Mathematics: The Language of Resilience and Logic A philosophical reflection on leadership, resilience, and the human condition.
By D. L. Dantes | November 8th, 2025
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Mathematics: The Language of Resilience and Logic
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Riding on the bus rn I just saw a sign that said “Euclid ave”
WHAAAT BILL’S DAD GETS AN AVENUE?!
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La imagen del mes de ESA/Hubble presenta una espectacular colaboración entre dos grandes observatorios espaciales: el telescopio espacial Hubble Space Telescope, fruto de la cooperación entre NASA y European Space Agency, y el telescopio europeo Euclid. Juntos ofrecen una nueva perspectiva de uno de los restos estelares más complejos y fascinantes conocidos: la Nebulosa ojo de gato.
Nebulosa Ojo de Gato: una mirada combinada de Hubble y Euclid a la muerte de una estrella
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Due telescopi, due prospettive. Vecchio e nuovo che collaborano, si cercano, si integrano. Ognuno dice all'altro quello che l'altro non può sapere, non può dire. Insieme, vedono meglio, superando ognuno le parzialità dell'altro.
Hubble ed Euclid, il primo lanciato nel 1990, il secondo nel 2023. Il primo ormai anziano, l'altro giovanissimo. Insieme. Si parlano, si cercano, capiscono il cosmo insieme.
Camminare soli a volte è necessario, ma spesso non è la cosa ottimale.
Questa nebulosa si chiama Occhio di gatto, si trova (ce l'ha detto la sonda Gaia) a 4300 anni luce da noi. Il guscio di gas e polveri di una stella che si avvia alla fine, ma spara tutti i suoi colori, segnando il cosmo con un evento unico (ogni nebulosa è diversa).
Hubble offre immagini ad alta risoluzione, rivelando i dettagli più intricati.
Euclid offre un grande campo visivo, immergendo la nebulosa nel suo contesto cosmico.
L'immagine combinata Hubble-Euclid è spettacolare ma anche ricca di informazioni sulla dinamica dei venti stellare e sull'evoluzione di stelle di massa intermedia. Soprattutto, è qualcosa che si realizza soltanto in un abbraccio di diversi punti di vista, nell'integrazione di diverse possibilità.
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¿Cómo vemos lo invisible? Dr. Diana Scognamiglio sobre la materia oscura y el futuro de la cosmología
En la cosmología contemporánea, el desafío ya no reside simplemente en observar el Universo, sino en reconstruir lo invisible. A medida que los estudios de nueva generación generan volúmenes de datos sin precedentes, los astrofísicos desarrollan métodos cada vez más sofisticados para cartografiar la distribución invisible de la materia oscura, controlar las incertidumbres sistemáticas y extraer…
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Just run it back, give me five whole minutes
I am thick tar on the inside burning
I’ve got a ghost in the hallway grinning
And a heavy head that won’t stop turning
If my fate is a bad collision And if my mind is an open highway
Give me the twilight two-way vision
Give me one last ride on a sunset skylane
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Listening to Infinite Baths and then Euclid should be mandatory, I think I’m ascending to another plane rn
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“Are you okay”
No I’ve been listening to vessels isolated vocals from Euclid on repeat for days now
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One of my settlements, Aybritt’s Hope, sent me a message to check on a black hole that’d suddenly appeared in the system. A few scans told me it was an anomalous black hole that’d disappear soon. Being what I am, of course I went into it. I think it sent me clear across Euclid in one jump!
A ringed capped/fungal world was the first thing to grab my attention. They’re probably my favorite exotic planet and finding a lush, green one was a nice surprise. The resident fauna weren’t as numerous as my home planet, but they were gorgeous as always.
Two of the planets had salvageable scrap, so I decided to check out the one with life first. It’s turned out to be this very alien-looking icey planet. The flatness of the tundra mixed with the giant mushrooms and spikes isn’t something I’ve seen before.
The local Vy'keen also tolerated my presence at the local archive long enough for me to take a few pictures.
The second salvage planet was a dead one. The beautiful night sky more then made up for the lack of fauna or flora.
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History of Philosophy: Logic
ALTBy original raster version: Farcasterrecreated English vector version: Nyqlatest, simplified version: Phlsph7 - File:Argument_terminology_used_in_logic_(en).svg, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=128118136
Logic is the branch of philosophy that studies reasoning, deduction, critical thinking, including both formal and informal logic systems. Formal logic consists of premises that lead to a conclusion, such as ‘the sun is up’ and 'if the sun is up, it is daytime’ which leads to the conclusion 'it is daytime’, which can all be evaluated for truthiness or falseness. These statements must follow a specific internal structure that is linked by a particular logic vocabulary which also has particular characters that might make them look like a math equation, such as ∧ (and) or → (if…then). The truth of the full argument, or full equation, depends on the truthiness of all the parts, leading to it being correct or incorrect, with correct ones supporting the conclusion, also known as deductive arguments. Arguments can also be 'ampliative’, which means the conclusion adds to the premises, such as inductive reasoning, where the premises offer a probability that the conclusion is correct, but isn’t certain like deductive reasoning is, and abductive reasoning, which seeks the simplest, rather than the most correct, conclusion from observations. Ampliative arguments are common in the sciences and everyday discourse. Informal logic is focused on 'natural language’ and explores fallacies such as false dilemmas and begging the question among others, critical thinking, and argumentation theory, which is studying how conclusions can be undermined or supported by the premises presented, such as in debate.
