Achilles And The Tortoise Paradox


It has been a while since I have gone off on a random tangent, so here we are. Today we are going to be learning about a very old paradox which was proposed by a fifteenth century BCE Greek philosopher named Zeno

The Paradox of Achilles and the Tortoise is one of a number of theoretical discussions of movement put forward by the Greek philosopher Zeno of Elea in the 5th century BC. It begins with the great hero Achilles challenging a tortoise to a footrace. To keep things fair, he agrees to give the tortoise a head start of, say, 500m. When the race begins, Achilles unsurprisingly starts running at a speed much faster than the tortoise, so that by the time he has reached the 500m mark, the tortoise has only walked 50m further than him. But by the time Achilles has reached the 550m mark, the tortoise has walked another 5m. And by the time he has reached the 555m mark, the tortoise has walked another 0.5m, then 0.25m, then 0.125m, and so on. This process continues again and again over an infinite series of smaller and smaller distances, with the tortoise always moving forwards while Achilles always plays catch up.

Logically, this seems to prove that Achilles can never overtake the tortoise—whenever he reaches somewhere the tortoise has been, he will always have some distance still left to go no matter how small it might be. Except, of course, we know intuitively that he can overtake the tortoise. The trick here is not to think of Zeno’s Achilles Paradox in terms of distances and races, but rather as an example of how any finite value can always be divided an infinite number of times, no matter how small its divisions might become.

If you would like to learn more about the Achilles and the tortoise paradox, then I would suggest watching this video or checking out this link. It will give you a good depth of understanding about how this paradox still impacts us today.

Dark Energy and Reflections Upon My Existence


Greetings, and welcome back to yet another lengthy blog post. I am currently typing this because I have managed to work myself into a funk about the endless winding road that is PLP reflections. Don’t get me wrong, undertaking this procedure is essential to the learning operation. Although 54 blog posts into my second high school year? That is approximately 30 blog posts in my eighth grade year, and seeing as there are 10 months of school that brings us to a sum total of three blog posts every month, which is equal to one every ten days. Sitting down in the same location, beginning with the same opening sentence and ending line has me yearning for a more purposeful reflection method.

I am currently procrastinating completing two different blog posts and all of the work that they entail. Seeing as this is the case, I have decided to do twenty minute of research on the modern knowledge of dark energy. I hope this pleases you folks. Enjoy my weapon of mass procrastination.

Dark Energy is a hypothetical form of energy that exerts a negative, repulsive pressure, behaving like the opposite of gravity. It has been hypothesised to account for the observational properties of distant type Ia supernovae, which show the universe going through an accelerated period of expansion. Like Dark Matter, Dark Energy is not directly observed, but rather inferred from observations of gravitational interactions between astronomical objects.

Proportion of matter in Universe

Schematic representation of the total mass-energy density in the universe.
Credit: Swinburne

Dark Energy makes up 72% of the total mass-energy density of the universe. The other dominant contributor is Dark Matter, and a small amount is due to atoms or baryonic matter.

In 1998 two teams of astronomers announced that distant, z~1 type Ia supernovae were slightly too faint than model predictions of an expanding (yet slowing) universe. To be fainter, the supernovae must be farther away and this requires that the expansion of the Universe was slower in the past. Both teams agreed that the universe is going through a phase of accelerated expansion. Dark Energy was invoked to drive this acceleration.

Ok I am still not in the mood to work, although a stress-free weekend is calling my name. If you happen to be one of the few people reading this before it is archived, then congratulations and welcome to the elite.

“Good morning, and in case I don’t see ya, good afternoon, good evening and goodnight” – The Truman Show

Reinventing The Magic of Star Wars

A bad Star Wars pun to start your day off

    If extravagant fictitious action movies were a system of rule, then the Star Wars franchise would be top dog. The newest addition to this scintillating ensemble is the masterpiece directed by JJ Abrams, ‘The Force Awakens’. Now, much like most Star Wars movies, two things are true about ‘The Force Awakens’: it is instantly engaging, yet at the same time conventional.

   If you’re the type of person who wants an intellectually stimulating movie that challenges your knowledge, then ‘The Force Awakens’ is not for you. On the contrary, if you happen to love movies full of action, classic quotes, laugh-out-loud moments and the occasional sprinkling of romance then this film is ideal. Perhaps no movie so far exemplifies the same carefully crafted nuances as this one.

  That said, while certain parodies may be more original than this movie, it is a must watch for dedicated Star Wars fans and newcomers alike. And therein lies the true magic of The Force Awakens and other movies of its ilk; both retro and post modern in their self-awareness. Throughout ‘The Force Awakens’ that radiates through in the energy of the music, and the engagement of the cast not to mention the iconically well done special effects. The Millennium Falcon scene is the perfect example.  Sand plumes into the air as gunshots are fired, but the partnership of authentic acting and light humour featuring laser noises and explosions will have you referencing the scene for weeks. This trend continues in every scene, combining the formulaic hero’s journey with modern effects to create a film that you will inevitably enjoying.

