“And all else is the work of man”....

Because we insist on having a definition for something that is not definable or that even has a true, rational relationship, we have contrived arithmetical expressions to describe the clinically insane.

22 units as a circumference and 7 units for a diameter are truly not numbers that are perfectly related as another number.

So we write this as a numerical approximation. The ratio of integers is most closely approximated to 3, a true number that God gave us along with integers that make up the contrived ratio of 22 to 7. It doesn’t “add up,” which is another way of saying “make sense,” because all arithmetic is unary addition in disguise.

In 22 / 7, we have a nonsensical garbage dump quantity left over that is not a number. It’s a “state of undefinable, interminable insanity,” also known as Room E409 at Cantor’s insane asylum. Irrational = insane. Insane = Jihad. Opposite of God’s clean, innocent, orderly, beautiful integer invention is the machinating mind of a race of grotesque, addicted, violent, irrational, competitive and ultimately rotting and dying creatures on their hind legs. Of course, that’s the hand we’re dealt, and we’ve made the world more automated and inhabitable, by inventing technology that is convenient, but at the same time senseless, filling our minds with plenty of irrationality and making us less truly unified and often miserable. The remainder in that division is not an independent godly number, it’s the “numeric expression of irrational, unterminating dependency, addiction, and lunacy.”

Similar to sqrt(2). There is no TRUE relationship between the squares and the diagonal, though we so desperately want there to be, and “it’s close enough.” So we invented, yet again, an arithmetic expression to discretize or number the non-numeric.

Same is true for sqrt(-1). That is a contrivance whose solution is not a true, or real, number whatsoever. It’s “i” for imaginary. Because it’s not based in how reality works.

We’re bent on putting infinitudes into finitudes.

So I take it back. There is no ℝ. There is only God’s beautiful integers, and Man’s numeric contrivances and PROCESSES to relate God’s numbers that don’t have any true relationship, and are largely found in ℝ, but a workable one, however, while we’re dying. To compare the cardinality of ℝ to ℕ, as if ℝ is a set of comparable stand alone numbers, is the height of the blasphemy of our Dahmer’d minds.

So congratulations... unary and “f*ck you, Rene” FTW (with all due respect). The line should have been called U for Unreal.

To create a true ToE based on the way things are, we need to disabuse ourselves of man-made machinations and consider the most elemental, independent phenomena of Godnecker first, before we fold in numeric approximation processes.

 

Ah, you see here's the problem! TABULA RASA to the best we can. What, TRULY, is a digit other than the UNARY GRUNT from our most elemental place where we build on???

A digit is a symbol in a high level language, like letters in an alphabet. These are high level, nth-order states we're talking about; we're no where near the ground floor with digits.

 

A digit is a symbol in a high level language, like letters in an alphabet. These are high level, nth-order states we're talking about; we're no where near the ground floor with digits.

Agreed. Although I would call a unary 1 a TRUE digit, no? Digit == digital == finger “digits” == “digital computer”. As in, all other uses are actually derivative?

 

I'm so utterly insistent on getting down to grunts so we can truly attempt to unify all phenomena at the lowest of rational levels. Pi is grunts. Groupings of grunts. If we see the unary/binary "numberless" element, we can build a definition for digits themselves from the hardware, as in some kind of presence of a voltage for unary representation. This is what a computer is doing (and why I believe truth states and numbers are related through the "grunt"), and why they are calculating "grunt digits."

It seems like you're saying that the computer's circuitry is the ground floor, but it is many flights up! Consider a single flip-flop in the computer. As an electrical component, built from even more basic electrical components (transistors, capacitors, resistors, etc.), the flip-flop resides on a high level of abstraction in the state hierarchy. And this is just considering the flip-flop as a physical device. The model of the flip-flop as a boolean state machine sits at an even higher level of abstraction.

But to make a computer, we connect a bunch of flip-flops together, grouping and organizing them by function, and tie them to a CPU, which is itself an nth-order state machine. A computer -- just as a physical device -- is a much higher level of abstraction than a single flip-flop.

Then we have the CPU's low-level language, it's instruction set architecture, which adds another layer of abstraction. Each instruction maps a set of physically realizable states (voltages across flip-flops) to an abstract action ("move the value stored here to there"). The CPU works on all layers of the abstraction hierarchy at the same time.

