This needs its own thread:

1) You may be the ONLY person on planet earth that says a calculator doesn't work with numbers. What, pray tell, is a calculator working with and "doing" again? It's adding/subtracting/dividing/multiplying ...?
You want to say that the LED that displays "8, 7, 9" is fundamentally DIFFERENT from the bits that drive the pixels to display those things? Under what authority of your machine/bit QED's early on are you magic-wanding such capacity?

2) There are NO "symbols" in the bit-processing machine, like there are no axioms. There are 1D bits that have nothing to do with each other. "Alpha-numeric" to a machine/brain = numeric only. I was using "axioms" to bracket "symbols" in. Symbols as in A, B, C are nothing more than user-defined 1D bit sequences that have NO basis to the machine outside of nondescript conglomerations of bits vs. other nondescript conglomerations of bits.

In any case, with respect to #1, I MAY be onboard with calling a "number" a "symbological representation of a unique set of bits"... though to say that in base 2, I can't also call 110111010 "442" is a little... <insert word for vexing>. And it ain't certainly anything your brain or Siri can do per #2. Its "utterance" of 442 or display of such on a screen is NOT the same thing, because there is no conceptual emulsification of any of the bits into any abstraction.

 

In a padded-room plumbing of my mind, I'm going to declare this, and again, it may be "new ground" burn-down, so tabula-rasa this deal:

The use of + and OR as an equality is both TRUE AND FALSE at the same time, in the same way TRUE + TRUE = TRUE AND FALSE is (as I discussed earlier).

When it comes to 0's and 1's with NO abstract noun suffix (like "bananas," "cars", etc), their use is equal (and 100% convinced of this due to every hardware gate being traced to aggregates of base OR or a modulation of its output as !OR).

When it comes to them suffixed, like 10101 bananas + 100101 more bananas, though you can treat the bit portion in the same way—and you now have 0111010 bananas via OR/+—in this case, you have MORE bananas in the same general space, and no need to "spawn" a concatenated computation.

So 21 + 37 bananas here is truly ADDING to the total and creating a "non-carry" total of 58, and one has 58 bananas. You don't have "21 bananas" OR "37 bananas" in the same way you don't walk to school or carry your lunch. You have added 21 to 37 to get 58 bananas. It functions more like an "and" of sorts — if I add 21 "and" 37, I get 58.

For the record, I think this is due to the nature of INFINITY and its connection to discrete symbologies and axioms when married to bits.

And now if you will excuse me, I shall inject myself with 300mg Thorazine and strap back into the gurney.

 

Just wanted to say that I love this paragraph.

 

To a bit-processing machine, it's only the relations that matter, not the bits. The bits are just canvas, devoid of information; the relationships between the bits conveys information. Get that through your noodle before continuing!

Of course, by responding to this we are furthering finding the keys to charming the 43 snakes that have just appeared in the last page.

But again — again! You make it sound like "there IS some special relation." Like there's some kind of "magical emergence of personhood" amidst the circuit and the registers. There is ZERO relation! What "relation" is there between a bank of binaries in Siri that shifts one array to another? "WHO" cares about it? Siri certainly doesn't, but she doesn't exist! Does Mario care that his arm was animated up? Mario doesn't exist.

There is no YOU or ME in between the states, and no one knowing anything different between the bits and where they are in the hardware! I don't understand why you are showing Harry Potterhood with respect to the states, as if "something is real" between them. Nothing is!

There is ZERO difference between a computer and old telegraphing machines telegraphing messages from one hub to the next. A computer is a sophisticated morse coding recording and playback device. There is NO one home anywhere, and NO partiality to be found between where the bits are now, and where the bits are t seconds from now!

 

It doesn't break the arithmetic: it "extends" it into undefined territory — that's what I'm proposing.

I have no problem with defining a new arithmetic, but it has to be self-consistent. The problem with your proposal is that it requires two mutually exclusive theorems: 'OR is equivalent to "+"' and '1 + 1 = 0'. The only way to remove the inconsistency is to change the properties of the OR operation, but then it's no longer OR, so why call it that? In fact, we have a perfectly good and compatible operation already: XOR.

An entanglement is false and true at the same time, and it's precisely what's happening here.

This is a popular but untenable way to think of quantum entanglement. The cogent way to think of entanglement is as a mixing of state. When we say that two electrons -- call them A and B -- are in pure states, we mean that we can describe the electrons independently from each other. However, should the electrons interact and become entangled, we mean only that it has become impossible to describe the state of A independently from the state of B (and vice versa).

