I'm talking about the notion of infinity RIGHT HERE. The continuum element that "cannot be defined" I insist is the VERY thing that is the basis of continuous geometric form.

But every element in the continuum of ℝ is perfectly finite. This is because ℝ is a well-ordered field. Let x be any element from ℝ. Then, we can always find a y ∈ ℕ such that x < y.

The integers are infinite. ℝ is infinite. ℝ is nothing more than fancy concatenated integers.

This is a terribly ignorant statement.

Consider before "set ℝ" was made and before decimals were created (tabula freaking rasa!). What were there? Countable integers. 1, 2, 3, 4, 5... ad infinitum. From there, another concept was born, and that was to create "fractions" of these very things, that are tagged onto each of those elements to create "hybridized" integers of rational and irrational form. Same things, they just happen to group them into a thing called ℝ. Very simple.

There is nothing "very simple" about ℝ. Please stop making things up.

 

O. to the M. to the G. This right here I think is the seminal post of this discussion, and my goodness, the very source of my contention.

You literally believe you exist as Javier, with all of your molecules spread out all over the Atlantic.

Am I reading that right?

You're right that this speaks to the heart of your "presence/non-presence" false dichotomy, but not for the reasons you think it does. Start taking away grains of sand from a heap of sand -- at what point is it no longer a heap?

The instant of my death, I am essentially the same group of molecules that I was an instant before. As time passes, without a working immune system to keep things in check, the bacteria in my body start feasting, breaking down the molecular bonds of my soft tissue. Is this putrefying cadaver still me? According to the medical examiner, and the unfortunate family member who has to identify me, it surely is.

At what point does the cadaver stop being me? After twenty years, when I'm just a pile of hair and bones in a grave, are they my hair and bones? If I have to be exhumed for some reason -- maybe to take a DNA test to solve a long-standing cold case -- they will be considered my hair and bones. What of the carbon, nitrogen, and oxygen that leached from my body into the environment, are they mine? Were they ever mine?

In my model, there are just states and transformations between states. Before I was born there were states; after I die there will be states. Whatever I am -- whether a living thing or a cadaver or a pile of bones -- can be described by a set of particular state configurations and various transformations. At some point, say in a million years, the set of states that once were associated with "me" will no longer be recognizable as having anything to do with me.

Now, using your presence/no-presence model, explain the precise instant where I become "no-presence".

 

1 = the set of all uniquely named infinities; 5, 9, 22, 3828, etc. and concatenated versions is just 1 in disguise, with unique relationships to each other.

How many elements does "set" 1 have? If it doesn't have a single element, then why are you calling it "1"?

You say that 5 is an infinity. So, if I have 5 beers, I have an infinity of beers?

 

I believe there is a "continuous" form of experience and knowledge acquisition one might define as analog FEEL (and I feel this is the "ghost in the machine" element we'll get to).

You're saying that humans FEEL experience while computers don't, yes? So let's speak directly to that. What does it mean to FEEL experience? Please don't just give examples of "feeling" as it is commonly understood; describe the unique properties of FEEL that are impossible for a computer to have.

Note that "analog vs digital" or "continuous vs discrete" is not a sufficient description, as any analog/continuous process can be perfectly characterized by a digital/discrete process (sampling theorem, et al).

 

But every element in the continuum of ℝ is perfectly finite. This is because ℝ is a well-ordered field. Let x be any element from ℝ. Then, we can always find a y ∈ ℕ such that x < y.


This is a terribly ignorant statement.


There is nothing "very simple" about ℝ. Please stop making things up.

Well, tell that to Pythagorus that basically said 1 is the master number all are built on.

Before there were fractions and decimals, there were counting numbers.

We decided to CREATE a 2-part number. The integer PLUS the fraction that is irrational or rational. There is ARITHMETIC built into any real to represent it! 1 PLUS 5/8!

Why not create a 2-decimal-point number and call that a “fundamental?” 2.6.8?

It’s an illusion that’s why. Every single binary computer using just 2 values can do any form of discrete or continuous mathematics. It does it with a binary set O. Or hell, your u-it set, which is Pythagorus all day long! QED. Reals are their own form of complex arbitrary amalgamation for measuring purposes. It’s specifically so we can apply the same fractional nomenclature across every integer. 4.58457 or 99.58457. The mantissa is uniform in nomenclature so we don’t have to invent a new name for each whole’s potential appendage. And the irrationals are simply “mini infinities” in between each whole.

 

You're right that this speaks to the heart of your "presence/non-presence" false dichotomy, but not for the reasons you think it does. Start taking away grains of sand from a heap of sand -- at what point is it no longer a heap?

