Why I don't like attending exhibition openings

I generally avoid such events, but find myself occasionally obliging a friend and accompanying them with the only consolation being the hope that the experience may prove my convictions inaccurate. Alas those hopes prove to be futile at every such chance attendance.

There's the experiential aspect, which even with the aid of empathy, understanding and careful reflection fails to provide more than painful frustration; during the fake and polite interactions equally ungenuine inquiries arise: "So what do you do?” The frustration emerges primarily from the realization of my cowardice which prevents me from actively defying customary conformity - knowing with certainty the pure formal nature of the inquiry, devoid of no more genuine interest then required to satisfy a curiosity which attempts to avoid boredom and dullness by engaging in mild and superficial intellectual entertainment (the conversation), I find myself pretending that this empty shell of an inquiry is of substance and respond accordingly - with symmetrical pretension. The only way I can withstand the half hour or so of my physical presence at such events is by erecting a hermetic and pseudo philosophical wall around me which relates insincerely to the exhibited pieces, or physically avoiding any interactions by inspecting the exhibited works repeatedly with ostentatious interest that would excuse my lack of socializing. Whilst exercising those evasive tactics I'm always astonished by my paranoia that time has slowed almost to a stop. This behavioral device tends to temporarily fend off those excruciatingly vacuous inquiries into the content of my person.

It would be tempting to at least engage in the consolatory activity of amusing myself by observing the career hungry crowd, seeking mutual attention of only those who in its mind can contribute to the elevation of either the ego or what's more important the factual career status. Sadly I no longer find it amusing. I'm saddened by this and inescapably forced into reflections on the human condition in general - how we will readily crawl, hop or sing in a bad chorus - ready to take those desperate measures if only their performance, no matter how pathetic and degrading, would deliver but a glimmer of a promise of bringing closer the illusory goal that we have chosen to endow with value.

A Bus Encounter

On that day, the bus of the 171 line was full as usual, but Joseph didn't mind standing for the twenty minutes or so since the reminder of his day would be spent sitting in on lectures at the local university. During the journey he would occasionally take his eyes away from the busy city-scape rushing past beyond the nearest window and observe the faces of other passengers, every now and then allowing his gaze to linger on a more interesting one.

While engaging in one of those lazy inspections of his fellow passengers Joseph was unsettled by a pair of blue and mysterious eyes meeting his. Those blue eyes were framed by a pleasant face of a young woman partially visible through a narrow gap between other passenger's heads. Not used to such confrontations from the depersonalized and anonymous crowd, Joseph attempted to conceal his voyeuristic intentions by nonchalantly continuing to turn his head, as if intending to look through a window on the opposite side of the bus. He was sure that during this momentary encounter when their gazes met, a latent smile appeared on her pale and calm face. After composing himself, he glanced back at this mysterious stranger and surely enough she had maintained the same subtle smile and what seemed particularly unusual was how her unmoved gaze welcomed his, as if expecting him to indeed glance back. Prompted by a sudden adrenaline rush Joseph looked away once more.

Not usually forward by nature, he generally avoided making spontaneous acquaintances with strangers, and women especially. Furthermore, he reserved those morning commuting intervals primarily for planning and reflection. Joseph, it seems, desired to suppress and control spontaneity despite seeing its value. It was welcome, but not on a bus. This brief encounter however unsettled his rigid convictions, and the appearance of this mysterious girl tempted him to break his strict habit, only if to learn her name. He made a decision. As the bus would approach the city center where most people would disembark, he would then have the necessary space to approach this newly potential non-stranger and make an acquaintance. This certainly wouldn't require too much effort on his part, since he felt that a subtle yet definite invitation had already been granted.

