Theory of Everything

bogosort

Joined Sep 24, 2011
696
I told you, you can ignore all my boldings and italics — I need living emotion and this text-only is suffocating at times. ;--D Therein lies the difference between a computer and a person. A living person "feels" desire, intention, etc. Not just computes. A non-living person does not, nor does a computer, nor n red and white blood cells. Because life is not the machine. Life is IN the machine.
What is preventing a computer from feeling desire or fear?

It seems like you're changing your stance on blood cells. Do they "feel"or not?

"Concepts" of numbers?? I thought a number was a concept!
A number is a concept. And when we start exploring and investigating numbers, we develop concepts of numbers.
 

bogosort

Joined Sep 24, 2011
696
This conversation has been very fun, stimulating, entertaining, etc. But it's going to go on forever in as many areas as pi has decimal-10 digits, and I'm sure you agree, we gotta get more ordered if it's going to actually be productive.

And formalizing is 100% your gift and shtick.

So I'm now going to look to you to direct the flow of questions in a formal manner so we stay ultra disciplined in one area of focus to arrive at *actual agreed conclusions*.

Cool? We need to get down to parity of abstraction with hardware, unary, voltage, etc...
Agreed, all the Pi and ℝ stuff is a distraction.

Ok, let's start here: You attach a special significance to "feeling", so I'd like to calibrate the boundaries of what that means. Does a blood cell feel? Does an amoeba? Where is the line draw?
 

bogosort

Joined Sep 24, 2011
696
Nah, they study "sets of numeric expressions." "There are only grunts, and if necessary, one grunt set. All else is the work of man." ;)
Dear Kronecker, you old so and so,

Perhaps it is true that god gave us the integers. Fine and solid things, they are. But the stuff that humans made are far more interesting.

Sincerely,
j

P.S. Tell Cantor he owes me an uncountable number of beers.
 

bogosort

Joined Sep 24, 2011
696
First, calling it a "CPU" from you as a machine yourself, is an "nth" order abstraction that doesn't really exist outside of Harry Potter. The "CPU" is a spatial catch-all term for a thing in reality you don't really know what is made of.
We agree that a CPU is a physical machine, yes? We agree that it is made out of the same stuff that we are made out of, just in different proportions and such, yes? You believe that we have extra stuff, but that's ok at this point, so long as we can agree that the CPU is a physical machine.

So CPUs are fair game for discussion, yes?

Second, it's all 1st order for me until you can prove other abstractions earn the right to be called nth order.
The sand on the beach is a big collection of 1st order states, yes? If a crab digs a hole in the sand, makes a nice little home with a berm and such, can you agree that the sand in the crab's home now has another level of information? By organizing the sand, there's a new level of state -- we can describe the state of the house as being well-kept, or tidy, or whatever. Agreed?

Can you see how different orders of state correspond to different levels of information? Each grain of sand has its own state. The collection of sand grains gives rise to another level of state -- in this state we find information about mostly stochastic processes like the wind and waves and such. Organizing the sand into a home (or sand castle, for sophisticated crabs) confers even more state.

The CPU has flip flops that register state value changes. Those flip-flops are the only thing that would qualify as knowing anything, if you were to use the term "know."
Let's say that the state of a particular flip-flop determines whether the CPU adds or subtracts two values. Let's say you ask the CPU to compute "4 + 1" and the CPU responds with "5". If the CPU didn't know the state of the flip-flop, how did it know to respond with "5" and not "3"?

A registration of a change of state is no different than saying the paper knows it has a check in a checkbox.
The difference is -- and I think you will agree -- that the CPU can do one thing if the checkbox is checked, and another thing if it is unchecked.

"Awareness" implies some kind of innateness to it, I will not ascribe to papers or switches that have no idea why their state changed.
What do you mean by "innateness"?

I propose feeling is independent of information, and is the very mystery element responsible for "knowing" the dog is something independent of information.
If "feeling" is independent of information (which seems weird to me; if I found out that a friend died, that information would give me very strong feelings), then what influences feeling? What makes you feel this versus that?

The CPU is a componental device. Just because there are wires between each portion of the salad's carrots, onions, tomatoes, and lettuce, and some power source sent enough juice between them to alter their states into quasi-melted elements, means nothing. In short, level of functionality is not "knowing."
Define "knowing".
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
Agreed, all the Pi and ℝ stuff is a distraction.

Ok, let's start here: You attach a special significance to "feeling", so I'd like to calibrate the boundaries of what that means. Does a blood cell feel? Does an amoeba? Where is the line draw?
I'm not sure we can start in "feeling-land" especially since I feel the mechanism is not intrinsic to the physicality (which you do not share). I also "feel" like we have to start with the limitations of our brain as an information processors, and then we "eliminatively" arrive at a definition for feeling. Perhaps even starting with "life" first. That a "living brain" does things, but a "non-living one" doesn't. We have to assume somehow that the brain is a unary or binary device to get anywhere I feel.

