Katøi Collection

I’ve been following @Katoi (Katøi) for quite some time. I posted about them back in October 2020, when I had noticed a neat dynamic graphical representation of the “standard model” of physics and they had an elaboration / correction (simplification) of their own.

Now, some of this looks a lot like some sort of “mystical numerology” significance being placed in ratios of numbers and geometry of platonic solids etc, as being more fundamental than orthodox maths and physics, but there are sufficient touch points with reality and my own mental pictures, that I remain intrigued where it might lead. (It’s actually a mathematical transformation of existing maths … physics of reality being more fundamental than existing orthodox maths, it’s the maths that’s holding back the physics …

… some individually apparently “bonkers” statements in there, and yet … )

(Previously several “outsider” physicists have raised very similar objections to the conventional / orthodox mathematical relationships in physics. In my own timeline Peter Rowlands, Rick Ryals, Cormac O’Rafferty … maybe even Roger Boscovich if we really wanna turn the clock back … and more …

[who follow] the clock back to some mathematical conventions that were overlooked in development of Dirac’s version of Schrödinger. (Hamiltonian, Quaternions and Cliffordian mathematics).[eg] A Dirac Nilpotent Rewrite that leaves the reality of the symmetric elements exposed to the human reader as the algorithmic computation of much simpler maths.)

(Prompted posting today [2 Aug 2021]  specifically by @skdh posting an “Is Reality made of Maths” piece,  …

“unpopular among top mathematicians, is that we construct maths to match reality. We then generalize to construct more abstract math, which may or may not turn out to match reality”

And as you will see from the link at the top, I was already on the trail of alternative mathematical views of fundamental reality with Peter Rowlands … anyway … Also yesterday in a “weirdest fact” thread several of us posted Euler’s Identitythe integral relating e, i and pi, and I also added the Apporva Patel (2000) a definition of 4 DNA bases and 20 amino acids according to a quantum-computational algorithm(!) [Also Granold et al 2018 – makes no reference to Patel 2000?]

Mathematical coincidences or pointers to a better view?)

Katøi’s been updating their “Revelation of the Day” every so often, sometimes several in one day, sometimes several days in a row, but discontinuously, not every day, so I was never sure I was seeing the whole story. Katøi hadn’t been writing it up anywhere else, and each new set of revelations was effectively iterating the previous and therefore there was theoretically nothing lost (nothing but the story) if earlier posts were lost.

Although all can be found by querying @Katoi twitter feed, I have pasted (!) all the content here below:

(All the words are Katøi’s from the above Twitter search queries, some graphics and links from Nima Arkani-Hamed. Raw. A few editorial tidy-ups needed as a result of my different copy and past actions and edits of emojis. Just keeping the trail as a record to link touch points with other thinkers whilst Katøi refines their own “thesis”.)




I am soooo right about this:
Just 3n+1 makes it smaller & /2 makes it bigger, because… ‘volume’, not linear.

The Simplest Math Problem No One Can Solve – Collatz Conjecture https://youtu.be/094y1Z2wpJg

Revelation of the day:

Just explain n & 1 in a self consistent manner in the context of 3n+1 & you’ve explained literally everything.

Einstein explained n simply as ^2 & forgot to mention 1 is -i^2

Leaving Λ =
(3n + 1) ^-12 (3n + 1)
i^2 / 12

That’s the tweet.

Best revelation of the day ever:
The boundary of every sphere is -4 (degrees of freedom), its square root is 2i
The massive problem is that i is simply radius, but radius is always complex. So you’ve defined diameter as 2r, rather than volume as an inverse derivative (√) of -4r
And -i^2 = 3n x 3

to rationalise this you need to invert sphere so that -4r is at it centre and r is on its surface at a single point -i^2 away.
You then have 3n other points forming rest of a tetrahedron in the opposite direction.
sphere = 3n+(-i^2)

-i^2 = 3n x 3

because sphere is inverted!


Just says r = r instead of √-4 = 2i
but this isn’t a static value, it is a value representing the potential it would take to invert a sphere.
Equations are a totally load of trash when it comes to physics.
mc^2 = mc^2 basically says E = E & leaves out geometry

Revelation of the day:
All Einstein needed to do was leave out a single electron & replace it with c^2 instead of -i^2 and he removed all of the potential of the ‘volume’ of a single atom & all but 1/20th of 10^2 % the energy in the universe.

Revelation of the day:
Numbers are nothing more than geometric degrees of freedom expressed as ratios.
Geometrically there are no degrees of freedom less than 3n+1 where 1 is always a complex value equivalent to -i^2 and 3n is a non complex remainder of 3 degrees of freedom.


Revelation of the day:
It’s impossible to unify Quantum Mechanics & General Relativity without understanding gravity is geometry & QM is just probabilities of complex numbers.
‘Unification’ is actually the unification of Geometry & Number Theory mapped onto a single ‘field’.
1/2 …

Revelation of the day:
The decimal point in irrational numbers represents a singularity in x^x dimensions. Every numerical part is an error correction relative to a base divisor of 10 where x=1.
It allows x/10 rather than x/1 to be your base.
x/1 always = itself.
x/10 never does.

