Infinity-ception

My mind is a swirling maelstrom of facts, useless information, questions, opinions, and dreams. There is one question that seems to pop out every now and then, and every time I manage to find the answer, I become so afraid of it that the question goes into remission for a while until I decide to look up the answer again. It’s the kind of question that kind of makes you think about the meta-magnitude of mathematics.

For those of you who aren’t necessarily mathematically-minded, let me give you a refresher.

We all know about numbers, but remember that all the numbers are divided into sets that fit into one another.

One such set is the set of integers. Integers are whole numbers that stretch from positive infinity to negative infinity; think of the number line, and picture the middle of it as 0. It extends eternally to the left and right, with negative integers on the left and positive integers on the right.

The set of integers is part of the set of real numbers, which contain rational (numbers that can be represented as a fraction, or ratio) and irrational numbers (that can’t be expressed as a ratio, such as the popular mathematical constant π).

Back to the question I was talking about earlier. Clear your mind, and really think about this one, because I’ll give you one answer I received to it, and I want to know whether or not you agree and why. Either way, I find it interesting. The question is:

Which set is larger… the set of all integers, or the set of all real numbers between 0 and 1?

I submit that the answer is the latter.

Is your mind blown yet?
No? Let me help it along a little.

Let’s consider, first, the size of the set of all integers. As I said before, it stretches from negative infinity to positive infinity, and contains whole numbers. It can’t be quantified, but if you had an infinite amount of time, you could count them, even if you started at an immensely large x and stopped at –x.

However, what about between 0 and 1? At first, one would say, “Nothing. When counting, you start with 0, and go to 1.” But remember, I said the set of all real numbers, and that includes fractions and irrational numbers. So to keep it simple, I can give you two numbers between 0 and 1; let’s go with 0.25 and 0.26. Not even realizing the fact that if you stay at that number of significant digits, you still have a wide berth between 0 and 1, but there are numbers between those… 0.251 and 0.252. The set of integers doesn’t have this problem. With integers, if you have x, you have nothing between it and x + 1.

Hopefully you see where I’m going with that. No matter which two decimals you compare, you can always go down one further layer of granularity and get a real number between the two. So not only do you have an infinity between 0 and 1, but you have an infinity between every set of decimals you can possibly postulate. Therefore, the set of real numbers between 0 and 1 is a much larger set.

A bit of research has led me to something called Aleph Numbers, and how set sizes are described with cardinality.

Even if you aren’t good at math, go down the rabbit hole for a little while, and see how infinitely deep it is.

Cool Story, Bro

Or, non-sarcastically, “awesome timing, bro.”

So today I went to the local Renaissance fair, King Richard’s Faire, with a few friends. It was a pretty good time; drank some beer, watched some shows, and fired some arrows. (Not necessarily in that order, though…) We also saw the cutest little tiger cubs, which oddly was the highlight of the day.

Naturally, in the middle of all the walking and sightseeing, we got hungry. One of the things that the Faire is known for (heck, I think pretty much any ren fair is known for) is their giant turkey legs. They’re pretty big. Mastodon-sized drumsticks, they are. Salted meat with a crispy skin that for some reason attracts all the bees in the vicinity. We saw these things everywhere, and decided that we absolutely had to get one. They just smelled so darn tasty.

After buying our food tickets, the three of us were lucky enough to get in line at a window that opened up when a girl behind it shouted that turkey legs were available from it. My two friends handed me the food tickets to get the turkey legs we were all craving.

As we were walking away, we heard this loud and clear announcement:

“Lords and ladies, we are sorry, but we no longer have any turkey legs available!”

My friends and I turned to each other. “Holy shit,” I remarked. “I feel terrible now. We got the last three.”

“Turkey leg high-five!!”

And we did. And we feasted and rejoiced in our good fortune.

Today was a good day.

Saving is Important

So I was playing Final Fantasy X the other night. I was doing some level grinding in the Omega Ruins for the first time, after feeling like I was ready due to obtaining Caladbolg, Nirvana, and all the summons.

…before I continue, for those of you who don’t know:

• The Omega Ruins is an optional dungeon in the game and is filled with powerful fiends, although not nearly as difficult as some of the stuff that the Monster Arena holds.
• Caladbolg is Tidus’ ultimate weapon, and Nirvana is Yuna’s.
• Yes, all the summons. It wasn’t at all difficult to obtain the Magus Sisters.