I'll give my take on feeling in post #1247.

Btw, on a side-note, I wanted to mention... the total confusion with this whole "numbers and representations" thing is due to my not fully clarifying, perhaps, that I'm coming at it literally from "discrete unary or binary voltages" mentality. A "!," as we said, would be a truth state of a voltage presence, not even a number (unless we equate it to 1). I want to know what Pi is as a function of these !'s.

It's !!! + some amount of additional !'s. How many additional !'s?
 
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Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
We agree that a CPU is a physical machine, yes? We agree that it is made out of the same stuff that we are made out of, just in different proportions and such, yes? You believe that we have extra stuff, but that's ok at this point, so long as we can agree that the CPU is a physical machine.

So CPUs are fair game for discussion, yes?


The sand on the beach is a big collection of 1st order states, yes? If a crab digs a hole in the sand, makes a nice little home with a berm and such, can you agree that the sand in the crab's home now has another level of information? By organizing the sand, there's a new level of state -- we can describe the state of the house as being well-kept, or tidy, or whatever. Agreed?

Can you see how different orders of state correspond to different levels of information? Each grain of sand has its own state. The collection of sand grains gives rise to another level of state -- in this state we find information about mostly stochastic processes like the wind and waves and such. Organizing the sand into a home (or sand castle, for sophisticated crabs) confers even more state.


Let's say that the state of a particular flip-flop determines whether the CPU adds or subtracts two values. Let's say you ask the CPU to compute "4 + 1" and the CPU responds with "5". If the CPU didn't know the state of the flip-flop, how did it know to respond with "5" and not "3"?

Agreed on the "state" definitions above, and I knew that's how you were using them. I would also call that "information contextualization," which requires hella programmer intention to file all of it to be interrelated.

However, the problem I have is, unless information has some kind of true spatiality to it, all of it is 1D points, and this doesn't cut it for me without a spatiality element. The dog is more than 1D because the information coming from the dog is minimally 2D requiring a 2D grid to see it, but then the information is stored in 1D? Why does the brain insist on reconstituting this image to be 2d as reflecting the dog? Until the information is spatially reconstituted on a screen, there is no spatiality to that information. The problem is, there is no 2D or 3D screen within the being, and there's also no actual connection between that information.

Seriously, WHAT is the software running that is insisting that be reconstituted to 2D to reflect the same dog, and any additional information anyone else speaks about "that dog" in space? There must be an innate understanding of what the dog (or any other object) in physical space, some kind of 1D to 2D to 3D mapper.

Furthermore, if we get a video of the backside of the dog in the same region, we now have 3D spatial information concerning the same dog, from a separate light source potentially, and this new information is precisely filed in relation to the same dog in 1D banks. Spatiality is entirely some kind of innate phenomenon when it comes to physical space. We might not know what the dog "is" precisely, but we know it has some kind of spatiality based on 2 or more angles. But no matter how you cut it, the data points are discrete photon bits that are filed.

We don't know what the dog is, how do we know what physical space the dog is in is? If we insist the dog is "in" this space, certainly the space itself must be minimally 3D to handle a 2D dog?

What is this strange-ass connection between 1D and 2D and 3D?
 
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Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
For a human being, the terms meaning, context, and feeling are very much intertwined.

To understand the "meaning" of these words, we have to take a slightly anthro-centric track, because we have only observed humans using such terms. The only true way to understand what they mean is to observe how a human uses them in various contexts to get a "feel" for their "meaning."

It could be said that feeling is used to contrast the non-flowing, repetitious or monolithic mechanicality element of a machine. Feeling could be said to be the opposite of machine-like functioning.

(Incidentally, this is altogether strange—if a person or being is simply a mechanical machine and nothing more—and is a rather curious notion for a machine to even define or care about as one of the key elements of what it means to be a living being.)

If a person were to perform a piece of piano music at a dinner party with no feeling, and only play the functionally correct notes, the party would want to kick him out and hire someone that does. The piece would carry no meaning without feeling. So what does it mean to play with feeling vs. none? It means to "experience" the notes at variable rates to reflect experiential intention upon the instrument beyond a uniform mechanical rate. It involves the notion of variable force, so that each note is played in context with variable intention to invoke a positive experience from the information.

A person might comment on the non-feeling music to another person, and they would completely grok immediately: "The person plays with no feeling, they have no heart, no spirit, no life to their music. They sound like a mere machine or computer that's functioning. There is no musicality. No passion, no fire. No burn. It's like they're not even alive." "Yes, I agree."

