer", I can use "GF(2)". Fair's fair!

Ok, no integers! “Number” only!

 

Again, none of it exists, lol. We must write from what we agreed to earlier! We have no knowledge of frameworks!
We call it “base whatever” AFTER. We have 2 sets all computers work with. Assume qubits are nested bits. They are still digital computers, just more bits per space.

You wrote up that lovely proof tabula RASA. same here!

You agree to it, then you default back to Banachian transgendered ordinals of the 4th order of a Timbuckthree. I'm not trying to put any of that down(!) But you agreed to simple reasoning, simple inference, simple arithmetic, for a REASON that you share with me, or you wouldn't have agreed it was a good starting point. ;--)

You're defending your choice of two-element computing by invoking XOR and binary computers. I'm showing that XOR-less unary computers are possible. How is that not allowed?

 

FALSE, though this is far more nuanced than you might think. First, we have to be clear about what a "mathematical statement" means. By definition, a mathematical theorem is always true and a mathematical contradiction is always false. But, in general, mathematical expressions do not carry truth values. For instance, the polynomial \( x^2 -3x + 1\) is neither true nor false. We can put it into an equation and make it look like a statement: \[ x^2 -3x + 1 = 0 \] But, again, the equation itself is neither true nor false. It is not a proposition.

Truth values are the domain of logic systems. Thus, to make an arbitrary mathematical expression have a truth value, we need to frame it as a statement in some system of logic. A naive way of doing this is to simply couch a mathematical expression in a propositional statement:

It is true that "y = 2x"

But whether that statement is true, false, or undefined depends on the domain of discourse and what we mean by 'y', 'x', and the '=' symbol. We can choose any number of models in which the statement is true, false, or undefined. We can even choose a model in which the statement is neither true nor false nor undefined (e.g., as the definition of a function). Therefore, the truthness of this mathematical statement depends on the given model.

And this brings up several subtle and important issues. Assuming we fix a model, can every mathematical statement -- i.e., every logical statement about mathematics -- be said to have a TRUE or FALSE value? The answer, unfortunately, is no.

In basic boolean (propositional) logic, every statement is decidable. That is, for any propositional statement -- no matter how complex -- we can decide whether it is true or false within the model. This is a very nice property of boolean logic (especially suitable for designing computer circuits). Alas, the price of decidability is lack of expressive power. For example, basic boolean logic is not powerful enough to make general statements about the natural numbers ℕ. We can't, for instance, express the notion of an "even number" within propositional logic. So, if we wanted to make a truthy mathematical statement about even numbers -- say, "every even number has the form 2k for any integer k" -- we can't do it in propositional logic.

To get more power into propositional logic, we have to extend it with quantification over variables, giving us predicate logic. Instead of just "A" and "not A" and such, we can express ideas like "for all A". But with this power comes a dark side -- first-order logics (like predicate logic) necessarily include statements that are undecidable. That is, there are statements for which we cannot say whether they are true or false, regardless of the chosen model.

In short, we need (at least) first-order logic to make truth statements about "complicated" mathematical theories, and any such logic necessarily contains undecidable statements. For example, a famous open problem in mathematics is the Goldbach conjecture: every integer larger than 2 can be expressed as the sum of two primes. We can write this as a statement in first-order logic. Let \( \mathbb{P} \) be the set of primes, then \[ (\forall n \in \mathbb{N}_{> 2})(\exists p,q \in \mathbb{P})( n = p + q) \] We don't know if this statement is true or false. It may turn out to be undecidable.

Are you Javier? Do you have a family? True?

If we can’t QED that using “good old fashioned” empirical observation, we have no hope. (pan to the purpose of my 2 humorous story snippets)

 

You're defending your choice of two-element computing by invoking XOR and binary computers. I'm showing that XOR-less unary computers are possible. How is that not allowed?

That XOR thing was tangential and in response to your invocation of f(). I was effectively saying binary reasoning is necessary to show distinction, or everything is TRUE. Nevertheless, it’s “true” (lol) we’re both guilty. Rasa 100% for me too!

 

You're defending your choice of two-element computing by invoking XOR and binary computers. I'm showing that XOR-less unary computers are possible. How is that not allowed?

