But what you’re not factoring is that you are only dealing with 2 states in your brain: high and low.

Sigh. We are 100% certain that your PC is a binary machine, yes? And your PC, using strictly binary logic, can represent and calculate numbers using any base we please, yes? In case you dispute this, type in "0x10 + 0x10" in google and you will get the correct answer, 0x20. Type in "7 + 6" and you will get the correct answer, 13. No human is translating those strings into binary behind the scenes, right?

So, if a strictly binary computer can use any number base, why do you think my human brain could not do the same?

Numbers are independent of their representation.

Whether we use 16 or 0x10 or 0b10000, we are referring to the same number. Whether the underlying circuitry is designed as base-10 or base-16 or base-2, the result is always the same: a number that can be represented in any base we like.

Your concept of 342 in your brain is composed of precisely 10 voltage states that you take as “1 unit”: 0101010110

Of all the possible state representations that my brain may be using to hold the concept of 342, it is almost CERTAINLY not ten on/off voltage states. You are confusing the base-2 representation of a number with the CONCEPT of that number. Do you really think that somewhere in my brain there are ten neurons that represent the number 342?!? If a surgeon kills these neurons with a laser, will I stop knowing what 342 is?!?

If you actually believe this, then we need to address this ASAP as this is a profoundly important misconception.

 

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.

"Evolve over time??" Eventually you "evolve" into the dirt you came from.

 

Nah. I appreciate the wigglerrhea, but no.

"Wigglerrhea"

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.

I couldn't disagree more. I might agree with you if we interpreted our visual field as a bunch of uniform, discrete blocks of stuff. Block of stuff there, or block of stuff not there. Only blocks of stuff around here.

But we don't interpret our visual field that way. There is an enormous amount of information being conveyed by the light that hits our eyes (I remember an estimation of 2 GB per second). While each photoreceptor in our eye is independent, behaving pretty much like a simple on/off switch, the photons in the light are not independent -- they each carry a bit of information from the multi-bit scene that's playing out in our field of view.

The light coming through the tree canopy casts a complex shadow filled with shapes that move in complicated ways as the tree sways in the wind. It's absurd to suggest that my brain takes in this information and responds "SORT OF CRESCENT-MOON SHAPE" or "NO SORT OF CRESCENT-MOON SHAPE" every instant for every patch of space.

That's not at all how it works.

 

Sigh. We are 100% certain that your PC is a binary machine, yes? And your PC, using strictly binary logic, can represent and calculate numbers using any base we please, yes? In case you dispute this, type in "0x10 + 0x10" in google and you will get the correct answer, 0x20. Type in "7 + 6" and you will get the correct answer, 13. No human is translating those strings into binary behind the scenes, right?

So, if a strictly binary computer can use any number base, why do you think my human brain could not do the same?

Numbers are independent of their representation.

This is the confusing element.

Whether we use 16 or 0x10 or 0b10000, we are referring to the same number. Whether the underlying circuitry is designed as base-10 or base-16 or base-2, the result is always the same: a number that can be represented in any base we like.

Of all the possible state representations that my brain may be using to hold the concept of 342, it is almost CERTAINLY not ten on/off voltage states. You are confusing the base-2 representation of a number with the CONCEPT of that number. Do you really think that somewhere in my brain there are ten neurons that represent the number 342?!? If a surgeon kills these neurons with a laser, will I stop knowing what 342 is?!?

If you actually believe this, then we need to address this ASAP as this is a profoundly important misconception.

This is a great zoom level—let's stay right here!

"Whether we use 16 or 0x10 or 0b10000, we are referring to the same number."

10,000% TRUE ALL DAY LONG.

Let's take it one thought at a time from here.

Number 342. The number ITSELF is what precisely in your binary brain? Be VERY specific, please.

 

"Wigglerrhea"


I couldn't disagree more. I might agree with you if we interpreted our visual field as a bunch of uniform, discrete blocks of stuff. Block of stuff there, or block of stuff not there. Only blocks of stuff around here.

But we don't interpret our visual field that way. There is an enormous amount of information being conveyed by the light that hits our eyes (I remember an estimation of 2 GB per second). While each photoreceptor in our eye is independent, behaving pretty much like a simple on/off switch, the photons in the light are not independent -- they each carry a bit of information from the multi-bit scene that's playing out in our field of view.

