Posts
By Sebastiaan
Well I finally finished Eternal Sonata (for the 360) yesterday, helped by a friend of mine.
All in all, a brilliant game, with a very innovative battle system. Only once or twice was the camera system a bit awkward. Another weird thing was the ending scene - it's three quarters of an hour and you'll have a whole bunch of clichés thrown at you.
The story is beautiful, the world is beautiful, the graphics-style is gorgeous (though the animations are sometimes a bit static)... And the biggest plus: it's a game about Chopin. It makes me want to read the biography I wanted and got for my birthday.
The game is not expensive, it scores pretty decent. If you like a good Japanese RPG, get this one. You might even learn something.
Tuesday, December 29, 2009
Friday, December 25, 2009
Math Puzzle: Solution
By Sebastiaan
This is the solution to this post.
The answer is 22 hours.
You can look at it in different ways, for example: n0 = 1. Then ni+1 = ni * 3 + 1. So then we just enter the numbers, and work our way towards the answer.
One could also get the following formula: ni+1 = 4*ni - 3*n - 3 with n0 = 1.
Lets take a closer look a the second formula. If you take a big n, say, 20, what does it look like? If n is that big, the second term (3*n) is insignificant, not even speaking of - 3. But what is 4*ni? It's four times the previous n, which is four times the previous n, etc... The first term is 4*1 (so, 41), the second 4*4 (so, 42), the third is 4*16, you can guess where we're going: 4n. This is a quick way to see how fast this progresses, within a day everyone knows what the secret is. But it does not provide you with the exact answer (22), since it's only an estimate.
If you calculate exactly, or use something like this calculating programme, you can easily find the answer. First number would be 1, the common ratio 3, and n is 22. Try progressing n up to 22, and see how fast it goes up.
This is the solution to this post.
The answer is 22 hours.
You can look at it in different ways, for example: n0 = 1. Then ni+1 = ni * 3 + 1. So then we just enter the numbers, and work our way towards the answer.
One could also get the following formula: ni+1 = 4*ni - 3*n - 3 with n0 = 1.
Lets take a closer look a the second formula. If you take a big n, say, 20, what does it look like? If n is that big, the second term (3*n) is insignificant, not even speaking of - 3. But what is 4*ni? It's four times the previous n, which is four times the previous n, etc... The first term is 4*1 (so, 41), the second 4*4 (so, 42), the third is 4*16, you can guess where we're going: 4n. This is a quick way to see how fast this progresses, within a day everyone knows what the secret is. But it does not provide you with the exact answer (22), since it's only an estimate.
If you calculate exactly, or use something like this calculating programme, you can easily find the answer. First number would be 1, the common ratio 3, and n is 22. Try progressing n up to 22, and see how fast it goes up.
Tuesday, December 22, 2009
Guitar Hero 5: First Impressions
By Sebastiaan
I recently got Guitar Hero 5 for my birthday, the XBOX360 version, and I have been playing it, well, frankly, a LOT, especially since Sunday.
Now, I have played Guitar Hero III: Legends of Rock, with my brother, we finished all songs in the co-op career except for two songs. Then, after a few months, we got World Tour, including a new guitar, a drum-set and a microphone. We played hell out of it, I perfected a few songs, and went on-line with Live Gold after a few months, when the community was, well, dead, but still had a lot of fun. Then I decided it was time to get the new Guitar Hero, for that sole purpose: going on-line. And of course, the convincing set-list (Nirvana, Muse, 3 Doors Down, Johnny Cash, to name a few). Though as with each Guitar Hero, I know less songs than that I do know...
First thing we did when we got it, was play Ring of Fire, by Johnny Cash. I played straight on expert on guitar, my brother sang on expert as well, and my father did bass on easy. I really like the new Star Power system, you can synchronize activating it better, though it has a disadvantage - when a band member is in trouble, he can't spend your star power, as he could with World Tour, though this is easily solved. If one band member is struggling, his instrument 'breaks', and you have to convince the crowd in order to let him continue. If you use star power when convincing the crowd, hit a few notes, your friend can play along again.
