By Sebastiaan
Here's another poem!
Truths
This is not a poem
of lively rejoice -
this is of truth,
the whole and only.
What is this if not
a call-out, shout-out,
fearful, frightful song
of lonely truth?
Might I see thy face,
once more, once again?
Might I hear thy voice
singing in my ear?
Yet all that remains
is the memory of you,
'till we meet again,
I'll always remain truthful to myself.
Life may not always be fair,
it may not always fare well -
yet fair it has been never,
still this is what we're thrown into.
You remain ingraspable,
as always -
we may be sinners,
we may be saints -
though that is all we'll ever be,
saints can sin and sinners can be saints,
the sinful saint should sanctify the sinner's way -
sinful truths still speak truth and wisdom forever on.
Saturday, September 18, 2010
Wednesday, September 15, 2010
Nameless
By Sebastiaan
Here's a poem for you!
Nameless
Where's your heart at
for it's not with me.
Residing in mine
is a flood that keeps me bleeding.
I'm weeping red for salvation -
you don't even know my name.
I call you starlight,
you call me smart -
I call you moonlight,
you take the compliment right.
Calling out to you -
yet I still remain nameless.
Here's a poem for you!
Nameless
Where's your heart at
for it's not with me.
Residing in mine
is a flood that keeps me bleeding.
I'm weeping red for salvation -
you don't even know my name.
I call you starlight,
you call me smart -
I call you moonlight,
you take the compliment right.
Calling out to you -
yet I still remain nameless.
Saturday, September 4, 2010
It Seems Today
By Sebastiaan
It seems today's
the day of my departure
from oblivion.
It seems the fires,
the flames of my hell,
will be cast out.
It seems today
...purification...
will lead me to
reality.
It seems today's
the day of my departure
from oblivion.
It seems the fires,
the flames of my hell,
will be cast out.
It seems today
...purification...
will lead me to
reality.
Sunday, August 22, 2010
Murmur
By Sebastiaan
Murmur
Quiet and speechless -
out of breath.
I have fallen into recess -
no more to forget.
"Your silent murmurs never reached me -
your tears, deeply drawn into your skin, wasted."
This ring, diamond set,
could never steal your heart;
yours is unmet,
mine merely foiled.
"Whispers are all they'll ever be -
though lakes of salt opened up to me,
I could never be
what you needed to see."
Murmur
Quiet and speechless -
out of breath.
I have fallen into recess -
no more to forget.
"Your silent murmurs never reached me -
your tears, deeply drawn into your skin, wasted."
This ring, diamond set,
could never steal your heart;
yours is unmet,
mine merely foiled.
"Whispers are all they'll ever be -
though lakes of salt opened up to me,
I could never be
what you needed to see."
Wednesday, July 14, 2010
Desert Sands
By Sebastiaan
Again I present you with a poem.
Desert sands
Whilst the wind whistles through the sands
we try to make amends
with past in the present
for a future so pleasant.
Whilst the wind wails sandstorms
howling we find forms
of writing in our minds
together this binds
words together as if attached with strings
with more value than gold rings
they create these things
called poetry.
Again I present you with a poem.
Desert sands
Whilst the wind whistles through the sands
we try to make amends
with past in the present
for a future so pleasant.
Whilst the wind wails sandstorms
howling we find forms
of writing in our minds
together this binds
words together as if attached with strings
with more value than gold rings
they create these things
called poetry.
Tuesday, July 13, 2010
Experimental Poem
By Sebastiaan
I always like to make my poems with a little twist, a play on words, for example. Here's another experiment:
Rightful heart, brightly
light my weighted burden,
light pathways stretched before
lightning strikes between
our hearts, filled,
our love, enticing flightfull
hour of dreams, fight
for painless façade.
Please end this charade,
release my hurting shackles,
unleash the darkest shade.
Make my paleness leave,
take bleeding broken leaves
wake me with love.
I always like to make my poems with a little twist, a play on words, for example. Here's another experiment:
Rightful heart, brightly
light my weighted burden,
light pathways stretched before
lightning strikes between
our hearts, filled,
our love, enticing flightfull
hour of dreams, fight
for painless façade.
Please end this charade,
release my hurting shackles,
unleash the darkest shade.
Make my paleness leave,
take bleeding broken leaves
wake me with love.
Ineffable
By Sebastiaan
Here's one more poem for you.
Ineffable
Ineffable, my feelings for you,
normal words, like fire,
cannot be used like heart's passion,
to show what I aspire.
Indescribable, my lover's lovely face,
for it is not one but many,
that seek to represent, for I resent,
the idea of the one that is mine.
"Alliterate all you want, lover boy,
all the figures you speak,
it is of no use to define me,
ineffable, indescribable, universal lover of thee."
Here's one more poem for you.
Ineffable
Ineffable, my feelings for you,
normal words, like fire,
cannot be used like heart's passion,
to show what I aspire.