But even all of this abstraction is insufficient to express any notion of Pi. For that, we need a program, a directed sequence of CPU instructions designed to produce a desired output. Programs -- and I'm only talking of machine languages here -- introduce a yet higher level of abstraction, and this level is especially complex because this is where all the abstract power resides. This is the level of Turing machines, of universal computation, of undecidable programs. This is where any notion of Pi exists in a computer, not at the flip-flop level. If flip-flops are ℕ, then programs are ℝ.

In short, a computation -- any computation, whether calculating digits of Pi or comparing two values -- is an nth-order state transformation across all n levels of state. An (n+1)th level question is asked -- e.g., what's the 100th digit of Pi? -- and a transformation is put into motion. From the state of a program, to the state of a CPU, to the state of groups of flip-flips, to the state of electrical components, to the state of first-order physical states, the transformation changes all of the states. However, the interpretation of the result of the computation -- e.g., the 100th digit of Pi is "9" -- necessarily occurs at the (n+1)th level.

So, when you ask what Pi "is" at some low level in the hierarchy, there is no satisfying answer. In particular, the set of states that can answer the question "What's the 100th digit of Pi?" are provably not unique. Such questions require a program to answer, and programs that output the same result can be written in many different ways. Likewise, the states are not unique at the hardware level (as evidenced by the various though computationally equivalent CPU architectures, e.g., Intel, ARM, MIPS, etc.). Likewise, the states are not unique at the electrical component level, or even the base physical level.

How does that sit with you?

For the record, I do know what I'm talking about in terms of the importance of getting *beneath* the abstraction and complexification. In the same way you want to compare a "red blood" cell to a human. Exact same simplification angle. Does a "red blood cell" feel? If consciousness and life is a function of a metaphysical property, and not a function of nth order physical complexity, then "conceivably" based on that, but the way we use "feel" in a human sense is way more telling because there's way more detail on how it behaves with respect to information.

Yes, yes, when I said that you don't know what you're talking about, I strictly meant with respect to ℝ (and Pi being an infinite number). You're clearly (obviously?) a very intelligent and knowledgeable person, and this dialogue has greatly helped me clarify and frame my own thoughts for myself. Of course, I still think you're full of sh!t on the ℝ stuff.

As for blood cells and consciousness, I do think it's an issue of complexity, but I'm quite open to challenging that notion. I just think it's easier to start from the bottom, as it were, then at the top with our peculiarly human ways of experience.

 

Using Grunt OS again, where a grunt is a blast of voltage, what is the most elementary way any Shannon-sanctioned binary digital computer (assuming binary is just "unary with spatial efficiency") is "seeing a digit?"

The state of one flip-flop as high or low.

100% disagree! A single flip-flop cannot encode all of the information necessary to express the notion of digit. Digits, like alphabets, are symbols in high level languages, which are far too complex to encode in some small amount of flip-flops.

I think it's very important we come to agreement on this, as it gets to the heart of what I consider a big source of confusion.

 

So the concept "4" in you is either this:

@@@@ (unary)
or
100 (binary)​

Nope, the concept of the number 4 is a whole bunch of associated states in my brain. It is entirely wrong to think that somewhere in my brain there are three or four neurons that directly encode the base-2 or base-1 representation of 4.

You say "pi" can't be baseless, but it most certainly can be with unary "1's" alone! UNARY is not base-1, it is its own foundational deal.

I never said "Pi can't be baseless", because I believe that all numbers are independent of any base -- they are all fundamentally baseless. To make them concrete we use symbols, and so we choose a base. But any such choice is a representation, not the number itself.

Unary, as we've been using it -- i.e., @@@@ represents four -- is a base-1 representation.

 

But you are calling PI a FINITE number independent of the base.

Absolutely and categorically. It is indisputable,

You want to call pi a finite number even at the unary or binary levels. It is an expression. It is NOT a finite number, and it is NON-terminating expression at the UNARY and BINARY levels where sh*t gets REAL.

Again, you are confusing the digits of Pi (a representation) with the number Pi. We have expressions for calculating digits of Pi, but these digits don't uniquely characterize Pi! It is extremely important that you understand that!

In order to uniquely characterize Pi we use its properties. For example, Pi is the unique number \( \pi \) such that

• a circle of radius \( r \) has a circumference of \( \pi r^2 \)
• the fundamental period of sine is \( 2\pi \)
• \( e^{\pi i} = -1 \)

These properties are why we even bother labeling an otherwise uninteresting number that sits somewhere between 3.14 and 3.15.

