Um... I didn’t say that? I said the repeating mantissa is *one* unit to NOT be truncated, or you lose its definitiom as 1/3. Of course it can be written in decimal form.

Such confusion. 1/3 does not have a mantissa. The IEEE754 floating-point representation of 1/3 has a mantissa (but so does the floating-point representation of 0,1,2, etc.!).

You're correct that, in base-10, we cannot truncate the decimal expansion of 1/3. But this is also true of Pi -- truncating the decimal expansion of Pi gives you a different number. So, what's the difference?!

The moment you truncate it, you’ve jeopardized its identity as a repeating decimal and now it is not representing 1/3 properly.

Same with Pi.

Point missed. We don’t divide 1/3 there! We MULTIPLY the man-made measurement algorithm 1/3 by the value, notice? 33 gallons, what is 1/3 of it? 1 TIMES 33 divide by 11. That is 3. And proper reasoning. :—)

I'll have what she's having. I'm going to give you the benefit of the doubt and assume you were high AF when you wrote this, lol.

1/3 is not a number. It’s a numeric dividing measurement process designed to create another. 1/3 of what? A fractional expression is a utilitarian process to make measuring easier, so we can stay in a given unit, and don’t have to use whole numbers for every measurement and change units (1.5 feet instead of 18 inches). That’s why we invented them.

It's hilarious to me how you insist that 80,000 Ph.D.'s will disagree with half (one-third?) of the things I say, while claiming with a straight face that 1/3 is not a number.

See above. Fractions are NOT numbers, they are two-number processes: their purpose is to yield another number or process for convenient measurement purposes... You can say 1.5 feet and remain in feet units instead of having to switch to another label expressed as a number (e.g., 18 inches). Mathematics goes beyond “REAL” in its semantic f*ckery, I tell you.

I fully and genuinely believe in your freedom to choose not to call rational numbers "numbers". I, however, will continue to fruitfully recognize number sets of all color and creed. #rationallivesmatter

I only see base 1 and base 2 as the TRUE expression of numbers, as a computer does, which is an overlap of logic states and quantity metrics, and where the divide between quantitative value and spatial representation effectively disappears by seeing them as amalgamations of logic states.

"The TRUE expression of numbers" -- spoken like a TRUE zealot! Analog computers are the devil's work!

Pi in this elementary definition is still a “resolving” process, NOT a number. It has a dimmer switch at its basest “representation”. Base-7 is as useless as understanding it as calling it a day with “π”

Sigh. 22/7 and Pi are different numbers. You claim that 22/7 has a dimmer switch, but that dimmer switch somehow disappears when we write it in base-7. "Oh, but base-7 is useless". No, your argument is useless. Anything you can write in base-1 or base-2, I can write in base-7 and use less paper while doing it.

Again, they are NOT numbers. They are fractional arithmetic expressions invented for measurement conveniences using the integers with operator concatenations.

"Fractional arithmetic expressions". You don't seem to realize that we can write 1, 2, etc. as fractional arithmetic expressions. In particular, we can write them as non-terminating fractional arithmetic expressions and they describe the same number.

I'm curious, do you believe that negative values are numbers? Is -5 a number?

To write the chord out using 2D glyphs is dimensional, #1. No awareness of the chord without such.
Secondly, no chord without 3D objects (strings) making it. Thirdly, the wave itself is dimensional.

So, you're saying that my conception of a Bb maj7 chord refers to a specific set of waves borne from vibrating strings? Which set exactly?

Fallacious notion! Euclid‘s definitions are entirely geometric first, as you learned them first! they were taught drawing on a 2D chalkboard! You can’t even discuss vectors and spaces (spatial any one??) until you discuss lines and points. And vectors are also written as 2D arrows and arrays!

You've probably never studied linear algebra, and that's fine. But a vector space is an abstract space with no geometrical objects. There are no lines or points in a vector space. In order to induce a geometry on a vector space, you need additional structure, namely, a compatible inner product. Using this inner product, you can define the notions of line, point, angle, etc.

Vector spaces are more fundamental than geometries. In physics classes, teachers use arrows on graphs to represent vectors in \( \mathbb{R}^2 \) or \( \mathbb{R}^3 \), but this is purely didactic in purpose, a way to help students get a concrete sense of the physics involved. In math classes, a vector is just an element of a vector space. It has no shape. It doesn't even have coordinates until we pick a basis set. But the choice of basis is arbitrary. Just as with numbers and bases, a vector is independent of any basis. Yet, somehow, I am able to conceive of such a thing without any reference to spatiality.

