If they don’t have shape, what is this about? The man who is one of the most extensive record-breaking number cognizers, does so as shapes to do it:

https://www.ted.com/talks/daniel_tammet_different_ways_of_knowing/transcript?language=en#t-216540

Notice that you don't need to be a "record-breaking number cognizer" to associate those glyphs with numbers. That he chooses one set of squiggles over another set (e.g., {0,1,2,3,4,...}) is of no consequence.

For the eleventy-third time: numbers are independent of their representation.

(he says pi is an infinite number, it goes on forever, btw)

Which proves that he doesn't know much about math.

 

How do we “know” the length of a line then, if all points are zero length?

Very easily: if a is a point on the line, and b is another point on the line, then the length of the segment defined by the points is |b - a|.

If between point A and point B are infinite zero-length points, what is measurement?

To make the notion of length rigorous in such domains, we need the machinery of measure theory. The Lebesgue measure has all the necessary machinery to give us the intuitive result: |b - a|.

 

1/3 = .9 repeating = 1 = infinity (one particular incarnation). Each point has zero AND infinite length at the same time.

What you just wrote is mathematically nonsense. By the way, 1/3 is very clearly not 0.999..., it's one third of that.

 

If INFINITY is ultimately outside the numeric as a definition, why can’t its adjective form be used to describe the true nature of ℕ as having infinite numbers?

"Having infinite numbers" is not a technically precise phrase, but in colloquial speech it gets the point across.

 

So INFINITY is not a base token, like “ADDITION,” it’s triangulated, or somehow tangentially a “byproduct?“

Not sure what a base token is. The arithmetic operation of addition, like INFINITY, is derived from the counting process.

 

Very easily: if a is a point on the line, and b is another point on the line, then the length of the segment defined by the points is |b - a|.


To make the notion of length rigorous in such domains, we need the machinery of measure theory. The Lebesgue measure has all the necessary machinery to give us the intuitive result: |b - a|.

There is still no line when each point is 0 length. It deosn’t matter the representation (which, btw, is more 0D information!) from pi to 5, what is the “length?” If you say any number, the number has no length!

 

How are they characterized if they are dimensionless? Dimensionless is shapeless, so this is my contention from the get go. :—)

Huh? We don't need to draw shapes to characterize shapes. The best descriptions we have of shapes are mathematical equations, which don't look anything like the thing they describe!

In an information processor, where information has no dimension, there is no innate shape of any kind. Correct? How is Daniel Tammet insisting they’re separate, and using “feel” to describe the shapes?

Who is Tammet? The "number cognizer" dude? What do geometric shapes have to do with numbers? The symbol most people use for zero looks like a circle -- so what?

 

I mean, what do you feel about it... you can reckon a “beginning,” God, infinity, numbers, etc. without invoking set theory (just a general conceptualization prior to deep math...temporarily assuming “feeling” potentially separate from knowable math).

Lol, well, let me put it this way. Before I learned set theory (and a whole bunch of mathematics), I felt utterly confused about this stuff.

 

Btw, it’s not that I don’t understand any of the stuff... I am arguing from a different Pythagorean and Newtonian purview that infinity is a non-emergent, non-tangential, stand-alone, elemental source, involving true spatiality and “token feel and meaning” (which science knows little about).

The thing is, when you say things like "Pi is an infinite number", I can't believe that you do understand this stuff.

Perhaps transfinite has merit, but “trans” is still a modulating prefix to elemental “infinite” no matter how the cake is cut, and I do not believe it’s spurious to grok INFINITY as an innate extra-numeric concept with properties that are not mathematically “boxable.”

The "trans" in transfinite is modulating finite, not infinite. When I learned set theory, we defined infinite sets in terms of finite sets. Finite is the ground floor, INFINITY lives up above.

 

You’ll notice we’re right in the zone with my original “true cube” question... dimensionless information yielding perceived spatial dimensiom. Either the dimension exists, or everything is one big discrete dimensionless 1D array.

Either way, it doesn't really matter, since information is dimensionless.

 

What you just wrote is mathematically nonsense. By the way, 1/3 is very clearly not 0.999..., it's one third of that.

Correct, I wrote it quickly on the way out the door. LOL.

1/3 is clearly not .999.. — I was thinking of the proof concerning 1 = .9 repeating:

 

The thing is, when you say things like "Pi is an infinite number", I can't believe that you do understand this stuff.

I know... but I'm using the term differently than "mainstream."

Consider me as Edna Van Halen who understands the guitar with no lessons or other various elements, but no one dare question her ability to FEEL the guitar fully — a term science has no concept of, and its true connection to meaning and information, infinity and the numeric. No one understands ANY of that in terms of making a ToE, period. There are bizarre overlaps and all sorts of things that are bunged up in semantic implications of words, that are tied to information, but information is separate from what is being described, which implies what's being described is not information, which implies words themselves have more to them than just information!!

