You are wrong. Let A and B represent natural numbers. Your circuit will add them. Now let A and B represent rational numbers; your circuit will fail to add them. Now let A and B represent complex numbers; your circuit will fail to add them. Now let A and B be square real-valued matrices; your circuit will fail to add them.

In order to properly implement addition, a computer needs to know how to perform the computation, and that depends on the types of things being added. You need to let go of the mistaken idea that "+" means one thing and one thing only. Arithmetic is bigger than what you learned in elementary school.

But remember, I don't see those things as numbers. ;--) I bracket higher degrees of abstraction from the innate counting numbers that are used to concoct them from combinatorial arithmetic expressions. How can we call something like "5" a "number" and then also say 5.42 is a number, when 42/100's is a completely separate system of expression? Makes no sense to me. They are apples and oranges. At what point do you not call it a number? Why isn't 5.1993.23901/4901 a number?

And the reason the circuit will add the natural numbers is because they ARE foundational elements of ontology and not derivative systems! And ALSO because there is a connection at a foundational level between logic and numbers. I know you see them as separate systems, and I'm sure you can see them that way, but I don't believe it's entirely some 100% "separate" phenomena at its core, especially if the nature of information has an innate spatial element.

 

Seriously, if it wasn't so empirically in practice at this moment, it would be up for debate to me. But all knowledge and information on this globe is being represented by 0's and 1's through a global network of computers doing it.

This isn't strictly true. The global network of computers communicate to each other using multi-level protocols. If binary is necessary and sufficient, then why do we have, e.g., 16-level Ethernet? We have it because information theory tells us that we can transmit information more efficiently when we use more encoding levels. Efficiency is a convenience. But convenience is exactly why we use binary computers in the first place -- they're cheaper to build and more reliable than analog computers.

The point is, there's no "privileged" coding scheme. Any scheme is as capable as any other for storing or computing information. Binary is just currently a convenient choice for general purpose computing. But we're running up on hardware limits for how fast and dense we can make our binary machines. In the future, we'll likely have entirely different architectures, and it's entirely possible that they will not be binary.

 

No, I have repeatedly said analog continuous computing is the other foundation, but its PURPOSE is to yield discrete values to us in the end ultimately.

Ugh, no. Consider an analog computer whose output controls the speed of a motor -- where is the discrete value?

It’s either digital discrete (unary or binary at foundation) or continuous.

Our models of computation are discrete or continuous, period.

 

Binary computers are employing laws of nature.

Every machine (including humans!) uses the laws of physics to work. Otherwise they wouldn't work. ;--)

 

Number bases are based in unary or binary as their foundation. I showed that in 1472 if you read it.

I read 1472 and you did not in any way show that. There is nothing "foundational" about base-1 or base-2. They are arbitrary choices. Just because you can tell a story about how you think children learn to count using unary does not make it a foundational truth.

 

One of the base formal definitions of geometry is shape. I am not being careless there. I am using the most rasa definition in any dictionary (Oxford, etc.) as “the shape and relative arrangement of the parts of something.” “The geometry of the house.” Given you know where I’m coming from, and you know what I meant, you need to chide me for being informal here??

No, you are wrong and being obstinate about it. The base formal definition of geometry pertains to a mathematical system. That people colloquially use the word "geometry" to mean shape is of no consequence to a high-level discourse. Sensitivity to language, please.

 

Every machine (including humans!) uses the laws of physics to work. Otherwise they wouldn't work. ;--)

I just don't understand this statement, because I'm trying to grok your partiality to different types of truths. What laws of physics? Aren't they something in the

This isn't strictly true. The global network of computers communicate to each other using multi-level protocols. If binary is necessary and sufficient, then why do we have, e.g., 16-level Ethernet? We have it because information theory tells us that we can transmit information more efficiently when we use more encoding levels. Efficiency is a convenience. But convenience is exactly why we use binary computers in the first place -- they're cheaper to build and more reliable than analog computers.

The point is, there's no "privileged" coding scheme. Any scheme is as capable as any other for storing or computing information. Binary is just currently a convenient choice for general purpose computing. But we're running up on hardware limits for how fast and dense we can make our binary machines. In the future, we'll likely have entirely different architectures, and it's entirely possible that they will not be binary.