Also, if you will say a statement is “QED or not” as your basis of rationale, you can’t show partiality to any output of a unary computer. It’s all TRUE, which means a QED cannot be had from it, which means unary is out the window, and we must use binary thought of TRUE or FALSE to reason and declare QED's.

 

FALSE, though this is far more nuanced than you might think. First, we have to be clear about what a "mathematical statement" means. By definition, a mathematical theorem is always true and a mathematical contradiction is always false. But, in general, mathematical expressions do not carry truth values. For instance, the polynomial \( x^2 -3x + 1\) is neither true nor false. We can put it into an equation and make it look like a statement: \[ x^2 -3x + 1 = 0 \] But, again, the equation itself is neither true nor false. It is not a proposition.

Truth values are the domain of logic systems. Thus, to make an arbitrary mathematical expression have a truth value, we need to frame it as a statement in some system of logic. A naive way of doing this is to simply couch a mathematical expression in a propositional statement:

It is true that "y = 2x"

But whether that statement is true, false, or undefined depends on the domain of discourse and what we mean by 'y', 'x', and the '=' symbol. We can choose any number of models in which the statement is true, false, or undefined. We can even choose a model in which the statement is neither true nor false nor undefined (e.g., as the definition of a function). Therefore, the truthness of this mathematical statement depends on the given model.

And this brings up several subtle and important issues. Assuming we fix a model, can every mathematical statement -- i.e., every logical statement about mathematics -- be said to have a TRUE or FALSE value? The answer, unfortunately, is no.

In basic boolean (propositional) logic, every statement is decidable. That is, for any propositional statement -- no matter how complex -- we can decide whether it is true or false within the model. This is a very nice property of boolean logic (especially suitable for designing computer circuits). Alas, the price of decidability is lack of expressive power. For example, basic boolean logic is not powerful enough to make general statements about the natural numbers ℕ. We can't, for instance, express the notion of an "even number" within propositional logic. So, if we wanted to make a truthy mathematical statement about even numbers -- say, "every even number has the form 2k for any integer k" -- we can't do it in propositional logic.

To get more power into propositional logic, we have to extend it with quantification over variables, giving us predicate logic. Instead of just "A" and "not A" and such, we can express ideas like "for all A". But with this power comes a dark side -- first-order logics (like predicate logic) necessarily include statements that are undecidable. That is, there are statements for which we cannot say whether they are true or false, regardless of the chosen model.

In short, we need (at least) first-order logic to make truth statements about "complicated" mathematical theories, and any such logic necessarily contains undecidable statements. For example, a famous open problem in mathematics is the Goldbach conjecture: every integer larger than 2 can be expressed as the sum of two primes. We can write this as a statement in first-order logic. Let \( \mathbb{P} \) be the set of primes, then \[ (\forall n \in \mathbb{N}_{> 2})(\exists p,q \in \mathbb{P})( n = p + q) \] We don't know if this statement is true or false. It may turn out to be undecidable.

It still has an elemental TRUTH state! It’s TRUE that it’s undecided! Otherwise you can’t do any more inquiry on it to find whether or not it’s true or false as a QED!

 

You say that you begin with the tenet "There is Information "as your starting point, which essentially means, "that's all there is": there is no such thing as a separate "knowable element" aside from it.

When did I say that? A theory builds its theorems -- its separable knowable elements -- from its axioms. The axioms aren't the only things in a theory.

In particular, I say that there are states, which -- by their configurations and changes in configurations -- convey information. There are information processors -- state machines with memory -- that organize information. In this organization, all the interesting stuff happens.

If any fellow reasonable human being asks you, "Is your name Javier?" . . .

(42 other yes/no questions ellided.)

That we have "yes/no" questions is not a problem with my theory. I clearly stated that we can represent information using sequences of binary bits. So, demonstrating a bunch of "yes/no" questions doesn't change anything.

On the other hand, as you claim that there is ONE TRUE REPRESENTATIONAL MODALITY -- the TRUE/FALSE MOTHER -- how do you answer non-"yes/no" questions?

You make the statement "There is information" as your starting point. But what you're really saying "It is TRUE there is information."

