Paradoxes: Be Logical, Yet Illogical

I was trying to daydream, but my mind kept wandering. ~Stephen Wright

I love paradoxes. They simply boggle the mind. Despite being built upon sound premises, they ultimately lead to senseless, illogical or self-contradictory conclusions. Here’s one of the best one I have come across.

Ever heard of Zeno of Elea, the bearded Greek guy? Well, it happened that he did not only come up with philosophies but is also accredited with creating several famous paradoxes. I’m sure you have heard of the race between the tortoise and the hare but try this: “The Paradox of the Tortoise and Achilles”. The former anecdote tells of how the hare lost the race due to his arrogance despite having the advantage against the tortoise. In Zeno’s version of the story, the race did not actually take place. But the tortoise did predict he will win the race. He argued with Achilles with seemingly logical reasoning till the simple-minded Achilles eventually believed him! The simplified version of the story goes thus. Judge for youself how ‘logical’ is the Tortoise.

It came to past that the Tortoise challenged Achilles to a race, claming that he would win as long as Achilles gave him a headstart. Being a mighty warrior swift of foot, Achilles was certain he would win.

“How far do you need?” asked Achilles.

“Ten metres.”

Upon hearing this reply, Achilles grew in confidence. Rolling on the floor and laughing away, he replied, “Be my guest then!”

The Tortoise, however, replied seriously. He claimed that he would win the race nevertheless and could prove it by a simple argument. He argued that no matter how fast Achilles could cover the initial ten metre between both of them, he should have covered a distance albeit a short one, say, one metre, during the interval. Now, Achilles would have to cover the one metre. No matter how fast he could go, the Tortoise would have gone a little farther away. Achilles would then have to cover that distance to catch up with the Tortoise. And while he was doing so, the Tortoise should have added another new distance between him and Achilles.

“So you see, everytime you are catching up the distance between us, I would keep moving so that you have to cover a new distance, however small it is, for you to catch up again. The process will go on ad infinitum and you shall never catch up with me!” the Tortoise elucidated.

And so, our mighty hero, Achilles conceded defeat.

While the argument given by the Tortoise seems sound, it does not sound to logic at all. The flaw in the logic, however cannot be easily pointed out for the logic of the situation seems impossibly assailable! The Tortoise would win the race! Yet, we know he woudn’t.

There are also several quotations by famous persons which make good examples of paradoxical statements and not without a touch of humour. American president, Abraham Lincoln wrote, “I’m sorry I wrote such a long letter. I did not have the time to write a short one.” Pablo Picasso, the famous Spanish artist and painter declared that he would like to be “a poor man with lots of money”; while Stephen Wright claimed to be having “amnesia and déjà vu at the same time”.

Believe me or not, it is possible to tell a lie without telling a lie! In philosophies, liar paradoxes are common. Consider this sentence: “This statement is false”. Or imagine someone appraoching you and tells, “I am lying.” Well, think it over… Are you still with me?

I also happened to stumble upon this mind-boggling brain teaser, which serves as an addendum to Zeno’s paradox. Take this paradox of Thompson’s Lamp away with you.

“Consider a lamp initially turned off. Let us imagine there is a being with supernatural powers who likes to play with the lamp as follows. First, he turns it on. At the end of one minute, he turns it off. At the end of half a minute, he turns it on again. At the end of a quarter of a aminute, he turns it off. In one eighth of a minute, he turns it on again. And so on, hitting the switch each time after waiting exactly one-half the time he wated before hiting it the last time.”

It can be easily deduced that all these infinitely many time intervals add up to exactly two minutes. The question is: At the end of two minutes, is the lamp on, or off?

Here the lamp started out being off. Would it have made any difference if it had started out being on?

So, welcome to the world of paradoxes! There are actually a lot of examples of paradoxes available. To include all of them here would be impossible! Maybe some other time!

The Scales of Libra

Diplomatic and urbane
Romantic and charming
Easygoing and sociable
Idealistic and peaceable”

“Indecisive and changeable
Gullible and easily influenced
Flirtatious and self-indulgence
~Traditional Libra traits

Reading the newspaper has ben my daily routine since young. The first thing I usually do when I get my hands on a newspaper isn’t flipping toe the sports section or reading celebrity gossips on the latest scandal. My top priority, however, is to get my daily dosage of horoscope.

No, no, no. I hardly qualify as a great follower of astrology. It is just the curious mind that drives me to find out what the stars have in store for me. Well, it does calm you to have foreknowledge of what looms ahead, doesn’t it? However 99% of the time, I am sceptical over astrological predictions. However, the astrological part that explains the personalites of different people under different zodiac signs is quite agreeable more than half ot the time. Here, I make my own interpretations of the signs (only Libra, actually, since I am proudly one) based on personal observations and what is said by astrologers. The stargazing part is, of course, skipped.