For example, "REAL" as you agree, is a misguided term for that number line, and what if that very term is one of the keys to understanding feeling and form? "Countable" is ALSO a bullsh*t linguistic ascription, straight up. People who work with the math are NOT necessarily linguists. Numbers are not countable. Numbers COUNT and are used for counting. "Countable" has incredible degrees of semantic horsesh*t attached to it, including the wherewithal of she/he who counts. I'm coming from this very ground-floor on purpose.. I could very easily cloud my mind with everyone else's thinking. I've kept my self very purposely "dumb terminal" with terminology because I know to understand the very elements requires an unclouded interface to them. I wouldn't bother pursuing this with you unless you too were a linguist (problem with "real," definition of Euclid's point, etc.)

"Pi" is "considered a finite number", "a point on that line that's 0D length," but I believe it's also infinite at the same time. There's hella more to the story when it comes to the true nature of existence and its connection to such things.

By tabula rasa, you'll have to bare with this element, because I want to build from as much a ground-floor as possible, with the cleanest implication...

 

If information is independent of its representation, and representation is the symbology used, then perhaps the symbology itself is tied to the word “feel” and has some kind of true spatiality? Otherwise is not representation just more dimensionless info? Why insist they’re separate?

I have zero doubt that symbology is connected to "feel". There's an entire field of academic research on that connection (semiotics). I don't, however, see what "feel" has to do with spatiality. The various layers of abstraction are all dimensionless.

Why insist they're separate layers? Because it seems like they are. Remember the sand grain? It conveys information, but when grouped with a bunch of other grains, the collection conveys even more information. If a finger writes a message in that sand -- a higher level of abstraction -- we get even more information.

Is the representation not “2D” spatial elements describing dimensionless info that permits meaning, grokking, and feeling toward it?

Are you're asking if it's the representation -- the symbols -- that gives meaning to an otherwise meaningless hunk of information? I don't think so. Symbols give information "concreteness", that's true, but there are so many examples where the choice of symbols makes no difference whatsoever, that it's difficult to think that the symbol is what matters. For instance, I don't get different meaning from the base-2 representation of a number versus its base-10 representation.

That's not to say that the symbols chosen can't introduce yet another level of abstraction that carries its own level of information. We see this all the time in marketing materials, where things like the choice of font makes a significant difference. But I see this is a meta-layer, not the fundamental thing.

 

The thing is, when you say things like "Pi is an infinite number", I can't believe that you do understand this stuff.


The "trans" in transfinite is modulating finite, not infinite. When I learned set theory, we defined infinite sets in terms of finite sets. Finite is the ground floor, INFINITY lives up above.

Yes, exactly. And literally truckloads of puppies die with this sh*t, I'm sorry. And I am not alone with this. The greatest mathematical minds would agree to this. We are putting God in a box with this, and taking what may be the very cornerstone of the origin of everything and putting it in convenient "transfinite" boxes of various cardinalities.

 

There is still no line when each point is 0 length. It deosn’t matter the representation (which, btw, is more 0D information!) from pi to 5, what is the “length?” If you say any number, the number has no length!

The length of a line segment (or a stick) is a magnitude, which we can express with numbers. How do we do that? We associate to each point on the segment a number in ℝ. Then, to find the magnitude, we read off the number at one end of the segment, and the number on the other end of the segment, and subtract them. For example, the length of a segment from Pi to 5 is \(5 - \pi \).

Now, if you want to argue that there are no lines, that's fine, but your beloved Euclid would disagree.

 

Correct, I wrote it quickly on the way out the door. LOL.

1/3 is clearly not .999.. — I was thinking of the proof concerning 1 = .9 repeating:

Gotcha. And I fully endorse the conclusion: 1.000... = 0.999....

 

The length of a line segment (or a stick) is a magnitude, which we can express with numbers. How do we do that? We associate to each point on the segment a number in ℝ. Then, to find the magnitude, we read off the number at one end of the segment, and the number on the other end of the segment, and subtract them. For example, the length of a segment from Pi to 5 is \(5 - \pi \).

Now, if you want to argue that there are no lines, that's fine, but your beloved Euclid would disagree.

Ahhhh...

Let's run with this for a moment. Every piece of information, including numbers are 0D, yes?

There are no lines of any length when everything is 0D length, right?

 

So as I said, I believe a ToE is found in the engine of meaning, words, semantics and the nature of their connection to discrete and continuous phenomena, and the understanding of innate intelligence vs. acquired as it respects "dogs in lights" in this "physical space" that is separate from 0D information, but that we are using to insist there's more than 0D on a daily basis.

Until one makes a delineation between information, the "information about the information" (its "representation") and ("physical space" — "something else"), the pursuit is futile.

Therefore, there are existing disciplines co-opting words that are not truly applicable to this end. Math is not exempt from this, as you know. The "RENE" line is one of them. It is not "real." And yet mathematics is very much FOUNDED on this nonsense term!

