How's this for a syllogistic definition for bits-as-numbers:

1) Bits are the fundamental unit of information.

2) Digital computers work with bits.

3) Digital computers compute.

4) Computing is done with numbers.

5) Bits are numbers.

 

Again, as you have not defined what it means to "know", I cannot answer the question.

In my view, the condition of knowing something is a big, complicated abstraction with many layers of connotation. "You know your friends, but do you really know them?" Etc.

None of this "knowing" stuff is necessary to accurately describe the transmission and storage of information. Here's a heuristic that can help us along: If the question you ask cannot also be asked of a camera, then it's not a well-posed question.


I don't know what you mean by this. The framework is the model, yes? Then I believe things can exist in models; indeed, I'm partial to models that have things in them.


Choosing a model means choosing a logical system (the rules) and applying semantics (the meaning) to the system. For example, in physics we typically model motion using differential equations. The equations are a mathematical model of a physical phenomenon. Choosing a different set of equations gives us a different model (different semantics). In no sense is the model the phenomenon; they are always distinct.


I don't understand your emphasis on pronouns. Using the heuristic mentioned above, if I take the CCD chip out of the camera, keep it powered so that it's "alive", what happens? The sensors in the CCD continue to respond to light, but without the rest of the camera circuitry, that's the end of the line -- no bitmaps are produced.

Ha! Well, okay then...

Perhaps we need to pursue a definition of "to know" first.

If information hits the CCD concerning the dog, the CCD circuitry then transfers the bits to various temporal registers and long-term storage devices, where the bits are then stored.

"CCD, do you know what the image is you just captured?"

"No."

"What kindly gives you the right to discuss it as though you do again?"

 

How's this for a syllogistic definition for bits-as-numbers:

Terrible.

1) Bits are the fundamental unit of information.

Check.

2) Digital computers work with bits.

Check.

3) Digital computers compute.

Sure.

4) Computing is done with numbers.

Bzzzt. Computation is a physical act, which means the one thing it cannot use is numbers. We can compute with voltages, gears, rocks, water levels, whatever -- but we cannot compute with numbers.

What about when you add 24 and 95 in your head? That's your brain using voltages, not numbers.

 

Ha! Well, okay then...

Perhaps we need to pursue a definition of "to know" first.

If information hits the CCD concerning the dog, the CCD circuitry then transfers the bits to various temporal registers and long-term storage devices, where the bits are then stored.

"CCD, do you know what the image is you just captured?"

"No."

"What kindly gives you the right to discuss it as though you do again?"

Notice that the question is completely irrelevant to the fact. For example, my camera is a cheap old thing that captures images and stores them on a compact flash card. Your camera, on the other hand, is a brand new model that includes state-of-the-art machine learning algorithms to categorize your images as you take them. Ask your camera what the image is, and it will put it in the "dog" folder.

So, how does "knowing" what the image is change the fact that both our cameras do the same physical thing? "Knowing" allows a greater level of storage organization -- our memories are probably far richer than, say, a fly's -- but so what? The fundamental process is the same for both the dumb camera and the smart camera, for the dumb fly and the "smart" human.

 

Notice that the question is completely irrelevant to the fact. For example, my camera is a cheap old thing that captures images and stores them on a compact flash card. Your camera, on the other hand, is a brand new model that includes state-of-the-art machine learning algorithms to categorize your images as you take them. Ask your camera what the image is, and it will put it in the "dog" folder.

So, how does "knowing" what the image is change the fact that both our cameras do the same physical thing? "Knowing" allows a greater level of storage organization -- our memories are probably far richer than, say, a fly's -- but so what? The fundamental process is the same for both the dumb camera and the smart camera, for the dumb fly and the "smart" human.

Oh, not at all......

I was literally thinking in my mind of the most elementary possible v1.0 CCD, as in like the Fairchild Kodak from the late 70's that's stored to a digital cassette.

I asked the CCD the question, not the storage medium. So kindly please re-read that question from that perspective, because, agreed, the sophistication level of the tech doesn't change the question in reality.

 

Terrible.


Check.


Check.


Sure.


