221st book of science by AP New Geometry Calculus-- the factorial as a circuit motion This book is in conjunction with my Potential Energy book. I noticed that physics has a difficult time in having physical meaning of a number as large as
7k views
to Plutonium Atom Universe

221st book of science by AP

New Geometry Calculus-- the factorial as a circuit motion

This book is in conjunction with my Potential Energy book.

I noticed that physics has a difficult time in having physical meaning of a number as large as 1*10^604 and as small as 1*10^-604.

There is nothing in Old Physics that reaches these numbers, except for factorial. And especially the factorial of nucleons position in say Element 118..

So here in Element 118 we can reach 296 nucleons and when we do a 296! we reach 10^604.

And there is a geometry meaning to factorial.

The easiest geometry is seating arrangements. So if you have 10 people to seat at a dinner table, what is the total number of possible arrangements? And the answer is 10!.

But notice also, that the factorial seems to be a go around phenomenon, a circuit like in physics electric current.

So, can we build the factorial multiplication as a new form of calculus?

A calculus that is geometrical but also quantitative. The quantity is simply the factorial arithmetic. The geometry is the total arrangements. And those total arrangements have a motion, a motion that is so crucial for calculus.

So when I publish this book on Potential Energy of Physics, I am going to simultaneously or concurrent or in conjunction publish this book on mathematics geometry of the missing geometry concept of factorial as a geometrical calculus of circuit motion.

So as we think of magnetic monopoles or dipoles of current in a electric circuit, we can also think of that current as a factorial. The current is in motion and the factorial geometry is all possible arrangements and those arrangements are begot from the motion of discrete particles.

So for example, we have a current of electricity of 3 monopoles of 0.5MeV each. In factorial that is 3! = 1x2x3 = 6. So we have a circuit of 6 waves going around.

Physics needs the factorial multiplication to reach infinity borderline. Math needs that factorial to complete multiplication for geometry.

The exponent is unable to reach 10^604 in physics concepts for volume is multiplication by 3 terms length, width, depth. But the factorial is not encumbered with 3 terms.

AP, King of Science, especially Physics
Archimedes Plutonium's profile photo
Archimedes Plutonium<plutonium.archimedes@gmail.com>
Dec 9, 2021, 3:10:02 AM (yesterday)



to Plutonium Atom Universe
Alright, let me enrich this geometry calculus. For volume is a static number begot from the multiplication of 3 parameters in 3rd dimension. While Factorial is a geometry of motion, as I said earlier, think of 10 people around a table to be seated and all the possible arrangements is exactly 10!. Quite amazing that all possible arrangements is a multiplication of that number.

But that is with counting numbers, so let us enrich this new geometry motion concept into that of Decimal Grid Systems, and make it a full bodied concept.

So in 10 Grid and all other grid systems we define the Factorial to be a multiplication of all the numbers in between an interval.

So in 10 Grid, what is the factorial for interval 1.0 to 1.3? This would be 1 x 1.1 x 1.2 x 1.3 = 1.716. And our answer is not a 10 Grid number but belongs in the 1000 Decimal Grid System. But that is no worry.

Now our interpretation of 1.716 is that it is a circuit of electricity go around as a current in that circuit. Just as our interpretation of 10! in Counting numbers is a table circuit and 10 people arranged in 10! possible ways.

So in Decimal Grid Systems we enrich the Geometry Calculus, the calculus of motion in a circuit by having factorial apply to all Decimal Grid Systems.

Now we ask for an answer to a simple question.

1) If we allow for this definition of factorial placed on all Decimal Grid Systems, do we have a Completeness theorem? What I mean is whether every decimal Grid number comes from a factorial calculus? Are the factorials complete in Decimal Grid Numbers Systems. For example is there a factorial that achieves the number 1.9 ? or the number 237.877? Or are their holes and gaps of numbers that cannot be obtained from factorial?

Archimedes Plutonium's profile photo
Archimedes Plutonium<plutonium.archimedes@gmail.com>
Dec 9, 2021, 3:27:29 PM (13 hours ago)



to Plutonium Atom Universe
Now the Factorial is a geometry operator and different from the Algebra operators of mathematics. As we easily can see that the back and forth movement of 10 people being seated in various arrangements around a dinner table. Which is 10!, and is a motion, wavelike motion of Geometry. It is the derivative wavelike motion of geometry, not algebra.