What is 16-level Ethernet? I don't even see it as a Google search. Is it not just a network protocol using binary values that are abstracted into layers?

 

No, you are wrong and being obstinate about it. The base formal definition of geometry pertains to a mathematical system. That people colloquially use the word "geometry" to mean shape is of no consequence to a high-level discourse. Sensitivity to language, please.

For someone who doesn't like absolutes, you are quite absolute at times. ;--)

 

In the end, any proof, no matter how complex, has to FEEL good or bad to have any worth. It has to “sit right” in the being. It either works (T) or it doesn’t (F).

Too simplistic. A computer can determine if a simple proof is correct or not without any notion of feeling or worth. There are many examples of proofs that humans don't quite know how to "feel" about. The four-color theorem was proven by a computer, but it used something like a million pages of brute-force calculations to do it. It works, but it doesn't "feel" very good to a mathematician because the proof isn't enlightening in any way.

Then there are the proofs that we simply don't understand. Most mathematicians can't understand Wiles' proof of Femat's last theorem. It's not that it's inelegant or too long, it's just that the math is really hard.

Then there's the issue that in any sufficiently complex system, there will be theorems that can't be proved or disproved. How does that "feel"? Why does it matter?

Digital computers, and even analog are an extension of how we reason. In the end, we need a VALUE.

No we don't! The result of a computation can be anything. A Fourier transform is not a value. A protein folding sequence is not a value. You're treating this far too simplistically.

That value is “good” or “bad” feeling-wise.

This makes no sense to me. What feeling does 2+3 = 5 impart? How is that feeling different from the feeling imparted by 3+4 = 7? What does the computer feel when it does the computations?

As a toddler, “feeling the goodness” of playing with a spatial block is the basis, then a “presence” indicator is attributed.

This doesn't make causal sense to me. A child doesn't play with a block unless it sees the block, which means "presence" comes before "feeling goodness".

 

Axiom 1: Information is a measurable quantity
Axiom 2: Feeling is an experiential sensation of goodness or absence thereof
Axiom 3: Meaning is feeling from information
Axiom 4: Information may be denoted as TRUE (T) or FALSE (F) and is a reflection of the presence or absence of meaning

Yuck. You don't define "goodness". If meaning comes from "goodness" or "absence of goodness", then there are only two possible meanings -- "good" or "not good". That seems rather limited.

Axiom 4 states that information is true if it has meaning -- feels good -- and false otherwise. What about information that feels neither good nor bad? Indifferent information is not information?

This "feels" like a mess to me.

 

Yuck. You don't define "goodness". If meaning comes from "goodness" or "absence of goodness", then there are only two possible meanings -- "good" or "not good". That seems rather limited.

Axiom 4 states that information is true if it has meaning -- feels good -- and false otherwise. What about information that feels neither good nor bad? Indifferent information is not information?

This "feels" like a mess to me.

Precisely the point, though — you are rejecting it because it "feels" like a mess. If it didn't "feel" like a mess, you'd have a different take toward it potentially. How much is "feeling" some base line element of "this works" is part of the picture?

 

Too simplistic. A computer can determine if a simple proof is correct or not without any notion of feeling or worth. There are many examples of proofs that humans don't quite know how to "feel" about. The four-color theorem was proven by a computer, but it used something like a million pages of brute-force calculations to do it. It works, but it doesn't "feel" very good to a mathematician because the proof isn't enlightening in any way.

What the computer does is, as you've said, up to its programmer. What "value" is computed is solely a function of human attribution to it, and human's direct intention to place values through gates to arrive at other values.

No we don't! The result of a computation can be anything. A Fourier transform is not a value. A protein folding sequence is not a value. You're treating this far too simplistically.

"Information is a measurable quantity" someone once said. No quantity, no information. A fourier transform is a multiplicity of values. When you make a fourier transform in a computer, the computer has broken down the mathematically describable wave values into constituent-part wave values that are ALL represented as stored values. There is no value unless there is measure. Measurability is value. A protein folding sequence is certainly, again, multiplicity of values. "Continuity" vs. "discrete" is STILL value. Analog and digital computers are doing the same thing — yielding information.

