I can now finally see what you are doing in pages 6, 7 and in the 1+ table.
You are really just encoding integers in wave-packages with frequencies of powers of 2.
The encoding is such that the time to transmit the signal would remain constant no matter how large the integer. Though to transmit higher and higher integers, you need to generate higher and higher frequencies and so to transmit infinity, you'd need an infinite amount of energy. - at some point long before that, though, you'd just reach the energy density limit.
It indeed isn't that hard but the lack of explanations makes it incredibly obscure.
Your notation is absolutely terrible although there is some twisted logic to it once it becomes clear what you even mean.
Now what I still do not get at all is the Jewelz Sets of yours. They are super weird, funky and unnecessarily complex.
So what you do is, you apply the following algorithm:
You keep halving your values, dropping the stuff past the dot:
It took four steps to do it, so s, the number of "physical wave sequences" is 4.
A different way to calculate this would be
(where
is the ceiling-function and means you must round up.)
The way your encoding works, integers take at most two frequencies, the higher of which being double the lower frequency. That's what you mean by "Total High" and "Low Physical frequencies" respectively. - That's how many repetitions of full cycles of the higher / lower frequency you need to represent your number, respectively.
You find these values with a couple more calculations:
First you find what you call the "low wave potential" which is the frequency of the lower of the two waves (so the "high wave potential" would automatically be twice that).
so for the above example,
.
From there you find the number of repetitions of the higher frequency through the simple formula
where we just calculated L' and T is the original integer, so
.
Now, from the original number and the number of high frequency repetitions needed, you calculate the number of low frequency repetitions.
So now we know that you need L=7 repetitions of a L'=8 Hz wave and H=2 repetitions of a H'=2L'=16 Hz wave (if you choose your frequency unit to be Hz)
In other words, you can write "9" as
th seconds of a 16Hz wave followed by
th seconds of an 8Hz wave.
You write this as
For some reason you choose to write your waves high first low last while, in the fraction notation, you use low first high last. This seems a little inconsistent but ok, if that was the only problem with your notation, it wouldn't be nearly as confusing. I'd probably write this as something like
or, since the denominators are always powers of 2, one could also write
or, since the lower frequency always is twice the higher frequency, one could also write
and the notation would be well-defined without redundancies. The subscript simply denotes what power of two the higher frequency should be. So you need
full cycles of a
Hz wave, followed by
cycles of a
Hz wave.
Furthermore, you add an extra step. I'm not quite sure at this point whether you add it because the "low wave potential" L' doesn't always equal the necessary lower frequency, and it just so happens to do so in case of 9 or this step (step 7) is redundant.
Ok so to summarize, you found an interesting way to write down any integer in a compact form that always just needs two "digits" of varying power.
And you found a pattern of addition of integers in a table. (The "+1 table").
All fine and dandy.
But what is that supposed to do? A new, convoluted way to write down numbers. Woo.Hoo.
How do those numbers help at all with addition?
How do you do multiplication, division, powers or any other interesting operation?
How do you write down fractions or decimal numbers or...?
And other than that pi defines half the edge-length of a full circle which is linked to cycles and waves, what does all this have to do with pi?
Even after this frankly over-patient effort to understand, most of this seems overly complex or redundant and there is nothing explaining your two "Periodic Table of Charged Elements"s.
I still don't get what half of your notation even means - it appears redundant.
Note that I managed to write the equations I grasped above in straight forward, traditional notation just fine. I even shortened your apparently purely iterative approach to find L' to a single function call. It's less redundant and it's clearer.
Perhaps you, hopefully understanding yourself what you even mean, can write down the rest of the content in the posted pages in a more traditional, less redundant manner?
Edit:
Here is an example arbitrarily chosen for 1337:
I bet (though I didn't attempt to actually read that) this Jewelz Set is something like an iteration on the above:
You could convert 626 and 711 in a similar fashion:
and having those two you could also write
etc. and you could repeat that until you get minimal values everywhere. This causes a tree of sorts of notations which, in your convoluted notation, might approach something that looks like those Jewelz Sets.
Edit: Apparently the TeX plugin is confused as to how it decides to show \lceil and \rceil. I don't think I've done anything to cause it to alternate between single and double bar. Not sure what's up with that. I'm still hoping you'll eventually adopt the much better-looking math-jax. I know you don't like additional java scripts and what not but the TeX plugin this forum uses just is so finnicky. It can't even ignore multi-spaces. It just reads them as syntax error. And then it does weird formatting nonsense like the above.