Another big advantage for most gamers, is that all tracks are available from the start of the game. Still, I'm playing through career, just because I like the challenges, which are new as well. In career mode, each song has a challenge. This can be a challenge for guitar only, for the band as a whole, or for bass, drum or vocals. With this challenge you can win up to 3 extra stars, on top of the possible 5 (6 if you perfect a song, which I did for the first time today) stars you can win by playing well.
Multi-player offers a lot of cool game modes, which I haven't even played through yet, at least not all of them.
The fifth part of Guitar Hero doesn't contain a lot of difficult songs for me as an experienced Guitar Hero player, of the approximately 35 songs I've played so far, I could finish over 30 in my first try, and one in second, and well, only one or two I find too difficult and I'm too lazy to go into practice just yet... Though Judith by A Perfect Circle, which I find pretty brilliant, will be a challenge to complete on expert... And Santana will be a challenge as well, I think, though I haven't had the guts to try that one yet. A quick glance through the track list on quickplay taught me it's going to be a big nut to crack.
The complete list of songs in Guitar Hero 5 can be found here. A big plus for most of you will be that over half of the songs are from the last decade.
At the moment I have over 170 stars, of which I collected 150 in the last two days... I'm going to try and max it out, with help from my brother.
I really like this new game in the franchise, 10/10 in my opinion!
I recently got Guitar Hero 5 for my birthday, the XBOX360 version, and I have been playing it, well, frankly, a LOT, especially since Sunday.
Now, I have played Guitar Hero III: Legends of Rock, with my brother, we finished all songs in the co-op career except for two songs. Then, after a few months, we got World Tour, including a new guitar, a drum-set and a microphone. We played hell out of it, I perfected a few songs, and went on-line with Live Gold after a few months, when the community was, well, dead, but still had a lot of fun. Then I decided it was time to get the new Guitar Hero, for that sole purpose: going on-line. And of course, the convincing set-list (Nirvana, Muse, 3 Doors Down, Johnny Cash, to name a few). Though as with each Guitar Hero, I know less songs than that I do know...
First thing we did when we got it, was play Ring of Fire, by Johnny Cash. I played straight on expert on guitar, my brother sang on expert as well, and my father did bass on easy. I really like the new Star Power system, you can synchronize activating it better, though it has a disadvantage - when a band member is in trouble, he can't spend your star power, as he could with World Tour, though this is easily solved. If one band member is struggling, his instrument 'breaks', and you have to convince the crowd in order to let him continue. If you use star power when convincing the crowd, hit a few notes, your friend can play along again.
Another big advantage for most gamers, is that all tracks are available from the start of the game. Still, I'm playing through career, just because I like the challenges, which are new as well. In career mode, each song has a challenge. This can be a challenge for guitar only, for the band as a whole, or for bass, drum or vocals. With this challenge you can win up to 3 extra stars, on top of the possible 5 (6 if you perfect a song, which I did for the first time today) stars you can win by playing well.
Multi-player offers a lot of cool game modes, which I haven't even played through yet, at least not all of them.
The fifth part of Guitar Hero doesn't contain a lot of difficult songs for me as an experienced Guitar Hero player, of the approximately 35 songs I've played so far, I could finish over 30 in my first try, and one in second, and well, only one or two I find too difficult and I'm too lazy to go into practice just yet... Though Judith by A Perfect Circle, which I find pretty brilliant, will be a challenge to complete on expert... And Santana will be a challenge as well, I think, though I haven't had the guts to try that one yet. A quick glance through the track list on quickplay taught me it's going to be a big nut to crack.
The complete list of songs in Guitar Hero 5 can be found here. A big plus for most of you will be that over half of the songs are from the last decade.
At the moment I have over 170 stars, of which I collected 150 in the last two days... I'm going to try and max it out, with help from my brother.
I really like this new game in the franchise, 10/10 in my opinion!
Monday, December 21, 2009
Finding Grace
By Alouette
Walking along
the sea shore,
I find grace
in pebbles no more.
Wind flowing
through my hair,
and when everything
is forgotten,
I still won't care.
Hiding behind you
and running along,
it seems like nothing
will ever turn wrong.
But everything changed
at the place
where I often come
to find my grace.
