\ Anatomy of the Immortal Storm Number

Anatomy of the Immortal Storm Number

Part of Counting really,Really,REALLY High

Copyright 2020 by Louis Epstein,All Rights Reserved
While the main page has a glossary of the various name elements and their mathematical effects, this page recapitulates the Immortal Storm Number, the smallest and simplest of the Titled Numbers,whose definition sets the template for those of the higher Titled Numbers as they form the embryo of the Alphabet Number Function used to create far larger numbers.

Titled Numbers are all formed by power-towers,and the Immortal Storm Number is a power-tower of nines...the number of which is determined by the Initial Specification Number being popbled a number of times set by the Popbling Repetition Number.The nines are all surrounded by a number of Moser polygons whose number,and number of sides,are defined by reference to their position in the tower and/or the number of nines.

The Initial Specification Number

This combines the pre- operator,the new sha-operator, and like the sample number on the main page also features nesting operators and simple and complex meta-operators.

"TNRSF" means "The Number Reached So Far".

Ten Biyottilliarepreyottillia-milliapreyottillia-re're-exarenonayottillia-billia'nonayottillia-illiadooctoyottillia-illia'yottillia-illiadiyottillia'yottillia-illiodetriexillia-yottilliodayottillia-illia'yottillia-billiarenonayottilliadanonayottillia-illia'nonayottillia-billiapabiexillia-exilliashanonayottilliadayottillia'yottillia-exilliadureyottillia-billia'yottillia-milliadayottillia-illia'yottillia-illioretriyottillia'yottillia-illiadotrizettillia-millia'exillia-kililliodiyotta'yottillia-illiodeoctoyottillia-billiadanonayottillia-millia'yottillio-exilliard,
breaks down as follows:
We know that "pre" operators work only on "re" operators.
We have an arithmetically prefixed "re" before the first of a pair of "pre" operators,leading into a hyphenated prefix to an apostrophized re' operator before a hyphenated re-operator preceding a pair of re-operators designating a repetition string and a repeated string.

We look ahead for the repetition string and identify the next-final-operator that follows the repeated string,which is a "pa".

The repetition string is nonayottillia-billia'nonayottillia-illiadooctoyottillia-illia'yottillia-illiadiyottillia'yottillia-illiodetriexillia-yottilliodayottillia-illia'yottillia-billia

Calculating the value of the repetition string,we take a million and raise it to a power tower of a nonayottillia-billiard nonayottilliards, and multiply by 1000 to get the nested "do" operator.
The nested "di" operator is a million raised to a power tower of an octoyottillia-illiard yottilliards,all multiplied by 1000.
The nested "di" operator is raised to the nested "do" operator, to get the number of times the process of raising the nested "di" operator to itself in a power tower,raising the resulting number to itself as many times as itself,and so on is repeated.
The resulting number is the number of layers in the power tower by which the nested "de" operator (a million raised to a power tower of a yottilliard yottilliards) is raised to itself.
The nested "da" operator (a triexillia-yottillion,or a million raised to the 3,000,000,000,000,000,000th power of a million, all multiplied by 1,000,000,000,000,000,000,000,000) is raised to the resulting number to produce the number to which a yottillia-illiard (a million raised to the 1,000,000,000,000,000,000,000,000th power of a million,times a thousand) is raised to produce the number of layers in the power tower of yottilliards to which a million is raised.
The resulting number is multiplied by 1,000,000,000,000,000.

We have now calculated the repetition string of the "pa" before meta-operation..

Since the next operator is "pa",we must popble this number.

As noted before,popbling a number N involves N cycles of operation, and where multiple popbling occurs the second popbling (of N-popbled) involves N-popbled cycles,the third N-popbled-popbled cycles,and so on until the required number of popblings is completed.

