Our problem is that I’m obeying our tabula rasa directive, but you haven’t uninstalled at least 14 apps, so all my terms are butting up against your existing glossary, rather than a base, intelligently derived sensible “map of the dog,” one we can build from scratch and then see how it interfaces with the existing one.

Pfft. Your terms have no rasa whatsoever. I'm just helping you keep your assumptions in that bulging closet full of assumptions.

 

Just, wtf on the sine waves not being binary. The entire information revolution is built on polar vibrations (frequencies) that yield binary sequential instructions in a circuit!!! If they weren’t binary, we could have no binary instructions or data!!

This isn't a flex, but I know a thing or two about sine waves and information. And this isn't mansplaining, but binary means "two". Sine is a function from ℝ to [-1, 1] ∈ ℝ, that is, it takes on an uncountable infinity of values in any single period. Very different types of things.

We can try to hash out the confusion if you want.

Also, btw, when you’re thinking about nullifying those QED’s using words built out of waves superpositioned with symmetrically undulating sine waves, please tell me precisely how you plan on generating the sequential instructions from your unary computer? I.e., you need a clock source (quartz?) that vibrates with binary polarity (crest and trough) at a certain “frequency” that allow you to generate the sequential binary address codes to release the u-its. Do you have access to a crestless wave that vibrates, or can we admit that the heartbeat of your unary computer would require binary sine waves?

Erm, the most obvious way to clock a unary computer is to generate a periodic sequence of "@"s. In my implementation example, this would correspond to pulses of, say, 5 V. What's the problem?

 

A friend of mine tracking the thread recommended we make a shared doc with things we agree on + elements of discussion.

Someone else is reading this thread? Egads!

You deftly QED’d information and state transfer and computation based on 2^n. I’ve been rolling from that place. Now you want to say it’s not “legit” and are arguing for base 9843 for info processors. What’s up, dude?

Ah, true, true. I started this journey happy to use base-2 representation for everything, as it is the lingua franca of comp sci and information theory.

But, as I slowly learned of your wretched base-2 fundamentalism, I developed an aversion to using binary strings for fear that they would take you deeper into the dark side. Simple as that.

My guiding principle, then and now, is that Numbers are Independent of their Representation.

 

Someone you know might have written these at some point... if you have any info on his whereabouts, please call 1-800-DI-LEMMA:

LOL. I'll have you note, however, that even way back then I clearly showed representation agnosticism. To wit:

Axiom 4: A bit is a discrete unit of information; we measure information by counting bits.

"A bit is a discrete unit of information", not the discrete unit of information.

A convenient representation for bits is sequences of 1s and 0s; we call such sequences bit strings.

"A convenient representation", not "the one, true, unique representation".

 

Dear Euclid-definitions-suck, Tesla-was-a-syphilitic-addict, and Rene-DesCartes-had-no-sense-in-nomenclature,

Hexadecimal is base-16 and represents the binary-states of the flip-flops and is derivative of them. Same is true for any other bases — they're based on what's in the flip-flops. QED.

<Snicker> Dear Confuses-geometrical-concepts-with-information-concepts, managing partner of No-Idea-What-Numbers-Are,

Base-16 representation existed long before flip-flops were invented. Indeed, you'll find that Sumerians used base-60 thousands of years before anyone ever found utility in base-2. It is the the Great Universal Liberty to be able to use whatsoever number base we feel like.

We have to f*ck this abstractive cloudy lollygaggery here. Your QED reflects the hardware. The hardware uses piezoelectric effect of an oscillating phenomenon (high and low!) to create a clock signal that generates the flip-flop switches to unlock the flip-flop-stored-high-or-low-binary-state instructions at them. No clock? No digital computer. Full stop. Quantum or otherwise. Unary computers don’t exist because you need a binary clock signal to generate unique binary strings that represent addresses. QED.

First, a computer doesn't need a clock (check out asynchronous CPUs). Second, one can easily make a unary clock: it's just a pulse train of voltages. Unary computers are just as possible as binary or ternary or whatever-ary computers. There's literally no way to dispute this, so I'm confused why you keep trying.

Oscillation is about "oscillating from high to low." Binary. QED.

Such tunnel vision. An oscillator makes a good binary clock source, but that doesn't mean all clock sources are necessarily binary.

Any one on this board would agree. QED.

Sigh, like such a thing would matter. The math is indisputable.

