Antonio E. Porreca 🐳

@aeporreca

Maître de conférences (lecturer) at & researcher at 🐗🇫🇷 • Natural computing, discrete dynamical systems & complexity • Down with generative AI • I like (human) languages • This is a pandemic, y’all 😷 • aeporreca.org

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Antonio E. Porreca 🐳@aeporreca· Jul 11

It’s #Caturday and Loki wants you to draw him like one of your French kitties.

Loki, a really pretty Euro-Armenian cat with black and white cow-like fur, is lying sphinx-like (but with a stretched-out leg) on a teal-coloured pouf and making a cute expression while looking slightly to his left.

Antonio E. Porreca 🐳@aeporreca· Jul 11

Here she is (sorry for the low quality picture, my phone only has 2x optical zoom).

Antonio E. Porreca 🐳@aeporreca· Jul 10

Loki also has a (slightly more modern) house like that.

Loki, a super cute black and white European cat, rests inside his cardboard house with scratching floor. The windows on the side of his house are open.

Antonio E. Porreca 🐳@aeporreca· Jul 8

At my parents’ place there should still be this (as far as I can recall) awesome 1987 book, which is full of pictures like these.

The 1980s-style cover of the Italian book ”Il grande libro dell’informatica: Dai numero al computer” (“The great book of computer science: From numbers to the computer”) by Mariagiovanna Sami, Arnoldo Mondadori Editore, 1987.

Antonio E. Porreca 🐳@aeporreca· Jul 6

It’s a very hot day to be so fluffy so one needs refreshment.

A very fluffy black cat (with ginger highlights and very pretty) drinking water in the sun from a large glass bowl placed under a tree.

Antonio E. Porreca 🐳@aeporreca· Jul 6

The code I’m writing right now is almost like this.

Some Python code:

def solve_diophantine(equation):
if (equation.degree() >= 4 and
equation.nvars() >= 58):
raise NotImplementedError(
'''unable to solve unless the
Church-Turing thesis is false''')
...

Antonio E. Porreca 🐳@aeporreca· Jul 4

And now on the cupboard.

Loki, the pretty European black and white cat, is sitting on the cupboard waiting for someone to feed him. He’s making a cute face and his belly is visible, showing his fluffy hair.

Antonio E. Porreca 🐳@aeporreca· Jul 4

And now on the floor.

Loki, who is still a pretty black and white European cat (even though of Armenian upbringing) is lying on the floor, his rear legs stretched but his front paws bent under him. He looks toward the right rather than toward the camera.

Antonio E. Porreca 🐳@aeporreca· Jul 4

Le voilà on the windowsill.

Loki, super cute black and white cat, laying with his head on the windowsill with his eyes barely open since he’s sleepy.

Antonio E. Porreca 🐳@aeporreca· Jul 4

It’s #Caturday and Loki has learned how to open the door (which was temporarily closed so it could not escape the house) by using the doorstopper as a lever. #MechanicalEngineering

Loki, a pretty black and white cat, is trying to open the door by pulling the doorstopper with his paw.

Antonio E. Porreca 🐳@aeporreca· Jul 2

C’est Marseille bébé. (Source : www.tiktok.com/@imaninita/v...)

Antonio E. Porreca 🐳@aeporreca· Jun 25

Grothendieck is that you?

A page from Deane Lent, Análisis y proyecto de mecanismos, Editorial Reverte, 1974.

Probando 56/1 × 1/55, el mínimo común múltiplo de 57 y 56 es 3192.
Nos queda:
[cálculos]
de nuevo contiene razones que no se pueden reducir a los engranajes disponibles (57 es un número primo).

Antonio E. Porreca 🐳@aeporreca· Jun 25

Watch me use barn machinery gears (including a scan of the 1849 book) as an example of synchronous dynamical systems in my next talk instead of traffic lights.

A slide titled “Equations with + and ×” that shows the synchronous execution (times) of two traffic lights as the alternative execution (plus) of four systems, depending on the initial state.

Antonio E. Porreca 🐳@aeporreca· Jun 25

Here’s the complete title (babel.hathitrust.org/cgi/pt?id=uc...)

THE FARM ENGINEER:
A Treatise on Barn Machinery,
PARTICULARLY ON THE
APPLICATION OF STEAM AND OTHER MOTIVE POWERS
TO THE
THRASHING MACHINE;
EMBRACING AN ACCOUNT OF THE METHODS PRACTISED IN ANCIENT AND MODERN TIMES FOR THRASHING AND WINNOWING GRAIN;
WITH
DESCRIPTIONS OF THE DIFFERENT STEAM ENGINES NOW USED AND PROJECTED FOR AGRICULTURAL PURPOSES;
AND THE
EXTENDED APPLICATION OF STEAM AS A MOTIVE POWER AT FARMS.
BY ROBERT RITCHIE, C.E., EDINBURGH,
ASSOCIATE OF THE INSTITUTION OF CIVIL ENGINEERS; YELLOW OF THE ROYAL SCOTTISH SOCIETY OF ARTS;
AND AUTHOT OF "RAILWAYS, THEIR RISE, PROGRESS, AND CONSTRUCTION," ETC.
Illustrated by numerous Engravings and Wood Cuts.
BLACKIE AND SON:
QUEEN STREET, GLASGOW; SOUTH COLLEGE STREET, EDINBURGH;
AND WARWICK SQUARE, LONDON.
MDCCCXLIX.