The light coming through the tree canopy casts a complex shadow filled with shapes that move in complicated ways as the tree sways in the wind. It's absurd to suggest that my brain takes in this information and responds "SORT OF CRESCENT-MOON SHAPE" or "NO SORT OF CRESCENT-MOON SHAPE" every instant for every patch of space.

That's not at all how it works.

Correct, because Newton would hit you over the head with a medieval dowel he made out of cow fat and say "Ohv cohse! Eet is in the foyv D!"

There are no continuous forms in the discrete-bit brain as described, QED all day long. Think about any form, close your eyes, and no such form exists. A car? A cow? A dog? Where is the actual contiguous-bit form in the brain? No where. No different than if you spread the bits out over 300 miles.

There are discrete bits, not continuous forms.

This cannot be argued. YOu must prove to me that when you think of any "slobbering dog form on Subjectus street" that the form you are looking at in your mind exists as your are describing it. It simply doesn't! Because THIS is the basis of mystery "conscious meaning," which is as the intersection of digital, infinite, and geometric. A state machine has discrete bits that can ONLY represent continuum.

There are NO sine waves in the brain!!

There are bits that represent the sine wave it heard! And SOMETHING had to tell the brain to discretize the continuous wave in a way to store the bits. Again, nondescript bits, that have NO IDEA they correlate to the wave!!

 

Mr Irℝational-as-Freudian-slip?,

Nah, a show of solidarity to my brothers and sisters in { ℝ - ℚ }.

I appreciate the Banachionics — very clear.

Thanks.

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

The sobering truth is that we don't know how to compose the vast majority of numbers in ℝ. Here is an easy to follow proof.

Any algorithm to compose a number in ℝ can be implemented as a computer program. For example, a program to calculate the digits of Pi is trivial to write. (We don't care that the program will never finish, we just care that there is an algorithm.)

Any program can be written as a unique binary string, e.g., "01101001000101" but much longer.

The set of all such strings is a countable infinity. That is, we can create a one-to-one correspondence between a program and a unique natural number, for every possible program.

The cardinality of ℝ is uncountable.

Thus, there are vastly more numbers in ℝ than there are possible programs.

Therefore, most numbers in ℝ cannot be composed. QED.

Incidentally, this same argument shows you why we can't use integers to compose every number in ℝ (there are exactly as many integers as there are possible computer programs: both map uniquely to binary strings).

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.

But you ignore all the scientific reasons why forces are considered old-fashioned. It's not an aesthetic decision.

Oh, and FYI, I have no problem whatsoever with Michael Faraday. The guy intuited fields with barely any mathematical training, I'd definitely buy him a beer. His "lines of force" explanation was obviously a product of its times. I don't judge him for it at all.

BTW, you should check out Feynman's lecture where he explains how the magnetic field is actually the relativistic effect of the electric field, though I don't know if you'll be thrilled or horrified. ;-)

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?)???

I have always said that number base is irrelevant, so yes, of course we can represent any of these numerical ideas in any base we want, including base-2. My proof above used base-2. Base-2 is a lovely number base.

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

Dear Herr Doktor Kronecker,

Peter Dirichlet would like to have a few words with you.

Sincerely,
Georg Cantor

 

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?

Hrm? I haven't ascribed a geometry to any of this; that's your bag of soup.

 

"Evolve over time??" Eventually you "evolve" into the dirt you came from.

And?

 

And?

You are too much!

So when your Uncle Friedrich died, and they put him in an urn and his ashes were thrown over the Atlantic, is he still "evolving" as we speak, because I just wan... <<PAGING DOCTOR BROWN TO THE E-WING, DOCTOR BROWN>> want to know exactly what you mean by the fact that your patent decomposition is a "form of evolution?"

 

Hrm? I haven't ascribed a geometry to any of this; that's your bag of soup.

We were talking about that dog™ earlier, and how generally speaking a QED for most intelligent human beings is that the thing exists in 3 measurable, observable dimensions of x, y, z. Your explanation for how the dog's "3D" data gets represented as 1D is that the "dog isn't really 3D." Science has traditionally used empirical observation as part of the scientific method to define things. I know actual sensory observation is sooooo 15th century, but humor me here. ;--)

You are not really a 3D element in nature, according to your definitions, because a "real form does not exist" independent of your states.

You? Nail? iPhone? These things are not real 3D objects to you.

 

This is a great zoom level—let's stay right here!

"Whether we use 16 or 0x10 or 0b10000, we are referring to the same number."

10,000% TRUE ALL DAY LONG.

Let's take it one thought at a time from here.

Number 342. The number ITSELF is what precisely in your binary brain? Be VERY specific, please.

