Case in point: the creation of your Euclidean plane algorithm above. That you would deem as math.

But what if the implementation and employment of that algorithm's results using numbers (calculation) afforded you the ability to create more algorithms?

You would not deem that as part of the definition of "math?"

To divorce the use and implementation of the creation of the algorithm from the employment of it is where the word "vain" pops up on my semantic dashboard (as in "unnecessary adherence to form over function"). This is why "doing the math" comes naturally, or "the math says..." comes naturally to everyone, because the purpose of the math is the ability to use it in reality, and often that leads to the ability to create more algorithms to "do more math."

To me, it's like making a hammer but saying the term hammering is not proper, because the use of it to create more hammers is not to be confused with the ability to create hammers.

 

...that said—and sorry for the 19th message on this, just don't want you to miss it:

I completely grok your contention from a practical perspective concerning the "coolness" x-factor of the term math "effectively" about the "creation of the algorithms only."

It's akin to Eddie Van Halen creating what could be the "audible algorithm" of Jump's solo in real time, burning up the stage with 32nd notes that defy understanding and burn a hole in your chest.

This in stark contrast to the 4th-year guitar student practicing the notational transcription one-note-at-a-time... and he gets it, you know—pretty good. Sounds like a quantized MIDI note-reader, but, you know—it's "Jump!"

It's like — "which one is MUSIC, though, man!???" "That second thing really isn't MUSIC compared to Eddie, FFS!"

Same here. Technically it is "music" but... I mean—really.

The ability to identify and sculpt mathematical symbology to represent nature's underlying phenomena, or machinery derived from it, is a real mathematician, and frankly you shouldn't be called a mathematician if that's not how you define it.

So it really should have its own superset term, like "Algorithmitist" because in reality it's just so far and away above the ability to plug a few numbers into the Pythagorean theorem and call it "math."

 

And by the way, just to add formally: I hold to your definition. I just think extending it into the calculation doesn't harm this definition. I believe it includes the underlying recipes AND the execution of them, because "calculation" has no meaning without the recipe, and the purpose of the recipe is the ability to do the calculation with it.

Is that legit to you?

Long division is to math as Windows 10 is to computer science. Operating system theory is definitely (applied) computer science, but using Windows 10 isn't "doing CS", is it? You agree that It would be ridiculous to extend the definition of computer science to include "using Facebook", yes? For me, it is equally absurd to extend the definition of mathematics to include "doing calculations".

We can build machines can do calculations, because no thought is required to follow a recipe. Mathematics requires creative and novel thinking, i.e., intelligence. We cannot build machines to do math.

 

Case in point: the creation of your Euclidean plane algorithm above. That you would deem as math.

I think I see the problem. An algorithm is a sequence of instructions, a recipe, to produce a desired result. Using linear algebra to define Euclidean geometry is the opposite of algorithmic! It takes incredibly high-level thinking to realize that what Euclid constructed by visual analogy with the physical world could be defined entirely abstractly, without any reference to our physical senses. Higher still is the recognition that, because the two constructions -- one physical, the other abstract -- are exactly equivalent, the physical construction has no privileged status. This, in turn, suggests that Euclid's model need not be the geometrical model. Indeed, we know now that Euclidean geometry is but one particularly simple type among innumerable other geometries.

In short, that entire process is "doing math". There's no algorithm for that; one must use deep, creative thinking. I suspect you called my original description of it an algorithm because I laid it out in steps: first, do this; then, using that definition, we can do this; and so on. My description of how to define Euclidean geometry with linear algebra was algorithmic. But my description was not "doing math"; it was merely a re-telling of the highlights of doing math.

This is how actual math gets disseminated. Professional mathematicians sit at their desks thinking. They are doing math. Once the math has been done -- once they've figured out how to prove the thing they've discovered -- they write it down algorithmically: "Let x be a real number, and f(x) a monotinic real-valued function . . ." They do this so that other mathematicians can easily follow the proof. Reading the proof slowly, line by line, the reader "does math" in between the lines to verify what's being said. By the end of the proof, the reader will have done the minimal amount of math necessary to understand the proof. (The writer of the proof, almost invariably, will have done far more math just trying to figure out the proof.)

Reading the proof is not sufficient to understand it; one must "do the math" whilst reading, and this almost never means doing calculations. In the vast majority of proofs, there will be precisely zero calculations; in the few cases where there are calculations, mathematicians will take them as given. The important stuff -- the hard stuff that needs mathematical thought -- is the ideas.

 

It's like — "which one is MUSIC, though, man!???" "That second thing really isn't MUSIC compared to Eddie, FFS!"