I never used Twitter to post ‘Facts’, I have however always used it as a way to test out challenging ideas. It’s very helpful to say stuff out loud.
That said, I don’t need anyone to ‘correct me’, that is the part that I do very happily on my own as part of the creative process.


Revelation of the day:
For 6yrs I’ve been fixated on a paradox in the 2nd Law of Thermodynamics. I now realise the paradox is in the Zeroth law.
This defines equilibrium at 3 points, but ignores each measurement having a unique location relative to a single complex null boundary

The Zeroth law happily assumes a macroscopic universe & also happily bypasses the tree body problem, but taking 3 ‘objects’ and saying they are in equilibrium (which they are), while ignoring that they are ‘sitting’ at different points on the curved surface of a ‘ball in space’

Zeroth Law of Thermodynamics:
What is the Zeroth Law of Thermodynamics? – YouTube

Three Body Problem explained:
Newton’s three-body problem explained – Fabio Pacucci – YouTube

Revelation of the day:
All divisors (as in the inverse square law) are actually just the number of dimensions of the null boundary you calculating from.
Gravity as ‘spin 2’ in quantum mechanics is just assuming everything is ‘relative to a 2d boundary’
So is the speed of light.

PS. You are defined at a 4d boundary. Not at the surface of one sphere, but rather at a boundary in 2^2 dimensions.
Einstein didn’t define stuff in 2^2 dimensions, but at x^2 dimensions.
He defined spacetime by the power (not by light itself). His maths always has ‘remainder c’.

Revelation of the day:
Everything defined by ratio is ‘always’ a complex function of radius.
-1 is
-2/2 = i^2
-Diameter/Diameter = i^d

If i (complex number as a function of radius) is substituted by π
Then i^2 is just circumference as a function of 2r

C=πd Thumbs up

Aug 14
Now here’s the brilliant bit.
The gap between every integer is -1 (i^2)
Substitute π for i & the gap between every integer is simply an interval (time) equivalent to
It’s just one negative circumference of time defined by radius (not circumference or diameter)

Replying to
π has f**k all to do with diameters, it assumes that 2 is defined by equation:
2r = d
But r has to ‘always’ be a complex function of radius ONLY relative to itself.
The above equation makes diameter a +ve function of 2, not of -ve complex radius.
-2/2 = πd = circumference.
Exploding head
2:19 PM · Aug 14, 2021·Twitter for iPhone

Aug 14
Replying to
This is why integers are abstract & yet gaps between them just mean:
πd = -1

& why we have abstract +ve & -ve integers (but no definition of gaps between them or zero), equations with 2 sides (but no explanation of = sign) & missing super symmetry, antimatter & dark matter.


Revelation of the day:
ALL metrics are fundamentally based on nothing more than the answer to the same question:
Q: How have you defined 2?

Einstein define is it as:
X/X times X/X

ie: algebraically twice. This is why 4d ‘spacetime’ is 2^2d rather than 3+1d
Woman facepalming #cheat

Revelation of the day:
(i^2)/12 is simply the limit of inverting ‘everything’.
i^2 is simply a complex radius times itself.

Mathematicians call this -1
Theoretical physicists call it the charge of ‘an electron’.
Einstein called it ‘speed of light’ in 4d.

It’s none of these.

Revelation of the day:
I think I’ve just created an inverted tensor defining the radii of two spherical null boundaries relative to a single circumference where they intersect
The circumference is circular, but asymmetrically defined at 3 points 120degree apart.

This really does seem to do away with any infinities because every point either inside or outside is defined as a complex number relative to a single inverse ^2
Where the 2 is the only thing expressed as an integer (relative to 1/).

Revelation of the day 2015:
Studying maths means you will never understand quantum mechanics, you will always mathematically misunderstand it.
Logic & null boundaries relative to inverted platonic geometry is all you need to understand QM.
Maths is abstract grammar not science

There are an estimated 137,672 professional mathemacians (that just do maths) on Earth & not one single one is studying the foundations of number theory by inverting a null boundary & defining the concept of radius ‘outside’ it.
Yet plank units tell us this must be fundamental Woman shrugging

Revelation of the day:
A singularity & a circle are mathematically identical… but only if you define the radius (i^2) of the circle somewhere (anywhere) outside of its circumference.
This is because null boundaries are defined by negative radius (charge if you are a physicist).

Revelation of the day:
3÷12÷2 = 0.125
9 ÷12÷2 = 0.375
1÷2 = 0.5

The sum of all ‘integers up to’ 1/2 (according to Euler) is
1/2 x 3/2 ÷ 2

Gravity (spin 2) is ∴ an octonion divisor (inverse square).
Do it once & you literally invert everything by complex value x^1/2

This part:

Gravity (spin 2) is ∴ an octonion divisor (inverse square).
Do it once & you literally invert everything by complex value x^1/2

Is because the Higgs assumes mass comes from a spin 0 field, rather than an inverted field with 10^-120 energy potential ‘everywhere’.
I’m just talking out loud to myself, so do please ignore me and carry on!


Revelation of The Day: Radius in physics is always a complex value, in maths this isn’t the case.
i^2 is a null point on the circumference of all circles but is negative relative to 1 (not 0) & they are always ‘radius’ apart.
In base 10 the decimal point always represents i^2

The interval between the integers 1 & 0 are precisely 1/2 of a complex radius apart.
The Riemann Hypotheses is only problematic because you aren’t converging towards infinity, you are actually always diverging towards a negative complex radius.