If you knew all that, great. Moving on.

So I was level grinding. Things were going rather smoothly; I had made it to the point in the dungeon where you have to defeat Ultima Weapon to move to the sub-basement of the ruins. Knocked him out no sweat after stealing 30 Doors to Tomorrow. I knew in the next section I would be ambushed by Great Marlboros, so I decided to make a run back to the start. I had pretty good armor on my party, but NOTHING that had No Encounters, so it wouldn’t be an easy trip.

I was starting to feel good about how well I was filling up the Sphere Grid. Kimahri moved into Auron’s section to get more defense and strength, while Lulu had learned Flare and Osmose (despite the fact that her spells only used 1 MP at a time…). I teleported Tidus over to Wakka’s section because I felt his strength was lacking. All in all, about a couple hours or so worth of effort, stolen items (Rikku’s Auto-Haste targe helped here), and a few close calls.

I get halfway back, and as I feared, I’m ambushed by a Great Marlboro. And again, before I continue, I should let anyone who doesn’t know that Great Marlboros are a pain in the ass. Not only are they incredibly difficult to defeat, but they always ambush you (except if one of your active party members has a weapon with First Strike) and start the battle with “Putrid Breath”. This attack puts Poison, Confusion, Darkness, Silence, and Berserk on your entire party. Unless you have armor that wards or makes you immune to these effects, the Great Marlboro doesn’t even have to touch you; your party members will uncontrollably attack themselves, and even if they miss, lose health anyway. And there’ll be virtually nothing you can do about it.

I got cocky, though. Kimahri survived the attack without Confusion and Berserk and was able to activate Auto-Med with a Remedy to bring his status back to normal. I switched him out for Yuna, healed everyone as best as I could, and got to work pounding the Great Marlboro for items with Rikku. The battle was tough, but I figured I’d come out on top and decided it might be a good idea to capture this thing for the Monster Arena.

That, in retrospect, was a terrible decision.

Auron had the capturing weapon and was clean, so I switched him in and started attacking. As if it could read my mind, the fiend used Putrid Breath again. None of my active characters had Berserk or Confuse Ward on, so they all started flailing wildly at both themselves and the beast. Yuna actually landed a few hits, but she might as well have been swinging a wet noodle.

And then, after about 15 seconds, Game Over.

I’ll never get those hours back.

Ever had an experience like that?

Game Reviews: Bioshock Infinite

The wait proved to be worth it; Bioshock Infinite is a fantastic adventure that delivers on all fronts. It will be lionized for years to come as the standard to which other first person shooter games should hope to achieve.

For the record, FPS is definitely not my genre of choice, mainly because I pretty much suck at shooting things and prioritizing my targets. (Unless, of course, there’s one really big one, and I just fire at its weak point until it’s dead.) Also, I didn’t finish the first Bioshock, nor did I play its sequel. When I first saw previews for this game, however, I knew that I had to experience it. I was right; not only did I have to experience it, but I’ve been highly recommending the experience to anyone I know that has even picked up a next-gen controller. You HAVE to play this game, because gamers will be talking about it. I’m going to keep this review short, because others (including Adam Sessler) have done a much better job of singing its praises.

Graphics: 10/10
Bioshock Infinite is, for lack of a better term, downright gorgeous. You are immersed in the majesty and beauty of the sky city of Columbia only a few minutes into the start of the game, and even when the game is turned off you still can’t pull yourself away from it.

Environments are colorful, vibrant, and even when they are dreary and rainy, they are teeming with activity and life. There were points where I just had to stop and take a look around in awe at the utopia that Irrational Games had created… between the people, buildings, sidewalks, vendor booths, and even faraway structures, I had never seen such unparalleled detail and creativity.

Story: 10/10
Few games could keep me as captivated with their story as Bioshock Infinite did. You play the role of Booker DeWitt (brilliantly voiced by Troy Baker, known for playing Snow Villiers), a disenfranchised Pinkerton agent sent to retrieve a girl named Elizabeth (voiced by Courtnee Draper) from the sky city of Columbia. The story from the very start is as immersive as the world you are looking at, so I will go no further to spoil details that you could very easily find out on your own. It does a fantastic job of mixing plot twists, drama, action, and deep thought of an existentialist nature.