Formal logic developed independently in ancient Greece, India, and China in antiquity. While valid reasoning predates the formal studying of logic, with geometry and other mathematics being the first studied such as when the ancient Egyptians developed formula to find the volume of truncated pyramids. The ancient Babylonians also used logic within medical diagnostics, such as in Esagil-kin-apli’s Diagnostic Handbook from the 11th century BCE. They also used logic to develop a predictive system for the location of the planets in the sky in the 8th-7th centuries BCE. The pre-Socratic Greeks added to the understanding of geometry that the ancient Egyptians had by developing geometric proofs, as well as developing principles for those proofs, rules that proofs must follow to be valid as written of by Euclid of Alexandria, who lived around the 300s BCE and whose text, The Elements, was used for thousands of years.
Aristotle, who lived from 384-322 BCE, is considered to have the greatest impact on Western logic and thought as well as the 'first formal logician, in that he demonstrated the principles of reasoning by employing variables to show the underlying logical form of an argument’. His works, the Organon, a collection of six works on logical analysis and dialectic, or reasoning by dialogue. He also developed a theory of non-formal logical fallacies. The Stoics. especially the Megarian school of the 4th century BCE, especially as formalized by Chrysippus of Soli, who lived from about 278-206 BCE, and reportedly wrote over 700 works, with 300 on logic alone, but almost none of them survive, possibly due to hostility toward the Stoics. They did, however, manage to make a mark on Western logic with their modal thinking with what is known as the Master argument of Diodorus Cronus, 'which states that each pair of the following propositions contradicts the third proposition:
Everything that is past is true and necessary.
The impossible does not follow from the possible.
What neither is nor will be is possible.’
The second contribution they made was the conditional statement, with Diodorus and his student Philo of Megara, who developed the system of 'let T0 and T1 be true statements, and let F0 and F1 be false statements; then, according to Philo, each of the following conditionals is a true statement, because it is not the case that the consequent is false while the antecedent is true (it is not the case that a false statement is asserted to follow from a true statement):
If T0, then T1
If F0, then T0
If F0, then F1
The following conditional does not meet this requirement, and is therefore a false statement according to Philo:
If T0, then F0’
The third contribution they made was the distinction between utterances (phone), which might just be noise, speech (lexis), which is 'articulate but which may be meaningless’, and actual discourse (logos), which is meaningful utterances.
Within the Rigveda, written between 1500-1000 BCE, contains a speculation that was later formalized as 'A’, 'not A’, 'A and “not A”’, and 'not A and not not A’ known as catuṣkoṭi. Logic continued to develop in India independently from Greek logic. Public debate was considered considered a form of rational inquiry, as were assemblies of relevant experts 'were regularly convened to deliberate on a variety of matters, including administrative, legal and religious matters’. Pāṇini, who lived in about the 5th century BCE, developed a form of Boolean logic, which uses whether something is true or false and operators such as AND, OR, and NOR to evaluate two statements against each other. Jains contributed to logic by focusing on epistemological, or focusing on the nature of knowledge, and 'Jains have doctrines of relativity used for logic and reasoning:
Anekāntavāda – the theory of relative pluralism or manifoldness;
Syādvāda – the theory of conditioned predication and;
Nayavāda – The theory of partial standpoints.
These concepts in Jain philosophy made important contributions to the thought, especially in the areas of skepticism and relativity’.
Chinese logic, with the country’s long isolation from both the West and India, developed independently as well. Mozi, who lived about 470-391 BCE, was the first to write about valid inference and correct conclusions, though they were considered 'non productive and not integrated into chinese science or mathematics’. Mohist logic focused rhetorical analogies based on three fa, 'methods of drawing distinctions between kinds of things’, and was based on syllogism, or two propositions that are asserted to be true to reach a conclusion. During the Qin dynasty, Mohism was suppressed by Legalism, as did the study of logic until it was reintroduced by Buddhists from India.
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🌌🔭 Un hito clave en nuestra comprensión de cómo se “encienden” los agujeros negros supermasivos en galaxias lejanas… 🔭🌌
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(So many expeditions coming up… I’m happy they’re rerunning the ones from this year but I keep hoping they rerun older ones at some point. Anyway, please enjoy my Beachhead Expedition vacation(?) photos.)