This makes no sense to me. What feeling does 2+3 = 5 impart? How is that feeling different from the feeling imparted by 3+4 = 7? What does the computer feel when it does the computations?

Again, precisely why I won't use the term "know." A computer doesn't "KNOW" it's doing any computations. It's a machine doing precisely what it's designed by living humans to do. Voltages are sent through gates to yield voltages. It's simply doing precisely what it's designed to do. There is no experience. This is why a human, living, conscious being is hella different than an 8088, and not just a function of state-processing complexity.

Gradations and types of feeling are different than "presence of any feeling." 2+3=5 registers as "true" on SOME level experientially. It may be miniscule, and it ain't hardly a heart-throb feeling you get hand-gliding, but there is a measurability of "acknowledgement" in the being, otherwise 2+3=7. Who is to say anything is related?

This doesn't make causal sense to me. A child doesn't play with a block unless it sees the block, which means "presence" comes before "feeling goodness".

The child sees the block and has a sense of "feeling of goodness attributed to the presence and potentiality of interacting with it." Playing with the block is an extension of that desire upon the object.

 

There appear to be 3 different “types” of what we might call “truth”... don’t think you’re expecting this either. Lol. What is your feeling on this:

Non-dimensional informational truths: These are born out of innate mathematical theorems that use “innate” laws to derive proofs from the relationships of sets of items and their characteristics to others using formal language to delineate axioms and inferences from them. This is a form of knowledge unto itself that only involves the senses as a utility but not as the final arbiter of what is deemed truth. E.g., “ℕ is the set of counting numbers. Prove the TRUTH that any two numbers when added yields another element of set ℕ.” Nothing to do with physical space as an entity separate from information as the basis. Information itself contains the question and the “answer.”

Qualitative, personal truths: “The apple is good!” “That was a great ride!” These involve “physical space” and the use of information to report on the value of what a thing in this space means. “Was is it TRUE that the apple was good to you? Yes!”

Spatial truths: The “physical space” in which we live, where one might even use the term “reality” and “real” with them, but they’re born in what we perceive to be true based in what information waves and photons carry to us concerning the referrent. Information is used as a means to an end: ”There is a block on the ground. It is TRUE there is a REAL block “there.” I have “one block”. The use of the term ”proof” in this case (as in consensual “court”) is again perceived based on direct sensory feedback from stimulus. It involves “objects” and what one might call “OJBECTive“ truth, since we all share access to the same physical space and objects. ”It is TRUE the boss’ last name is Realman. He is a REAL person, not just informational concept. He works at 123 Spatial Avenue in Jupiter, Fl. He has a dog named Banach. He likes LCD Zeppelin. He rubs lotion on his skin before he goes to bed.” Post #1472 is exploring this definition of truth (And a good question to explore is why this can’t hold equal value to the first definition of truth above).

In all 3 cases, experiential value of feeling to ascribe weight to the data is the arbiter of truth value.

Agreed?

The use of "truth" outside of a formal logic system is problematic for me. The first category is compatible with formal truth, but the other two aren't. I prefer "judgement" for these.

I judge that the apple tastes good. I judge that there is a block on the ground.

Judgement speaks to the subjective nature of the experience, whereas "truth" implies a certainty that is not possible. Just because I see a block on the ground doesn't mean that my assessment is necessarily accurate. Truth implies necessity.

 

But no matter how you cut the cake, you are divorcing information from physical space, correct? What is the true nature and origin of this divorcement, and how is it being made?

A system of logic is completely abstract. When I, as an information processor, think of logic systems, I am referring entirely to internal states.

Further, if you will say that physical space is the origin of information, how is it that information seems to hearken back to physical space as a referent?

External states (physical space) and internal states convey information. The referents of logic systems are entirely internal.

Is it intellectualy "legal" to divorce them and make the arbiter of truth just information's self-consistency?

Sure, why not?