Gameplay: 10/10
As I said before, first-person shooters are not my thing. But damn, this game was fun as hell to play, even when it got the most frustrating. Elements from the previous Bioshock games are returned in the form of Vigors, which give Booker powers that emanate from his left hand to disable, damage, and manipulate enemies in whatever style you choose. Throughout most of the game, Elizabeth accompanies you, and not only does she stay out of harm’s way (so no ‘protecting the damsel’ nonsense), but during battle, and oftentimes when you are in most need of it, she’ll toss health, ammo, and Salts (for your vigors) to you that she finds. Outside of battle, she’ll find money and perform lockpicking to give you access to areas off the beaten path. Throw in the large collection of weapons available to suit any play style and you’ve got a great formula for the ideal shoot-‘em-up. Dying isn’t even that much of an inconvenience; you lose a little bit of money, and Elizabeth resurrects you in a safe zone away from where you fell. Throughout the entire game, you are pushed to keep going.

The most fun part about combat, though, is when you get a chance to be on the Skylines that are found throughout the world. They’re Columbia’s main form of transportation, and their addition to your strategy is nothing short of pure bliss. Hop on a Skyline and start wailing away at helpless targets below, zooming or coasting along as you please, or target an enemy on the ground and hurl toward them with a melee deathstrike. Some enemies also have the ability to follow you onto the Skylines, but it’s still just as fun shooting them off.

Overall: 10/10
I feel privileged that I got the chance to play Bioshock Infinite. Surpassing the excellence of the original Bioshock was probably a very difficult feat to pull off, but the developers managed to do it, and I’m sure they’re revelling in it at this point. If you’ve read any of my game reviews, you’ll see that I have not yet given any games I’ve played a perfect score like this. Bioshock Infinite is an experience that even the most casual gamer should attempt, as I’m willing to bet they’ll get as lost in it as I did.

For my favorite review of this game, see the YouTube channel Rev3Games review that Adam Sessler did here.

Prayer-a-thon

Two explosions in Boston today at the finish line of the Boston Marathon prompted an influx of media coverage and a flood to my facebook timeline of messages of hope for those affected by the tragedy.

And given how local it is (much like the shootings in Newtown earlier this year), my heart goes out to anyone who was personally affected or knows someone who was critically injured.

However, you’re not going to see me praying about it or requesting that others do the same. Prayer isn’t going to bring the two confirmed casualties back. It’s also not going to cause the amputees from the blast to regrow their limbs. As a matter of fact, prayer is not going to do anything except bolster the self-righteousness of those who announce that they’re doing it or begging others to do the same, only so they can join in on a sanctimonious circlejerk by co-opting yet another national tragedy to broadcast their façade of piousness. The only people the prayers are really helping are those who are doing it in the first place… and even then, there’s no tangible, relevant effects.

This alludes to what I said earlier today about the National Day of Prayer and how unnecessary it is. What about a National Day of Charity, or a National Day of Science, or a National Day of Compassion? Why are the theocrats who gave birth to such a sanctimonious national holiday not encouraging something that oh, I don’t know, CHRIST would advocate? Because compassion and action are what is needed right now.

Give money, even if it’s a little. Give blood, because you’re giving life.

Because if all you’re going to give is prayer, all you’re giving is the message that you want to help, but you’d rather plea to the whims of a deity that would invariably be responsible for letting the event happen in the first place.

Facebook Has ADD

I remember when I first joined Facebook back in 2006, it looked like a great way to connect with people in my life and share my thoughts, musings, and reminisce with them. Seven years later, it feels like it’s strayed so far from that. I have to wade through my news feed to see posts made by friends and acquaintances… the rest are advertisements, pages, “SHARE THIS NOW” spam, unimpressive pictures, and sometimes unfathomable stupidity.

It’s like reddit, except it takes up more room.

Facebook, for me, was a much simpler way for me to connect with people. It’s not something I can do as easily out of doors; I can’t just go to a bar or club and strike up a conversation with a total stranger. Hell, I can barely keep up mindless banter unless I’m with people I’m really close to.

It’s left me to wonder… what has become of Facebook as we once knew it? Do people really connect on it as much as they used to, or is it nothing more than a medium for pushing pictures of cats and pay-to-play fetchquest game requests? I added “things I like” to my profile so that my friends and acquaintances could find discussions through common interests, but as it turns out it’s just inundated my front page with things I’d rather just scroll past.

First there was Friendster, then there was Myspace, and now we have Facebook and Twitter. These our our social networks, but I can’t shake the feeling that my generation is ready to move on at this point to something better, just like we did 7 years ago.