Indescribable, my lover's lovely face,
for it is not one but many,
that seek to represent, for I resent,
the idea of the one that is mine.
"Alliterate all you want, lover boy,
all the figures you speak,
it is of no use to define me,
ineffable, indescribable, universal lover of thee."
Sunday, July 4, 2010
Pascal's Triangle In Motion
By Sebastiaan
I recently created this Flash video for my (upcoming, nearly finished) site. It shows Pascal's Triangle in motion:
(If the space above is empty, you do not have QuickTime installed)
For more information on Pascal's Triangle, take a look at my previous post on this subject.
I recently created this Flash video for my (upcoming, nearly finished) site. It shows Pascal's Triangle in motion:
(If the space above is empty, you do not have QuickTime installed)
For more information on Pascal's Triangle, take a look at my previous post on this subject.
Wednesday, June 30, 2010
Short Story: Lightning Struck, Part Five
By Sebastiaan
The fifth and final part to my story.
Lightning Struck, Part Five
If only it had been a dream...
There we were, with the overcast sky howling thunder at us. We argued, I was mad at you for acting so strange. That's when I changed, I lost myself. After all, it should have been you who was mad at me for acting strange.
I threw you out of the car and drove away. But I drove blindly, right into a tree. I was knocked unconscious.
When I woke up, it all seemed a bad dream. A doctor was hanging over me. "Good morning," he said. "Sleep well?" And it was here that the recovery process had started.
It is only now that I understand what beast lures inside me.
"I hope you can hear me, I hope you can see me," I called out loud on top of the hill were we last were. The car was standing next to me, a new car. I looked at the sky, which was rapidly turning a dark shade of grey. "It's these three words: I am sorry." I sat down, and waited for the thunderstorm to get here.
Lightning struck again.
Dust to dust... I thought. Storm clouds gathered all over my head.
Ashes to...
The fifth and final part to my story.
Lightning Struck, Part Five
If only it had been a dream...
There we were, with the overcast sky howling thunder at us. We argued, I was mad at you for acting so strange. That's when I changed, I lost myself. After all, it should have been you who was mad at me for acting strange.
I threw you out of the car and drove away. But I drove blindly, right into a tree. I was knocked unconscious.
When I woke up, it all seemed a bad dream. A doctor was hanging over me. "Good morning," he said. "Sleep well?" And it was here that the recovery process had started.
It is only now that I understand what beast lures inside me.
"I hope you can hear me, I hope you can see me," I called out loud on top of the hill were we last were. The car was standing next to me, a new car. I looked at the sky, which was rapidly turning a dark shade of grey. "It's these three words: I am sorry." I sat down, and waited for the thunderstorm to get here.
Lightning struck again.
Dust to dust... I thought. Storm clouds gathered all over my head.
Ashes to...
Friday, June 11, 2010
Short Story: Lightning Struck, Part Four
By Sebastiaan
Part four to my story.
Lightning Struck, Part Four
Perhaps it's time I came to terms with it.
"You don't have to. Tell us, I mean."
I stared him blankly in the eye.
"Are you still with us?"
"Yes I am, doctor Sherman," he answered.
Sherman whispered something in the ear of the man next to him, who then slowly walked forwards and started talking: "This won't hurt, it's just to get you to focus. Do you understand?"
"I certainly do," he replied.
"Good, then..." the man started, but he was interrupted by a smack to his face.
Doctor Sherman stood up and grabbed the sedative from the man who just fell to the floor. "You wouldn't hurt me, now, would you."
"I have... a name..." he hissed through his teeth.
"Yes, murderer is your name. You murdered your wife, remember?"
His eyes turned big. "Liar!" In rage he charged forwards, but the doctor avoided the attack.
Next thing I knew I woke up, bound to a bed... There was something.. vague.. about coming to terms... "Help!" I screamed. A man with a black eye came inside, he looked at me sourly. "That seems painful."
"It is," he said, grinding his teeth.
Then doctor Sherman came inside. "Good, you're awake. I'm sorry we had to bind you. We can't take another risk."
"I'm sorry, but I do not... understand..." I said hesitantly. "Oh.. oh... hey man, I'm sorry... I..." I said looking to the black-eyed man.
"You remember?" Sherman asked uncertain.
"Yes... I think I do." A flash shot through my mind, lighting everything. It was a bright flash. I shook wildly with my head, and then it dawned on me. "No.... no! No!!!" I started screaming. The doctor and the black-eyed man left the room.
Lightning struck again...
Part four to my story.
Lightning Struck, Part Four
Perhaps it's time I came to terms with it.
"You don't have to. Tell us, I mean."
I stared him blankly in the eye.
"Are you still with us?"
"Yes I am, doctor Sherman," he answered.
Sherman whispered something in the ear of the man next to him, who then slowly walked forwards and started talking: "This won't hurt, it's just to get you to focus. Do you understand?"
"I certainly do," he replied.
"Good, then..." the man started, but he was interrupted by a smack to his face.