And? It is true that I believe there is information. So what? You are pointing to a chair and saying, "See! I told you so, a chair!"

Further, you need to assume it is TRUE that light EXISTS independent of information, or you can't know anything more. You can't say "maybe" it exists, or "maybe information exists." LIGHT exists in order for you to KNOW and COMPUTE. You must start from a binary place of YES or NO. QED.

In my theory, "light" is just a label for a particular set of states and transformations on those states. I don't make any claims for why it (or anything else) exists. You can say "QED" all you want, but you have not shown a necessary conclusion. This is effectively what you're saying: The universe has something that I call light. Therefore, I must start with YES or NO. Lol.

You cannot know what anything is until you output a true or false about whether or not it exists. QED.

This sentence is absurd. Before I can know something, I have to "output a true or false about whether or not it exists". If it didn't exist, I wouldn't have anything to know about, would I?

I'll ask you again: when you look at the complex, ever-changing shapes in the shadow underneath a tree in bright sunlight, what exactly is "there/not-there"? How exactly are you perceiving the shadow?

We have nothing more than voltage on the line or not on the line. The voltage exists or it does not.

That's a unary system you just described. In a binary system, there are two valid voltage states: HIGH or LOW. LOW voltage does not mean "no voltage"; LOW voltage means a specific range of voltage values, say, between -0.25 and 0.25 V.

This is not an insignificant detail.

You can't say BASE-384 until you say IT IS TRUE it exists from a binary place.

I would never say that base-384 (or any number base) is true or false. A number base is not a truth statement.

A qubit is nothing more than a state processor that is evaluating more states per second than a classical system (proof below). It's superpositional Shannon bits all day long. A qubit is still outputting ZEROES and ONES, or FALSE OR TRUES *in the end*, or you can't get any reasonable data from it. Quantum computers use binary, but each switch can have multiple binary states at the same time.

Sigh. If each switch in a quantum computer "can have multiple binary states at the same time", then how the f*ck can you call the switch "binary" with a straight face? The definition of binary is precisely two states.

A QED *IS* an undeniable... TRUTH. QED. You must make the statement, "It is true I exist," before you make any mathematical inquiry.

There's an enormous difference between logical TRUTH and ontological TRUTH. The statement "If 4 = 5 then I am god" is 100%, undeniably TRUE in boolean logic. But it makes no assertion to any ontological notion of truth.

 

Qubits are described in terms of binary states, because TRUE or FALSE is the foundational basis of sane, mathematical reasoning!

Huh? Qubits cannot be described in terms of binary states -- that's what makes them qubits and not regular bits.

You seem to be confusing the fact that we can compare qubits with bits, which is fine as they're both units of information.

If you want an out from quantum hell -- which I'd completely understand, since quantum computing completely destroys your binary MOTHER theory -- you can just point to the fact that we're not yet certain that quantum computation is indeed more powerful than classical computation. You'd be invoking the extended Church-Turing thesis, which -- as of yet -- has not been disproved. The recent result from Google's quantum computer is still up for debate.

 

Ok, no integers! “Number” only!

Great. Define "number".

 

Are you Javier? Do you have a family? True?

I certainly believe that I'm a human named Javier with a family. If I'm in a simulation programmed to be believe it, is it still "true"? F*ck if I know.

This is one reason why I don't like absolutes. I can make (truthy) statements about my experiences. I can make (truthy) statements in formal systems, like logic and math. I have no idea whether any of those statements are ontologically true. I suspect some are, but I can't know. And that's fine. I don't need to describe the universe "as it really is". I just need to describe the universe in a reasonable way.

 

Also, if you will say a statement is “QED or not” as your basis of rationale, you can’t show partiality to any output of a unary computer. It’s all TRUE, which means a QED cannot be had from it, which means unary is out the window, and we must use binary thought of TRUE or FALSE to reason and declare QED's.

Again with your binary bias. "True" is not the unit of a unary computer, so it's not "all true".

What is 2 + 3 in unary? @@ + @@@ = @@@@@

What is the logical result of "if (@@ == @@)"? @

What is the logical result of "if (@@ == @@@)"? <anything besides @>

This can all be formalized and implemented in a physical circuit. Nary a TRUE to be found.