 

But remember, I don't see those things as numbers. ;--)

You may not see them as numbers, but other humans do. And these other humans use computers to add them together. Or are you suggesting that a computer can't compute 2/5 + 3/4?

How can we call something like "5" a "number" and then also say 5.42 is a number, when 42/100's is a completely separate system of expression?

Because 5 = 10/2 = 100/20 = ...

There's no sense in which the number 5 in N is different from the number 5 in Q. Indeed, N is a subset of Q, which means that every one of your beloved counting numbers has a p/q expression.

And the reason the circuit will add the natural numbers is because they ARE foundational elements of ontology and not derivative systems!

Uh, no. The reason an ALU will add natural numbers is because we designed them specifically to perform the "+" of boolean rings. Computers can also add two complex numbers, but they just need a different circuit. BECAUSE THE "+" IS DIFFERENT.

And ALSO because there is a connection at a foundational level between logic and numbers. I know you see them as separate systems, and I'm sure you can see them that way, but I don't believe it's entirely some 100% "separate" phenomena at its core, especially if the nature of information has an innate spatial element.

You have yet to demonstrate this foundational connection. In the most distilled, pure, elemental forms of expressing numbers and logic, we find that they are very different types of things. Statements of logic do not at all look like statements of numbers. You assume that because we can represent numbers in base-2, and binary logic has two states, that this trivial fact is some kind of fundamental connection. It's not.

A statement of logic has no mathematical meaning. "IF A OR B THEN C" -- what is that saying mathematically? Nothing.

An arithmetical statement has no logical meaning. "12 + 3 = 15" -- that's not even a valid statement in any logical system.

You are confusing domains based on a trivial coincidence.

 

If you don't say so yourself. ;--)

Hear, hear.

 

You may not see them as numbers, but other humans do. And these other humans use computers to add them together. Or are you suggesting that a computer can't compute 2/5 + 3/4?


Because 5 = 10/2 = 100/20 = ...

There's no sense in which the number 5 in N is different from the number 5 in Q. Indeed, N is a subset of Q, which means that every one of your beloved counting numbers has a p/q expression.


Uh, no. The reason an ALU will add natural numbers is because we designed them specifically to perform the "+" of boolean rings. Computers can also add two complex numbers, but they just need a different circuit. BECAUSE THE "+" IS DIFFERENT.


You have yet to demonstrate this foundational connection. In the most distilled, pure, elemental forms of expressing numbers and logic, we find that they are very different types of things. Statements of logic do not at all look like statements of numbers. You assume that because we can represent numbers in base-2, and binary logic has two states, that this trivial fact is some kind of fundamental connection. It's not.

A statement of logic has no mathematical meaning. "IF A OR B THEN C" -- what is that saying mathematically? Nothing.

An arithmetical statement has no logical meaning. "12 + 3 = 15" -- that's not even a valid statement in any logical system.

You are confusing domains based on a trivial coincidence.

Let us say you were tasked to demonstrate that on some level there WAS a deep unified connection between addition of numbers 1 and 0 and the logic states 1 and 0. How would you go about doing this using a proof-based approach (which I am coming up to speed with as we speak)?

 

Hear, hear.

"Information is independent of who wrote it." Who says I'm taking pride in such things? I claim it's elegant and simple. One of you could have written it, I'd say the exact same thing, because I believe in objective truth (ducks).

 

I just don't understand this statement, because I'm trying to grok your partiality to different types of truths. What laws of physics? Aren't they something in the

You didn't finish your thought, and I can't figure out what you don't understand. A machine is designed to do work by using the laws of physics.

What is 16-level Ethernet? I don't even see it as a Google search. Is it not just a network protocol using binary values that are abstracted into layers?

For instance, high-speed (e.g., 50 Gbps) Ethernet uses PAM-16 encoding for transmission. Remember, the universe is analog -- to send a message we have to agree on what the voltage levels represent. Using two voltage levels is fine for storing information, but it's way too inefficient for transmitting information. So we've developed a bunch of multi-level encoding schemes in our never ending quest for faster speeds.

 

For someone who doesn't like absolutes, you are quite absolute at times. ;--)

Absolutes are fair game in formal systems. :--)