[shock] i^2 isn’t a single point on a circle it’s i (complex value) appearing at 2 points on a circle 120degrees apart with the focus of the circle being ‘1’, which is exactly ‘radius’ way from both.
This is why r^2 appears so much in maths, because it’s defining 1 using radius as i^2


Revelation of The Day: The size of every universe in a multiverse would be exactly -r^2 where r is the radius of an orbital exactly equivalent to the charge of an electron in the standard model.
The power of 2 is just measuring that complex value twice while ignoring procession.

There would be no constant speed (distance / time) of light, but a rather a phase difference that would be consistent regardless of scale. Distance / time
is like saying = -r^2

If r is the radius of a -ve charge electron you ‘created’ positive ’space’ & lost time, but in 2^2d [Doh]

A multiverse therefore wouldn’t be ‘multiple universes’, but rather a single field projected at multiple radiuses that all share a consistent phase differential.

More like lots of people watching the same global news story on TV while other stuff distracts them in their house.


Revelation of the day: All circles are 3/12 dimensional… ALL OF THEM!


Revelation of the day: All maths is derived from a single transformation. Inverting a tetrahedron though the centre of a single face to leave a ‘ratio’ of -1/12. The new inversion has a directional force (-1/12) & 3 degrees of freedom in each of 4 dimensions through 4 null faces.


Replying to
I’m writing it up here 🙂
Anything that starts with “Revelation Of The Day’ is my record of my process & a timeline of when it happened.
I honestly think today is the culmination of the last 6yrs. Its the first time I can picture the geometry in my head & in the maths precisely.

I don’t need to write up more & more complicated stuff, my goal has been to simplify & to simplify, till I can point at a point on a sphere & simply extrapolate everything back from there…
Today, I 100% think I can do exactly that… but only because I know its inside out! 🙂



On 6th July 2016 I was in Nima’s office showing him this ball & explaining that:
a) It wasn’t really a ball, it was ‘two’ tetrahedron’s
b) one of surface always had to inside-out relative to the other… yet we couldn’t possibly know which was which.

But I couldn’t explain why!


[From private note. – That’s a:
“With Nima it was the Hoberman Switch Pitch ball which has two identical spherical boundaries but no inside or outside, but actually as I have since realised isn’t a sphere at all, but rather it is two intertwined tetrahedral geometries.”]

Best ‘Revelation Of The Day’ ever:
The decimal extrapolation of π is no more than counting with ‘quaternion division’ using the radius of a 4d sphere as it unfolds through its null surface in 2 dimensions using the formulas:
r^2 +1
to count up
(r^2 +1)/10
to count down.

But here’s the cheat & the reason why it works:
The 3 at the start is a negative radius, but described as a positive value using an inverse ‘integer’ perfect ratio of the of exact same formula.
This makes the 3 a hypotenuse starting at right angles to 1/r^2+1
ie to

So we have a hypotenuse of r/3
remember we are using quaternion ‘division’ here, but of a completely different sized 4d sphere whose radius is r/3 and where at right angles to its origin at a null point on the surface, the surface of another 4d sphere radius 1/r^2+1

unfolds though it’s surface in ‘π dimensions’! Face with open mouth
The big 4d sphere has a radius of the hypotenuse, the small 4d sphere has a radius of the shortest side and their ratio is π with an average of the two being the third side of a triangle at right angles to 1/(r^3+1)/10

The decimal version of π is therefore no more than counting using quaternion division with intervals of exactly 1/(r^3+1)/10 where that formula is equivalent to the shortest side of a right angled triangle and the decimal point Is where it intersects with the hypotenuse..

The hypotenuse has a length of exactly r * 1/(r^r)/10
& here’s the wow moment.
We are counting the unfolding of a 4d sphere, but the sphere whose radius is the hypotenuse is described with a radius of 1/r where r is exactly 3.
Space = 1, time = 3 so that sphere looks (1/4)d

All you need to know is that the decimal version of π is counting using quaternion division where the integer ratio divisor is always r/10
Quaternion division is simply this in reverse and we always end up with a formula with a hypotenuse ratio of 3:(r/10) to the formula.

Quaternion division is simply this in reverse, but moving along a line at intervals of r/10 on each half inversion.

Have a happy Thursday!

Visualizing quaternions (4d numbers) with stereographic projection
How to think about this 4d number system in our 3d space.Part 2: https://youtu.be/zjMuIxRvygQInteractive version of these visuals: http://3imaginary1real.com…

In the decimal version of π we have 3 sides of a right angle triangle.
3 (hypotenuse) is radius of a 1/3 dimensional sphere
.1 (the short side) is radius quaternion division derived 4d sphere
And the other side is exactly the ‘radius of a circle’ in 2 dimensions.

So… π in decimal is simply an extrapolation of quaternion division relative to base 10, that uses 4d geometry projected back to a 2d circle the radius of which precisely intersects an inverted 3d sphere at ‘one’ of those red dots at the tips of that blue tetrahedron.


