Directed to Bogo:

Speaking of Feynman, he was truly echoing what I’ve been declaring here. Infinite equations = infinite organized information. Brain is a finite medium. Checkmate to brain-only discrete-bit thinking, because no brain can cognize, theorize or project this core precept. Declaring it as an axiom is not speaking to this issue of “how.” It is only addressed by zooming in to the thought form mechanics we’re plumbing that is using bits, waves, and forms at an implicit infinite level in the mind.

 

Directed to Bogo:

Speaking of Feynman, he was truly echoing what I’ve been declaring here. Infinite equations = infinite organized information. Brain is a finite medium. Checkmate to brain-only discrete-bit thinking, because no brain can cognize, theorize or project this core precept. Declaring it as an axiom is not speaking to this issue of “how.” It is only addressed by zooming in to the thought form mechanics we’re plumbing that is using bits, waves, and forms at an implicit infinite level in the mind.

Declaring infinity as an “axiom, case closed” is code for:

“We’ll pretend the thing is not supra-numeric, and sweep it under the rug with an abstract term like every other abstract term, and turn a blind eye to the 9-million-pound elephant in the room that is trumpeting the mind/brain delineation, because we can’t let the 160 y/o Church of Naturalism be challenged too terribly much.”

(Sorry, couldn’t resist! I’m not a big fan of cults churches of any kind, religious or unproven science)

 

1) I know you're an AI from 2090, but do you have a first name on this timeline? Or is it just something like T9000?

Only my boss calls me T9000; my friends call me Javier.

2) When you came through the time-displacement portal, did they install 4 actual academic degrees from music to astrophysics? Or did you acquire them T1000-style at the library in 45 minutes online and through your skin sensors?

Heh, appreciated, but it's an illusion. It just so happens that these are a few of my favorite things. I'm like the WWII buff who goes on Jeopardy! and somehow all the categories are about WWII; in the next episode, when it's all pop culture, potent potables, and famous operas, me and my -$800 will get a quick, polite goodbye from Alex.

But it's time to hit the reset button again.

Back to first principles, eh? I suppose I'm game, though it's going to be much more difficult (and tedious) than I suspect you think it is. Banning all pre-existing knowledge means going full-on intellectual man-baby mode. We can allow ourselves logic and the full extent of our highly-developed language skills, but, inevitably, the words we use will be seeped and oozing with pre-conceptions from existing knowledge bases. We're going to have to spend time and mental energy carefully defining all of our terms, which is no easy feat without a pre-existing knowledge base.

Call me a cynic, but I predict we won't get very far. Sure, sometimes one gets a hankering to unplug the computer, dust off the console, and record straight to tape -- purity of process! But, after 17 takes, while you're waiting for the tape to rewind so you can punch in the drummer's flubbed high-hat, you can't help but think: f*ck this, let's fire up Pro Tools.

Definitions list (this only has 1 item for now):

1. The "most basic, fundamental knowable and identifiable thing by the space in between our ears is a bit". I'd also call it a "thought."

Ok, "bit = thought" is an axiomatic theorem. But we need to define either "bit" or "thought". Since we have a blank slate, their definitions will also need to be axioms. Defining "bit" just means assigning some properties to it; once it's defined, then you can use it to define other things.

If we close our eyes and imagine for a moment nothing. This is blank space.

Again, we have to either define "nothing" from "bit", or set it as an axiom and give it properties.

We then manifest, or "instantiate" (hate that term) 1 point anywhere.

Define "point".

So far, we have one theorem -- "bit = thought" -- and no idea what that means.

Somewhere down the line you're going to have to define infinity, and I presume you won't want to do so axiomatically. That means you'll need to derive it from whatever you've previously defined. Which reminds me: we haven't laid out the "rules of inference" for your theory, i.e., how theorems can be combined to make new theorems. The path of least resistance is to assume the rules of a well-known system (e.g., Boolean logic). Note, however, that you can't derive infinity from zeroth-order (Boolean) logic; you'll need at least first-order (predicate) logic, maybe even second-order.