Now it could be said that certain metronomic or machine-like music has feeling, but the intention is to create a certain feeling by WAY of that specific intention. Nine Inch Nails does such things to great effect. For example, in a thriller movie, one might hear robotic tones to convey the feeling of a robot after someone else. The feeling created by the robotism soundtracks the movement of the robot. It is commonly and universally observed that robots make certain noise. So using a trumpet blast for such conveyance doesn't work, unless there's a specific context to do so.

At this same dinner party, one might use the term "feel" to describe the atmosphere of the room, the people, the dress, the music, the type of people there. The "qualia" or qualitative elements of the information is associated with "feeling and meaning." Without saying anything informational about the room, one could say "the party gave me a 1930's, gangster, speak-easy vibe." One might ask, "Why?" They would then rattle off facts within the set "room" responsible to evoke such a feeling within themselves, and see if perhaps the other person shares the same sentiment or feeling.

The same person might be accosted by someone at the dinner party whom they do not know, whom they have never shared prior information exchanged, and whom therefore is of no meaning to them, or also expressed as "one for whom they have no prior experiential feeling." To talk to them would mean there was no shared context of meaning and feeling for the information. Small talk is considered universally to be of minimal shared feeling and experiential value. It is of "shallow experiential worth." Only when you get to know someone does the information take on greater feeling and meaning.

If a person's old fling was found at the party, and came up to him, a completely different experiential feeling would come up within the person, typically in the center of his being (which is quite curious, that information might be found in the brain, but feeling is found in the heart region). The historical information exchange between these two parties yields a context of information exchange, whose purpose it is to feel each other's mutual opinion on new information, concerning any potential shared topic. Laughter is a good sign of positive information exchange, and laughter is a form of feeling attached to various information exchanges.

Strangely, the power of the term feeling as contrastive to machinery can be observed if a human-like terminator machine from the movie came up to both parties and spoke in monotone, uniform voice: "Hello. My name is T-800, let me make your acquaintance," and moved his eyes back and forth robot-wise, and his limbs moved up and down without context to each other—both persons would feel utterly terrified that a machine is in their presence that appears like a human. If the machine acted with feeling, in that its speech was not monotone and had variable inflection and intensity combined with emotive appearance, the "uncanny valley" might be breached and he might be treated as a "feeling human" vs. just a mechanical machine. The concept of "feeling" and "meaning" is explored in the movie Ex Machina, where machine "Ava" invokes feelings from Caleb who is a subject commissioned to interact with it. Caleb develops feeling for the robot that acts like a human.

To interact with feeling and use words with feeling is to understand context and tone, and the feel and inner atmosphere that words may invoke. One word within a sentence not having contextual connection to the prior can throw off the continuity of feeling for the sentence. For humans, there is a certain degree of baseline universality in the laws of feeling with words, being shared objects that we use to communicate. Those who can "feel deeply" are sensitive to such contextuality, where we might say there is a distinction between science and art, though there are overlaps.

When someone knows how to write with feeling, they understand how to express themselves colorfully with words using the proper cadence and also be sensitive to what feeling they are imparting to another. Just one word out of context can create a feeling-difference instantly, like if I were to abruptly say THE PUPPY WAS SHOT BY EVIL NAZIS — the caps implying shouting, or variable intensity of vocal force — and then decided to go back to normal as if that were considered "proper" with continuity of feeling of the prior sentences. So the notion of information flow and its contextualization with variable force over time is involved with the mechanics feeling.

The movie Shawshank Redemption is almost universally acclaimed by all who watch it as a movie that conveys realism — or a parity of 2D representation of behavior in the (minimally) 3D space we live inas well as hopefulness. Would the same universal sense of feeling people share with this movie be had if a Klezmer band were to appear every 2 minutes in various scenes in the background playing a completely non-contextual kazoo choir and yelling "RED LIVES MATTER?" One would ask "What does that mean?" "Why are they doing that?" "Why" or "reason" is tied to feeling and meaning. There is no meaning to such behavior because the feeling is interrupted with non-contextual "craziness" one might say. Without sufficient context or reason for the next placement of information, no feeling is had.

The man and woman at the dinner party might use the term "love" where feeling between them is sufficiently shared. Love is considered to be a feeling, and love is used to denote positive feeling toward something or someone and the shared informational context between them. Many might readily say, "I LOVE" that movie above, it invokes great feeling within me. The worth of the information is the feeling it conveys.

Whereas functioning invokes semantic elements of processing discrete numbers, computing, machinating, grinding, even masticating. Feeling invokes a sense of continuity, experiential worth, artfulness, context, love.