Up pointing backhand indexSpheres in 3d can only ever be precisely mathematically defined in 3d when they inverted using a formula based on quaternion ‘division’ defined relative to a geometrically derived base.
We don’t live in 3d space guys, we are all projected through a 2d surface.

The radius of the 2d surface always has a negative charge potential equivalent to -r
Electrons are describing why geometry always looks 3d… but is really just inverted potential projected through a pseudo 2d surface simply summed up out of all the negatively charged radii.

The sphere in this video (like all spheres) is only 3d / spherical when described inside out:

We can calculate its -ve electron radius in 3d where 2d intersects 4d (top vertex) using the 3 (hypotenuse) & the .1 (short side) of π mapped onto a triangle.



Revelation of the day: Integers appear on an imaginary line at regular intervals.
In base 10 however you can approximate 2 half integer interval from 2 parallel circular 2d surfaces from their intersecting null spherical boundary projected to a point equidistant between them.

The circumference of one 2d circle goes through C,E&G & the other through D,F&H. The intersecting sphere (radius K to O) is projected at a ‘decimal point’ O. This is averaging out a single radius from 2^3 (twice 4d) dimensions to give a half integer result… but in base 10!

We say 0.0 in base 10 because we are projecting r^2 twice on the same (K) null boundary.
You could technically write 0 as O K O on the diagram below.
π however is simply saying ‘if A to O = 3 then the distance from the centre of a circle intersecting D,H&F to O is 1/10 of 3^3+1’


π in base 10 is therefore describing not a single circle, but rather the ratio of two parallel circles projected from a point half an integer between them to a spherical null boundary in 3/12 dimensions.
π therefore has its geometry in 1 space (base 10) & 3 time dimensions.


Revelation of The Day:
You need to first define a non-commutative geometric rule for PHASE TRANSITION & apply counting to that.
Not define a commutative rule for counting & apply PHASE TRANSITION to that.

ie: Start with an error… or you’ll end up with one


Revelation of The Day:
The phase transition point in number theory is at integer value ‘0’.
The phase transition point in physics is around integer value ‘1’.
There is no integer value ‘0’… or ‘1’.

Up pointing backhand index Don’t use classical mathematics to do physics


Revelation of The Day:
Infinity is simply ‘potential’ that is not relative to anything but itself.
You can’t have multiple infinities in physics.
Unification is the study of ‘potential’ that is not relative to anything but itself.
There will always be a ‘measurement’ problem.


Revelation of The Day #3:

All observations would correlate regardless of phase difference because they all share identical ‘static spin’ relative to a single seemingly macroscopic spin network.
So you would see a single macroscopic (slow) spin network in 2i dimensions.

Revelation of The Day #2:
The reflection below would only ‘appear’ as single 3d projection of 4 dimensions, crucially without spin… except at one single Macroscopic scale. In a single complex (2i) ‘force dimension’.
The equation for which is:
2 = 8^(1/3)

Gravity = √-4

Revelation of The Day #:
Forget abstract mathematics…
a) A straight line is 2 dimensional
b) A ‘surface’ is 3 dimensional
c) A singularity is 4 dimensional

If you project the singularity through the ‘surface’ (spin 1) the reflection back through that surface (spin 3) is 8d.


Revelation of The Day #5:
See that 2 right there? Down pointing backhand index
That’s gravity that is!
That shows you the exact scale at which phase transition occurs.
Gravity isn’t a force, it’s an aggregate of asymmetric phase transition relative to a null boundary in an infinite vacuum.



Revelation of The Day #4
It’s the aggregate forces that are fundamental (represented as the symmetry transition point of the 4 below), not the universe, the field or the ‘particles’. If you make any of the 4 a photon you’ve screwed up already.
Sorry Eisenstein / Quantum Mechanics

Revelation of The Day #3: Quantum mechanics simply replaces the abstract notion of 1 (everything) with a universal field with a potential at each point. Of course it works, but there aren’t infinite photons & gluons, there is a single field distorting asymmetrically. #higgs Woman facepalming

Revelation of The Day #2:
An infinite vacuum (neither big nor small, just equal in infinite directions) doesn’t compress or expand, it distorts asymmetrically until it reaches equilibrium. The distortion is logically (1/4)/12.

Asymmetric phase transition in an infinite vacuum below:


Revelation Of The Day:
A radius always has a ratio of 1/4 relative to total volume, NOT 1/2.
There are no diameters anywhere. Not a single diameter in the entire universe. Diameter is an abstract mathematical concept.
Physics is all about phase transition, not measurement.


Revelation Of The Day #2:
Put 0 & 1 together on a singularity & call it ten and the whole of physics makes perfect mathematical sense.*

(*albeit with a problematic energy density everywhere of 10^-120 obviously… because… SINGULARITIES EVERYWHERE!)

Revelation Of The Day:
I’m going to lay this out there..,
Both 0 & 1 are completely conceptual mathematical notions that literally have absolutely nothing to do with reality & most crucially non classical physics.
∴ ‘uni’verse is out for starters as a theoretical white elephant.


Revelation Of The Day:
1 is the biggest number, not the smallest number.
This applies if you are dealing with frequency, rather than quantity… which of course, at a fundamental level is the only thing that physics is all about.