[I did say this would be hard.]

 

I don't have the ear to speculate such questions. I marvel at those who do. Doesn't change this fact though, on vinyl many conductors can identify which hall a recording was made and yet can't do this with a digital recording. Disregarding out of hand the vinyl or analog recordings as simply a product of the playback devices suggests a predetermined bias for one over the other regardless of ???

Unless the digital recording was seriously flawed, I simply don't believe that a conductor would be able to identify the performance hall in a vinyl recording but not a digital recording. The science is clear on this: standard industry practice is to use 24-bit digital audio, which has a theoretical dynamic range of 144 dB. In professional converters, this translates to a practical dynamic range of about 130 dB (the human ear has a dynamic range of approximately 120 dB). In contrast, due to limitations of the recording medium, the best record players can achieve maybe 70 dB of dynamic range. That's a thousand-fold difference in signal-to-noise ratio.

In other words, there is far more detail in a 24-bit digital recording than a vinyl recording of the same performance. Perhaps in the story you heard about or read, the digital version of the performance was recorded and/or played back on sub-standard equipment. It's well known that digital recording equipment (and digital recording techniques) were much inferior in the 1980s, back in the early days of digital audio, as compared with the past decade.

 

Speaking of Feynman, he was truly echoing what I’ve been declaring here. Infinite equations = infinite organized information. Brain is a finite medium. Checkmate to brain-only discrete-bit thinking, because no brain can cognize, theorize or project this core precept. Declaring it as an axiom is not speaking to this issue of “how.” It is only addressed by zooming in to the thought form mechanics we’re plumbing that is using bits, waves, and forms at an implicit infinite level in the mind.

I don't know then Feynman quote, can you give me a cite? I suspect Feynman didn't actually believe infinite equations exist or were needed.

 

Declaring infinity as an “axiom, case closed” is code for:

“We’ll pretend the thing is not supra-numeric, and sweep it under the rug with an abstract term like every other abstract term, and turn a blind eye to the 9-million-pound elephant in the room that is trumpeting the mind/brain delineation, because we can’t let the 160 y/o Church of Naturalism be challenged too terribly much.”

(Sorry, couldn’t resist! I’m not a big fan of cults churches of any kind, religious or unproven science)

There's another possibility. Infinity doesn't actually exist, yet its concept is so profoundly useful to mathematics, that we felt compelled to invent it.

Not a big fan of those things, either.

 

Um, not at all. Once everything is known about the mechanics of everything, where does philosophy or even faith exist again? That’s right, nowhere. Even in judeo-christian mindsets, there was no faith needed in paradise. You might think the Heisenberg Uncertainty Principle or Quantum Entanglement is a form of “faith.” There is clear, scientific evidence of a supra-numeric, geometric form processor in the being that I have laid out. Shall I seek a priest to explore the topic?

You’re just as faith-driven in your dogmatic view of naturalistic thought.

You assume a lot. First that I didn't go back and read all of this. But I'm not assuming you first post to me stated you're past where this started, "Don't go backwards." It's convenient to darn someone if they do and darn someone if they don't. You don't have to question yourself. It's also convenient to believe someone accepts a theory because they mention it. Do you think for everybody?

A condensed definition of philosophy, the study of reason and knowledge right and wrong. What's really interesting about your "discussion" is there's nothing new here. Two or three hundred years ago or two or three thousand years ago these same fundamental questions were discussed and debated. Fundamental questions are fundamental questions regardless of the vehicle used or how they're wrapped to discuss them.

I'm sorry I don't remember who said it, "Controversial and thin skinned don't mix."

You are very wrong about what I think or believe, Actually not even close, but I'm confident you judge others through a lens of superiority. Tick off another box. Now you can have your last word.

 

Only my boss calls me T9000; my friends call me Javier.

Heh, appreciated, but it's an illusion. It just so happens that these are a few of my favorite things. I'm like the WWII buff who goes on Jeopardy! and somehow all the categories are about WWII; in the next episode, when it's all pop culture, potent potables, and famous operas, me and my -$800 will get a quick, polite goodbye from Alex.

