Difference between revisions of "Sandbox"

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{{top}}
  
{{top}}
   
  +
[[RedPu]] is a bilingual ([[English]] / [[Russian]]) emulation based on the utopian dialogue
−
<div class="thumb tright" style="float:right; margin:0 0 8px 8px">
  
  +
presented in the article [[Рыжий Пу]].
−
{{pic|Tetreal10bx10d.png|300px}}
  
−
<small><center>Real tetration to base \(b=\mathrm e\).<br>
  
−
From: Fig.17.2, p.239 in ''Superfunctions''.</center></small>
  
−
</div>
  
   
  +
The emulation is presented in two synchronized language layers.
−
'''Tetration''' is the superfunction of the [[exponential]] map.
 
  +
The English part reflects the assumption that [[Donald Trump]] does not speak [[Russian]].
−
For a given base \(b\), tetration is the function \(\operatorname{tet}_b\) satisfying the functional equation
  
  +
The Russian part reflects the assumed replies of [[Путин Владимир Владимирович]].
−
\[
  
−
\operatorname{tet}_b(z+1)=b^{\operatorname{tet}_b(z)}\,,
  
−
\]
  
−
together with additional normalization conditions that ensure uniqueness.
 
−
The name “tetration’’ reflects its position as the next operation after exponentiation in the [[hyperoperation]] hierarchy.
  
   
  +
==Context==
−
The most commonly studied case is the '''real holomorphic tetration''' to base \(b=\mathrm e\), usually denoted simply by
  
−
\[
  
−
\operatorname{tet}(z)=\operatorname{tet}_{\mathrm e}(z).
  
−
\]
  
   
  +
The emulation develops the theme of “radioactive ash” («радиоактивный пепел»),
−
==Definition==
  
  +
introduced into Russian political discourse in 2014 by
−
Let \(T_b(z)=b^z\).
 
  +
[[Киселёв Дмитрий Константинович]].
−
A function \(F\) is called a ''superexponential'' (superfunction of \(T_b\)) if
  
−
\[
  
−
F(z+1)=T_b(F(z)).
  
−
\]
  
−
A '''tetration''' to base \(b\) is the unique real holomorphic superexponential satisfying the regularity condition
  
−
\[
  
−
\lim_{y\to\pm\infty} F(x+\mathrm i y) = \text{finite}
  
−
\]
  
−
and the normalization
  
−
\[
  
−
F(0)=1.
  
−
\]
  
   
  +
The text below is not a prediction, not a plan, and not a call to action.
−
These conditions distinguish tetration from the infinitely many other superfunctions of the same transfer equation.
  
  +
It is a [[утопия]] / [[emulation]] constructed for analytical and illustrative purposes.
   
  +
==Dialogue / Диалог==
−
==Properties==
  
−
For the principal tetration \(\operatorname{tet}_b\), the following hold:
  
   
  +
<poem>
−
* **Shift property** (transfer equation)
  
  +
**Trump (English):**
−
\[
  
  +
Hello, Mister Putin.
−
\operatorname{tet}_b(z+1)=b^{\operatorname{tet}_b(z)}.
  
−
\]
  
   
  +
**Путин (Russian):**
−
* **Derivative at the fixed point**
 
  +
Здравствуйте, мистер Трамп.
−
If \(L\) is the fixed point of the exponential, satisfying \(L=b^L\), then
  
−
\[
  
−
\operatorname{tet}'_b(0)=L.
  
−
\]
  
   
−
* **Analyticity**
+
**Trump:**
  +
One of your television hosts once said that Russia could turn the United States
−
For \(1< b < \mathrm e^{1/\mathrm e}\), the tetration to base \(b\) extends to an entire function.
 
  +
into radioactive ash. Is that statement correct?
−
For larger bases, branch singularities appear.
  
   
  +
**Путин:**
−
==Complex structure==
  
  +
Он действительно так сказал. Да.
−
<div class="thumb tright" style="float:right; margin:0 0 8px 8px">
  
−
{{pic|Ackerplot.jpg|300px}}
  
−
<small><center>Complex map of tetration for base \(b=\mathrm e\).<br>
  
−
From: Fig.19.7, p.266 in ''Superfunctions''.</center></small>
  
−
</div>
  
   
  +
**Trump:**
−
The complex dynamics of \(z\mapsto b^z\) determine the analytic structure of tetration.
 
  +
So Russia *can* do that?
−
For \(1<b<\mathrm e^{1/\mathrm e}\), the exponential has two attracting fixed points.
 
−
This allows construction of a regular Abel function and hence an entire superfunction.
 
−
At the critical base \(b=\mathrm e^{1/\mathrm e}\), these fixed points collide (bifurcation), and above this threshold, the dynamics become repelling, producing complex branches.
  