Even more to the point: what EVH (or any other musician) does when he creates music, no machine can do. Machines can only follow algorithms (do calculations), they cannot create (do math).

The connection between music and math has long been recognized. It seems like the perfect way to draw the conceptual line between math and calculation: you should be as willing to admit calculation into "doing math" as you would be to admit computer-generated MIDI notes as "doing music".

So it really should have its own superset term, like "Algorithmitist" because in reality it's just so far and away above the ability to plug a few numbers into the Pythagorean theorem and call it "math."

Creating algorithms is one tiny subsection of mathematics, so no. But your example with the Pythagorean theorem is spot-on: there needs to be an enormous distinction between doing math and plugging numbers into a formula.

 

Even more to the point: what EVH (or any other musician) does when he creates music, no machine can do. Machines can only follow algorithms (do calculations), they cannot create (do math).

Ummm...that whole “machine vs. human” thing. Not sure why your vantage point legally differentiates. Modern naturalist brain-only science does not. Brain = bit processing machine. Body is functional interface. Maybe it has something to do with that undefined “life” token in the mind’s “BIOS” that we’ll get to.

There are plenty of EVH Quantum substrate AI replicants at “Guitar HoloCenter 2090” doing plenty of “creating” from the naturalist brain-only perspective. We haven’t differentiated man from machine, reality or observer, because we haven’t defined either, or the “meaning” mechanism that differentiates between signal and noise to quantify it, but—and is central to my impetus here—is as much non-philosophical “science” as any equation made by a mathematician. From my perspective, the mathematician hasn’t “created” the equation. He’s “identified its existence” and crystalized it into 3rd order symbology to communicate it to others.

The connection between music and math has long been recognized. It seems like the perfect way to draw the conceptual line between math and calculation: you should be as willing to admit calculation into "doing math" as you would be to admit computer-generated MIDI notes as "doing music".

I am. But it’s as purest as adhering to the 8-track in the prior example in my estimation, due to many even graduate mathematicians agreeing (you said you are in the minority!). You want to make a distinction with abstract “feeling” and “heart” and other terms that aren’t what Mario uses to play an iGuitar, or what the Terminator might. We aren’t there yet, it’s where I want to go.

But your example with the Pythagorean theorem is spot-on: there needs to be an enormous distinction between doing math and plugging numbers into a formula.

Agreed. But we’ll nitpick this thing into next year’s quarantine. Can we get back on the Interstate now?

 

Why I am so hellbent on differentiating bits vs. what the bits represent in a living person is this question right here:

What, from your to-the-death, naturalist, math-is-it vantage point, differentiates a living human bit-processing EVH with living brain from the iEVH of 2090 grown by Cyberdyne that entirely breaches the uncanny value for you—sweat, beers, concert riders, cigarettes, etc.—performances are identical, personality 100% modeled. Or even the real EVH in a casket that died from tongue cancer in 2030?

What “level of bits” in the earth-based physical medium is the difference?

See, it’s here that my reasoning begins, and where real science I feel needs to. Not in mathematical models, but in “meaning and life”, both of which are undefined scientifically, but I believe can be with a thorough exploration of the mind’s “BIOS” firmware definitions that science has heretofore selectively cherry-picked terms out of to work with, but ignored myriad others.

We don’t even define what a question is as different from a DOS prompt scientifically!

 

. . . that entirely breaches the uncanny value for you . . .

Side note: is "uncanny value" an uber linguistic play on "uncanny valley"? If so, bravo!

What “level of bits” in the earth-based physical medium is the difference?

Honestly, I have no idea. I don't know what it is that distinguishes human brains (that can do music and math) from other types of machines. Complexity seems to be a factor, though I very much doubt it's the only factor: we could build an enormously complex array of random circuits, with more nodes than brains have neurons, and I very much doubt it would become conscious when we turned it on.

They call it the hard problem of consciousness for a reason.

We don’t even define what a question is as different from a DOS prompt scientifically!

 

Side note: is "uncanny value" an uber linguistic play on "uncanny valley"? If so, bravo!

It is now!

Honestly, I have no idea. I don't know what it is that distinguishes human brains (that can do music and math) from other types of machines. Complexity seems to be a factor, though I very much doubt it's the only factor: we could build an enormously complex array of random circuits, with more nodes than brains have neurons, and I very much doubt it would become conscious when we turned it on.

OR!....OR!

