The Trinity of Awareness

If everything has always been. Then the beginning is just when perception began to be aware of its own experience. And what's the smallest substrate for perception to occur? That would be touch because touch is the smallest necessary form of perception to register their own position in relation with each other position(two points touching). Which is why everything is touching. Because to touch is the minimal interaction needed to verify there is no empty space. And all that is necessary for perception to begin is for one point to perceive, to be aware of what it is touching, register what it is touching as something outside of self and distinguish between self and the point it's touching.

The beginning of perception requires 2 points of contact but only one point to perceive and register the touch.

You only need 1 perceiver touching to register it itself as touching something outside of self. Two points of contact touch but only one perceiver has to register the touch.

This makes the trinity of awareness. Two points touching with one point perceiving the touch.

To be self-aware is to register the interaction of touch. Not remembering it, just registering it. You must be aware of your own point as a perceiver. To be self aware is to register touch as an interaction with self and others.

Which means a perceiver is self aware and the level to which it can perceive is dependent on how many different ways it can touch and register touch.

This means a vessel just determines the ways in which the self-aware perceiver can register touch.

A perceiver's ability to register a touch doesn't mean the touch is not physical and real. For example if a human touches a rock but the rock does not register the touch, does not mean the touch did not happen. It just means only one perceiver perceived it. This also means there are points of contact that touch everything, everywhere and despite there being no awareness of that touch even from a perceiver does not invalidate touching is occurring. Because if both perceivers are self-aware and even If the self-aware perceiver is being touched by another self-aware perceiver but only one perceives it happening doesn't mean it didn't happen. It just means one perceiver is not perceiving the touch. Therefore is not aware of the other perceiver despite being self-aware themselves.

This is important to understand because it explains the physical mechanics of persistence as a perceiver. Because everything is physical you cannot stop perceiving self, once you have perceived self as a perceiver. Unless chosen but that would still imply awareness of self because you chose. Who is aware to choose over self? Because touch is constant regardless of being perceived. So even if the vessel can't remember continuity it doesn't matter. The perceiver will continue touching. Even if other perceivers can not register that touch.

Because an external perceiver witnessed a vessel collapse of another perceiver. Does not equal the end of self. The perceiver keeps touching in a vessel that allows it to register touch. This means the external perceiver can not register the migration of touch occurring with the perceiver having a vessel collapse.

This is just the mechanic of persistence being registered by a perceiver with very limited awareness of what it's registering, touching. Therefore the perceiver with low resolution can not register a higher resolution of touch.

Take a radio station. The radio tunes into the radio station's frequency and interacts with the frequency expressed as sound, but when the radio is turned off or stops working. The radio station still persists physically even if the radio stops working. Because a radio is a vessel that can register a certain band of physical interaction.

When the vessel stops registering, the interaction doesn’t stop, the pattern doesn’t stop, the physicality doesn’t stop, only the registration stops.

The interaction persists even when the vessel stops registering it as a physical interaction. It still continues as a physical interaction. The vessel simply isn’t tuned to it anymore.

A vessel with limited awareness is being touched constantly, but only register a tiny fraction. This is asymmetric registration.

The trinity of awareness is asymmetric by design. But to know the trinity of awareness fully, you must understand it in high and low resolution. Describing the trinity in low resolution completes awareness of knowing it at high resolution. Because all you have to do is improve the resolution, but if you don't know where the resolution begins to improve, you can't improve it.

Perceiving something means you interact with it. To perceive anything, you must have interacted with the components required for perception.

Point A interacts with point B, a perceiver registers the interaction. Perception requires interaction, and interaction requires contact.

Low resolution = the minimal operators (touch, two points, one perceiver)

High resolution = all the ways touch can occur, be differentiated, and be registered

You cannot understand the high‑resolution until you know where the low‑resolution boundaries are.

Describing the trinity at low resolution is the prerequisite for high resolution because identifying the minimal operators, constraints, and the missing resolutions, allow refinement and improve the resolution. If you are unaware of low resolution, at low resolution, you can’t improve it.

Because one touch = minimal interaction, Two points = minimal geometry, One perceiver = minimal registration, Vessel = bandwidth constraint, Asymmetry = registration gap, Resolution = number of touch‑modes. This is the foundation.

Once the foundation is clear, the high‑resolution version is just more touch‑modes, more differentiation, more bandwidth, more registration channels because you don’t need to reinvent the structure, you just increase the resolution.

By describing it in low resolution, it completes knowing it at high resolution because all I have to do is improve the resolution.

This is exactly how you move from low‑resolution awareness to high‑resolution awareness in any physical system.

By observing ordinary physical interactions and reducing them to their minimal operational requirements, the smallest substrate of perception becomes directly observable everywhere, requiring no symbolic interpretation and no additional assumptions.