There's no mathematical or logical inconsistency in quantum entanglement. When Schrodinger semi-jokingly described the cat as both dead and alive, he meant that the cat's state was a superposition (sum) of the pure dead state and the pure alive state. The implication is not that the cat is both dead and alive at the same time, rather that it's current state cannot be described without reference to both states. This superposition of states is a non-classical phenomenon, so we don't have an intuitive way to describe it other than mathematically. But we can definitively say that it does not mean "true and false at the same time", as that's a logical contradiction: TRUE AND FALSE = TRUE.

It is 1 AND 0 because they are both necessary to continue the calculation of the string. IF not, how can we justify seeing strings of bits as having any connection? 010101110 only can be seen as legit because the far right 0 is connected to the next 1 to the left, etc. How do we connect them? Through the arithmetic of OR foundationals which yields superposition of true and false as manifested via a carry-bit.

There are lots of different ways of appending bits to a string. More to the point, there is no inherent notion of string or "connection" between bits. When a digital circuit seems to treat a group of bits as a connected sequence, it's only because we designed it that way. Fundamentally, every bit in every computation is an independent entity; any apparent "grouping" is a design choice.

One must see the inverter ontologically separate from the gate, because they exist functionally separate from each other axiom-wise.

An inverter is a gate. It is the physical implementation of the logical NOT operation. As I see it, the (abstract) logical operations are more fundamental than the (physical) constructions that implement them. This seems clear if we consider that, for any given logical operation, there are innumerable ways to physically implement it (diodes, transistors, water valves, sand traps, etc.). There's no sense in which a transistor AND gate is more fundamental than a water valve AND gate. Since they both share the irreducible property of performing the logical AND operation, the logical operation must be more fundamental.

So yes, an OR gate is functionally more elemental because the NOR requires another element. The AND gate is composed of negated NANDS, and OR's can be made of negated NAND's, but the NAND's are componental. QED.

I think you missed my point when you responded. The NOR gate is not, as you suggest, an OR gate with the addition of an inverter. Look up NOR and OR gate schematics and you'll see that NOR gate is its own implementation (with no OR to be found). In fact, depending on the transistor technology used, a NOR gate requires the same number or less transistors than an OR gate. In other words, in some implementations, an OR gate has more elements than NOR. By your reckoning, then, the NOR gate is more fundamental.

But that's silly. The only reasonable way to categorize these things is by their logical operation. There are precisely 16 binary logical operations -- each axiomatic in propositional logic -- and each is as fundamental as the other.

It feels like you're trying to force an ontological hierarchy to this to appease your theory. It's a big red flag for a theory when it finds itself trying to push square pegs into round holes. Just sayin'.

Again, ontological observation, though—because in the axiomatic world we can build ANYTHING. Where's the "trit" in the presence/absence element of the natural world? The natural world has a bit defined as a high or low voltage. A trit is...? Nowhere.

We can define trit as positive, zero, negative voltage. There's nothing more "natural" about bit than trit. Again, forcing a hierarchy where none exists is unnatural and a red flag.

 

Must have slipped through, because I'm not on board. STATE and PROCESS are not elemental enough to be "SOMETHING" as in "dog" or "RED." A "dog"/noun can be in multiple states THROUGH process. E.g. the concept of a dog being put into a state of sleep via the process of tranquilization.

I don't see the problem. The CONCEPT of putting a dog to sleep and the PROCESS of putting a dog to sleep are two different things. There many more PROCESSes than there are CONCEPTs, so that isn't an issue.

What's more elemental than STATE?

 

And that is entirely not a function of bits or chemicals without a metanatural component . . .

Prove it!

. . . because the guy on the gurney ain't experiencing anything, and watson couldn't care less about the laughter in this discussion.

Prove it!

What is an amoeba's experience of pain? If I build a bot and program it to do everything it can do to avoid the wall with red paint on it, and then I push it toward the red wall, what's different from the amoeba's experience of pain? How different is the amoeba from an insect; an insect from a mouse; a mouse from a dog; a dog from a human?

Is there a distinguishing line somewhere? What does it look like?

 

I don't see the problem. The CONCEPT of putting a dog to sleep and the PROCESS of putting a dog to sleep are two different things. There many more PROCESSes than there are CONCEPTs, so that isn't an issue.

What's more elemental than STATE?

