I'm in a class this semester called Puzzle, Games and Algorithms. Originally I thought it would just be an easy class that I would take for essentially free Comp. Sci. credit. It hasn't been terribly difficult, but Friday of last week shared some information that rightly blew my mind.
We were discussing a random deck of cards and Professor Snapp made the claim that if he were to shuffle the cards, then the specific permutation of cards that his shuffle would yield would never have been seen before. Most of the class disagreed with him. I agreed with him, but only because I thought he must know something that I didn't and not because I genuinely thought that the average shuffle yielded a unique deck. Well, here was the proof:
Since there are 52 distinguishable cards in a standard deck of playing cards (13 different numbers, repeated four times, but each time in a different suit), then the number of distinguishable permutations for the deck is 52!.
If you aren't sure about factorials, 52! (read 52 factorial) is equal to 52 * 51 * 50 * 49 * ... * 3 * 2 * 1 = 8 * 10^67
To put that in a little perspective he offered us a few estimates for other objects:
• Number of seconds in a century = 4.5 × 10^9.
• Number of human beings alive on Earth = 6.7 × 10^9.
• Number of Oreo cookies sold since 1912 = 4.9 × 10^11.
• Federal debt (est. in US$ on 9/10/07) = 9.0 × 10^12.
• Number of seconds that have elapsed since the Big Bang = 4 × 10^17.
• Number of distinct positions in a 3 × 3 × 3 Rubik’s cube = 4 × 10^19.
• Number of grains of sand on the earth = 10^21.
• Number of stars in the visible universe (Simon Driver, 2003) = 7 × 10^22.
• Number of atoms in a human body = 10^28.
• Mass of the sun (in kilograms) = 10^30.
• Number of legal chess positions = 10^40.
• Number of distinct positions in a 4 × 4 × 4 Rubik’s Revenge = 10^45.
• Number of permutations of 52 playing cards = 8 × 10^67.
• Number of distinct positions in a 5 × 5 × 5 Rubik’s Ultimate Cube = 10^74.
• Number of physical particles in the universe (inflationary model) = 10^80.
• Number of distinguishable games of go = 10^768
(These were copied from the PowerPoint presentation used during the lecture, found at http://www.cs.uvm.edu/~snapp/puzzles/)
Basically, even if everyone (today's population) on the earth had been shuffling a deck of cards once a second from the very instant of the Big Bang, we wouldn't have seen all the possible combinations. In fact, if every star in the visible universe had a planet just like the Earth with exactly as many people and all of those people were shuffling 52-card decks once a second beginning the second of the Big Bang, even then we would have only seen 1.876 * 10^50 diferent shuffles, leaving the rest of the 8 x 10^67 unseen. And that is a great number of unseen permutations.
And that's all I have to say.
Tuesday, September 22, 2009
Monday, September 14, 2009
How long has it been since I posted?
I have successfully completed the second week of my stint as a sophomore Computer Science major at UVM. I wrote my first program for Intermediate Programming in Java (I hope that I remember all the syntax soon, else the upcoming projects are going to suck). I am really quite confused about boolean circuits and what, exactly, they are doing. I see lines and then lines coming off of lines and lines going into gates and out of gates and into other gates and I am simply lost. Ho hum.
Three of my courses appear to be near-carbon copies, too. Two of them, incidentally, are taught by the same professor (Snapp, if you were curious). They all basically have taken the ideas of computer logic and are just applying it slightly differently. One looks at the actual structures of computer math, another at applications of computer-style math in the real world and the third looks that the probability that computer-math-based programs and processes will work (among other things, though).
The courses, since you asked (I don't think I actually have any readers, but whatever) are Discrete Structures (called Discrete Mathematics by most universities), Probability and Statistics for Computer Science Majors and Puzzles, Games and Algorithms. Puzzles, Games and Algorithms is probably my most interesting (and, incidentally, easiest) course this semester. We're going to the Great Corn Maze in the Northeast Kingdom of Vermont on the 26th of this month. If I remember to, I'll post about it.
As a shameless plugs, I would like to invite everyone to use Blackle.com as much as possible as opposed to Google. It is powered by Google but uses a black screen which saves kilowatt-hours (but only in a significant amount if a great many people use it).
