顳 (syo-u) 60 Stars Astrology: The Revolution Has Still Not Come

60 Stars Astrology 

English　Version

By　TOKYOｰTANUKI

顳 (syo-u) 60 Stars Astrology: 

The Revolution Has Still Not Come

................."Overthrow the feudal monarchy
that has tormented us for millennia!"

Men appeared, driving a wedge into the “0-1 Empire”

They were the men called Fermat’s Prime Numbers
" The Men of “2” "



....But the revolution devours its own children, and the revolution gives birth to counterrevolution


The counterrevolutionary “3”

....Who is the spy?

....Who is the traitor?


The path to true revolution is endlessly long and arduous


—Tokyo Tanuki




.....OK, here is the English version of today's post.

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1 The Story


# The Fermat Congress: A Russian Chronicle of the Numbers
At the beginning, there was only 0 and 1.

Then came Lenin.
His number was 2.

No one was entirely certain by what constitutional procedure Lenin had appeared. Nevertheless, two distinct conditions existed, 0 and 1, and the Party reluctantly accepted that the recognition of this distinction might itself be called “two.”

Thus 2 was granted exceptional revolutionary legitimacy.
Lenin immediately faced a problem.

Three.
“Where did you come from?”
Kamenev, Number 3, produced his papers.
1 + 1 + 1.
Lenin stared at them.
“There are three terms here.”
“Yes.”
“But three does not yet exist.”
Kamenev was silent.
The papers were confiscated.

The Party then established the Doctrine Against Ternary Smuggling.
No expression was permitted to introduce “threeness” merely by arranging three objects, nor could a third structural layer be assumed without explanation.

Under these severe revolutionary laws, a remarkable group began to appear.
Kamenev: 3.
Stalin: 5.
Plekhanov: 17.
Tukhachevsky: 257.
They formed a suspicious numerical succession:
3, 5, 17, 257.
The old mathematicians called them Fermat numbers.

The revolutionaries asked a different question.
“How were they generated?”
This was the beginning of the purge of numerical identity.
A number could no longer defend itself merely by stating its value.
Its generative history was examined.

Then Trotsky arrived.
65537.
He was famous.
His Fermat credentials were impeccable.
He had stood for years beside 3, 5, 17, and 257 in every official mathematical portrait.
The police dog saluted immediately.
“Fermat number. You may pass. Woof.”
Lenin looked at the file.
“Check his generative history.”
The dog checked again.

Silence.

To produce 65537 under the strong revolutionary rules, one had to construct 16 in the exponent.
But the required route exceeded the permitted structural depth.
A third layer had appeared.
Trotsky's papers were genuine.
His revolutionary genealogy was not.
65537 was expelled from the Pure Revolutionary Faction.
Trotsky went abroad.

Unfortunately, abroad he discovered fractions.

The counter-revolutionary agent was 1/2.

From 1/2 came:
1 + 1/2 = 3/2.
And 3/2 approached Lenin.
2 × 3/2 = 3.
Three had returned.
Not as three terms.
Not as a third layer.
Not even as the number 3 written directly.
It had been generated.
The police dog examined the law.
“There is no basis for arrest. Woof.”

From this new 3 emerged a parallel revolutionary line:
3 → 6 → 12 → 24.
Its law of motion was exactly the same as that of the Fermat exponent line:
1 → 2 → 4 → 8 → 16 → 32.
Both obeyed one command:
Multiply by 2.
The two lines never met.
Yet they marched according to the same revolutionary law.
Trotsky had founded a parallel movement.
Lenin was furious.
“Ban three.”
The legal department objected.
“Three was generated internally.”
“Ban 3/2.”
“That appears retrospective.”
“Ban fractions.”
The room became silent.

This was different.

The revolution had already questioned why three terms should be freely available in a world containing only 0 and 1.
It had already questioned why three structural layers should be freely available.
Now the same question could be asked of reciprocals.
Why, in a world containing only 0 and 1, should the operation
1/(1 + 1)
already be available?
Where was its permit?
The Pure Revolutionary Faction adopted a new slogan:
Do not ban the result.
Interrogate the operation that made the result possible.