If a machine can acquire information, tabulate, and compute with it, it could be said that "feeling" is the human experience involving these things.

Words are universal tokens of feeling between human beings, and their use is mathematically rigid, requiring very specific shared discourse universes to convey meaning and feeling. Words are used to convey mathematically-based order vs. disorder, so that feeling and meaning can be had. In print, the use of punctuation conveys tone and pause, to set off the feel or mood. A "good writer" understands the mathematical laws of contextualization and word use to create meaning and feeling within a given language.

It could be said "feeling is the ontological experience of information." It is one of the principal elements of human meaning, and involves the notion of experiencing the form and movement of objects in space with respect to their environment.

I would call it a "meta-knowledge", the basis of consciousness, a "feeling of what one knows."
 
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Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
(Just a curious side-note: did pi exist before it became part of a set? Therefore, if your definition of a number is “that which is part of a set”, what would have been your definition for this number in use prior to it being classified?)
 
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bogosort

Joined Sep 24, 2011
696
Btw, on a side-note, I wanted to mention... the total confusion with this whole "numbers and representations" thing is due to my not fully clarifying, perhaps, that I'm coming at it literally from "discrete unary or binary voltages" mentality. A "!," as we said, would be a truth state of a voltage presence, not even a number (unless we equate it to 1). I want to know what Pi is as a function of these !'s.

It's !!! + some amount of additional !'s. How many additional !'s?
Confusion still remains. A truth state cannot be equated to a number because they belong to different domains. The instant you say "1 = T", where "T" is the symbol for a truth value, you've necessarily stripped all numeric properties from the symbol "1".
You're declaring that symbol "1" stands for a truth value, not a number. Truth values belong to logical systems; they do not have numeric properties. We can't validly ask "What's the next truth value after 'T'?" or "Is 'T' even or odd?"

The representation of numbers is a different level of abstraction. I think it'd be helpful for you to try to visualize what a number might look like. Forget computers and ToEs for now, step outside of any models, and just try to picture what the number represented by the symbol "3" looks like. What "looks" different about it as compared with the number represented by the symbol "2"?

When I try to visualize these things, I end up picturing three sheep or three balls or something. I always end up concretizing the number with physical objects. No matter how hard I try, I cannot put a face to the numbers themselves. This speaks to the pure abstractness of numbers -- they are not physical things. But, in order to use numbers in the physical world, we have to give them some physical representation: notches on sticks, marks on paper, voltage levels on a circuit. And herein lies a big problem: there are far more abstract numbers than there are possible physical representations. We have a pigeonhole problem: too many pigeons, not enough holes to put them in.

No matter what representation we choose, we won't be able to express every number. We do, however, have a say in how we organize our pigeonholes. Effectively, we chose a single number to use as a reference for the representation of every other number. In base-10, we use ten symbols to relate a number to multiples of ten. In base-2, we use two symbols to relate a number to multiples of two, and so on. It is this decision -- which base to use -- that determines whether a representation is non-terminating or not. If the denominator of a number has prime factors that are not prime factors of the base, then that number will have a non-terminating representation in the base. Notice that this is strictly a property of the chosen base, not of the number itself.

For example, ten has prime factors two and five. So, in base-10, the number "one-sixth" is non-terminating because six has a prime factor of three, which is not a factor of ten. In base-10, we have to write "one-sixth" as a non-terminating decimal: 1.6666... In base-12, however, "one-sixth" has a terminating representation: \[ \frac{1}{6}_{\text{base-10}} = 2 \times 12^{-1} = 0.2_{\text{base-12}} \] Terminating or non-terminating are properties of bases (representations), not numbers. So, when you ask what the decimal expansion of Pi is in base-1, I'm nonplussed. That base-1 is a particularly terrible base to represent irrational numbers speaks only to the base, not the numbers themselves. In base-Pi, Pi has a terminating representation: 10.
 

bogosort

Joined Sep 24, 2011
696
Agreed on the "state" definitions above, and I knew that's how you were using them. I would also call that "information contextualization," which requires hella programmer intention to file all of it to be interrelated.
I disagree with your last sentence. Each grain of sand has first-order state by virtue of it being a physical thing. This first-order state conveys information. The grains of sand, however, are not alone -- they are part of a larger structure of sand. This larger structure itself has 2nd-order state and conveys different information than what each grain conveys. This is physically true, whether or not there is an information processor around to notice. In other words, the universe itself is set up as increasing orders of state complexity.

Simple information processors, such as sensors, interact with only one level of state. Sophisticated information processors interact with multiple levels.

