Lucid Sententia XX

A finite length of time, no matter how great, pales in comparison with infinitude. Seconds are in the same class as centuries. In this sense each moment is like an entire lifetime.

LETHAL SPELL ABILITY thought experiment.

I had thought of this interesting hypothetical scenario recently, which could easily be extended to a thought experiment. Imagine that each person, over the age of, say, 16 was given the magical ability of having another person drop dead by thought alone, e.g. 'Adolf!', and Adolf drops dead. The ability would entail perfect concealment of he act, i.e. it would be impossible to know who had cast the deadly spell. This part is important, so those exercising this magical power would do so with full knowledge of its effectiveness, and impunity. Moreover, I believe that to many, only the presence of such anonymity would be a necessary condition for casting the spell at all.

This is interesting for a number of reasons. I wonder how many people would go ahead and actually use the spell? Also, suppose the version of the magic ability such that the total number of spells was unlimited, with perhaps some daily limit. And that each spell would have to be cast at an individual, e.g. general spells like "may all people above 6 feet drop dead" would be disallowed, which doesn't mean that one couldn't find out who the people like this are and cast the spell on them. At what rate and in what sorts of patterns would people start dropping dead? 

I have been thinking about this, and wondering what kind of people would jump at the opportunity of exercising such power.

For example, suppose that in the original scenario (of having a single spell only), we let the time to cast the spell last for a month. The point being that existing grudges, prejudices, and feelings of hate would be sorted out right away, so to speak, instead of having the scenario allow to wait for a time when an otherwise unwilling to use the spell person would be forced to do so in self defense. 
So suppose a month goes by and all the spells had been cast. It follows that we're left with a population that is at most smaller than before by the whole number of people (magicians) who were endowed with the ability to cast the spell (the case when no magicians are killed before casting their own spell), and roughly (±1) at least smaller than before by half the number of magicians (the case when half the magicians are killed before casting their spell).

Now imagine 2 alternative outcome-worlds:
--world 1 consisting of all the spell casters and the remaining youth under 16. So this world is left with those that though it to be better to cleanse it one way or another. And those who got eliminated no longer exist.
--world 2 consisting of all the spell victims, and all of the under 16 that were present before any spell was cast, i.e. the original, under 16 population. So basically this world consists of everyone minus the spell-casters.

I wonder how those worlds would evolve in time. World 1 has less people remaining, but let's suppose the populations to be sufficiently large, as not to be in danger of extinction after the cleansing process. I wonder how those worlds would differ, given what kind of people occupy it.

I also wonder if people would just annihilate themselves into extinction, on the version of the scenario where there would be no limit on the number of lethal spells. It would be like giving anyone access today to the current nuclear arsenal deployment.

I'm sure there are other aspects of this thought experiment that I haven't raised, and which could be quite interesting. I'm thinking of writing a short story based on this scenario as the underlying premise. No prizes for guessing that Borges and Lem are among my inspirations! 

I've identified an interesting semi-group in Australian slang ;)

(G, * )

G  = {yeah, nah}

Closure
yeah nah = nah
nah yeah = yeah
nah nah = nah
yeah yeah = yeah

Associativity
(yeah nah) yeah = yeah
yeah (nah yeah) = yeah

(yeah yeah) nah = nah
yeah (yeah nah) = nah

(nah yeah) nah = nah
nah (yeah nah) = nah

(nah nah) yeah = yeah
nah (nah yeah) = yeah

The above structure can be extended to a monoid, if we add the empty word as the identity element.

ECHO

Echo: "What he said."

ALOSZA I DRZWI

Mój szczur po prostu nie radzi sobie z pojęciem drzwi. Jak są zamknięte to je obwąchuje z ewidentną ciekawością. Gdy drzwi są otwarte to jego zdziwienie wcale nie ustaje---obwąchuje próg i framugę z zaciekawieniem; rozgląda się z widocznym osłupieniem: jak to może być, że perspektywa wcześniej nie widoczna, nagle się ujawnia? Nagła zmiana w topologii podłogi musi robić wrażenie. Ale, mimo trudności z ogarnięciem swoim szczurzym umysłem pojęcia drzwi, trzeba temu ciekawskiemu gryzoniowi przyznać godną pochwały wytrwałość.

MAJOWY WIECZÓR

W lipowym zagajniku, z nad usłanej puszystyą bielą trawy unoszą swoje główki delikatne dmuchawce, jakby chciały odgadnąć które to gwiazdy wskazują skierowane ku niebu stożkowe kandelabry kwiatów samotnego kasztanowca.

Asortyment Nieskończoności

Jest to prezentacja Powerpoint, prelekcji której udzieliłem w Otwartej Kolonii (filii Wolskiego Centrum Kultury) 20 kwietnia. Ten wykład to krótka historia pojęcia niskończoności, oraz wstęp do arytmetyki liczb kardynalnych poprzez prezentację dowodów Cantora na równoliczność zbiorów nieskończonych. Poniższa prezentacja zawiera trochę definicji oraz pomocy ilustracyjnych, ale oczywiście brakuje jej niezbędnej narracji która wyjaśnia wszystkie pojęcia oraz ich relacje.

Asortyment Nieskończoności PDF by Mariusz Popieluch on Scribd