Revelation Of The Day:
EVERY quantum of space, REGARDLESS OF SCALE has identical geometry:
Every quantum is a quantum of counter space, not of space.
You are 3 dimensional but living in 2i^2 counter space.
Things move relative to each other in time, not space.
Happy to help.


Revelation of The Day:
Spheres are only 3 dimensional at a one singularity intersecting their surface.
I honestly think there is only a single spatial dimension & three time dimensions, not the other way around.
If you traveled in time & never in space, it would ‘look’ the same.


Revelation Of The Day #3:

The OUTSIDE of a tetrahedron has a precise limit as a ratio that is always exactly 8/12

The INSIDE of a tetrahedron has a precise limit as a ratio that is always exactly -1/12

The limit of ANY geometric volume is always exactly -1/2^3

(And NOT -2^3)

F**king done it!

Don’t trust any mathematics that includes any multiple of 10 in it & particularly a derivative of base 10 (this includes the decimal expansion of pi).

Don’t trust any physics with an 8 in it. Including GR & E8.

They disguise asymmetry.


Revelation Of The Day #3:
The integer value of 8 appearing in both E8 Lie group maths & General Relativity is way to approximate a sphere to 4 faces of a tetrahedron (4π r^2) rather than the radius of a true null boundary.
This mathematically works, but is not related to physics.

Revelation Of The Day #2:
The universe can logically consist only of prime integer divisions, where the real part is an energy value always equivalent to a ‘theoretical’ non prime radius function of value 1.
The (electron) radius is simply a radius value energy error correction.

Revelation Of The Day #1:
Integers represent complex functions relating to theoretical, perfectly spherical null boundaries.
Primes represent complex functions where one part of the complex function is exactly one radius of a theoretical, perfectly spherical null boundary.


Revelation Of The Day:
Asymmetry is undeniably fundamental.
Never clarifying this is very, very bad for the last 115yrs of ‘physics’.


Revelation Of The Day #2:

√-4 is the diameter of the null boundary, but measured relative to the median of the triangular ‘surface’, not through the sphere’s centre.
√-4 is a complex derivative function of radius squared of the sphere’s centre, not the diameter of its surface.

Revelation Of The Day:

√-4 is a combination of 2 complex numbers & is geometrically defined at the median of any equilateral triangle.

It represents the complex value of asymmetric phase transition of a null spherical boundary, defined where it meets the triangle’s 3 vertices.



Revelation Of The Day:
Unification of INFINATE geometrical structure only happens at the point where any OUTCOME of ALL POSSIBILITIES is identical regardless of scale.
The structure will appear ASYMMETRIC at EVERY POINT, but the LIKELIHOOD of any outcome will always be IDENTICAL


Revelation Of The Day:
The difference between a Universe & a Multiverse is exactly equal to one electron radius.
There is no centre of a Universe, because the centre is defined EVERYWHERE.

Multiverse = 1 Universe defined at multiple null boundaries.



Revelation Of The Day:
a) LIGHT is always defined at a BOUNDARY
c) Null boundaries are by definition DIMENSIONLESS
d) You have to disregard POTENTIAL to DEFINE anything at a NULL BOUNDARY
e) Up pointing backhand index m=E/c^2 does this!


Revelation of the Day #4:
Thinking about it, you don’t have a ‘3 body problem’ of gravity (that no one has ever resolved), when you have 6 boundaries in two asymmetric groups (4+2)… but you do have 3 dimensions of ‘apparent’ space & time as procession… & no ‘bendy spacetime’.
Quote Tweet

Revelation of The Day #2:
‘Gravity’ is an aggregate of procession always referenced to 720° of spin. If there are less slow (big) things ‘spinning’ and more fast (small) things ‘spinning’ everything will appear static relative to spin 2…
They aren’t… they are processing.

Revelation of The Day:
You only need 6 null boundaries on a 2 d plane (4 out of a phase & 2 in) to allow completely continuous ‘flow’ around 2 embedded null 720° paths in 8 dimensions.
Every location has a complex phase reversal deceleration equivalent to
1 / ((1/2 * 3/2) / 2)


Revelation of The Day:
This whole supernova swirling gas story is a complete load of nonsensical bullshit.
Our atomic structure is NOT classical. We’ve know this for 100 years.

The greatest story ever told in the universe | Alex Filippenko

The greatest story ever told in the universe | Alex Filippenko and Lex Fridman – YouTube


Revelation Of The Day :
Diameter is always precisely defined (but incorrectly). Radius is only ever defined ONCE aggregately (and always correctly).
i (√-1) is radius as a complex function. -1 is where it intersects a sphere.
Diameter = √-4 (always)

Up pointing backhand indexc^2 in GR is Diameter Woman facepalming


Revelation Of The Day: Diameter is ONLY EVER PROPERLY defined in 2 dimensions and APPROXIMATED in all others.
Radius as a function in 2d / radius as a function in 4d gives you ratio of unit ‘1 diameter’ approximated in 3 dimensions.