Walking along
the sea shore,
I find grace
in pebbles no more.
Wind flowing
through my hair,
and when everything
is forgotten,
I still won't care.
Hiding behind you
and running along,
it seems like nothing
will ever turn wrong.
But everything changed
at the place
where I often come
to find my grace.
Sunday, December 20, 2009
Daylight Poem
By Sebastiaan
I am an intense poetry lover, and occasionally I write my own poems. I'd like to share my latest creation with you.
Daylight Poem
Beaming sunlight shines on my face,
my thoughts slip away,
and I find myself astray,
fading out.
Beaming sunlight reaches my face,
though barely, as I drift
further from you, left
with but a staring gaze.
Inhaling, deep breath,
one more second,
then you're dead,
sunlight burning away your face.
I am an intense poetry lover, and occasionally I write my own poems. I'd like to share my latest creation with you.
Daylight Poem
Beaming sunlight shines on my face,
my thoughts slip away,
and I find myself astray,
fading out.
Beaming sunlight reaches my face,
though barely, as I drift
further from you, left
with but a staring gaze.
Inhaling, deep breath,
one more second,
then you're dead,
sunlight burning away your face.
Tuesday, December 15, 2009
Engel: Melodic Metal, Superb Song Texts, And One Hell Of An (Absolute) Design!
By Sebastiaan
Another find from the budget corner: one, single euro for a CD by the melodic death metal band Engel, the album Absolute Design. I listened to it almost right away, and no, I did not know they existed, nor that they were this good. The CD cover design just intrigued me. Now, a few months later, I'm listening once more, and this time, some of the lyrics are really impressing me. I already noticed this the first time listening, but I didn't care to look them up in the booklet. Well, I finally did.
The lyrics at the top of the post are from Casket Closing, the second track of the album. It's the chorus, and what a chorus it is! To me, it's about coming to terms with having to let go of someone, which a lot of us have to go through at a certain point in their lives, because of illness, or at the end of a friend/relationship, or because of both. Or because of any number of reasons...
These lyrics are from the third track of the album, again, the chorus. For me this one means, well, literally turning the page: getting on with my life. Again, I am surely not the only one who has had to do this. In fact, I believe everyone is constantly turning pages: while you are reading, you enjoy life, but at the end of the page, the story turns sad, and you have to turn the page but it's really hard to do so, because you're afraid the story will continue to be sad, even though in fact the story has not yet been written. You write your own story. It's not about standing still, waiting for the next page or chapter to unfold - you stand in the middle of your life, it's your call. So make the most of it. Now.
Overall, the Absolute Design album has a nice metal sound to it: mostly fast drums, nice guitar riffs, grunting when it's necessary, and a very melodic sound to it.
Plus, the cover design is absolutely brilliant!
Listen here.
Some more nice lyrics with which I will leave you:
I want you to leave me far behind,From: Casket Closing.
To start over and create something new.
I want you to be free from me and find,
Someone special to call your own.
Another find from the budget corner: one, single euro for a CD by the melodic death metal band Engel, the album Absolute Design. I listened to it almost right away, and no, I did not know they existed, nor that they were this good. The CD cover design just intrigued me. Now, a few months later, I'm listening once more, and this time, some of the lyrics are really impressing me. I already noticed this the first time listening, but I didn't care to look them up in the booklet. Well, I finally did.
The lyrics at the top of the post are from Casket Closing, the second track of the album. It's the chorus, and what a chorus it is! To me, it's about coming to terms with having to let go of someone, which a lot of us have to go through at a certain point in their lives, because of illness, or at the end of a friend/relationship, or because of both. Or because of any number of reasons...
Oh, everything I've been fighting for,From: Next Closed Door.
Is behind the next closed door.
I've been fighting all my life,
I want to turn this page around.
These lyrics are from the third track of the album, again, the chorus. For me this one means, well, literally turning the page: getting on with my life. Again, I am surely not the only one who has had to do this. In fact, I believe everyone is constantly turning pages: while you are reading, you enjoy life, but at the end of the page, the story turns sad, and you have to turn the page but it's really hard to do so, because you're afraid the story will continue to be sad, even though in fact the story has not yet been written. You write your own story. It's not about standing still, waiting for the next page or chapter to unfold - you stand in the middle of your life, it's your call. So make the most of it. Now.