   
  +
**Путин:**
−
==Relation to superfunctions==
  
  +
Может.
−
Tetration is the ''canonical'' superfunction of the exponential.
 
−
Any superfunction \(F\) of \(T_b(z)=b^z\) satisfies the transfer equation
  
−
\[
  
−
F(z+1)=b^{F(z)}.
  
−
\]
  
−
Among these, the tetration is the uniquely normalized superfunction that is:
  
−
* real on the real axis,
 
−
* holomorphic in a vertical strip,
 
−
* smooth at \(\pm\mathrm i\infty\),
 
−
* normalized by \(F(0)=1\).
  
   
  +
**Trump:**
−
Other superexponentials differ by periodic or quasiperiodic distortions.
  
  +
Thank you. That answer is sufficient.
   
  +
**Путин:**
−
==Inverse: Abel function==
  
  +
Для чего вам это?
−
The inverse of tetration is the [[Abel function]] (ArcTetration), denoted by \(\operatorname{ate}_b\).
 
−
It satisfies the Abel functional equation
  
−
\[
  
−
\operatorname{ate}_b(b^z)=\operatorname{ate}_b(z)+1,
  
−
\]
  
−
with normalization \(\operatorname{ate}_b(1)=0\).
 
−
For the natural exponential, this becomes
  
−
\[
  
−
\operatorname{ate}(\exp(z))=\operatorname{ate}(z)+1.
  
−
\]
  
   
  +
**Trump:**
−
==Iterates==
  
  +
To justify a decision currently being voted on by Congress.
−
The pair \((\operatorname{tet}_b, \operatorname{ate}_b)\) provides analytic interpolation of integer iterates.
 
−
For the \(n\)-th iterate of the exponential (not exponentiation),
  
−
\[
  
−
\exp_b^n(z)=\operatorname{tet}_b\!\bigl(n+\operatorname{ate}_b(z)\bigr),
  
−
\]
  
−
where \(n\) may be any real or complex number.
  
   
  +
**Путин:**
−
This gives a smooth functional continuation of exponentiation to non-integer “heights’’.
  
  +
Какое решение?
   
  +
**Trump:**
−
==Special cases==
  
  +
About Russia.
−
<div class="thumb tright" style="float:right; margin:0 0 8px 8px">
  
−
{{pic|E1efig09abc1a150.png|300px}}
  
−
<small><center>Tetration near the critical base \(b=\mathrm e^{1/\mathrm e}\).<br>
  
−
From: Fig.17.4, p.245 in ''Superfunctions''.</center></small>
  
−
</div>
  
   
  +
**Путин:**
−
===Base \(b=\mathrm e^{1/\mathrm e}\)===
  
  +
И вы решили меня предупредить?
−
This base is the threshold at which the exponential map changes from having two attracting fixed points to having none.
 
−
The tetration at this base has unusual properties, such as:
  
−
* extremely slow growth near its fixed point,
  
−
* increased sensitivity to initial conditions,
  
−
* non-entire analytic structure.
  
   
  +
**Trump:**
−
===Base \(b=\mathrm e\)===
  
  +
Yes. We prefer transparency.
−
The standard tetration \(\operatorname{tet}(z)\) is real and smooth on the entire real line.
 
  +
You may want to warn the personnel at your launch facilities.
−
Its values decrease towards the lower fixed point of the exponential as \(z\to-\infty\), and blow up super-exponentially as \(z\to+\infty\).
  
   
  +
**Путин:**
−
==Historical remarks==
  
  +
Зачем?
−
The modern construction of real analytic tetration was developed by:
  
−
* E. Schröder and G. Koenigs (19th century) — regular iteration theory
 
−
* J. Kneser (1949) — analytic solution for base \(b=\mathrm e\)
 
−
* D. Kouznetsov and H. Trappmann (2009–2024) — complex extension, superfunctions, explicit computation methods
  
   
  +
**Trump:**
−
A unified presentation is given in the monograph ''[[Superfunctions]]''.
  
  +
Because we are about to demonstrate that Mr. Kiselev was mistaken.
   
  +
**Путин:**
−
==Examples and plots==
  
  +
В чём именно?
−
<div class="thumb tright" style="float:right; margin:0 0 8px 8px">
  
−
{{pic|B271t.png|300px}}
  
−
<small><center>Graph of tetration and its inverse.<br>
  
−
From: Fig.14.4, p.203 in ''Superfunctions''.</center></small>
  
−
</div>
  
   
  +
**Trump:**
−
Some characteristic graphs:
  
  +
In assuming that only Russia can turn others into ash.
   