Bzzzt. Computation is a physical act, which means the one thing it cannot use is numbers. We can compute with voltages, gears, rocks, water levels, whatever -- but we cannot compute with numbers.

What about when you add 24 and 95 in your head? That's your brain using voltages, not numbers.

If we're discussing a number, what proof do you have that the abstraction is not the same as the voltage? We haven't defined what anything is yet, remember?? Ha...

 

I don't know what you mean by this. The framework is the model, yes? Then I believe things can exist in models; indeed, I'm partial to models that have things in them.

But in the case of ontological models, I would argue we have a catch-22.

If the model is mathematically based and the math has not defined "what something is," how can it be partial to "having things in them" if they cannot be defined by the bits that refer to them? The dog is manifest as some kind of other elements that compose the definition, namely a "form" in some kind of "space," otherwise, the dog is a bag of spatial-less bits and not one of the bits care 1 bit about any other.

 

Oh, not at all......

I was literally thinking in my mind of the most elementary possible v1.0 CCD, as in like the Fairchild Kodak from the late 70's that's stored to a digital cassette.

I asked the CCD the question, not the storage medium. So kindly please re-read that question from that perspective, because, agreed, the sophistication level of the tech doesn't change the question in reality.

Further (and I like having these smaller messages to keep track of various sub-elements rather than having them all in one big unwieldy page) — I asked the question to the CCD using "words."

If I ask you the question, "Where is the dog in the light?" I'm using words here, which assume cannibalization to bits.

An information processing device is instructed to represent the word as bits because a human told it to do so; typically in a binary system the word is 8 bits.

Where is the dog in the light; and if you say it's somewhere in:

01010111 01101000 01100101 01110010 01100101 00100000 01101001 01110011 00100000 01110100 01101000 01100101 00100000 01100100 01101111 01100111 00100000 01101001 01101110 00100000 01110100 01101000 01100101 00100000 01101100 01101001 01100111 01101000 01110100 00111111

The more relevant question to you and the CCD is, where is the concept of dog, light and image thereof vs. potential actual in the above if you only have something other than more bits to define and distinguish at your disposable?

 

If we're discussing a number, what proof do you have that the abstraction is not the same as the voltage? We haven't defined what anything is yet, remember?? Ha...

What proof do I have that the abstraction that we call number is not the same as the abstraction that we call voltage? None, as proof is only possible within mathematics/logic, and the notions of numbers and voltages as abstractions are not in the mathematical domain. But I have plenty of evidence that the two are not equivalent. I can rattle off properties of numbers that can never be applied to voltages, but that would be boring and gross overkill. What makes you think they are the same?

 

What proof do I have that the abstraction that we call number is not the same as the abstraction that we call voltage? None, as proof is only possible within mathematics/logic, and the notions of numbers and voltages as abstractions are not in the mathematical domain. But I have plenty of evidence that the two are not equivalent. I can rattle off properties of numbers that can never be applied to voltages, but that would be boring and gross overkill. What makes you think they are the same?

Because we have not defined anything outside of bits, an abstraction itself is not a bit, but essentially another "universe of thinkable thoughts" in my mind, which we have yet to define by anything, because words haven't been defined outside of bits. A number may carry voltages within it—we have not defined what something is, so an abstraction is something if we're not going to call it more bits.

Because of this, my syllogistic proof I believe still stands—I show partiality to the existence of something outside of nondescript bits, and you don't (yet).

 

But in the case of ontological models, I would argue we have a catch-22.

Lol! However, if we were being super careful, I bet we could describe objects within an ontological model with needing to posit their existence outside the model, even if the model is specifically about everything that actually exists. Funny shit, what brains can do. Turtles all the way down.

If the model is mathematically based and the math has not defined "what something is," how can it be partial to "having things in them" if they cannot be defined by the bits that refer to them? The dog is manifest as some kind of other elements that compose the definition, namely a "form" in some kind of "space," otherwise, the dog is a bag of spatial-less bits and not one of the bits care 1 bit about any other.

I'm not following you. In mathematical models of motion, the equations describe the movements that can happen without ever needing to define what's actually moving. For example, Newton's pithy "F = ma" tells us that an object of mass 'm', experiencing a force 'F', will accelerate a quantity 'a'. Under certain restrictions, this fact applies to any object, and so defining the object is delightfully unnecessary. If it were the case that the various objects in the universe each obeyed different laws of physics, we'd have as many models as we have objects. Fortunately, this is not the case.