It is worth noticing that Libra is the only inanimate sign of the zodiac; all the others are represented either by humans or animals. Libra, being represented by the Scales of Justice, tends to be diplomatic and impartial in making decisions. The reason of choosing an inanimate object as Libra’s sign is perhaps the traits mentioned above are hardly possessed by mortals, for each and every living creature tends to place their concerns atop the others’.

I can’t agree more on the statement that Librans are often idealistic. Whatever they venture in, they will make sure the results are of perfect standard. Being perfectionists implies that they refuse to entrust hefty responsibilties to the others. They prefer to handle the job by themselves so as to attain the best results. I used to be a perfectionist but as I grow up, I came to learn that pursuing ideals is not so realistic after all. The idealistic part of me slowly fades… So as a Libran, I may be a perfectionist – just not a perfect one, though. (Get the punchline?)

Another part that I must agree is that Librans are very sociable beings. I am an erstwhile introvert but in these few years, I have slightly inclined to be an extrovert. I wonder if this have something to do with the position of the stars?

It is odd that astrologers classify Librans as romantic and sometimes flirtatious. Ruled by the planet Venus, Libra is know far and wide as the Zodiacal Lover. This really does perturb me as it is vaguely suggesting that Librans have the characteristics of a Casanova or a Don Juan to a certain extent. Heck, I don’t even have the chance of indulging myself in love! This is simply incredulous! Absurd!

Librans’ cast of mind is artistic rather than intellectual. To me, the reality seems to be the other way round. I am terrible in art compared to solving math and physics problems. I always find my right brain to be somehow devoid of artistic skills and imagination. The next thing closest to art which I can boast of is the skill of writing. Writing out the contents of your heart can really relieve the dishevelled soul of its burdens.

So, you can see that not everything astrologers say is true. At least iin my case. Perhaps, the scales of young Librans hasn’t much achieved equilibrium during the turbulent teenage years. After all, scales can tilt!

Anyway, it comforts me to know that Librans are charming. Even though I am yet to hear such a compliment from the people around me, it really gives a boost to my ego and morale! *Grin*
Last but not least, I remind you that all of the aforementioned are the conclusions made based on my personal obseravations. If you have a Libran friend or if you are one, do let me know if I am correct. As for the astrological predictions, I’m still working on them. You know, the sky today is cloudy and the crystal ball is murky. Some other time, perhaps. Some other time… *Wink*

In the meantime, I hope I won’t draw any flak from any astrology advocates out there for presenting my own version of the signs!


P/s: I initially planned to post this blog last night. Unfortunately, for some unknown reasons, my stomach was against the idea. It made me spend an hour in the toilet. And when I retired to bed, the upset tummy kept me awake. *Growl*

Confessions of a Teenager

It takes a minute to like someone, an hour to love someone, but to forget someone takes a lifetime. ~Unknown Author

Once in a while, when Venus, the ruling planet of Libra has its greatest influence, the sentimental side of a Libran will predominate. The epiphany came on one of those days, perchance. It began with a casual eye contact with her, which somehow liberated me from the ennui of the day. There was a gush of emotion so foreign, yet overwhelming, accompanied by an irrepressible onslaught of energy. The diagnosis, of course, was clear-cut: I had a crush.

Well, I have read about countless accounts of such a phenomenon in the youth column; it is something typical amongst hormone-charged teenagers; something I used to dismiss as nonsense. I told myself I have better things to do than to impetuously plunge into a game of puppy love. At least not now. Love can wait.

Just as I thought I was susceptible neither to Cupid’s arrows nor Aphrodite’s spells, Love crept up on me at the least expected moment. This girl whom had not drawn my attention suddenly became so attractive. Convivial and phlegmatic by nature, she has a great number of friends. Her looks may be modest but she exudes a certain je ne sais quoi which results in a lot of secret admirers gravitating towards her, with me recently joining their rank. Perhaps, it has to do with her opaque eyes which reflect unfeigned sincerity and are able to heal the wounded soul of any mortal man who set eyes upon them. In short, she is a paragon, if not, an earthly angel. She is the one, I told myself.

I tried approaching her, for starters; chatting with her to find out more about her interests, likes and dislikes. I was tongue-tied most of the time, thanks to the overwhelming level of adrenaline. Anyway, every moment spent with her is a moment of treasure. Hence, a perfect example of Einstein’s theory of relativity put in layman’s terms: when you are sitting beside a nice girl, and hour seems like a second; when you are sitting on a red-hot cinder, a second seems like an hour.

Unfortunately, Fate has the cruel habit of playing around with mortals’ feelings. The girl happens to be dating a boy with gusto, who turns out to be an acquaintance of mine. Should I make my confession and wreck their relationship? Heck, I did not even have the confidence of winning her heart. I may be pessimistic but there was obviously the possibility of me being rejected. After all, I’m no Prince Charming and by no chance the answer to the prayers of a maiden.