However, the problem I have is, unless information has some kind of true spatiality to it, all of it is 1D points, and this doesn't cut it for me without a spatiality element. The dog is more than 1D because the information coming from the dog is minimally 2D requiring a 2D grid to see it, but then the information is stored in 1D?
Before we continue further, we need to get this straight to both our satisfaction. You say that the information coming from the dog is minimally 2D, but this seems inaccurate. Each photon of light carries 1 bit of information, yes?

If you disagree, then we need to stop here and figure out why. If you agree that each photon carries 1 bit of information, then we have only two possibilities at the retina. Either
  1. Each photoreceptor is conveying 1 bit of information, and so we think of the collection of receptors as a collection of 1-bit data sources.
  2. Each receptor is conveying 1 bit of information; if there are a million receptors, then we have a million bits of information.
Option 1 is the "1D" model; option 2 is the "1,000,000D" model. Notice that neither "2D" nor "3D" is a possibility, because bits of information are not geometrical.

Before we continue, we need to be in perfect agreement about this. I believe the "1,000,000D" model is the proper model because the information conveyed by each receptor is dependent on the information conveyed by the other receptors. In other words, the "1D" model implies that the million bits of information is random -- each bit of information is completely independent and has no relation to the rest of them. But the information conveyed by the receptors comes from physical states that are related to each other. Therefore, the "mega model" is the correct way to think about it.

Thoughts?
 

bogosort

Joined Sep 24, 2011
696
To understand the "meaning" of these words, we have to take a slightly anthro-centric track, because we have only observed humans using such terms. The only true way to understand what they mean is to observe how a human uses them in various contexts to get a "feel" for their "meaning."
It seems pretty clear to me that the human experience is, well, human. The only way for a computer to have the human experience -- to have feeling and meaning as humans do -- is to be human, which presumably cannot happen. So, I 100% agree that computers and such do not experience the world as we do. Never in dispute.

The same is true, of course, for dogs. But when I hang out with dogs, I can't help but notice "human-like" aspects, as if they have their own canine version of feeling and meaning. Their version and our version are undoubtedly different, but they seem more similar than different. The difference grows when I consider the reptilian version of feeling and meaning. It grows bigger still when I consider the insectoid version. Nonetheless, there seems to be a spectrum of feeling and meaning, a range of properties that a human might consider and think to herself, "Yeah, I can relate to that".

This is what I'm trying to get at. Not the unique way that humans experience the world, but the commonalities that seem to be present in most living organisms. We say that the single guy at the dinner party is "peacocking" because we find commonality in mating rituals. I want to see if we can pinpoint where the specialness of experience arises. Is it a fundamental property of biological organisms? Is it a consequence of complexity? I see more similar than different between a computer and a blood cell, so what's the critical difference?
 

bogosort

Joined Sep 24, 2011
696
(Just a curious side-note: did pi exist before it became part of a set? Therefore, if your definition of a number is “that which is part of a set”, what would have been your definition for this number in use prior to it being classified?)
Can't let go of the Pi, eh? :) It's definitely a tangent, though I'm happy to continue discussing it.

"Did Pi exist before it became part of a set?" That's a grammatically loaded question, lol. Consider this question: "Did humans exist before they were called Homo sapiens?" if we take "Homo spaiens" as referring to a particular classification, then yes: the definition of homo sapiens is of relatively recent vintage, and humans existed long before then. But if we take "Homo sapiens" to refer to the people so-defined, then no, there were no humans before the people that we now call Homo sapiens.

Likewise with Pi. I would say that to "know Pi" is to know it as a member of ℝ. The ancient Egyptians had a notion of Pi, but they didn't know Pi like we know it today. If I didn't know anything about ℝ, and you asked me for a definition of Pi, I would probably mumble something about the relation between a circle's radius to its circumference. This might be a sufficient definition for, say, agricultural uses of Pi, but it is insufficient in more general mathematical contexts. Which is why we now have ℝ.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
Confusion still remains. A truth state cannot be equated to a number because they belong to different domains. The instant you say "1 = T", where "T" is the symbol for a truth value, you've necessarily stripped all numeric properties from the symbol "1".
You're declaring that symbol "1" stands for a truth value, not a number. Truth values belong to logical systems; they do not have numeric properties. We can't validly ask "What's the next truth value after 'T'?" or "Is 'T' even or odd?"

The representation of numbers is a different level of abstraction. I think it'd be helpful for you to try to visualize what a number might look like. Forget computers and ToEs for now, step outside of any models, and just try to picture what the number represented by the symbol "3" looks like. What "looks" different about it as compared with the number represented by the symbol "2"?