Also, I would like to post this video for your enjoyment (it's quite old and I've seen it countless times):
Three of my courses appear to be near-carbon copies, too. Two of them, incidentally, are taught by the same professor (Snapp, if you were curious). They all basically have taken the ideas of computer logic and are just applying it slightly differently. One looks at the actual structures of computer math, another at applications of computer-style math in the real world and the third looks that the probability that computer-math-based programs and processes will work (among other things, though).
The courses, since you asked (I don't think I actually have any readers, but whatever) are Discrete Structures (called Discrete Mathematics by most universities), Probability and Statistics for Computer Science Majors and Puzzles, Games and Algorithms. Puzzles, Games and Algorithms is probably my most interesting (and, incidentally, easiest) course this semester. We're going to the Great Corn Maze in the Northeast Kingdom of Vermont on the 26th of this month. If I remember to, I'll post about it.
As a shameless plugs, I would like to invite everyone to use Blackle.com as much as possible as opposed to Google. It is powered by Google but uses a black screen which saves kilowatt-hours (but only in a significant amount if a great many people use it).
Also, I would like to post this video for your enjoyment (it's quite old and I've seen it countless times):
Friday, September 4, 2009
The post that contains the monologue about the decent friend
What, exactly, is a decent friend? There are fun friends, silly friends, obnoxious friends, outgoing friends, introverted friends, useless friends, caring friends, casual friends, reliable friends, etc. But what, exactly, is a decent friend?
This is a question that bugs me every time I take a facebook survey that asks me if I have a best friend. Surely, before I can honestly name a "best" friend I must have a concept of a decent friend.
To be honest, tonight I was talking to one of my more compassionate friends (who, unfortunately, is no longer near to me geographically) and it came about that I was called a decent friend. I had to take issue with that because I haven't made for myself a clear definition of a decent friend. I will try to now. I didn't say I would come up with a definition, mind, just that I'd try.
Out of all of the friend-types, the caring friend is almost always considered the best. But I don't know that I can accept that as an absolute. Sometimes it isn't enough to care, but the caring must necessarily translate into always doing the right thing. But is it even necessary for a decent friend to always do the right thing for the other friends? I can't help but to say no, since that would seem to indicate a "perfect" friend, and that's an abstract that is absolutely impossible.
So, I think that what I have to settle on is a friend that, whenever possible (or, perhaps just more than seventy-five percent of the time that it's possible) does what s/he has to for a friend in need. A decent friend doesn't have to like doing nice things or doesn't have to enjoy being there for a friend, but the decent friend will always set him/herself aside (or, again, the majority of the time) in order to help his/her friends.
There aren't many decent friends, are there?
This is a video that I particularly enjoy:
This is a question that bugs me every time I take a facebook survey that asks me if I have a best friend. Surely, before I can honestly name a "best" friend I must have a concept of a decent friend.
To be honest, tonight I was talking to one of my more compassionate friends (who, unfortunately, is no longer near to me geographically) and it came about that I was called a decent friend. I had to take issue with that because I haven't made for myself a clear definition of a decent friend. I will try to now. I didn't say I would come up with a definition, mind, just that I'd try.
Out of all of the friend-types, the caring friend is almost always considered the best. But I don't know that I can accept that as an absolute. Sometimes it isn't enough to care, but the caring must necessarily translate into always doing the right thing. But is it even necessary for a decent friend to always do the right thing for the other friends? I can't help but to say no, since that would seem to indicate a "perfect" friend, and that's an abstract that is absolutely impossible.
So, I think that what I have to settle on is a friend that, whenever possible (or, perhaps just more than seventy-five percent of the time that it's possible) does what s/he has to for a friend in need. A decent friend doesn't have to like doing nice things or doesn't have to enjoy being there for a friend, but the decent friend will always set him/herself aside (or, again, the majority of the time) in order to help his/her friends.
There aren't many decent friends, are there?
This is a video that I particularly enjoy:
Tuesday, August 25, 2009
School-ward bound
All summer, sadly, I have been looking forward to returning to school in the fall. I say sadly because I remember well how much I looked forward to summer vacation as a child. Now, though, I can't help but to feel that I have outgrown the town I live in (as anyone who lives here will eventually do). This creates a lot of frustration for me when I have to go back for breaks or spend any significant length of time in the town. It isn't that I feel as though I'm too good for the town (and not just because I have such a hard time with that particular abstract noun) but I just get so bored when I am here with nothing to do and that makes me tired. And being tired all the time is draining on a person. Thus, I have been eagerly awaiting the day that I get to leave again.