As we have yet to map out exactly how the brain works, this is a guess. But I can imagine how I would teach a computer about the number 342 and then extrapolate to my circuits.

Before I can hold the concept of the number represented by 342, I need to have the concept of number. That comes from the concept of counting, and includes INFINITY and some other useful stuff. So, now that I have a bunch of number-associated concepts, I can begin formulating concepts of specific numbers. Of course, I have zero concept of most numbers, simply because there are far more of them than I have memory, and most of numbers are uninteresting to me. For example, the number 3846758489373829104 is not in my head. I typed random numbers for a second or two and didn't even bother to consider what order of magnitude the number is.

Now, the number 342 seems rather pedestrian to me and probably doesn't hold much conceptual value. It is, however, a "human-sized" number and so carries with it some conceptual luggage. For instance, 342 pounds is a fat person but a light glider (as in engine-less airplane); $342 a week is a sh!tty paycheck, but $342 an hour is great. So, though I don't think much specifically about 342 (besides a few simple properties like "it's even", "it follows 341", etc.), it does carry a few associations. In particular, our having shone a spotlight directly on 342 in the context of this discourse induces a few more associations.

So, I'd say that, architecturally, the situation in my brain looks something like this: the symbols "342" act like pointers to several concepts. A few of these concepts -- NUMBER, "conversation with Jennifer about numbers" -- provide the most conceptual weight, the things that I most strongly associate with the number 342. There is a also a pointer to short-term memory (cache?) where I hold the states representing the symbols themselves and a few other relevant details, like the contents of my current thought process, most of which at this moment relate to 342 in some way or another.

In contrast, the number Pi has a lot more associations and requires a lot more storage space in my brain. This has nothing to do with its length -- I can only remember Pi to a few decimal digits -- rather it's a function of its importance to me. In engineering, Pi shows its face frequently. Then, there's the whole "mysterious" aspect of Pi that people seem to love ("contains all the plays of Shakespeare!") and makes me cranky for some reason.

I'd say that Pi's digits -- the four or five I can remember -- are probably stored in a big network of neurons that represent "memorized numerals" that are specifically associated with the concept of numbers (as opposed to, e.g., the big matrix of "memorized telephone digits" neurons). I can practically guarantee that the digits "3.141" or whatever are not stored as a short binary sequence of on/off voltages in a handful of neurons.

 

There are no continuous forms in the discrete-bit brain as described, QED all day long. Think about any form, close your eyes, and no such form exists. A car? A cow? A dog? Where is the actual contiguous-bit form in the brain? No where. No different than if you spread the bits out over 300 miles.

I don't understand what you're saying.

Here's where I'm at: you say that the universe is binary, that fundamentally there is "presence" or "no-presence". You claim this is how our brains work, too: I see a dog or I don't see a dog.

I say that the brain does not work that way. I gave the speckled tree shadow example to refute the binary nature of experience.

You replied with the above, and I don't understand what you're saying.

YOu must prove to me that when you think of any "slobbering dog form on Subjectus street" that the form you are looking at in your mind exists as your are describing it.

I have to prove what now? When I imagine a dog, what I am visualizing doesn't exist externally. What am I supposed to prove?

 

Nah, a show of solidarity to my brothers and sisters in { ℝ - ℚ }.


Thanks.


The sobering truth is that we don't know how to compose the vast majority of numbers in ℝ. Here is an easy to follow proof.

Any algorithm to compose a number in ℝ can be implemented as a computer program. For example, a program to calculate the digits of Pi is trivial to write. (We don't care that the program will never finish, we just care that there is an algorithm.)

Any program can be written as a unique binary string, e.g., "01101001000101" but much longer.

The set of all such strings is a countable infinity. That is, we can create a one-to-one correspondence between a program and a unique natural number, for every possible program.

The cardinality of ℝ is uncountable.

Thus, there are vastly more numbers in ℝ than there are possible programs.

Therefore, most numbers in ℝ cannot be composed. QED.

Incidentally, this same argument shows you why we can't use integers to compose every number in ℝ (there are exactly as many integers as there are possible computer programs: both map uniquely to binary strings).


But you ignore all the scientific reasons why forces are considered old-fashioned. It's not an aesthetic decision.

Oh, and FYI, I have no problem whatsoever with Michael Faraday. The guy intuited fields with barely any mathematical training, I'd definitely buy him a beer. His "lines of force" explanation was obviously a product of its times. I don't judge him for it at all.