Because STATE is essentially an adjective that only makes sense when it’s ultimately connected to a noun/medium. The “state” of the flip-flip, the “state” of the dog, the “state” of an observable ontology. In this case, we’re chiefly discussing neurons.

 

Prove it!

Prove it!

What is an amoeba's experience of pain? If I build a bot and program it to do everything it can do to avoid the wall with red paint on it, and then I push it toward the red wall, what's different from the amoeba's experience of pain? How different is the amoeba from an insect; an insect from a mouse; a mouse from a dog; a dog from a human?

Is there a distinguishing line somewhere? What does it look like?

There’s evidence, but a proof is on line 493 of the ToE.

 

Back to working on #3 (will respond to the other post):

1) We have machinery/bits QED;
2) INFINITY not a number;

INFINITY is therefore a CONCEPT/AXIOM/SYMBOL, or some combination of them.

Question is, what are those to the #1’s QED with respect to a natural world information processor? And what precisely, is the mechanism asking the question or distinguishing between #1 and #2? And how does this differ from a bit vs. number to the machine?

 

Consider this tabula rasa for a moment. The base concept we're dealing with here is "TRUE + TRUE = FALSE."

Sigh. The "+" operation is arithmetical, meaning it deals with counting. We add magnitudes, not truth values! What is the square root of TRUTH?

It implies, "If I have a voltage OR I have another voltage" I have NO VOLTAGE. That makes NO sense, and is patently conceptually insane.

You keep making type errors. "voltageA + voltageB = 0" is totally legit because we are adding magnitudes: "5 + (-5) = 0".

But you're saying "5 OR (-5) = 0", which of course makes no sense, as OR is a logical operation whose domain is truth values. We cannot use OR to add.

"I have a voltage, OR I have another voltage which would ordinarily equal 'having a voltage,' but because I cannot augment the definition of voltage to contain "more" voltage for truth-state purposes

The bolded part says it all. Of course we can express a voltage as having "more" voltage: 5 V + 2 V = 7 V. This is perfectly valid in the domain of arithmetic. It is entirely nonsensical in the domain of truth values. This why you end up having to do crazy conceptual gymnastics, trying to invoke entanglement and infinity to explain a very simple idea.

This is not a feature of your theory, it's a bug. I don't know why you're clinging so strongly to the OR = "+" idea, but is untenable.

We are in the business here of rolling new architecture to describe the VERY unintuitive elements of reality like entanglement and nonlocation. We are trying to get at relationships in nature that involve untapped definitions and overlaps. So I would say "be open to seeing this in a very new light where the moon can disappear just by looking at it." lol

If we truly want to account for quantum effects, then we're going to need a quantum theory. More than that, whatever theory we come up with will necessarily require quantum mechanics (the mathematical framework) as its foundation. This is a proven fact of our universe (see Bell's inequalities). Do we really want to go there at this point?

More generally, I think it's important to note that -- whatever we come up with -- it cannot contradict anything that humanity already knows to be true. If our ToE ends up with the theorem "1 = 2", then we're f*cked. Game over. Likewise, all the results of the "old" architectures have to be frameable in the new architecture. Relativity didn't overturn Newtonian physics, it extended it. GR gives precisely the same result as SR in the limit as gravity goes to zero, and SR gives precisely the same results as Newtonian physics for velocities significantly less than c. Similarly, quantum physics gives the same results as classical physics in the limit ħ → 0.

New theories do not topple old theories, they only augment them. While the idea of "burning it all down" is exciting, there are only two possible outcomes: either 1) we end up re-building what we already knew, or 2) we invent a monstrosity that has no relation to this universe. And though the latter sounds kind of fun, it's actually really hard to do well. Plus, don't we want to talk about this universe?

The information theoretic approach seems like a great way to go. It's a relatively new perspective that's nonetheless frameable in the old architectures. This almost guarantees that it's both valid and rich in fresh insights.

And W to the T to the F, and boy does this ever prove my point: this makes zero sense that the "abstract world of logic" is not reflecting the reality of the ontology and hardware — or you couldn't make BOOLEAN-based circuits!!

You've got it backwards. The "abstract world of logic" is primary; the physical implementation, as an imperfect construction, is secondary. The axiom of OR -- its definition -- is abstract. We can build a machine (a gate) that implements OR under very specific conditions, but the machine is not axiomatic. Indeed, we have many choices in how we implement OR, and all are equally valid.