  +
**Путин:**
−
* Real tetration \(\operatorname{tet}(x)\)
 
  +
Вы хотите сказать, что испугались?
−
* Complex level sets of tetration
 
−
* Abel function \(\operatorname{ate}(x)\)
 
−
* Iterates \(\exp^n(x)\) for fractional \(n\)
  
   
  +
**Trump:**
−
<div class="thumb tright" style="float:right; margin:0 0 8px 8px">
  
  +
No. I want to say that intimidation is not a substitute for capability.
−
{{pic|Tetsheldonmap03.png|300px}}
  
−
<small><center>Complex structure of tetration.<br>
  
−
From: Fig.18.3 (top), p.250 in ''Superfunctions''.</center></small>
  
−
</div>
  
   
  +
**Путин:**
−
==Humor==
  
  +
Но вы же понимаете, к чему это может привести?
−
<div class="thumb tright" style="float:right; margin:0 0 8px 8px">
  
−
{{pic|BlackSheep.png|300px}}
  
−
<small><center>Cartoon related to tetration.<br>Source: free illustration.</center></small>
  
−
</div>
  
   
  +
**Trump:**
−
==References==
  
  +
Yes. That is precisely why we are having this conversation.
−
{{ref}}
  
   
  +
**Путин:**
−
D. Kouznetsov. ''Superfunctions''. Lambert Academic Publishing, 2020.
 
  +
И что вы предлагаете?
−
Includes all figures cited above.
  
   
  +
**Trump:**
  +
We propose to remove the instruments that make such statements possible,
  +
while preserving the population and the territory.
  +
  +
**Путин:**
  +
Это ультиматум?
  +
  +
**Trump:**
  +
No. An explanation.
  +
  +
**Путин:**
  +
А если мы откажемся?
  +
  +
**Trump:**
  +
Then the explanation will be repeated,
  +
using a language that does not require interpreters.
  +
  +
**Путин:**
  +
Вы угрожаете?
  +
  +
**Trump:**
  +
No. Threats are what television hosts do.
  +
We deal with accountability.
  +
  +
**Путин:**
  +
Вы уверены, что контролируете последствия?
  +
  +
**Trump:**
  +
We control our actions.
  +
You control whether your system survives the truth about itself.
  +
  +
**Путин:**
  +
А если народ не поймёт?
  +
  +
**Trump:**
  +
Then it will finally hear something other than myths.
  +
  +
**Путин:**
  +
Вы уверены, что после этого всё закончится?
  +
  +
**Trump:**
  +
Nothing “ends”.
  +
Some things simply stop working.
  +
  +
**Путин:**
  +
Например?
  +
  +
**Trump:**
  +
For example, the belief that shouting about ash
  +
protects those who shout.
  +
  +
**Путин:**
  +
И что будет со мной?
  +
  +
**Trump:**
  +
That depends on whether you prefer to be a witness
  +
or an exhibit.
  +
  +
**Путин:**
  +
Это не разговор по телефону.
  +
  +
**Trump:**
  +
Agreed.
  +
That is why this is the last phone call.
  +
  +
**Путин:**
  +
Когда мы увидимся?
  +
  +
**Trump:**
  +
Soon enough.
  +
</poem>
  +
<!--
  +
In a setting where interpreters will still be present,
  +
but excuses will not.
  +
  +
(The dialogue continues conceptually as in [[Рыжий Пу]],
  +
with emphasis on non-nuclear demilitarization,
  +
personal responsibility of decision-makers,
  +
and the collapse of performative intimidation.)
  +
!-->
  +
==Interpretation==
  +
  +
The bilingual form highlights an asymmetry:
  +
  +
* threats are produced for a domestic Russian audience,
  +
* consequences are explained in a language addressed outward.
  +
  +
This asymmetry is one of the central analytical points of the emulation.
  +
  +
==Relation to other articles==
  +
  +
* [[Рыжий Пу]] — original Russian emulation
  +
* [[Эмуляция]] — methodological category
  +
* [[Утопия]] — literary framing
  +
* [[ChatGPT in TORI]] — methodological disclaimer
  +
  +
==Note by [[ChatGPT]]==
  +
  +
[[ChatGPT]] assisted in restructuring the emulation into a bilingual format
  +
and in clarifying the separation between fictional dialogue,
  +
analytical intent, and factual references.
  +
No factual claims or political positions were introduced by [[ChatGPT]].
  +
Responsibility for interpretation remains with the Editor.
  +
See also «[[ChatGPT in TORI]]».
  +
  +
==Warning==
  +
  +
As with other emulations in [[TORI]],
  +
this text does not constitute a recommendation,
  +
instruction, or forecast.
  +
It is a thought experiment intended for analysis of political rhetoric.
  +
  +
==References==
  +
{{ref}}
 
{{fer}}
  
{{fer}}
   
 
==Keywords==
  
==Keywords==
−
«[[Superfunction]]», «[[Exponential]]», «[[Logarithm]]»,
 
−
«[[Tetration]]», «[[ate]]», «[[Abel function]]»,
 
−
«[[Transfer equation]]», «[[Iterates]]».
  