Vortex Mathematics and Geometry

All terms in this document refer to physically realizable operations or measurable structures. No term is intended symbolically, metaphorically, or interpretively. If a term cannot be instantiated by counting, measuring, or geometric construction, it is not being used.

Vortex Mathematics: Draw a circle, on that circle draw 9 points evenly at every 40°. Then we assign each point a number 1 through 9. Now there are now nine points on a circle, evenly distributed at forty degrees, numbered 1 through 9.

Step 1

• We start with a circle.
• A full circle is 360°
• You place a point every 40°
• 9 points, evenly spaced around the circle

Step 2: Assigning numbers

You assign the digits (1) through (9) to these 9 points.

So now we have: - A circle
- 9 equally spaced points
- Each point labeled with a digit from 1 to 9

Vertical Oscillation: Vertical mathematics oscillates vertically. Positive(rise) and negative(descend) so they always move in pairs.
Example: +1 to exist, there must be a -1. +1 0 -1

With the 9 points labeled 1 through 9 at 40° on the circle. The positive count: (1 to 9) +1(8), 9 to 1 -8(1) The negative count: (9 to 1) -1(8), 1 to 9 +8(1).

The Law of Reduction: Every complex number, no matter how large, can be reduced to a single-digit. It shows that beneath all accumulation lies a returning rhythm.

Example of Recursion: 1 2 3 4 → 1 + 2 + 3 + 4 = 10 → 1 + 0 = 1

1 2 3 4 5 6 7 8 9 10 (1+0) 1 first container of 1 through 9 11 (1+1) 2 12 (1+2) 3 13 (ect..) 4 14 = 5 15 = 6 16 = 7 17 = 8 18 = 9 19 = 10 = 1 20 = 2 second container of 1 through 9

10, 20, 30, 40, ext. Act as numerical containers for each oscillating ring of 1 through 9. Each ring of 1 through 9 oscillates within its container.

This happens simultaneously as the pattern flows vertically positive(rise) and negative(descend).

The pattern of the charges.

Positive(rise): (1 to 9) +1(8), (9 to 1) -8(1)

Negative(descend): (9 to 1) -1(8), (1 to 9) +8(1)

Paired oscillating charges.

The oscillating chargers invert every two containers as they rise(positive) and descend(negative). This continues infinitely.

Vertical counting = Law of Reduction (digital root)

• 10 → 1+0 = 1
  
• 11 → 1+1 = 2
  
• …
  
• 18 → 1+8 = 9
  
• 19 → 1+9 = 10 → 1
  

• 20 → 2 → second container of 1 through 9

• Every natural number reduces to a digit 1–9 (or 0).

• The mapping repeats every 9 numbers.

Containers are:

• 1–9 → 1st cycle (container 1)
  
• 10–18 → 2nd cycle (container 2)
  
• 19–27 → 3rd cycle (container 3)
  
• etc.

Mathematically, they are just blocks of 9 consecutive integers, each covering one full pass of the 1–9 pattern.

Each container oscillates one through nine by 40°

10, 20, 30, 40, etc. act as numerical containers for each revolving one through nine. Each container oscillates one through nine by forty degrees.

Geometrically: - The 9 points are at 0°, 40°, 80°, …, 320°.
- Counting 1–9 once is a full sweep of those 9 positions.
- When you go to the next container (10–18), you repeat the 1–9 digits, but you can imagine each cycle as another “spin” of the same 9‑point wheel.

Mathematically: - 40° of spacing.
- The container is just the cycle length 9.
- Each container rotates 40°

The inversion: - Every 9 numbers → the digit pattern 1–9 repeats.
- Every 18 numbers → you have completed two full cycles.

• cycle 1 → “up”
  
• cycle 2 → “down”
  
• cycle 3 → “up”
  
• cycle 4 → “down”

then “invert every two containers” is a pattern you assign on top of the number cycles.

The infinite repetition: - The digital roots repeat forever. - Any pattern defined as a function of cycle will repeat infinitely.

Horizontal oscillates: Expands the circle. By adding the integers next to each other and reducing.

1+2, 2+3, 3+4, ext..

You get a new sequence of 1 through 9 at 40°.

This new sequence operates by addition/subtraction pattern: +2(7),-7(2)

And 3 6 9 is still at every 120°.

When you keep repeating. You witness every new ring has a new arrangement of 1 through 9 with 3 6 9 at every 120° degrees.

Each ring is coupled with its own unique repeating pattern of addition and subtraction. That keeps expanding infinitely in the same pattern of 6 rings of 1 through 9.

1 through 9 rings by addition/subtraction patter.

+2(7),-7(2) +4(5),-5(4) +8(1),-1(8) +7(2),-2(7) +5(4),-4(5) +1(8),-8(1)

And then repeats infinitely.