Back to first principles, eh? I suppose I'm game, though it's going to be much more difficult (and tedious) than I suspect you think it is. Banning all pre-existing knowledge means going full-on intellectual man-baby mode. We can allow ourselves logic and the full extent of our highly-developed language skills, but, inevitably, the words we use will be seeped and oozing with pre-conceptions from existing knowledge bases. We're going to have to spend time and mental energy carefully defining all of our terms, which is no easy feat without a pre-existing knowledge base.

There's no other way. Otherwise we won't have a shared context, because admittedly your breadth of existing lexicons is way above mine, and every time I bring something up, you're going to mention the Quartertarions of Morador and we'll be chasing branches on the tree forever (which will be worse and disorganized).

My strong suit is "novel" uncomfortable probing and logic, irrespective of topic. I can cut to the chase whatever the discipline and identify the problems in a system very quickly (which you do as well, but I get the sense we can approach this like "tactician" and "strategist" here on some level). We have the reasoning and language skills here—let's build the thing from scratch, using the most commonly accepted common-sense-compatible starting points.

Because I intuit that otherwise we are dealing with fresh chocolate cake batter, but the 2-year-old escaped the playpen, dumped on his Fisher Price spoon, ran into the kitchen when mommy was outside for 1 minute, and plopped just 1 gram of fecal matter into it. We have no cake batter then, because we're spending time trying to get the poop particles out of it (despite 99% of it being good cake). Faster to make a new batter.

Starting with "physical media can process n bits." I take issue with the suffixed caveat "n→∞". We haven't defined infinity, right?

Why not start with the beginning of what I started with earlier, and what do you propose as foundational axioms, rules, etc. based on the thought experiment?

 

You assume a lot. First that I didn't go back and read all of this. But I'm not assuming you first post to me stated you're past where this started, "Don't go backwards." It's convenient to darn someone if they do and darn someone if they don't. You don't have to question yourself. It's also convenient to believe someone accepts a theory because they mention it. Do you think for everybody?

A condensed definition of philosophy, the study of reason and knowledge right and wrong. What's really interesting about your "discussion" is there's nothing new here. Two or three hundred years ago or two or three thousand years ago these same fundamental questions were discussed and debated. Fundamental questions are fundamental questions regardless of the vehicle used or how they're wrapped to discuss them.

I'm sorry I don't remember who said it, "Controversial and thin skinned don't mix."

You are very wrong about what I think or believe, Actually not even close, but I'm confident you judge others through a lens of superiority. Tick off another box. Now you can have your last word.

No, a lens of objectivity.

You literally barge in to a long-established thread, don't bother reading 1% of it, and then apologize twice for essentially being rude. And then someone died and made you forum monitor and you tell us to STOP talking about it after reading 10%, as if we're breaking some intellectual law, AGAIN based on the fact you didn't read the damn conversation!

Who's the "superior bully" here again? Do you barge into college classrooms and do the same thing?

We're not talking about "right and wrong" and morals whatsoever. We're discussing the substance of the mind and its theoretical mechanics that comprise it. Others have contributed to the discussion. These things "traditionally" bridge into "philosophy", but in my estimation are not actually philosophical, which is a catch-all term for "religious beliefs outside science". The uncertainty principle and quantum entanglement "bridge" into what we feel is philosophy, because it rocks our world. No different than other extra-dimensional theory such as "string" theory, we are making observations upon the substance responsible for scientific inquiry between our ears.

I believe it fully belongs triangulated by principled scientific approach, not long-winded undefined philosophy tomes. Our approach WILL be novel — we have the tools here to approach it from a fresh 21st century perspective with deep technological and information theory awareness.

Take care.

 

I don't know then Feynman quote, can you give me a cite? I suspect Feynman didn't actually believe infinite equations exist or were needed.