 

Absolutely. Dog == human, except a dog uses monotonic elements and is not reporting on any spatial “thought“ using the likes of words, advanced gesticulations, chalkboards, chalk, and videos. It’s more much ...unary? Lol. Dog can “know” someone’s there, maintains memory of its relationship to that someone, can signal basic needs from that someone, show affection etc. But there’s insufficient variety of communication to characterize any higher spatiality in it its being.

So where's the line? You say it's not an issue of complexity, but then what is an issue of? Does a blood cell feel? A virus? Where's the line?

 

Such confusion. 1/3 does not have a mantissa. The IEEE754 floating-point representation of 1/3 has a mantissa (but so does the floating-point representation of 0,1,2, etc.!).

You're correct that, in base-10, we cannot truncate the decimal expansion of 1/3. But this is also true of Pi -- truncating the decimal expansion of Pi gives you a different number. So, what's the difference?!


Same with Pi.


I'll have what she's having. I'm going to give you the benefit of the doubt and assume you were high AF when you wrote this, lol.


It's hilarious to me how you insist that 80,000 Ph.D.'s will disagree with half (one-third?) of the things I say, while claiming with a straight face that 1/3 is not a number.


I fully and genuinely believe in your freedom to choose not to call rational numbers "numbers". I, however, will continue to fruitfully recognize number sets of all color and creed. #rationallivesmatter


"The TRUE expression of numbers" -- spoken like a TRUE zealot! Analog computers are the devil's work!


Sigh. 22/7 and Pi are different numbers. You claim that 22/7 has a dimmer switch, but that dimmer switch somehow disappears when we write it in base-7. "Oh, but base-7 is useless". No, your argument is useless. Anything you can write in base-1 or base-2, I can write in base-7 and use less paper while doing it.


"Fractional arithmetic expressions". You don't seem to realize that we can write 1, 2, etc. as fractional arithmetic expressions. In particular, we can write them as non-terminating fractional arithmetic expressions and they describe the same number.

I'm curious, do you believe that negative values are numbers? Is -5 a number?


So, you're saying that my conception of a Bb maj7 chord refers to a specific set of waves borne from vibrating strings? Which set exactly?


You've probably never studied linear algebra, and that's fine. But a vector space is an abstract space with no geometrical objects. There are no lines or points in a vector space. In order to induce a geometry on a vector space, you need additional structure, namely, a compatible inner product. Using this inner product, you can define the notions of line, point, angle, etc.

Vector spaces are more fundamental than geometries. In physics classes, teachers use arrows on graphs to represent vectors in \( \mathbb{R}^2 \) or \( \mathbb{R}^3 \), but this is purely didactic in purpose, a way to help students get a concrete sense of the physics involved. In math classes, a vector is just an element of a vector space. It has no shape. It doesn't even have coordinates until we pick a basis set. But the choice of basis is arbitrary. Just as with numbers and bases, a vector is independent of any basis. Yet, somehow, I am able to conceive of such a thing without any reference to spatiality.

Seriously, can you please do me a favor and read #1472 from a completely UNINSTALLED place. Bare arithmetic, observation, and inference. And then you will see where I'm coming from. There are foundational truths that exist at lower levels of abstraction that get muddled at higher levels.

If we have to "build a new framework," so be it! But you will see that what I have to say is hella rational, because it couches these things in relation to things that are empirically observable but not necessarily scientifically defined.
I address the whole issue of what I feel is the true nature of fractions in it.

 

Yeah, no. I spin ZERO narrative.

And yet you persist.

Check out none other than Professor Georg Cantor’s words:

Besides the fact that those weren't Cantor's own words, we all know that Cantor was a loon. Now, I personally don't care if Cantor believed that the source of his math was a strudel that he carried in his pocket, his math speaks for itself. But since you are trying to associate these men with your ontology, well, you've just associated yourself with a certifiable crazy person. Seems fitting, maybe?

There are tons of quotes from Newton alone on the topic about God being a personal source of everything, including knowledge of nature:

Sigh. You offer two quotes that show that Newton believed in god. So what? Newton believed god created the universe like he would create a clock, intricate yet precise and deterministic. The whole point of doing science is to figure out how the clock works, and that's what Newton set out to do. But all of this is irrelevant to the fact that Newton clearly separated his spiritual beliefs from his scientific work. I only care about Newton's science and math. Dragging his religion in here causes me to question why you would do such a thing. You think it buoys your stance, but it has the opposite effect on me.

