Math and Philosophy

This is actually from Semester 1 of Grade 10, but I read it again and I’m genuinely proud of it so I’m posting it here so it may be immortalized on the internet. 

The link between mathematics and philosophy was my entire inquiry project, so I apologize if you don’t read something incredibly profound about how math is actually grounded in unanswerable questions, just like philosophy. If you are looking for that, please see my inquiry project write-up. Instead, I’m going to go really in depth into specific mathematically philosophical questions.

Language is one of those human concepts that are simultaneously infuriating in its limits and exhilarating in its possibilities. I’ve often felt betrayed by the English language, as I search for a word that perfectly describes what I’m feeling, only to discover that it doesn’t exist. However, as a lover of literature, it’s difficult to stay angry for long. Humans are able to describe nearly everything in our visible universe, and we like to feel that we know everything there is that needs to be known, and then some. But that feeling doesn’t really matter to discoverers and inventors, so it inevitably always gets ignored. Us humans have the concept of infinity, defined as something with no ends and no limits. It just goes on and on and on (like me!), and it is impossible for humans to fully grasp this concept. We rely so heavily on physical representations of ideas, thus making complex concepts, like time travel and infinity, unimaginable to us. We can’t imagine something that doesn’t exist to us, and that is to be expected. So, why do we talk about the infinite so much, when it doesn’t even apply to us?

One perspective is the mathematical side. We use concepts like infinity in, say, graphing, because we logically know that there no boundaries to a function like x + 1 = y. We can represent this on a graph or in a table of values, but all the values of y are impossible to list, because they’re infinite. You can add one to any number an infinite number of times, and you will still get a possible y value. This concept also applies to fractions and negative integers, even irrational numbers. Pi plus one is just π + 1, shortened to 4.1415… Even irrational numbers, that we use so often in mathematics, go on infinitely! An irrational number is defined as a non-terminating, non-repeating decimal, therefore it goes on infinitely. We use these little infinities constantly: pi, phi, certain ratios and fractions. We also find these irrational numbers in nature – the Golden Ratio can be seen almost everywhere in nature, and is directly linked to the Fibonacci sequence. Therefore, this tells us that some form of infinity must exist outside of humans, that there are situations where never-ending and limitless concepts exist.

However, (there’re a lot of those in this little composition) we can also look at infinity philosophically. When we talk about something that never ends, we begin to erase the basic aspects of life itself – as morbid as it sounds, death and decay. If, for example, human beings were infinite, we would either never die or our bodies would never decompose. Either one. But then there’s the idea of souls, or some sort of aspect of humanity that is separate than the total sum of our parts. It is my belief that, if one were to completely clone a living person, give them the exact same memories and emotions as the original, you would still get someone completely different. This new person would not be the old one in all shapes and forms, but that missing aspect is unknown. I’m not sure if this missing aspect is infinite in its existence, but it’s definitely possible. We can also think about infinite time philosophically. Often, we ask ourselves if anything we do is worth it, if it’s all towards some purpose or if it’s even going to remain. Logically, we may know that whatever we make and everything we do will eventually disappear, but we don’t know when. Our brains are hardwired so that the idea of humanity perishing, of us just ceasing to exist, terrifies us. There’s the survival instinct, of not wanting to die, but we also don’t like the idea of putting all this work, effort, and time into the things we’re proud of, and thinking that they will have been for nought. I know I don’t like thinking about it.

Our brains tell us that time isn’t infinite, but science tells us that the universe itself might be. According to multiple theories, proposed by those much more educated than I, there are an infinite number of possibilities in an infinite number of dimensions in an infinite universe. This is described as the multiverse theory, and it gives a certain amount of hope that things are better somewhere in our supposedly infinite universe. Although, this also means that things are worse, but good and bad are all relative and depend on our definitions, so it’s inevitably a language issue, which I touched on earlier, and this whole mind-screwing idea is a topic for another composition. Anyway, according to this theory, literally anything is possible, and that sounds like something you’d see on a poster with a sunset in the background, but it’s also a mathematical goldmine. In inequalities that state x ≥ y, x can be equal to or larger than y, meaning x can be equal to almost anything other than y. However, if y is equal to negative infinity (-∞) x can be anything, including negative infinity. Because infinity (even negative infinity) is, you know, infinite.