In the information model that we've been discussing, the important parts of dog->light->camera are 100% equivalent to cat->sound->ear, or teepee->smoke-signal->teepee. We don't need to define "dog" or 'cat" or "teepee" to quantify information, just as we don't need to define "marbles" or "rocks" to quantify the physics of motion.

 

Further (and I like having these smaller messages to keep track of various sub-elements rather than having them all in one big unwieldy page) — I asked the question to the CCD using "words."

Small chunks of elephant are easier to eat than whole elephants, so I agree.

If I ask you the question, "Where is the dog in the light?" I'm using words here, which assume cannibalization to bits.

An information processing device is instructed to represent the word as bits because a human told it to do so; typically in a binary system the word is 8 bits.

I'm not following you. There seems to be an implicit model shift happening, where the question "Where is the dog in the light?" has switched roles from use to denote (as it did in this very sentence). Zooming in and out of logical systems gets confusing really quickly (ever read Hofstadter's Godel, Escher, Bach?), so slow it down for me by explaining each step. What do words have to do with this? What do words have to do with bits? You also seem to be using "words" in two ways: 1) as natural language units (dictionary words, etc.), and 2) as computer language units (32-bit words, etc.).

 

Small chunks of elephant are easier to eat than whole elephants, so I agree.


I'm not following you. There seems to be an implicit model shift happening, where the question "Where is the dog in the light?" has switched roles from use to denote (as it did in this very sentence). Zooming in and out of logical systems gets confusing really quickly (ever read Hofstadter's Godel, Escher, Bach?), so slow it down for me by explaining each step. What do words have to do with this? What do words have to do with bits? You also seem to be using "words" in two ways: 1) as natural language units (dictionary words, etc.), and 2) as computer language units (32-bit words, etc.).

Holy zoom levels, batman. I think you're an AI from 2060.

You're admittedly the living Brittanica here—I conventionally work in a "long term" investigative modality where I plumb depths of many disciplines with specific questions in mind to get at specific answers, as a lawyer might, to make a case. I feel original thought is from within in that good ol' "mysterious mind" that is "unlocked" (NOT the brain, dammit! ha), so I've touched on various authors' works in context to my studies. So as you've done thus far, you might have to continue to do some steering semantically in this Bonnie and Clyde pursuit here—but hopefully never to filibuster or cloud the simple point.

Anyway, back at the E-wing at Bellevue:

Brain. CCD. Both bit (as we defined) processors—correct?

If so, a group of bits is a byte, or "word" of arbitrary length.

But a word is also a geometric symbol to reference the group, yes?

 

Because we have not defined anything outside of bits, an abstraction itself is not a bit, but essentially another "universe of thinkable thoughts" in my mind, which we have yet to define by anything, because words haven't been defined outside of bits. A number may carry voltages within it—we have not defined what something is, so an abstraction is something if we're not going to call it more bits.

I thought we agreed our assumed model was common sense? Don't words (and other things) have common sense definitions and ontological status? If you really want to start from first principles and rigorously define everything as we go, then we're going to be here for a few years, at least. Personally, I'd rather assume the basics and work from there. I'm fine if something specific needs to be completely fleshed out, but just starting with bits and deriving everything else sounds tedious as hell.

Anyway, to me, an abstraction is just another way of representing something. Usually, an abstraction simplifies the thing being abstracted, at the cost of complicating the bigger picture (every abstraction adds another layer of complexity). The concept of voltage is an abstraction of a physical phenomenon -- talking about voltage is a convenient way for us to talk about the physical phenomenon that we associate with the concept. Likewise, bits lets us abstract the notion of "quantity of information" in a convenient and quantifiable way. Though the concept of bits and voltages are abstractions, the things they refer to (the abstractant?) are physically real.

Numbers (and the myriad other mathematical objects) seem different. They are, in a sense, the ultimate abstraction -- perfectly distilled from the physical world -- yet they don't have an obvious referent (as it were). The "it" of a voltage is an empirical phenomenon; the "it" of bits is a quantity of information. What is the "it" of a number? It's entirely possible that mathematical objects abstract the very stuff of the universe, but who knows.

