220th book of science by AP

Physics Potential Energy equals Mathematics factorial in all possible permutation arrangements

Whilst in a discussion of infinity borderline and the lack of anything in physics for a number as large as 10^604, I come to realize that this number is more than amply met up with in physics by the concept of Potential Energy.

Especially the heaviest known nucleosynthesized elements such as element 118. So if we have all possible arrangements of 299 nucleons we have infinity..

So M = N ln N. If N = 10^603, then we have:
>    ln N = ln(10^603) 
>           = 603(ln 10) 
>           = 1388.458811...

Ln(10^604) 604(ln10) = 604 * 2.302 = 1390.7

ln10 = 2.302 x/lnx for 10^607/ 1.390*10^3 = approx 10^604 so 3 place values to capture primes 1*10^608

253! = 5.1734609926400789218043308997295e+499

300! = 3.0605751221644063603537046129727e+614

19^(22x22) = 8.2554901045277384397095530071882e+618

22^(22x22) = 5.4022853245302743024619692001681e+649

In Old Physics, potential energy was always a shadowy, murky subject. Time we bring it to light.

Archimedes Plutonium<plutonium.archimedes@gmail.com>
Dec 5, 2021, 2:25 AM
to Plutonium Atom Universe

You need to define "infinity" better. Not just a assumption or opinion as "never ending".

A better definition is to say -- where does finite end and infinity begin-- a borderline.

In the history of mathematics, there was a genius named Huygens who studied the tractrix movement of a pocketwatch across a graph paper and the curve that it outlined as he dragged it. That curve is a tractrix, very amazing curve for it is a finite curve but stretches to infinity itself.

So when you compare a tractrix with a circle area, you can find where the infinity borderline is located, and it is located at 1*10^604 in large scale or in the tiny microscopic scale it is 1*10^-604.

Now you ask for a Physics comparison to reach infinity. And obviously nothing of 9.3*10^10 light years is going to get you numbers on the order of 10^604 or -604 exp.

Nothing in physics is this large or that small in scale. The Planck numbers at best reach 10^80 at most 10^160.

However, there are physics numbers that easily reach 10^604 in the idea of mathematics permutations. Such as Jacobs example of how many ways can you seat 11 people at a diner table is a very big number, as 11 factorial.

But now you have the nucleons of atoms of elements from plutonium to americium to element 118. And if you take the factorial of element 118 you easily reach 10^604, as Huygens-AP infinity borderline.

But what does a all possible arrangements of nucleons actually physically mean?

Clearly, you can arrange those nucleons of element 118 as equal to infinity..

253! = 5.1734609926400789218043308997295e+499
300! = 3.0605751221644063603537046129727e+614
19^(22x22) = 8.2554901045277384397095530071882e+618 
22^(22x22) = 5.4022853245302743024619692001681e+649

You are never going to get infinity from small numbers like 93 billion light years.

So can we make total arrangements be something on the order of a Speed in Physics. Or can we make arrangements be distance in physics? Or can we make time be total possible arrangements.

I suspect time is the easiest to convert to total possible arrangements.

Then we would need a unit time. A time of 1. and count from 1 to 10^604.

AP, King of Science, especially Physics

Back in the 1990s, they had no available calculators for such large factorials as they do now on the web.

296! = 3.855*10^604

295! = 1.302*10^602

🐁 of Math and 🐀 of Physics Archimedes "failure" Plutonium
<plutonium.archimedes@gmail.com> fails at math and science:
> In Old Physics, potential energy was always a shadowy, murky subject. Time we bring it to light.
>
> AP, Drag Queen of Science, especially Physics
>
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