That day, as it happens, is this Sunday. I plan to leave very early in the morning and get to school as soon as possible. In fact, I have even started packing already (and that's big for me) because, well, there's nothing else to do.
I would not be in such dire straits if my car hadn't been murdered by my brother's fiancée (about whom a blog could be kept to track all of the stupid actions she performs during any gien day). Without a car, it's impossible to get a job in this town (as there are literally only three places to work and none of them are ever hiring). The cycle continues because no car means no job means no money means no car means no job.
But Sunday it's all done!
That day, as it happens, is this Sunday. I plan to leave very early in the morning and get to school as soon as possible. In fact, I have even started packing already (and that's big for me) because, well, there's nothing else to do.
I would not be in such dire straits if my car hadn't been murdered by my brother's fiancée (about whom a blog could be kept to track all of the stupid actions she performs during any gien day). Without a car, it's impossible to get a job in this town (as there are literally only three places to work and none of them are ever hiring). The cycle continues because no car means no job means no money means no car means no job.
But Sunday it's all done!
Tuesday, August 11, 2009
Wretched Racko
This morning I was awoken, yet again, by my all-too-noisy cousin Chris singing on his way up the stairs. Good morning, world. Nine o'clock in the morning in the waning days of a summer vacation (a day with no plans except sleeping in, no less) is far too early an hour to be rudely awakened. And upon being woken up, I was harassed by several people into a game of Racko. I haven't played it in a long time, and apparently it has been a long-enough time for me to forget my intense hatred of that game.
When I was younger, I used to have to spend one weekend every few weeks at my grandmother's. She is card-obsessed and I used to have to play Racko several times a day, at least, for the entire duration of the weekend. A nine-year-old who only wants to go outside and play (which I only really wanted to do at my grandmother's, probably as a result of the card-playing alternative) is not mollified by endless games of Racko, golf, rummy, 21, Skip-Bo and Uno. The only three of those games for which I acquired a long-lasting dislike are Racko, golf and rummy.
But this morning I forgot that Racko was on that list. About forty seconds into the game, I was hit by the recollection of my deep-seated hatred of that game. My family, however, has the policy that if you start a game you have to see it through. I was stuck. I'm sure everyone knows the feeling.
The problem was compounded by the fact that everyone's patterns shared at least one card with another player's. The game went on and on, with everyone picking up cards and immediately discarding them. Everyone knew what was going on, but, true to form, no one acknowledged the ugly truth. It became a waiting game, with all four players hoping someone else would crack first and try for an entirely new pattern. Since everyone was only one or two cards from winning, though, no one was willing to try to get a whole new pattern as they knew they'd not have the time and each card thrown out from their rack risked the game for them.
The end result was that everyone got tired of the game and everyone decided to end it so that nobody won. It sounds a lot like some government plans that have been implemented, but the events are on such a different scale that it would be a superficial connection anyway.
I guess that's it for now.
When I was younger, I used to have to spend one weekend every few weeks at my grandmother's. She is card-obsessed and I used to have to play Racko several times a day, at least, for the entire duration of the weekend. A nine-year-old who only wants to go outside and play (which I only really wanted to do at my grandmother's, probably as a result of the card-playing alternative) is not mollified by endless games of Racko, golf, rummy, 21, Skip-Bo and Uno. The only three of those games for which I acquired a long-lasting dislike are Racko, golf and rummy.
But this morning I forgot that Racko was on that list. About forty seconds into the game, I was hit by the recollection of my deep-seated hatred of that game. My family, however, has the policy that if you start a game you have to see it through. I was stuck. I'm sure everyone knows the feeling.
The problem was compounded by the fact that everyone's patterns shared at least one card with another player's. The game went on and on, with everyone picking up cards and immediately discarding them. Everyone knew what was going on, but, true to form, no one acknowledged the ugly truth. It became a waiting game, with all four players hoping someone else would crack first and try for an entirely new pattern. Since everyone was only one or two cards from winning, though, no one was willing to try to get a whole new pattern as they knew they'd not have the time and each card thrown out from their rack risked the game for them.
