This is a review.
For each sequence of picture gave rise to a pattern which gave further rise to a formula. As practice find the formula for each example and you may express the answer in the blog.
Wednesday, November 14, 2007
Pattens review
This is a review.
For each sequence of picture gave rise to a pattern which gave further rise to a formula. As practice find the formula for each example and you may express the answer in the blog.
Tuesday, November 13, 2007
Exercises to practice Fibonacci in n dimensions part 1
Exercises to help get a feel for the N-dimensional Fibonacci numbers:
Please write your answers here.
1. Pick a number from 2 to 6 (it actually can be bigger also, but for practical purposes we want to stop here) Call the number n
2. Define a new number m=2*n + 1
3. write the numbers 1 n times in a raw. For example if n=3 write (1,1,1) if n=4 write (1,1,1,1) etc. Pick up an English letter that defines this list with an index=1. For example I picked the letter W and for me W1=(1,1,1,1)
4. Keep creating W2,W3,W4,W5,W6 (you can continue but it is good to stop at 6 or some other point) based on the following rule: This is just an example:
If W3 is something like (a,b,c,d) then W4 will be (d,d+c,d+c+b,d+c+b+a) Do you understand the rule? Ask.
5. Create a new sequence from the Pick another letter of the alphabet and create another sequence made out of the ratios of the one you picked before where you always divide by the first member. For example I picked the letter V and got:
For example if W3=(a,b,c,d) then V3=(1,b/a,c/a,d/a) Express your answer as a decimal in three cases and the rest leave as fraction
Please write your answers here.
1. Pick a number from 2 to 6 (it actually can be bigger also, but for practical purposes we want to stop here) Call the number n
2. Define a new number m=2*n + 1
3. write the numbers 1 n times in a raw. For example if n=3 write (1,1,1) if n=4 write (1,1,1,1) etc. Pick up an English letter that defines this list with an index=1. For example I picked the letter W and for me W1=(1,1,1,1)
4. Keep creating W2,W3,W4,W5,W6 (you can continue but it is good to stop at 6 or some other point) based on the following rule: This is just an example:
If W3 is something like (a,b,c,d) then W4 will be (d,d+c,d+c+b,d+c+b+a) Do you understand the rule? Ask.
5. Create a new sequence from the Pick another letter of the alphabet and create another sequence made out of the ratios of the one you picked before where you always divide by the first member. For example I picked the letter V and got:
For example if W3=(a,b,c,d) then V3=(1,b/a,c/a,d/a) Express your answer as a decimal in three cases and the rest leave as fraction
Monday, November 12, 2007
Grading and attendance clarification
Here are some guidelines about grading.
First of all there are different kinds of situations in the class.
Some of you are processing emotional stuff and growing and this is very important and certainly part of your overall education. If someone the situation is really difficult and you cannot come to class, keep an email touch with me and so your connection will not be broken. My letter was not aimed towards these students but if you are in the catogory I recommend that you od not skip class or if you do come and see me individually
There are other very rare situation were students could not come to class for unusual reasons and I am dealing with each students on a 1-1 individual basis. My letter was not aimed towards them either.
Also my letter was not aimed towards students who for rare occasions did not come to class for various reasons.
My letter was aimed towards students who
1. Either think that this class in bullshit and a waste of their time and this is why they do not come to class. If you are in the category I suggest you withdraw now before you get an F or
2. Students who think this is a wonderful class but think that the instructor is such a good guy that he will give them a good grade any way. For these students, I suggest that they do not skip a single class and start adding to the class themselves even more then they have been doing until now.
Now about final requirements.
I decided to give a final in the class. I looked at the math content of the course and it was very beautiful and not too difficult. Here are some dates where the content of the final was discussed and we will enrich it and deepen our understanding for the rest of the semester in addition of presentations. To present to the class is a privilege and if you don't want to do it I will not force you but the grade is going to include everything you learned and did in the course. The dates are 9/30 10/1,29,31 11/7,9 In addition we devoted several class times to the seelogo movie presentation that expresses Fibonacci numbers in a higher dimension and I will put it in the final for sure and we will review. Look at the blogs.
This being said I want to add two things:
1. That I do not want you to feel that something changed in my intent and style. Most of you are doing just fine and I know that you are learning a lot all the time. We had many magical moments in the class and this is not going to go away. It is all part of the experience. We are just adding a twist, a little whirl, a dragon that is going to turn into a crysal.
2. I was listening to some music a few minutes ago. Strings. It was amazing patterns and enery in them. I realized that this is all about. patterns. Our class, the test, all the math that we did and will do this semester is about patterns and energy. I invite you to see it that way including this seemingly new twist...