Overall, the Absolute Design album has a nice metal sound to it: mostly fast drums, nice guitar riffs, grunting when it's necessary, and a very melodic sound to it.
Plus, the cover design is absolutely brilliant!
Listen here.
Some more nice lyrics with which I will leave you:
Split my flesh to revealFrom: Trial and Error.
There's nothing left to curse.
Tearing my wounds in vain
when seeking for myself in pain.
Calling out so I'll change my ways,From: Calling Out.
working hard to turn me in to someone else,
they don't see why I choose to be me,
trying hard to end the reason of my life.
Watch Out! Explosions In The Sky
By Sietse
A little over a month ago I decided to go out to a shop and buy a post-rock album. I didn't know if they would have one and I certainly didn't know what band it would be, but since no band in the genre has ever disappointed me yet, I was just going to buy the first thing I would find. Though when I talked to a friend about it he said that he had seen a Explosions in the Sky album and that it was only 10 euros.
The next day when I went to the shop, that friend, Almar, came with me to check if the CD was still there. Well, it was and it looked just awesome. I took the album and glared at it for awhile to check it out, because the cover was just amazing. It appears to be a cover with some (awesomely) drawn burning trees and random words on it, line after line after line. However, when you take a closer look, you'll see that those random words actually form the album title: "The world is not a cold dead place". Thing became even cooler when I turned the album around and saw the repeated words yet again, but this time some of the words were coloured red and spelled out the 5 track titles. It seems short, but the post-rock genre is notorious for its long tracks and indeed the album is still 45 minutes long, with the shortest song coming in at 8:18.
So naturally I wanted to buy it and grabbed my wallet at which Almar suddenly remarked: "Damn, I should've not told you about that album, I should've waited untill I had the money to buy it myself." Which made the pleasure of purchasing it even greater as it was really fun hearing him mock about it. Then even at the counter the guy who sold me the album complimented me on my taste for such a young guy and he started talking about when he listened to the album. He said: "I listened to it whilst flying from America, but maybe that was entice the gods" enticing the gods being a translated Dutch saying which means something like "to ask for problems".
The album is a real beauty with nicely distorted guitars, great drums that help build up the song and they didn't use any vocals at all, which is normal for the post-rock genre and it brings a lot more creativity to the sound of the instruments. Yet even without the vocals the songs present you with a story. Yes, they present you with a story that you can make up for yourself. I recommend to just sit there, have a drink and listen to the music, without doing anything else. It's a great experience.
The next day when I went to the shop, that friend, Almar, came with me to check if the CD was still there. Well, it was and it looked just awesome. I took the album and glared at it for awhile to check it out, because the cover was just amazing. It appears to be a cover with some (awesomely) drawn burning trees and random words on it, line after line after line. However, when you take a closer look, you'll see that those random words actually form the album title: "The world is not a cold dead place". Thing became even cooler when I turned the album around and saw the repeated words yet again, but this time some of the words were coloured red and spelled out the 5 track titles. It seems short, but the post-rock genre is notorious for its long tracks and indeed the album is still 45 minutes long, with the shortest song coming in at 8:18.
So naturally I wanted to buy it and grabbed my wallet at which Almar suddenly remarked: "Damn, I should've not told you about that album, I should've waited untill I had the money to buy it myself." Which made the pleasure of purchasing it even greater as it was really fun hearing him mock about it. Then even at the counter the guy who sold me the album complimented me on my taste for such a young guy and he started talking about when he listened to the album. He said: "I listened to it whilst flying from America, but maybe that was entice the gods" enticing the gods being a translated Dutch saying which means something like "to ask for problems".
The album is a real beauty with nicely distorted guitars, great drums that help build up the song and they didn't use any vocals at all, which is normal for the post-rock genre and it brings a lot more creativity to the sound of the instruments. Yet even without the vocals the songs present you with a story. Yes, they present you with a story that you can make up for yourself. I recommend to just sit there, have a drink and listen to the music, without doing anything else. It's a great experience.