Antonio E. Porreca 🐳@aeporreca· Jun 25

Applications of number theory pre-70s (which are, incidentally, or rather fatalistically, related to the factorisation of dynamical systems wrt synchronous execution that we’re working on). Love the source: Robert Ritchie, The Farm Engineer: A Treatise on Barn Machinery […], Blackie and Son, 1849.

Another point of importance in working wheels is, that the same teeth should not always come together; when this occurs, it must produce inequality of wear. To avoid the latter fault, it is the practice to make the number of teeth in the wheel what is termed "prime" * to the number of teeth in the pinion;

* One number is prime to another, when no number except unity will divide them without a remainder; thus 9 is prime to 10, having no common divisor. A prime number is 11, 13, 17, and so on, which, if multiplied by an even number, will produce an even number. The least number divisible by two prime numbers, or by two numbers prime to each other, is their product; as an example, 15 and 8, the factors of 15, are 3 and 5; the factors of 8, are 2 and 2 and 2; hence the least number divisible by 15 and 8 must be divisible by their factors, 3, 5, 2, 2, 2, or is their continued product, or 8 × 15 = 120. Less importance is now attached than formerly to making wheels prime to each other.

Antonio E. Porreca 🐳@aeporreca· Jun 24

Fluffy Luminy cat. 🐈‍⬛

A black (female?) cat walking. She has medium-long hair and is very fluffy, especially the tail.

Antonio E. Porreca 🐳@aeporreca· Jun 22

This slide courtesy of @joshuagrochow.bsky.social.

Thank you for hosting remote talks! 🙂

• Many researchers cannot travel because of:
• The current pandemic
• Family or work responsibilities
• Disability or other health issues
• Climate change and environmental cost
• Lack of funding
• Visa issues…
• Remote talks help keeping the community connected

based on a slide by Joshua Grochow

Antonio E. Porreca 🐳@aeporreca· Jun 22

New talk: “Polynomial equations over bĳective dynamical systems and their semiring extensions”, just presented at the Workshop on Cellular Automata and Boolean Automata Networks at Unconventional Computation and Natural Computation (UCNC 2026) aeporreca.org/talks/polyno...

🚧 Polynomial equations over bĳective dynamical systems and their semiring extensions 🚧
Rocco Ascone • Antonio E. Porreca • Marius Rolland
Aix-Marseille Université & LIS, Marseille, France
Workshop on Cellular Automata and Boolean Automata Networks

Antonio E. Porreca 🐳@aeporreca· Jun 21

Even if it’s not #Caturday Loki is still rubbing himself against my backpack.

Antonio E. Porreca 🐳@aeporreca· Jun 19

When people “ask ChatGPT” (source: www.instagram.com/p/BY6UzGugDfD/)

A comic from Safely Endangered:

First panel: a person, keeping a black ball in his hands, asks: “Magic 8-ball, am I stupid?”

Second panel: the black ball is revealed to actually be a bowling ball.

Antonio E. Porreca 🐳@aeporreca· Jun 13

It’s #Caturday and Loki is posing on the windowsill doing his best ☺️ face.

Loki, a European black and white cow-patterned cat who happens to be very pretty and fluffy, is sitting on the windowsill on a sunny late spring afternoon, doing a very cute expression with his eyes closed.

Antonio E. Porreca 🐳@aeporreca· Jun 11

Pigeon qui fait le cosplay d’un gabian. / Pigeon cosplaying as a seagull.

A white pigeon with grey wings who kinda looks like a seagull.

Antonio E. Porreca 🐳@aeporreca· Jun 11

My phone thinks that the coefficients of this polynomial are phone numbers. I’m pretty sure that if we call them we can contact the algebraists of the past and ask one question to each of them.

X=C(7) + C(5) + C(3) + C(2)
Polynomials of degree 13.
[Poly(1, -102, 4609, -121550, 2074039, -23977514, 191011755, -1044297386, 3820688124, -8853993720, 11611101600, -6477408000, 0)]

Antonio E. Porreca 🐳@aeporreca· Jun 6

It’s #Caturday and Loki is playing with my backpack, as he often does.

Antonio E. Porreca 🐳@aeporreca· May 30

It’s #Caturday and it’s already the second time this week I meet this good boy taking a nap on his car.