  Ultimately, I appreciate how Abrams has carefully crafted every aspect of this legacy, and the result is outstanding. The jury in charge of awarding Oscars had rightfully so put this movie on the nominee list, yet even though ‘The Force Awakens’ did not win an award, this movie has risen above all expectations to deliver a message that we all know and love, and make all of the past.

  Though the movie is very mimetic it’s predecessors, being part of a series does not mean that the movie is epigonic; it’s just the superlative equivalent of the Fast and the Furious. Sometimes, it is ok to set aside complex thrillers and indulge yourself in a repetitive series highlighting montages of propensity. You wouldn’t have gone to the theatre to see an avant-garde film. Similarly, sometimes you need to ignore the more ingenious side of the film industry, sit down with your popcorn and enjoy one hundred and thirty five minutes of laughter, lasers and Han Solo yelling “Punch it Chewy!”

Is society becoming too sensitive and over reactive?

Perhaps more than else, this generation distinguishes itself as the “ age of freedom “. Which, in retrospect is quite fitting. The first ever telepathic communication device has been confirmed, the LGBTQ2S community has made vigorous advancements, and being yourself is finally legal in many places. It’s hard to imagine, but not long ago schools for the developmentally challenged were officially named “Schools for Idiots” or “Schools for Imbeciles.” Today we scratch our heads, wondering how people could have been so insensitive.

   With all of the horrors faced by previous generations, perhaps it is understandable that “ self esteem “ was not a popular term.

   But press the button of millennials, or the unnamed generation “Z”, and you might just find yourself in some trouble. The smallest insult will send these people over the edge. Yet, something that I admire is this because of this, they are always the first to an issue. Take the Jefree Star incident for example.

   Back in June 2017, Jeffree posted a video entitled “Racism”. He made some very horrifying comments in this video, attacking race and gender. In the 15-minute apology video, Jeffree apologised for his racist comments. Yet this was not enough for those of today. He continues to get hate comments and death threats. In this case, people were genuinely offended. This was DEFINITELY not okay. He should have known better than to make such comments. But death threats? Seriously?

  You may also remember the recent incident regarding our favourite reality tv setting, the White House. Just a few weeks ago, Supreme Court nominee Brett Kavanaugh was accused of supposed inappropriate touching of a women, just days before he would have possibly claimed a spot in as Supreme Court ruler.

Though, luckily for us, a woman by the name of Christine Ford spoke up, and Kavanaugh was put to the test in court. This again, I believe was a good call on Fords part. Thid case was in Cavanaugh’s past, but what was there rest of the worlds reaction. What was yours?

   What about the times when the media has actually over-reacted? Most likely, you know, or at least have heard of the name Chevy Chase. A popular comedian in the 70s, most commonly known for his over the top, offensively offensive jokes. But now Chase is being punished for his over the top, (funny) jokes. By who, you may ask? No one else but our favourite little judges. Today’s society. Is this ok? No. Certainly not. The 70s was a totally different age, and any equivalent jokes made today would certainly not be passable, or even seen as funny. But should Chase really be punished for a relatively funny joke in the 70s, that may offend those today? Sure. Maybe sitting in his kitchen ignoring this feedback and having his family speak for him is not a passable answer. But this is about us, not him. To back him up, he is a comedian. This is his job.  He is being judged way too harshly. Because, as the old saying says, a comedian’s gotta do what a comedian’s gotta do.


  In this situation, what the mature person would do is they would let go of his jokes. I fully aware, even as a little known bystander that Chevy is aware of his horrid reputation. But is this going to change his reaction to the situation? No. I will fully admit that I myself am frustrated by his ignorance to these comments, and of course if we are considering maturity, than Chases reaction must come in to play. But rather than wallowing in this disaster, lets instead be the adults in the room and move on. There are bigger more important subjects which must attain our interest.

  This knowledge and aspect of life angered me. If I was to ask for the aid of my fellow human beings, then I would hope that the children of earth would join me, for it is our views and interests that can change this for the better. Of all the amazing feats that have been accomplished today, yesterday and tomorrow this is one thing that the “age of freedom“ has yet to learn. But our kids do have one thing to remember. We have the right to speak, and the world has the right to hear our voices. So before you close this link and agonize the world with your slightly unnecessary opinion, let me part with one question. Should the word really be living other people’s lives? “My life, my choices, my mistakes and my lessons” seven billion brains with a story to tell and seven billion brains who are willing to listen can change the world.