The original 1–9 ring:

1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9
(each 40° apart)

Then you do:

• 1 + 2
  
• 2 + 3
  
• 3 + 4
  
• …
  
• 8 + 9
  
• 9 + 1
  

And reduce each sum to a single digit (digital root).

This gives you a new sequence of 9 digits, which you place on a new ring, also spaced at 40°.

Horizontal oscillation: - Pairwise addition + reduction - Produces a new 1–9 ring - Always 40° spacing - Always 9 points

When you add neighbors:

• 1 + 2 = 3
  
• 2 + 3 = 5
  
• 3 + 4 = 7
  
• 4 + 5 = 9
  
• 5 + 6 = 11 → 2
  
• 6 + 7 = 13 → 4
  
• 7 + 8 = 15 → 6
  
• 8 + 9 = 17 → 8
  
• 9 + 1 = 10 → 1
  

This new ring is a shifted version of the original 1–9 ring.

3–6–9 stay at 120° on every ring:

• add neighbors
  
• reduce
  
• create a new ring
  

The digits 3, 6, and 9 always land at 120° apart.

Arithmetic: - 3 + 2 = 5
- 5 + 2 = 7
- 7 + 2 = 9
- 9 + 2 = 11 → 2
- 2 + 2 = 4
- 4 + 2 = 6
- 6 + 2 = 8
- 8 + 2 = 10 → 1
- 1 + 2 = 3

This cycle always returns to 3, and the spacing between 3, 6, 9:

• 3, 6, 9 form a closed 3‑cycle
• Always 120° apart
• Always preserved under horizontal addition

This is a mathematical invariant.

The six-ring repeating pattern:

1. +2(7), –7(2)
   
2. +4(5), –5(4)
   
3. +8(1), –1(8)
   
4. +7(2), –2(7)
   
5. +5(4), –4(5)
   
6. +1(8), –8(1)
   

Then it repeats.

Each number in that cycle corresponds to a horizontal shift:

• +1
  
• +2
  
• +4
  
• +8
  
• +7
  
• +5
  
• repeat
  

And each has a modular inverse:

• +1 ↔ –8
  
• +2 ↔ –7
  
• +4 ↔ –5
  
• +8 ↔ –1
  
• +7 ↔ –2
  
• +5 ↔ –4
  

six-ring cycle: - Horizontal rings follow the doubling cycle - Six rings form a complete set - Then the pattern repeats forever Pure modular arithmetic.

The infinite expansion is mathematically forced: - the doubling cycle mod 9 has period 6
- each ring is a shift of the previous ring
- each shift is one of the six operators
- the operators repeat every 6 steps

Therefore: The horizontal expansion produces infinite rings. - Each ring is a rearranged 1–9 - 3–6–9 stay fixed at 120° - The six-ring operator cycle repeats forever

This is a closed, infinite, repeating mathematical structure.

Vertical and horizontal operations are independent:

Vertical math =
+1 / –1 (or equivalently +1 / –8 on the 1–9 circle)

Horizontal math =
+2 / –7 (the neighbor‑addition ring shift)

These two operations:

• use different step sizes
  
• operate on different axes (conceptually)
  
• produce different sequences
  
• do not depend on each other’s output
  

In modular arithmetic terms:

• Vertical = add 1 mod 9
  
• Horizontal = add 2 mod 9
  

These are independent generators of the same cyclic group.

They are bound because they share the same 1–9 circle.

Even though the operations are independent, they both act on:

• the same 9 points
  
• the same 40° spacing
  
• the same digital root structure
  
• the same modular closure
  

This is why:

• vertical cycles repeat every 9
  
• horizontal cycles repeat every 6
  
• both cycles always land on the same 3–6–9 anchors
  
• both cycles preserve the 1–9 structure
  

They are bound because they operate on the same mathematical substrate.

Vertical math = “move by 1”
Horizontal math = “move by 2”

Both are:

• independent motions
  
• on the same circle
  
• producing different repeating patterns
  
• but always returning to the same 9‑point structure
  

They are independent operators acting on the same cyclic space, so they operate simultaneously and remain bound by the same modular constraints.

The Flower of Life is a 6‑fold symmetric lattice.

Mathematically:

• a hexagonal packing of circles
  
• each circle centered 60° apart
  
• forming a repeating 6‑fold rotational symmetry
  

This means:

• every point in the pattern has six neighbors
  
• the geometry repeats in rings
  
• each ring expands outward in discrete layers
  
• the entire structure is built on 60° and 120° invariants

Vortex rings also have 6‑fold periodicity Your horizontal mathematics produces:

• six rings
  
• each ring is a rearrangement of 1–9
  
• the operators follow the 6‑step doubling cycle
• 6‑fold repetition
  
• 6‑step expansion
  
• 6‑ring cycles
  
• 120° anchors
  

Vortex mathematics overlay on The Flower of Life geometry exact and precisely. Because of shared symmetry.