With a circumference of 22 and a diameter of 7, the result is 3 AND "something else."

Great example. The rational number 22/7 has a non-terminating decimal representation in base-10: \[ \frac{22}{7} = 3.142857 142857 142857 ... \] Because ten doesn't share prime factors with seven, we cannot express 22/7 as a terminating decimal in base-10. In terms of the real line, base-10 means using tick marks that are spaced by multiples of ten. No matter how small we make the powers of 10, the point corresponding to 22/7 falls between two tick marks. So, using such a ruler, we can never line up a tick mark with the corresponding point.

But that's a problem with the ruler, not the number! Change the ruler to use tick marks at multiples of seven and they point does line up with a tick mark. Again, representations.

 

Re: CCD's — if you were to zoom in on the CCD grid, you would see a literal, visible mini 2D image of a dog, correct?

What? No. Zoom in to a single pixel on the CCD and you would see a sensor, not an image of the dog.

 

Because we insist on having a definition for something that is not definable or that even has a true, rational relationship, we have contrived arithmetical expressions to describe the clinically insane.

What undefinable things are you referring to? We have extremely precise, rigorous definitions of Pi, ℝ, aleph0, and all the rest. Furthermore, we have precise, rigorous relationships between these definitions.

22 units as a circumference and 7 units for a diameter are truly not numbers that are perfectly related as another number.

But 22/7 is a rational number, i.e., a ratio of two of god's beloved integers. If 22/7 is somehow not allowed, then your problem is with division. But if I have three apples, and two people to share them with, each person gets one and a half apples. Why shouldn't we be able to capture that notion with numbers?

To create a true ToE based on the way things are, we need to disabuse ourselves of man-made machinations and consider the most elemental, independent phenomena of Godnecker first, before we fold in numeric approximation processes.

My problem with this is that it feels just as much a machination to count things as it does to divide things.

 

Agreed. Although I would call a unary 1 a TRUE digit, no? Digit == digital == finger “digits” == “digital computer”. As in, all other uses are actually derivative?

The notion captured by "digit" as a finger is precisely the idea that we can symbolically represent the count of something with a physical thing (number → finger). In other words, a digit must be interpreted, and so exists on a higher level of abstraction than the physical thing being used as the symbol.

 

How do you define pi?

What? No. Zoom in to a single pixel on the CCD and you would see a sensor, not an image of the dog.

No, not a single pixel... I mean the whole thing. Could you see the grid and say "Look, image of dog!"

 

Absolutely and categorically. It is indisputable,


Again, you are confusing the digits of Pi (a representation) with the number Pi. We have expressions for calculating digits of Pi, but these digits don't uniquely characterize Pi! It is extremely important that you understand that!

In order to uniquely characterize Pi we use its properties. For example, Pi is the unique number \( \pi \) such that

• a circle of radius \( r \) has a circumference of \( \pi r^2 \)
• the fundamental period of sine is \( 2\pi \)
• \( e^{\pi i} = -1 \)

These properties are why we even bother labeling an otherwise uninteresting number that sits somewhere between 3.14 and 3.15.


Great example. The rational number 22/7 has a non-terminating decimal representation in base-10: \[ \frac{22}{7} = 3.142857 142857 142857 ... \] Because ten doesn't share prime factors with seven, we cannot express 22/7 as a terminating decimal in base-10. In terms of the real line, base-10 means using tick marks that are spaced by multiples of ten. No matter how small we make the powers of 10, the point corresponding to 22/7 falls between two tick marks. So, using such a ruler, we can never line up a tick mark with the corresponding point.

But that's a problem with the ruler, not the number! Change the ruler to use tick marks at multiples of seven and they point does line up with a tick mark. Again, representations.

Ok, I'm seeing what's going on here. I just put a VCR tape in the machine and discovered what the motel ℝoom is really about:

Pi is not a number. Let us get this straight. It's a PROCESS, a meta-MACHINE that's not a true number, as it's constantly trying to find its identity. We ascribed it one because it has enough of an identity to be workable. We call it a finite "number" that is a character within its horror movie ℝ (Number "line" my ass! It's a multi-dimensional mongrelization of ℕ, more befitting a plane, or some other geometric thing). Pi is like singing "Maria" in C from Westside Story, and staying on the F# from prior C and never hitting G. Kronecker is having a posthumous epileptic seizure in his casket at this moment at this disgusting semantic f*ckery.

