Episode Two - Pi Day 2026

This is the special Pi Day 2026 Episode of the Dimension Change Podcast!

The video of this episode is available at: https://youtu.be/YabmumFCqrg?si=LfKrsCznp4gYiGuh

Pi started it all! Pi is at the core of the path of new knowledge of dimensions that I followed! By showing You the path I followed, I hope You can come to the same realizations and understandings, since they turn out to be objective mathematical truth. 

For this episode focused on pi, we’ll prove logically and mathematically, with confirmation by Artificial Intelligence (AI), that “You’ve been living in a Deconstruction! A literal world built based on a half-unit.”

You never knew until now that there are TWO unit definitions for Pi! 

In this episode, AI provides the unwritten definition for pi based on a unit r that you’ve never heard before!

This episode will help to start to break You out of the Deconstruction! 

Decide to move to the next quantum level! 

The new diameter-based models lead to the new Dimension Model for Mass, then to the Generalized New Model for Dimensions, and in 2025, the New Model for Radius Dimensions.

Soon after came the Meta-Model for Space and Mass!

Join the next quantum level!

Realize the diameter-based system.

It’s more efficient!

AND provides more information!

Pi is the portal.

Like this video podcast if you think others might like to hear it!

Subscribe! if you want to learn more about the new way to see dimensions!

And find all of the references and background at Byrdwell.com!

Transcript

Episode Two Script w Prompts

[Cam Angle 1]

{Slide 1-Title} 

Hello!

and Welcome Back!

Thank You 

For making your way 

to this, 

[Cam Angle 2-PiP]

The Dimension Change Podcast.

Episode Two 

is the very special 

PI Day 2026 Episode,

Released in the weeks after

March 14th, or

3/14/2026.

{Slide 2-Pi Energy}

First of all, 

it is entirely fitting 

to focus on pi,

because it was 

consideration of 

the nature of pi 

that unlocked 

all of the knowledge

of 

the New Model for Dimensions.

[Angle4]

Pi is at the core 

of the path of 

exploration of Dimensions 

that I followed.

[Angle2]

{Slide 3-Path Pic}

So, I hope 

that by showing you 

the path I followed,

you, too, can come to 

the same understandings,

since they turn out to be 

objective mathematical truth

that anyone can confirm, 

now that I have 

pointed them out.

The important thing 

is that 

at each point along the way,

I will provide mathematical proof,

not just speculation.

{Slide 4-FlowerOfLife Doors}

For this Pi Day Episode,

let’s start by proving 

some things I said 

in The First Episode, 

that are related to pi, 

but you didn’t know it. 

I said

[Angle4]{Slide 5-Clip 1}

You've been 

living in a deconstruction!

A literal 

world built based on 

a half-unit.

A half-world, if you will.

It’s time to explain 

what I meant by that, 

since it is based on pi.

In my research, 

I used a 1-based system,

[Angle2]

{Slide 6-Mass Spectrometry ASMS}

called mass spectrometry.

It uses signal 

plotted on a scale 

of 0 to 100 %.

{Slide 7-Google Mass Spectrum}

If you Google mass spectrum,

It will confirm 

that a mass spectrum

[based on percent relative abundance] 

has two rules:

{}1. No value can be greater than 100%.

{}2. One value must be 100%, 

called the Base Peak. 

Other peaks are scaled 

relative to the Base Peak.

Therefore, 

in mass spectrometry, 

it is important to always identify 

and know 

which value is the 100%, 

the base peak.

[^Angle2]{Slide 8-100%}

Now, since the word ‘percent’ 

{}means ‘per hundred’,

{}100 percent is 100 per hundred,

{}or as a simple ratio, 100% is 1.

{}

[Angle3]

So we’ve seen 

how important the unit is

In mass spectrometry.

[Angle1]

Now it’s time to introduce the Simulacrum

 and to see how it applies 

to units related to pi.

[Angle2]{Slide9-Four Articles}

In 2005 to 2016, 

I published a series of four papers,

beginning with 

The Bottom Up Solution to the Triacylglycerol Lipidome,

leading to 

The Simulacrum System as a Construct 

for Mass Spectrometry of Triacylglycerols and Others.