Or maybe I’m just getting old.

In Defense of Marriage

I’ve said it on facebook, but it bears repeating. I’m a heterosexual, unmarried, humanist male. I don’t really plan on getting married anytime soon. Thing is, I don’t think it’s fair that I have a right to get married, but all my LGBTQ friends don’t. I’m not better than them. Why shouldn’t they have the same rights as other, heterosexual married couples?

Oh, what’s that? You’ve got reasons? Let’s see if I haven’t heard them before.

“God/The Bible says…”
No. Let’s just stop right here. I don’t give two flying shits about what your god or holy book has to say on the matter, because it’s irrelevant. We can get into a massive theological discussion about all the heinous stuff your god does allow, but most theists conveniently ignore when it doesn’t suit their agenda.

In America, especially, we have this fantastic thing called the Separation of Church and State. Not only does it mean freedom of religion, it means freedom from religion. It means that the government must remain neutral in affairs that have anything to do with religious belief. So if you’re against same-sex marriage because “God says it’s wrong", then so far you haven’t much of a leg to stand on in this country. God also says that eating shellfish is wrong, but that probably doesn’t stop your trips to Red Lobster.

“Marriage is supposed to be between a man and a woman. It’s a religious institution. This country was founded on Christian principles.”
Really? I guess you fell asleep in 4th grade history class, then. Marriage is really supposed to be a business transaction between landowners, given that young women, in the time where the practice originated, were viewed as property as well. Religion simply assimilated this tradition (like it has done for so many others) and redefined it to be about the commitment between a man and a woman. Governments decided that it would be a good idea to legally recognize these commitments and bring with them all sorts of benefits. And when you start getting into government, you start having to think about civil rights issues.

“Gay marriage will destroy the sanctity of marriage.”
What “sanctity”? Where is the sanctity of marriage in a country where the majority of them end in divorce? What’s so sacred about Kim Kardashian’s $10 million wedding that ended in divorce only 72 days later?

There are plenty more arguments out there that I’ve heard, but all of them, even the ones that are probably being thrown around in the SCOTUS right now, are as ridiculous as these three.

If you don’t agree with me, and you’re against same-sex marriage, then there’s probably nothing I can say that will convince you to change your mind.

Not that I need to. You’re just plain wrong. Just be wrong quietly. Same-sex marriage does not affect you. At all.

Unplanned Hiatus

So I just noticed that I haven’t contributed anything to my own damn blog for quite a long time. The last post I made was in May of 2012… it’s now February of 2013. Much time has passed, and many things have happened, but not anything that I believe hasn’t already been talked about elsewhere.

Furthermore, this blog isn’t really supposed to be a personal public journal… it’s the musings of my online persona. (And if you don’t know who that is, scroll to the top of the page.)

So in other words, I know I’ve been gone a long time, and I’m not sure if anyone really cares all that much except me. But we’ll find out soon enough.

Let’s get down to business. I need to start using this blog as a means to flex my writing muscles and display their prowess, and more importantly to receive feedback so that I can grow as a proficient writer. It is one of my more satisfying hobbies, but it isn’t a very lucrative one. It doesn’t even have to be financially, either… it’s how I validate both my intellect and any creativity I can pull from my right brain.

My series, “The Legend of Sylph Stridemoon”, has since faded from memory. I knew what I wanted to do with the characters, but I just couldn’t bring myself to find the time to make any decent plot development. I haven’t really had the motivation.

Since then, I’ve come up with two new characters as a result of my roleplaying adventures with friends. The first is Lance Lazrade, a freelance network security consultant by trade with inborn magical abilities revolving around the sphere of everything computers and networks. The second is Celso DeMedici, a Renaissance scientist sucked into time-travelling adventures with a motley crew of people he could have only encountered in dreams. I’ve created an entire backstory with the first, which I believe I have actually posted on this blog (forgive me if I haven’t). The second? Not so much. I can’t take credit for any of the adventures he has gone on so far, they have all been thought up by my GM. I’m slightly interested in what I could do with Celso, though.

Also, I’ve played dozens of video games since May, but I haven’t posted a review of a single one. I get the feeling those are actually going to become more sparse.

I guess what I really need is a kick in the pants. Something that will hold me to the obligation of updating this blog regularly. And I hope that if you are reading this, you can provide me with that motivation.