 

Dear information-as-existence, only-person-in-the-world-that-says-a-calculator-doesn't-use-numbers, no-dog-in-the-light, and cherry-pick-what-historical-figures-represent-as-actual-science,

Sine is a function from ℝ to [-1, 1] ∈ ℝ, that is, it takes on an uncountable infinity of values in any single period. Very different types of things.

Totally on board with that! Those values reach an EXTREME of essentially two polar states though! That's what an oscillation is about! I do know a thing or two about those things. Cue you with "But sine waves are not Banachian-symmetric over a spheroid 1024D plane!"

Did you know that the Maya used base 181,028,571,993?

Would you agree that those bases are hella more abstract than the most simple of "binary states?"

YES, I fully and am COMPLETELY in agreement that computation exists as a separate thing from REPRESENTATION. Got it. We don't need to go around that Big Ben again. I got some strange-ass issues I have to reckon with before I say "Siri knows the weather." You MAY convince me of the use of this term for this discrete-bits-only situation, but it may happen when I convince you to use REALITY. :--D

But, when it comes to NATURE(!) and not the MIND(!):

We are down to unary or binary as what's going on in nature, can. we. agree??? Is the dog there, not there, or NHETHEORER? At any given time, we can represent that space the dog is in as a BASE 2, no?? As in, "how many possible configurations we have for the dog in this "ONE COLUMN SPACE BEFORE WE NEED TO CARRY THE DOG."

 

Erm, the most obvious way to clock a unary computer is to generate a periodic sequence of "@"s. In my implementation example, this would correspond to pulses of, say, 5 V. What's the problem?

Answer me this question if you will:

In the adder you built, the clock generated a square wave of an oscillation that was essentially, what 5v vs. 1v? The flip-flops are flipped high with 5V on a line or flipped low with 1V, correct?

 

So, if I don't know the difference between ℕ and ℝ, please explain how I can say with full certainty that |ℕ| < |ℝ|?

Let me put on record to you, and for everyone watching, this statement:

|ℕ| < |ℝ|

"Is 100% complete and total David Copperfield smoke and mirrors Grade A bullshistics of the absolute highest of orders." — Jennifer Kronecker.

I would bet 4.7 trillion cash dollars on this point.

Here's my proof:

Values correspond to points. If you can label a point, you can make it a uniquely named "whole integer." How many infinite values are on a continuous, infinite-point sine wave? As many integers as you need to number each and every one of them.

I don't care if you call the point 2992, 12, 3,902,382,472.20284 or invoke hieroglyphics $*0148$( in base 3808310831.

There are unique points that one can label. They are ALL integers, period. And all of them can be uniquely represented by as many binary strings as you need.

The irrational numbers are not numbers. They are infinities in disguise. They go on forever like infinity. If they terminate, they're rational. If they're rational, they're integers appended by a fraction of some base 10 number.

Calling them ℕ or ℝ with that super cool Roman outline Trajan-esque movie font is entirely for convenience in calculations and measurements by fractionating values with decimal points.

"The integers are what's really going on, all else is manufactured."

Sincerely,

Kℝonecker's Secretary

 

<Snicker> Dear Confuses-geometrical-concepts-with-information-concepts, managing partner of No-Idea-What-Numbers-Are,

Literal LOL... they fired you at the firm, since you think numbers exist outside your bits that represent them.

My model sees geometrical and information as two sides of the same coin, as does your brain's bits. I see "true" geometry as infinite-value-continuum, and bits are representations of digital versions of these. We're not there yet. :==D

Do you realize that if you can't define the "dog in the light" as "something" that is existent apart from your states, that YOU YOURSELF don't exist??? I mean you're willing to call yourself a DOS prompt.

And you wonder why I think "you don't know what anything is" if you're just a brain??

"Coming up next on OntoloTV — Man found to be so intelligent, he doesn't exist!"

 

Dear Siri’s-roommate,

You would say you are _ALIVE and have _CONSCIOUSNESS right now.

Let’s say, Watson forbid, you end up in a casket in your local funeral home.

What is the specific difference between you now and the you in a casket?

versus

What is the difference between your smartphone now, and one that has had its battery removed and placed in another casket in an adjoining room.

Besides AMOUNT of data “you” can both process, the speed and complexity of your algorithms, would you consider yourself different from the phone in this respect? Tabula rasa, remember.