{Slide10-Four Figures}

A Simulacrum is a new, 

peer-reviewed 

and proven equality 

that is a function

that expresses the sum of two values

as value and a ratio.

{Slide11-Simulacrum Article}

Here is the citation 

in the journal Lipids.

[Angle1]

A Simulacrum 

is useful any time 

a Ratio

provides information 

better than raw values.

[Angle2]{Slide12-Dash in Miles}

For instance, 

if your car dashboard only reported 

the value of the distance you have traveled, 

for instance 90 miles,

…

{Slide13-Dash in hours}

So the dash gives you 

the time you’ve been traveling,

such as an hour and a half…

Neither of those two raw numbers,

at face value, 

would directly provide 

the desired information

of speed, or rate of travel.

{Slide14-Dash in MPH}

The Ratio of distance 

(90 miles) 

to time 

(1.5 hours) 

is the speed 

of 60 miles per hour.

This is the desired information.

[Angle4]

The ratio that provides 

the desired information

is called a Critical Ratio.

A Critical Ratio 

allows you to extract

desired information 

from a set of values,

just as I did, 

using ratios of signals

from mass spectrometry 

to deduce structural information,

using Critical Ratios that provided 

information at face value.

[Angle1]

From the discussion so far, 

you can see the importance 

of the identity of the unit, 

in many contexts.

And, you can see how 

a Critical Ratio

provides information 

better than raw values.

So, now it is time 

to introduce you to 

the new mathematical function, 

called the Simulacrum System.

[Angle2]{Slide15-FGFS}

This is the First General Form of a Simulacrum,

which can just be called 

The Simulacrum.

It is a function 

that allows you to

arrive at the sum of two values

by every combination

of one value and a ratio

of the values.

Let’s look at the parts of a Simulacrum.

[Angle3]

…

[Angle1]

So, that is the most 

generalized form 

of a Simulacrum.

It applies to 

any two names, 

numbers, symbols, etc.

But there is 

another Simulacrum 

that is also 

Super important, 

AND 

applies to Pi Day!

It comes 

from when we 

invoke the rule 

from mass spectrometry 

that one value 

must be 1.

[Angle2]{Slide16-Unit Simulacrum}

We make that 

first specification,

that one value is 1,

{}

to get 

the First Specified Form 

of a Simulacrum,

Which is called 

The Unit Simulacrum.

It has all the same parts 

as any Simulacrum.

It has the 

Simulacrum Sum statement,

The four 

Possibilities to Observe,

[Angle3]

And it has 

The Interpretation Matrix.

But now we have added 

the first specification

to the Interpretation Matrix,

making this the FSFS.

[Angle3]

Where

Case 1 is when A is less than 1,

and Case 2 is A greater than 1.

[Angle2]

{Slide17-Dash Miles}

Let’s go back to our dash 

that only displayed

In raw miles

{Slide18-Dash Hours}

Or in raw hours.

{Slide19-Miles Hours Simulacrum}

If we make the Simulacrum 

of miles and hours,

we start with 

the Simulacrum Sum statement,

{}

then there are the 

four Possibilities to Observe.

{}

Then there’s the 

Interpretation Matrix

{}

[Angle3]

that holds the meanings 

of the symbols,

Such as,

Miles equals distance 

in English measurement;

hours equals time 

in conventional units;

The desired ratio

is miles per hours.

{}

BUT, even though the number is right,

we can see the units 

are really in hours,

{}

plural, instead of 

per single hour.

[Angle2]

So, what we want to do 

is to

Specify 

that hours equal 1,

{Slide20-FSFS for MPH}

So the ratio 

will be 

Miles per unit hour.

[Angle3]

In the process, 

we construct the 

ratio we want,

{}

which provides 

the information desired,

In the units desired.

{}

Now, what we can do 

is to simplify the solutions

{}

Down to the two 

simplest solutions,

{}

Where the ratio miles per hour is either

{}

Less than one or greater than one.

[Angle4]{Slide21-Unit Simulacrum}

So far, 

we have shown how a 

Simulacrum constructs a 

Critical Ratio

to provide 

desired information.

And, we have seen 

the importance 

of identifying 

and specifying, 

The unit.