Some infinities are larger than other infinities, but that’s per our current definition of infinity. This definition might change with more concepts introduced over time or more “mathematical evidence”, but it always just comes down to language and how we interpret it. When I think of the word “infinity”, I think of the multiverse theory. Other people might think of infinite time, of wormholes, of graphs. The thoughts that come into our minds when we think of infinity are, dare I say it, endless. Does this imply our own thoughts, the little electric shocks zooming through our brains at thousands of miles per hour, are infinite? Who knows? Why do we even care? If they are infinite, why? Why wouldn’t they be? I can come up with multiple answers to each of those questions, but none of them are definitive, which is really cool. This implies that even our most logical field, mathematics, isn’t definitive. It implies that current science isn’t definitive, and it’s all just theory, when you really think about it. Philosophy as we know it has managed to worm its way into every aspect of logic with its unanswerable questions, almost always beginning with “why”. Maybe this explains why we use “y” as a variable. Maybe it doesn’t, but that’s okay. (If the multiverse theory is to be believed, then there is a Sara who knows why, or has at least convinced herself that she does.)

I think what I took away most from these philosophical discussions in math class was accepting that sometimes there isn’t an answer, that math isn’t necessarily the say-all, do-all. It’s mostly about discussion and exploring all these ideas. Maybe it’s naïve of me to think about, but how much could we do if we acknowledged that not everything is clean-cut with a simple answer and a picture? If we did things out of pure curiosity (as I do most of the time), and because we think there might be a positive outcome? Is there any better way of doing things?

TechTeamEdublog

  1. What Widgets and Plugins did you choose?
    1. Calendar+
    2. Footnotes
    3. Image Widget
  2. What are their strengths?
    1. Online platform to keep track of school events, tests, homework assignments, etc.
    2. Great for students to keep track of their sources and where information in their work is taken from, or for those like me who tend to put little comments in their work and don’t like using brackets.
    3. Offers opportunity for additional customization to blog (which I needed more of). Very user friendly and can add multiple additional images
  3. What are their weaknesses?
    1. No way to sync it with normal Calendar widget to make upcoming school events, tests, etc. public to those who view the blog. Widget is mostly for personal use.
    2. In the published version of a post with footnotes, there’s a less-than-aesthetically-pleasing blue symbol at the end of each footnote.
    3. No opportunity to preview how image looks on site, or add additional content without the presence of an image.
  4. Can these programs be used in a classroom setting to enhance student learning? Would you use it and/or recommend it?
    1. It’s good for students who would like an easy-to-use online platform to keep track of all their upcoming events and due dates. I wouldn’t personally use it because I use my phone calendar to keep track of these things, but to each their own.
    2. It’s an excellent tool for sourcing work (helps students keep track of what they used their sources for, etc.). Would definitely recommend.
    3. I would recommend it to students who want to add a bit more flair to their blog, especially those interested in photography/art and would like to show their work on their homepage.

Math 11 Sequences and Series Blog Post

 

Arithmetic
General Term: t_{n} = a + (n-1)d
To figure out the value of any given term (t_{n}), a (the first term), d (the common difference), or n (the term in which a certain value appears).
Sum of Terms: s_{n} = [(a+t_{n})n]\div2
To figure out the sum of any given arithmetic series (S_{n}), n (the last term), or a (the first term).

Geometric
General Term: t_{n} = ar^{n-1}
To figure out any given term (t_{n}), a (the first term), r (the common ratio), or n (the term in which a certain value appears).
Sum of Terms: S_{n} = [a(r^n-1)]\div (r-1)
To figure out the partial sum of any geometric series if not given the last term, the last term, the first term, or the common ratio OR
S_{n} = (rt_{n} - a)\div (r-1)
to do the same thing, but if given the last term of the series.