So this is why I believe "1" is devoid of all of the associations of sets and properties, and can characterize things in the purest of lights.

If you can tell me precisely what pi is in unary, I believe you will find that it is NOT a "finite machine." It is in a state of quantum-esque infinite HELL where it's chasing something it can never attain, because it is NOT a number, it is a meta-MACHINE that is not from this plane.

And this, ladies and gentlemen, is why I will declare openly why it appears I'm "full of sh*t" about ℝ. Why? Because ℝ is full of sh*t about itself. You can't create a set of numbers AND extended abstract processes and call it a "set of numbers that is comparable to ℕ in any way shape or form." And then, you CANNOT double down on such madness and have the Luciferian-grade moxie to call it REAL.
And you CERTAINLY can't do what I was trying to do, and that is make reality-based sense of that ill-named inferno.

So, ℝ does not stand for REAL. It stands for ℝENE. More precisely, as someone here once said:



...for co-opting a divine word for this mongrelized, MADDENING hell. We all forgive you, of course. But this very much pisses me off, because it is brazenly insane and has grotesque philosophical implications that could describe the atrocities on this planet in some Hilbert space.

The set should be called U for UNREAL, and not a set of NUMBERS, but a set of COMPONENTAL NUMERIC CONTRAPTIONS.

 

"Dimension"... just want to be sure we are using it in the same way, rasa-style:

1) Informational — there are 500,000 dimensions, or "unique characteristic points" to describe the head of a pin
2) Geometric — there are 3 dimensions to a cube (X, Y, Z)
3) Physical-Space Dimensions — "Measurable physical space dimension?" Similar to geometric, but sensory-empirical?

?

i-dimensions
g-dimensions
p-dimensions?

 

are we going for the longest post ever here ?

At times like these , Im reminded of the question, how many infinities are there.
If there's an infinite number of integers, and an infinite number of fractions between any two integers , how many numbers are there ?

if all else fails,

remember the ultimate answer is

42

https://en.wikipedia.org/wiki/42_(number)#The_Hitchhiker's_Guide_to_the_Galaxy

 

are we going for the longest post ever here ?

At times like these , Im reminded of the question, how many infinities are there.
If there's an infinite number of integers, and an infinite number of fractions between any two integers , how many numbers are there ?

if all else fails,

remember the ultimate answer is

42

https://en.wikipedia.org/wiki/42_(number)#The_Hitchhiker's_Guide_to_the_Galaxy

No, we're going for the most accurate and comprehensive as humanly possible. Small feat.

 

How do you define pi?

Like any other mathematical object, you define it by a list of properties.

No, not a single pixel... I mean the whole thing. Could you see the grid and say "Look, image of dog!"

No, of course not. The photo sensors transduce the energy from the light into a voltage or current, and we can't see voltage or current.

 

Pi is not a number. Let us get this straight. It's a PROCESS, a meta-MACHINE that's not a true number, as it's constantly trying to find its identity.

My problem with this is that counting is a process, and we get the numbers in ℕ from counting. And if we consider 1 as an element of ℝ, then it has a "process" very much like Pi: \[ 1 = 9 \times 10^{-1} + 9 \times 10^{-2} + 9 \times 10^{-3} + 9 \times 10^{-4} + \cdots \] If we're going to make boisterous claims about what is and what isn't a number, then we need bullet-proof justification.

Pi is like singing "Maria" in C from Westside Story, and staying on the F# from prior C and never hitting G.

I love tritones. =)

So this is why I believe "1" is devoid of all of the associations of sets and properties, and can characterize things in the purest of lights.

In the abstraction hierarchy, sets are at a much lower level than numbers. Numbers and arithmetic require a bunch of structure, whereas the language of sets has almost no structure, Sets are just collections of things. Sets are simpler and more basic than numbers.

Here's an analogy: in terms of complexity, sets are to numbers like air is to O2 molecules. With sets, we can't do much more than say "this is air" or "this is not air", which is the extent of the structures and definitions we can create with sets. But if we want to define what an O2 molecule is, we need a lot more structure, i.e., the full might of chemistry.

Sets are just bags of stuff. Numbers, like O2, require a lot more structure to describe and define.

If you can tell me precisely what pi is in unary, I believe you will find that it is NOT a "finite machine."

I don't understand why you keep emphasizing the unary (base-1) aspect, as if it makes any difference. Can we write the digits of Pi in base-1? Of course. Here's one way:

111
.
1
1111
1
11111
....