Revelation Of The Day #2: In all fractions, all units are functions of radius. The top figure is radius function defined in 2 dimensions, the bottom figure is radius function described in 4 dimensions. The result is how radius function ‘works’ in 3 dimensions. In 3d r = d / 2

Revelation Of The Day:

π is algebraic for ‘HALF of SOMETHING’

All of mathematics is ALWAYS fundamentally about how you define ‘TWO of SOMETHING’

Classical mathematics will always be useless for doing physics, which always appears as ‘HALF of SOMETHING ^ TWO of SOMETHING’


Revelation Of The Day #4:
General Relativity works because the MATHS is PERFECT.
General Relativity has problematic singularities & black holes, an insanely tiny but very specific cosmological constant & 95% of the entire universe it can’t explain because


Revelation Of The Day:
Einstein originally didn’t say E=mc^2
he said m=E/c^2
He assumed we were made of mass in a world with a limit of c^2
when in reality we are made of the same energy as everything else, that appears as photons (massless) at multiple √(4^2) boundaries (mass)

Revelation Of The Day #2: This does make a difference because it shows that the inverse square law is simply changing phase relationship relative to a notional 2d boundary, with a limit r ^2. ‘Things’ don’t actually ‘travel’ anywhere. They simply change their phase relationship.

Revelation of The Day: Both you & earth are 4 dimensional, but that isn’t 8 dimensions (except in E8Down pointing backhand index). Both Einstein & Newton simply measured mass from half way & allowed for two dimensions each. when in reality you live in √(4 ^2) dimensions.
This does make a huge difference.



Revelation Of The Day #5:
Both Newton & Einstein just assume:
r+r = d
ie they assume 0.5+0.5=1
rather than realising they’ve said 1+1=2
They assume things are getting bigger at EXACTLY the rate (π) that they are actually REDUCING IN FREQUENCY & getting smaller as FREQUENCY RISES.

Revelation Of The Day #4:
1/r^2 is a function of approaching the focus of a sphere from ANY POINT r=0 outside of that sphere.
The centre of mass is therefore not at the centre of the sphere, but relative to its surface.
1 is equivalent to diameter but r internally & r externally.

Revelation Of The Day #4: And that’s it folks. You don’t live in a 3+1d universe, you live in the the remainder of an (i^2) / 12 dimensional multiverse. Effectively we are all embedded inside and outside of each other. There are no discrete parts of a multiverse. We are all one!

Revelation Of The Day #3:
The 11 d space of string theory is actually just the integer value remainder of
(i^2) / 12 dimensional space.
In all of mathematics & physics the imaginary part of i^2 is always a function of radius relative to the function 4πr^2 projected down to 2D

Revelation Of The Day #2:
OMG! I have just for the first time understood what string theory is trying to explain… but can’t.
Those aren’t strings, those are 720° PATHS through 11 dimensional space, OUTSIDE the nucleus, but with a path that is UNIQUE to EACH electron radius.

Revelation Of The Day #1: I’ve just figured out how to project the FUNCTION 4πr^2 which has two solutions (one relative to 3 dimensions & one relative to 1 dimension) down to a 2D plane. This generates a clear zero dimensional 720° path that never crosses & a DIAMETER of
i ^2


Revelation of The Day #6:

1 = (e^(π* i))^2

Down pointing backhand indexAny thoughts?


Revelation of The Day #5:
I honestly think this makes way more sense that a circle being infinite and undefined.
Any physics professionals want to correct me on this, fire away.
Don’t be shy, let’s see if what you learned from someone else or what I’ve taught myself holds up best

Revelation Of The Day 4#:
Einstein ignored energy & calculate with a constant relative to a spherical boundary. If the boundary was accidentally a photon not a spherical planet, an inverse square would leave out atomic potential & infer black holes & singularities everywhere.

Revelation Of The Day 3#:
r^2 + r^2 = 4 π r^2 / 2
With the limit being defined relative to ‘any’ spherical boundary, is a far, far better proof of Fermat’s Last Theorem than Andrew Wiles one & a far less stupid proof of the Poincaré conjecture than Perlman’s.

Revelation Of The Day #2: All Platonic solids have a limit of r ^2 from any singularity relative to ‘aggregate potential surface’. When you describe any 1 of the 5 solids, you rule out all the r^2 potential of the other 4.
∴All volumes have a ‘potential’ limit of 4 π r ^2


Revelation Of The Day #1: There are only 5 Platonic solids because below a tetrahedron we logically have a circle & above dodecahedron we have a dimensionless singularity.
Both have a limit of r ^2 relative to ‘a potential surface’. Scale becomes irrelevant ‘potential’ doesn’t



Revelation Of The Day #6:
Quantum mechanics works beautifully not because it’s complete, but because it isn’t.
It does this by adding two (2) ‘hypothetical massless particles’ (photon/gluon)as force carriers, thus hiding the contribution of spin 2 (force of gravity) at all scales


Revelation Of The Day #5:
Einstein could accidentally hide spin 2 of gravity as the square of a constant, not because planets are spherical, but because non existent massless photons are. He didn’t notice because he left out a non spinning (unknown at the time) spin 0 Higgs field

Revelation Of The Day #4:
m=E/ c ^2

E=mc ^2

Therefore Einstein can do General relativity as geometry using a constant speed (distance/time) measured from the surface of a sphere & completely ignore E (energy).
the 2 in E=mc2 isn’t a square, it’s spin 2.
it’s gravity


Revelation Of The Day #3:
Einstein hid his error (ignoring the Higgs ‘spin’ of zero) and created a spin 2 gravity based model.
He hid the 2 in the square of the speed of light & therefore drew straight lines through a static space that aren’t there that he bent with geometry.