BTW, you should check out Feynman's lecture where he explains how the magnetic field is actually the relativistic effect of the electric field, though I don't know if you'll be thrilled or horrified. ;-)


I have always said that number base is irrelevant, so yes, of course we can represent any of these numerical ideas in any base we want, including base-2. My proof above used base-2. Base-2 is a lovely number base.


Dear Herr Doktor Kronecker,

Peter Dirichlet would like to have a few words with you.

Sincerely,
Georg Cantor

Tell Peter I'm not available, I'm busy talking to a 2D puddle in a forest who thinks he's 1D but can reference and store 3D info about a reality he doesn't think exists.

Therefore, most numbers in ℝ cannot be composed. QED.

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.

Incidentally, this same argument shows you why we can't use integers to compose every number in ℝ (there are exactly as many integers as there are possible computer programs: both map uniquely to binary strings).

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

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.

 

You are too much!

So when your Uncle Friedrich died, and they put him in an urn and his ashes were thrown over the Atlantic, is he still "evolving" as we speak, because I just wan... <<PAGING DOCTOR BROWN TO THE E-WING, DOCTOR BROWN>> want to know exactly what you mean by the fact that your patent decomposition is a "form of evolution?"

Of course. We don't stop existing (or changing!) when we die. Our states transform to other states. Ashes to ashes, and states to states.

What's the big deal?

 

Of course. We don't stop existing (or changing!) when we die. Our states transform to other states. Ashes to ashes, and states to states.

What's the big deal?

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?

 

We were talking about that dog™ earlier, and how generally speaking a QED for most intelligent human beings is that the thing exists in 3 measurable, observable dimensions of x, y, z. Your explanation for how the dog's "3D" data gets represented as 1D is that the "dog isn't really 3D."

I see. Ok, let me clarify. I said that we do not know the fundamental geometry of the universe, or even if such a thing can be cogently described. Science has shown us that, if we're going to use a geometry to characterize the universe, then we need at least a four-dimensional geometry. In other words, treating the dog as a "3D" object is, at best, a simplification. It's almost certainly not a fundamental truth.

More importantly, and this is where we should focus, bits are not 1D geometrical objects. We can use bits to hold the information of a geometry, but bits are not themselves geometrical. So, when you say things like "represent 3D data in 1D", you're not speaking cogently. You might as well be saying "represent square things in orange colors".

I know actual sensory observation is sooooo 15th century, but humor me here. ;--)

Literal lol!

You? Nail? iPhone? These things are not real 3D objects to you.

Let's assume, for argument's sake, that the universe is 11-dimensional. In that case, the nail, the iPhone, and my skull are all 11-dimensional. Why couldn't an 11D someone drive an 11D nail through my 11D skull?

 

I see. Ok, let me clarify. I said that we do not know the fundamental geometry of the universe, or even if such a thing can be cogently described. Science has shown us that, if we're going to use a geometry to characterize the universe, then we need at least a four-dimensional geometry. In other words, treating the dog as a "3D" object is, at best, a simplification. It's almost certainly not a fundamental truth.

More importantly, and this is where we should focus, bits are not 1D geometrical objects. We can use bits to hold the information of a geometry, but bits are not themselves geometrical. So, when you say things like "represent 3D data in 1D", you're not speaking cogently. You might as well be saying "represent square things in orange colors".

Literal lol!

Let's assume, for argument's sake, that the universe is 11-dimensional. In that case, the nail, the iPhone, and my skull are all 11-dimensional. Why couldn't an 11D someone drive an 11D nail through my 11D skull?

Ok, again the whole existing nomenclature "butt-up" issue.

But I feel we have found the proper zoom level (and actual hope for a better foundation) with this other post about you existing as Javier in "different states" over the Atlantic, because this is the exact kernel I've been trying to get to for us to frame the foundation of the house.

 

Sigh. We are 100% certain that your PC is a binary machine, yes? And your PC, using strictly binary logic, can represent and calculate numbers using any base we please, yes? In case you dispute this, type in "0x10 + 0x10" in google and you will get the correct answer, 0x20. Type in "7 + 6" and you will get the correct answer, 13. No human is translating those strings into binary behind the scenes, right?

So, if a strictly binary computer can use any number base, why do you think my human brain could not do the same?

Numbers are independent of their representation.

For the record, I believe there are 2 levels of representation, and that's the confusion here. We will get there starting from your ashes over the Atlantic.