The instant of my death, I am essentially the same group of molecules that I was an instant before. As time passes, without a working immune system to keep things in check, the bacteria in my body start feasting, breaking down the molecular bonds of my soft tissue. Is this putrefying cadaver still me? According to the medical examiner, and the unfortunate family member who has to identify me, it surely is.

At what point does the cadaver stop being me? After twenty years, when I'm just a pile of hair and bones in a grave, are they my hair and bones? If I have to be exhumed for some reason -- maybe to take a DNA test to solve a long-standing cold case -- they will be considered my hair and bones. What of the carbon, nitrogen, and oxygen that leached from my body into the environment, are they mine? Were they ever mine?

In my model, there are just states and transformations between states. Before I was born there were states; after I die there will be states. Whatever I am -- whether a living thing or a cadaver or a pile of bones -- can be described by a set of particular state configurations and various transformations. At some point, say in a million years, the set of states that once were associated with "me" will no longer be recognizable as having anything to do with me.

Now, using your presence/no-presence model, explain the precise instant where I become "no-presence".

By this logic, you cannot ever identify a thing. The dog in the light... is it a dog if it’s a cat? A few shiftings of bits from that contiguous “cluster” and you have Hillary Trump. You have no knowing capacity if everything is still existent without contiguity and bit clusterization, and therefore no computational capacity based on such knowledge.

 

How many elements does "set" 1 have? If it doesn't have a single element, then why are you calling it "1"?

You say that 5 is an infinity. So, if I have 5 beers, I have an infinity of beers?

Infinity is about “limitless quantity.” If it truly exists with respect to a sine wave’s infinite values, there is infinite quantity of bits or u-its stored in the wave. Or infinity doesn’t exist. That simple. You can pull any number of points you need out of that wave to create n or ∞ beers from it, but the wave remains a “wave.” And pan to the whole “states” vs. continuum argument with respect to defining “something” in the previous post.

Pythagoker thumbing that statement up all day long.

 

Ah, but they’re connected, and that’s what I’m driving at.

What is connected? What are the "they" that are connected? (Sometimes pronouns drive me crazy.)

1D as an informatic dimension (of discrete or indivisibly continuous reckoning) vs. discrete or continuous 3D geometric dimension. The 3D geometric dog is stored as 1D informatic bits (is there a specific term for non-geometric dimension?) and their arrangement in space is NOT retained in the brain as the 1D-bit processor brain stores them (that’s where you say the dog isn’t really 3D, etc).

What exactly do you mean by "the 3D geometric dog is stored as 1D informatic bits"? The "dog is stored"? Do you mean the information of the physical dog is stored?

BTW, dimension is more general than geometry. Spatial (geometric) dimension is only one particular type of dimension, though it's the most familiar (because that's what they teach high school.

A useful way to think of dimension is as the minimum number of parameters that can describe something. This, of course, depends both on the thing we're talking about and what we're trying to describe. For example, if we're talking about colors using the RGB model, then a color is a three-dimensional object in "RGB space", as we need three parameters -- reg, green, and blue intensities -- to describe any point (color) in the space. If we augment the RGB model with a new parameter, say the transparency of a color (as in GIFs), then colors become four-dimensional objects.

I believe there are precisely 5 dimensions that govern existence: 3 geometric and 2 informatic. The latter 2 play lots of magic tricks to create time and chance based on experiential illusion. Again, theory.

I've been wondering where the 5 in "5D" came from. What are the two informatic dimensions like?

 

Well, tell that to Pythagorus that basically said 1 is the master number all are built on.

So, you're on board with unary now?

We decided to CREATE a 2-part number. The integer PLUS the fraction that is irrational or rational.

A fraction cannot be irrational -- the definition of "irrational" is "non-fraction". Again, you're mistaking representation of a number for the number. Decimal representations have two parts, but the numbers they represent are not "2-part".

There is ARITHMETIC built into any real to represent it! 1 PLUS 5/8!

No, no, no. You are confusing decimal notation with numbers in ℝ. The closest thing to what you're describing is ℚ, wherein any number a/q, with a and q integers, can be expressed as an integer d with remainder r/q: \[ \frac{a}{q} = d + \frac{r}{q} \]

Why not create a 2-decimal-point number and call that a “fundamental?” 2.6.8?

You can make up any notation you want, but it's just a representation; the number it represents is unchanged.

 

So, you're on board with unary now?

I said provisionally.... I think binary is a more spatially compact unary in a sense, using 0 as a shadow 1 of sorts. It’s not entirely defined yet.

A fraction cannot be irrational -- the definition of "irrational" is "non-fraction". Again, you're mistaking representation of a number for the number. Decimal representations have two parts, but the numbers they represent are not "2-part".

Omg. Ok, right now? There are 93846382827 sets of numbers. Some have 14 decimal points like a Photoshop revision. I am uninstalling every one of them.