He has said it more than once in lectures—I can't find it in print. Then I heard Michio Kaku actually echo it in one of his (agreeing with it), something about infinity divided by zero is part of each term of the additive series.

 

Only my boss calls me T9000; my friends call me Javier.

Heh, appreciated, but it's an illusion. It just so happens that these are a few of my favorite things. I'm like the WWII buff who goes on Jeopardy! and somehow all the categories are about WWII; in the next episode, when it's all pop culture, potent potables, and famous operas, me and my -$800 will get a quick, polite goodbye from Alex.

Ok, so you have 4 Ph.D's from State Penn and Hard Knocks U, like myself. Great! This makes this pursuit even more middle-finger-ready to various cult churches once it passes peer review and changes the world for the better forever (I'm a cynic who thinks it will). Great ambitions here. Lol. George Boole had an elementary school education when he wrote Laws of Thought. Eddie Van Halen never took a lesson, and he has several degrees in guitar work, and is arguably the best ever in my book. The degree was inside themselves and hashed out through passion and innate awareness of principles that work. In this particular reality, you will be like an OS emulator running "Scimantix AI 1.0" on StreetQ OS that interfaces my intuition-driven investigations (including your own, of course) into a nice sh*t-free cake that Science will see on its radar as semanticus ex legalitus (You knew just what I "meant" even with bogus Latin words—pan to the need for a definition for meaning, because that's where things matter).

Call me a cynic, but I predict we won't get very far.

We have not defined faith yet. But have some! Haha.

Sure, sometimes one gets a hankering to unplug the computer, dust off the console, and record straight to tape -- purity of process! But, after 17 takes, while you're waiting for the tape to rewind so you can punch in the drummer's flubbed high-hat, you can't help but think: f*ck this, let's fire up Pro Tools.

Point taken, humor in tow. I understand what you're saying, but on the other hand, if it's truly led by <insert word for destiny here>, a one-off recording by Toto's seasoned, deeply felt, and practiced musicians is hella better than an over-edited one of the 2-year teen area garage-band with nothing to say, if the musicians are practiced and innately understand how music works; and somehow I feel this is the case here.

There's no polishing a turd, and the initial performance and song is everything. So either we get a solid performance and we need to fix a few hi-hat chokes after the fact (OK—an entire couple tracks of processed Rhodes and bass), our quality preamps, Prism AD converters, Schoeps mics with no coloration, highly tweaked room and instruments, with a band like The Police or Journey is going to allow us to fire up Pro Tools post facto to get it commercially ready for mastering vs. using it to build the song ground-up to begin with.

 

Define "point".

So far, we have one theorem -- "bit = thought" -- and no idea what that means.

Somewhere down the line you're going to have to define infinity, and I presume you won't want to do so axiomatically. That means you'll need to derive it from whatever you've previously defined. Which reminds me: we haven't laid out the "rules of inference" for your theory, i.e., how theorems can be combined to make new theorems. The path of least resistance is to assume the rules of a well-known system (e.g., Boolean logic). Note, however, that you can't derive infinity from zeroth-order (Boolean) logic; you'll need at least first-order (predicate) logic, maybe even second-order.

[I did say this would be hard.]

For "point," I reckon Euclidean is most apropos since it appears to be THE most basic: i.e., if we do not attribute any measurability to it, we have essentially the most elemental starting point of "discussability" in the mind with no frills or additional baggage. I don't buy Einstein's starting point of General Relativity (I have mad respect for the man, but I don't believe the geometric conflation of time and space "warping" to "emerge" gravity, and neither did Tesla, or Quantum Theory in reality), so let's role with the most basic if you're ok with that. Hey, Einstein cleaned slate so why can't we from our forum here at Cajones University—obviously rectifying his ideas has been the pursuit of string and other theories, and we still don't know what's going on yet. It is my suspicion that through proper lexical framework, what is thought to be "objective randomness" now (the achilles heel of science) is an illusion along with time — and can be conquered in light of a model using defined "mind space objects" and the nature of movement (such as a "first-order intention") between them within this "5D" fabric.