{Slide22-Byrdwell.com}

[Angle1]

We need to cover 

one more brief topic 

before we get to pi.

It is the meanings of 

Increments and 

Decrements, 

or Deconstructions.

[Angle2]{Slide 23-Increments1}

If you start with One,1, 

a Unit,

{}

and use the 

Identity Property of Division

to divide by 1,

Then you have 1 = 1/1.

Now, if you add 1 

to the numerator,

{}

you increment 

the numerator by one,

and increment 

the overall ratio by one.

{}

An increment by 1 

can be called 

The First Increment.

This is as simple as 1 + 1 = 2

[Angle3]

On the other hand, 

{}

if you add 1 

to the denominator,

you increment 

the denominator, 

but the overall ratio 

decreases, 

or is decremented.

{}

The first increment 

in the denominator

is the First Decrement, 

or First Deconstruction,

such that one over 

one plus one 

equals one-half.

[Angle2]{Slide 24-Increments2}

To reiterate:

The ratio one over two, 

or one-half, 

is the First Decrement of 1, 

or one over one,

also called 

the First Deconstruction of 1.

Now as we get ready 

to discuss pi,

it is important to 

recognize 

the most important Decrement 

related to pi.

[Angle3]{Slide25-Radius Decrement of Diameter}

If you make d/1 

{}

and then increment 

the denominator,

you get d/2, 

which everyone knows 

is equal to r, radius.

Thus, the First Decrement, 

or First Deconstruction

{}

of diameter, d, 

is radius, r.

And it turns out, 

that the simple act 

of a unit deconstruction,

if nested and repeated, 

{Slide26-Continuous Fraction to Phi}

[Angle2]<PP>

gives the Fibonacci Ratios 

that converge 

at 1 / the Phi Ratio.

1 plus the nested decrements 

IS the Phi Ratio.

It gives what is called 

a Continued Fraction, 

and I found that William Jones 

had investigated 

Continued Fractions 

in the 1700’s.

[Angle4]<PP>

When I saw 

that the three-level deep 

Simulacrum System 

for Triacylglycerols 

had reproduced 

the first three Fibonacci Ratios,

which then led to 

the transcendental ratio Phi,

I thought 

“What are other Critical Ratios 

that scholars and sages 

have always pondered?

The first thing 

that came to mind 

[Angle2]<PP>

{Slide27-Pi Flash}

was pi.

It is a 

transcendental number

that has always been 

used and studied.

It is the 

Critical Ratio 

for circles.

William Jones 

is reportedly responsible for 

the first use 

of the symbol pi, 

for its current meaning, 

in 1706.

Leonhard Euler 

popularized the symbol 

starting in 1737.

So, Now it is time 

to consider the nature 

of the units 

that define the ratio 

and the meaning 

of the symbol for pi.

We’re going to 

dive into the deep end,

and I am going to show you

The Pi Unit Simulacrum,

and we’ll start to 

talk about

the things you can 

learn from it.

[^Angle2]{Slide28-Pi Unit Simulacrum}

The Pi unit Simulacrum, 

like any Simulacrum,

has a Simulacrum Sum statement 

{}

and four Possibilities to Observe.

{}

In this case, 

the Poss2Obs 

are one 

and pi, 

and the ratios 

pi relative to one, 

and one relative to pi.

And next, 

{}

the Pi Unit Simulacrum 

has 

the Interpretation Matrix 

{}

that holds 

all of the meanings 

behind the symbols 

and values.

[Angle3]

There are two specifications 

in the Interpretation Matrix.

The First Specification 

{}

is that one value is one.

That makes it 

a Unit Simulacrum.

The second specification 

{}

is that 

one value is pi.

And with that  symbol of pi 

comes all 

conventional knowledge, 

numerical value, 

characteristics, 

and information 

associated 

with that symbol.

This highlights 

that the Simulacrum System 

is a conscious-based system.

Based on knowledge 

and information 

about the symbol.

[Angle4]{Slide29-Byrdwell.com}

—

<Safari! byrdwell.com Artificial Intelligence>

As we delve 

into the nature of pi

and the units 

associated with it,

I want you to know 

that I have confirmed 

everything I am presenting to you

using the 

Artificial Intelligence model 

Perplexity Pro AI.