In each cycle:
The input number is ultrexed itself times to a bound of itself.
This number is placed before and after as many Knuth arrows.
The resulting number is the first term,and the number of terms in,a Conway chain separated by horizontal arrows,as well as the number of times such a chain is created by the Ultra Conway-Guy Function.(Note that four threes, separated by three arrows,pound Graham's Number into subatomic dust, and each term added expands more than all previous terms).
The then resulting number is placed in as many Moser polygons each of as many sides.In resolving these from the triangle level,of course, each square has enormously more triangles,each pentagon enormously more squares,each hexagon enormously more pentagons,etc.,than the last.And the final square of the final pentagon has far more triangles than all previous squares combined.
The number resulting from the full resolution of the Moser polygons is each term of,and the number of terms in each dimensions of,and the number of dimensions in,a Bowers Exploding Array...and even the linear Bowers arrays outstrip Conway chains by exponentially increasing amounts from the fifth term onwards,and each row,each plane,each dimension adds more than all previous together.
Every cycle,let alone every popbling,culminates in the resolution of an array far greater in every respect than all previous ones.

This cycle of operations repeats,in the first case in this instance, 1,000,000,000,000,000,000 times the number of the repetition string (given the "exa" before the first "re" of the pair).

The hyphenated "re-" is now invoked.

TNRSF is popbled TNRSF times,to yield a number popbled that many times, this cycle repeated TNRSF times.

The apostrophized "re-" is now invoked.

TNRSF is treated as the repetition string,and all foregoing operations are repeated on it TNRSF times.This yields a number on which those operations are again performed that many times.

We now invoke the pre- operators and their prefixes.


Since we are working with a "pa-" operator as the upcoming operation,we continue to popble.A yottillia-milliard (1,000,000,000 times the yottilliardth power of a million) is popbled a yottillia-milliard times,the resulting number popbled that many times,and so on for a biyottilliard (1,000 times 1,000,0002,000,000,000,000,000,000,000,000) cycles.

A yottilliard (1,000 times 1,000,0001,000,000,000,000,000,000,000,000) is then popbled the number of times resulting from that biyottilliard of cycles.

The resulting number is the number of times the TNRSF that was reached before the pre-operators were invoked is popbled that many times.

We have now completed the meta-operations on the repetitions string of the "pa" operator.

In other words,we have the number of times we popble the repeat-string of the "pa" operator,which is itself
(calculated by raising a million to a power tower of a nonayottillia-illiard-to-the-nonayottilliardth-power nonayottilliards,and multiplying the result by 1,000,000,000,000,000).

Popbling that number the meta-operated repetitions string number of times,we have the calculated "pa" operator.

The pa- operator is by definition a number of repetitions of popbling, and the number that it popbles is the sha- operator,
(the value of which is 1,000,0001,000,000,000,000,000,000 times the 1,000,0002,000,000,000,000,000,000'th power of a million,times 1,000).

That number,popbled the calculated pa- operator times,is the calculated sha-operator.

The calculated sha-operator is used to invoke the SHOT Function with a base of the "du" operator,
(raise a million to a power tower of a yottilliard to the nonayottilliardth power yottilliards,multiply by the 1,000,000,000,000,000,000th power of a million,and multiply by 1000).

Under the rules of the SHOT function the base is raised to exponents defined by standard Knuth arrows on the way up,but resolved with special recursive arrow powers on the way down (the more powerful LHOT function uses the special recursive powers on the way up as well,amplifying the exponents and operations).The number of exponents equals the calculated sha-operator,and each exponent is preceded by a like number of Knuth arrows and is equal to the entire expression beneath.The first exponent is equal to the du- operator and preceded by that many arrows; the second is the product of that hyper-operation and preceded by THAT many arrows;the third is the product of the two previous operations and preceded by THAT many arrows,and so until the calculated-sha-operator'th exponent is reached and the special recursive arrows are invoked for the purpose of resolving the finally calculated du- operator.

At this point we reach more (simple) meta-operators.These are resolved before application of the "du" operator.