 

Dear 100%-discrete-AF-digital-bit-state-machine-with-hair-and-sneakers,

Where exactly do your finite, discrete number of states conceive, store, and process the notion that sine waves have infinite values between any two points, and what discrete mechanism in you harbors such discrete definitions?

Where are thought-to-be-grey-matter waves of variable frequency coming from in a discrete processor? What is vibrating the matter?

 

Totally on board with that! Those values reach an EXTREME of essentially two polar states though! That's what an oscillation is about!

Not quite. Oscillations are fluctuations about a single value. Consider the most common form of oscillation, a damped oscillator, which has an exponential decay. The extreme values are not constant, rather they converge to the central value over time.

Cue you with "But sine waves are not Banachian-symmetric over a spheroid 1024D plane!"

Lol, well, we don't need to get too fancy to see that knowing the extremes of a sine wave is not enough. For example, suppose you only know that a waveform oscillates periodically between 1 and -1. What waveform is it? You cannot say -- there are infnite different such waveforms. The unit sine wave, the unit square wave, the unit triangle wave, the unit sawtooth, the unit cosine -- these all oscillate between 1 and -1. What makes them different is what happens between the extremes.

Did you know that the Maya used base 181,028,571,993?

Would you agree that those bases are hella more abstract than the most simple of "binary states?"

This is insightful as it points directly at your bias. There is nothing "more abstract" about base-181028571993 versus base-2. Both forms are equally as abstract. But because the latter is easier for you to think about, you assume that it is more fundamental in some way. You're projecting your values and beliefs, but these are not universal! For a counter that has precisely 181,028,571,993 steps, base-181028571993 is the most "natural" choice of representation.

YES, I fully and am COMPLETELY in agreement that computation exists as a separate thing from REPRESENTATION. Got it.

Hallelujah!

But, when it comes to NATURE(!) and not the MIND(!):

We are down to unary or binary as what's going on in nature, can. we. agree???

No way. If some natural phenomenon is amenable to numeric representation, then we are free to describe it using whatever number base we desire. I may describe the state of some system using binary, octal, decimal, hexadecimal, or base-181028571993. My choice will reflect the representation most convenient for me at the time, but my choice will not affect the results. What I describe will be the same whether I use unary or hexadecimal.

I think it's important that we recognize that number bases and such are for human consumption. Number bases allow us to use positional notation, where the value of a digit depends on its position in a sequence. In base-10, for example, the first position is the value of the digit, and the second position is ten times the value of the digit. So, 25 is 2*10 + 5*1. Positional notation makes it much easier to perform calculations ("carry the one", and so forth). To see this firsthand, try to multiply 25 and 14 using Roman numerals, which are not positional.

But "nature" doesn't perform calculations symbolically; she doesn't need number bases. Nature isn't unary or binary or any-ary; she just is. We humans sometimes find it helpful to organize information numerically, and so we choose a convenient number base. But that's it. There's no ontological significance to number bases.

At any given time, we can represent that space the dog is in as a BASE 2, no?? As in, "how many possible configurations we have for the dog in this "ONE COLUMN SPACE BEFORE WE NEED TO CARRY THE DOG."

No. What you described is one possible (human) way of characterizing a section of space, but it is neither unique nor necessary. It all depends on what phenomena we're trying to describe, and it what detail. If we only care about one particular property of a section of space -- e.g., the color or the amount of gravity -- our description will surely be different than if we're trying to describe several properties at the same time -- e.g., the motion of an object through that section of space. In every case, there is no unique or necessary formulation that describes it.

 

This is insightful as it points directly at your bias. There is nothing "more abstract" about base-181028571993 versus base-2. Both forms are equally as abstract. But because the latter is easier for you to think about, you assume that it is more fundamental in some way. You're projecting your values and beliefs, but these are not universal! For a counter that has precisely 181,028,571,993 steps, base-181028571993 is the most "natural" choice of representation.

But what you’re not factoring is that you are only dealing with 2 states in your brain: high and low. You are using these ALONE to build other concepts and amalgamations. Your concept of 342 in your brain is composed of precisely 10 voltage states that you take as “1 unit”: 0101010110

I don’t care how you cut the cake, that IS your representation of “12” (and 12 to you is an arbitrary grouping of bits).

Your voltages at their absolute elementary only have TAS and TDS as their foundational states.