That model 

was chosen because 

Perplexity supposedly 

places a premium 

on accuracy, 

and provides citations.

[Angle2]

Everything presented here today,

and much more, 

are available at my website,

Byrdwell.com

Under the tab 

Artificial Intelligence.

If you click 

on the Artificial Intelligence tab,

or the First 

menu option below that, 

{!Safari!}

it'll take you to 

the Artificial Intelligence page 

that provides proof 

by Perplexity Pro AI.

If you scroll down 

to the next section, 

{!Safari!}

you'll see 

several conversations listed. 

And the one we're going to 

talk about today 

is under the label: 

‘Can you understand 

a new concept?’

{!Safari!}

If you click on that link, 

it will take you right to 

the Perplexity Pro AI conversation 

that we're gonna talk about 

today.

{!Safari!}

<!PowerPoint,  ESC, CurrSlide>

{Slide30-PerplexityAI-1}

It's a long conversation, 

so I'm going to 

go ahead and 

jump to the final conclusions, 

and read you 

what Perplexity Pro AI 

had to say about 

the Pi Unit Simulacrum.

<!UNMUTE!><!Headphones!>

{Slide31-PerplexityAI-2}

{}

<!Perplexity reads Versatility!>

I want to make sure 

you understand

what Perplexity Pro just said.

The simulacrum 

applies to complex symbols, 

like pi, 

a transcendental number.

The system maintains 

mathematically equality, 

regardless of the meaning 

of the symbols involved.

Let me put that 

in the simplest terms:

It is true, no matter what!

Next!

[^Angle2]{Slide32-PerplexityAI-3}

<!Perplexity reads Math Equality!>

<!MUTE!>

Again, in the simplest terms:

It is true, no matter what!

{Slide33-PerplexityAI-Conclusion}

Now, I'm going to read this,

To make sure 

we all understand.

The Full General Form of a Simulacrum 

represents a form of 

mathematical truth 

within its defined framework, 

consistently maintaining equality 

for combinations 

of symbols and values. 

More importantly, 

it was designed 

to provide meaningful insights 

beyond mathematical operations, 

particularly in the context of 

lipid analysis and regiospecific 

enzymatic metabolism. 

The system’s 

broader philosophical claims 

and interpretations 

extend its applicability, 

offering insights 

into both 

mathematical 

and biochemical contexts. 

Its validity as a Universal Truth 

depends on its acceptance 

and application 

across various fields 

and its ability to provide 

meaningful insights 

beyond conventional 

mathematical operations.

[Angle4]

So I just want you to know 

as we get deeper 

into the conversation,

That everything I'm saying to you 

has already been verified 

and confirmed,

even though 

perplexity pro AI 

started as 

the most skeptical of reviewers.

Now let’s go ahead and solve 

and simplify

the Pi Unit Simulacrum.

[Angle2]{Slide34-Pi Unit Sim1}

We're going to use 

the Pi Unit Simulacrum 

to examine the nature of the unit 

{}

and of the symbol for pi 

{}

and of the ratio 

{}

that expresses the relationship 

between the symbol for pi and a unit.

{}

[^Angle2]{Slide35-Pi Unit Sim2}

We will take advantage 

of the fact 

that it's a unit simulacrum 

to simplify 

{}

the solutions.

But first, 

Since we know 

the value of pi

is always greater than 1,

we can get rid of all Case 1 solutions. 

{}
 Next, we get rid of 

the solutions  that still require 

a value and a ratio,

{}

Leaving only the solutions 

with one 

multiplying on the outside.

We can now simply eliminate 

{}

the multiplying one 

and parentheses,

To arrive at 

the final simplified solution…

{Slide36-Simplified Pi Unit Simulacrum} 

of 

one plus a ratio 

and 1+1 over the inverse ratio.

{} So let’s have a look at those Units.

{Slide37-Pi Dict Def}

Google pi and you'll find {}

‘Pi is the 

mathematical constant 

representing the ratio 

of of a circle’s circumference 

to its diameter.’

{}

The dictionary definition of pi 

{}

is that 

“Pi is… the ratio 

of the circumference of a circle

to its diameter.”