Doctor Sherman stood up and grabbed the sedative from the man who just fell to the floor. "You wouldn't hurt me, now, would you."
"I have... a name..." he hissed through his teeth.
"Yes, murderer is your name. You murdered your wife, remember?"
His eyes turned big. "Liar!" In rage he charged forwards, but the doctor avoided the attack.
Next thing I knew I woke up, bound to a bed... There was something.. vague.. about coming to terms... "Help!" I screamed. A man with a black eye came inside, he looked at me sourly. "That seems painful."
"It is," he said, grinding his teeth.
Then doctor Sherman came inside. "Good, you're awake. I'm sorry we had to bind you. We can't take another risk."
"I'm sorry, but I do not... understand..." I said hesitantly. "Oh.. oh... hey man, I'm sorry... I..." I said looking to the black-eyed man.
"You remember?" Sherman asked uncertain.
"Yes... I think I do." A flash shot through my mind, lighting everything. It was a bright flash. I shook wildly with my head, and then it dawned on me. "No.... no! No!!!" I started screaming. The doctor and the black-eyed man left the room.
Lightning struck again...
Thursday, June 10, 2010
Short Story: Lightning Struck, Part Three
By Sebastiaan
Part three to my story.
Lightning Struck, Part Three
There was much going on. Mostly there was much confusion, but especially the striking resemblance between the two was remarkable! At least, that's how it looked towards the outside. What few noticed, was what was going on inside the, so to say, spacious cavern that was his. There was a lot of shouting back and forth, a lot of fighting. Yet few did understand...
Perhaps I should first make clear: he is not me. He is not even a part or facet of me. 'He' is just a bad dream, yet a dream I can't seem to control. At times I am not myself. It mostly seems to happen at night, which is why I sleep bad.
Yet perhaps I should first finish the story...
There I was, with you, in the car, remember? It wasn't too long ago, and we were simply waiting for the thunderstorm to pass over, for it was still right on top of us.
"I'm sorry..." you said. "It's just... you're so difficult to live with. Mood swings and such... you don't even seem to notice!"
I did indeed not understand what she was talking about, until much later, when it dawned on me that what seemed to here as mood swings... were...
"Please.. don't... be mad?" you asked. "Please forgive me..."
I stared blankly ahead, deeply in trance or such. Then I said: "It's okay, you have to do what you have to do." I understood perfectly what it was she would do next. Yet I didn't seem to care.
Amidst all the conversation, the storm seemed to grow. It was a perfect projection of what was going on inside the cavern.
"Goodbye." I watched you, as you slowly moved your hand away from me, towards the door of the car. With a soft click it opened, and you stepped outside. Then you shut the door. I couldn't watch. Yet still I knew.
It wasn't 'till much later, I realised this was not the way things had gone. This was my projection in the cavern, this was what my mind seemed to wish had happened...
Part three to my story.
Lightning Struck, Part Three
There was much going on. Mostly there was much confusion, but especially the striking resemblance between the two was remarkable! At least, that's how it looked towards the outside. What few noticed, was what was going on inside the, so to say, spacious cavern that was his. There was a lot of shouting back and forth, a lot of fighting. Yet few did understand...
Perhaps I should first make clear: he is not me. He is not even a part or facet of me. 'He' is just a bad dream, yet a dream I can't seem to control. At times I am not myself. It mostly seems to happen at night, which is why I sleep bad.
Yet perhaps I should first finish the story...
There I was, with you, in the car, remember? It wasn't too long ago, and we were simply waiting for the thunderstorm to pass over, for it was still right on top of us.
"I'm sorry..." you said. "It's just... you're so difficult to live with. Mood swings and such... you don't even seem to notice!"
I did indeed not understand what she was talking about, until much later, when it dawned on me that what seemed to here as mood swings... were...
"Please.. don't... be mad?" you asked. "Please forgive me..."
I stared blankly ahead, deeply in trance or such. Then I said: "It's okay, you have to do what you have to do." I understood perfectly what it was she would do next. Yet I didn't seem to care.
Amidst all the conversation, the storm seemed to grow. It was a perfect projection of what was going on inside the cavern.
"Goodbye." I watched you, as you slowly moved your hand away from me, towards the door of the car. With a soft click it opened, and you stepped outside. Then you shut the door. I couldn't watch. Yet still I knew.
It wasn't 'till much later, I realised this was not the way things had gone. This was my projection in the cavern, this was what my mind seemed to wish had happened...
Wednesday, June 9, 2010
Short Story: Lightning Struck, Part Two
By Sebastiaan
Here's part two to my short story.
Lightning Struck, Part Two
"What on earth are you doing?" you said.
"I... I don't know." he replied. "It's just like this body isn't mine, you know? You don't know, of course you don't. No one understands. No one..."
"You're not yourself," you said in a somewhat frightened voice.
"Yet.. I feel... so like myself. So much more myself."
"Snap out of it!"
He fell, face down on the floor. Snapped back to reality.