The BIOS of the Mind which we so brazenly use as "abstract starting points" to make sense of mathematical models with "well it's just an axiom!" Harry Potter-grade magic wands, has some additional, undefined tokens in it — you know, like "real," "know," "reality," "reason", "who", "what", "when," "how", "where" (you know, those basic questions we assume exist to do science—whatever they are) and... "living" and "being," and "observer" "random," "non-random," "chance," "intention," "non-intention," and how it seems to treat these things by default different from each other, with tokens "feeling" and "heart" and "spirit" and "passion" and "force" and that allows it to even broach the question, "Could there be something more than the bit-processing medulla substrate" that causes us to feel such things not in the locality of the grey matter(!) Say that again— but in the curious area of the "center of our chest" and even have it be a plausible question to it to begin with?!
Even the thought that the mind has tokens for the movement of things that it deems random vs. non-random is incredibly bizarre, considering a mechanical physical medium sure has hell doesn't know what bits are driving it or what they represent, or how they move.

And so in lies the pursuit — if we can objectively start building things from scratch rather than insisting all is a 2nd or 3rd order mathematical model for everything that is, rendering us about as existent as Pac-Man on an Arcade console (which we seem to "know" the difference concerning), we can start uncovering logical definitions for these things as a function of raw, unencumbered observation and pure, obvious inference rather than assuming the question is an eternal, unknowable, intractable bitch forever.

I'm waiting for your next move on that based on my starting place from a few messages back.

 

I read a couple of pages, but too many tangents.
what would make all this impossible is the consideration that those playing fret less instruments will have a percentage of players somewhat off key. A key change may not only bring about the potential for multiple players to be off, but our ear accepts or rejects the new tonal Center, regardless of its accuracy. If you asked the performers to notate where in the score they f’ up, you could probably isolate it.

 

I read a couple of pages, but too many tangents.
what would make all this impossible is the consideration that those playing fret less instruments will have a percentage of players somewhat off key. A key change may not only bring about the potential for multiple players to be off, but our ear accepts or rejects the new tonal Center, regardless of its accuracy. If you asked the performers to notate where in the score they f’ up, you could probably isolate it.

Thanks — actually, the original question morphed about 15 pages ago into a completely new consistent topic (1 main tangent).

 

Even then, and Im only speaking from limited experience, fretless players are constantly adjusting thier tone, rolling up or down toward tonal Center. That in itself is one of the reasons I love fretless stringed instruments (cello for me). Playing strict tones can get boring real quick. The instrument in the hands of the artist is what brings it to life.

 

Even then, and Im only speaking from limited experience, fretless players are constantly adjusting thier tone, rolling up or down toward tonal Center. That in itself is one of the reasons I love fretless stringed instruments (cello for me). Playing strict tones can get boring real quick. The instrument in the hands of the artist is what brings it to life.

That's great, man. Not to be a buttass, but we're past that now, though... if you could just go ahead and exit this topic and check out the new topic on page 3 and feel free to join if you have something new on it, that would be greeeeaat (as Lumberg would say in Office Space). Thanks!

 

It is now!


OR!....OR!

The BIOS of the Mind which we so brazenly use as "abstract starting points" to make sense of mathematical models with "well it's just an axiom!" Harry Potter-grade magic wands, has some additional, undefined tokens in it — you know, like "real," "know," "reality," "reason", "who", "what", "when," "how", "where" (you know, those basic questions we assume exist to do science—whatever they are) and... "living" and "being," and "observer" "random," "non-random," "chance," "intention," "non-intention," and how it seems to treat these things by default different from each other, with tokens "feeling" and "heart" and "spirit" and "passion" and "force" and that allows it to even broach the question, "Could there be something more than the bit-processing medulla substrate" that causes us to feel such things not in the locality of the grey matter(!) Say that again— but in the curious area of the "center of our chest" and even have it be a plausible question to it to begin with?!
Even the thought that the mind has tokens for the movement of things that it deems random vs. non-random is incredibly bizarre, considering a mechanical physical medium sure has hell doesn't know what bits are driving it or what they represent, or how they move.

And so in lies the pursuit — if we can objectively start building things from scratch rather than insisting all is a 2nd or 3rd order mathematical model for everything that is, rendering us about as existent as Pac-Man on an Arcade console (which we seem to "know" the difference concerning), we can start uncovering logical definitions for these things as a function of raw, unencumbered observation and pure, obvious inference rather than assuming the question is an eternal, unknowable, intractable bitch forever.

I'm waiting for your next move on that based on my starting place from a few messages back.

With this said, it actually opened up an even better starting question in my mind, that leads to the one initially posed...

Given our starting axiom of a physical material substrate processing n bits, what is the mechanism asking the question, "What is a point"?

This first investigates the very interrogative mechanism of the substrate as it is defined in accordance with our initial axiom that renders it on equal footing with any other mechanical bit-processing substrate.