Now talk to me.

There are integers and there are componental, arithmethic tack-ons using other integers. QED. PERL is not the same as assembly. PERL is BUILT from assembly. No more PERL to get to the hardware. PERL can’t see the elements.

 

By this logic, you cannot ever identify a thing. The dog in the light... is it a dog if it’s a cat? A few shiftings of bits from that contiguous “cluster” and you have Hillary Trump. You have no knowing capacity if everything is still existent without contiguity and bit clusterization, and therefore no computational capacity based on such knowledge.

You claim I cannot identify a thing, but provide no evidence. I've already mentioned the concept of identity, where one state is recognized to be equal to another. This leads to the concept of similarity, which is the degree to which two states are not identical. Computers that have visual recognition capability use the concept of similarity, and so it goes with us.

Everyday, I lose thousands of skin cells -- little pieces of me sloughing off into the void. But the states of me with and without the skin cells are very similar, and so my wife has no problem associating the two distinct states with the same concept of me. After I've been dead for twenty years, the states associated with "dead me" will not be very similar to the set of states of "living me". After a long enough period of time, there will be no more similarities.

You didn't answer the question: in your model, at what point do I become "non-presence"?

 

If it truly exists with respect to a sine wave’s infinite values, there is infinite quantity of bits or u-its stored in the wave. Or infinity doesn’t exist. That simple. You can pull any number of points you need out of that wave to create n or ∞ beers from it, but the wave remains a “wave.” And pan to the whole “states” vs. continuum argument with respect to defining “something” in the previous post.

So, um, first I'd point out that sine -- the function with infinite values -- is a mathematical object, not a physical wave. You'll never find a sine wave in nature. Physical waves cannot have infinite anything, as that would require infinite energy, and that's physically impossible. Let's not confuse mathematical functions with physical waves.

Second, I asked "if I have 5 beers, I have infinity beers?", which is a yes/no question. So, which is it?

 

There are integers and there are componental, arithmethic tack-ons using other integers. QED.

No. You call the elements of ℝ "arithmetical tack-ons using other integers" and expect me to accept it, but it's a provably false statement. You might as well be arguing that {0, 1} has five elements, as this is the same level of patent falseness.

PERL is not the same as assembly. PERL is BUILT from assembly. No more PERL to get to the hardware. PERL can’t see the elements.

Your analogy is invalid because ℝ is not built from ℤ. You don't seem to understand that if you removed every integer and every integer-like number from ℝ, you'd have removed exactly 0% of the numbers in ℝ.

 

You AGREED to tabula rasa. And you are NOT doing it!! Until such time, we are halted!

 

No. You call the elements of ℝ "arithmetical tack-ons using other integers" and expect me to accept it, but it's a provably false statement. You might as well be arguing that {0, 1} has five elements, as this is the same level of patent falseness.


Your analogy is invalid because ℝ is not built from ℤ. You don't seem to understand that if you removed every integer and every integer-like number from ℝ, you'd have removed exactly 0% of the numbers in ℝ.

So, um, first I'd point out that sine -- the function with infinite values -- is a mathematical object, not a physical wave. You'll never find a sine wave in nature. Physical waves cannot have infinite anything, as that would require infinite energy, and that's physically impossible. Let's not confuse mathematical functions with physical waves.

Second, I asked "if I have 5 beers, I have infinity beers?", which is a yes/no question. So, which is it?

And this is so amazing to me, because you insist you ARE essentially an extension of nature, so why are you showing partiality to a "conceptual" wave vs. a "physical one?" They're all states? You "know" the difference? And what is this business about "finding one in nature?" What's an oscillator? We can generate a simple sine-wave from one. We built it from nature. Obviously nature's vibrations can generate one. And if you insist that there is "infinite values" to a "conceptual sine wave" and you also insist it exists, then you are also insisting there is infinite storage somewhere to store that infinitude (the basis of my 5D reasoning).

Each beer is 1-infinity, 2-infinity, 3-infinity, 4-infinity, 5-infinity (for example). You have "5" of them.

If "5" is a word/wave token for a "unique infinity" then if you have 5 beers, you have essentially "5-infinity" of beers.

 

You AGREED to tabula rasa. And you are NOT doing it!! Until such time, we are halted!

Tabula rasa does not mean "make up facts about ℝ". If you're allowed to invoke ℝ, I get to use it, too.

 

Tabula rasa does not mean "make up facts about ℝ". If you're allowed to invoke ℝ, I get to use it, too.

You are right (although I do not believe I was doing that... I think it's simply an infinite number set like any other, and infinity is infinite). So we need to uninstall all number sets right now, together. Thank you. If you can say "f*ck you, Rene," then I can too (no disrespect Rene, we think you are a pillar, but we can't be afraid to step on toes. "Cool, folks — go for it!")