Revelation Of The Day #2:
The universe isn’t one single inflating ‘thing’, it’s an aggregation of ‘spin’.
Einstein is wrong but Nima Arkani-Hamed is right when he says this is literally all it’s possible to be made of. The only errors are the static values of gravity & the Higgs.


Revelation Of The Day: 4 yrs, 4 mths, 3 weeks & 1 day after meeting Nima Arkani-Hamed at Princeton, I realised the Higgs is defined not by 0, but by the r in 4π r^2
The universe is an average of 4+2 dimensions
Gravity is 4^1/2 (inverse square)
The r makes thisDown pointing backhand indexalgebraic.




Revelation of the day:
4π r2 is the ONLY mathematical function that actually IS an equation; because it explains two completely different geometries at once.
Both solutions are correct and yet the answer can only be either one solution or the other, not both at the same time.



Revelation Of The Day:
If the Riemann hypothesis is true (it is) you can’t count up from 0 only down from 1/2.
The 3 at the beginning of π ∴ isn’t an integer, it’s a POWER of 0.5

= 0.12500000…

0.5/0.125 is 4 ie. the dimensional limit of a sphere ratio π with a limit of ‘r’!

Replying to @AlisonMoyet
🙂 I’m so pleased you replied, because I ‘think’ that’s my greatest revelation of the day of them all & I’ve been working on this for 5.5yrs! π isn’t infinite Alison, it just says a sphere has a maximum of 4 dimensions. That’s all it’s saying… we live in 4 dimensions 🙂

@AlisonMoyet – I love that you had this revelation. I love the palpable excitement you reveal. Sometimes equations are just beautiful to look at even when you (me) have no earthly understanding. Wishing you a continuum of a happy day 🙂 xx


Revelation Of The Day: Both the fine structure constant & the cosmological constants are both unexpectedly odd numbers because they are both false (they are maths, not physics) aggregations of 8 internal electron radii projected out to 4 dimensions averaged out to 2 dimensions.


Revelation of the day: In physics (not maths) radius has an ‘infinitely’ higher energy value than diameter. Diameter always has no energy value because it’s energy limit is radius squared. radius squared has infinite energy at ‘r’… exactly where Einstein put centre of mass.


Revelation of the day 2/2
Answer: Pi is always COUNTING fractions, just that and nothing else.
But… The 3 at the beginning isn’t a fraction.
So… The ‘error’ in Pi is using an integer at the start, all of the other numbers are precisely correct.
The 3 in Pi is an error!

Revelation of the day 1/2: All of maths is just counting. We all it things like calculus or trigonometry, but at the end of the day it’s all just COUNTING.
Pi as a decimal is 3.141… COUNTING off to INFINITY.
But the diameter of that circle is just 1
Q: So WTF are we COUNTING?


Revelation of the day: Special Relativity disregards both the 3 or 4 dimensional geometry it takes place in & the fact that every observer is ‘part of’ the surface of a sphere, rather than separate to it. The two postulates are therefore describing something other than ‘reality’.


Revelation of the day:
Mathematics is the language in which God has written the universe
Galileo Galilei

This is garbage, you don’t explain physics with maths, you explain maths with physics and at the heart of all physics is a single unit of measurement… the electron radius.


Revelation of the day:
5+(3 ^5) = 248
This is why a 3 dimensional universe ‘looks to be’ 13.8bn years old & also why the cosmological constant 10^-120 appears’ to be so small if it was that old & infinitely ‘big’.
It’s actually the geometry of 4 dimensional internal reflection…



Revelation of the day:
We think about General Relativity as a description of the very big (macroscopic) & Quantum Mechanics of the very small (microscopic). This is wrong.
GR is a description of the very slow & QM of the very fast.
The difference is ‘time’ relative to frequency.


Revelation of the day:
The reason General Relativity & Quantum mechanics don’t work together is because both ignore the phase transition that occurs at the molecular level. The universal limit is defined not by the speed of light, but by net atomic RADIUS of ALL ionic bonds.


Revelation of the day:
The entire number line from zero to infinity is defined by the negative interval between 3 & 2 (i squared) not by the positive interval between 0 & 1 (+1).
Therefore the 3 in the decimal version of π is the approximation, the infinite fractions are precise.


Revelation of the Day:
The potential of Maxwells vector field is sourced by electro magnetism, Einstein’s vector field is sourced by density of matter. The potential of a final theory will be sourced by ‘energy’, not locally, but as aggregate potential across the entire field.


Revelation of the day:

The universe is no more written in the language of maths & equations, than Unicorns are written in the language of DNA.

Rather, the ‘universe’ & mathematics are limited by the same geometry. That geometry is as likely to be 3 dimensional as unicorns are.


Revelation of the day: a) There are an even number of photons in the universe b) Photons only come in multiples of prime numbers c) 2 isn’t a prime, it’s a pseudo prime that’s a twin prime happening at a single location d) That location can’t be spacial… it hast to be temporal


Revelation of the day: By imagineering spacetime all Einstein did was find a mathematical way to make 1 into a ‘pseudo prime’ to mathematically cheat geometric equivalence at every point.
All he needed was to ‘assume’ 2squared dimensions as a power of ‘c’, thus avoiding primes.