Next thing I saw was her face over mine. "You had a bad dream," came the words from your mouth.
I shook my head. "No, no, it wasn't a dream... Please, you have to believe me."
"All right, I will, but please, tell me what was in your dream."
"I saw... you, and, well, myself. It was as if I looked upon both of us... Yet.. it wasn't.. me?"
You shook your head, but I could tell from your face, you were bit shocked by me telling this. Yet your words contradicted this: "It was just a dream, come, let's go back to sleep."
"I... I don't think I can. I'll get a glass of water and do some crosswords."
"But... we've slept just over an hour!"
It was this, this last sentence of her, that triggered me. After I went downstairs, I looked at the time. 5:56 blinked the time. "Just over an hour?" I murmured. "And I had a dream in that one hour of sleep?" This can't be right. A great white flash blinded me. It came from outside the window. What to do...
Here's part two to my short story.
Lightning Struck, Part Two
"What on earth are you doing?" you said.
"I... I don't know." he replied. "It's just like this body isn't mine, you know? You don't know, of course you don't. No one understands. No one..."
"You're not yourself," you said in a somewhat frightened voice.
"Yet.. I feel... so like myself. So much more myself."
"Snap out of it!"
He fell, face down on the floor. Snapped back to reality.
Next thing I saw was her face over mine. "You had a bad dream," came the words from your mouth.
I shook my head. "No, no, it wasn't a dream... Please, you have to believe me."
"All right, I will, but please, tell me what was in your dream."
"I saw... you, and, well, myself. It was as if I looked upon both of us... Yet.. it wasn't.. me?"
You shook your head, but I could tell from your face, you were bit shocked by me telling this. Yet your words contradicted this: "It was just a dream, come, let's go back to sleep."
"I... I don't think I can. I'll get a glass of water and do some crosswords."
"But... we've slept just over an hour!"
It was this, this last sentence of her, that triggered me. After I went downstairs, I looked at the time. 5:56 blinked the time. "Just over an hour?" I murmured. "And I had a dream in that one hour of sleep?" This can't be right. A great white flash blinded me. It came from outside the window. What to do...
Tuesday, June 8, 2010
Odd Squares
By Sebastiaan
No, this is not a post about strange squares. It's all about odd squares though.
Warning! Non-mathematicians may find this post unreadable.
Let me list the first few:
12 = 1
32 = 9
52 = 25
72 = 49
92 = 81
At first glance, there does not seem to be a pattern. I got this puzzle from my school, where I study to be a mathematics teacher. It stated:
"The squares of all positive odd integers are eightfolds plus one."
First thing to do was translate this into proper mathematics language.
So, odd, would mean the integer can be written as "2k+1" with k any positive integer. Thus we get:
(2k+1)2
Also, an eightfold, is "8n" with n any positive integer. Thus we get:
(2k+1)2 = 8n + 1
Now let's work out the brackets...
4k2 + 4k + 1 = 8n + 1
4k2 + 4k = 8n
for all positive integers k and n.
So now we have a relatively simple statement to proof. First thing that springs to mind is induction, but if you look just a little bit further... you'll find a much simpler and more elegant proof.
So, let's first start by dividing by four.
k2 + k= 2n
What's left to proof is that the sum of an integer and its square is even. There are multiple approaches to solving this, I'll give you two.
Say, k is even. Then k2 is most certainly even, for (2p)2 is 4p2 which is a multiple of four and thus even. When you add another even integer, it will always remain even.
Say, k is odd. Then k2 is odd, for (2p+1)2 is 4p2 + 4p + 1, which are two even integers plus one, making it odd. Now add the same odd integer k, you will get an even integer, for two odds make an even.
So, for any positive integer k, we get an even integer. Thus every odd square is an eightfold plus one.
Q.E.D.
Another approach could be rewriting the left-hand of the equation, that would make k(k+1) = 2n. Now, an integer multiplied by the next integer, would always be 'odd' times 'even' or 'even' times 'odd'. This always makes even.
Q.E.D.
No, this is not a post about strange squares. It's all about odd squares though.
Warning! Non-mathematicians may find this post unreadable.
Let me list the first few:
12 = 1
32 = 9
52 = 25
72 = 49
92 = 81
At first glance, there does not seem to be a pattern. I got this puzzle from my school, where I study to be a mathematics teacher. It stated:
"The squares of all positive odd integers are eightfolds plus one."
First thing to do was translate this into proper mathematics language.
So, odd, would mean the integer can be written as "2k+1" with k any positive integer. Thus we get:
(2k+1)2
Also, an eightfold, is "8n" with n any positive integer. Thus we get:
(2k+1)2 = 8n + 1
Now let's work out the brackets...
4k2 + 4k + 1 = 8n + 1
4k2 + 4k = 8n
for all positive integers k and n.
So now we have a relatively simple statement to proof. First thing that springs to mind is induction, but if you look just a little bit further... you'll find a much simpler and more elegant proof.