An orange cat sleeping in a semi-sphinx position on the roof of a car. He’s very cute.

Antonio E. Porreca 🐳@aeporreca· May 29

We are working on finite dynamical systems (aka finite functions) up to isomorphism, where sum and product are categorical (disjoint union and Cartesian product, ∅ is 0 and singleton is 1). It has these properties (plus additive cancellation). It’s a pretty tough beast but we love it.

$Things we know about ⅅ • It is an integral semidomain 😊 (AB = 0 implies A = 0 or B = 0) • No unique factorisations nor cancellation 😡 (C₂C₂ = gcd(2,2) × C_{lcm(2,2)} = 2C₂) • Almost all systems are irreducible 🫤 (lim_{n → ∞} |reducibles of n states| / |all systems of n states| = 0) • There are no primes 🤷‍♂️ (P prime means P | AB implies P | A or P | B)$

Antonio E. Porreca 🐳@aeporreca· May 29

Ho ritrovato alcuni vecchi esercizi di algebra (di 19 anni fa 👀 a UniMiB, prof Thomas “Elemento Noitro” Weigel) in cui facevo proprio quello che vorremmo fare adesso con le nostre estensioni di semianelli (là era più facile però, scopri il vero valore della sottrazione solo quando l’hai persa 🙁).

$Istituzioni di Algebra (II modulo) Esercitazione 1 Antonio Enrico Porreca — matricola 078934 antonioenrico.porreca@studenti.unimib.it 15 marzo 2007 Esercizio 1. Computare $[\Q(\sqrt{2}, i) : \Q]$ e $[\Q(\sqrt[3]{2}, e^\frac{2 \pi i}{6}) : \Q]$. Soluzione. \begin{solution} Per la formula del grado vale \[ [\Q(\sqrt{2}, i) : \Q] = [\Q(\sqrt{2}, i) : \Q(\sqrt{2})] \cdot [\Q(\sqrt{2}) : \Q]. \] Calcoliamo, innanzitutto, il polinomio minimo di $\sqrt{2}$ su $\Q$. Sia $f = X^2 - 2$. Allora $f$ \`e monico e $f(\sqrt{2}) = 0$. Per il criterio di Eisenstein $f$ \`e irriducibile: infatti $2$ divide il termine noto ma non il coefficiente direttore, e $2^2 = 4$ non divide il termine noto. Dunque $f$ \`e il polinomio minimo di $\sqrt{2}$ su $\Q$; perci\`o $[\Q(\sqrt{2}) : \Q] = \deg f = 2$. Calcoliamo ora il polinomio minimo di $i$ su $\Q(\sqrt{2})$. Sia $g = X^2 + 1$; allora $g$ \`e monico e $g(i) = 0$. Se $g$ fosse riducibile, allora sarebbe prodotto di due polinomi lineari e dunque avrebbe una radice in $\Q(\sqrt{2})$. Ma $\Q(\sqrt{2}) \subseteq \R$, mentre le radici di $g$ sono $i, -i \notin \R$. Qundi $g$ \`e il polinomio minimo di $i$ su $\Q(\sqrt{2})$ e $[\Q(\sqrt{2}, i) : \Q(\sqrt{2})] = \deg g = 2$. Per quanto osservato in precedenza \[ [\Q(\sqrt{2}, i) : \Q] = [\Q(\sqrt{2}, i) : \Q(\sqrt{2})] \cdot [\Q(\sqrt{2}) : \Q] = 2 \cdot 2 = 4. \] Analogamente, nel secondo caso si ha \[ [\Q(\sqrt[3]{2}, e^\frac{2 \pi i}{6}) : \Q] = [\Q(\sqrt[3]{2}, e^\frac{2 \pi i}{6}) : \Q(\sqrt[3]{2})] \cdot [\Q(\sqrt[3]{2}) : \Q]. \] Il polinomio minimo di $\sqrt[3]{2}$ su $\Q$ \`e $f' = X^3 - 2$, perch\'e \`e monico, ha radice $\sqrt[3]{2}$ ed \`e irriducibile per il criterio di Eisenstein (esattamente come il polinomio $f$ di cui sopra). Perci\`o $[\Q(\sqrt[3]{2}) : \Q] = \deg f' = 3$.$

Antonio E. Porreca 🐳@aeporreca· May 28

This is OK for everyone, right?

Antonio E. Porreca 🐳@aeporreca· May 27

Sigh 😞

Received 21 March 2025
Accepted 18 February 2026
Published 27 May 2026

Antonio E. Porreca 🐳@aeporreca· May 27

New paper: Doré, F., Perrot, K., Porreca, A.E., Riva, S., Rolland, M.: Infinite trees for division and roots over finite discrete-time dynamical systems. Natural Computing. 25, 16 (2026). rdcu.be/fk2q0 (preprint aeporreca.org/papers/infin...)