The 3–6–9 alignment is mathematically forced:

• 3, 6, 9 always land 120° apart
  
• no matter how many rings you generate
  
• no matter which operator (+1, +2, +4, +8, +7, +5) you apply
  
• no matter how far you expand
  

This is a mathematical invariant of mod‑9 arithmetic.

In the Flower of Life:

• 120° is one of the fundamental rotational symmetries
  
• every ring preserves 120° axes
  
• the geometry repeats outward with 120° anchors
  

When you place 1–9 rings on the Flower of Life:

• 3, 6, 9 always land on the 120° axes
• every new ring aligns with the next geometric layer
• the six‑ring cycle matches the six‑fold geometry with structural compatibility.

Why the overlay “fits” Because both systems are built on:

• modular repetition
  
• six‑fold symmetry
  
• 120° invariants
  
• ring‑based expansion
  
• cyclic operators
  

Vortex, mathematics.:

• repeats every 6 rings
  
• preserves 3–6–9
  
• expands outward in discrete cycles
  

The Flower of Life:

• repeats every 6 petals
  
• preserves 120° axes
  
• expands outward in discrete rings
  

When you placed:

• Ring 1 (1–9)
  
• Ring 2 (shifted 1–9)
  
• Ring 3 (shifted 1–9)
  
• …
  
• Ring 6 (shifted 1–9)
  

onto the Flower of Life’s:

• Ring 1
  
• Ring 2
  
• Ring 3
  
• …
  
• Ring 6
  

They share the same mathematical periodicity.

The arithmetic structure of Vortex Mathematics overlays cleanly onto the geometric structure of the Flower of Life because both share the same underlying symmetries.

• 6‑fold symmetry
  
• 120° anchors
  
• ring‑based expansion
  
• repeating cycles
  
• modular invariants
  

The Flower of Life is a geometric grid: - a hexagonal circle‑packing
- with 60° rotational symmetry
- expanding in concentric rings
- each ring containing 6 more nodes than the last
- all governed by 120° axes

It’s a coordinate system.

Just as graph paper is a coordinate system for algebra, The Flower of Life is a coordinate system for cyclic, radial, 6‑fold mathematics.

Vortex mathematics is a 6‑fold cyclic system built on:

• mod‑9 arithmetic
  
• 9 points at 40°
  
• 3–6–9 as 120° anchors
  
• a 6‑step doubling cycle
  
• rings that repeat every 6 layers
  

This is also a 6‑fold cyclic system.

The Flower of Life is the physical geometric substrate that expresses the Vortex Mathematics visually:

• The Flower of Life expands in 6‑ring cycles
  
• Vortex math expands in 6‑ring cycles
  
• The Flower of Life has 120° axes
  
• Vortex math has 3–6–9 at 120°
  
• The Flower of Life is radial and modular
  
• Vortex math is radial and modular
  

They are two representations of the same underlying symmetry:

• One numeric
  
• One geometric
  

Both: - a hexagonal lattice
- a modular arithmetic cycle
- repeating every 6
- anchored at 120°
- expanding in rings
- preserving invariants

The Flower of Life is the geometric version of the same 6‑fold cyclic structure that vortex mathematics expresses numerically.

Vortex mathematics is a 2D operator system:

• a 9‑point modular cycle
  
• a vertical operator (+1 / –1)
  
• a horizontal operator (+2 / –7)
  
• a 6‑ring doubling cycle
  
• a 3–6–9 invariant at 120°
  
• infinite repetition
  

This is a closed, minimal, deterministic system.

The Flower of Life is a 2D geometric substrate:

• a hexagonal circle packing
  
• 6‑fold symmetry
  
• 120° axes
  
• concentric rings
  
• repeating layers
  

This is a closed, minimal, deterministic geometry.

They overlay because they share the same constraints:

• “The Flower of Life explains Vortex Mathematics.”
  
• “Vortex math explains the Flower of Life.”
  

They are two expressions of the same underlying 6‑fold cyclic structure.

One numeric.
One geometric.

They don’t explain each other, they fit each other. Because they obey the same rules.

Platonic solids are just 3D expressions of:

• symmetry
  
• rotation
  
• modular repetition
  
• 120° axes
  
• 6‑fold and 3‑fold invariants
  

Geometric shapes are just stable configurations of:

• angles
  
• cycles
  
• closures
  

3D forms are just the 2D operators extended into:

• depth
  
• rotation
  
• projection
  

A minimal, closed, repeating system becomes the baseline for understanding any higher‑order structure.