So, let's first start by dividing by four.
k2 + k= 2n
What's left to proof is that the sum of an integer and its square is even. There are multiple approaches to solving this, I'll give you two.
Say, k is even. Then k2 is most certainly even, for (2p)2 is 4p2 which is a multiple of four and thus even. When you add another even integer, it will always remain even.
Say, k is odd. Then k2 is odd, for (2p+1)2 is 4p2 + 4p + 1, which are two even integers plus one, making it odd. Now add the same odd integer k, you will get an even integer, for two odds make an even.
So, for any positive integer k, we get an even integer. Thus every odd square is an eightfold plus one.
Q.E.D.
Another approach could be rewriting the left-hand of the equation, that would make k(k+1) = 2n. Now, an integer multiplied by the next integer, would always be 'odd' times 'even' or 'even' times 'odd'. This always makes even.
Q.E.D.
Sunday, June 6, 2010
Short Story: Lightning Struck, Part One
By Sebastiaan
I'm as much a poet as I am a writer, so here's a short story for you. It's not based on real events, it's just an exercise in writing. I will be posting it in a few parts.
Lightning Struck, Part One
It all began with the thunder that night, a bolt of lightning striking down mere meters away from us. You shivered, I put my arm around you, lightly caressing your arm, but you shook my hand off.
"What's wrong?" I asked you.
"Nothing..." you said under your breath. Then lightning struck again, and I decided we should hurry towards the car, which was nearby.
Once we had entered the car, I asked once more: "Please, darling, what's wrong?".
"It's just the weather," you replied, looking away.
In retrospect, I should have known. And I guess I secretly knew all along things would never be the same again. Just not exactly how bad it was.
It actually didn't start with the lightning; it started a few months earlier, with, of all objects, a carrot. Such a small and simple vegetable, orange, mostly, with a little bit of green on the top. The dinner you made me was wonderful, but for one small, seemingly harmless thing. You put carrot in the salad.
To any outsider, this would have meant nothing. But even though you knew I hated carrots, you put them in the salad. I didn't mention it to you. Perhaps I should have, but I guess, in the end, it wouldn't have mattered. This time, I couldn't save you, me, or us.
Lightning struck again, you shivered in the car, once more. I noticed you glancing outside. I said: "It's okay, you're safe in here, there's no need to go outside." You looked at me and smiled. A smile I had not seen before. It wasn't your smile... and the glance, it wasn't your glance, yet it told me everything.
You had every reason to go outside. Yet I didn't know it yet.
To be continued...
I'm as much a poet as I am a writer, so here's a short story for you. It's not based on real events, it's just an exercise in writing. I will be posting it in a few parts.
Lightning Struck, Part One
It all began with the thunder that night, a bolt of lightning striking down mere meters away from us. You shivered, I put my arm around you, lightly caressing your arm, but you shook my hand off.
"What's wrong?" I asked you.
"Nothing..." you said under your breath. Then lightning struck again, and I decided we should hurry towards the car, which was nearby.
Once we had entered the car, I asked once more: "Please, darling, what's wrong?".
"It's just the weather," you replied, looking away.
In retrospect, I should have known. And I guess I secretly knew all along things would never be the same again. Just not exactly how bad it was.
It actually didn't start with the lightning; it started a few months earlier, with, of all objects, a carrot. Such a small and simple vegetable, orange, mostly, with a little bit of green on the top. The dinner you made me was wonderful, but for one small, seemingly harmless thing. You put carrot in the salad.
To any outsider, this would have meant nothing. But even though you knew I hated carrots, you put them in the salad. I didn't mention it to you. Perhaps I should have, but I guess, in the end, it wouldn't have mattered. This time, I couldn't save you, me, or us.
Lightning struck again, you shivered in the car, once more. I noticed you glancing outside. I said: "It's okay, you're safe in here, there's no need to go outside." You looked at me and smiled. A smile I had not seen before. It wasn't your smile... and the glance, it wasn't your glance, yet it told me everything.
You had every reason to go outside. Yet I didn't know it yet.
To be continued...
Current Activity
By Sebastiaan
Lately I've been working with flash to create some own material for my internship. I'm currently studying to become a mathematics teacher, thus I use the flash files in my lessons.
Also I've picked up building a website, which is currently on-line, with not much on there except the flash files, a picture of me and some links. I'll link to it anyway: http://www.famnijland.nl/Sebastiaan/home.htm. I'll update today or tomorrow, so that the flash files are easily accessible.
I've bought a book on Java recently and have made my way through it, and I will probably post some applets on my site. I'm guessing I can't add them in a blog post, so I'll just link once I have something up. I'll first have to convert some applications to applets before I can post them, but that should not pose much of a problem.
And to top all that, I've come across Project Euler, a combination of mathematics and programming. I've solved near 20 of the problems in a few weeks time, but it's getting pretty difficult now, not only the problems, but most of all finding the time and concentration to work on some good programming.
That's all for now.