I.e., what is the token "what?" mean with respect to an assumed and undefined environment ("space") it is speaking to *apart* from the substrate OR self-referencing another portion of the substrate, because elementary token what assumes something other than itself asking about something somewhere that exists, and is integrally tied to the other interrogative where (1 of 6) that also needs diamond hard definition. Bear in mind, assuming the same substrate asks the questions "what is a point," it may ask it with respect to, for example, a point of a pencil. The pencil (or anything else) isn't in the substrate, as you agreed.

 

Sneak peak of a potential trajectory: When you very first replied, you pinpointed the issue of trying to know “what something is.”

I propose we distill this question down from a Visual Basic-grade granularity level into an Assembly one to probe the BIOS’ built-in firmware lexicon. You, know in the same way we use “axiom” as a “built-in” token to wave a magic wand over token infinity to “badabing” it in to our digital math.

Token “what” → question on docket as proposed in previous post
Token “is” → infers a concept of existence of something “in” something something else (“where”)
Token “something” → infers existence of an indivisible entity

I say the final must comprise a (first-order, along with derivative order overlap) notion of Indivisibility, like infinity itself, which is key to it (and hearkens to my earlier references to the right side of Boole’s equation). Take n number of pixels out of Mario, and he’s no longer Mario as a reference point of the bit-processing substrate, because there’d be no more permanent reference point from which to define Mario.

Therefore, the first-order definition of Mario must contain ∞ bits, and again, we butt up against the limit of a physical substrate’s storage capacity. The brain is not an infinibit soft SSD. Even if in the far future we were to tap sub-quantum storage, we are still dealing with finite, countable storage elements/transistors, and still is divisible. Token INFINITY implies indivisibility other than being able to spawn another infinity from it, as it does already mathematically.

This also implies first-order Mario is an indivisible geometric form that cannnot be stored on the substrate itself. Pan to my original question: “Where is the cube in the brain as-described?”

I therefore say the first-order definition of token SOMETHING is in fact infinite, as Boole intimated in equating bits as unique “universe of thinkable thoughts” elements.

 

I propose we distill this question down from a Visual Basic-grade granularity level into an Assembly one to probe the BIOS’ built-in firmware lexicon. You, know in the same way we use “axiom” as a “built-in” token to wave a magic wand over token infinity to “badabing” it in to our digital math.

Token “what” → question on docket as proposed in previous post
Token “is” → infers a concept of existence of something “in” something something else (“where”)
Token “something” → infers existence of an indivisible entity

I say the final must comprise a notion of Indivisibility, like infinity itself, which is key to it (and hearkens to my earlier references to the right side of Boole’s equation). Take n number of pixels out of Mario, and he’s no longer Mario as a
reference point of the bit-processing substrate, because there’d be no more permanent reference point from which to define Mario.[/quote]
I'm confused about the model space. Your assembly analogy implies that the brain is a processor, which is a machine. But we haven't defined what a machine is. We're assuming bits, and nothing else, right? Before we can have an assembly language, we need an architecture. We need to get to a state where we can define what it means to "process bits".

I therefore say the first-order definition of token SOMETHING is in fact infinite, as Boole intimated in equating bits as unique “universe of thinkable thoughts” elements.

Until "infinite" is well-defined, it's a meaningless string of symbols. Same goes for "point" and every other foundational concept. Agreed?

 

I'm confused about the model space. Your assembly analogy implies that the brain is a processor, which is a machine. But we haven't defined what a machine is. We're assuming bits, and nothing else, right? Before we can have an assembly language, we need an architecture. We need to get to a state where we can define what it means to "process bits".

Sure... How about: any material-derived, physical, and thus componental or contraptional assembly that is able to derive unique sequences of bits from other bits?

Until "infinite" is well-defined, it's a meaningless string of symbols. Same goes for "point" and every other foundational concept. Agreed?

Yes. I was invoking existing usage of it as an axiom in my own linguistic ”Euclideck” for spiffballing a sneak-peak of where I’d like to go.

 

Sure... How about: any material-derived, physical, and thus componental or contraptional assembly that is able to derive unique sequences of bits from other bits?

This is the first iteration of a definition of machine, yes? What's "material"? What's "physical"? What does "derive" mean?

 

This is the first iteration of a definition of machine, yes? What's "material"? What's "physical"? What does "derive" mean?

Yes.

In order to do any scientific inquiry of any kind, as I'm sure you'll agree—and as you just actually employed by asking the above question—scientists first must assume science is, and we can do it (or we need to pack it in right now).

