The Infinite Regress

I’ve been thinking a lot lately about two specific things.  One is the statement “Everything happens for a reason,” and the other is the concept of fate – which I will define as a predetermined eventuality (which is, perhaps, not the most philosophically exhausted definition of fate, but it will do fine for this entry).  I usually tend to err on the side of optimism when it comes to the way the world works.  Though some of you who know me on a more personal level might describe me as pessimistic on a day-to-day basis, my view of the world in general, you have to admit, is slightly more upbeat.  That being said, I have always thought that everything happens for a reason – perhaps influenced by my christian upbringing and taught that God has a plan for everything.  And though the past few years have been probably the hardest of my life, I’ve always tried to convince myself that the events which took place happened for reasons unknown to me, but reasons none the less.

But what of fate?  I asked myself today “do you believe in fate,” and found to my surprise that the answer wasn’t “yes,” but also not “no”.  Let’s think about this…

Fate is, by my definition, a predetermined eventuality, meaning that no matter what one does with his life, eventually it will be in the place where this predetermined eventuality determines it to be.  When I say it like that, of course I don’t believe in that.  I’ve always subscribed to the notion that we, as human beings, have a freedom of will and a choice as to what to do with our lives.  Part of me wishes that fate does exist, because then I don’t have to worry about what to do so much, I’ll be where I’m going to be regardless of my choices.  In other words, if fate exists, all roads lead to X, where X is the place fate has predetermined you to be.  Pfft.  Yeah right.

But wait a minute… Let’s assume for a moment that I still believe that everything happens for a reason (a phrase I find myself losing faith in as of late) – does that statement presuppose the existence of fate?  I guess we would have to dissect the statement “everything happens for a reason”…  I don’t think the statement is talking about reasons like “you burned your hand on the stove because the stove was hot”.  I think we can agree that reasons is being used here in it’s profound and life-explanative sense (if that’s not a word then I just made it one).  But if that’s the case…isn’t that fate?  I’m not sure I’ve fully grasped these concepts yet, but my lunch break is over and I need to plan some lessons….or maybe I won’t plan them and in the long run it won’t matter because I’ll be in the same place if I had planned them..

A friend of mine recently prompted me to unearth the total secrecy that is my favorite number.  When I casually explained to him that there was no way for me, a graduate of mathematics, to pick just one of the many awesome numbers that exists, he told me to simply list some of them anyway.  As I began to list and explain my favorite numbers, he then said I should write a blog post about the many numbers that I like along with the reasons I like them.

So here we go.  Let’s do this – I’m psyched!  But before I begin I would like to say that there are some numbers I like for no particular reason at all other than I think they are cool… Now without further ado I present to you

#’s I <3

0 (zero) – zero is the identity of the real numbers under addition, which is to say for all x in the reals, x + 0 = x.  Zero reminds me of a number that yields to no other number in as far as multiplication. Sure he’s like a pushover when dealing with the operation of addition, but multiplication is like HIS place, you know?   Since the product of any number and zero is always zero I feel like zero secretly has a “pffft, you can’t mess with me, I’m ZERO” mentality.  Zero is also neither positive nor negative,  (0,0) marks the origin  (where the x and y axes intersect) , (o,o,o) marks the origin of a three dimensional Cartesian coordinate system (where the x, y, and z axes are coincident).  I often wonder if we graphed the universe on a three dimensional coordinate system what location would be considered the origin of the universe…where is (0,0,0) in our universe?  Speaking of the universe, it is rumored that if one successfully divides by zero that the universe explodes.

1 (one) – I like the number one because it is the unity of the commutative ring of real numbers under ordinary addition and multiplication, which means that it is simply the identity of the real numbers under multiplication.  Monists like Parmenides and Zeno believed that the only true being is “The One”, and that everything else we perceive is susceptible to corruption and deceit.  And this fact sparks a plethora of worth having philosophical debates.  There are also many properties in mathematics that produce the number one, such as:

.999… (.999 repeating) – since I like 1, I consequently also like .999… since .999… = 1.  The proof of this is as follows:

we know 1/3 = .333…

we also know that 1/3+1/3+1/3 = 1

therefore .333… + .333… + .333… = 1 by substitution

therefore .999… = 1 b/c .333.. + .333… + .333… = .999… by addition.