The bus arrived at the stop where most people usually leave. The commotion created by people heading for the doors was the cue Joseph had been waiting for which gave him the sufficient amount of courage to turn toward the young woman once more.  He was mildly amused upon noticing how his heart begun to beat faster during the composition of the introductory phrase. He approached tentatively, and just as the last of the people standing between them headed for the door leaving behind an empty and unobstructed space, Joseph experienced what could be best described as a cognitive jolt of disillusion, as his eyes fixed on the blind man's cane, which the young woman was holding closely by her side. Her gaze now suddenly stripped of its mystery, had dissolved into a blank and eerie stare into oblivion, and her Mona Lisa smile now equally demystified reduced to the calm and relaxed expression of a morning commuter.

Joseph stood there staring in disbelief for a few seconds, his lips parted with the preselected introductory phrase screaming inside his head. What finally brought him back from the paralysis of this epistemic anomaly was the realization of his asymmetric freedom of being able to look at the young woman, which he thought to be unfair and invasive. With that thought, amused by his imaginative powers of confabulation, he hopped off the bus just as the doors were beginning to close.

Lucid Sententia XVIII

Blows, unlike kisses, leave marks on both flesh and soul, as memories of their acquisition, thereby advising prudence to avoid them. Hence the impenetrable walls and protective shells gradually accreted with time. Those provide shelter from the lethal force of blows, but also are inadvertently impervious to the delicate brushes of kisses.

A Perfect World.

Lev, one of the most gifted graduates of The Academy of Unlimited Arts, with personal interests in Perpetual Omnipotence, decided to focus on universe creation in his postgraduate pursuits. The world he planned to make this time was meant to be unlike any other - a dynamic cosmos full of sentient and intelligent beings. The idea was to make it a perfect world; no pain, no sorrow, no longing, no broken hearts. No death. In short - ideal.

After all the world-making only one thing remained to be done - finding a fitting name for this wonderful creation. Lev was happy and content having finally settled on an appropriately adequate one - a perfect name. Upon completion of his cosmic project, Lev attached a plaque to its Luminiferous Aether, and on it an engraving in a particularly baroque font "A place with no dreams".

Beginning of the End

Elijah had been seeing Barbara for almost a month by then. The first few times they had met for coffee, drawn towards each other with a youthful curiosity and suppressed desire, days passed like hours. They relished in this new unexplored space of companionship. Immersed in philosophical conversations about life, exchanging views about what seemed most important, they managed, it seemed, to create their private realm outside of time which did not conform to the usual laws governing the universe. Before Elijah could realize, their quite lengthy acquaintance, for they had by then known each other for over a year, within no more than a few weeks evolved to a state which was an enchanted and exciting platform full of endless possibilities. Both quite shy, and careful not to spoil what grew out of what seemed like hours in their personal timeless world, enjoyed this curious state full of promise yet free from promises. Aside from Barbara’s cheerful, witty and energetic yet controlled demeanor which captivated with its reliably suitable degree of spontaneity, there was one other particular quality which Elijah admired. Unlike anyone he had met before, Barbara wholeheartedly engaged herself into any issue at hand, and with a particular and genuinely considerate approach when immersed in conversation with a colleague, or a friend. "She makes me feel present" was, Elijah felt the best characterization of her caring, engaging and non-selfish nature.
Barbara had a quintessentially feminine and beautiful Rubenesque figure, which sadly did not reflect her desired self image. This bitter dissonance between love expressed and actual self-love, was to become a blemish which would not only encroach into the blissful realm the two friends had conjured, but eventually mercilessly annihilate it.
The first cracks appeared during one of their many outings through the city’s major bookstores. Whilst strolling through the forest of towering bookshelves inside the city’s largest ‘used books’ store, and admiring the beautiful publications of Shakespeare’s works from the beginning of the 20th century, Elijah captured by an almost juvenile spontaneity with a trace of romantic intention, which he wouldn't deny, turned to Barbara and whispered among the colonnade of world’s major literary works: “Close our eyes, and let me lead you into a place within this forest where you will open them again only after you have blindly picked some book – one which you’ll promise to read”. Barbara agreed promptly – and soon, they were silently dancing through this symbolic storage room of millions of stories, fictional and actual lives, hopes and dreams. Upon stopping among some particularly tall bookshelves Elijah delicately twirled Barbara twice and lead her carefully as she blindly reached out for a book - this mysterious book, which they both anticipated to contain a magical spell which would embody everything that led to its emergence from the dormant and dusty forest. It would also bring a promise, a guide, or clue on this treasure hunt for true love. Barbara hesitated a little before allowing her fingers tentatively feel the spines of the books at shoulder level. She pulled a dusty book out, and after what appeared as having glanced at the title she silently turned with a jerk of the neck to Elijah who, not having seen the title himself only puzzled in horror at Barbara’s cold, narrowed eyes piercing him with a deadly and stern gaze out of the frame of a stone cold and fierce grimace which momentarily disfigured her face. She pushed the book into his chest, said “very funny” and marched off with an impatient glance at her watch. Elijah stood there in utter bewilderment at what had just happened, and his eyes widened as he read “Low fat cooking” - a title screaming at him with its colorful and boldface font from the dusty cover of the book.