Ontologically speaking, you definitely seem like a materialist, as you equate gates with logical operations and voltages with numbers. I suppose I lean toward the idealist side, equating logical operations and numbers with their abstract definitions. I don't know where that leaves us.

Ontologically and logically, there are two separate functions being married here in a NOR gate.

In the case of a NOR gate, the transistor setup is identical to an OR as its foundational structure, except that . . .

And then you go on to list a circuit that is not an OR gate.

Without appealing to physical implementations, can you describe what makes OR more foundational than any other binary logical operation, such as XOR?

But that's irrelevant to the ontology, because modern sophisticated implementations are abstractions and shortcuts that are not where the simple truth building blocks are found. I'm talking about THE most base of computational hardware, 1940 style, which is where the ontology is found that is implementing the boolean reality.

Before there was any hint of the idea of a computer, there were the 16 binary logical operations. They exist 100% independently from computers. A computer is just an electronic way of using the operations, but the operations are fundamental, not the computer!

Again, you're not seeing at the zoomed-in ontological level! "IF A THEN B" to a MACHINE is equivalent to:

"IF 10101010 = TRUE THEN 110101001," which is either a new stored state or the prompting of a new set of instructions.

No idea what you're trying to say. At the machine level, "IF A THEN B" looks more like "10010100101001011110100101010010101", i.e, a string of thirty-two zeros and ones that encode the IF instruction and the values of its operands. (Of course, at machine level there are no actual 1s and 0s, just voltages, but those are harder to write in ASCII.)

Machines do not work at an "ontologicial level". Machines work at the "physical level". We use the laws of physics to design machines, not ontology. The statement "IF A THEN B" is a convenient abstraction of the sequence of voltages that cause the machine to behave conditionally. The machine's just following the laws of physics; the English-like code makes it easier for us to set up the machine appropriately.

You are a brain according to you. You don't know what A and B are beyond the bits.

The second statement does not follow from the first. Suppose my brain is programming a computer to control the lights in the house. My brain decides to store the value of the bathroom light in a variable called "A". In the code, it writes "IF A THEN B". How does my brain not know what "A" is referring to? In a sub-set of states of my brain's memory, it is has associated the sub-set of states where it holds "bathroom light" with the sub-set of states where it holds that it has a variable labeled A" in a program. In what sense is this not "knowledge of A"?

Symbols are abstractions that DO NOT EXIST in the brain that is a bit processor per your QED!

A physical "z" symbol does not exist in my brain, but the CONCEPT of SYMBOL and the shape of "z" certainly do.

A subset of states in my brain holds the CONCEPT of SYMBOL, i.e., a thing that represents something else. In another section of my brain, it holds the CONCEPT of Z, which has many associations. One of these associations with Z is a set of optical sub-states that recognize the shapes "z" and "Z". The brain connects all these notions to "know" what the symbol "z" is.

There is ZERO alpha component to the ALPHANUMERIC phrase in a computer. It is ALL NUMERIC, ALL bits.

Gah. "Bit" is an abstraction; there are no bits in a computer. We physically implement a bit as a piece of wire, or as a capacitor tied to a variable impedance, or as a more complicated circuit. There are no numbers and no bits in computers. We just pretend there are. It's much more convenient to call those wires "bits" and those other wires "power". But, just like a number, you can't take a picture of a bit; it's an abstraction.

Your desire to make "symbols" and axioms out of bits is the equivalent of 400 bits of Mario's cartoon head spawning a pixelated "thought bubble" that "refers" to 210 bits of his arm as separate concepts. At no time is there any emulsifying agent to bits that you are referencing either IN the head, IN the arm, or ANY connection to them.

WTF? A CPU (or brain) can certainly take the 400 bits (or whatever) of cartoon Mario head and associate them with 210 other bits. That's the whole f*cking point. Processors change states depending on other states; processors impose relationship between states. That is the entire freaking point of processors.

Axioms and symbols are NOT bits in the same way INFINITY is NOT a number, NOR is it a bit.

You're using "bits" where I would use STATE. Axioms and symbols are states that are associated with other states; in particular, the other states are functions of the axiom states. That's what axioms do, they let us derive theorems (other states).

Notice that my state ontology is gregarious. All of these ideas -- axioms, symbols, infinity, numbers, concepts -- are just states. I don't need to impose arbitrary ontological rules for what this is made of as opposed to what that's made of. I just have states and functions (processes) to change them. Some of these processes create associations (dependencies); others merely transfer state. The collection of all the related states and processes is the "thing".