2 (two) – I love the number 2.  It is simultaneously the first positive even number and the first prime number.  Incidentally, it is the ONLY even prime number since every even number after 2 is divisible by 2!  In fact, the number 2 is part of the definition equations for even and odd numbers: 2n and 2n+1 respectively (where n is any integer).  very cool.  I’ve also heard that it takes two to tango, but I have yet to see a proof for this claim.

√2 (square root 2) - √2 is one of two irrational numbers that I like, the other being pi.  When I was in ring theory I did a project involving Z[√2]….or maybe it was Q[√2]…I don’t remember.  What do remember is becoming strangely attached the the number √2.  Another cool thing about √2 is that the diagonal of a 1×1 square is √2 using the Pythagorean theorem.

i (square root -1; the imaginary number) – all throughout elementary school and part of middle school I believe that taking the square root of a negative number was simply impossible…and then one day my teacher was like “okay so the square root of negative 1 is i,” and I was like “wait what…?”  And all of a sudden there was like this whole other realm of mathematics!  I like i because it is imaginary in an already abstract world.  If you think about it, our imagination produces objects or things/events outside of reality – they are abstract.  So when you are talking about mathematics (which is an abstract entity by nature) and you then talk about imaginary numbers, it’s like an abstraction in an abstraction.  i is also the main contributor to the construction of the complex numbers, which are of the form a + bi, where a and b are real numbers.

3 (three) - The number 3 is awesome because any three points define a plane (or said differently: any 3 points are coplanar).  It is also the number of vertices our first regular n-gon has, called an equilateral triangle.  I love the triangle.  You can make so many things out of the triangle (more on this below) – it’s awesome.  Also, “Three is a magic number.”

4 (four) – There are a lot of reasons I like the number 4, but probably the main reason is because of the tetrahedron.  The tetrahedron is the first of 5 platonic solids, but here’s the crazy part: it’s constructed using four equilateral triangles!  The number 3 when added 4 times produces a three dimensional object with 4 vertices!  Who would have ever thought!  In case you don’t know what a tetrahedron is, imagine folding the triforce up so that the empty middle triangle of the triforce is now the base of the tetrahedron and the 3 gold pieces are the “sides” which all meet at one point at the “top”….did that even help?  whatever.  The tetrahedron is my favorite platonic solid.

π (pi) – π is the second of my two favorite irrational numbers.  You can find π if you are given the radius and circumference of ANY circle by dividing the circumference by two times the radius (which is just the diameter of the circle).  There are people who can recite an insane amount of digits of pi, and I am certainly not one of them.

7 (seven) – seven is awesome because Final Fantasy VII will forever be the greatest installment in the Final Fantasy series.

24 (twenty four) and 27 (twenty seven) – there is no particular reason that I like these numbers…i just do.

1111 (one thousand, one hundred and eleven) - I like this number because 11:11 am and pm are the only times of the day that all four digits on a digital clock are the same.  It’s make a wish time!

25 (twenty five) – I like twenty five because it is a perfect square, and it was my graduation seat number when I graduated with my  masters degree =)

1.67 (one point six seven) – i don’t know why…but in high school this was the answer to like 65% of math problems

There are many more numbers that I like, and perhaps I can write about them another time.  But for now I hope you enjoyed reading about a select few of my favorite numbers!

Also, there is this one book that I don’t know the name of…nor do I know who wrote it…but it’s a book of a TON of numbers and why they are interesting.  It’s definitely worth trying to find.  If you find it let me know, because I’ve been looking for it with little success.

also http://en.wikipedia.org/wiki/Interesting_number_paradox just for funzies.

-mock

Hey readers, i just got back from a 4 day Christmas trip to Bend, OR to visit my fiancée and her family.  There was lots of snow, which made it pretty awesome.  The only downside to the trip was that i still felt like s$%* the whole time…damn you, UC.