When I try to visualize these things, I end up picturing three sheep or three balls or something. I always end up concretizing the number with physical objects. No matter how hard I try, I cannot put a face to the numbers themselves. This speaks to the pure abstractness of numbers -- they are not physical things. But, in order to use numbers in the physical world, we have to give them some physical representation: notches on sticks, marks on paper, voltage levels on a circuit. And herein lies a big problem: there are far more abstract numbers than there are possible physical representations. We have a pigeonhole problem: too many pigeons, not enough holes to put them in.

No matter what representation we choose, we won't be able to express every number. We do, however, have a say in how we organize our pigeonholes. Effectively, we chose a single number to use as a reference for the representation of every other number. In base-10, we use ten symbols to relate a number to multiples of ten. In base-2, we use two symbols to relate a number to multiples of two, and so on. It is this decision -- which base to use -- that determines whether a representation is non-terminating or not. If the denominator of a number has prime factors that are not prime factors of the base, then that number will have a non-terminating representation in the base. Notice that this is strictly a property of the chosen base, not of the number itself.

For example, ten has prime factors two and five. So, in base-10, the number "one-sixth" is non-terminating because six has a prime factor of three, which is not a factor of ten. In base-10, we have to write "one-sixth" as a non-terminating decimal: 1.6666... In base-12, however, "one-sixth" has a terminating representation: \[ \frac{1}{6}_{\text{base-10}} = 2 \times 12^{-1} = 0.2_{\text{base-12}} \] Terminating or non-terminating are properties of bases (representations), not numbers. So, when you ask what the decimal expansion of Pi is in base-1, I'm nonplussed. That base-1 is a particularly terrible base to represent irrational numbers speaks only to the base, not the numbers themselves. In base-Pi, Pi has a terminating representation: 10.
I appreciate the answer; the reason I'm coming back to this is because some of the core elements here are very key to agree on to get further, and some of this is philosophical regarding the true dragon-hood of the topic.

First, you do know literally thousands of mathematicians on the net will disagree with you!?? ;--) I've got a good friend whose a degreed math/logic guy and even he was taken aback and couldn't believe you are saying pi is a "finite" number with zero length, a single point in ℝ, no matter what the base.

So whatever "confusion" I'm sportin' here, bare in mind apparently most modern mathematicians have the same confusion (hey, I have similar thoughts in other areas about all sorts of things, so no biggy there!). But I have verified this to be the case. I have read and re-read your reasoning with a very open mind. Perhaps you have unorthodox takes on things, that's fine, of course. But your thinking on this is not mainstream. Thousands or millions of dollars are spent calculating pi in super computers. They are not doing it in base 10 or any base. They are doing it in baseless grunts. Every grunt is a flip-flop. Binary computers are representing the digits as voltages and switches at the very hardware level, with no additional "concept" abstractions. At the most elementary of hardware levels, pi is 3 unary states (represented as more compact binary; yes, you sold me on unary as even more fundamental, but I see binary as essentially unary sharing the same space) + something more. Symbols do not exist to me at the hardware level — just discrete, and fundamentally unrelated voltage states, unless a human knows the relationship.

Bare in mind you have a serious paradox you are saying above: You are a physical device. But you insist numbers exist as a non-physical things. That's like an FM radio saying its frequency dial is not physical. You don't know anything but physical. I must repeat this: You don't know anything but physical. So as a machine, where is the intellectual justification to say numbers exist outside of the literal wires, Vcc, and switches that you are. This is all you have to work with.

Though I'm 100% on board that numbers are NOT physical things, I believe they are represented in the 5D. I agree with Newton and Pythag and others that they are metaphysical things involving actual infinity, not as a process but as an actual origin stuff, the ℝ-stuff. I.e., ℝ is a real "thing" that exists somewhere, and it's not physically represented. It's not a process. It's the "stuff of infinity" that is the very basis of my model. I can't stress this enough and nor am I at odds with the greatest mathematicians of yore on this. I want to define infinity in the model as ℝ-stuff that is NOT a function of a function or process, but as something that exists perhaps in the 5D, that for example perhaps the DOG is made of. There is all of R in between 3.14 and 3.15!

So I need you to explain to me what you believe pi literally is from a PC's perspective. If you want to use 22 and 7 to do it, do it with u-its, bits, schlitz, but I can't see anything else. I assume, like Von Neumann, the brain is binary, no different than a PC we've built in our brain's image to work with binary states: You have a GRUNT and a GRUNT complement, or higher pitched GRUNT, or whatever you want to use.

I cannot rationally entertain any other abstract notion using 2D symbols — base "anything." They do not exist to me. I want the very simplest of grunts only, because I believe "integers" are all we have (and the monstrosity that is "ℝ stuff", that isn't a set of numbers, it is an indivisible numeric continuum where each interval contains 100% of itself), and the simplest form are grunts. Grunt for a voltage over a certain amount, grunt at a different pitch for a voltage under a certain amount. Computers can compute literally everything with 2-state grunts.