“From this fountain (the free will of God) it is those laws, which we call the laws of nature, have flowed, in which there appear many traces of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experimental. He who is presumptuous enough to think that he can find the true principles of physics and the laws of natural things by the force alone of his own mind, and the internal light of his reason, must either suppose the world exists by necessity, and by the same necessity follows the law proposed; or if the order of Nature was established by the will of God, the [man] himself, a miserable reptile, can tell what was fittest to be done.”

It's kind of funny that I can't tell which of the two options Newton sees himself as, the presumptuous man or the miserable reptile. Fortunately, his science was a lot clearer than his spirituality.

 

And yet you persist.


Besides the fact that those weren't Cantor's own words, we all know that Cantor was a loon. Now, I personally don't care if Cantor believed that the source of his math was a strudel that he carried in his pocket, his math speaks for itself. But since you are trying to associate these men with your ontology, well, you've just associated yourself with a certifiable crazy person. Seems fitting, maybe?


Sigh. You offer two quotes that show that Newton believed in god. So what? Newton believed god created the universe like he would create a clock, intricate yet precise and deterministic. The whole point of doing science is to figure out how the clock works, and that's what Newton set out to do. But all of this is irrelevant to the fact that Newton clearly separated his spiritual beliefs from his scientific work. I only care about Newton's science and math. Dragging his religion in here causes me to question why you would do such a thing. You think it buoys your stance, but it has the opposite effect on me.


It's kind of funny that I can't tell which of the two options Newton sees himself as, the presumptuous man or the miserable reptile. Fortunately, his science was a lot clearer than his spirituality.

You're missing my point.

If your starting point is that there is NOT a higher stand-alone source, there are inferences to that which include having to make sense of EVERYTHING without the possibility of anything "more" to inform it. For example, you insist INFINITY is ONLY a process, because it's only what you can make sense of. You're not open to insisting INFINITY is a "thing" or a stand-alone being, or a repository of "substance", "energy," or "points." It's hogwash to you, because you are implicitly biased AGAINST it. As is MOST of modern science. It was NOT to those men. That's allll I'm saying. It is NOT to me. I mention these men only to bolster the sense that many rational, scientific giants shared the same starting point, and that is, that INFINITY exists as "something" apart from the "computed" situation in which we live.

 

The digits of Pi cannot be base-less, by definition of what a digit is!

I think your assertion that the digits of pi are baseless is baseless.

You state that the digits are simply a series of flip flops. Well, if that’s the case, the base is binary.

I can’t understand your argument (in fact, many of your arguments). You often make contradictory statements, such as this one, to make your point.

I’m working on understanding you spatiality arguments. For I believe you are way off base here. That’s why I haven’t responded recently.

 

So where's the line? You say it's not an issue of complexity, but then what is an issue of? Does a blood cell feel? A virus? Where's the line?

In my estimation, anything that is alive, size-agnostic. "What is alive?" It's an innate token and requires no explanation. It just "is." Animated machinery is not a classification, no matter how complex.

 

They are only different things because we’ve been TAUGHT that. If you read it again with an open mind, tabula rasa, without all predispositions, it makes hella sense, I’m sorry. You make it sound like things can‘t come from a unified conceptual source! It’s incensing you can’t disabuse all frameworks to make basic observational sense. I start from a place that is WAY different from normal, using spatial meaning and logic on a bare plane. You claimed you would do that when you agreed to base inference, arithmetic. Instead, you say “no can do” due to prior “framework” knowledge. NONE is necessary to understand that.

It's incensing to me that you assume close-mindedness is the reason why I disagree. I completely get that your theory makes good sense to you. And I completely get that you think I disbelieve it because I was taught differently. But the actual reason I disagree is because I have studied the sh!t out of formal systems trying to understand how reason itself works. In all that effort, I have come to understand the intricately woven details that go on behind our abstractions. I know what a tangled mess it can be, and I have fought my way through it. Given our exchanges, I am fairly confident that you have not personally tangled with the concepts of numbers like I have.

You interpret my disbelief of your theory as close-mindedness, but to my eyes, your theory is naive and simplistic to the point of uselessness. I believe your lack of experience prevents you from recognizing this.

 

I think your assertion that the digits of pi are baseless is baseless.

You state that the digits are simply a series of flip flops. Well, if that’s the case, the base is binary.

I can’t understand your argument (in fact, many of your arguments). You often make contradictory statements, such as this one, to make your point.

I’m working on understanding you spatiality arguments. For I believe you are way off base here. That’s why I haven’t responded recently.