Because of this, my syllogistic proof I believe still stands—I show partiality to the existence of something outside of nondescript bits, and you don't (yet).

Naw. Bits are definitely not numbers. We can use numbers to count bits, but we can use numbers to count sheep, too. Are sheep numbers? I suppose I should have pointed this out many posts ago, but numbers are enormously complicated mathematical objects with jaw-dropping and mind-bending properties. There are so many, many different types of numbers -- natural, rational, real, complex, quaternions, octonions, p-adic, and the list goes on, and on, and on -- yet, there's only one type of bit. Bits are simple, numbers are pregnant with possibility. There's no possibility for equivalence.

 

Holy zoom levels, batman. I think you're an AI from 2060.

My reasonably educated guess is that the AI of 2060 will be noticably more flexible and adaptive than the AI of 2021, but nothing remotely close to what humans can do. Want to give me a Turing test?

You're admittedly the living Brittanica here—I conventionally work in a "long term" investigative modality where I plumb depths of many disciplines with specific questions in mind to get at specific answers, as a lawyer might, to make a case. I feel original thought is from within in that good ol' "mysterious mind" that is "unlocked" (NOT the brain, dammit! ha), so I've touched on various authors' works in context to my studies. So as you've done thus far, you might have to continue to do some steering semantically in this Bonnie and Clyde pursuit here—but hopefully never to filibuster or cloud the simple point.

I grok that modality, and I'll try to follow along as best as I can, provided you'll permit me AI-type questions.

Brain. CCD. Both bit (as we defined) processors—correct?

If so, a group of bits is a byte, or "word" of arbitrary length.

But a word is also a geometric symbol to reference the clump, yes?

Brain and CCD + microprocessor (not sure how relevant that technical detail is, but I'll throw it in) = bit processors.

A group of 8 bits is called a byte (a group of 4 bits a nybble, so clever those comp sci guys of old). A word, in CPU speak, is the size of the CPU's registers, which are its immediate storage areas. A CPU (the computer's brain) does its magic by moving data into and out of registers, and so CPUs work most efficiently when the data is in register-sized chunks: words. Your 64-bit CPU is called "64-bit" because that's its word size.

Terminology minutiae aside, we can pretty much dispense with such language when discussing information, as the only quantity that matters is the number of bits. Information is processor-agnositc, so CPU word size (or brain neuron-chunk size) doesn't matter. This is why you see cryptographic algorithms labeled as, e.g., AES-256 (for 256-bit key lengths), rather than AES-32 (i.e., 256 bits is 32 bytes) or AES-4 (256 bits is four 64-bit words).

Occasionally, you'll see the word "word" used to describe a binary string, such as "10010". That can be called a 5-bit "word", but if we're in a context where the word "word" could be used in the usual lexical sense, then it's best to reserve "word" for the lexical case, and call chunks of information (like the previous 5-bit sequence of symbols) "strings". Note that a string (in the information sense) can be comprised of any number and kind of symbols, not just 1s and 0s. We usually stick with 1s and 0s simply because it's more to the point (any sequence of symbols can always be bijectively mapped to a [longer] sequence of 1s and 0s).

TLDR; bits are all we need, and sequences of bits are called strings.

 

I thought we agreed our assumed model was common sense? Don't words (and other things) have common sense definitions and ontological status? If you really want to start from first principles and rigorously define everything as we go, then we're going to be here for a few years, at least. Personally, I'd rather assume the basics and work from there. I'm fine if something specific needs to be completely fleshed out, but just starting with bits and deriving everything else sounds tedious as hell.

We'll have to find equal-footing there, but I think we can get a working sketch pretty quickly.

Naw. Bits are definitely not numbers. We can use numbers to count bits, but we can use numbers to count sheep, too. Are sheep numbers? I suppose I should have pointed this out many posts ago, but numbers are enormously complicated mathematical objects with jaw-dropping and mind-bending properties. There are so many, many different types of numbers -- natural, rational, real, complex, quaternions, octonions, p-adic, and the list goes on, and on, and on -- yet, there's only one type of bit. Bits are simple, numbers are pregnant with possibility. There's no possibility for equivalence.