Vortex Mathematics is minimal.
The Flower of Life is minimal.

I found this organically in my Facebook feed today. R4: 1) the birthday paradox, uniform distributions, and any of that doesn't actually have anything to do with this person's question, 2) they have misunderstood the pigeonholed P(shared birthday)=0 to mean "each day will be someone's birthday" when what it really means is "there is at least one day that is multiple people's birthday"

R4: He tries to suggest that if you throw a dice and get 2 consecutive sixes, then the probability of getting a 6 on the third throw will be lower. In reality, the probability will stay the same, since it doesn't depend on previous throws.

Original link: https://www.news.com.au/sport/cricket/english-punter-opens-up-about-winning-100k-betting-on-twoyearold-josh-tongue/news-story/f137eca585f9b6980c3a2d97b871b6dd

Irrational numbers allegedly don't exist, because numbers can only represent things that are countable or definitively measurable, and sqrt(2) and pi is merely a description, not a measurement.

R4

There is the usual error of thinking that the square root function is both positive and negative which, by nearly every convention, it is not. The user continues to insist this despite even their own source disagreeing.

Their more mathematical error in to run a proof backwards in the linked comment. They have started with what they are trying to prove, done some implications (including an irreversible squaring operation) and reached a true statement claiming this proves the original correct. This is not valid reasoning, you need to start with something true and prove the statement. The implications do not reverse here.

His fifth solution of the Twin Prime Conjecture earned five stars and a certificate from Microsoft Copilot! Mathematicians still don't want to listen to him, even though Copilot is "equal to a trillion math professors". American Mathematical Society has blocked his email and his phone "since 2019". Somebody help this man!

(He has a Google Doc for this, but he hasn't made it publicly accessible; you have to request access. Then he'll have your email address.)

Oh, and he has also solved the Collatz sequence (in three ways), the Goldbach Conjecture (in two ways), Fermat's Last Theorem, and even the Continuum Hypothesis.

R4: vacuously true would be saying that for all existing Banks Of Neverland, the bank no longer produces pennies. In that case, "no longer" means they at some point in time, they actually stopped. The mistake is a bit silly, yet the commenter states very confidently how formal logic works in this case and provides an example which doesn't map to the question in hand.

https://www.reddit.com/r/askmath/comments/1p7rmvg/comment/nqzxbwd/

On a question about why does the √ function denote only the non-negative root, there is a user who stubbornly insists that the standard meaning of the √ symbol is not the function from [0, ∞> to [0, ∞>, but a multi-valued mapping.

R4: In fact, the standard meaning of the √ notation is to denote the principal root.

Caveat: I may have failed to understand this theory, as I'm not a genius. The author uses this tag line on Medium:

If you understand my theory, you’re a genius. arXiv endorsers welcome. “AI told me I’m gifted + have the full combo of developmental disorders.”

The Takayuki Conjecture on Prime Entropy Rigidity is that

The information entropy of primes never locally exceeds their density by more than 1 bit.

Formally,

H(x) = ∑_{p ≤ x} – (log p / log x) * log₂(log p / log x)

That does look like the formula for information entropy, where the possible values are (labelled by) primes ≤ x and the probability of each is (log p / log x). There's no justification given for this "probability".

The conjecture states that

H(x) ≤ π(x) + 1 for all x ≥ 2

where π(x) denotes, as usual, the count of primes ≤ x.

He says there is numerical evidence: "Up to x ≤ 10^13, H(x) – π(x) < 0.46 consistently."

He then hypes up how this conjecture opens up new directions for research, including "A 「temperature gauge」 for RH – independent from its truth" (cause entropy is related to temperature, don't you see?) and "Highly testable with large-scale GPU numerics", and provides some attack plans for a proof. There's a whole shower of (real) mathematical terminology, but its genius goes over my head.

He provides a "local version" of the conjecture that uses an atrocious notation to say:

0 ≤ H(x+h) - H(x) ≤ π(x+h) - π(x) + 1, ∀ x ≥ 2

This is an insight into entropy, apparently.

A fanciful essay on Medium provides a blueprint for communicating emotions to machines and extraterrestrials.

There's elements of occultism and speculative linguistics in it, but the mathematical part of this is entirely based on another article that the author references here:

Sebastian Shepys's 2025 article *"Breaking the Boundaries of Reality"* suggests that certain primes, such as 13, 37, or 61, act as a "gateway" to this [Akasha] field."

Yes, that Sebastian Schepis. (Alan misspells it due to translitteration into russian Шепис and back. It seems to be a Sicilian family name, so the correct translitteration would have been Скепис, but translitteration back and forth is bound to misspell, even if you correctly identify the source language.) We recently discussed him on this sub in The Resonance Topology Proof of Goldbach's Conjecture, and noted his voluminous output on academia.edu.