When I said {!,#} and "T" or "F", I should have said {#,!}... ignore the T/F element. The numbers are {#, !}-based n, discrete voltage states full-stop, nothing else.

Given the seriousness of other mathematicians disagreeing, and the fact that I only want to see this represented at THE lowest level, this is a very important question before we move forward.
 
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Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
I disagree with your last sentence. Each grain of sand has first-order state by virtue of it being a physical thing. This first-order state conveys information. The grains of sand, however, are not alone -- they are part of a larger structure of sand. This larger structure itself has 2nd-order state and conveys different information than what each grain conveys. This is physically true, whether or not there is an information processor around to notice. In other words, the universe itself is set up as increasing orders of state complexity.
But this sort of "nested state" situation is programmed by a programmer in a computer to be represented as such. If we laid out all of the transistors in a computer linearly to be n billion units long, we'd simply have certain flip flops high vs. low in a linear line. Their relationship is entirely user-defined to reflect any kind of "nested states" in physical reality.

Before we continue further, we need to get this straight to both our satisfaction. You say that the information coming from the dog is minimally 2D, but this seems inaccurate. Each photon of light carries 1 bit of information, yes?

If you disagree, then we need to stop here and figure out why. If you agree that each photon carries 1 bit of information, then we have only two possibilities at the retina. Either
  1. Each photoreceptor is conveying 1 bit of information, and so we think of the collection of receptors as a collection of 1-bit data sources.
  2. Each receptor is conveying 1 bit of information; if there are a million receptors, then we have a million bits of information.
Option 1 is the "1D" model; option 2 is the "1,000,000D" model. Notice that neither "2D" nor "3D" is a possibility, because bits of information are not geometrical.

Before we continue, we need to be in perfect agreement about this. I believe the "1,000,000D" model is the proper model because the information conveyed by each receptor is dependent on the information conveyed by the other receptors. In other words, the "1D" model implies that the million bits of information is random -- each bit of information is completely independent and has no relation to the rest of them. But the information conveyed by the receptors comes from physical states that are related to each other. Therefore, the "mega model" is the correct way to think about it.

Thoughts?

From what I can tell, like a retina, a 2D image appears on the literal spatial CCD's 2D grid elements?

If that is the case, the "order" of that image is a function of each grid element being populated sequentially in hardware flip flops, and other flip flops track the received data with respect to how it would be reconstructed to a spatial 2D screen. There is a fixed number of photons involved with the surface excitation of the CCD where the image is literally represented in spatial 2D, and physical wires run from the grid elements to actual physical latches.

Yes, this intimates that light is populating the grid with just the right photons at the right intensity to create the image! That has some seriously.... extended implications for light!
 
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Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
112
Without a process, INFINITY has no definition. It is undefined and cannot be used in the model.
As I mentioned above, ℝ-stuff infinity. That's where the secret sauce is. ;--) The infinitude of ℝ, with its 100% of itself between each interval is not a process. What if the dog outside the window is made of the ℝ-stuff?
 
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bogosort

Joined Sep 24, 2011
696
First, you do know literally thousands of mathematicians on the net will disagree with you!?? ;--)
Show me. If thousands of mathematicians disagree with me, it should be easy to post a few links.

I've got a good friend whose a degreed math/logic guy and even he was taken aback and couldn't believe you are saying pi is a "finite" number with zero length, a single point in ℝ, no matter what the base.
Ask your friend how an "infinite number" can be smaller than 4. If your friend is indeed a math guy, then he will know what this question means: What's the Lebesgue measure of Pi?

Perhaps you have unorthodox takes on things, that's fine, of course. But your thinking on this is not mainstream.
My views on mathematics are so orthodox, they have curly sideburns and refuse to work on the Sabbath. Seriously, unlike most things, I'm 100% mainstream in mathematics.

Thousands or millions of dollars are spent calculating pi in super computers.
Lol, no one cares about digits of Pi. In its orbital calculations, the JPL rounds Pi to its 15th digit: https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/

In that link, they point out that with just 40 digits of Pi, we can calculate a universe-sized circumference to within an error less than the width of a hydrogen atom. The only reason people compute lots of digits of Pi is to test new hardware or new algorithms. Digits of Pi is a good test because the nth digit is easily checked. But no one cares about the actual digits.

Bare in mind you have a serious paradox you are saying above: You are a physical device. But you insist numbers exist as a non-physical things.
The "paradox" is easily resolved.