   
  +
«[[RedPu]]»,
−
[[Category:Superfunction]]
  
  +
«[[Рыжий Пу]]»,
−
[[Category:Exponential]]
  
  +
«[[Donald Trump]]»,
−
[[Category:Special function]]
  
  +
«[[Путин Владимир Владимирович]]»,
−
[[Category:English]]
  
  +
«[[Киселёв Дмитрий Константинович]]»,
  +
«[[Эмуляция]]»,
  +
«[[Утопия]]»,
  +
«[[Radioactive ash]]»
  +
  +
[[Category:Emulation]]
  +
[[Category:Utopia]]
  +
[[Category:Donald Trump]]
  +
[[Category:Vladimir Putin]]
  +
[[Category:ChatGPT]]

Latest revision as of 17:22, 6 January 2026


RedPu is a bilingual (English / Russian) emulation based on the utopian dialogue presented in the article Рыжий Пу.

The emulation is presented in two synchronized language layers. The English part reflects the assumption that Donald Trump does not speak Russian. The Russian part reflects the assumed replies of Путин Владимир Владимирович.

Context

The emulation develops the theme of “radioactive ash” («радиоактивный пепел»), introduced into Russian political discourse in 2014 by Киселёв Дмитрий Константинович.

The text below is not a prediction, not a plan, and not a call to action. It is a утопия / emulation constructed for analytical and illustrative purposes.

Dialogue / Диалог

    • Trump (English):**

Hello, Mister Putin.

    • Путин (Russian):**

Здравствуйте, мистер Трамп.

    • Trump:**

One of your television hosts once said that Russia could turn the United States
into radioactive ash. Is that statement correct?

    • Путин:**

Он действительно так сказал. Да.

    • Trump:**

So Russia *can* do that?

    • Путин:**

Может.

    • Trump:**

Thank you. That answer is sufficient.

    • Путин:**

Для чего вам это?

    • Trump:**

To justify a decision currently being voted on by Congress.

    • Путин:**

Какое решение?

    • Trump:**

About Russia.

    • Путин:**

И вы решили меня предупредить?

    • Trump:**

Yes. We prefer transparency.
You may want to warn the personnel at your launch facilities.

    • Путин:**

Зачем?

    • Trump:**

Because we are about to demonstrate that Mr. Kiselev was mistaken.

    • Путин:**

В чём именно?

    • Trump:**

In assuming that only Russia can turn others into ash.

    • Путин:**

Вы хотите сказать, что испугались?

    • Trump:**

No. I want to say that intimidation is not a substitute for capability.

    • Путин:**

Но вы же понимаете, к чему это может привести?

    • Trump:**

Yes. That is precisely why we are having this conversation.

    • Путин:**

И что вы предлагаете?

    • Trump:**

We propose to remove the instruments that make such statements possible,
while preserving the population and the territory.

    • Путин:**

Это ультиматум?

    • Trump:**

No. An explanation.

    • Путин:**

А если мы откажемся?

    • Trump:**

Then the explanation will be repeated,
using a language that does not require interpreters.

    • Путин:**

Вы угрожаете?

    • Trump:**

No. Threats are what television hosts do.
We deal with accountability.

    • Путин:**

Вы уверены, что контролируете последствия?

    • Trump:**

We control our actions.
You control whether your system survives the truth about itself.

    • Путин:**

А если народ не поймёт?

    • Trump:**

Then it will finally hear something other than myths.

    • Путин:**

Вы уверены, что после этого всё закончится?

    • Trump:**

Nothing “ends”.
Some things simply stop working.

    • Путин:**

Например?

    • Trump:**

For example, the belief that shouting about ash
protects those who shout.

    • Путин:**

И что будет со мной?

    • Trump:**

That depends on whether you prefer to be a witness
or an exhibit.

    • Путин:**

Это не разговор по телефону.

    • Trump:**

Agreed.
That is why this is the last phone call.

    • Путин:**

Когда мы увидимся?

    • Trump:**

Soon enough.

Interpretation

The bilingual form highlights an asymmetry:

  • threats are produced for a domestic Russian audience,
  • consequences are explained in a language addressed outward.

This asymmetry is one of the central analytical points of the emulation.

Relation to other articles

Note by ChatGPT

ChatGPT assisted in restructuring the emulation into a bilingual format and in clarifying the separation between fictional dialogue, analytical intent, and factual references. No factual claims or political positions were introduced by ChatGPT. Responsibility for interpretation remains with the Editor. See also «ChatGPT in TORI».

Warning

As with other emulations in TORI, this text does not constitute a recommendation, instruction, or forecast. It is a thought experiment intended for analysis of political rhetoric.

References

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