Anyway we were out one day just walkin’ around in downtown bend when Steph decided to stop by some girly-girl shop to see if they still had some $300 wooden beatles poster which read “All you need is love, love is all you need” – quite possibly the most redundant lyric ever, but whatever tickles your fancy i suppose.  Once inside she immediately started gazing upon the last remaining poster, which gave me time to look around the cute shop.  I was reading some funny magnets defining sex (seks) in a humorous way when i stumbled upon a small piece of wood hanging on the wall which read:

“The most important things in life are not things.”

Now, overly redundant beatles posters are one issue, but this particular signage was on a whole other level.  It doesn’t make any sense – plain and simple.  This really bothered me, throughout the whole day actually, and even clear through the next.  It bothered me so much that i had to dedicate a blog post to its nonsensical shenanigans and explain how it doesn’t make sense on any level of cognitive thought.  First, let’s try to define a ‘thing’.  For now, let’s say that a ‘thing’ is some sort of existing object (and don’t worry if you don’t like this definition – you’ll see why soon).  I will now write the quote substituting our tentative definition in for the word “things”:

The most important existing objects in life are not  existing objects.

Okay so that doesn’t help.  Let’s change the definition of a ‘thing’ to be “something abstract”; be it a thought, a plan of action, an event, whatever.  Something that is not comprised of matter – that is what we will take to be our new definition.  Again, i will rewrite the sentence using this new definition:

The most important abstract entities in life are not abstract entities.

By now you should see where i’m going with this; I could repeat this same process for any definition given by google (here) and get the same sort of nonsensical sentence.  In other words, it doesn’t matter what the definition of “thing” is, this sentence will never make sense.  Ultimately, “thing” is a set which contains a seemingly infinite number of elements; in mathematical terms:

Thing = T:={x|x is a thing}, and we’ll also define a subset of T, let’s call it M, where M = Most important things:={x|x is in T and x is dubbed important}

So essentially the sentence reads “The most important elements of set T are not elements of set T” or perhaps more precisely “for any x in T, x is not in M” which is just outright false by the definition of M itself.  Actually the only way the previous statement would be true is if M was the empty set, but who would agree that there are no important things in life?

The only way i can look at this sentence and see it’s truth is if the definition of thing is different in both listings of the word; and by this i mean i read it like “the most important things (the general definition which encompasses every possible definition of the word thing) in life are not things (material possessions)”.  But i feel, as a mathematics graduate, that that angle of perception (if intended to be viewed that way) is not at all implied.

My point is this: the sentence is way to vague, and provably false; therefore it should not be an item for sale.  I will pay for statements that make sense, but people should not hang logically false statements on their walls unless they are free.

\end{rant}.

Sorry it took so long to get this started!!  It took me a while to figure out how to get everything i needed for WinEdit and LaTeX to work on my personal computer as opposed to the remote desktop linked to my old college provided desktop…if that makes any sense.  Either way, i’ve got it up and running!

special thanks to: Scott Kouchi.

Unemployed? Tired of being ridiculously bored around the house, pacing from one room to the next? Constantly checking your facebook page to see if anyone has updated his/her status in the last 4 seconds since you last checked? Sleeping because there is nothing else to do? Finding joy out of counting the number of little bumps on your ceiling? Male? Female? If you answered yes to any of the questions preceding this sentence, then I have just the answer for you!!! Study!!!

For the past few months I have literally done very little in as far as self improvement. Granted, I can check off a couple more Anime on my “to watch” list, and i’m a pretty good shot with an m16 on Call of Duty: Black Ops, but when it comes things which improve my cognitive and or physical (insofar as conditioning) capabilities, I have basically done nothing. It was a few weeks ago when I really began to notice that I have, as a result of doing nothing productive (aside from looking for jobs), become somewhat disconnected from my previously owned academia – if that is even a word…I will assume it’s not and define it: I will henceforth refer to academia as a state in which one is dedicated to learning academic knowledge. Does that make any sense….? Whatever.

My point is, after having done nothing but go to school for 17+ years, doing nothing for 4 months makes me feel like I’m slowly forgetting more and more of my education by not using any of it. So a buddy of mine agreed to do an hour of study time with me at a local library. It was awesome. Aside from the fact that I realized I had forgotten almost everything when I was re-reading chapter 0 (no that’s not a typo) in my Abstract Algebra Book, it really felt good to sit down and try to learn (or in my case re-learn) some content!