A state is a physical thing. How a state is configured depends on how it interacts with other states. For example, the state of my visual cortex depends on the state of my retina, which depends on the state of the light entering the retina. This is an example of an internal state (visual cortex) that is dependent on external states (the outside world). We associate physical things with states that have external reference.

In contrast, some states are dependent primarily on other internal states. These states, like the concept of numbers, have no direct external reference. We associate abstract things with such states.

Both types of states are physical. There is no paradox.

There is all of R in between 3.14 and 3.15, and also 3.141 is less than 3.14!
The precise way of saying the first part of your conjunction is that the cardinality of [3.14, 3.15] equals the cardinality of ℝ -- i.e., there is a bijection between the elements of both sets. Slightly less formally, we can say there are as many elements in the interval as there are in all of ℝ. But we cannot say that 3.141 < 3.14. Proof: \[ \begin{align} 3.141 < 3.14 \qquad \implies \qquad \frac{3141}{1000} &< \frac{314}{100} \\ 3141 &< \frac{314}{100} \times 1000 \\ 3141 &< 314 \times 10 \\ 3141 &< 3140 \end{align} \] So, unless you're willing to defend that 3141 is less than 3140, you've clearly made an error.

So I need you to explain to me what you believe pi literally is from a PC's perspective. If you want to use 22 and 7 to do it, do it with u-its, bits, schlitz, but I can't see anything else.
I'm not sure how to parse the phrase "what Pi literally is". Pi is literally a number, an element of ℝ. It has certain properties that allow us to recognize it. Most of these properties can be easily encoded in a language that is usable by a computer. For example, the property \( 3.14 < \pi < 3.15 \) is easily encodable. The property "is a transcendental number" is easily encodable. Even the property of its decimal expansion is easily encodable -- there are thousands of algorithms that calculate digits of Pi.

What's not encodable? The last digit of Pi's decimal expansion in an integer base. This is not encodable in any language.

How does this apply to computers? In the vast majority of practical applications of Pi, the computer is not using Pi at all. Rather, it is using a rational approximation to Pi (like 22/7). In these applications, the only property that matters is the value (magnitude). And since it is such a small number (almost zero!), the vast majority of applications need only a few bits of precision to approximate its value. A computer algebra system (like Mathematica or Maple) will use various properties of Pi beyond just its numerical value, but these are rare exceptions.

In other words, most computer applications don't use Pi at all, so they don't need to know what it "literally is".
 

bogosort

Joined Sep 24, 2011
696
But this sort of "nested state" situation is programmed by a programmer in a computer to be represented as such. If we laid out all of the transistors in a computer linearly to be n billion units long, we'd simply have certain flip flops high vs. low in a linear line. Their relationship is entirely user-defined to reflect any kind of "nested states" in physical reality.
No, the nested state situation is a property of the universe. If you disagree, then explain how a pile of sand is different from a grain of sand.

From what I can tell, like a retina, a 2D image appears on the literal spatial CCD's 2D grid elements?
Each element in the retina/CCD is an independent thing. Each individual photoreceptor and phototransistor can hold one bit's worth of information. Using your parlance, these are all "1D", yes?

When interpreting the data, the information processor (brain/CPU) treats the independent, individual elements as being dependent. This forms a larger system (retina/CCD) out of many tiny subsystems (individual receptors/transistors). In your parlance, this larger system is nD, for n individual elements in the system. Yes? A megapixel CCD has about a million individual sensing elements. The human retina has about a million sensing elements. Both are "mega-D" systems.

There is a fixed number of photons involved with the surface excitation of the CCD where the image is literally represented in spatial 2D, and physical wires run from the grid elements to actual physical latches.
You say "the image is literally represented in spatial 2D" -- what do you mean by "literally represented"? The accurate way to say it is that the information processor interprets the data as a 2D spatial image. In other words, it treats the data from the million independent sensors as if each datum was dependent on all the others. Note that it need not be this way -- if we attach a random source of photons to each individual element, the resulting 2D matrix would not be a spatial image -- it'd be a million points of random data!

Yes, this intimates that light is populating the grid with just the right photons at the right intensity to create the image! That has some seriously.... extended implications for light!
You act as if this is magical, but it's no different than what happens all along the chain. Light strikes an object and interacts with it, causing the state of the light to change based on the physical properties of the object. Some of the light goes through the object, some of it gets absorbed by the object (heating it up), and some of it gets reflected. Of the reflected light, some of it will have the correct angle to strike the lens of your eye, which focuses it on your retina. This light, having been reflected off the object, carries with it information about the object, which your photoreceptors receive and transmit to your brain.

If all of the light goes through the object, or all of the reflected light misses your eye, or if there's not enough light to stimulate your receptors -- well, then you simply don't see the object. :)
 
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