Monday, December 14, 2009
Wallace Stevens
By Sebastiaan
This poetry book has been in my possession for some time now. It's a collection with Dutch translations, which I don't read, of some poems by Wallace Stevens. I would like to share the following stanza with you:
EDIT: This stanza is the last one of the poem "Snow Man".
This poetry book has been in my possession for some time now. It's a collection with Dutch translations, which I don't read, of some poems by Wallace Stevens. I would like to share the following stanza with you:
For the listener, who listens in the snow,Just think about it, read it another time.
And, nothing himself, beholds
Nothing that is not there and the nothing that is.
EDIT: This stanza is the last one of the poem "Snow Man".
First CD
By Sebastiaan
Nearly ten years ago, I got my very own "real" CD (so not a children's sing-a-long disc). It was the single Supergirl by Reamonn, which was quite popular at the time. I listened to the radio every evening in those days, and this song was on quite frequently.
We had to bring along a CD to school, and I choose this one. I don't remember exactly how I got it, perhaps we even bought it especially for this occasion.
Anyway, while I was cleaning my room I stumbled upon it again, covered with a layer of dust. I'm listening to it right now... Nostalgia.
German homepage.
English homepage.
MySpace.
We had to bring along a CD to school, and I choose this one. I don't remember exactly how I got it, perhaps we even bought it especially for this occasion.
Anyway, while I was cleaning my room I stumbled upon it again, covered with a layer of dust. I'm listening to it right now... Nostalgia.
German homepage.
English homepage.
MySpace.
Art: Desire
By Sebastiaan
A few weeks ago, I was feeling like painting something. A friend of mine gave me a subject: "Smachten", which translates to "Desire". Thought I'd share this one with you:
Fun fact: my mother formed the final idea in me, painting an island. I ended up giving it to her as a birthday present.
More of my artwork will be (is) posted on DeviantART.
A few weeks ago, I was feeling like painting something. A friend of mine gave me a subject: "Smachten", which translates to "Desire". Thought I'd share this one with you:
Fun fact: my mother formed the final idea in me, painting an island. I ended up giving it to her as a birthday present.
More of my artwork will be (is) posted on DeviantART.
Sunday, December 13, 2009
Munchkin
By Sebastiaan
A little something about one of the most epic games ever. This is no video game; I'm talking about the card/board game Munchkin.
Over the years, this game has grown into something pretty big. There are six expansion packs for the card game alone, not counting the eight stand-alone games and Blender, which is ideal for mixing multiple sets of cards, with each their own expansion packs.
We have a pretty big Munchkin collection, though it is not yet complete. I will post a photo of our collection soon. EDIT: photo posted. Excluded from the photo is Munchkin Blender, we put it in the Star Munchkin box. Most of our games are in Dutch (1-4, Munchkin Bites and Cthulhu).
Yesterday we played Munchkin Quest, the board game version, for the first time. We had to get used to the rules a bit, there are some significant differences with the card game, although it has all the power of the card game (especially the humour). A lot of the cards are direct imports from the card game, but there are also some I don't recognize. Could be because most of our card sets are in Dutch, I'm not quite sure. But does it really matter? The game remains brilliant.
It's quite inspiring, I will probably go and create my own set of cards, purely for home-use.
For the Munchkin-players reading this: we had an epic final boss battle, in which we had to scrape every last resource as a bonus from our hand and cards in play. We being me and the second master of Zwollywood, my brother. We teamed up for the final battle, coming to a total of 55, not counting dices, versus 63 for the boss (and a wandering level 17 monster). Then I rolled pretty badly, and my brother rolled pretty good for the monsters. I used my bobble-head, a loaded die, and found that I could throw another die for a card. This had to be a three for us to win, but it was a two... Then we noticed the monsters still had a minus 4 penalty, and thus we were able to win...
Right, that was unreadable for non-Munchkiners, and probably all the more boring.
A little something about one of the most epic games ever. This is no video game; I'm talking about the card/board game Munchkin.
Over the years, this game has grown into something pretty big. There are six expansion packs for the card game alone, not counting the eight stand-alone games and Blender, which is ideal for mixing multiple sets of cards, with each their own expansion packs.
