Back to the problem of the Periodic Table, I found some of David Halprin's old articles in a stack of paper Rainer handed me, which included a formula on how to calculate the atomic number from Larson's A-B-C notation. I've made this, and some other papers, available on ReciprocalSystem.org:
Atomic Number Equation Based on Larson's Triplets
I did test Halprin's equation out on the entire Periodic Table, and it does work. It is based on the way Larson calculations atomic number as a recursion of temporal displacements. Motion in the time region works more like layers of an onion or atomic energy levels. So what you end up doing, is summing up all the rotations from 1 to where you are. For example, take copper, element #29, with displacements of 3-3-(7). Since atomic numbers were created arbitrarily, and in the RS the temporal displacement is actually mass, the numbers are off by 2, so one needs to subtract 2 from the total to get the atomic number.
A=3, B=3, C=-7
First, sum up to
one less than A, using the 2n
2 relationship:
2 *1
2 + 2*2
2 = 10
Then sum up B, all the way:
2*1
2 + 2*2
2 + 2*3
2 = 28
Then add C
10+28+(-7) = 31
Then subtract 2:
31 - 2 = 29
Halprin's equation works equally well, without having to resort to summation. But it does point out another issue with the Periodic Table: why aren't the actual displacements used in the calculation, why 1 less for the principle rotation? That would mean copper is actually 2-3-(7).
One of the big issues with working with Larson's triplets is that they don't all mean the same thing. And this is not obvious in his books. For example, one sees hydrogen listed as 1½-1½-(2) and also as 2-1-(1). Which is right? The answer is
both, since the former is in
subatomic notation, and the latter in
atomic notation. Yep, he uses two, different notational systems for particles and atoms. And it gets worse, because the photon is done as displacement, not subatomic notation. So that's three. And when calculating atomic number, the 1-less notation is used, so that's 4. And if you get into
Basic Properties of Matter, he then introduces "vibration 2" and another half-unit based notation. So that's 5. And don't forget the original units are
speed, not displacement, so that's 6 different notational systems!
It all comes down to problems created by the
rotational base, that "rotational equivalent of nothing," that we did away with in RS2 by using angular velocity (0-180 is a unit of angular motion, which does a direction reversal from 180-0, creating a rotation).
The 1D rotational base is 1-0-0. If we add an electric rotation to that, we get the positron, 1-0-1, which is how Larson originally expressed it. Then he revised the notation to make the rotational base 0-0-0 so the positron became 0-0-1, hiding the underlying rotational base, which did nothing because it was the rotational equivalent of nothing.
When it came to atoms, there were two rotational bases involved, originally 1-1-0, but that got knocked down to 0-0-0 as well. So the atomic notation hides 2 rotational bases. That's why you end up with two, different ways to view hydrogen and 6 different notational systems. I find it very confusing!
Right now, I'm looking at a way to standardize notation, so it would be the same "across the board" for computer simulations. Since all measurement is taken relative to the progression,
displacement seems to be the logical point of standardization. But that gives rise to other problems, as the resulting notation no longer provides the values necessary for chemical interaction, as described in NBM. So there is something wrong, here.
I also found, which Halprin hints at in his paper, that there are some problems at the start of the Periodic Table. I've looked at this before in RS2, and concluded that Atomic Number 1 is deuterium, NOT hydrogen, and that does seem to be the case as it is a more logical fit. Deuterium can be expressed doubly as 2-1-(1) or 1-1-1, the latter being a structure that Larson tends to avoid, along with 1-1-0. I agree with Halprin that the 1-1-0 particle is the deuteron, atomic number 0.
But remember how we had to subtract 2, simply because of convention? If we add that back in for a more realistic atomic number, that makes helium #4, deuterium #3, the deuteron #2, and at the top of the periodic table... the
proton as #1. Since hydrogen is a compound particle of proton + electron neutrino, and as discussed in BPOM, the electron neutrino is responsible for isotopic mass, it turns out that hydrogen is an
isotope of the proton, in the RS.
So this essentially rewrites the Periodic Table to be:
1: proton, 1-0-1 or 1-1-(1); with an isotope of hydrogen 1½-1½-(2)
2: deuteron, 1-1-0
3: deuterium, 1-1-1 or 2-1-(1)
4. helium, 2-1-0
... etc...