 

It still has an elemental TRUTH state! It’s TRUE that it’s undecided! Otherwise you can’t do any more inquiry on it to find whether or not it’s true or false as a QED!

Lol, nice try, except that we don't know, for instance, if Goldbach's conjecture, or P = NP, or the Riemann hypotheses, are decidable. These statements may or may not have a truth value, which means that we cannot say that is TRUE (or FALSE) that they are undecidable!

 

Lol, nice try, except that we don't know, for instance, if Goldbach's conjecture, or P = NP, or the Riemann hypotheses, are decidable. These statements may or may not have a truth value, which means that we cannot say that is TRUE (or FALSE) that they are undecidable!

Dear Goldbach, you don't exist in this discourse. Thanks for your input. ;--)

I certainly believe that I'm a human named Javier with a family. If I'm in a simulation programmed to be believe it, is it still "true"? F*ck if I know.

This is one reason why I don't like absolutes. I can make (truthy) statements about my experiences. I can make (truthy) statements in formal systems, like logic and math. I have no idea whether any of those statements are ontologically true. I suspect some are, but I can't know. And that's fine. I don't need to describe the universe "as it really is". I just need to describe the universe in a reasonable way.

Ok, GREAT! Agreed.

Just so you know, ontological "truth" that we can reasonably know is the only thing that matters to me. But the observational senses have something to do with it; I just want to build the foundation using the simplest components. If we have to re-invent the foundation of certain assumptions, so be it.

For example, the proof you made based on the assumption of a "bit" is super ontologically applicable. You were VERY readily on it until I insisted "It was the way it is." Well, I'm saying existence may be both unary and binary at THE most rudimentary level, but I believe binary is the basis of "meaningful reasonability about things."

It's VERY reasonable to assume a physical substrate with "wires" to represent things, can represents either unary or binary logic. You wrote the proof based on it, let's roll forward with it. It's "reasonable."

Let's start there, and there are no Goldbachs to be found, no Riemann manifolds, no Cantoral oratorios. We are using "Truthy" as our basis alone (if you want to call it that) by insisting on some basic things like you did in the proof.

You started the proof before using binary, let's continue it, if you're game, from a very simple, Feynmantic "map of the cat" level.

 

Just as a side-note (the thinking behind "crazy talk of" 0, 1, and infinity's relation):

Not to name drop, but just to show for the record (and which I know you know) that extremely intelligent scientific minds such as Newton, Pythagoras, Leibniz, Galilei, Einstein, Heisenberg, Maxwell, Planck and many other very astute intellects—even Darwin(!)—maintain a starting proposition for reason that there is an "origination source point" outside of what we know as physical existence.

(I don't want to start there, btw — I'm just saying we may end up "getting there" logically if we plumb the core BIOS).

Whatever you want to call it—"God" or "Dog." "Dog" might be God in some foreign language. These are just wave tokens to describe something indescribable, like the infinite quality of ℝ and its ultimate relationship to the discreteness of numeric quantities. This thing is both "something" and "the something required to describe something (information)."

Therefore, let us assume for a minute, this element is the source of the term and definition of infinity and "number", and that all things are derived from this "parent source." Assume there was a "beginning" to the universe (a "big bang" or what have you), "before this time" there was just this "infinity source" of both continuous and discrete "things". What was "before that?" It's like saying "what's after infinity." There just "always was existence."

If you could describe the "source thing" you'd say it has 4 minimal properties:

1) 1 THING THERE
2) INFINITE AMOUNTS OF "IT" (A "parent" substance)
3) IT HAS CONTINUOUS FORM OF ANY KIND (A circle, a triangle, a dog)
4) IT HAS NO GEOMETRIC SIZE (i.e., size is a derivative construct of it)

Whatever is "there," it is both "one" and it's infinite. The moment something comes from it — i.e., it "divided" itself — there is now "another infinity" spawned, because infinity still remains infinite wherever it "is".

You could call this new element also "1" and INFINITE just the same. Or "11" and INFINITE just the same. Or you could call it "2" and INFINITE. If another thing came from the source, it would be called "3" and INFINITE, etc. We can readily observe this concept in a mathematical sine wave having infinite values. The wave is "1", but it has infinite values that comprise it. If we examine a different sine wave, we may call it "2," but it also has infinite values that comprise it.