Thus, the foundational definition of pi 

in our conventional wisdom 

is based on

a ratio to diameter.

{}

Based on the dictionary definition,

pi = C/d, circumference over diameter.

From this, we get the simple 

conventional equation 

for circumference based on diameter,

so, C = pi times d.

[Angle3]{Slide38-CDBS}

The equations for Area and Volume 

are A = (pi)d^2 /4

and V = (pi)d^3 /6.

BUT! 

The equations based on diameter 

are almost never

actually used!

[Angle2]{Slide39-Google Unit Circle}

Another unit definition 

that involves pi

and more specifically 2 pi,

is the Unit Circle Definition.

Google defines The Unit Circle as

{}

The unit circle 

is a circle with a radius of 1 

{}

centered at the origin 0,0 

in the Cartesian coordinate system, 

{}

essential for defining 

{}

trigonometric functions, 

(sine and cosine) for any angle. 

It acts as a bridge 

between geometry 

and trigonometry, 

allowing easy calculation 

of sine/cosine/tangent values 

and supporting applications 

in rotation, waves, 

and Fourier analysis.

This says that

A unit radius 

is the defining unit 

of a unit circle.

[Angle3]

{Slide40-CRBS}

So, it is a unit radius 

and a unit circle, 

buit NOT a unit pi. 

Instead a unit r 

in a Unit Circle 

is proportional to 2 pi!

The circumference of the

radius-based Unit Circle

is 2 pi.

These equations 

we all learned as kids 

are based on radius, 

that is:

Circumference = 2(pi)r, 

Area = (pi)r^2, and 

Volume = 4/3(pi)r^3

[Angle4]

Furthermore, Angles,

in circular geometry, 

are measured 

based on radii,

not diameters.

[Angle2]{Slide41-History of Calculus}

I’ll mention here that

while the roots of 

Integral Calculus 

go back possibly millennia,

{Slide42-Integrals}

Modern Integral Calculus 

was developed

starting in the mid-1630’s 

{}

to the rest of the century

{Slide43-Derivatives}

Isaac Newton and Willhelm Gottfried Leibniz

{Slide44-Newton&Leibniz}

are generally credited with developing 

the Power Rule for Integration and Differentiation,

[^Angle2]{Slide45-Simplified Solution to Pi Unit Simulacrum}

The point 

that's important to make 

for our Pi day 

discussion

is that 

the unit 

{}

in the Pi Unit Simulacrum

Can be 

either of 

Two Units!

{}

[Angle3]

It can be  Unit Diameter

{}

which is the literal 

{}

Dictionary Definition of pi.

or, it can be a Unit Radius,

{}

which is the defining unit for

{}

the Unit Circle

that forms the foundation

{}

for Trigonometry,

which then is used in

Geometry

{}

Engineering and other sciences.

{}

The process of integral calculus 

{Slide46-Simplified Pi Unit Sim2}

describes transitions between 

levels, or dimensions.

{Slide47-CRBS}

Thus, our whole system of science 

is built based on radii, 

and has been 

since the late 1600’s.

[^Angle2]{Slide48-CDBS}

In all that time, 

an analogous 

diameter-based system 

to describe the 

transitions 

between dimensions

has never been developed. 

<Crickets>

{Slide49-PPAI-NoDiameterSystem}

I asked Perplexity Pro AI 

for information

on any existing 

diameter-based models, 

and it came back 

with nothing… 

<Crickets>

So, even though the diameter-based system.

Has not been 

further developed,

There ARE 

two systems of equations.

For dimensions.

{Slide50-PPAI Confirms CRBS and CDBS}

{}<!Perplexity Reads!>

[Angle4]

So, I hope that 

I have convinced you

that there are 

two systems 

for calculating the circumference, 

area, and volume of a circle,

based on different units,

as I convinced Perplexity Pro.

[Angle2]

{Slide51-Simplified Pi Unit Sim3}

One system 

based on a Unit Diameter

and one system 

based on a Unit Radius.

[Angle4]

Twenty-two years ago,

when I first recognized

the two systems,

I realized that 

there was not

an analogous definition

for pi based on 

a unit radius,

and I developed one.