This is not my bias. This is nature’s bias! I really don’t understand how you can argue this!

You insist C is separate from zero and one foot pedals, but they are not in the end! C IS an amalgamative abstraction of the pedals! The pedals are the observed voltage states that make C possible!

 

No. What you described is one possible (human) way of characterizing a section of space, but it is neither unique nor necessary. It all depends on what phenomena we're trying to describe, and it what detail. If we only care about one particular property of a section of space -- e.g., the color or the amount of gravity -- our description will surely be different than if we're trying to describe several properties at the same time -- e.g., the motion of an object through that section of space. In every case, there is no unique or necessary formulation that describes it.

Nah. I appreciate the wigglerrhea, but no. You are occluding the Feynmantic simplicity with your Banachian scalar matrix transfinite ordinals.

Before you start in with the “qualia” and the dog’s fur color, and his saliva color, and his paw shape, you must first speak to its PRESENCE or ABSENCE, and its components’ PRESENCE or ABSENCE.

We literally have no hope here if you won’t agree to the fact that your CCD picked up an image or didn’t. It is signal or it is noise.

You agree to it or you don’t. The “kinda sorta” is only because you’re missing facts or disagree with them to arrive at the dog being there or not.

Your house is at 39572 Subjective Dr. in Florida or it is not.

You even defaulted to QED’ing it that way, because you know physical substrates work that way.

And now you want to wiggle out of it by saying every base is the same abstraction.

N to the O to the P to the E! Claude Shannon, John Von Neumann, George Boole, Frege, etc. would agree.

 

Answer me this question if you will:

In the adder you built, the clock generated a square wave of an oscillation that was essentially, what 5v vs. 1v? The flip-flops are flipped high with 5V on a line or flipped low with 1V, correct?

The clock generates voltage pulses, though you could of course use any waveform (sine, square, triangle, whatever) at the output to represent the pulse -- the clocked circuitry is designed to ignore any voltage less than what "@" is defined as.

Note that two-state flip-flops would not be appropriate for unary circuits. This isn't a problem, of course, as flip-flops aren't required for computation.

 

Let me put on record to you, and for everyone watching, this statement:

|ℕ| < |ℝ|

"Is 100% complete and total David Copperfield smoke and mirrors Grade A bullshistics of the absolute highest of orders." — Jennifer Kronecker.

I would bet 4.7 trillion cash dollars on this point.

I'm glad for you that bets placed on a forum post aren't legally binding.

Here's my proof:

Values correspond to points. If you can label a point, you can make it a uniquely named "whole integer."

First mistake. Visualize a square of unit length (each side has length 1 in whatever units you care to use). Starting at one corner of the square, draw a line segment through the center of the square, terminating at the opposite corner. You've just drawn one of the square's diagonals.

Now, imagine a horizontal number line. Each point on the line corresponds to a number in ℝ. Imagine rotating your square such that the diagonal rests on top of the number line, with the left-most end of the diagonal resting directly on the point 0. What point does the right-most end of the diagonal touch? Pythagoras told us how to solve this: \[ \text{diagonal} = \sqrt{1^2 + 1^2} = \sqrt{2} \] Can we label the point \( \sqrt{2} \in \mathbb{R}\) ? Of course, we just did. Can we associate it with an integer? NO!

Let's assume that we could associate \( \sqrt{2} \) with a unique integer. Because a square's diagonal is longer than its sides (the triangle inequality), we know that -- whatever integer we use -- it must be larger than 1. A reasonable first guess is the next largest integer, 2. But this is problematic, as it breaks the rules of multiplication, implying that 2 equals 4: \[ \sqrt{2} = 2 \qquad \implies \qquad 2 = 4 \] Indeed, any integer we choose to represent \( \sqrt{2} \) will lead us to some contradictory statement (2 = 9, 2 = 16, etc.).

And since what leads us to contradiction is specifically the assumption that \( \sqrt{2} \) could be associated with an integer, the assumption itself must be wrong. Therefore, there is no unique integer that can be associated with \( \sqrt{2} \). And, since your claim applies to all elements of ℝ, a single counterexample -- which we found -- refutes your claim. QED

In case you are tempted to claim that "any point in ℝ can be uniquely named by a ratio of integers", let me save you the trouble. It is easily proved that an irrational number, such as \( \sqrt{2} \), can not be represented by a ratio of integers.