Lately I've been working with flash to create some own material for my internship. I'm currently studying to become a mathematics teacher, thus I use the flash files in my lessons.
Also I've picked up building a website, which is currently on-line, with not much on there except the flash files, a picture of me and some links. I'll link to it anyway: http://www.famnijland.nl/Sebastiaan/home.htm. I'll update today or tomorrow, so that the flash files are easily accessible.
I've bought a book on Java recently and have made my way through it, and I will probably post some applets on my site. I'm guessing I can't add them in a blog post, so I'll just link once I have something up. I'll first have to convert some applications to applets before I can post them, but that should not pose much of a problem.
And to top all that, I've come across Project Euler, a combination of mathematics and programming. I've solved near 20 of the problems in a few weeks time, but it's getting pretty difficult now, not only the problems, but most of all finding the time and concentration to work on some good programming.
That's all for now.
Symmetry
By Sebastiaan
Symmetry is a wondrous subject, which one not only finds in mathematics, but in other subjects as well, and of course, in nature.
First, let's start by defining symmetry. There are different kinds of symmetry, but the one that springs immediately to mind, is reflection symmetry. Look at the following kite:
It has a clear axis of symmetry right through the centre. But we could also look at a star like this one:
This one also has the symmetry axis, but as you can see, it can also be rotated - this is called rotational symmetry.
But there are other forms of symmetry too. What about palindromes? They are found in words, numbers or sequences of words and numbers... Here are a few examples:
eye
never odd or even
1475741
etcetera..
I absolutely love playing with words and numbers. That's why I love symmetry. You can find symmetry in many places, if you look hard enough. Gorgeous symmetry can be found inside music. In the lyrics, but most definitely in the instruments too. But that's for some future post.
Symmetry is a wondrous subject, which one not only finds in mathematics, but in other subjects as well, and of course, in nature.
First, let's start by defining symmetry. There are different kinds of symmetry, but the one that springs immediately to mind, is reflection symmetry. Look at the following kite:
It has a clear axis of symmetry right through the centre. But we could also look at a star like this one:
This one also has the symmetry axis, but as you can see, it can also be rotated - this is called rotational symmetry.
But there are other forms of symmetry too. What about palindromes? They are found in words, numbers or sequences of words and numbers... Here are a few examples:
eye
never odd or even
1475741
etcetera..
I absolutely love playing with words and numbers. That's why I love symmetry. You can find symmetry in many places, if you look hard enough. Gorgeous symmetry can be found inside music. In the lyrics, but most definitely in the instruments too. But that's for some future post.
Tuesday, February 9, 2010
The Question Why
By Sebastiaan
Another poem:
The Question Why
Linear time passes equally dull
as all other times -
straight forward,
immer gerade aus.
What's new becomes old
over time and
in symphonic obedience
of listening, telling, and
knowing what to do,
I startle, and question
why?
Another poem:
The Question Why
Linear time passes equally dull
as all other times -
straight forward,
immer gerade aus.
What's new becomes old
over time and
in symphonic obedience
of listening, telling, and
knowing what to do,
I startle, and question
why?
Monday, February 8, 2010
Pythagorean Theorem
By Sebastiaan
It's been long since I wrote about math, so here's a rather simple subject which almost everyone knows of, but taken to a bit higher level. I'm talking about the Pythagorean Theorem.
Let me first bring back the long ago acquired knowledge of the theorem. When you have a right-angled triangle, or simply a right triangle, the theorem states that the sum of the squares of the legs belonging to the right angle are equal to the square of the side opposite the right angle.
Right, that's a pretty large piece of information, but what I'm actually saying is, with reference to the picture above, that:
AB2 + AC2 = BC2
or
b2 + c2 = a2
The classic example is AB = 3 and AC = 4. The squares of these sum up to 25 (9 + 16 = 25), and the square root of 25 is 5. So BC = 5.
Now, a more interesting question comes up when one asks oneself, "why?". For most of us this is pure magic, but it is most definately proveable. Not only is it proveable, it has been proven in many, many different ways. I will actually try to take some of these proofs and show them to you, in understandable language.
This first 'proof', is actually just to make the matter a bit more comprehensible. It's good to get a bit more knowledge about the theorem.
With reference to the picture above:
If AC = 3, then the area of the square with side AC, is 3 x 3 = 9.
If AB = 4, then the area of the square with side AB, is 4 x 4 = 16.
If AC = 5, then the area of the square with side BC, is 5 x 5 = 25, which is indeed 9 + 16. If you work this out neatly, you'll find by measuring that this is indeed true.
But this doesn't actually prove the theorem. If you replace '3' with 'b' and '4' with 'c' and '5' with 'a', then you get b2 + c2 = a2.
A nicer prove, in my opinion, is the following:
With reference to the above picture:
(1) The area of each of the triangles are given by 1/2 times a times b, so 1/2*(a + b), so all four triangles sum up to 4*(1/2*(a + b)) which is 2*a*b or simply 2ab.