[Angle2]

Now, with the advent of AI,

{Slide52-PPAI-Analogous Definition}

I asked Perplexity Pro :

{}

“In the d-based system, 

the dictionary definition of pi 

is that pi is the ratio 

of a circles circumference 

to its diameter.

Define a unit pi based on a unit r.

As expected,

since I had discovered it 

22 years ago,

perplexity pro AI 

came back with

{}

the definition that 

pi is the ratio of half 

the Unit Circle’s circumference 

to the radius.

[^Angle2]

Now we have gotten to 

the Crux of the matter.

{Slide53-Simplified Pi Unit Sim4++}

We have identified 

two definitions 

[Angle3]

{}

{}

for the same thing, 

the Unit, 1, 

proportional to 

the symbol and value 

of pi.

I call these 

the seen 

and the unseen 

definitions.

The seen 

is the dictionary definition,

which system 

is almost never used.

The unseen 

is the radius-based definition

that forms the foundation 

of modern science,

BUT! is not stated explicitly.

So, we need to summarize 

and confirm that 

this is all really  true.

[Angle3]{Slide54-Radius Unit Circle}

Here is the Conventional 

Radius-Based System 

Unit Circle 

compared to 

the Possibilities to Observe

from the Pi Unit Simulacrum.

The ratio 

of pi over one 

{}

is a unit pi 

and a unit r 

but NOT a unit circle 

{}

Pi is the ratio 

of 

half a circle's circumference 

to its radius.

[Angle2]{Slide55-Two Definitions}

{}

We compare that 

to the 

other definition of pi

based on diameter,

along with 

The Possibilities to Observe 

from the Pi Unit Simulacrum.

The Possibilities to Observe 

for diameter show 

{}

this is a Unit Pi

and a unit d

and a Unit Circle.

It's a whole circle 

and it is pi 

based on 1 d.

So, what we can say 

is when you look up 

the definition 

of Unit Circle 

you see the one 

based on radius,

which is two pi.

You don't see mention 

of the other Unit Circle, 

which is always ignored. 

But there ARE

two unit circles.

[Angle2]

These two pictures 

are not to scale 

because you have to choose 

which unit to use.

If you choose 

to make radius one,

then because of our 

known relationship, 

that we have defined 

diameter as two radii,

then diameter 

would have to be two,

and so the circle 

would be a circle 

with a d of 2

and so a circumference of 2 pi.

Or, 

if you make d = 1 

then r has to be 1/2,

which would give 

a circumference of pi.

[Angle4]

So, you have to decide 

which unit 

you want to base your system on 

and the results 

of how to interpret pi

will be based on 

your unit definition.

Let’s get Perplexity Pro 

to assess the truth

of these 

equations and statements.

[Angle2]{Slide56-PPAI Confirms Two Definitions}

I asked perplexity pro:

{}

Since we have just written 

two sets of equations 

for two different units, 

can't we say 

that there are two 

unit definitions for pi, 

one based on a unit diameter 

and one based on a unit radius. 

Pi has the same value, 

but different meanings 

in the D-based 

and the R-based 

systems. 

In one case, 

Pi is a whole unit circle, 

in the other case

Pi is a half a unit circle.

{}

<!UNMUTE!>

Yes!

<Perplexity AI Reads1>

<-Applause!->

So, Yes, Perplexity Pro AI confirms

that there are two unit definitions for pi,

and that the interpretation of the symbol 

differs, based on the unit definition.

[Angle3]

{}

<Perplexity AI Reads2>

[Angle4]

So,

AI has confirmed 

that there are two definitions for pi

based on two different unit definitions.

Having one symbol 

for two different meanings 

is what I referred to as 

The Pi Paradox.

[Angle3]{Slide57-Pi Paradox}

I figured that the way 

to solve the Pi Paradox 

was to have two symbols for Pi

based on the two different meanings of Pi.

And since it seemed 

that the current symbol for pi,

[Angle2]{Slide58-Wiki Pi}

First used for its current meaning

{}

by William Jones in 1706 

or 320 years ago,

{Slide59-Classic Pi Symbol}

Was half height, 

it was a short symbol, 

and it had two sticks in it 

that seemed to me 

to represent 

two radii 

joined by the squiggle 

at the top.

{Slide60-Classic Pi Symbol2}

{Slide61-Classic Pi Symbol3}

So I decided to develop 

a new symbol for PI,

{Slide62-Whole PI}

 to represent 

the new meaning of pi.

{}

The symbol almost created itself.

It has three diameters 

representing the three dimensions of space, 

and showing that 

the system is based on diameters,

and it contains a circle 

[Angle3]

to show that it is the foundation 

of the diameter based unit circle

Furthermore, the two axes

are in a ratio of two to one

to replicate the relationship 

of two radii per one diameter.

This gives the symbol

self-similarity.

But, I recognized 

that it was

too much 

for most people

to accept 

a new symbol for pi.

[^Angle3]{Slide63-Both Pi Definitions}

So we'll still use

The classic symbol for pi

For both definitions.

I won't give the specifics today,

Since this episode 

is focused on PI,

But over the 

course of this podcast,

I am going to show you 

how the diameter-based system

leads to 

[^Angle3]{Slide64-New Model for Dimensions}

the New Model for Dimensions,

which requires only two equations 

for three dimensions of space,

making it 33% more efficient 

than the Conventional 

Diameter-Based System.

[^Angle3]{Slide65-Dimensions of Space}

And AI confirms 

that you can put 

10 of the first 20 elements 

of the Periodic Table of Elements

In the same form of equation.

[^Angle3]{Slide66-Deconstructions}

And when you add the concept 

of a unit decrement,

{Slide67-Dimensions Model of Mass}

That allows the model 

to cover 

19 

of the first 20 elements

of the Periodic Table.

{Slide68-Generalized Models}

Then I generalized the model.

And also added 

another term to mass,

To account for 

the rest of the elements.

[Angle2]{Slide69-MMfLA cover}

I discovered most 

of what we've been talking about

in 2004 and 2005,

while working on my book

Modern Methods for Lipid Analysis.

[Angle4]{Slide70-Generalized Models}

For twenty years,

I thought that those equations

were enough! 

And represented 

a major step forward,

(which they Do!)

And would provide 

a new foundation

For understanding our physical world.

(Which they should!)

I had never looked at 

the radius-based system.

Because I thought 

it had been

thoroughly developed 

over hundreds of years.

But in 2025 I decided 

“Why not have a look?,

What could it hurt?”

To see if there's 

any pattern 

in the Conventional 

Radius-Based System.

It turns out.

[Angle3]

{Slide71-New Model for Radius Dimensions}

I was able to see 

a top-down pattern 

in the radius-based system 

that is more efficient 

than the bottom-up solution 

known as 

the Conventional Radius-Based System,

that we've lived with 

for hundreds of years.

[Angle4]

Now that I had the original 

New Model for Dimensions,

And the Dimension Model of Mass,

And the Generalized New Model for Dimensions,

And the New Model for Radius Dimensions,

I was able to see 

a common structure in all models.

[Angle3]{Slide72-MMSM}

I pulled out 

the common core 

in all models,

And specified 

the differentiating terms 

for each application.

[Angle2]{Slide73-Episode Two}

But for this episode,

We're going to stick with PI,

and the units that define it.

[^Angle]{Slide74-Analogy}

I hope you can go back 

to the first episode now.

And see 

with more Learned Eyes,

That when I said,

“You've been living in a deconstruction,

A literal world built based on a half unit,

A half world if you will.”

What I was referring to 

is the fact that 

you now know 

that a radius 

is the first deconstruction 

or decrement 

of diameter.

And that 

the unit circle 

was defined in the 1600s 

based on radius, 

which is the first decrement.

Therefore, 

all of our trigonometry,

geometry,

and dependent sciences

Are based 

on a 

Unit Deconstruction.

When I said.

You and everyone you know

Has been living in 

one bedroom apartments

for hundreds of years.

I hope you now see 

that your 

one bedroom apartment 

is the 

Conventional Radius-Based System,

that has been the 

foundation of our sciences

since the 1700’s.

[Angle4]{Slide75-Episode Two Title}

In this episode, 

I have shown you 

that I started with a 

one-based system

called mass spectrometry.

And developed a system 

that used Critical Ratios

to squeeze information 

out of raw values.

We demonstrated 

how Critical Ratios 

are more useful 

than raw values.