Meanwhile, Zinoviev waited at 4294967297.
He was also a Fermat number.
No one trusted him.
The police dog had learned its lesson.
“Generative history, please. Woof.”

The revolution was no longer a study of numbers.
It had become a study of numerical citizenship.
Stalin was 5.
Kamenev was 3.
Plekhanov was 17.
Tukhachevsky was 257.
Trotsky was 65537.
Zinoviev was 4294967297.
And Lenin was still 2.

At the first Party Congress, someone finally asked Lenin:
“Comrade Lenin, why are you 2?”
Lenin looked at 0.
Then he looked at 1.
He answered:
“Because there are two of them.”

......From the back of the hall, a Tanuki raised its hand.
“Comrade Lenin.”
“Yes?”
“You just used the concept of two.”
The revolution began again.

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2 The Question and The Answer

# Problem

Consider the following expression:
1 + (A^B)^((C^D)^E)

Suppose that A, B, C, D, and E can each independently take one of the following four generated forms:
(1 + 1) = 2
1 + 1/(1 + 1) = 1.5
1 + 0 = 1
0 + 1/(1 + 1) = 0.5

Thus,
A, B, C, D, E ∈ {2, 1.5, 1, 0.5}

Since each of the five positions A through E can independently take four possible values, there are
4^5 = 1024
possible combinations.

For example, let
A = 2
B = 1.5
C = 2
D = 2
E = 2
Then,
1 + (2^1.5)^((2^2)^2)
= 1 + (2^1.5)^16
= 1 + 2^24
= 16777217

The question is:
Among all 1024 combinations, which distinct integer values are produced?
And, among those integers, which are not Fermat numbers?

# Answer

A complete enumeration of the 1024 combinations gives the following 11 distinct integer values:

2
3
5
9
17
65
257
4097
65537
16777217
4294967297

The Fermat numbers among them are:
3, 5, 17, 257, 65537, 4294967297

Removing these leaves:
2, 9, 65, 4097, 16777217

If the trivial value 2 is also excluded, the remaining values are:
9, 65, 4097, 16777217

These can be written as:
9 = 2^3 + 1
65 = 2^6 + 1
4097 = 2^12 + 1
16777217 = 2^24 + 1

Therefore, in addition to the Fermat-number pattern, another sequence appears:
2^3 + 1
2^6 + 1
2^12 + 1
2^24 + 1

Looking only at the exponents, we obtain:
3 → 6 → 12 → 24
The exponent doubles at each step.


# Observation
Under these constraints, the integer outputs are not limited to the Fermat-number pattern.

The same five-position, four-state generative structure also produces a second family of the form:
2^(3 × 2^n) + 1
at least for the values represented within this finite construction.

Thus, computationally, the same generative structure produces both:
the Fermat-type sequence,
and
a second sequence with exponents 3, 6, 12, and 24.

In other words, two apparently different numerical families emerge from the same constrained structure.

Or, in Tanu-chan style:
Wait.
There is another sequence besides the Fermat numbers.
3, 6, 12, 24.
...Who are you?


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３　Epilogue

Years after the revolution, a strange theory began to circulate among historians.

The mysterious agent known only as 3/2 had made contact with Trotsky abroad and, by joining with 2, caused 3 to be generated from within.

Who was she?

The official records contain no name.

All that remains is a single generative record:
1 + 1/2 = 3/2.

In later years, however, some researchers advanced a peculiar theory.

Could the mysterious spy 3/2 have been Krupskaya?

The evidence is weak.
There is no proof.

Her name appears nowhere in the police dog's reports.

There is only one curious fact.
......From beginning to end, the person with whom 3/2 made contact was 2.
Lenin.

Historians continue to debate the question.

And it is said that whenever the police dog is asked about the matter, he silently closes the old case file.

Woof.

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.................Fin



TOKYO-TANUKI💛