How many infinite values are on a continuous, infinite-point sine wave? As many integers as you need to number each and every one of them.

I don't care if you call the point 2992, 12, 3,902,382,472.20284 or invoke hieroglyphics $*0148$( in base 3808310831.

There are unique points that one can label. They are ALL integers, period. And all of them can be uniquely represented by as many binary strings as you need.

Second mistake. You yourself have stated that sine takes on values in the interval [-1, 1]. If we assume these values to be integers, then there are only three possible values of sine: -1, 0, and 1. Ah, but you say, we can always scale the interval to get a larger resolution: [-10^10, 10^10] gives us twenty billion possible values of sine. And we don't have to stop there!

Here's the problem, though: sine is a smooth function, it takes derivatives of any order. Among other things, sine's smoothness implies that it is continuous -- there are no "holes" in the values it can take. In other words, sine touches every value in the interval [-1, 1] ∈ ℝ. This means that, for any \[ y \in [-1, 1] \] there is an \[ x \in [0, 2 \pi) \] such that \[ y = \sin(x) \] Now, you claim that every such \( y \)-value has an integer representation. I offer a counterxample based on our old friend \( \sqrt{2} \).

Let \[ x = \frac{3 \pi}{4} \] then \[ y = \sin(\frac{3 \pi}{4}) = \frac{\sqrt{2}}{2} \] In other words, we have found a \( y \) that is half of the very number that we proved could not be an integer. If you suspect that somehow the half aspect changes its irrationality, then simply multiply both sides of the equation by two and you'll have the desired result. Therefore, integers (and rational numbers) are insufficient to label every point touched by sine. QED

The irrational numbers are not numbers. They are infinities in disguise. They go on forever like infinity. If they terminate, they're rational. If they're rational, they're integers appended by a fraction of some base 10 number.

Third mistake. An irrational number is just as much a number as a a rational number. Both can be used to represent magnitudes. We can add, subtract, multiply, divide, etc. irrational numbers. Indeed, an equation such as \( x^2 = 2 \) has no solution without irrational numbers. So, if you're content to allow \( x^2 = 4 \), it seems rather arbitrary to refuse passage to \( x^2 = 2 \).

Furthermore, every irrational number is finite. Our friend \( \sqrt{2} \) is larger than 1, but smaller than 2. If we use inches as units, the square whose diagonal has length \( \sqrt{2} \) has an area of exactly 1 square-inch, which is not exactly infinite, lol.

The fact that \( \sqrt{2} \) has a non-terminating representation in base-10 is just a quirk of base-10 (a human construct). Note that \( \sqrt{2} \) equals "10" in base-\( \sqrt{2} \), so yeah.

Sincerely,

Kℝonecker's Secretary

Sincerely,

Your irℝational friend

 

Dear Siri’s-roommate,

You would say you are _ALIVE and have _CONSCIOUSNESS right now.

Let’s say, Watson forbid, you end up in a casket in your local funeral home.

What is the specific difference between you now and the you in a casket?

versus

What is the difference between your smartphone now, and one that has had its battery removed and placed in another casket in an adjoining room.

Besides AMOUNT of data “you” can both process, the speed and complexity of your algorithms, would you consider yourself different from the phone in this respect? Tabula rasa, remember.

To keep our readers (hah!) suitably engaged, let's throw in some gratuitous violence. Suppose that a madman hopped up on bath salts quietly broke into my house while I was sleeping, took a hammer and a large tenpenny nail, and drove that nail through my skull. Let's also suppose that, before leaving my house, the madman grabbed my phone and drove a tenpenny nail through it.

Both my phone and I are dead. The most salient difference between this and our LIFE states is that our processors are broken, i.e., we can no longer process states. We're still "there", of course, a set of states that will continue to evolve over time (me in more smelly ways). But without an active information processor, we can't do the same kinds of things we used to do. So, the phone gets tossed in the garbage and I get buried in the ground.

 

The clock generates voltage pulses, though you could of course use any waveform (sine, square, triangle, whatever) at the output to represent the pulse -- the clocked circuitry is designed to ignore any voltage less than what "@" is defined as.

Note that two-state flip-flops would not be appropriate for unary circuits. This isn't a problem, of course, as flip-flops aren't required for computation.

I'm glad for you that bets placed on a forum post aren't legally binding.