Chance's Revenge

Joseph was known to occasionally bewilder random strangers, mostly those unfortunate enough to travel on the same train as him, by unexpectedly turning to them and reciting some lengthy and arbitrary Latin sentence. This exercise in buffoonery was mostly intended to evoke a laugh from his friends who shared his appreciation for the hilarity of the kaleidoscopic mixture of puzzlement, amusement and horror - all inevitably provided by his victim's faces.

Yesterday morning Joseph, up to his usual mischief did just that - while conversing with his typically extroverted group he suddenly turned around without warning and uttered a preselected Latin phrase to the young woman sitting behind him - "You are the most beautiful girl I have ever seen in my not so quite short life". This time something odd happened however. Whilst uttering this provocative sentence he slowed down half way through and what began as a nonchalant and lively baritone quietened to a quivering whisper, for at that very moment Joseph realized that what he was saying was true. The jest backfired, and Chance took her revenge on him.

N>1 roots of primes are irrational

The question came up in a conversation recently, and although it seemed intuitively true, I couldn't find a proof online. Many of you reading this are probably familar with the proof for the irrationality of √2. Well, this is a more general version for all n integer roots of any prime.

Theorem

Proof

Euclid's first theorem states that for a, b ∈ Z and any prime p:

p|ab  →   p|a  or  p|b 

An immediate corollary of it is, for a, 1 ≤ n ∈ Z and any prime p:

p|aⁿ   →   p|a

Since

p|aⁿ = aa^n-1    →  p|a  or  p|a^n-1

but,

p|a^n-1 = aa^n-2   →   p|a  or  p|a^n-2

:

p|a^n-(n-2) = a² = aa   →   p|a  or  p|a

→  p|a  or  p|a  or  p|a  or... p|a  ( n times )   →   p|a

* * *

Now suppose for contradiction that

∃a,b,2≤n∈ Z, p∈P (p^1/n = a / b), where a nad b have no common factor.

p^1/n = a / b   →   p =  aⁿ / bⁿ 

→   pbⁿ =  aⁿ  →   p|aⁿ   by def. of divides, since bⁿ∈ Z

→  p|a by Corollary to Euclid's first theorem.

Hence a = pk ,  k∈ Z by def. of p|a.        (1)

But  p^1/n = a / b   →   a = p^1/nb = pk   →   pbⁿ = pⁿkⁿ 

→ bⁿ = p( p^n-2kⁿ )  →   p|bⁿ   by def. of divides, since p^n-2kⁿ∈ Z

→ p|b by Corollary to Euclid's first theorem.

Hence b = pm ,  m∈ Z by def. of p|b.     (2)

Statements (1) and (2) jointly contradict the statement that "a and b have no common factor".

Hence ∀a,b,2≤n∈ Z, p∈P (p^1/n ≠ a / b)  q.e.d.