You can have two types of geometric series: convergent (terms come closer together) or divergent (terms become further apart).
When you have a convergent series, the common ratio is greater than -1 but smaller than 1 (and cannot equal zero). Convergent series have infinite sums (the number in which the sum of all the terms converge at), which can be calculated with the formula S_{\infty} = a\div (1-r).
Divergent series don’t have infinite sums.

Langston Hughes, Poetic Genius

I think Langston Hughes wrote about the African-American experience of the early 20th century best because his poem, “The Negro Speaks of Rivers”, is directly emotional. It is a poem that is meant to be quickly understood, and the feelings within it comprehended by those who share the same struggle. Hughes wrote the poem in simpler language so his purpose isn’t lost in complicated vocabulary and allusion. In a few short lines, Hughes uses broad allusions and emotional phrases to emphasize a point. He conveys the emotions of his ancestors and the weight he feels from his own history, making “The Negro Speaks of Rivers” an incredibly powerful poem.

Photo 

When Men Find Comfort in the Land of Mice

When Men Find Comfort in the Land of Mice

The novella Of Mice and Men would be a fast-paced tragedy, arrival of the main characters quickly giving way to darkness, if it weren’t for how author John Steinbeck inserts long paragraphs with vivid descriptions of nature. This describing of forests, swamps, and animals tend to be the only peaceful points in the story, with every setting outside of nature plagued by distress and worry.

Steinbeck uses this method, of writing his story so that nature is almost synonymous with calm, incredibly well and, frequently, not so explicitly. One of the first scenes of the story features the two main characters, George and Lennie, lounging next to a pond as the day winds down. George begins to talk about a farm that he and Lennie will one day have, with “a big vegetable patch and a rabbit hutch and chickens,” (p.14). This dream is a recurring element of the story, with George detailing it multiple times throughout the novella and Lennie speaking about how he will get to tend the rabbits.

For Lennie, the farm is an opportunity for him to pet soft things whenever he pleases, but for George, it is something to look forward to. Typically quite angry, George calms down when he thinks of his farm (“[George’s] voice was growing warmer. ‘An’ we could have a few pigs. I could build a smoke house the one gran’pa had…’” p.57). After Candy’s dog is brought out to be shot, George eventually begins to talk about the farm, with Candy himself catching on to the idea: “We’ll fix up that little old place an’ we’ll go live there.’ […] They all sat still, all bemused by the beauty of the thing, each mind was popped into the future when this lovely thing should come about,” (p.60).

Aside from the farm, however, the nature in the character’s current environment of Soledad is a more physical source of refuge. After Lennie kills Curley’s wife, he runs to the spring where he and George first arrived. He kneels down and drinks the water, and Steinbeck sets the scene acutely differently to the chaos of the barn: “When a little bird skittered over the dry leaves behind him, his head jerked up and he strained toward the sound with eyes and ears until he saw the bird, and then he dropped his head and drank again.” (p.100)

But why did Steinbeck create an environment where the characters’ only salvation from their struggles is nature? It’s possible he was attempting to answer the question of what is man’s connection with nature. In Of Mice and Men, Steinbeck relates nature to a life without struggle, an outlet for serenity. Perhaps, nature is a way for man to detach himself from a life of hard-work with nothing to yield. Perhaps Steinbeck thought that the forests and ravines are places to go when in need of a refresh, a way to return to our roots. Regardless, it’s clear that the author instills a sense of importance to man’s unique connection with nature; despite consistently being deprived of it, nature is almost always a way for us to find salvation from the hardships of human existence.

 

Photo courtesy of: mtran on serendip studios. 

Narrative Essay: “The Eye of the Storm”

Things I Did Well:

  • Description/Visual

I’m quite proud of how I described the event and that I was successful in helping the reader visualize it. I used to have a lot of trouble in providing good descriptions and showing vs telling, so I’m very happy that I apparently did it quite well in my narrative essay.