(2) The area of the square with sides equal to c is given by c*c, or c2.
(3) The area of the square with sides equal to a + b is (a + b)*(a + b) or (a + b)2.
(4) The area of the square is also given by combining (1) and (2), which makes c2 + 2ab.
Now we can combine (3) and (4), and you get, magically (or perhaps not so magically?), the Pythagorean Theorem:
(a + b)2 = c2 + 2ab
a2 + b2 + 2ab = c2 + 2ab
a2 + b2 = c2
I will probably post more proofs, hopefuly more elegant ones, in the future.
It's been long since I wrote about math, so here's a rather simple subject which almost everyone knows of, but taken to a bit higher level. I'm talking about the Pythagorean Theorem.
Let me first bring back the long ago acquired knowledge of the theorem. When you have a right-angled triangle, or simply a right triangle, the theorem states that the sum of the squares of the legs belonging to the right angle are equal to the square of the side opposite the right angle.
Right, that's a pretty large piece of information, but what I'm actually saying is, with reference to the picture above, that:
AB2 + AC2 = BC2
or
b2 + c2 = a2
The classic example is AB = 3 and AC = 4. The squares of these sum up to 25 (9 + 16 = 25), and the square root of 25 is 5. So BC = 5.
Now, a more interesting question comes up when one asks oneself, "why?". For most of us this is pure magic, but it is most definately proveable. Not only is it proveable, it has been proven in many, many different ways. I will actually try to take some of these proofs and show them to you, in understandable language.
This first 'proof', is actually just to make the matter a bit more comprehensible. It's good to get a bit more knowledge about the theorem.
With reference to the picture above:
If AC = 3, then the area of the square with side AC, is 3 x 3 = 9.
If AB = 4, then the area of the square with side AB, is 4 x 4 = 16.
If AC = 5, then the area of the square with side BC, is 5 x 5 = 25, which is indeed 9 + 16. If you work this out neatly, you'll find by measuring that this is indeed true.
But this doesn't actually prove the theorem. If you replace '3' with 'b' and '4' with 'c' and '5' with 'a', then you get b2 + c2 = a2.
A nicer prove, in my opinion, is the following:
With reference to the above picture:
(1) The area of each of the triangles are given by 1/2 times a times b, so 1/2*(a + b), so all four triangles sum up to 4*(1/2*(a + b)) which is 2*a*b or simply 2ab.
(2) The area of the square with sides equal to c is given by c*c, or c2.
(3) The area of the square with sides equal to a + b is (a + b)*(a + b) or (a + b)2.
(4) The area of the square is also given by combining (1) and (2), which makes c2 + 2ab.
Now we can combine (3) and (4), and you get, magically (or perhaps not so magically?), the Pythagorean Theorem:
(a + b)2 = c2 + 2ab
a2 + b2 + 2ab = c2 + 2ab
a2 + b2 = c2
I will probably post more proofs, hopefuly more elegant ones, in the future.
Sunday, January 24, 2010
Moonshine
By Sebastiaan
This is a poem to go along with the previous post by Jolanda.
Moonshine
This is triumphant calling
over graceful islands -
bubbles of sea
surrounded by land.
Triumphant he shouted
over tearful drops of water -
bubbles of snow
surrounded by heat.
Endless wailing
of the full moon - wants
to hear, to see,
the ground beneath its hand.
Triumphant was crowded,
triumphant the land,
triumphant the sea,
triumphant drops of water
in snowy landscapes
of me -
moonshine.
This is a poem to go along with the previous post by Jolanda.
Moonshine
This is triumphant calling
over graceful islands -
bubbles of sea
surrounded by land.
Triumphant he shouted
over tearful drops of water -
bubbles of snow
surrounded by heat.
Endless wailing
of the full moon - wants
to hear, to see,
the ground beneath its hand.
Triumphant was crowded,
triumphant the land,
triumphant the sea,
triumphant drops of water
in snowy landscapes
of me -
moonshine.
Wednesday, January 20, 2010
Nightshine Poem
By Sebastiaan
Sunny days
and moonlit skies
divided darkened nights
with lies
of tomorrow,
of the future,
an end to sorrow.
Sunny nights
and dimly lit oceans
divided blackened land
and took our sight
of tomorrow,
of the future,
and refuelled our sorrow.
Sunny days
and moonlit skies
divided darkened nights
with lies
of tomorrow,
of the future,
an end to sorrow.
Sunny nights
and dimly lit oceans
divided blackened land
and took our sight
of tomorrow,
of the future,
and refuelled our sorrow.
Friday, January 15, 2010
Progressive Rock Artist
By Sebastiaan
I'd like to say a few words about a very talented guitarist and composer, Jasper van Emmerik. He also happens to be a good friend of mine, and we've had some collaborations in the past, jamming, recording, or just sharing musical thoughts.