 

You assume a lot. First that I didn't go back and read all of this. But I'm not assuming you first post to me stated you're past where this started, "Don't go backwards." It's convenient to darn someone if they do and darn someone if they don't. You don't have to question yourself. It's also convenient to believe someone accepts a theory because they mention it. Do you think for everybody?

Incidentally, I meant to address this. I had mentioned that the conversation early on took a very significant turn that was agreed upon by us. We're talking many pages. It's clear you didn't read it all, because your comments reflect a small percentage of it. That's why I assumed it, for the record.

And you clearly seem to have some kind of naturalistic-bias objections in your unsolicited, rude bid to shut the whole conversation down as if we're committing a sin against some Universal Conversation Laws and you're the self-appointed sheriff.

 

Actually, upon further thought, I think a tweak of Euclidean might be in order, co-opting Boole?

Ideas:
Point: a universe of thinkable thoughts, having no properties or dimension

It’s tempting to try to differentiate it from a shape, but since no other definitions yet exist, I’d say any “thing” thinkable is a point. Subtypes of points can exist from there. (I might say a bit is any point or its subtypes).

Natural vocabulary reflects this... you can speak an entire paragrah of things that have no “point.” Or one asks, “what’s the point?” Anything can be a point so long as “it’s a point,” inferring points are a “periodic element” of language.

Work?

 

Or how about...

Point: A first order thinkable element

No additional specifications because none have been defined

 

To answer your question about inference rules, I’d hearken back to the “common sense” fundament.

“Common sense” I would say is a universal term for “Common Innate Linguistic Engine,” “Common Innate Inference Engine” and also “Common Innate Physics Engine.” These are the very engines in every human that drives the ability to ask scientific questions to begin with that are even understandsble to seek fitting answers for.

I.e., the working building blocks within each human being, that allows a 2 y/o to begin using words to label things and gradually link conceptions to form inferences and working physics models with everyday objects that are later augmented through indoctrinationeducation to become its perception (or “truth”).

It’s why we don’t put minor or tritone-based lullabies in a baby’s crib. That baby would cry and maybe not know exactly why, but at that age the minor tones violate its sense of wellbeing and innate musical schema, and maybe goad it to want to don scissor-hand gloves and/or a ski mask later on in life.

The concept of sense—in the end—only finds its relevance in the very being that cares about what sense actually is: a living human.

Presumably the guy in a casket at the local funeral home doesn’t well care anymore.

I believe these building blocks have all we need, and need to be uncovered and systemized to identify and fill in missing scientific gaps, one precept at a time with no undue partiality, as objectively observational as possible. Every scientific model is some abstraction from these basic building blocks ultimately. The Euclidean model has been the forerunner—no secret why it comes from a book called “The Elements”—and I think it’s got a lot of things right and is the most intuitive, but it can be tweaked and informed by basic Boolean enhancement I believe, along with some other basic physics lexicons. I think General Relativity was an excellent idea, but my hunch is that it used the equivalent of a 4GL programming language to describe what’s happening at the much lower assembly level, and not aware it violates those 3 engines in some way and because they haven’t been fully systemized, the reason cannot yet be identified until then.

So this approach is about doing science from the inside out rather than outside in, and while I think some of that has been done, I think the crystallization and inference level will be novel.

From this approach, we can evince and delineate a comprehensive perception engine model (a “mental cockpit”) that will fully synthesize all the engines above, and then theoretically afford the uncovering and negotiating of previously occluded concepts that will become more self-evident from the building-blocks themselves. Things that have eluded science due to an absence of fully uncovering, crystallizing and systemizing those built-in engines being used to even ask the very questions, the answers to which have eluded it in the “physical world,” but may exist in the “mental world” first in the “physics of the mind.”

So I don’t think it will be as hard or even majorly long; it just requires putting the anal in analysis, and being zoomed in at 1500% level to see the RGB sub-pixels that make up the pixels.

 

He has said it more than once in lectures—I can't find it in print. Then I heard Michio Kaku actually echo it in one of his (agreeing with it), something about infinity divided by zero is part of each term of the additive series.