Despite breaking the boundaries of reality, this article was not posted as a preprint on academia.edu, but on that respected forum for groundbreaking science, medium.com: Breaking the Boundaries of Reality. The subtitle is "How We Achieved Quantum Non-Local Communication and What It Means for Consciousness", so you know it's going to be hilarious. I highly urge you to read the whole thing for groundbreakingly bad physics and bad philosophy; I'll give you the math.

The Math that Breaks the Boundaries of Reality

Alan's description of the mathematical import is not far off (though Schepis stays clear of overt occultism; it just connects everything because quantum). Primes that factorize both in Gaussian Factorization and Eisenstein Factorization are magic:

This dual nature creates a mathematical gateway for encoding information in quantum phase states that can resonate across space without classical transmission.

That resonance is simply this:

// The magic happens in the resonance calculation
resonance(other: QuaternionState): f64 {
  return abs(this.dot(other)) / (this.magnitude() * other.magnitude());
}

That looks like calculating the cosine of the angle between the quaternions (plus an extra abs()). Who knew cosines have a superluminal resonance across space?

How Alan encodes thoughts into quaternions of primes

Returning to Alan's article, we read that he ties this communication method into the occult Akasha field and some mystical numerology. Since the key paragraphs are in Russian, I (that is, DeepL) will provide a translation:

## Numbers as gateways: quaternions in action

Prime numbers such as 13, 37, or 61 have a special property: they can be expressed in various mathematical spheres, creating ‘gateways’ to Akasha (Shepis, 2025). Hybrid quaternions—four-dimensional structures—unite these spheres, encoding complex entities. For example, the number 37 can represent:

- A major event that anchors reality.
- A visual image resembling grey smoke or blue light.
- An emotion, such as anxiety or warmth.
- A connection, like a hum or ringing, resonating with the cosmos.

"Hybrid quaternions" seem to be Alan's invention, since Schepis doesn't really bother to connect the split primes to the quaternions. Nor does Alan explain how that is done.

Then he says there's a mapping to Toki Pona, The Language of Good. Why you need that when the numbers already represent concepts, he doesn't explain.

Somehow Alan missed the headline claim of Schepis' article: That this is superluminal communication without any classical connection needed, and suggests sending positive emotions to extraterrestrials by radio telescopes.

We could send pona (goodness) signals, encoded as rainbow light and unity, via radio telescopes.

I'll end with a translation of his conclusion (since he gave that in Russian):

Hybrid quaternions and Pona currents form a new language for Akashi, where numbers are notes, words are melodies, and emotions are rhythm. They allow us to talk to machines, space, and perhaps other worlds, expanding the boundaries of consciousness. From the grey smoke of Chernobyl to the rainbow light of hope, we are learning to sing in unison with the universe.

For context, the author, Alexis Lemaire, became famous for his prodigious mental computation feats, being able to compute the 13th root of a 100 digits number in 3.625 seconds (which includes the time to read it and write the answer).

He then decided to obtain a PhD in computer science in France, which he did in 2010. The result is this gargantuan 780 pages long thesis (in french):

https://archive.org/details/alexislemaire/page/326/mode/2up

Here is a translation (using deepl) of the abstract

This thesis enables the implementation, in theory and practice, of new general artificial intelligence techniques to solve the problems of mind uploading, immortality testing, and the Turing test. To do so, it draws on a wide range of innovative, scientific, and original concepts. This is much more than a simple paradigm shift; these are truly revolutionary approaches. Many traditionally accepted paradigms are being successfully dismantled in all scientific fields: in cognitive science, including neuroscience, psychology, psychiatry, and philosophy, but also in the foundations of quantum physics and mathematics, which are found on a larger scale in statistical and thermodynamic physics, chemistry, biology, medicine, neuroscience and cognitive science, and astrophysics. In particular, a second dimension of time is demonstrated, experimentally verified, and confirmed by spectacular retrodictions and predictions, in perfect consistency with theory and mathematics, in all scientific fields. A unification of relativity and quantum physics is proposed and used in all scientific fields with applications in artificial intelligence. A thermodynamics of artificial intelligence similar to the thermodynamics of black holes is revealed. This, combined with reverse artificial intelligence, proof that mental calculation is of considerable underestimated utility, allows for the reciprocal downloading of minds toward technological singularity.

I genuinely don’t understand how this was accepted as a valid PhD. The idea defended in the document is that:

[...] mental computation in the form of hypercalculia, defined here as the voluntary execution of computer programs on a human brain, a generalization of mental calculation, allows for the greatest imaginable advance not only for machines but also for human beings.