So if I said "such and such is not REAL" but was using the term with respect to physical space, where EVERYONE ELSE inherently uses the term effortlessly and intrinsically, well then "she doesn't understand what she's talking about." No, she understands fully. The mathematics discipline does not understand this clearly, and theories can be built with misnamed things that are "self-consistent" but can also be ontologically blind. Why does that matter? It matters if you believe math's primary PURPOSE is to describe the world in which we live.

You also have said Euclid's "point" definition sucks. These are considered staples in mathematics, so you are not at odds with the above.

So when you make a QED out of certain terminology, and it's not necessarily ontologically applicable, the QED is NOT the full story. It's "self-contained consistent," but it is NOT the full scope.

For example, what if space is NOT bent at all, and gravity is NOT an effect ontologically. Despite ALL the math that appears to reflect this ontology, what does that render all of those sophisticated tensor-calculus equations that are all "undeniable"? That sound and look so utterly infallible and holy? It's very sophisticated bullsh*t, no disrespect to Einstein.

I have issues with the use of the term "infinite." To call pi a "finite number" mathematically, even if "true," is a "REAL" criminal "point" in full effect.

In the context of mathematical frameworks, "pi" is a "finite number, a point on a number line." Sure, got it. I understand all about it. But I can grok instantly that this is linguistically akin to having a child who was learning violin, and she can play one Mozart minuet and one Bach in two keys memorized, and the parent just went ahead and bragged about her being a "musician."

Is she a musician? Absolutely!™

Or how about going out with someone twice, and talking 4-5 times. Is she your girlfriend?

She might not think so, but you do!™

So calling "pi a finite number on the REAL line" without knowing what "meaning" is — literally, the VERY TERM that is used to denote the engine of how meta-information-representation and our human INNATE "axiomatic" generator maps to information which maps to ontology properly; and how words truly create value from distinguishing between physical space, their objects (of which we have NO understanding, how we are even addressing things dimensionally from a 0D array!), infinitude, finitude, numeric, "true continuous," "faux continuous," and how these words truly work ontologically is what I would call a brand new set today:



It stands for "Bullsh*t Truths."

The set of all Bullsh*t Truths has a one-to-one bijection with the arrest record of pedophile priests.

These truths don't really tell the story with sufficient depth about what's REALLY going on (there's that term again "REAL"), and though they provisionally work as a truth, and are pitched as such, they aren't really one once framed in the full context of the word.

So just be alert to this issue as we move forward here. Like I said, I want to burn the house down, starting with "REAL", rename it to Rene or E for Numeric Expressions. We may have to burn down some of Euclid's work.

No offense, guys... you might have done the same when you pushed things forward.

The "simple machinery is not found in a mathematical statement," said Feynman. This implies the model involves deep plumbing in the very way we think and reason that alerts us there's even a "potential ToE to begin with."

 

The number line is a geometric object. Each point is not a "result", it's just a point on the line. There is a bijective map between the elements in ℝ and the points on a line, so we call such a map "the real number line". It's as if we labeled each point on a line. That's it; no computations involved, no results.


Of course.


You're talking about applications ("rocket use"), but that's an (n+m)th order affair. The number Pi -- an nth order abstraction -- has nothing to do with rockets; there are no properties of Pi that include "rockets". Lol.

From the application perspective, the rocket guidance system doesn't use the number Pi. Instead, it uses a rational approximation that is sufficient for the application. This is no different than any other number used in an application. If, at some particular stage of flight, the engineers calculate that the rocket's acceleration will be 5 km/s^2, they know that the probability of it being exactly 5 km/s^2 is zero, because the number 5.0000000... has FAR more precision than the system is capable of. This is why careful scientists and engineers don't specify numbers, they specify ranges. The acceleration is not 5, it's 5.0 +/- 0.5.


ℝ is not a line (its elements can be mapped to one), but it is a set. Sets do not have geometric dimensions. The numbers in ℝ are not results, and they are not computed -- indeed, the vast majority of numbers in ℝ cannot be computed!

How do you figure they are not results?

Anything derived from a process can be termed results. ℝ elements are the results of multiple-level abstract arithmetic computation beyond counting that results in non-integers.

And this here is entirely what I’ve been saying since day 1 in Wiki:

“A model for the real number system consists of a set ℝ, two distinct elements 0 and 1 of ℝ, two binary operations + and × on ℝ (called addition and multiplication, respectively), and a binary relation ≤ on ℝ.”

“A model using the two most elemental numbers, 0 and 1 represented as binary bit elements (compact unary). No advanced frameworks necessary. All non-ℕ numbers and sets are the results of computation on the integers.“ — L. Kronecker II

Even sqrt(-1).

ℝ is not a geometric line unless mapped, sure—but it is an implied conceptual one, if it has any kind of mappable sequentiality.

 

Huh? We don't need to draw shapes to characterize shapes. The best descriptions we have of shapes are mathematical equations, which don't look anything like the thing they describe!

As young children, we first see, feel, and draw shapes in physical space before there is any further abstract informational characterization of any kind.