Most "things" are fairly simple, like rocks. Rocks do not have many processes other than a base set that we associate with its physical properties. Some "things" (like CPUs) have more interesting processes, i.e., processes that are more transformative-oriented. And some other "things" (like brains) have really interesting and complex processes. But it's all just a bunch of states. In fact, we could look at the universe as a single (very complicated) state with a single (very complicated) process, and everything is just the time evolution of this single universal state.

I don't care how many bits you have, at no time does a computer "know" any one bit or "group" of bits as representing anything, anywhere at anytime!

Wrong! My computer knows that at location 0xF9F20 in RAM there is a 1024x768 group of bits that are all related. It also knows that these bits represent an image compressed with the JPEG algorithm. It also knows that this image is called "jav_holding_a_beer.jpg". It knows all of this because I told it so and, in response, it made the necessary associations in its internal set of states.

If what you are saying were true, then your computer would be useless!

Why are you drawing "conceptual distinctions between:

100101010101011000111010101010

and

111001010011010100110001010100

????

Top is RED, bottom is JOE BIDEN. You don't know what either are, and you claim you can bracket them and "conceptualize them" because one group happens to be stored on an network drive, and the other is stored on a flash drive, but you Harry Potter them together in this discourse by saying "CONCEPT" and "AXIOM"!!

I know the difference between RED and JOE BIDEN because they share very few of the same sub-set associations in my brain. Why is that so difficult to accept?

 

I want to speak to the comment you made about bias. As I'm sure you will agree, anyone who is seeking objective truth does so first from some kind of conjectural intuition, or hypothesis.

For example, it was known for centuries that light was a wave. Einstein and potentially others suspected an additional particulate property that led to the modern wave-particle duality theorem.

To posit such a ground-breaker meant that, though Einstein stood on the shoulders of giants (per Newton's quote), he couldn't be afraid to inadvertently step on their toes to get up there. I wouldn't call his intuitive sense that light was a duality as a "bias," because even though that is technically "correct," the word "bias" can carry a slightly negative connotation.

I would say he had a starting, deep intuition, not a "bias."

Talking about the nature of disjunction or "+" operators is several pages in to where we're going, and I got ahead of myself, admittedly. You are a seasoned expert with the existing nomenclatures. I have a working knowledge of them. Where this discussion works is in the co-shared raw reasoning power. So as we probe forward, I will look to you to see how we can best augment or replace the existing stuff.

In order to move things forward, we have to seriously examine the relationship between axiom #1 and axiom #2.

You keep using terms like "concept," but I would argue that any use of any term is actually based in the ability to _DEFINE them as separate from the voltages. I have never seen a bag of voltages care about bringing "shape" or "form" to something as a living human being does.

So I'm thinking even at a more elementary level at this point, in that, we have voltages in a brain, which essentially are "neuronal states." I don't see these states any different than a future Watson or Siri's classic-computing or quantum or any other computing form. At no time is Siri "defining" anything, or cordoning off any group of bits vs. any other to make them "different." You are invoking a "cordoning" function and separating "yourself" from the voltages to show partiality to certain groups, and defining some groups as numeric, some groups as conceptual, and some groups as axiomatic. There will "never" be a "dog" to you that exists. "RED" and "JOE BIDEN" to you are no different — bags of voltages on a random car hood somewhere on a street corner in some nondescript town.

Until you can prove to me you can do this magical thing as a function of voltages, I don't see the legal right to do it.

So our next level here is to get at the relationship between our axioms #1 and #2, and this is where a lot of my reasoning lies with respect to discussing the intersection of "adding" and "disjunction" (and potentially bridging truth states with infinity and numbers) at a level that is beyond the logic tables and at the level of bridging #1 and #2 with respect to these issues. I'm aware that TRUE or FALSE in the case of entanglement is about their interdependence (I'd like to say codependence, but that's a psych term only). I would argue Boolean rings are doing just that when you start using concatenation in "01 + 01". You are concatenating states to make sense of 1+1=0. I'm getting at the same sort of thing in a different manner. But that's a digression.

Bottom line, we need to get on expounding on #1 and #2 with respect to my prior post... I'm awaiting what you have to say on that

 

1) You may be the ONLY person on planet earth that says a calculator doesn't work with numbers.

I've actually built an adder with my own two hands. I put switches on one end (the input), a couple of 7-segment LED displays at the other end (output), and wired a bunch of logic gates -- made up of transistors -- together in between.