And within this statement science is, and we can do it, we have to be free to use some Crayon-grade starting elements. If this weren't true, then the question above couldn’t even be fashioned for me to answer.

So, to even ask the question, you employed some basic elements to paint with—including a canvas itself, a brush and some basic colors. We're assuming we have some kind of CMYK (Cyan, Magenta, Yellow, Black) here as our starting color pallet, and then we can build a swatch of "official" colors (discrete definitions) off it.

Then we can hopefully build an offset press, where we synergize the CMYK and the swatch colors to publish a white paper called The 5D Semantic Framework: A New Starting Point for Modern Science (or something similar to agree upon—which is the very reason you came here from 2090, and which, to submit to any Goliath of scientific body will require a King David with the cajones of a man with elephantitis of the nuts {to quote John Bender of The Breakfast Club}—because it will be a Renaissance-grade paper, which will win the 2020 Nobel Prize for a novel approach to the problems of science. And then we get to use the sharp corners of the prize trophy to pop our egos! Sound like a plan? Good! It's nice to have goals.)

Now then:

We were able to agree upon our initial axiom concerning the properties of physical substrates due to the mind's built-in Reserved Keywords if you will. They integrally involve and comprise the ontology of what it means to define and thus do science as a human being. So perhaps Ontological Reserved Keyword(s), or "ORK" for short? I just used another ORK typedef-esque function of the BIOS to make a "processed" keyword called ORK that you can cognize.

I would say "no effort to understand by the baseline human cognizance system" is a property of every ORK (again, "object" being an ORK element to mean "any thing, agnostic of its properties").

For example, "Where is the cube as described" or "Where in the light is the dog" are using ORK's with science's existing "processed colors." Where I would say is an ORK, and dog is a subset of animal which too is an ORK. The point at which "what is that?" is exhausted to arrive at a definition could also be part of it. E.g., "What is an icon? A clickable object. What is a clickable object? A program. What's a program? An executable piece of bit-processing software. What is software? Instructions on a medium. What's a medium? A physical substance." We reached the ORK "physical substance" when it's a base-observed element requiring no further parsing: they are self-evidentiary.

Perhaps the core semantic engine could be a Periodic Table of the Scientific Semantic Elements? (PTSSE) Essentially that's what it is.

Certain verbs like "derive" don't need to be further defined, because, like where or what, certain essential verbs are also part of the PTSSE.

So, to your question: What's physical? The basis of science: the observed elements of the natural world. What's material? Same thing. These are ORK's because they're essential to do science with. Machine is a little more "blurry" on the other hand, I would think, because the ORK function has two entries, one of verb and one of noun, denoting ability to productively move or output. In math, functions are defined as machines, and indeed, a mathematician discovers the very functions or machinery of nature.

Agreed?

 

In order to do any scientific inquiry of any kind, as I'm sure you'll agree—and as you just actually employed by asking the above question—scientists first must assume science is, and we can do it (or we need to pack it in right now).

I think we've established that there are (at least) two modalities or "channels" in our discourse: intra-model and extra-model. When we're talking about the model, we're no longer within the model and so are using the extra-model channel. In this modality we can use whatever words and concepts are necessary to communicate our thoughts.

On the other hand, when we're defining or otherwise using the model, we're in the intra-model channel. Here, we're only allowed to use words and concepts that have been previously defined, given as axioms, or come from a pre-agreed background context (e.g., English and logic). So, while in the model, we don't have to define what "what" means, nor do we have to derive logical inferences such as "if A then B; A; therefore B". But we do have to define (or give as axioms) the words and concepts that are used to build the model.

When I asked what "physical" means, I was using the extra-model channel. Your answer can use the extra-model channel for "out-of-band" discussion, but at some point, if the concept of "physical" is an element of the model, you need to provide a definition within the model.

By my last count, our model has "bits" as a fuzzily-defined axiom. There's no definition of "natural world", "science", or "observers", so these can't be used to define "physical". If you feel the urge to protest that we all know what "physical" means, then it should be easy to formally include in the model. For this endeavor to have any hope of success, we need to be precise and clear about what we're actually saying within the model.

BTW, let's call a spade a spade: what you call ORKs are axioms. There's nothing wrong with axioms; you can't build a model without them because we have to start somewhere. So, we should probably start with defining a few axioms.

[intra-model channel]
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: \[ S \to P(I) \to I \] 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 \( 2^n \) 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.

[/intra-model channel]

So far, this is a very small model -- with only 4 axioms, a single lemma, and a single theorem -- but it's already pretty powerful: we can quantify the information in any state.

What do you think about this approach?