I’m sure there is something that you, the reader, have wanted to teach yourself but just can’t find the time for. If you are the everyday working person, then I know that there are like a million things that you have to do during the day and the last thing you want to do when you get a break is exhaust more time and effort into learning something new – something which takes concentration! My solution: make a designated time for it. It can’t be impromptu like my sophomore year speech on Rocky Balboa…or this blog entry; it has to be planned out because let’s face it: you’re not in school anymore, nothing is forcing you to study – unless of course you are in school, but then why would you be reading this!!?? Go study for your test tomorrow for the love of God!!!! As for the rest of you, if there is something that you want to teach yourself/learn, then I have found that it is easier when you plan a time for it.

If, however, you are like me and have nothing going on, there really is no excuse for not doing the things you wish you could do/learn – is what I would say if I wanted to be a ginormous hypocrite. Finding motivation has been a huge hurdle for me, and it took two of us (my friend and I) to dig ourselves out of this motivationless slump. Ultimately the guilt of not remembering how to prove if a specifically given relation is an equivalence relation on some set S got me to open my old college books…well it was that and the fact that my own mathematics senior project looks like a foreign language that got me to open them (don’t tell my old professors…I’m ashamed).

I guess the moral of today’s post is this: if you have something that you have wanted to do, make time and do it. The last thing you want to have happen to you is looking back on your life and saying “man I wish I had made time to learn how to x”, where x is an element of the set which contains all things you have wanted or will want to do. Yeah…re-reading this post I have no idea how one could have derived that moral from the above paragraphs had I not just explicitly stated it…but there ya go.

Happy Monday.

[mock]

by the way べんきょう means “study” in Japanese. You learned something new today. Unless you already knew that…in which case my favorite color changes constantly, but it is definitely NOT anything neon. There, now you have definitely learned something new today.

that took forever…

I am writing this post to cleanse my mind. In its current state there is a whirlwind of thoughts, each of which extend their reach to the depths of my mind reserved for calming purposes – the part that allows me to rest and sleep. Thus, I feel that writing out some of my thoughts would be an appropriate response to combat the chaos.

Those of you who know me know that these past four months have brought about dramatic change in my life; in my every day life even. For those who don’t know what I’m talking about I’ll spare you the story for now, but it’s safe to assume that the events have left me somewhat lost – and I use the word ‘lost’ here with its profound and existential (almost spiritual) sense in mind. I’ve been thinking a lot about fairness and how it does or does not exist in life. When you think about fairness, what comes to mind? For me I always think of a little boy who when his parents give his sister some 50 dollar birthday present, and then get him a 20 dollar birthday present exclaims “that’s not fair, you spent more money on her,” or something like that. So I have to ask myself, how is the word ‘fair’ being used in this example? There is a comparison which is taking place, i.e. the 50 dollar gift versus the 20 dollar gift – so does that mean when anyone uses the word ‘fair’ they are comparing one thing to another? I guess what i’m trying to say is that in this example, what would be considered “fair” is if the parents spent an equal amount of money on their offspring. Therefore, the word “fair” here is being used as term for “balance” or “equality”.

But i’m not convinced that this is the true meaning of fairness. To me, fairness needs to have in its definition something about equal opportunity. For example, it would be fair for an employer to abandon bias opinions of applicants based on their physical characteristics and instead decide who to hire based on who is intellectually more qualified. It would be fair if presidential candidates talked only about their own beliefs instead of slandering the beliefs and past doings of other candidates. It would be fair if runners with asthma were allowed a head start in races to level the competition. This is the kind of equal opportunity I am talking about when I think about fairness. But of course, none of these things happen in society – we’ve all heard it said that “life is not fair”. Take finding a job as an example; it’s mostly done through networking, your degree means nothing if you don’t know the right people. Or look at models, if you are not attractive there is a slim chance you will become a model. Equal opportunity rarely exists in society – but isn’t that what our society is trying to create? All throughout school I was taught that everyone deserves equal rights and equal opportunities – but these things are unachievable on a fundamental level (at least the equal opportunity part is – I don’t want to get into an equal rights debate). Human beings are all born differently – each and every one of us is unique. Some people are born into a house of poverty and disease, while others are born into wealth and good looks. Fairness (using the definition of equal opportunity) fails to exist at the beginning of life. It would be outrageous to say that a woman born with one leg has equal opportunity in life to become an Olympic athlete as one who is born with both her legs.