  • Voice

As someone who has done quite a bit of writing in the past, I know how hard it is to maintain your own voice in your writing, especially doing an essay. There sort of has to be a sense of formality, and it’s really easy to dissolve into long words you never typically use and start to tell the story from a perspective that isn’t your own. I think I managed to maintain my point of view during the essay and tell the story the way I saw it happen and how I felt about it at the time (and how I still feel about it), while still keeping it from becoming conversational.

Things I Can Improve:

  • Purpose

I understand my purpose of writing the essay might have been a bit vague – I’ve always had trouble in conveying the message of the story. I don’t want to explicitly state it, but I should probably try to hint at it a bit more. When we verbally tell stories, we don’t really focus on the meaning or lesson we learned from the experience, but instead focus on telling it in the most interesting way possible. I’m also a bit more used to journalism articles and humorous writing now, so it was difficult to put myself in the mindset of “I’m writing something important”.

  • Conciseness

The first draft of this was probably about 1000 words. I cut down a lot, but I realize in trying to describe a lot of stuff, I lose the point of the story. I’ve definitely become a lot better with being concise and effective in my writing over the years (“cutting the dead wood” as you say), but there is absolutely still work to be done!

 

BONUS:

What the classroom looked like when we left (all necessary layers of brick for walls, floor completed, inside walls covered. What rests is the roof and indoor decor.)

 

What the classroom looks like now – second from left. (Currently in use for children between grades 1 – 8.)


Images courtesy of @tylerknott and banksy and me and @metowe 

TechTeamO365

  1. What do you think of Office 365?
    1. I think it’s a great tool for those who need to know how to use a variety of computer programs. It’s comprehensive and easy to navigate while still permitting the user to accomplish complicated tasks.
    2. Office 365 makes it very easy to access files from multiple devices and share information with a variety of people. It’s best suited to a school/work environment.
  2. Why do you think that?
    1. The homepage has automatic access to many Microsoft programs and makes it easy to download the applications to your desktop. Also, upon entering a program for the first time, it gives you basic rundowns on how the program works and cool features you have access to. There is also always access to a help centre if needed.
    2. I rely very heavily on OneDrive for a lot of my school work – I can save something on my computer and open it on a school computer within a minute. However, I’m not sure how useful this is in a purely home/personal environment.
  3. What are the strengths of this program?
    1. Easy to navigate/maneuver
    2. Large variety of capabilities to accomplish an even larger variety of tasks
    3. I just have a high opinion of Microsoft/Windows programs. I think their strength lies in their compatibility with any device and other programs, and making it very easy to share files and information across many platforms.
      1. I wonder if Microsoft is going to follow Amazon’s example and open-source Cortana. That would be cool.
    4. What are the weaknesses of this program?
      1. There are quite a few redundant programs
        1. Sure, Sway is kind of fancy but it’s complicated and at times, confusing to use. PowerPoint is perfectly capable of accomplishing what Sway can, and people actually know how to use PPT!
      2. There are some glitches, like with all programs. OneDrive Online will occasionally not sync with the OneDrive downloaded program, OneNote will need log-in on numerous occasions.
    5. How can this program be used in a classroom setting to enhance student learning?
      1. Besides the obvious – Word is great, PowerPoint makes presentations not cringeworthy, Excel is my actual life saver – Office365 has a lot of potential to be incredibly capable of being fully integrated into student learning.
      2. I’ve said it before and I’ll say it again: OneDrive is I have the app on my phone, and it’s so much more convenient than sending myself documents and audio files. It cuts presentation-making and group-project time in half.
      3. I’ve also used OneNote frequently in class, and while it’s little difficult to get the whole class up and running, it proves very effective in getting documents out to the whole class, doing group projects, and taking notes.
    6. What suggestions do you have to improve the program?
      1. Overall, I like the program. I think minimizing the number of programs available on a student account would make everything a little bit less confusing, or making it easier to mold elements from each program.
      2. Currently, it’s difficult to transfer formatting from Word to Powerpoint and vice versa. I’m not sure if this a problem with any other programs (I know Sway isn’t very versatile when it comes to their formatting) but providing more ease of access between the two most popular programs would be beneficial.
      3. Also, what is up with Sway? It would be a much better program if it was possible to change the layout of the templates, resize things, and combine different types of media seamlessly. But that’s a whole different essay.
    7. Do you have any questions about the program?
      1. What’s the difference between a student account and a teacher account? I know the permissions are different, but are the programs changed?
        1. If so, this could potentially be the source of a lot of confusion between the teacher and the class when it comes to the online programs.
        2. That, or Wi-Fi.
      2. Are there any voice-automated/artificial intelligence assistant systems accessible with Office365?
        1. If so, how?
        2. If not, are there plans for this? Cortana is great.