We have a pretty big Munchkin collection, though it is not yet complete. Yesterday we played Munchkin Quest, the board game version, for the first time. We had to get used to the rules a bit, there are some significant differences with the card game, although it has all the power of the card game (especially the humour). A lot of the cards are direct imports from the card game, but there are also some I don't recognize. Could be because most of our card sets are in Dutch, I'm not quite sure. But does it really matter? The game remains brilliant.
It's quite inspiring, I will probably go and create my own set of cards, purely for home-use.
For the Munchkin-players reading this: we had an epic final boss battle, in which we had to scrape every last resource as a bonus from our hand and cards in play. We being me and the second master of Zwollywood, my brother. We teamed up for the final battle, coming to a total of 55, not counting dices, versus 63 for the boss (and a wandering level 17 monster). Then I rolled pretty badly, and my brother rolled pretty good for the monsters. I used my bobble-head, a loaded die, and found that I could throw another die for a card. This had to be a three for us to win, but it was a two... Then we noticed the monsters still had a minus 4 penalty, and thus we were able to win...
Right, that was unreadable for non-Munchkiners, and probably all the more boring.
Thursday, December 10, 2009
Harrisons: Britpop As It Should Be
By Sebastiaan
Way back in September 2009, I found this CD by the britpop group Harrisons: No Fighting in the War Room. I had never heard of them, but was feeling lucky, and the CD was in the discount corner - five, yes five CD's for just one euro each - and it had a bonus DVD! How cheap can it get.
Well, three long, musically filled months passed, and I've finally listened to the CD. I am Amazed (yes, Amazed, with a capital A)! This CD is brilliant! It has a nice, britpop/indie sound to it, how shall I put it... the true britpop sound, the way it should be. It has everything you would expect from a britpop band.
On first listening, I didn't really have ear for the lyrics, then I grabbed the inner sleeve and started reading along... A lot of the texts are absolutely brilliant. Allow me to quote:
Really love the alliteration in this, "car crashing kids", and of course the rhyme in"stink of drink and think".
Definitely worth buying, or, listen on MySpace.
Well, three long, musically filled months passed, and I've finally listened to the CD. I am Amazed (yes, Amazed, with a capital A)! This CD is brilliant! It has a nice, britpop/indie sound to it, how shall I put it... the true britpop sound, the way it should be. It has everything you would expect from a britpop band.
On first listening, I didn't really have ear for the lyrics, then I grabbed the inner sleeve and started reading along... A lot of the texts are absolutely brilliant. Allow me to quote:
The kicking punching
Trigger happy car crashing kids
Stink of drink and think
That it is just the way life is.
Really love the alliteration in this, "car crashing kids", and of course the rhyme in"stink of drink and think".
Definitely worth buying, or, listen on MySpace.
Math Puzzle
By Sebastiaan
I came across a puzzle a few days ago. It is part of the (Dutch) National Science Quiz, my brother was reading the question out loud. I hadn't given it much thought, until now.
I came across a puzzle a few days ago. It is part of the (Dutch) National Science Quiz, my brother was reading the question out loud. I hadn't given it much thought, until now.
It is as follows: one person knows some sort of secret, he/she then tells three others. This takes an hour. Now these three others will each pass the secret on to again three others, which takes another hour. This process continues this way, until everyone in the world knows about the secret. Only the persons who were told about the secret last, can tell three more persons. How long will it take for the secret to be known by everyone in the world?
In the quiz, you can choose between a day, weekend or a week.
In the quiz, you can choose between a day, weekend or a week.
I won't give the answer to this problem, not just yet. I will wait until the 22nd of December, for then the quiz doesn't take entries anymore. I will post the answer (at least, what I assume is the answer) before the 27th, the day the official quiz answers are given.
So, let's take a look at the progress in this problem.
1 person knows about the secret. After 1 hour, 4 persons know about the secret. After 2 hours, 13 persons know about the secret.
So. in maths language:
n0 = 1
n1 = 4
n2 = 13
Can we find a formula describing this process?