Naw. Heh. I'd argue we're using bits to count the sheep just the same.

5 sheep over in field A + 7 sheep over in field B is 12 sheep in total.

Binary equivalent:

0101 field-A sheep + 0111 field-B sheep = 01100 sheep

100% equal to 5+7 = 12 sheep

Strung-together logic states = computable numbers.

I argue until we define something outside of the bits (in the other post), they're no different.

It's simply base 2 vs. base 10, where base 2 is composed of 2 bits per number, and where each bit is itself a number (like saying "TRUE I have something" vs. "FALSE I have something". There is an implicit isometry of logic states and the most elementary quantities there, in my estimation).

All the different types of numbers are qualitative descriptions. In the end, we have quantities that are added, subtracted, multiplied or divided (or simply just "fanciful addition"). Their characteristics are abstractions external to the numbers themselves.

Yes or no?

 

My reasonably educated guess is that the AI of 2060 will be noticably more flexible and adaptive than the AI of 2021, but nothing remotely close to what humans can do. Want to give me a Turing test?


I grok that modality, and I'll try to follow along as best as I can, provided you'll permit me AI-type questions.


Brain and CCD + microprocessor (not sure how relevant that technical detail is, but I'll throw it in) = bit processors.

A group of 8 bits is called a byte (a group of 4 bits a nybble, so clever those comp sci guys of old). A word, in CPU speak, is the size of the CPU's registers, which are its immediate storage areas. A CPU (the computer's brain) does its magic by moving data into and out of registers, and so CPUs work most efficiently when the data is in register-sized chunks: words. Your 64-bit CPU is called "64-bit" because that's its word size.

Terminology minutiae aside, we can pretty much dispense with such language when discussing information, as the only quantity that matters is the number of bits. Information is processor-agnositc, so CPU word size (or brain neuron-chunk size) doesn't matter. This is why you see cryptographic algorithms labeled as, e.g., AES-256 (for 256-bit key lengths), rather than AES-32 (i.e., 256 bits is 32 bytes) or AES-4 (256 bits is four 64-bit words).

Occasionally, you'll see the word "word" used to describe a binary string, such as "10010". That can be called a 5-bit "word", but if we're in a context where the word "word" could be used in the usual lexical sense, then it's best to reserve "word" for the lexical case, and call chunks of information (like the previous 5-bit sequence of symbols) "strings". Note that a string (in the information sense) can be comprised of any number and kind of symbols, not just 1s and 0s. We usually stick with 1s and 0s simply because it's more to the point (any sequence of symbols can always be bijectively mapped to a [longer] sequence of 1s and 0s).

TLDR; bits are all we need, and sequences of bits are called strings.

Yes, I'm very familiar with all that nomenclature (Have a 30-year background in all things IT since C-64, so I've investigated those elements at one point or another).

Agreed, let's dispense with the IT element then, since it's not germane to developing the framework now anyway. I went there because I maintain a fundamental bit-number-equivalency theorem, and it might be relevant in the end if it could be integrated.

We are using words (as in linguistic, dictionary-style) to communicate about everything right now. Each word is composed of a letter on the screen; each letter is an array of pixels, controlled by individual programmed bits in the GPU.

The computer is agnostic to the shapes it's creating on the screen that we are reading to communicate.

Implicitly, bits are creating forms that we are distinguishing from other bits in real time.

Would you agree:

Forms are required to make sense of bits, correct? Otherwise bits are context-less and therefore meaningless to other bits?

 

My reasonably educated guess is that the AI of 2060 will be noticably more flexible and adaptive than the AI of 2021, but nothing remotely close to what humans can do. Want to give me a Turing test?

Ok, 2090 then? I think when Ken Jennings won against "Watson" in Jeopardy, it was really just you in the back, and instead of showing the time-displacement tech you came here in, they showed pictures of a generic datacenter room. I may just give you that test at some point!

I grok that modality, and I'll try to follow along as best as I can, provided you'll permit me AI-type questions.

Yes, feel free... that's how this arrangement is working out quite well in the pursuit of a true Theory for Everything (TBA Spring, 2026).