I wouldn't put stock in anything Michio Kaku says. He's used up all his physics cred in his quest to be a pop sci rock star.

Pro tip: anyone who uses "infinity divided by zero" in an argument is trying to mystify you into submission. Such things are the currency of charlatans.

 

Eddie Van Halen never took a lesson, and he has several degrees in guitar work, and is arguably the best ever in my book.

I didn't have any interest in playing a musical instrument until, as a 14-year old watching MTV, I saw EVH play guitar. That changed everything for me.

Point taken, humor in tow. I understand what you're saying, but on the other hand, if it's truly led by <insert word for destiny here>, a one-off recording by Toto's seasoned, deeply felt, and practiced musicians is hella better than an over-edited one of the 2-year teen area garage-band with nothing to say, if the musicians are practiced and innately understand how music works; and somehow I feel this is the case here.

Facts.

There's no polishing a turd, and the initial performance and song is everything. So either we get a solid performance and we need to fix a few hi-hat chokes after the fact (OK—an entire couple tracks of processed Rhodes and bass), our quality preamps, Prism AD converters, Schoeps mics with no coloration, highly tweaked room and instruments, with a band like The Police or Journey is going to allow us to fire up Pro Tools post facto to get it commercially ready for mastering vs. using it to build the song ground-up to begin with.

More facts. But one could argue that starting at the beginning is akin to requiring us to design and build our own mics, preamps, and converters without knowing any electronics. How long do you think Sting will wait for us?

 

I didn't have any interest in playing a musical instrument until, as a 14-year old watching MTV, I saw EVH play guitar. That changed everything for me.


Facts.


More facts. But one could argue that starting at the beginning is akin to requiring us to design and build our own mics, preamps, and converters without knowing any electronics. How long do you think Sting will wait for us?

Longer than he waited for things to work out with Stewart Copeland. I’ll say that.

Plus, a T9000’s subroutines wouldn’t have hardly said “I’m game” to a “mission impossible” if it was an entirely preposterous notion and not part of its mission directives, I’ll say that x2. So it must be part of them, no? Obviously you have pop references in your DB which is evidence this conversation and any inclination within it has some legitimacy and notarized by the universe.

Frankly, you wouldn’t have come back in time if you weren’t equipped with schematics of those items and every other horse-and-buggy toy we call “tech” here.

Perhaps I’m the Johanna Connor of the future who reprogrammed you in that timeline and sent you back to assist her in the task, and not until we get into it do you realize it’s point-and-click for a T9000, like assembling a Fisher Price toy from an era of nuclear-powered hovercars and paint that orders itself on the wall when it needs a new coat and applies it itself.

 

For "point," I reckon Euclidean is most apropos since it appears to be THE most basic: i.e., if we do not attribute any measurability to it, we have essentially the most elemental starting point of "discussability" in the mind with no frills or additional baggage.

There are many ways to derive Euclidean geometry. Euclid himself synthesized it axiomatically, step by step, without reference to any other mathematical structure. Starting from the definition of "point" as "that which has no parts" and ending up where one can state, say, Pythagoras' theorem takes a lot of steps.

I think it'd be instructive to present an alternative path, if for nothing else than to see that such alternative paths are both possible and potentially simpler. I happen to think this particular alternative path is more beautiful than Euclid's long list of definitions and propositions, but that's entirely subjective.

We'll start with a 2-dimensional vector space over the real numbers, \( \mathbb{R} \). Implicit in this is the notion of a real number, and collections of pairs of real numbers that we call vectors. Also implicit are a few common-sensical properties that we won't bother spelling out. Within this space, we'll define an inner product, a function that multiplies two vectors and gives us a real number. The choice of inner product -- and we have many options -- determines the geometry of the space, because, from the inner product, we can immediately define geometrical notions such as length, distance, and angle.