It's an inefficient use of space, but it conveys precisely the same information that "3.1415..." does. But, as I've repeated many times now, any sequence of digits of Pi -- no matter what the base -- does not uniquely characterize Pi. There are an uncountable amount of numbers whose decimal digit representation starts with "3.1415...". This is true whether we use twenty or twenty trillion digits. What makes Pi unique is its properties, not its digits.

So, ℝ does not stand for REAL. It stands for ℝENE. More precisely, as someone here once said:

LOL! I want that shirt!

 

1) Informational — there are 500,000 dimensions, or "unique characteristic points" to describe the head of a pin

"Informational dimension" is apparently an esoteric technical metric related to information entropy that seems outside the scope of this discourse, so I'd prefer we not use the phrase. I think what we've been trying to express with the "dimensions" of information is better expressed in terms of strings of bits. That is, what we actually mean by dimensions of infromation is amount of information.

For example, the information in an m-by-n matrix of on/off values is perfectly encoded by an mn-bit string, Instead of saying the matrix has mn dimensions of information, we simply say it has mn bits of information. This is not only clearer, it's easier to write and, most importantly, it has the advantage of not overloading the word "dimension", which is most commonly associated with the geometric concept.

What do you think?

2) Geometric — there are 3 dimensions to a cube (X, Y, Z)

Yes, geometric dimension refers to the minimum number of coordinates necessary to label a point in a geometric space.

3) Physical-Space Dimensions — "Measurable physical space dimension?" Similar to geometric, but sensory-empirical?

This is problematic. First, we can't measure physical space directly -- we measure distance and such by reference to objects and then infer the properties of space. Second, what we're actually inferring is our perception of physical space.

I don't think we can cogently say anything about the "actual geometry" of physical space, at least not from first principles. But, if we can agree that whenever we refer to the geometry of physical space we do so with implicit acknowledgment that we're talking about the perceived geometry of physical space, then I'm fine with it.

 

I'm going to take another stab at the counting element from another angle, because, though counting is a "process," I do not believe it can be held on the same order of higher abstraction.

The issue with pi is very much touching on the "information" element we're discussing. I emphasize unary because for some reason I thought perhaps it might change the angle, but it didn't, so that's good.

The problem I have with "finite" as I do with "real" or "countable" (for other reasons), etc. is that you seem to be saying the "expansion" element has nothing to do with its underlying properties. But at the same time you're say each term is "adding additional precision" forever. The number 3 is static. It's not in any kind of "flux." Whereas the portion of pi that is "in a perpetual state of adding more precision" cannot semantically be described as "finite" whatsoever to me. It's either finite and rational (like 3) or it's approaching finite and irrational like pi. If it's approaching finite, how can it literally be finite? It's finite as we USE pi effectively, of course. But I'm talking about its native, isolated unstable state.

So either we have a semantic glitch in the matrix, or the term "finite" has some kind of alternate meaning in very high mathematics that I cannot buy without some kind of thesis. If we disregard all sets, and discuss the number 200 years ago, what are we saying about it?

 

"Informational dimension" is apparently an esoteric technical metric related to information entropy that seems outside the scope of this discourse, so I'd prefer we not use the phrase. I think what we've been trying to express with the "dimensions" of information is better expressed in terms of strings of bits. That is, what we actually mean by dimensions of infromation is amount of information.

For example, the information in an m-by-n matrix of on/off values is perfectly encoded by an mn-bit string, Instead of saying the matrix has mn dimensions of information, we simply say it has mn bits of information. This is not only clearer, it's easier to write and, most importantly, it has the advantage of not overloading the word "dimension", which is most commonly associated with the geometric concept.

What do you think?


Yes, geometric dimension refers to the minimum number of coordinates necessary to label a point in a geometric space.


This is problematic. First, we can't measure physical space directly -- we measure distance and such by reference to objects and then infer the properties of space. Second, what we're actually inferring is our perception of physical space.

I don't think we can cogently say anything about the "actual geometry" of physical space, at least not from first principles. But, if we can agree that whenever we refer to the geometry of physical space we do so with implicit acknowledgment that we're talking about the perceived geometry of physical space, then I'm fine with it.

That sounds fine... So then all information shouldn't be called "1D" or "2D" or... at all? What about a matrix you describe above as being called a 2D array in comp. sci. space?