At no point in my construction did I have to sprinkle numbers into the circuit to make it work. So, I ask you, where did the numbers come from? Where they already present in the components? If so, what part of the components hold the numbers? How did my use of switches "push" a number into the circuit? Please explain.

What, pray tell, is a calculator working with and "doing" again? It's adding/subtracting/dividing/multiplying ...?

A couple of pages ago I showed how logical XOR is compatible with boolean addition. In other words, with a suitable mapping, XOR logic behaves as if it were adding. Of course, XOR is not adding anything. But since the result is compatible with what we call boolean addition, we can cogently interpret it as addition.

This goes for all arithmetical operations. A calculator or computer is not doing division/multiplication/etc. What's actually going on under the hood is that we've figured out how to string logical operations together that have results that are compatible with an arithmetic operation.

You want to say that the LED that displays "8, 7, 9" is fundamentally DIFFERENT from the bits that drive the pixels to display those things?

On the contrary, both the LED and the bits of RAM that drive it (or a monitor or whatever) are just states. A processor uses the state of the RAM to configure the state of the LEDs. In neither the RAM nor the LED are there any numbers, just states.

2) There are NO "symbols" in the bit-processing machine, like there are no axioms. There are 1D bits that have nothing to do with each other.

Repeating myself here, but for posterity: a symbol is a particular configuration of a state that is associated by a processor with other states. Nothing fancy here.

As for bit independence, each possible configuration of state can be mapped to a sequence of bits, and each bit can be independently configured. This independence is the blank canvas. Once a processor associates a group of bits with a particular state, the bits are no longer independent -- the relation between them is the state.

In any case, with respect to #1, I MAY be onboard with calling a "number" a "symbological representation of a unique set of bits"... though to say that in base 2, I can't also call 110111010 "442" is a little... <insert word for vexing>.

A number is not a symbolic representation. Numbers are purely abstract -- abstractions of the counting process -- and have no definitive representation. "442" is one particular symbolic representation of the number that has all the properties that we associate with it. "Four-hundred and forty-two" is another symbolic representation of the same number.

And it ain't certainly anything your brain or Siri can do per #2. Its "utterance" of 442 or display of such on a screen is NOT the same thing, because there is no conceptual emulsification of any of the bits into any abstraction.

Nonsense. The "emulsification" is given by the processor itself. Siri most certainly emulsifies the bits that represent your spoken commands. If she didn't, she wouldn't know the difference between the words you say and some random section of her memory.

 

There is ZERO difference between a computer and old telegraphing machines telegraphing messages from one hub to the next.

Exactly right! Both are information processors. The brain, too, is an information processor. If no one is home in the computer, then no one is home in the brain. Can we accept this as a possibility? I don't see why we shouldn't.

Alternatively, perhaps "someone" is home in the telegraph, the computer, and the brain. The telegraph, as an information processor, is quite simple and has no where near the processing capabilities of even a modest computer, much less a human brain. So, the "someone" home in a telegraph is very much a simpleton. In this regard, the "someone" home in a brain is far more sophisticated, and likes the taste of fine wine. What's the problem with this notion?

 

Because STATE is essentially an adjective that only makes sense when it’s ultimately connected to a noun/medium. The “state” of the flip-flip, the “state” of the dog, the “state” of an observable ontology. In this case, we’re chiefly discussing neurons.

Erm, state as we've been using it is a noun. "The state of the pixels" refers to a particular configuration (noun) of pixels. The great utility of STATE is that it does not need to be connected to a medium or anything else concrete. We can use the same set of tools to analyze the state of my brain or the state of RAM. This is a hallmark of a good abstraction.

 

Back to working on #3 (will respond to the other post):

1) We have machinery/bits QED;
2) INFINITY not a number;

INFINITY is therefore a CONCEPT/AXIOM/SYMBOL, or some combination of them.

Question is, what are those to the #1’s QED with respect to a natural world information processor? And what precisely, is the mechanism asking the question or distinguishing between #1 and #2? And how does this differ from a bit vs. number to the machine?

INFINITY is a CONCEPT, not an AXIOM. We have a SYMBOL ('∞') that represents the CONCEPT, but that's not important.

I've already given a possible mechanism by which the INFINITY CONCEPT arises, but basically it goes like this: Assume an information processor that is 1) powerful enough to count and 2) has enough memory to keep track of its counting (as well as store many other states). Such a processor is capable of associating various CONCEPTs about counting, including the notion of NUMBER as the abstraction of the thing being counted.