This then implies that Geometry has a integral calculus also. In Algebra we know the derivative and integral of Algebra from dy x dx is the integral of area under a graph in a particular interval and as dy/dx for the derivative.

In Geometry calculus, the factorial is derivative of motion in a wavelike manner, back and forth in different seating arrangements of 10 items (people, boxes, prisms, plants, trees).

In Geometry calculus we now need the integral of geometry, and since the factorial is derivative we can expect that some form of division is the integral of geometry calculus. A division that has say Universal Space is volume x times y times z. And divide a factorial from that Universal Space.

Completeness of Factorial

Now yesterday I discussed whether the factorial of Decimal Grid Systems is a complete algebra. Meaning: are all numbers in Decimal Grid System able to be produced from a particular factorial?

We know that in Counting Numbers we cannot access numbers like -- any odd number after 1. Not access 4, 8, 10, 12, .... and many others.

So having fractional decimal numbers, does that ease the list of ommissions? I would say somewhat because a number such as 0.7 in 10 Grid would be accepted as 0.72 in a higher Grid where we delete the 0.02 portion.

The question of Completeness will depend on the definition of a factorial. Do I define it as any consecutive string of numbers that is 2 or more numbers. So that a singlet number is not a factorial. So that 0.9 x 1.0 is a factorial but not 0.9 x 0.9. This raises the question of whether I must bring in exponential A^2, A^3 etc in order to well define factorial and whether it is a Completeness algebra.

Archimedes Plutonium's profile photo
Archimedes Plutonium<plutonium.archimedes@gmail.com>
12:03 AM (4 hours ago)



to Plutonium Atom Universe
Now do not hold me to this as yet, for still trying to figure it out. For I suspect the Geometry Calculus Integral is like a "complement set of the universal set.

The Geometry Calculus Derivative is the Factorial which is a motion of going around such as 10! is the motion generated by 10 people in all possible seating arrangements at a dinner table with 10 seats.

The Geometry Calculus Integral of this 10! would be a the entire universe as a factorial subtract 10!. The entire universe is 296! and hence the integral of 10! would be 296! - 10!.

The arithmetic of geometry calculus is far far easier than the arithmetic involved in Algebraic calculus and their use of dy/dx, dy*dx, the power rules.

AP


Archimedes Plutonium's profile photo
Archimedes Plutonium<plutonium.archimedes@gmail.com>
4:06 AM (now)



to Plutonium Atom Universe
No, the integral geometry is not the Complement set, but rather the Power set in number of subsets. That formula is 2^k where k is the cardinality of members.

So for 2^296 since our Element 118 has 296 nucleons we have total number of subsets as being 1.273..*10^89.

Now the square root of that is 3.5*10^44 for the Schrodinger equation psi function.

Now looking up Planck units for force I have in Newtons 1.2*10^44 and for frequency I have 1.8*10^43 seconds. Newton is of course kg(meter)(second^-2).. A conversion to eV involves 10^19.

So what I am beginning to see in the Geometry Integral is a circuit of various sizes of sets of particles ranging with the empty set to sets of 296 nucleons.

The Geometry derivative is a circuit of waves where 296! = 3.855*10^604.


So here, the question has to be at what 2^n at what n value is 2^n = 3.855*10^604 or in that neighborhood of values.

Alright, I do not know where this mistake crept in but 2^604 is about 10^181, not that of 10^89.

4.149* 10^180 = 2^600

6.639* 10^181 = 2^604

And that is a number much much better, for in physics the Old Physics had a number 10^186 as the largest number of physics significance as 10^186 approximate number of Planck volumes in the observable universe. (source Wikipedia in orders of magnitude (numbers))

Physics: 7*10^245 approximate spacetime volume of the history of the observable universe in Planck units. (source Wikipedia).

Now of course the last isotope of plutonium is Pu244.

The last isotope of Element 118 is 296

So here we maybe able to see some connections between Geometry Derivative of 296! = approx 10^604 and Geometry Integral of 2^604 = approx 10^180.

So in some sense, do we have an inverse relationship brewing here? Not to say a Fundamental Theorem of Geometry Calculus between factorial and that of all possible subsets in a power set formula of 2^k.

AP, King of Science, especially Physics

So, every day now I am beginning to like this more and more. But I am still confused as to how Calculus can have a derivative and integral for Algebra and also have a derivative and integral for Geometry.