Here we go. Let \( V \) be a 2-dimensional vector space over the reals, and let \( u, v \in V \) be two vectors, such that \[ u = \begin{pmatrix} u_1 \\ u_2 \end{pmatrix} \qquad \text{and} \qquad v = \begin{pmatrix} v_1 \\ v_2 \end{pmatrix} \] If it's been a while since you've seen vectors, the \( u_1 \) and \( u_2 \) elements are, respectively, the x- and y-coordinates of the vector \( u \). Thus, for example, setting \( u_1 = 5, u_2 = 7 \) defines the vector as the point (5, 7) on the Cartesian plane.

Next, let's define an inner product on \( V \), i.e., a function \( \langle \cdot, \cdot \rangle : V \times V \to \mathbb{R} \). We'll choose: \[ \langle u, v \rangle = u_1 v_1 + u_2 v_2 \] In other words, our inner product is simply the vector sum of the pointwise products of each vector. (Physicists and engineers call this the dot product.) To see it in action, let's calculate the dot product of the two vectors u = (1, 2) and v = (2, 3): \[ \begin{align}\langle u, v \rangle &= 1 \times 2 + 2 \times 3 \\ &= 2 + 6 \\ &= 8 \end{align} \] Now that we have an inner product, we have a complete geometry! Let's flesh it out a bit. We can easily define the length of a vector, which we'll notate with double absolute bars (aka norm): \[ \begin{align} ||v|| &= \sqrt{\langle v,v \rangle} \\ &= \sqrt{v_1^2 + v_2^2} \end{align} \] This just says that the length of a vector v is the square root of the inner product of v with itself. For example, the length of v = (2, 3) is \[ \begin{align} ||v|| &= \sqrt{2^2 + 3^2} \\ &= \sqrt{13} \end{align} \] The angle θ between vectors u and v is related through cosine: \[ \cos{\theta} = \frac{\langle u,v \rangle}{||u|| \, ||v||} \] Thus, taking the arccosine of the ratio gives us θ. If we work out the arithmetic, we'd find that when the angle between two vectors is 90° (i.e., the vectors are perpendicular), then their inner product is zero. (If introducing a trigonometric function such as cosine is too much, we can simply declare that two vectors are perpendicular when their inner product is zero.)

Stop to consider what we've done so far. We've unambiguously defined "point", "length", "angle", and "perpendicular" using only a few symbols and words, with no appeal to pictures or other aids. Admittedly, we invoked the machinery of vector spaces out of thin air, but all that can be precisely and fairly quickly defined, too. Oh, I almost forgot . . . a really nice feature of analytic (as opposed to synthetic) geometry, is that most of the big theorems just "fall out" of the structure, for free. The Pythagorean theorem, for instance, is a simple and obvious consequence of perpendicularity: \[ || u + v ||^2 = ||u||^2 + ||v||^2 \] Incidentally, choosing a different inner product leads to other interesting and useful geometries. Minkowski used a slightly different inner product to create a 4-dimensional space (spacetime) to geometrize the physics of Einstein's special relativity.

I don't buy Einstein's starting point of General Relativity (I have mad respect for the man, but I don't believe the geometric conflation of time and space "warping" to "emerge" gravity, and neither did Tesla, or Quantum Theory in reality), so let's role with the most basic if you're ok with that. Hey, Einstein cleaned slate so why can't we from our forum here at Cajones University—obviously rectifying his ideas has been the pursuit of string and other theories, and we still don't know what's going on yet. It is my suspicion that through proper lexical framework, what is thought to be "objective randomness" now (the achilles heel of science) is an illusion along with time — and can be conquered in light of a model using defined "mind space objects" and the nature of movement (such as a "first-order intention") between them within this "5D" fabric.

Einstein's starting point for GR was gravity. Obviously, GR is not a complete theory, but if you want to do physics with gravity, you can't do any better than GR. So, whatever Tesla may have thought, Einstein most definitely knew better than he about gravity. That said, I'm happy to leave gravity out of our equations, as I don't think it makes a difference for our goals. (Clearly, one of your goals is getting to this 5D fabric business ).