NON-existence is an illusion from this place. Everything just is. In essence, there is just "1" and "infinite existence." In this basic sense, UNARY state of TRUE is what is going on everywhere. Everything is going on. It's true that everything is there.

This is also THE most rudimentary thinking possible.

Given the source is infinite, there are infinite possible spawnings of infinity and infinite numbers to describe such spawnings.

Binary thought, or "reasoning" could therefore be considered a derivative "construct" that arose from the unary TRUTH of "1"/INFINITY.

What if the "source" wanted to represent "non-existence?" It would have to spawn some kind of "unidentifiable" substrate that would at least have to provisionally contrast between "thing" and "no thing there." This I would call "0" or "the potential for another infinite thing that has not yet manifested in that specific locality related to another."

It's really also "1" and INFINITE, but some kind of "incarnation" that permits contrast against other "things" as the basis of the notion of "FALSE."

What if the "source" wanted to represent "finitude"? It would have to create an object of a "componental or contraptional nature" perhaps composed of "many discrete infinities". Then create an interpretation mechanism that "triangulates" the difference between "that thing" and minimal qualifications for when that thing is not "there" any more, or the concept of "variable size" based on other things.

There is a LOT of sense to be made when we consider the potential for an infinite point source, just sayin'.

 

Great. Define "number".

I did in my “grunt” thesis! That was the whole point: A number is essentially a wildcard label for any one thing, and there is no cardinality or ordinality to them until a user-defined relationship is made between them. Yes?

 

When did I say that? A theory builds its theorems -- its separable knowable elements -- from its axioms. The axioms aren't the only things in a theory. In particular, I say that there are states, which -- by their configurations and changes in configurations -- convey information. There are information processors -- state machines with memory -- that organize information. In this organization, all the interesting stuff happens.

You said it earlier.... there’s no objective truth or reality, just information/states.

(42 other yes/no questions ellided.)

That we have "yes/no" questions is not a problem with my theory. I clearly stated that we can represent information using sequences of binary bits. So, demonstrating a bunch of "yes/no" questions doesn't change anything.

On the other hand, as you claim that there is ONE TRUE REPRESENTATIONAL MODALITY -- the TRUE/FALSE MOTHER -- how do you answer non-"yes/no" questions?

How does Watson or any other high-level binary-based system? It does so exclusively with binary-based Shannon bits and searching and parsing! Consider Watson beat Ken Jennings and can answer all sorts of non yes/no questions, utilizing servers in a datacenter using a binary basis to establish a complete informatic framework. How does a driverless car drive? Same thing. I’m not sure why you think binary can’t literally answer everything outside qualitative “feel” elements (“do you like the strawberry?”) and “beliefs” (Does God exist?)... all other things can be done Watson-style. What is Watson in 2040? Ava from Ex Machina.

And? It is true that I believe there is information. So what? You are pointing to a chair and saying, "See! I told you so, a chair!"

Because it speaks to the utter basic, brass tacks, fundamental element of “knowing.” You need to say “It is true X exists” before you start discussing states of X!

In my theory, "light" is just a label for a particular set of states and transformations on those states. I don't make any claims for why it (or anything else) exists. You can say "QED" all you want, but you have not shown a necessary conclusion. This is effectively what you're saying: The universe has something that I call light. Therefore, I must start with YES or NO. Lol.

What is a “state??” States are NOT existence. States DESCRIBE the STATE of existence. I have a “dog.” He is state hungry.
The dog exists, INFORMATION concerning HIM reflects the STATE of his existence and what he’s doing!

This sentence is absurd. Before I can know something, I have to "output a true or false about whether or not it exists".

Absurd? Please tell me all about that red parrot you own.

No parrot?? No data. How about your job as a bellydancer? No job as a bellydancer? No data. How about this conversation? Oh, it’s TRUE it exists to you? Data now, and only now, can be had. "The stuff must have existence apart from the information for there to be any meaningful awareness of it." All data about things comes first from a basic TRUE/FALSE acknowledgment of its existence! I mean really, the "dog in the light" — does it exist or not? If it does, you can know about it, if it doesn't, you can't. The concept of truth or truthiness HAS to have some kind of externality to it, or what's the point?