First mistake. Visualize a square of unit length (each side has length 1 in whatever units you care to use). Starting at one corner of the square, draw a line segment through the center of the square, terminating at the opposite corner. You've just drawn one of the square's diagonals.

Now, imagine a horizontal number line. Each point on the line corresponds to a number in ℝ. Imagine rotating your square such that the diagonal rests on top of the number line, with the left-most end of the diagonal resting directly on the point 0. What point does the right-most end of the diagonal touch? Pythagoras told us how to solve this: \[ \text{diagonal} = \sqrt{1^2 + 1^2} = \sqrt{2} \] Can we label the point \( \sqrt{2} \in \mathbb{R}\) ? Of course, we just did. Can we associate it with an integer? NO!

Let's assume that we could associate \( \sqrt{2} \) with a unique integer. Because a square's diagonal is longer than its sides (the triangle inequality), we know that -- whatever integer we use -- it must be larger than 1. A reasonable first guess is the next largest integer, 2. But this is problematic, as it breaks the rules of multiplication, implying that 2 equals 4: \[ \sqrt{2} = 2 \qquad \implies \qquad 2 = 4 \] Indeed, any integer we choose to represent \( \sqrt{2} \) will lead us to some contradictory statement (2 = 9, 2 = 16, etc.).

And since what leads us to contradiction is specifically the assumption that \( \sqrt{2} \) could be associated with an integer, the assumption itself must be wrong. Therefore, there is no unique integer that can be associated with \( \sqrt{2} \). And, since your claim applies to all elements of ℝ, a single counterexample -- which we found -- refutes your claim. QED

In case you are tempted to claim that "any point in ℝ can be uniquely named by a ratio of integers", let me save you the trouble. It is easily proved that an irrational number, such as \( \sqrt{2} \), can not be represented by a ratio of integers.


Second mistake. You yourself have stated that sine takes on values in the interval [-1, 1]. If we assume these values to be integers, then there are only three possible values of sine: -1, 0, and 1. Ah, but you say, we can always scale the interval to get a larger resolution: [-10^10, 10^10] gives us twenty billion possible values of sine. And we don't have to stop there!

Here's the problem, though: sine is a smooth function, it takes derivatives of any order. Among other things, sine's smoothness implies that it is continuous -- there are no "holes" in the values it can take. In other words, sine touches every value in the interval [-1, 1] ∈ ℝ. This means that, for any \[ y \in [-1, 1] \] there is an \[ x \in [0, 2 \pi) \] such that \[ y = \sin(x) \] Now, you claim that every such \( y \)-value has an integer representation. I offer a counterxample based on our old friend \( \sqrt{2} \).

Let \[ x = \frac{3 \pi}{4} \] then \[ y = \sin(\frac{3 \pi}{4}) = \frac{\sqrt{2}}{2} \] In other words, we have found a \( y \) that is half of the very number that we proved could not be an integer. If you suspect that somehow the half aspect changes its irrationality, then simply multiply both sides of the equation by two and you'll have the desired result. Therefore, integers (and rational numbers) are insufficient to label every point touched by sine. QED


Third mistake. An irrational number is just as much a number as a a rational number. Both can be used to represent magnitudes. We can add, subtract, multiply, divide, etc. irrational numbers. Indeed, an equation such as \( x^2 = 2 \) has no solution without irrational numbers. So, if you're content to allow \( x^2 = 4 \), it seems rather arbitrary to refuse passage to \( x^2 = 2 \).

Furthermore, every irrational number is finite. Our friend \( \sqrt{2} \) is larger than 1, but smaller than 2. If we use inches as units, the square whose diagonal has length \( \sqrt{2} \) has an area of exactly 1 square-inch, which is not exactly infinite, lol.

The fact that \( \sqrt{2} \) has a non-terminating representation in base-10 is just a quirk of base-10 (a human construct). Note that \( \sqrt{2} \) equals "10" in base-\( \sqrt{2} \), so yeah.


Sincerely,

Your irℝational friend

Mr Irℝational-as-Freudian-slip?,

I appreciate the Banachionics — very clear. That's all, of course, true.

However, I need to clarify my exact meaning.

I believe the REALS are COMPOSED of essentially concatenated and combined integers in various configurations.

You think it's silly, because you only think in 7GL languages. You don't want to deal with forces, because you only like dealing with fields because "forces are just soooo old tech." You completely can't stand the fact that fields were INVENTED by the guy to create "unique sets of forces." You just want to see the field and ignore what he was trying to make.