I guess I’m still confused about when one is accurately able to use the word ‘fair’ as I have defined it. If we take it to mean equal opportunity, is the word fair only used to describe situations in which equal opportunity applies? Let me see if I can even come up with one of these situations. Hmmmm….. Ok how about this: Rock, Paper, Scissors. In this game, each player has an equal opportunity of winning. It is a fair game – each player can make the same three choices. It would be unfair if one player was allowed a fourth choice, which defeated both rock and paper for instance. So now what? Does fairness only pertain to man-made “games”? What about basketball? Is basketball a fair game? Technically yes, each player is bound by the same rules that an other player on the court is bound to; however, when you consider physical capability fairness dissipates. How is it fair that some players are physically able to jump much higher than other players simply because of how their body is built? I’m beginning to suspect that fairness can be rarely applied, or perhaps only applied to situations which are abstracted from the physical world, like the concept of flipping a coin or the game of rock, paper, scissors.

Therefore, I’m beginning to think that fairness does not exist on a human level. People are born with different IQ’s, different eye color, different strength, different disorders, etcetera. So the question I find myself asking is….why? Why is life so fundamentally unfair? Why do some people get to have awesome opportunities while others do not? This isn’t a question about how hard someone works to achieve their goals. This question transcends hard work and determination. I’ll agree that some people work damn hard in life to get what they want, and they deserve an appropriate reward, but this questions is about the uncontrollable. Things happen in life which we cannot control – like the diagnosis of a disease. Why do these things happen to some but not others? Why is life not fair in this regard?

Am I just complaining? Am I just asking these things because I feel like I have been robbed somehow? Am I playing the “why me God…why me?!?!” card? Maybe. But even if I wasn’t I think I would still be curious to know why equal opportunity does not exist. I won’t settle for “that’s just the way the universe is.” Nor will I settle for a long scientific explanation of chromosome and DNA mechanics. I’m asking why the universe itself is unfair from a perspective of virtue and not of scientific fact. Comments would be much appreciated.

Konbanwa ladies and ‘gents. From the time of creation, this website has waited for one individual to fill its empty canvas with images and paragraphs depicting tales of epic proportions, describing amazing feats of courage and dedication, and portraying to you, the reader, how awesome and thrilling the adventures of life are. But alas, the words did not appear, the pictures did not come, and the stories of old remained untold and forgotten. It came as somewhat of a shock to realize that a blog does not write itself and that a photo gallery does not manifest the albums in your head onto a viewing window. So the answer to the very subtly suggested question is yes – yes I now realize that if I want a website of my own, then I need to put time into it.

To those of you who know who I am, I’m sure you are thinking “OMG Mock posted something!” while simultaneously taking bets on how long it takes me to lose interest in blogging. I want in. Put me down for one month. To those of you whom I do not know, abandon the whole “judge a blog by its first post” rule of thumb that you would normally use and let me get myself warmed up for this – it takes me a while… Well, that and the only “writing” I’ve done in the past few months is “fury war lfg.” SO cut me some slack for this first week…or couple weeks….actually lets make it the first 4 posts, just to be safe – that way I should just be getting into the groove of blogging when I lose interest. Sounds about right (spoiler alert, this might just be one of my phases). But until that time feel free to read over any and all things you may find in this website!! On the top bar there is a “Math” link where you will currently find nothing! There is also an “Anime” tab which when clicked on contains nothing! And finally there is a “Pictures” tab which if clicked on expecting to see pictures will severely disappoint you as there is nothing there!… I’m working on it…slowly. My advice would be to check back here on a random basis instead of a regular one so as to maximize your chances of viewing something new!

Anyway, to save this post from being totally spontaneous and slightly pessimistic, the real reason I wanted to write was to christen this website!! YAY for finally getting this started *smashes bottle of champagne*! I’ll write something new up in the near future when I’m not so hungry and have my thoughts more organized!

[mock]