I'll ask you again: when you look at the complex, ever-changing shapes in the shadow underneath a tree in bright sunlight, what exactly is "there/not-there"? How exactly are you perceiving the shadow?

The same way a face detecting algorithm works or a song ID algorithm works! It progressively matches truth statements in its database concerning components of what it’s picking up via camera or microphone and determining if something is there! How is this not obvious?? We have algorithms doing it in binary systems right now!

That's a unary system you just described. In a binary system, there are two valid voltage states: HIGH or LOW. LOW voltage does not mean "no voltage"; LOW voltage means a specific range of voltage values, say, between -0.25 and 0.25 V.

Again, it’s about contrast of voltage to represent two elemental states. I can take all of the data about the dog and morse code that data to you with dots and dashes.

Sigh. If each switch in a quantum computer "can have multiple binary states at the same time", then how the f*ck can you call the switch "binary" with a straight face? The definition of binary is precisely two states.

Sigh!??
The switch itself is not binary, the data is binary being stored in a super positional “switch” representing essentially more compact binary processing of 0’s and 1’s! We are STILL working with binary data!! Literally undisputable. Look up any scholarly article on it. The qubits are essentially Shannon “super bits.” If I have a binary string k as 101010110111101010, and I can encode that with 18 flip flops in a classical system, but in a quantum system I can encode those binary states AND string j as 10101101010100, I can do hella more computations per second because I can do way more processing on way more Shannon bits! Shannon bits are true or false!

There's an enormous difference between logical TRUTH and ontological TRUTH. The statement "If 4 = 5 then I am god" is 100%, undeniably TRUE in boolean logic. But it makes no assertion to any ontological notion of truth.

Correct. And “if 4=5 then I am god” is complete and utter nonsense, and its truth value is WORTHLESS to a human being where meaning IS ontological. Come on! What good is it to not make ontological truth the basis??? Zero!

 

Again with "reality". If you're definition of REALITY is different than "the universe; everything that is", then you need to spell it out clearly and specifically. Otherwise, there's no need to use the word "reality"; it's always and entirely implied. Instead of "reality has stuff" one might say "there is stuff" or, even better, "we perceive stuff".

We perceive stuff is an intellectually honest starting point, a single fruitful seed that can sprout an entire ontology. Sure, "we", "perceive", and "stuff" have to be defined and explained, but that's where the ontology grows.

I took a different path, starting with "There is information". On my path, perception comes way later, but I think both paths lead to the same inevitable spooky mansion at the end of the road: the universe is an information processing state machine.

"There is information" is your starting point from an older post, above.

Mine is: "stuff" exists independent of information, and information's sole purpose is to describe it.

The "stuff" itself is not information. There is no point of any kind of inquiry unless the "stuff" exists independent of the information. This is the basis of "truth" to the "degree that we can know it": when the "stuff" in one's mind reflects the condition of what's going on outside it, there's "truth" about it.

There is "stuff" and then there is "states" about the stuff. To say the "stuff == states" doesn't make any sense to me. The TV exists. It can be in "state on" or "state off." The channels are states, etc. But states are behavioral elements, not existential "actualities."

 

I've not read through all this lot,

so this could have been said, and is probably not relevant.

BUT any way....


Two things.

The world as we know it is digital.... because we always quantise to a level. Its just the way we see everything.

Quantum entanglement...

Its all about how we try to mimic the real world, we can make it as easy or as hard as we like,

 

The greatest computational QED of the last 10 years shows 100% fundamental, classical computer Shannonic binaries can simulate the 6 human interrogatives as a function of smart parsing only:

In total, the system has 2,880 POWER7 processor threads and 16 terabytes of RAM. According to John Rennie, Watson can process 500 gigabytes, the equivalent of a million books, per second.

Take the same algorithms, tweak them to work with real-time audio and visual data, use a quantum system TO PARSE THE SAME KIND OF REAL WORLD BINARIES at exabyte/second throughput and you have a 2040:

Samantha:

And Ava: