Going back to the 1st book, on pg. 138, I just re-read something that I think is rather important and yet another indicator of the veracity of the Ra material,
I'm not sure if many people here are familiar with Euler's Identity (e^(i*π) + 1 = 0), but if you are then you're probably aware that the exponential function e^z can be defined as the limit of (1 + z/N)^N, as N approaches infinity, and thus e^iπ is the limit of (1 + iπ/N)^N.
So, in the below animation, N takes various increasing values from 1 to 100. Thus the computation of (1 + iπ/N)^N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 + iπ/N)^N. It can then be seen that as N gets larger (1 + iπ/N)^N it approaches the limit of −1.
![[Image: ExpIPi.gif]](http://upload.wikimedia.org/wikipedia/commons/0/0e/ExpIPi.gif)
What this shows is going from an otherwise straight line we naturally converge on the geometric curved representation of π. This is exactly what Ra is describing, "the infinite whole paradoxically described by the straight line ... This paradox is responsible for the shape of the various physical illusion entities you call solar systems, galaxies, and planets of revolving and tending towards the lenticular."
I find this so compelling because when I first started exploring S.H. I intuitively saw it implied all things were a single unit. To understand this I imagined a logarithmic spiral coming from 0 as the starting point creating a circle or the polar coordinate system.
To try and illustrate this on a more abstract level to a group of mathematically-minded friends, I threw together the following demonstration:
(1) a + b = a - b ⇒
(2) b = (a - a) - b ⇒
(3) 2b = (a - a) ⇒
(4) b = (a - a) / 2 ⇒
(5) b = 0
where b = 0 is the additive identity. What many neglect to notice however is that even though,
(6) a + 3 = a - 3, is a false statement, we can say that since ∀A: ∅ ⊆ A, we know 3 has in it the empty set (∅). This means we have a mechanism to make the statement meaningful. We evaluate this by taking the false terms and allow them nullify each other:
(7) +3 = -3, is false, and thus A ≠ A, implies the terms cancel leaving us with ∅.
In standard set-theoretic definition of natural numbers, we use sets to model the natural numbers. So in this context, zero (or the additive identity as equal to 'b') is modeled by the empty set and therefore (7) as a member of the empty set allows for the statement:
(8) 3 ≈ b (proof), in step (1). Which then allows us to evaluate step (6) to say:
(9) a = a, because ∀A: A ∪ ∅ = A.
Thus,
(10) 'b', as the additive identity, is approximately equal to any and all ℂ and ℝ values.
Working from step (4) we can solve for 2:
(11) 2 = (a - a) / b or (0 - 0) / 0.
This seems to make no sense, because how can 0 / 0 = 2? The simplest way to understand this is by reformulating (11) like so:
(12) 2 = a(1 - 1) / b ⇒
(13) 2 = a / 1, because (c * y) / (d * y) ⇒ c / d
The problem with this though is 'a' was free to equal anything in (1), but here in (13) 'a' becomes restricted exclusively to 2. A more robust way to understand how (a - a) / b can equal 2 is through the following evaluation:
(14) b = (a - a) / 2, (as seen in (4))
(15) 2 = (a - a) / b
Substitute 2 for b and b for 2. This gives:
(16)![[Image: 41b104202bdd.png]](http://files.abovetopsecret.com/images/member/41b104202bdd.png)
If you notice what this shows is 0/0 ... 0/2. These things are end-points of an infinitely long line!
![[Image: 74760efadc87.png]](http://files.abovetopsecret.com/images/member/74760efadc87.png)
The formulation of the line is as follows :
(17) (a - b) / c = (a - b) - c. Note that (a - b) - c is the same formulation as seen in (2) and (a - b) / c is the same formulation as seen in (4). Thus, when (a - b) = c^2,
(18) c = c^2 - c, such that c = 0 and c = 2!
The equation that's being observed here is this:
(19)![[Image: 4ee3e8670a06.gif]](http://files.abovetopsecret.com/images/member/4ee3e8670a06.gif)
The length of this line can be evaluated as:
(20) Lim c→0 (a - b) / c = Lim c→0 (a - b) - c ⇒
(21) ∞(a - b) = (a - b)
So this line in (16) reflects an infinite length.
(22) What this seems to show is that 2 as seen in (11) represents all positives as one quantity and all negatives as another. Since the additive identity can be shown to be similar to all reals by steps (6) through (10), it's not too difficult to see it's implied that (a - a) / b, as seen in (11), or simplified 0 / 0, causes disambiguation allowing for the properties expressed symbolically as (+a -a) to be qualitatively-quantitated (+a as 1 and -a as 1 = 2) rather than quantitatively-quantitated away (+a -a ⇒ 0).
What do I mean by quantitated versus qualitated? In a technical sense I mean A = A allows for quantization and A ≠ A allows for differentiation between quantitative & qualitative terms. This might sound complex, but really it's just a way to distinguish between two elements that otherwise would appear to be identical when in fact they're not.
For instance in step (15) we see (a - a) / b which simplified represents 0 / 0. The difficulty in understanding this is that we're dealing with two different types of zeros. Sounds weird I know but consider +0 = -0 ⇒ 0 isn't nothing it's actually the culmination of both the positive and the negative (i.e. 3 + 0 = 3 - 0 ⇒ 3 = 3 because this 0 has inside it the notion of both positive and negative allowing for cancellation). If you have a hard time understanding this remember: a + b = a - b ⇒ 2b = (a - a) ⇒ 2 = (a - a) / b; where b = 0! So we can see dividing (+a - a = 0) by a similar 0 (the additive identity, meaning +0 = -0) gives us the + & - components (or 2).
Thus,
0 (as the empty set) ≠ 0 (as the summation of + & -)
Or put another way 0 as representing abstract nothing, the empty set, is different from actual zero (+ & - summed). The way I think of + & - summed is by imagining a noble gas like Helium that has 2 electrons in its outer valence level making it stable.
To better grasp this it's easier to understand all of these ideas of nothingness and somethingness when viewed as a continuum. For instance ask a schooled philosopher, "What is the opposite of love?" 9 times out of 10 the answer will be apathy. Ask an average person off the street and you'll get, "Hate." Who's right?
Apathy is the absence of love or hate. Love is a passion (i.e. 1), and can only be countered by a passion from the opposite end of the spectrum, that is hate (i.e. -1). Apathy is that point in the middle (or 0 as representing the summation). Another possibility that's commonly ignored is the idea of not even having a feeling towards the situation because none has been created yet. This is clearly different from apathy, but also represents 0 (as abstract nothingness).
For a more technical treatment of this idea and how it works, see here.
Now if you scroll back up and re-read (22) you'll see that what I'm saying here is that splitting any zero that isn't the empty-set (∅) or a type-of ∞ will result in two parts.
This has important ramifications even in the physical world. Consider energy and matter are interchangeable, but it takes a huge amount of energy to create matter. Even ignoring that hurdle this is still difficult because ...
What this is showing is that even the physical universe obeys this rule of going from 0 to 2, because when we convert energy to matter we get two parts as - & +.
This seems to suggest that eventually these points must curve back in on themselves (as seen in first animation) towards 0. And what'a ya know this is exactly what happens when the 2nd law of thermodynamics runs its full course. Viewed another way it hints we can cross the infinity of points on this straight line by curving space as seen in (19).
When you start to think this way what you realize is that numbers are recursive descriptions of other elements. Put another way -1 is 1. They're on the same continuum. IE/ Hate (-1) is love (1) perverted and love is the insanity of hate without the violence.
Likewise no number can be defined without 1. For instance if you have all Real numbers available to you, but 1 is removed from the domain then 2 * 3 ≠ 6 because 6 ≠ 6 since 6 / 6 ≠ 1. Meaning 6 is not a component of itself, because 1 is undefined. So unless 1 holds no number holds.
This suggests for any element to exist all other things must exist simultaneously. Thus for a = a there must be elements that simultaneously do & don't equal themselves (i.e. 0 and infinity – Complex ∞ ≠ Directed ∞ ).
Meaning that 0 is both a bijective function, where all reals & complex numbers represent a set equinumerous to the values found inside 0 as qualitative terms (i.e. think of 0.5 as a component of 0 but at the same time as a mapping to 5); and in the second interpretation the values as inside 0 actually represent several states. Such that they can either be 0, as the empty set, *or* any real or complex number. In this way 0 can be seen as surjective meaning that it can literally transmute anything in to anything else through the empty set and infinity.
Summed up this represents the very heart of the Law of One that all things are an integral part of the whole; where all things are unique, but fundamentally representations of the same thing, i.e. see (10).
Quote:Questioner: Then can you tell me how the galaxy and planetary systems were formed?
Ra: I am Ra. You must imagine a great leap of thought in this query, for at the last query the physical, as you call, it, universes were not yet born. The energies moved in increasingly intelligent patterns until the individualization of various energies emanating from the creative principle of intelligent infinity became such as to be co-Creators. Thus the so-called physical matter began. The concept of light is instrumental in grasping this great leap of thought as this vibrational distortion of infinity is the building block of that which is known as matter, the light being intelligent and full of energy, thus being the first distortion of intelligent infinity which was called by the creative principle.
This light of love was made to have in its occurrences of being certain characteristics, among them the infinite whole paradoxically described by the straight line, as you would call it. This paradox is responsible for the shape of the various physical illusion entities you call solar systems, galaxies, and planets of revolving and tending towards the lenticular.
I'm not sure if many people here are familiar with Euler's Identity (e^(i*π) + 1 = 0), but if you are then you're probably aware that the exponential function e^z can be defined as the limit of (1 + z/N)^N, as N approaches infinity, and thus e^iπ is the limit of (1 + iπ/N)^N.
So, in the below animation, N takes various increasing values from 1 to 100. Thus the computation of (1 + iπ/N)^N is displayed as the combined effect of N repeated multiplications in the complex plane, with the final point being the actual value of (1 + iπ/N)^N. It can then be seen that as N gets larger (1 + iπ/N)^N it approaches the limit of −1.
What this shows is going from an otherwise straight line we naturally converge on the geometric curved representation of π. This is exactly what Ra is describing, "the infinite whole paradoxically described by the straight line ... This paradox is responsible for the shape of the various physical illusion entities you call solar systems, galaxies, and planets of revolving and tending towards the lenticular."
I find this so compelling because when I first started exploring S.H. I intuitively saw it implied all things were a single unit. To understand this I imagined a logarithmic spiral coming from 0 as the starting point creating a circle or the polar coordinate system.
To try and illustrate this on a more abstract level to a group of mathematically-minded friends, I threw together the following demonstration:
(1) a + b = a - b ⇒
(2) b = (a - a) - b ⇒
(3) 2b = (a - a) ⇒
(4) b = (a - a) / 2 ⇒
(5) b = 0
where b = 0 is the additive identity. What many neglect to notice however is that even though,
(6) a + 3 = a - 3, is a false statement, we can say that since ∀A: ∅ ⊆ A, we know 3 has in it the empty set (∅). This means we have a mechanism to make the statement meaningful. We evaluate this by taking the false terms and allow them nullify each other:
(7) +3 = -3, is false, and thus A ≠ A, implies the terms cancel leaving us with ∅.
In standard set-theoretic definition of natural numbers, we use sets to model the natural numbers. So in this context, zero (or the additive identity as equal to 'b') is modeled by the empty set and therefore (7) as a member of the empty set allows for the statement:
(8) 3 ≈ b (proof), in step (1). Which then allows us to evaluate step (6) to say:
(9) a = a, because ∀A: A ∪ ∅ = A.
Thus,
(10) 'b', as the additive identity, is approximately equal to any and all ℂ and ℝ values.
Working from step (4) we can solve for 2:
(11) 2 = (a - a) / b or (0 - 0) / 0.
This seems to make no sense, because how can 0 / 0 = 2? The simplest way to understand this is by reformulating (11) like so:
(12) 2 = a(1 - 1) / b ⇒
(13) 2 = a / 1, because (c * y) / (d * y) ⇒ c / d
The problem with this though is 'a' was free to equal anything in (1), but here in (13) 'a' becomes restricted exclusively to 2. A more robust way to understand how (a - a) / b can equal 2 is through the following evaluation:
(14) b = (a - a) / 2, (as seen in (4))
(15) 2 = (a - a) / b
Substitute 2 for b and b for 2. This gives:
(16)
If you notice what this shows is 0/0 ... 0/2. These things are end-points of an infinitely long line!
The formulation of the line is as follows :
(17) (a - b) / c = (a - b) - c. Note that (a - b) - c is the same formulation as seen in (2) and (a - b) / c is the same formulation as seen in (4). Thus, when (a - b) = c^2,
(18) c = c^2 - c, such that c = 0 and c = 2!
The equation that's being observed here is this:
(19)
The length of this line can be evaluated as:
(20) Lim c→0 (a - b) / c = Lim c→0 (a - b) - c ⇒
(21) ∞(a - b) = (a - b)
So this line in (16) reflects an infinite length.
(22) What this seems to show is that 2 as seen in (11) represents all positives as one quantity and all negatives as another. Since the additive identity can be shown to be similar to all reals by steps (6) through (10), it's not too difficult to see it's implied that (a - a) / b, as seen in (11), or simplified 0 / 0, causes disambiguation allowing for the properties expressed symbolically as (+a -a) to be qualitatively-quantitated (+a as 1 and -a as 1 = 2) rather than quantitatively-quantitated away (+a -a ⇒ 0).
What do I mean by quantitated versus qualitated? In a technical sense I mean A = A allows for quantization and A ≠ A allows for differentiation between quantitative & qualitative terms. This might sound complex, but really it's just a way to distinguish between two elements that otherwise would appear to be identical when in fact they're not.
For instance in step (15) we see (a - a) / b which simplified represents 0 / 0. The difficulty in understanding this is that we're dealing with two different types of zeros. Sounds weird I know but consider +0 = -0 ⇒ 0 isn't nothing it's actually the culmination of both the positive and the negative (i.e. 3 + 0 = 3 - 0 ⇒ 3 = 3 because this 0 has inside it the notion of both positive and negative allowing for cancellation). If you have a hard time understanding this remember: a + b = a - b ⇒ 2b = (a - a) ⇒ 2 = (a - a) / b; where b = 0! So we can see dividing (+a - a = 0) by a similar 0 (the additive identity, meaning +0 = -0) gives us the + & - components (or 2).
Thus,
0 (as the empty set) ≠ 0 (as the summation of + & -)
Or put another way 0 as representing abstract nothing, the empty set, is different from actual zero (+ & - summed). The way I think of + & - summed is by imagining a noble gas like Helium that has 2 electrons in its outer valence level making it stable.
To better grasp this it's easier to understand all of these ideas of nothingness and somethingness when viewed as a continuum. For instance ask a schooled philosopher, "What is the opposite of love?" 9 times out of 10 the answer will be apathy. Ask an average person off the street and you'll get, "Hate." Who's right?
Apathy is the absence of love or hate. Love is a passion (i.e. 1), and can only be countered by a passion from the opposite end of the spectrum, that is hate (i.e. -1). Apathy is that point in the middle (or 0 as representing the summation). Another possibility that's commonly ignored is the idea of not even having a feeling towards the situation because none has been created yet. This is clearly different from apathy, but also represents 0 (as abstract nothingness).
For a more technical treatment of this idea and how it works, see here.
Now if you scroll back up and re-read (22) you'll see that what I'm saying here is that splitting any zero that isn't the empty-set (∅) or a type-of ∞ will result in two parts.
This has important ramifications even in the physical world. Consider energy and matter are interchangeable, but it takes a huge amount of energy to create matter. Even ignoring that hurdle this is still difficult because ...
Quote:... in a technical sense, you cannot just create matter out of energy: there are various 'conservation laws' of electric charges, the number of leptons (electron-like particles) etc., which means that you can only create matter / anti-matter pairs out of energy. Anti-matter, however, has the unfortunate tendency to combine with matter and turn itself back into energy. Even though physicists have managed to safely trap a small amount of anti-matter using magnetic fields, this is not easy to do. (source)
What this is showing is that even the physical universe obeys this rule of going from 0 to 2, because when we convert energy to matter we get two parts as - & +.
This seems to suggest that eventually these points must curve back in on themselves (as seen in first animation) towards 0. And what'a ya know this is exactly what happens when the 2nd law of thermodynamics runs its full course. Viewed another way it hints we can cross the infinity of points on this straight line by curving space as seen in (19).
When you start to think this way what you realize is that numbers are recursive descriptions of other elements. Put another way -1 is 1. They're on the same continuum. IE/ Hate (-1) is love (1) perverted and love is the insanity of hate without the violence.
Likewise no number can be defined without 1. For instance if you have all Real numbers available to you, but 1 is removed from the domain then 2 * 3 ≠ 6 because 6 ≠ 6 since 6 / 6 ≠ 1. Meaning 6 is not a component of itself, because 1 is undefined. So unless 1 holds no number holds.
This suggests for any element to exist all other things must exist simultaneously. Thus for a = a there must be elements that simultaneously do & don't equal themselves (i.e. 0 and infinity – Complex ∞ ≠ Directed ∞ ).
Meaning that 0 is both a bijective function, where all reals & complex numbers represent a set equinumerous to the values found inside 0 as qualitative terms (i.e. think of 0.5 as a component of 0 but at the same time as a mapping to 5); and in the second interpretation the values as inside 0 actually represent several states. Such that they can either be 0, as the empty set, *or* any real or complex number. In this way 0 can be seen as surjective meaning that it can literally transmute anything in to anything else through the empty set and infinity.
Summed up this represents the very heart of the Law of One that all things are an integral part of the whole; where all things are unique, but fundamentally representations of the same thing, i.e. see (10).