 

5 sheep over in field A + 7 sheep over in field B is 12 sheep in total.

Binary equivalent:

0101 field-A sheep + 0111 field-B sheep = 01100 sheep

100% equal to 5+7 = 12.

Counting bits and counting sheep. The string "0101" has precisely four bits of information. If we count bits in the usual way, that particular string represents the number 5: \[ 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 5 \] But we can count the bits differently: \[ 0 \times 2^{-1} + 1 \times 2^{-2} + 0 \times 2^{-3} + 1 \times 2^{-4} = 0.25 \] The same sequence of bits can represent the number 0.25, or indeed something entirely different. Anything that has at most four bits of information can be represented by that string.

Strung-together logic states = computable numbers.

Nope. We naturally associate counting (and logic states) with countable numbers, i.e., 0, 1, 2, 3, ... But most numbers are not countable. What logic state corresponds to \( \pi \)? How do you count \( \sqrt{2} \) sheep? Indeed, the vast majority of numbers aren't even computable in principle, whereas bits are always countable (and hence computable). So, how can they be the same if the size of one set (numbers) absolutely dwarfs the size of the other set (bits)?

All the different types of numbers are qualitative descriptions. In the end, we have quantities that are added, subtracted, multiplied or divided (or simply just "fanciful addition). Their characteristics are abstractions external to the numbers themselves.

I think I see what you mean, and I agree to a point. This is one of those instances where the technical stuff is important. Numbers, as complicated as they are, do not include any notion of adding, subtracting, etc. Numbers have properties, that's it. If we want to perform operations on numbers -- adding, subtracting, etc. -- then we have to bolt on extra, even more complicated models. This is where we get into algebraic structures, like groups, rings, fields, etc. The structure of the numbers by themselves does not permit operations, but by imposing richer structure, such as a ring structure, then we can include things like addition and multiplication. But a ring isn't a number, and the "same" number behaves very differently in different algebraic structures. In boolean rings, 1 + 1 = 0 is a true statement.

I say all of this to convey the idea that counting, adding, numbers, bits -- they're all very different things, each their own deep discipline. Admittedly, our everyday language makes it all the more confusing because we informally mix and match the various concepts. But if we look carefully, as we should in such endeavors, we see far more distinction than sameness.

 

Yes, I'm very familiar with all that nomenclature (Have a 30-year background in all things IT since C-64, so I've investigated those elements at one point or another).

Nice, I started on C-64 myself.

The computer is agnostic to the shapes it's creating on the screen that we are reading to communicate.

Implicitly, bits are creating forms that we are distinguishing from other bits in real time.

Would you agree:

Forms are required to make sense of bits, correct? Otherwise bits are context-less and therefore meaningless to other bits?

This is precisely like the "0101" example. How we should interpret the symbols -- the semantics -- is arbitrary, informationally-speaking. Whether "0101" means 5, 0.25, or "Monday" it costs the same (informationally-speaking) to transmit, process, and store the message. Likewise, an 8-bit 256x256 pixel bitmap has a maximum information capacity, regardless of the image it displays. One might argue that the image itself, when processed by a suitable brain, can convey more information. For example, if every pixel in the the bitmap was a random 8-bit number, the image would be a fuzzy mess, seemingly conveying zero information. On the other hand, a bitmap that was just a white background showing a formula for generating the digits of PI would seem to hold a lot more information than could possibly fit in a 256x256 image (infinite digits worth of information!).

But, and here's the important part, the random bitmap contains a lot more information than the image of the formula for PI does. How do we know? Because to describe the random image exactly as it is, we'd have to describe every pixel exactly as it is. Whereas, with the PI image, to describe the complete bitmap we can use a few words, like "white background, formula for PI in black in middle". What about the fact that the formula for PI seems to contain within it an infinite source of information? It actually doesn't, because PI has a very simple structure -- so simple, in fact, that we can describe it entirely (!) with a few symbols. That is to say, PI is patterned, and patterns are information shortcuts. An endless string of "001001001001..." has barely more information than the string "001".

It's crucial that we recognize that the information is completely independent of the semantics given to it, whether by man or machine.