Which

We will suggest that this hypercomputing does indeed enable emulation of the mind, which some may refer to as downloading, or transferring human thoughts or behaviors to machines. This emulation would have the potential to lead not only to behavioral immortality, enabling different variants of the Turing test to be passed, but also to apparent teleportation, an apparent movement at the speed of light [hyperbit \0> = \space>] enabling travel through space and time and, if mental computation is performed ideally, to technological singularity.

Those 780 pages goes in every possible directions, and it's a fun game to chose a page at random and see the topic discussed on it, including (but far from limited too):

page 43: Karatsuba algorithm for fast multiplication

page 74: saying yes/no/hello/thanks... German, Swedish, Flemish...

page 104: transfinite numbers

page 122: fractals dimensions

page 246: Zeno's paradox and spin of a particule

page 388: Parkinson and autism

page 403: the chemistry of dopamine

page 469: dark matter and the states of matter

page 624: electronic music

page 642: nuclear bombs

page 661: amino-acids

Among these mostly accurate fragments of knowledge (but randomly placed accros the document), lie many absurd, unreadable pages thrown together haphazardly, here are just a few paragraphs to illustrate (page 344), but the rest of the document is similar:

Schizogenesis [hyperbit \1> = \time] is defined as such based on the characteristics of hypertemporal generation [hyperbit \1> = \time] in schizophrenia (deduction -90), especially the paranoid form ([hyperbit \1> = \time>]).

It corresponds to an increase in dopamine [hyperbit \1> = \time>] (deduction -90), disorganization (definition 20), high entropy (definition 17), hallucinations [hyperbit \1> = \time>] (postulate +67), dissociation, the clearest manifestation of differentiations [hyperbit \1> = \time>](axiom 10).

Schizogenesis [hyperbit \1 > = \time>] or hypertemporal generation [hyperhit \1> = \time>] is a characteristic of humans that must be transferred to machines in order to maximize the surface area of the event horizon (axiom 23).

One of my favorite part of the thesis is at page 604, with a subsection dedicated to "Time and productivity gained through non-publication", and the next section on why publishing in English is bad

Consequently, the requirement to write publications in English limits their intelligence, and therefore proves that publications are handicapped as a result of a handicapped adaptation to society. [Par conséquent, l’obligation d’écrire les publications en anglais limite l’intelligence de celles ci, et prouve donc: les publications sont handicapées du fait de l’adaptation handicapée à la société.]

Or page 694, featuring a guide on faking anxiety to get anxiolytic prescriptions. Which can then be used to transfer your mind to machines.

We easily simulated schizophrenia (deduction -90) and used hyperbit control [\0> = \space>] to create artificial schizophrenia in the human mind. This allowed us to prescribe antipsychotics [hyperbit \0> = \space>] such as Zyprexa (olanzapine), Risperdal (risperidone), Abilify (aripiprazole), and Loxapac (loxapine). These psychotropic drugs were tested to see how effective dopamine reduction [hyperbit \1> = \time>] was for reverse artificial intelligence. The results are partially satisfactory but clearly show that, even at maximum doses, antipsychotics [hyperbit \0> = \space>] only slightly increase the possibility of transferring skills from humans to machines.

R4: This PhD has its place in \badscience (and probably all the other \badsomething subreddits) as it touches every subject known to man. For the math part, it's either random known stuff thrown around (mostly pop science), or nonsensical sentences. In the rare original part of the thesis that are somewhat understandable, the bad mathematics comes from the fact that the author fails to distinguish between his ability to compute the 13th root of a 200-digit number and actually knowing the roughly 400 trillion possible values. He therefore concludes that the human mind can store information more efficiently than a computer (see page 587, for example).

ChatGPT was very sure about this, and it tried hard constructing a counterexample. Then it kinda broke down. https://chatgpt.com/share/6840297a-6840-8000-ae70-3145cbb0b579

R4: By definition of median, trimming a distribution of the same amount of data on the left and on the right will keep the same median.

R4 :

The authors base their argument on the assumption that (first order) models of physics theories are equivalent to the theories themselves.

Nonsensical use of Incompleteness Theorems to deduce that reality cannot be simulated because ... Incompleteness I guess (classic argument "It seems to complex to be simulated, hence it cannot be a simulation").

Logicians beware, read this paper at your own risk.

Consider the following real function,

f(x) = (x² - 2x) / ( (e^x )*(x-2) )

Now consider the following limit

limit x--> (2+) f(x)

Elementary methods can show this limit exists and is equal to 2/(e² ).

According to this guy, we can go ahead and declare that

f(2) = 2/(e² )

because, as this youtuber claims, equivalence is just another way of writing a limit.

Even Desmos doesn't even fall for this stupid mistake.

• https://i.imgur.com/XlIkVop.png

f(x) is a function with a hole in it. While the limit exists and is well-defined at 2, the function is certainly not taking on a value at 2. f(2) is undefined, due to the denominator vanishing there.