I'm going to write up my thoughts on numbers, tabula rasa style, starting from grunting neanderthal level, you can rip it to shreds, and we'll see what we arrive with, and how it intersects.

Good?

 

And this is so amazing to me, because you insist you ARE essentially an extension of nature, so why are you showing partiality to a "conceptual" wave vs. a "physical one?" They're all states?

Because the states associated with mathematical waves are entirely different from the states associated with physical waves. They are not the same kinds of things.

And what is this business about "finding one in nature?" What's an oscillator? We can generate a simple sine-wave from one.

No, we cannot. There has never been, nor will there ever be, an oscillator that can generate a single-frequency sine wave.

Oscillators generate physical waveforms that necessarily have finite duration. Mathematically, we can model such waveforms as a pulsed sine, i.e., the product of a sine and a rectangle waveform of duration T: \[ x(t) = \text{rect}(\frac{t}{T}) \sin(\omega_0 t) \] Taking the Fourier transform of this will show that the result is a continuous sinc (not sine) function in frequency, i.e., it contains many more than just the single frequency of a true sine.

You may protest that this is quibbling, but we need to be precise. You're attempting to argue that (mathematical) sines have infinite values, therefore (physical) waveforms must also have infinite values. This is the kind of invalid reasoning that can happen with loose terminology. We must be precise about what exactly we're describing.

And if you insist that there is "infinite values" to a "conceptual sine wave" and you also insist it exists, then you are also insisting there is infinite storage somewhere to store that infinitude (the basis of my 5D reasoning).

No, I do not believe that we must store every value of sine in order for us to know the concept of sine. This seems pretty obvious to me. In any single period, I know maybe three or four values of sine off the top of my head, yet I know very well what sine is. The infinite values of sine are far less important than the properties of sine. We can't even label most values of sine.

In the same way, I know ℝ quite well, though I can't even describe the vast majority of its members.

In the same way, I can know a dog pretty well, though I couldn't tell you what a single one of its molecules was doing.

Each beer is 1-infinity, 2-infinity, 3-infinity, 4-infinity, 5-infinity (for example). You have "5" of them.

If "5" is a word/wave token for a "unique infinity" then if you have 5 beers, you have essentially "5-infinity" of beers.

Sorry, but this is nonsense.

 

I'm going to write up my thoughts on numbers, tabula rasa style, starting from grunting neanderthal level, you can rip it to shreds, and we'll see what we arrive with, and how it intersects.

Good?

Sure.

 

Because the states associated with mathematical waves are entirely different from the states associated with physical waves. They are not the same kinds of things.


No, we cannot. There has never been, nor will there ever be, an oscillator that can generate a single-frequency sine wave.

Oscillators generate physical waveforms that necessarily have finite duration. Mathematically, we can model such waveforms as a pulsed sine, i.e., the product of a sine and a rectangle waveform of duration T: \[ x(t) = \text{rect}(\frac{t}{T}) \sin(\omega_0 t) \] Taking the Fourier transform of this will show that the result is a continuous sinc (not sine) function in frequency, i.e., it contains many more than just the single frequency of a true sine.

You may protest that this is quibbling, but we need to be precise. You're attempting to argue that (mathematical) sines have infinite values, therefore (physical) waveforms must also have infinite values. This is the kind of invalid reasoning that can happen with loose terminology. We must be precise about what exactly we're describing.


No, I do not believe that we must store every value of sine in order for us to know the concept of sine. This seems pretty obvious to me. In any single period, I know maybe three or four values of sine off the top of my head, yet I know very well what sine is. The infinite values of sine are far less important than the properties of sine. We can't even label most values of sine.

In the same way, I know ℝ quite well, though I can't even describe the vast majority of its members.

In the same way, I can know a dog pretty well, though I couldn't tell you what a single one of its molecules was doing.


Sorry, but this is nonsense.

But as a physical device, you have no “right” separating the math from the physical. You are the physical. You are the math.

Our terms need to be precise, but also not presumptive. “Concepts” are bits of highs and lows. You’re a brain made out of dirt. Math is literally neurons. Abstractions are groups of highs and lows. Must see from the most granular or conclusions and “proofs” can be made that do not reflect the physicality.

Also, I want to say again, please ignore my capital letters, bolds, exclamation points as anything other than an attempt to inject passion into the arguable dispassionate machinery. Anything sounding like an ass is toward the frustration of communication and wanting to see my intuition proven alone, and not at all toward you. I very much appreciate your taking the time to delineate stuff with such detail. It’s a pleasure discussing these things with you, even though I want to uninstall 35% of certain software you came through time with.