The digits of pi are BINARY or UNARY, like any number, correct. I said "baseless" perhaps in reference to UNARY, which is often not considered "base-1" but its own foundational concept (since all bases include 0, and start from the number before the base, so "base-1" would only include "0" semantically)... I clarify all this in post 1472 if you can take a gander.

(Base-4 = {3, 2, 1, 0}; base-3 = {2, 1, 0}; base-2={1, 0}; base-1 = {0}? No.)

 

You're missing my point.

If your starting point is that there is NOT a higher stand-alone source, there are inferences to that which include having to make sense of EVERYTHING without the possibility of anything "more" to inform it. For example, you insist INFINITY is ONLY a process, because it's only what you can make sense of. You're not open to insisting INFINITY is a "thing" or a stand-alone being, or a repository of "substance", "energy," or "points." It's hogwash to you, because you are implicitly biased AGAINST it. As is MOST of modern science. It was NOT to those men. That's allll I'm saying. It is NOT to me. I mention these men only to bolster the sense that many rational, scientific giants shared the same starting point, and that is, that INFINITY exists as "something" apart from the "computed" situation in which we live.

Newton did not equate god or energy with the mathematical concept of infinity. That's my point.

It does us no good to use one word to mean multiple things. If you want to include some unbounded energy source that is the genesis of everything, then don't call it INFINITY; call it what it is, god. Then please proceed to define its properties and such.

 

In my estimation, anything that is alive, size-agnostic. "What is alive?" It's an innate token and requires no explanation. It just "is." Animated machinery is not a classification, no matter how complex.

"Alive" must have properties that are different from "non-alive". So, what are those properties. More importantly, which of those properties can silicon machinery not have? (Note that every biological creature is an animated machine.)

 

It's incensing to me that you assume close-mindedness is the reason why I disagree. I completely get that your theory makes good sense to you. And I completely get that you think I disbelieve it because I was taught differently. But the actual reason I disagree is because I have studied the sh!t out of formal systems trying to understand how reason itself works. In all that effort, I have come to understand the intricately woven details that go on behind our abstractions. I know what a tangled mess it can be, and I have fought my way through it. Given our exchanges, I am fairly confident that you have not personally tangled with the concepts of numbers like I have.

You interpret my disbelief of your theory as close-mindedness, but to my eyes, your theory is naive and simplistic to the point of uselessness. I believe your lack of experience prevents you from recognizing this.

If you think everything you've studied and been taught is 100% infallible, then you are close-minded to a new foundation, which is at odds with what you originally agreed to. You 100% explicitly agreed to baseline knowledge, arithmetic, and inference, and then we will see how it works into other formal systems later on.

You have NOT studied any of this stuff with respect to ontology and MEANING. These things are UNDEFINED. Connecting the number "1" to blocks and FEELING and these things being possibly their own brand of knowledge? You have not studied that whatsoever, guaranteed. It is not taught.

So if you will read it from that place, it's a different bag. But I don't think you want to.

 

Newton did not equate god or energy with the mathematical concept of infinity. That's my point.

It does us no good to use one word to mean multiple things. If you want to include some unbounded energy source that is the genesis of everything, then don't call it INFINITY; call it what it is, god. Then please proceed to define its properties and such.

Why is this? If Cantor can use the word to describe it? And Newton? And tons of others? Why must we only assume INFINITY is a "process?" In fact, I've never heard of it described that way.

 

The digits of pi are BINARY or UNARY, like any number, correct. I said "baseless" perhaps in reference to UNARY, which is often not considered "base-1" but its own foundational concept (since all bases include 0, and start from the number before the base, so "base-1" would only include "0" semantically)... I clarify all this in post 1272 if you can take a gander.

(Base-4 = {3, 2, 1, 0}; base-3 = {2, 1, 0}; base-2={1, 0}; base-1 = {0}? No.)

It's confusing to use binary and unary as synonyms for base-2 and base-1. I suggest we strictly call number bases by their base-n name.

BTW, you keep mentioning post 1272 but that's like 50 pages back. Can you provide a direct link?

 

"Alive" must have properties that are different from "non-alive". So, what are those properties. More importantly, which of those properties can silicon machinery not have? (Note that every biological creature is an animated machine.)

Talk about using "senses only" to make a claim though (as in, "JUST an animated machine")!? First it is well known that there is no specific scientific definition for "life". There is no difference between a dead frog and a living one any more than a Ferris Wheel that is stopped is less alive than a moving one.

The chief property of ALIVE I would say is spatial-based experience. The capacity to report on this is a separate matter.