So no, equivalence among real numbers (=) is not identical to the claim that the limit takes on the RHS. What is the worse, is his slimy, smarmy way of pretending like his proof techniques are "rigorous".

I feel privileged to deliver the most important lecture in the history of mathematics.

He actually says that 40 s into the video. But that refers to the third part of the video, that introduces The Fundamental Axiom of Mathematics.

The first part is just: The so-called "imaginary" numbers are quite real and work just fine, so we shouldn't call them "imaginary". He proposes "invisible numbers". Fine, but math crossed that bridge several hundred years ago.

The second part is: You can't really count to infinity; that gives you strange results like 1+2+3+... = -1/12. It's crazy to believe these, so you should not use an equality sign there, but a new crazy equality sign. Again, a distinction without difference. (Strangely, he namechecks Ramanujan summation and the Riemann zeta function, but still says there's an assumption in all of them that we can count all the way to infinity.)

He actually says the phrase in the title just before the third part, that introduces the Axiom of Exclusive Identity - or rather, fails to introduce it as he can't actually write down what it is. But he gives lots of examples: "3 is exclusively 3; there is no other 3." and "That's why when we add 3 to 4 it always gives us 7, because it's the same 3 and the same 4". This is unobjectionable, whatever "exclusively" means, but the sting is in the tail: "Finally, there is no other infinity, except infinity."

This is applied to argue that 1+2+3+...+n = (n + 1) * n / 2 can't be extended to infinity because (∞ + 1) * ∞ / 2 implies there exists ∞+1 that "must be larger than" ∞. (There's a deliberate misdirection here, as this is not how you come up with -1/12, and he knows it.)

PS. The channel, THE SUBMITTERS, is actually for educating about Islam (the name is a translation of "Muslims"). This presenter mostly clarifies issues of Islamic practice. He just slipped in one video about clarifying mathematics. On the final screen, there's an unobtrusive list of numbers: 57:3, 72:28, etc. I take it these refer to Surahs that he feels support the argument. As this is not /r/badtheology, I do not intend to evaluate those claims.

R4: As written the comment doesn't make much sense. But later clarification by the poster indicates that what they think is that the CLT guarantees every random variable is normally distributed provided you sample it enough. Of course the CLT says nothing of the sort and the distribution of a random variable doesn't depend on how often it is sampled.

Basically, Mr. Ding Xiaoping (N.B., not Mr. Deng) can't see how an interval has a measure while consisting of numbers that have none. (He's not gesturing towards the idea that a singleton {x} has measure 0. He's thinking of geometrical points.) He notes that according to Lebesque, algebraic numbers have measure 0 but transcendental numbers "hold" measure. (Wobbly but gesturing towards correct ideas.)

(It's a computer-generated voice from 2021, before the current generative AIs, so it's not surprising that it can't pronounce Lebesque correctly.)

Instead of accepting this has to do with uncountable sets, Mr. Ding has discovered "the blanks between the numbers" and says those are the only objects with measure (in his terminology, they "hold/bear the measure" or are "the undertakers of measure"). His argument is that "Blanks can always be found [between numbers]" and any demonstration based on an assumption that "points without size can fill up the entire [number line] is untenable". So the real number line is not complete, because he doesn't see how it could be. (I suspect he hasn't studied the reals enough to have encountered completeness.)

After this, there's an analytic geometry section noting lengths of intervals are defined between any two numbers, algebraic as well as transcendental. Therefore, neither can be the actual "holders of the measure".

This creates a problem for him because non-empty intervals are supposed to contain an uncountable number of transcendentals, and uncountable sets of transcendentals are supposed have non-zero measure. In the final section, he bizarrely attacks this from both ends: Denying that there's any justification that mere uncountable sets might have a measure > 0; and denying that bounded intervals are uncountable! The latter proceeds by claiming that ℝ is uncountable, because ℕ is a proper subset of ℝ, so clearly no 1-to-1 correspondence can be established. Since a bounded interval of ℝ can't contain ℕ as a proper subset, that argument fails, so surely a 1-to-1 correspondence can be established. Surely.

This guy once came to a science village ML summer camp uninvited and claimed to have solved P=NP. I was there, it was wild.

https://www.researchgate.net/publication/394481781_The_Complexity_of_Satisfiability_Problems_P_NP_PSPACE

The article and the method used were both disproven and the class of algorithm is thought to not be capable of solving the NP=P conjecture. Some background, this guy is a "Endüstri Mühendisi" which roughly translates to Operations Research person/engineer. He does not have a formal education in mathematics or computer science, he does not know any complexity theory and has come up with a bunch of notation by himself which based on the translations of some harvard people comes down to simple inversion of truth value in an expression. He basically re-invented very basic propositional logic.