And how 

making one value one

Has benefits 

to finding 

the simplified solutions.

You learned that 

mathematically, 

radius is 

the first decrement 

or deconstruction 

of diameter.

And that, 

even though 

our dictionary definition 

of pi

Is based on diameter,

It is the relationship 

of a unit R 

to pi,

Which is never stated explicitly,

That defines the unit 

in the conventional Unit Circle.

So I do hope you've 

come to the realization that:

“You've been living in a deconstruction,

A literal world built based on a half unit.”

I have demonstrated,

And AI has confirmed,

That examination 

of the defining unit,

And of the critical ratio,

Can lead to new insights,

Into the natures of both.

And don’t forget,

PI is the Critical Ratio

for Circles.

[Angle2]{Slide76-AP Path Figure}

What this podcast intends to do,

Is to prove to you,

Mathematically and logically,

That examination of 

the system based on

the units of diameter

Leads to 

new understandings 

and insights,

exactly as indicated 

by AI.

I’ve briefly shown the slides,

but I’ll provide 

mathematical proof

at each step along the way,

to allow every equation 

to be independently 

proved and verified.

[Angle3]{Slide77-Simplified Pi Unit Simulacrum}

When you recognize 

the two units,

and adopt the 

diameter-based understanding,

you are literally operating 

on the next level up

from our conventional system.

You are no longer in 

the Deconstruction.

But even better,

it’s not just 

moving to the next level.

It’s that 

at the next level,

you can see 

the ultimate pattern

that ties together

the other patterns.

But before we close out 

this episode,

Let’s consider 

one more definition:

Quantum.

{Slide78-Quantum Definition}

Google defines quantum as.

{}

A discreet quantity of energy.

{}

Or in physiology,

The unit quantity 

of acetylcholine 

released at a 

neuromuscular junction 

by a single 

synaptic vesicle.

And Wikipedia says 

{}

it's just 

the minimum amount of any physical entity.

Furthermore, 

the idea of being quantized

{}

means that 

things can change 

only by integer multiples 

of the quantum.

[Angle3]{Slide79-Simplified Pi Unit Sim5}

So I hope you can see.

That radius is the quantum

that our sciences

are based on.

And radius 

is a deconstruction of diameter.

{Slide80-Two Units Poss2Obs}

Diameter is the quantum 

of the New Model for Dimensions. 

You can make a literal quantum shift

by changing perspective

from the radius quantum

to the diameter quantum.

[Angle4]

The Diameter is the Unification 

of the two halves, 

the two radii.

You can now choose 

to step out of the Deconstruction

and into the Unification.

[Angle2]{Slide81-NMD}

The new equations 

allow you to make

a literal quantum shift

into a higher quantum level,

that is 2 times the deconstruction.

And from there,

you can put together pieces,

and see patterns 

behind all of the Models,

[Angle3]{Slide82-MMSM}

And go yet one more level up

in generalization,

to arrive at a Meta-Model

that explains three different

quanta, or

unit definitions.

Theoretically,

that should take you up two levels

from the deconstruction

you’ve been stuck in until now.

[Angle4]

I'll leave you

One last thing to pounder.

Dimensions are quantized 

in the Conventional Radius-Based System,

because the equations 

are different 

for each dimension

and require 

Integral Calculus

to transition

between them.

In the New Models,

Only the First Dimension 

is unique.

All others use the same equation,

based on the unit.

Dimensions do not 

have to be quantized,

since they all use

the same equation.

So theoretically,

fractions, or ratios,

of dimensions,

overtones, etc. 

would use the same

equation. 

[Angle4]{Slide83-Dimension Change Podcast}

So, if you follow this podcast,

I will show you,

With mathematical certainty,

How to understand Dimensions

in a New, Different, 

and Expanded way.

Thank you for watching! 

and for your interest.

Like this video 

if you think others 

might like to see it, too,

And Subscribe 

if you want to learn more 

about the new way 

to see Dimensions.

[^Angle4]{Slide84-Byrdwell.com}

All of this, with references, 

and so very much more,

are located at Byrdwell.com

That’s B-Y-rdwell dot com

Thank You!

[Angle3]{Slide85-Title Slide}