At some point in its counting, the processor will run out of "raw counting memory". If it has kept track of its counting state in another area of memory, it will be able to continue counting from where it left off. This is the notion of "n + 1", where n is the last number it reached before it ran out of raw counting memory.

Such a processor may associate the "n + 1" CONCEPT in another area of memory: when n is reached, store the last number and start the count over, this time adding the count to n. Eventually, of course, this would use up all of its memory.

Perhaps, however, the processor has developed a COUNTERFACTUAL CONCEPT that lets it consider possibilities that are not currently true. This leads to an association: "If I had more memory, then I could keep counting higher." How much higher? By associating "n + 1" with its counterfactual "more memory", the CONCEPT of INFINITY is born: "if I have an unbounded amount of memory, I can count an unbounded amount of numbers."

Whether such a processor actually derives these CONCEPTs on its own depends entirely on its design. I cannot imagine a calculator, with such a focused design, ever doing it. But it's not difficult for me to imagine that the human brain, filled with such general capability to derive complex associations, does something similar when it first conceives of INFINITY.

 

I want to speak to the comment you made about bias. As I'm sure you will agree, anyone who is seeking objective truth does so first from some kind of conjectural intuition, or hypothesis.

Quite right. I'd point out, however, that good science means never being married to the hypothesis -- the data must always guide the conclusion, not a sense of what should be the conclusion. One of the primary goals of the scientific method is to remove as much human bias out of an experiment as possible (in recognition of just how biased we truly are). It can never be 100% bias-free, but discipline and strict adherence to best practices are a good step.

For example, it was known for centuries that light was a wave. Einstein and potentially others suspected an additional particulate property that led to the modern wave-particle duality theorem.

Neither here nor there, but the platitudes of pop-sci are a pet peeve of mine, and "wave-particle duality" is one of those. As a quantum phenomenon, light is neither wave nor particle (and it certainly is not "both at the same time"). Wave and particle are classical ideas that have no analogue in the quantum world. Whatever we imagine as being wave-like or particle-like classically, none of that is happening at the quantum level. There is indeed a sense in which quantum stuff is best associated with "waves", but these are not physical waves, they are mathematical (Schrodinger's wave equation).

Anyway, like I said, just an off-topic nit.

Talking about the nature of disjunction or "+" operators is several pages in to where we're going, and I got ahead of myself, admittedly. You are a seasoned expert with the existing nomenclatures. I have a working knowledge of them. Where this discussion works is in the co-shared raw reasoning power. So as we probe forward, I will look to you to see how we can best augment or replace the existing stuff.

Agreed. If I seem unreasonably stubborn (or full of myself) on some technical issue, it comes from a place of seeking clarity. I'm all too familiar with the conceptual spaghetti that results from trying to weave a basket of ambiguous and semi-understood notions. I've made a lot of spaghetti baskets over the years, and I will make many more. But I try hard not to repeat the same mistakes.

In order to move things forward, we have to seriously examine the relationship between axiom #1 and axiom #2.

Can we restate the axioms? I'm not even sure what they are at this point.

You keep using terms like "concept," but I would argue that any use of any term is actually based in the ability to _DEFINE them as separate from the voltages. I have never seen a bag of voltages care about bringing "shape" or "form" to something as a living human being does.

So, I'm confused because in the model as I've been tracking it, we don't have any voltages or human beings in them yet. I've been trying to stick to INFORMATION, STATE, BIT, PROCESS, and CONCEPT. Voltages and humans are way more complicated phenomena and would require a slew of dictionary definitions to get to. Things like "shape" and "form" are ok as CONCEPTs.

At no time is Siri "defining" anything, or cordoning off any group of bits vs. any other to make them "different."

FYI: when you say "Siri", I mentally replace it with "information processor of moderate complexity". And, yes, Siri assuredly is cordoning off groups of bits. Your phone wouldn't work, otherwise! How is she doing that? Her programmers taught her where everything goes: put your weather data over here, put your speech-to-text stuff over there, etc. How do brains do it? A couple hundred years of mammalian evolution wired us this way. Vision stuff in the back, motor stuff in the middle, abstract reasoning stuff in the front.