You don't want to see that "ZOFP" (I'm using that for now on to represent "Zero and One Foot Pedal) is what's actually happening in this thing called REALITY which you don't want to define at all. You want to make conclusions concerning the BIOS based on a 7GL language. You know, TelepathSDK® from 2090, a language that you can just walk over the computer and send it a telephathic printf statement, and it creates an entire GUI in 24-bit color in 3 seconds. "See? We can create all sorts of abstractions with our our brains!"

You don't want to talk about the brass tacks levels of the fact that you brain is 2-state, representing TAS and TDS, "high and "low" and all binary computers are such, and John Von Neumann, FFS(!) agreed the brain is binary, which essentially yields 2 states, high, low, for each bit, each bit is essentially representing 2^n base 2 possibilities (again, representing integers 0 and 1, because in the end, those strings arithmetically manipulated and can be converted to higher symbolic concepts called "numbers" which are BIT AMALGAMATERS).

Beyond that you have abstractions and magical amalgations, and you love using 9549 different number sets composed of foundational truths, and interrelating them and calling them different names, which is YOUR magic wand (we all have them — MINE is that there is a 5D continuous wave processor that permits amalgamation of any 2 bits into discretized continuous form, one effectively shared by Newton). You think bits can be referred to together and called things by using other arbitrary bits to do this, and say it has to do with consciousness, but don't define consciousness, etc.

In short, you have not won the bet above. You have simply deflected to your 7GL language rather than seeing that "what we call REALS" are sophisticated concatenations of the set of infinite whole integers (set {0, 1} really just 0's and 1's) that "effectively" go from -∞ to ∞, and we just don't have names for all the ones we need, so we have created another set for the purpose of making convenient measurable concatenations called decimals.

It's the SAME argument you are using with you u-it deal. It's really all u-its or bits at baseline level!

Do you see that a BINARY computer can literally do everything you delineated above using discrete bits, each bit storing a 0 or 1 (which double as integers 0 and 1?)??? QED! That is NOT inductive!

Sincerely,

THE SECRETARY IS WITH OTHER CLIENTS, THIS IS KRONECKER BACK FROM THE DEAD HIMSELF

 

To keep our readers (hah!) suitably engaged, let's throw in some gratuitous violence. Suppose that a madman hopped up on bath salts quietly broke into my house while I was sleeping, took a hammer and a large tenpenny nail, and drove that nail through my skull. Let's also suppose that, before leaving my house, the madman grabbed my phone and drove a tenpenny nail through it.

Both my phone and I are dead. The most salient difference between this and our LIFE states is that our processors are broken, i.e., we can no longer process states. We're still "there", of course, a set of states that will continue to evolve over time (me in more smelly ways). But without an active information processor, we can't do the same kinds of things we used to do. So, the phone gets tossed in the garbage and I get buried in the ground.

Here's the big problem: neither you NOR iPhone NOR the nail exist beyond 2D, by your own admission, so I don't see how the nail is going into your 3D head??? Or how you claim such is happening, as if any one group of bits truly knows you have a 3D form that a nail can go into?

 

Where exactly do your finite, discrete number of states conceive, store, and process the notion that sine waves have infinite values between any two points, and what discrete mechanism in you harbors such discrete definitions?

I've already explained how the concept of INFINITY arises from the concept of counting (through the n+1 induction). This concept is simple enough that I expect most people have a decent notion of this type of infinity.

On the other hand, the concept of an uncountable infinity, such as ℝ, is much more sophisticated and requires significant effort to develop. I don't think the average person has a clear notion of ℝ.

Nonetheless, we can store the properties of uncountable infinities (and ℝ) on a computer, so the properties themselves are certainly discretizable. Using these properties, we can program computers to reason about uncountable infinities. For instance, using a proof engine and a suitable set of properties, a computer can conclude that \( |\mathbb{R}^3| = |\mathbb{R}| \) without being told specifically that the cardinality of the cube equals the cardinality of the line. At the very least, this suggests that reasoning about uncountable infinities can be discretized.

Where are thought-to-be-grey-matter waves of variable frequency coming from in a discrete processor? What is vibrating the matter?

Why does something need to vibrate? The salient aspect of vibration is periodic change, and change can come in many forms.