The end result was that everyone got tired of the game and everyone decided to end it so that nobody won. It sounds a lot like some government plans that have been implemented, but the events are on such a different scale that it would be a superficial connection anyway.
I guess that's it for now.
Monday, August 10, 2009
Short-term happiness from one petty act.
A few months ago, in (what passes for me as) a fit of rage, I posted a definition on the Urban Dictionary website (urbandictionary.com, oddly) for the name of my brother's fiancee, Noel, on the site with a lengthy and scathing definition. It pretty much attacked everything about her and made me feel better. I know about their screening process and "inside jokes" are supposedly rejected in the review process, so I never actually expected it to make it to the site. And I proceeded to forget all about it. Until today.
Facebook is a wonderful tool for me to look at, because many times my friends' statuses jog my memory about something I either did, forgot to do, should have done but decided to put off or had simply refused to do but (upon being reminded ofsaid "something") had a change of heart which caused me to do whatever it was about which I had refused. Today my friend's status referred to a new favorite non-word ("Rumsfail," if you're curious). That reminded me of my post and I went on the site immediately to see what had become of it. I found my definition and was pleased at once. In a rare act of nostalgia, I read through it, grinning all the while. Until I noticed one sentence missing a comma at the end of the third paragraph (I tend to ramble).
My happiness dissolved at once and I tried to edit the post, but I couldn't for the life of me remember the password for the account I'd made, so any possibility of that was dashed.
I guess the moral of this story is to always use the same password for everything, despite what the Internet security people say about hacking. In retrospect, if they got the password to my online banking, it really doesn't change anything if they get the password for my Urban Dictionary account as well.
Three cheers for bad foresight. Also, enjoy this:
(I do so enjoy kitties).
Facebook is a wonderful tool for me to look at, because many times my friends' statuses jog my memory about something I either did, forgot to do, should have done but decided to put off or had simply refused to do but (upon being reminded ofsaid "something") had a change of heart which caused me to do whatever it was about which I had refused. Today my friend's status referred to a new favorite non-word ("Rumsfail," if you're curious). That reminded me of my post and I went on the site immediately to see what had become of it. I found my definition and was pleased at once. In a rare act of nostalgia, I read through it, grinning all the while. Until I noticed one sentence missing a comma at the end of the third paragraph (I tend to ramble).
My happiness dissolved at once and I tried to edit the post, but I couldn't for the life of me remember the password for the account I'd made, so any possibility of that was dashed.
I guess the moral of this story is to always use the same password for everything, despite what the Internet security people say about hacking. In retrospect, if they got the password to my online banking, it really doesn't change anything if they get the password for my Urban Dictionary account as well.
Three cheers for bad foresight. Also, enjoy this:
(I do so enjoy kitties).
Friday, August 7, 2009
Back in Business and Izzard.
Well, last night I had a really strange dream involving the Hitler balloon in Aqua Teen Hunger Force, and I have decided to take up blogging again. The two events are totally unrelated, but that doesn't change the validity of either.
Since I lack anything real to blog about, I have decided to write about Eddie Izzard. Though he's been a performing comedian for a number of years now (you can tell from the outfits that he wears, assuming he doesn't enjoy dressing in all the hottest out-of-fashions), I have only recently been introduced to his comedy. My favorite excerpt from one of his shows so far will now be posted:
This is pretty representative of his comedic style. As an aside, Izzard identifies as a straight transvestite, and seems to enjoy the gamut of reactions his clothing draws.
If you're unfamiliar with Izzard, I would definitely recommend watching some of the clips on YouTube and familiarizing yourself. If you opt out, I won't lose sleep over it, though.
Since I lack anything real to blog about, I have decided to write about Eddie Izzard. Though he's been a performing comedian for a number of years now (you can tell from the outfits that he wears, assuming he doesn't enjoy dressing in all the hottest out-of-fashions), I have only recently been introduced to his comedy. My favorite excerpt from one of his shows so far will now be posted:
This is pretty representative of his comedic style. As an aside, Izzard identifies as a straight transvestite, and seems to enjoy the gamut of reactions his clothing draws.
If you're unfamiliar with Izzard, I would definitely recommend watching some of the clips on YouTube and familiarizing yourself. If you opt out, I won't lose sleep over it, though.
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