Aside from playing well together, he also composes a lot of songs on his own, using his guitar, his mac, and input from his friends. You will be able to download some of his musical ideas for free from his site (which has a complete English translation available for you) in the near future. Meanwhile you can listen to them there, or download them from his last.fm artist page.
Happy listening!
I'd like to say a few words about a very talented guitarist and composer, Jasper van Emmerik. He also happens to be a good friend of mine, and we've had some collaborations in the past, jamming, recording, or just sharing musical thoughts.
Aside from playing well together, he also composes a lot of songs on his own, using his guitar, his mac, and input from his friends. You will be able to download some of his musical ideas for free from his site (which has a complete English translation available for you) in the near future. Meanwhile you can listen to them there, or download them from his last.fm artist page.
Happy listening!
Wednesday, January 13, 2010
Believe
By Sebastiaan
Here's another poem for you, made by myself:
Believe
Hold high hopes and have faith,
believe and sorrow,
from black to white,
can shift out of the grey,
out of the night,
into the light.
Try to think of things that turn tomorrow
from dark to bright,
believe,
everything will turn out right.
Here's another poem for you, made by myself:
Believe
Hold high hopes and have faith,
believe and sorrow,
from black to white,
can shift out of the grey,
out of the night,
into the light.
Try to think of things that turn tomorrow
from dark to bright,
believe,
everything will turn out right.
Monday, January 11, 2010
More Quick Poems
By Sebastiaan
Number 5. is actually a translation of one my Dutch poems.
4.
Light turns dark
is black turns
grey turns white
is light.
5.
Night turns to red
light lies light in lines
stretched out over land -
let us walk, hand in hand.
6.
No more light,
no more right,
no more fight,
this is the quiet.
Number 5. is actually a translation of one my Dutch poems.
4.
Light turns dark
is black turns
grey turns white
is light.
5.
Night turns to red
light lies light in lines
stretched out over land -
let us walk, hand in hand.
6.
No more light,
no more right,
no more fight,
this is the quiet.
Wednesday, January 6, 2010
Guitar Hero 5: Progress Update
By Sebastiaan
Just a progress update, I'm about halfway through the 360 achievements, and halfway through the campaign as well. Met some really great people on-line with whom I did achieve a whole bunch of stars.
Just have to finish Rush - The Spirit of Radio on guitar, solo, then I'll be satisfied and call it 'finished'. I can get the intro at ~65% now, but, well, that's in practice mode, and the intro riff is found in other sections of the song as well. But I'm confident I'll finish it soon.
Anyone who wants to play with me can add me as a friend, my gamer tag is The Wise Dragon. I'll also compete with you, if you'd like.
Just a progress update, I'm about halfway through the 360 achievements, and halfway through the campaign as well. Met some really great people on-line with whom I did achieve a whole bunch of stars.
Just have to finish Rush - The Spirit of Radio on guitar, solo, then I'll be satisfied and call it 'finished'. I can get the intro at ~65% now, but, well, that's in practice mode, and the intro riff is found in other sections of the song as well. But I'm confident I'll finish it soon.
Anyone who wants to play with me can add me as a friend, my gamer tag is The Wise Dragon. I'll also compete with you, if you'd like.
Tuesday, January 5, 2010
Quick Poems
By Sebastiaan
Quick poems, I don't know if it's a term, but to me they're like haiku's - real short poetry that does not have to rhyme, and, unlike haiku's, does not have any form. Here's some for you:
1.
Morning red shines on
mourning black dress.
Wept tears to tie
the knots back together.
2.
In terms of leaving,
coming, going and being there,
someone shouts
"just passing through."
3.
Dreaming deafening sounds,
sound defeat,
sound the retreat,
I'm homebound.
Quick poems, I don't know if it's a term, but to me they're like haiku's - real short poetry that does not have to rhyme, and, unlike haiku's, does not have any form. Here's some for you:
1.
Morning red shines on
mourning black dress.
Wept tears to tie
the knots back together.
2.
In terms of leaving,
coming, going and being there,
someone shouts
"just passing through."
3.
Dreaming deafening sounds,
sound defeat,
sound the retreat,
I'm homebound.
Friday, January 1, 2010
Happy New Year!
By Sebastiaan
Would like to wish all of you a happy 2010, may it be your year.
Or rather: may you make it your year. It's something you have in hand. Here's a little poem:
To someone special.
In dreams absolve the pain,
find comfort and regain
your spiritual strength,
for nothing is in vain.
Do and live,
don't give up,
fight, stand strong,
it's your own life you live.
Twenty-nine was not the end,
twenty-ten is no beginning,
live your life -
you're winning.
Would like to wish all of you a happy 2010, may it be your year.
Or rather: may you make it your year. It's something you have in hand. Here's a little poem:
To someone special.
In dreams absolve the pain,
find comfort and regain
your spiritual strength,
for nothing is in vain.
Do and live,
don't give up,
fight, stand strong,
it's your own life you live.
Twenty-nine was not the end,
twenty-ten is no beginning,
live your life -
you're winning.
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