It is plain to see, and to sense and feel that there is motion in a factorial and motion in a Power Set rule of 2^k. The motion in factorial is 10 people to be seated at a dinner table allows for the possibility of 10! arrangements which we can see in our minds as a circuit as each arrangement circuits through the table. We also sense motion in the Power set rule of 2^k where given a set of size cardinality k, that it has 2^k possible subsets. And here we sense the motion of speeding through all sizes of subsets starting with the null set, until we reach the final given set, and all sets in between. We can see the factorial as a circuit of electromagnetic theory of physics and a derivative of math, and each arrangement as a wavelet. We can see the 2^k as a integral of math and as a increasing volume starting out with empty set (null set) and increasing in volume size to the original set of k members.

So I am rather surprised and proud of myself in this discovery. But I am a bit worried as to whether this means math has 8 operators for before, I claimed math can only have 6 operators since physics has only 6 laws. That is why I am careful and saying this is calculus of geometry, while the power rules for derivative and integral on polynomials is calculus of algebra.

So I have just 6 operators of add, subtract, multiply, divide, derivative, integral. So we have many forms of addition, addition of angles as well as addition of numbers, so why not say we have two forms of derivative, the dy/dx and the factorial. Why not say we have two forms of integral, the dy*dx and the 2^k.

So I do not want to say we have 4 operators in Calculus, but rather a derivative for algebra and one for geometry, a integral for algebra and one for geometry. And who knows, I may just be able to prove they are equivalent.

AP, King of Science, especially Physics

Excellent new idea in mathematical physics, that Geometry has a derivative and integral different from Algebra derivative and integral.

So let me start a graph using only Counting numbers and start it at 1, not 0.

The derivative geometry is N! and the integral geometry is 2^N.

So the graphs would be {1 to 1, 2 to 2, 3 to 6, 4 to 24, etc} for derivative geometry.

And {1 to 2, 2 to 4, 3 to 8, 4 to 16, etc } for the integral geometry.

Now we can justify this as saying that 1 and beyond is the visible while between 0 and 1 is the invisible calculus.

And later on we can tinker with the formulas of N! or 2^N, by such things as perhaps N!+1 or N! - 1, or 2^N plus or minus 1. And one of the reasons being to obtain odd numbers for some sort of Completeness.

There is no doubt, and no mistaking the fact that N! and 2^N have internal Motion, the motion that physics calculus so much depends upon.

AP, King of Science, especially Physics

Already a call for a change, for there really is no such thing as the empty set. There is reality of "nothing" but a set of nothing is illogical. So here we have to define set as having members. And the crux of the definition of set is the membership. So the smallest set possible is a set of 1 member. This then forces the Power Set formula to be (2^N) - 1. And that formula gives odd numbers.

Now looking at the factorial we see those are all even numbers beyond 1. And here we have to ask a profound question as to why always even number when seating people at a table in all possible arrangements. Why must that be a even number? I mean if we had 5 people of a seating arrangement which is 5! = 120, why even when 5 is odd? A puzzling question probably deserves a puzzling answer.

AP

Now I am trying to picture the Motion Flow in both the Geometry Derivative Factorial k! and the Geometry Integral (2^k)-1.

So the Geometry derivative is seen as a circuit (dinner table) with seats around and then the arrangements. Is there a way of counting the arrangements, so that one does not miss any? And this tactic may lead to some clarity in computer science feigning to be math problems (halting).

So in the Geometry integral is seen as a building up from set of 1 member to the set with k members.

I see a ordering in the geometry integral, although dicey once you get into large numbers of k.

But I see no means of ordering in counting the derivative k! arrangements. I see no way of making it easy to count the arrangements, just start listing and hope you do not list duplicates.

So here I am asking for a Means of Ordering.

AP

💀 of Math and ☠️ of Physics Archimedes "Putin's Stooge" Plutonium
<plutonium.archimedes@gmail.com> blithered:
> I see a ordering in the geometry integral, although dicey once you get into large numbers of k.
>
> But I see no means of ordering in counting the derivative k! arrangements. I see no way of making it easy to count the arrangements, just start listing and hope you do not list duplicates.
>
> So here I am asking for a Means of Ordering.

The letters in "Archimedes Plutonium" can be rearranged to write: "I am
the purloined scum"