I realized there was no chance of kindling a relationship with me being so passive and unconfident. All the while, I am only sitting on a bench, observing her as her love story unfurls before me. I thought I would leap into the picture as soon as opportunity presents itself, but it turns out that the longer I waited, the thinner my chances get. At last, I decided to forget every little thing about her. However, this is easier said than done. For the first time in my eighteen years of life, my Libran analytical mind fails to weigh the situation and let her go so that I could continue with my life. Love that we cannot have is the one that lasts the longest, hurts the deepest and feels the strongest.

Love, as I found out, is a curious thing. Researchers have tried to poke into this primitive emotion, trying to understand the chemistry of love but found themselves no closer to an answer. Love is a miraculous feeling which may be initiated by simple actions: a casual eye contact, a gentle touch or a friendly conversation; Love is a magical feeling which stimulates the brain into producing feel-good hormones, thus placing lovers in a constant rapture; Love can also be a motivation and an impetus which drives mortals into achieving great things - or relieves them of a sound mind as they go gaga. To put it in Jules Renord’s famous words, “love is like an hour glass, with the heart filling up as the brain empties.”

Do I regret giving up? I lost the game but won in the other way. This epoch-making event has changed my philosophies on life. In my humble opinion, life is all about making choices. Upon reaching a fork in one’s path, dilemma ensues as to which one to tread. Robert Frost’s poem “The Road Not Taken” best sums up the doubts of a person making a difficult choice. By taking the path of my choice, I was denied the opportunity to discover the other possibility. I was proud to be able to make my decision; yet, I pined deep down. Life does have its crests and troughs which every mortal has to tread.

However, the hope of kindling a relationship with her still glows faintly within my heart. “Let providence decide,” I told myself. Let providence decide...

New Year Blues: On Friendship and Love

"We will open the book. Its pages are blank. We are going to put words on them ourselves. The book is called Opportunity and its first Chapter is New Year's Day." ~ Edith Lovejoy Pierce

It has been a week since Christmas and a mere hour left before the year draws to an end. There will not be much pomp and ceremony to usher in the new year as a mark of respect for the tens of thousands of victims killed in the most destructive tsunami recorded in the past forty years. No matter. I will spend the next hour alone in the room with one of my favourite songs playing in the background to keep me company.

I am a Libran who seriously believe that when the stars upon the heaven are arranged in a particular fashion, I get helplessly sentimental. This is at least the only explanation I can come up with for getting surges of nostalgia and depression especially during this time of the year. There is a subject close to my heart which I must put into words and bottled up feelings which I must confide.

As an erstwhile introvert, I used to cling to the belief that having friends is a luxury; one may live without any. This holds true provided that work or studies is the sole raison d’etre to one. Blame it on the genes if you want to, for we have been programmed since million years ago to live in communities. No man is an island unless he or she is willing to befriend loneliness.

It is sad but true that more often than not, we do not show enough concern for the friends around us, as was my case. Being able to see them everyday, I took them for granted. Because of my blinding ignorance, I failed to see that as time slips by, there will eventually come the day when we will be walking separate forks of the road, pursuing different dreams and aspirations; I failed to extend my appreciation to them for being a tower of support in dire hours.

Here, I wish to toast everyone a happy new year. May it pave the way for you to greater happiness and success. To my friends and ex-classmates: you guys and gals are a wonderful company. Thanks! To my intimate pals and confidants: “good friends are like stars… You don’t always see them, but you know they are always there.” Friends forever!

There is, however, something I have not mentioned to anyone – no, not even to my closest of friends – that is the aspect of love. I have always remained indifferent on the subject of whether it is advisable to kindle a relationship at this age. While it is healthy to do so provided that one knows where to draw the line, I am of a different opinion from those who impetuously plunge into puppy love.

However, never had I the notion that I would join the ranks of teenagers going gaga over a crush so soon. Heck! Blame it on the raging hormones! This is an example of the often ironical reality, considering that I used to believe that I am susceptible neither to Aphrodite’s spells nor Cupid’s arrows. Don’t get me wrong, though. I am not destitute of romantic love. After all, I am a Libran – whose romantic side is yet to be discovered by the special “one”!

Frankly speaking, I have been hit several times by the irrepressible onslaught of feeling so foreign, yet so overwhelming. Robert Frost said it right, “Love is an irresistible desire to be irresistibly desired.” Of this aspect, I do not wish to venture any further for I am not sure of my parents reaction over this matter should they find out about it! I would perhaps have to sit through mom’s long sermons while I shall never divine what is going around in dad’s mind, the man with little words.

Sigh, I have to wrap this topic up for now anyway. It is New Year’s Day! Embrace yourselves for a challenging year ahead!