Please do not comment any answers.
n0 = 1
n1 = 4
n2 = 13
Can we find a formula describing this process?
Please do not comment any answers.
Wednesday, December 9, 2009
First Encounter With Math: Pascal's Triangle
By Sebastiaan
Thinking back, the first time I fell in love with mathematics must have been reading the magnificent book "De Telduivel", the dutch translation of "The Number Devil" by H.M. Enzensberger.
The part I found most fascinating, was what I later learned is called "Pascal's Triangle" named after Blaise Pascal, a famous western mathematician, physicist and religious philosopher.
First let me explain a bit about the triangle. "1" is our top number, which comes in the uppermost 'corner' of the triangle. Then we go downwards and left, where we put another "1" and we go downwards right, where we put a third "1". Let me sketch the situation for you:
Thinking back, the first time I fell in love with mathematics must have been reading the magnificent book "De Telduivel", the dutch translation of "The Number Devil" by H.M. Enzensberger.
The part I found most fascinating, was what I later learned is called "Pascal's Triangle" named after Blaise Pascal, a famous western mathematician, physicist and religious philosopher.
First let me explain a bit about the triangle. "1" is our top number, which comes in the uppermost 'corner' of the triangle. Then we go downwards and left, where we put another "1" and we go downwards right, where we put a third "1". Let me sketch the situation for you:
1
1 1
Now, we go down-left, and down-right from both ones. The number we put in the space, is the sum of both numbers above it, and in the leftmost and rightmost spaces we just put a "1". Continuing this process infinitely, we get Pascal's Triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
You get the general idea.
Now, the most interesting thing about the triangle, is that it has a wide variety of uses. (I understand that almost everyone who reads this will lose interest in a few moments, but I still would like to share this)
One practical use is found in the calculation of combinations. Say, we are looking for the number of combination of n things taken k at a time. Mathematicians call this n choose k. Let's take a practical example, which we find in the game of poker.
Take a look at my example: we have n = 52, for there are 52 cards in a deck of cards, and let's say k = 5 because we have a poker hand with 5 cards. We now have 52 choose 5. The official formula for combinations is n! divided by k! times (n-k)!, so let's put that into perspective...
...which means there are 2,598,960 combinations of poker hands.
Could we not have found this answer in a differnet way? The answer is yes. Take a look at the following -much simpler- example: 3 choose 1. After a few calculations we find the answer is the simple "3". Take a look at the 3rd row of Pascal's Triangle (don't count the top "1" as a row, this can be seen as the starting number, or row 0), and then the first number that isn't one (for that would be 3 choose 0). This is also 3!
This works for all combinations. 7 choose 3 would be 35, according to the triangle. According to the formula this is 7! (so 7 times 6 times 5 times 4 ..... times 1) divided by 3!4!:
(7 x 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1 x 4 x 3 x 2 x 1)
...which is indeed 35.
As a kid, I used to write down the triangle as far as I could, which mostly meant 'till I ran out of paper... I especially used to do this during the more boring classes in primary school. It's ages ago, though I remember it as if it were yesterday.
I will probably post more about the triangle later on, since I so dearly love it. There are some great patterns in it...
Florian Wolff
By Sebastiaan
I recently bought the newest CD by Florian Wolff, entitled: Catching up, standing still after seeing him perform some live, acoustic songs. Didn't have a chance to listen to it 'till last weekend, and I must say, it's got a few jewels! This is a very promising singer-songwriter.
Oh, my copy is a signed one! Pretty neat.
You can listen to four of his songs here, and buy the cd here.
I recently bought the newest CD by Florian Wolff, entitled: Catching up, standing still after seeing him perform some live, acoustic songs. Didn't have a chance to listen to it 'till last weekend, and I must say, it's got a few jewels! This is a very promising singer-songwriter.
Oh, my copy is a signed one! Pretty neat.
You can listen to four of his songs here, and buy the cd here.
A Romantic Favourite...
By Sebastiaan
Classical music has recently grown to one of my biggest addictions. I've collected (bought, or received as a gift) many CD's, and my Chopin collection has nearly reached completion.
There are two words in that sentence I'd like to pick out and indulge on: "Chopin" and "completion". Let's start with the latter.