Revelation of the day: 355/113 is a better description of π than it’s base 10 equivalent, not because it’s more accurate, but because it its only correct to a value of 10*-8 This isn’t giving new information about π, but is telling us loads about radii & their relation to base 10


4 thoughts on “Katøi Collection”

  1. Since we’re into long, weird speculation anyway, I’ll share an old musing hanging around my hard drive. You may recall a discussion somewhere back there on your site about the nature of point-particles, where I’d said something like:

    ‘The article says at one point, “Some have argued that there is nothing more to particles than their relations, but intuition rebels at this claim. For there to be a relation, there must be two things being related.” I think this is an objection the author is trying to answer.

    ‘This goes to the heart of the question. There are not necessarily two point-particle “things,” which exist independently and come into a relationship. After all, what would it mean for a thing to “exist independently” without reference to any relationships, and then somehow come into a relationship?

    ‘Instead the proposal is that a relationship forms between two concerns relative to one another, and out of this relationship emerges what may at times appear to be point-particles. This approach has the advantage that the concerns are not necessarily reified as single point-particles. A concern could evolve into multiple relationships or interactions with other concerns, explaining quantum entanglement — that is, the relationship of “point-particles” in ways not limited by the space and time to which their reification would otherwise commit us.’

    Well, there’s more, in a file dated 2020-11-25 that invokes, among other things, imaginary numbers. I’m no mathematician, and I was probably smoking drugs when I came up with these thoughts, but they seemed to make sense at the time. Here it is, for what it’s worth:

    What does it mean for a concern to have a wavefunction? This is possibly the phase of operation of the concern. As I understand Whitehead, the concern alternates between phases where it receives information, and phases where it acts in response, sending out information of its own to other concerns. Presumably, its response depends on the positive opportunities in the wavefunction; the other half of the time it is taking information in, and to anything looking for a response, it appears to be non-existent.

    This would cast the practical probabilities entirely in one half of the waveform, unless there are such things as “negative probabilities.” This might explain why we have to square the probability to calculate the wavefunction, and why we have to use imaginary numbers. It might be fruitful to base the wavefunction symmetrically on a centre point, below which something like “anti-probability” occurs. This is the part of the waveform below the zero line, the part expressing negative values; to describe them properly, we need imaginary numbers, which describe the anti-probability, an area in negative space, the time when the concern is taking in the response cycles of other concerns.

    This is perhaps why only two concerns can exist in some atomic circumstances, why there are two types of spin: exactly two concerns, and no more, can cycle in push-pull mode to be present and responding and also receiving and reflecting in every cycle, not just every other cycle.

    The concern can respond to more than one other concern at a time. For example, when it interacts with a concern that is blocking it (a slit), it could also respond elsewhere to another concern that is blocking it (another slit), if such a slit is present. What it does depends, systematically in this case, on the ways it can respond to the apparatus, or rather, to a set of concerns represented by the apparatus. If the wavefunctions of the apparatus happen to synchronize with the wavefunctions of the concerns in a certain way, then there is potential to sense and respond between the two concerns.

    If this is true, then the wavefunctions of certain atoms that do not interact, such as the inert gases, might be in some way offbeat or dissonant compared to ones that do, such as oxygen or carbon. We could test for this.

    We say the valence bands are full, but we need to understand how each new band affects the possibilities for rhythmic synchronization. It’s possible that as the atoms get larger and larger, they reach a wavefunction saturation where (for fractal reasons, maybe) we have white or pink noise, and no signal in the cycle of reception and
    response. At that point we need a higher energy signal, which would correspond to a more massive nucleus, a new valance band, a louder instrument perhaps, signalling a new recognizable rhythm with which to interact with other concerns at the same level.

    Gravity is possibly the deliberate synchronizing of concerns, adjusting the rhythm of one very slightly to match another. When a mass of concerns meets another mass, each compensates in order to synchronize; but the larger mass is less able to compensate due to its inertia (momentum), so the smaller mass accelerates, which is to say, it alters its timeframe continuously, as it were leaping ahead with each crest, to synchronize with the timeframe of the greater mass.

    This is entirely testable in math, I’m sure, but I haven’t a clue how.

  2. We certainly have talked on this before.

    On point particles – that was my passing reference to Boscovich in the intro, but very Bohr / Whitehead also. Points defined only by their (relative) relations to other points, the only relations really being their separation in space-time. Which of course makes those relations dynamic, so easy to imagine waves and resonances described this way.

    I have no trouble treating imaginary “i” as real in a geometric sense – a quarter-turn rotation (and “pi” as the half-turn).
    Also like that “concern” language for an arbitrary object – an arrangement or pattern of inter-related “points”.
    Concern suggests the idea of “relevant information” as opposed to a necessarily materialised object.

    Going to have to mull over those other thoughts about relative frequencies and amplitudes explaining the inter-particle forces atomic and gravitational (the resonances & phase shifts explanation of gravity) – though of course that’s what Boscovich was doing – relating the relations to forces (in his case by some madcap formulae, long before we had 20th C physics).

    Fascinating stuff

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