Also, there is one man who exactly parallels my intuition: Pythagoras. My thoughts are Pythagorean more than even Kroneckarian. I believe 1 is the only true integer, and the rest are contrivances, and the real numbers are even derivative of those.

1 is “Assembly”
Integers are “MS Basic”
Reals are C#

There is a proof buried somewhere, but 1 is essentially the set of all numbers. 0 is the potential for the set.

A modern computer proves the representation of all mathematical operations and number sets, using 1 and its complement as the sole basis. QED.

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.

 

I don't understand what you're saying.

Here's where I'm at: you say that the universe is binary, that fundamentally there is "presence" or "no-presence". You claim this is how our brains work, too: I see a dog or I don't see a dog.

I say that the brain does not work that way. I gave the speckled tree shadow example to refute the binary nature of experience.

You replied with the above, and I don't understand what you're saying.

I don't understand what you're saying.



Here's where I'm at: you say that the universe is binary, that fundamentally there is "presence" or "no-presence". You claim this is how our brains work, too: I see a dog or I don't see a dog.



I say that the brain does not work that way. I gave the speckled tree shadow example to refute the binary nature of experience.



You replied with the above, and I don't understand what you're saying.

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). And then there is a binary form of experience one might call COMPUTATION, that can essentially REPRESENT the FEEL element in binary data. One might roughly correspond the right hemisphere to FEEL, and the left to DIGITAL COMPUTE. The computation of the numbers and the numbers themselves are irrespective of the representation of the experiential data, though "base experiential worth" is tied to "meaning" which is tied to what the numbers are representing.

In my model, there is a 3D dog in physical space, and a continuous form in the 5D mind and ALSO numbers that correspond to both! Just sharing theory right now.

The "data acquisition scenes" of James Cameron's Terminator 2 are the perfect explanation of how a state machine is progressively "matching" using binary true/false states to determine what it's programmed to look for is a match. But "feeling" has nothing to do with it.

The machine's "reasoning" is entirely "on and off"-based to arrive at "what the machine needs". I do not think this is farfetched whatsoever, and is based on the computational procedure a human might do:

He's got 3 functions running:

acquire_motorcycle();
acquire_boots();
acquire_clothes();

This is precisely how Watson beat Ken Jennings in Jeopardy. Watson is a very basic concept of reasoning using highly tuned classification and collation of data to syphon relevancies and arrive at a "score" on a score card.

Watson's reference point was all of Wikipedia. So breaking down the query into progressively smaller or zeroed-down "compartments" of data is how it fetched the relevant info from the database.

A person might go into a store with acquire_shirt(). Man A, using almost no feeling or sense of style will go into the store with "subjective feeling" having almost nothing to do with the variables. He's no different than the terminator above.

He walks in with acquire_shirt() running. To determine a shirt is actually "a shirt" is by way of the same brute force sequence. It may be eliminative in nature. where_am_i() == store? -> department store TRUE -> electronics dept == true? re-route() --> men's department TRUE -> current_item==shoe OR shirt OR pants OR belt TRUE -> shirt probability = 98.43% -> run shirt-specific data-acquisition subroutines.

Utility of the shirt is all the function is looking at. Shirt.color can be white or blue. Shirt.pattern can be plain or plaid. Shirt.fabric can be cotton or polyester. Shirt.size can be large. First shirt that matches TRUE to all 4 criteria means buy_now().

All that is needed is a LOT of presence/absence data like the Terminator or Watson. If Watson was in a compact quantum computer from 2040, what's the difference between the algorithms that beat Ken Jennings? Nothing, just optimized and hella faster. It's simply high speed binary logic data matching. The brain can most certainly behave in this manner, as John Von Neumann believed (and who can get any more qualified to say it).

And the more data available to match, the more you have potential for "grey area" fuzzy AI elements.

 

I see. Ok, let me clarify. I said that we do not know the fundamental geometry of the universe, or even if such a thing can be cogently described. Science has shown us that, if we're going to use a geometry to characterize the universe, then we need at least a four-dimensional geometry. In other words, treating the dog as a "3D" object is, at best, a simplification. It's almost certainly not a fundamental truth.

More importantly, and this is where we should focus, bits are not 1D geometrical objects. We can use bits to hold the information of a geometry, but bits are not themselves geometrical. So, when you say things like "represent 3D data in 1D", you're not speaking cogently. You might as well be saying "represent square things in orange colors".

Ah, but they’re connected, and that’s what I’m driving at. Yes, I’m aware a bit has no geometric form, lol. 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).

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.