 

In that adder you made, I argue the numbers are there in their basest of forms, represented as 0's and 1's (i.e., my conceptual "O" number set from the graphic). That overlaps in _DEFINITION with strings of logic states, and one of the very points I'm getting at. The string of logic states have no meaning until you call them a "number". The number "IS" the string of logic states FIRST — 10111 — before it becomes the abstract symbol "23" (as you literally prove in the hardware, and what is reflected as individual voltage states in your brain). (In which case, if there IS an overlap, then there is an implicit overlap conceptually in the logic and arithmetical operations, which I’m ALSO trying to get at!)

You are insisting they are entirely separate, and for the life of me, I don't know how based on what you define yourself as—a coil of grey matter comprising neurons of discrete voltages. I'm insisting they're the same, based on this observable physicality. Voltage high or low = logic state OR number. Why do you have a "different word" to describe "logic state" vs. "number" when the same set of neurons can represent both?

That said, in the same vein, you have repeatedly declared "there is no dog in the light" in the brain. But you are, again, a collection of voltages in grey matter. So why do you insist there's "no dog in the light" in the brain? Why do you show partiality to something "outside" those voltages? Do your voltages know the difference somehow?

That said, I feel we are seriously in need of a working lexicon to continue, so what do you think about one- or two-lining the below words with respect to how you are using them (in relation to your brain's physicality as a reference point, where possible) so we can consensually and precisely reference them without equivocation from here on out; I think that would be excellent:

BIT ____________
NUMBER ___________
INFORMATION ___________
MACHINE ____________
CONCEPT ____________
SYMBOL _____________
AXIOM ______________
YOU _____________

 

Axioms so far (although "information" I feel is ontologically incomplete as defined below):

Axiom 1: Information is a measurable quantity.
Axiom 2: A state is a particular configuration or arrangement of measurable quantities.
Axiom 3: A process is a mapping between states. Some process P transforms state A to state B according to some rule.

As a measurable quantity, information can be processed. Examples of information processes are transferring and storage, wherein state is copied and saved. Let I represent some particular configuration of information. To transfer and store I, then, means to configure the storage state S to that of I:S→P(I)→IS→P(I)→I

Axiom 4: A bit is a discrete unit of information; we measure information by counting bits.

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

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

Lemma 1: There is a one-to-one correspondence between any state of n possible configurations and a bit string of log2(n) bits.
Proof: A string of n-bits can represent 2n2n different configurations. Taking the base-2 logarithm of both sides gives us the lemma. QED.

Theorem 1: The information capacity of a state is given by the count of bits in its corresponding bit string.
Proof: Using Lemma 1, map the state to a k-bit bit string. Then, by axiom 4, the state has k bits of information. QED.

Axiom 5: INFINITY is a non-numeric element representing unbounded n

 

Also:

FACT___________
OBJECTIVE TRUTH__________

Science, and the CONCEPT of this discussion revolves around the ability for us to agree to what the objective truth is, vs. what we “think” it is.

The “dog in the light” notion is simply a CONCEPT that we are discussing. Since science makes a distinction between _SOMETHING happening vs. _NOTHING to achieve this, these are axiomatic elements.

The dog would like to ask you a few candid questions about himself as a thought experiment, if you will be so kind to oblige him:

“Why do you insist I’m not in your mind if, as a collection of voltage states in matter, that’s all I am to you, and there’s nothing outside those voltages to you (you don’t know the source of them, whether captured from eye sensors or uploaded via flash drive in your neck). If there’s nothing outside those voltages, how do you make a distinction between _OBJECTIVETRUTH of my presence or absence in the light, or know that Jennifer is asking about me vs. something else with respect to her own mind and the same “light” you claim I’m either “in” or “not in”? And how do you know you are being asked such a question, or the difference between you and her asking it, or me for that matter, if there’s no dog (me) in the light to begin with, or no Jennifer to ask? If your concept of dogs to begin with are states, how is it that collection of states is not in reference to another dog, if you insist none of us exist outside your mind to even differentiate the facts, thereby coming to the _OBJECTIVETRUTH concerning the matter? Frankly, I’m offended you don’t think I exist, and now I’m going to bark. Where is the barking happening in relation to a real-time truth you are observing vs. the solipsistic idea you adhere to? If I were to show up next your computer and bark, you’d claim I wasn’t there, and you wouldn’t feed me? Would you deny the _OBJECTIVETRUTH that you observed me outside your self to Jennifer or anyone else that asked the question, and insist there’s only a solipsistic state dog as I starve because you don’t think I exist outside brain states and ‘kant’ know I do?”