One can never quite complete ones collection of classical music: there is a wide, wide variety of performers of each piece of classical music. Think of the great Artur Rubinstein, one of the, if not the, most talented Chopin performers. Yet as I skim through my collection of CD's, names as Evgeny Kissin (Ballades) and Elisabeth Leonskaja (I really love her performance of the Nocturnes) cannot be excluded.
Frédéric François Chopin (born 1810, his only known photograph to the left, taken in the year of his death, 1849) is my all-time favourite composer. Now, let me make one thing clear: overall, I've listened to pop, rock and metal a lot more than classical music, yet it is a good fourth, and Chopin is among my top artists (momentarily 23rd on last.fm).
Chopin has composed in the "Romantic genre", so to say, but he has composed a variety of pieces. Among my favourites are the Nocturnes, which are pieces inspired by the night, the Waltzes, which is a ballroom/folk dance, and of course the Ballades, or rather: the Instrumental Ballades, a new musical form which Chopin invented.
I love Chopin's music for its subtlety, the nuances, the expression, the melancholy, though there are of course many dramatic pieces, and lovely melodies... All in all, I love his music for its variety.
I am still looking for a nice biography of Chopin. For those interested in Chopin, yet not into reading: check out Eternal Sonata, it's a very nice Japanese RPG for Xbox 360 and PlayStation 3, about the last days of Chopin. I'm probably going to post a more extensive post on the game when I've finished playing it (now in the last chapter, I believe).
Classical music has recently grown to one of my biggest addictions. I've collected (bought, or received as a gift) many CD's, and my Chopin collection has nearly reached completion.
There are two words in that sentence I'd like to pick out and indulge on: "Chopin" and "completion". Let's start with the latter.
One can never quite complete ones collection of classical music: there is a wide, wide variety of performers of each piece of classical music. Think of the great Artur Rubinstein, one of the, if not the, most talented Chopin performers. Yet as I skim through my collection of CD's, names as Evgeny Kissin (Ballades) and Elisabeth Leonskaja (I really love her performance of the Nocturnes) cannot be excluded.
Frédéric François Chopin (born 1810, his only known photograph to the left, taken in the year of his death, 1849) is my all-time favourite composer. Now, let me make one thing clear: overall, I've listened to pop, rock and metal a lot more than classical music, yet it is a good fourth, and Chopin is among my top artists (momentarily 23rd on last.fm).Chopin has composed in the "Romantic genre", so to say, but he has composed a variety of pieces. Among my favourites are the Nocturnes, which are pieces inspired by the night, the Waltzes, which is a ballroom/folk dance, and of course the Ballades, or rather: the Instrumental Ballades, a new musical form which Chopin invented.
I love Chopin's music for its subtlety, the nuances, the expression, the melancholy, though there are of course many dramatic pieces, and lovely melodies... All in all, I love his music for its variety.
I am still looking for a nice biography of Chopin. For those interested in Chopin, yet not into reading: check out Eternal Sonata, it's a very nice Japanese RPG for Xbox 360 and PlayStation 3, about the last days of Chopin. I'm probably going to post a more extensive post on the game when I've finished playing it (now in the last chapter, I believe).
Tuesday, December 8, 2009
First Blood
By Sebastiaan
Hello everybody,
I've tried blogging in the past, didn't work out for me. Yet I've always wanted to try and attain a longer blogging streak, so here goes another shot...
In short, what's this blog about?
It's about everything that interests, puzzles and confuses me, that keeps me busy, going onwards. From daily events, to quotes, to things I read, news articles, twitter, other blogs, webcomics.... It's about Mathematics, Games, Music, and all the other things you find in this world.
Bye!
Hello everybody,
I've tried blogging in the past, didn't work out for me. Yet I've always wanted to try and attain a longer blogging streak, so here goes another shot...
In short, what's this blog about?
It's about everything that interests, puzzles and confuses me, that keeps me busy, going onwards. From daily events, to quotes, to things I read, news articles, twitter, other blogs, webcomics.... It's about Mathematics, Games, Music, and all the other things you find in this world.
Bye!
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