 

What motivates us to do incredible things?

“[…]the only people for me are the mad ones, the ones who are mad to live, mad to talk, mad to be saved, desirous of everything at the same time, the ones who never yawn or say a commonplace thing, but burn, burn, burn like fabulous yellow roman candles exploding like spiders across the stars and in the middle you see the blue centerlight pop and everybody goes “Awww!” – Jack Kerouac, On the Road.

 

The above passage is from one of my favourite books of all time. The book itself deals with a lot of complex stuff: youth (especially when it’s fleeting), human relationships, self-discovery, morality. But this passage really gets to me, and it always has.

There isn’t really a context for it. He’s talking about how he got into the whole mess of travelling America with Dean Moriarty, and while it’s from the point of view of the fictional Sal Paradise, it really is based on Kerouac’s own experiences with Neal Cassady, so it’s a valid hypothesis that these are his real sentiments. He writes about how he’s attracted to those wild people nearly everyone knows, the ones that are adventurous and always have a story to tell. He’s attracted to people that are interesting, yet he acknowledges that they aren’t always the most stable, likening them to exploding roman candles. In the book, Sal Paradise talks about how complexly flawed and wonderful Dean Moriarty is, and he wishes he could be part of that special brand of madness. And I think that’s what a lot of people crave.

We read books and watch movies and create fiction because it depicts people who are fascinating enough to have other people care about what they have to say. And deep down, I think we all sometimes want to be that sort of person. When we’re in the presence of such remarkable stories, such adventurous souls, we may begin to wish for that uniqueness, and that’s OK. It’s normal to want to settle down and live comfortably, but all too often, the greatest experiences in life aren’t ones that make us money – they’re the ones we sought out with madness and liveliness in our hearts. Humans want to be remembered, in a way that is so crippling because our fear of oblivion is so strong. We know we will die, and maybe it drives us to do incredible things and along the way, we become incredible people.

LAVA BOMBS (and associated products)

If you’re like me, the picture above is reminiscent of someone stabbing someone else in the neck with pen in a Quentin Tarantino movie. It’s a fair comparison: incredibly bright red liquid spurts out of a hole, sending streams of said bright red liquid up, only to sail back down. However, this particular brand of, for lack of a better word, spurting, isn’t the result of purposefully comedic SFX.

Classified as a Strombolian eruption, the upwards lava explosions are caused by large gas bubbles bursting, which travel up until they reach a vent. The spurting (oh god I hate this word) effect is further emphasized by the results (also known as tephras): solid bits of lava (splatter), solid bits of bubbly lava (scoria), lava bombs (which are just as cool and badass as they sound), and whole chunks of solidified lava. 

To make them even cooler, Strombolian eruptions are named for the Italian island Stromboli, which has a lot of volcanoes that produce this particular kind of eruption.

And you thought volcanoes couldn’t get any better.

 

Photo courtesy of: 

volcanoes4. Volcanoes. 28 September 2014. 18 January 2017. <https://volcanoes4.wikispaces.com/Volcanoes>.

Info courtesy of:

Ball, Jessica. Types of Volcanic Eruptions. n.d. 18 January 2017. <http://geology.com/volcanoes/types-of-volcanic-eruptions/>.