 

It's confusing to use binary and unary as synonyms for base-2 and base-1. I suggest we strictly call number bases by their base-n name.

BTW, you keep mentioning post 1272 but that's like 50 pages back. Can you provide a direct link?

FFS, I meant 1472, sorry!

 

djfantasi: if you happened to read that post before I edited it, I meant post 1472 has the clarification.

 

If you think everything you've studied and been taught is 100% infallible . . .

That you would even suggest this is telling. My point was not that I learned a bunch of facts; my point was that I have personally struggled with these things and have an intimate understanding of what's involved. I am talking about my experience.

You have NOT studied any of this stuff with respect to ontology and MEANING.

I really, really LOVE when people tell me what I have or have not done. Before I studied math, science, and engineering, I studied philosophy. My search for ontology and meaning drove me to math and science. The only thing I do is search for meaning in math and science.

 

Such confusion. 1/3 does not have a mantissa. The IEEE754 floating-point representation of 1/3 has a mantissa (but so does the floating-point representation of 0,1,2, etc.!).

You're correct that, in base-10, we cannot truncate the decimal expansion of 1/3. But this is also true of Pi -- truncating the decimal expansion of Pi gives you a different number. So, what's the difference?!


Same with Pi.


I'll have what she's having. I'm going to give you the benefit of the doubt and assume you were high AF when you wrote this, lol.


It's hilarious to me how you insist that 80,000 Ph.D.'s will disagree with half (one-third?) of the things I say, while claiming with a straight face that 1/3 is not a number.


I fully and genuinely believe in your freedom to choose not to call rational numbers "numbers". I, however, will continue to fruitfully recognize number sets of all color and creed. #rationallivesmatter


"The TRUE expression of numbers" -- spoken like a TRUE zealot! Analog computers are the devil's work!


Sigh. 22/7 and Pi are different numbers. You claim that 22/7 has a dimmer switch, but that dimmer switch somehow disappears when we write it in base-7. "Oh, but base-7 is useless". No, your argument is useless. Anything you can write in base-1 or base-2, I can write in base-7 and use less paper while doing it.


"Fractional arithmetic expressions". You don't seem to realize that we can write 1, 2, etc. as fractional arithmetic expressions. In particular, we can write them as non-terminating fractional arithmetic expressions and they describe the same number.

I'm curious, do you believe that negative values are numbers? Is -5 a number?


So, you're saying that my conception of a Bb maj7 chord refers to a specific set of waves borne from vibrating strings? Which set exactly?


You've probably never studied linear algebra, and that's fine. But a vector space is an abstract space with no geometrical objects. There are no lines or points in a vector space. In order to induce a geometry on a vector space, you need additional structure, namely, a compatible inner product. Using this inner product, you can define the notions of line, point, angle, etc.

Vector spaces are more fundamental than geometries. In physics classes, teachers use arrows on graphs to represent vectors in \( \mathbb{R}^2 \) or \( \mathbb{R}^3 \), but this is purely didactic in purpose, a way to help students get a concrete sense of the physics involved. In math classes, a vector is just an element of a vector space. It has no shape. It doesn't even have coordinates until we pick a basis set. But the choice of basis is arbitrary. Just as with numbers and bases, a vector is independent of any basis. Yet, somehow, I am able to conceive of such a thing without any reference to spatiality.

Mathematics is about points and machinery that maps points to other places, and shifting of points over time. The machinery is arithmetical in nature, and all arithmetic is addition at different rates in disguise. There's nothing more going on there.

Vector spaces are not "spaces" in my estimation. Another f*cked up word. Spaces are about spatiality, and spatiality is a geometric and physio-geometric term. A better term is "forum" or something that implies non-geometric relationality.

 

That you would even suggest this is telling. My point was not that I learned a bunch of facts; my point was that I have personally struggled with these things and have an intimate understanding of what's involved. I am talking about my experience.


I really, really LOVE when people tell me what I have or have not done. Before I studied math, science, and engineering, I studied philosophy. My search for ontology and meaning drove me to math and science. The only thing I do is search for meaning in math and science.

I'm speaking colloquially. There is NO definition to these things— you know this... this is why we're discussing it and why you're open to working with some "chick on the internet" to make a ToE. "Meaning" and "Feeling" and various other things are all "up in the air," and a principled approach to connecting things like basic logic, feeling, meaning, arithmetic I have NOT found. If you simply read 1472 from a very basic clean-slate place, and uninstall everything, you will find it is insanely on-point. And I'm not bragging. It just is.