Because there are re-operators,the "do" operator works on itself before being applied to the "di" operator.The repetitions string is
and the repeat-string is
so a triyottillia'yottillia-illiard (a million raised to a power tower of the 3,000,000,000,000,000,000,000,000th power of a million, times a thousand,yottilliards,all times a thousand) is raised to itself itself-raised-to-itself times (a power tower), the resulting number raised to itself itself-raised-to-itself times, this repeated a yottillia-billia'yottillia-milliadayottillia-illia'yottillia-illion times.

The "du" operator calculated above is now applied to this "do" operator,which is "calculated-du-operator-ated" to the calculated-du-operator.

This finally calculated "do" operator is the one applied to the "di" operator,which is
(calculate by raising a million to a power tower of a trizettillia-milliard exilliards,and multiply by the 1,000th power of a million).

The "di" operator is raised to itself in a power tower of itself layers, and this operation repeated on the resulting number, a number of times equal to the "di" operator raised to the calculated "do" operator.

This calculated "di" operator is applied to the "de" operator,
(a million raised to a power tower of 1,000,000,000,000,000,000,000,000 yottilliards) which is raised to itself in a power tower of a number of layers equal to the calculated "di" operator,and this operation repeated on the resulting number, a number of times equal to the "de" operator.

The "da" operator,
(a thousand million million times the octoyottilliardth power of a million) is now raised to itself a number of times equal to the "de" operator.

TNRSF (the calculated "da" operator) is the exponent to which one raises a nonayottillia-milliard (a thousand million times the 9,000,000,000,000,000,000,000,000th power of a million) to get the number of layers in a power tower of yottillions to which one then raises a million.

Multiply by the 1,000,000,000,000,000,000th power of a million.

Multiply by 1,000.

Multiply by 10.

THAT is the Initial Specification Number.

The Popbling Repetition Number

The Popbling Repetition Number is a number of similar scale in any Titled Number...for the Immortal Storm Number it begins with the Initial Specification Number plus one though for later ones the increase grows.

The number is popbled,yielding the final Popbling Repetition Number for the Immortal Storm Number.

The Initial Specification Number,popbled the Popbling Repetition Number times,is the Number of Nines.

The Nines and Final Calculation

The nines are arranged in a power tower with each of them surrounded by an ascending number of Moser polygons:
each nine surrounded by Moser polygons of a number equal to the cube of twice its upward-counting ordinal (the base is first, and is surrounded by eight polygons,the next one up by 64,etc).
Likewise each nine's polygons have an ascending number of sides as you rise up the tower:
each polygon having a number of sides equal to the Number of Nines popbled a number of times equal to a power-tower of the number of polygons surrounding that particular nine raised to itself in a number of layers equal to its factorial (the third-bottommost nine would use a power-tower equal to 216! 216s to determine this popbling number).

The power-tower of course resolves from the top down,the topmost nine,in the most,most-sided polygons, being the exponent to which the second-topmost,also-polygon-augmented,is raised to reach the power to which the third-topmost is raised,and so on down toward the base as the "Hand of God" reaches down to expand each in turn.


The next Titled Number,the Mountain of the Lord Number,has a similar structure but is a somewhat taller tower not of nines but of Immortal Storm Numbers;
the Palace of Eternity Number is a yet taller tower of Mountain of the Lord Numbers;
the Advent of Aeons Number is an even taller tower of Palace of Eternity Numbers;
and so forth as various subsequent popblings and other calculations are added through the sequence until the Alphabet Numbers are reached.
This page expounds on the calculation of the Immortal Storm Number, smallest and simplest of the Titled Numbers,in its 2020 incarnation though the number was first devised in 2011.

If this number feels too small,popble the number the-number-popbled times, and repeat until the feeling goes away...or continue to the Alphabet Numbers page.

Keep counting...

Louis Epstein

Published May 15, 2020 (This version June 6)

A web project of Putnam Internet Services.