Sincerely,
--Dani
First of all there are different kinds of situations in the class.
Some of you are processing emotional stuff and growing and this is very important and certainly part of your overall education. If someone the situation is really difficult and you cannot come to class, keep an email touch with me and so your connection will not be broken. My letter was not aimed towards these students but if you are in the catogory I recommend that you od not skip class or if you do come and see me individually
There are other very rare situation were students could not come to class for unusual reasons and I am dealing with each students on a 1-1 individual basis. My letter was not aimed towards them either.
Also my letter was not aimed towards students who for rare occasions did not come to class for various reasons.
My letter was aimed towards students who
1. Either think that this class in bullshit and a waste of their time and this is why they do not come to class. If you are in the category I suggest you withdraw now before you get an F or
2. Students who think this is a wonderful class but think that the instructor is such a good guy that he will give them a good grade any way. For these students, I suggest that they do not skip a single class and start adding to the class themselves even more then they have been doing until now.
Now about final requirements.
I decided to give a final in the class. I looked at the math content of the course and it was very beautiful and not too difficult. Here are some dates where the content of the final was discussed and we will enrich it and deepen our understanding for the rest of the semester in addition of presentations. To present to the class is a privilege and if you don't want to do it I will not force you but the grade is going to include everything you learned and did in the course. The dates are 9/30 10/1,29,31 11/7,9 In addition we devoted several class times to the seelogo movie presentation that expresses Fibonacci numbers in a higher dimension and I will put it in the final for sure and we will review. Look at the blogs.
This being said I want to add two things:
1. That I do not want you to feel that something changed in my intent and style. Most of you are doing just fine and I know that you are learning a lot all the time. We had many magical moments in the class and this is not going to go away. It is all part of the experience. We are just adding a twist, a little whirl, a dragon that is going to turn into a crysal.
2. I was listening to some music a few minutes ago. Strings. It was amazing patterns and enery in them. I realized that this is all about. patterns. Our class, the test, all the math that we did and will do this semester is about patterns and energy. I invite you to see it that way including this seemingly new twist...
Sincerely,
--Dani
Friday, November 9, 2007
Volume patterns HW for the weekend
This activity connects between patterns and ideas of calculus and can give deep insight and be fun also.
Take a peace of paper (8,5''X11'') and cut the four equal squares from the 4 corners. Fold it to make it into a box w/o top. Keep doing this 4 times and each time cut a square of a different size. Put the boxes side by side and look at the pattern of the volume of the boxes.
Each time you get a different volume isn't it? When the small squares are very tiny the base of the box is big but the hight is small. The volume will then be small, isn't it? On the other side of the spectrum, if the square that you cut is large the height of the box is large but the area of the base becomes quite tiny so again the volume is small. Do you remember by the way the formula of area and volume?
Area= Length times Width and
Volume = Area times Height which is the same as
Volume= Length Times Width Times Height.
So here we are with patterns again, for each square we cut we get a different volume. Draw this pattern on paper, write about it, find a formula...play with it. Now you are hired by a company to make the box with a largest volume. What size square would you cut?
Wednesday, November 7, 2007
Patterns and Inverse patterns
Last time we had fun with pattern.
Many patterns do have an inverse pattern.
For example the pattern (1,4) (2,6) (3,8), (4,10).... We found last class the crystallization of the pattern that was the formula (x,2*x+2)
The inverse pattern has some pairs like (4,1), (6,2) (8,3) (10,4) but this is not a complete picture. How do we complete? Why?
(1,__), (2,__),(3,__) (4,1),(5,___), (6,2).... How do we find that pattern?
Would you be interested to explore it further? We created from shapes last time 3 patterns where the above one was the first. How about finding inverse patterns for the other two patterns: I think the second one is very difficult yet not beyond your mind and if you want I can explain to those who are interested. The third one is medium difficulty. How about using the patterns from last time also?
Many patterns do have an inverse pattern.
For example the pattern (1,4) (2,6) (3,8), (4,10).... We found last class the crystallization of the pattern that was the formula (x,2*x+2)
The inverse pattern has some pairs like (4,1), (6,2) (8,3) (10,4) but this is not a complete picture. How do we complete? Why?
(1,__), (2,__),(3,__) (4,1),(5,___), (6,2).... How do we find that pattern?
Would you be interested to explore it further? We created from shapes last time 3 patterns where the above one was the first. How about finding inverse patterns for the other two patterns: I think the second one is very difficult yet not beyond your mind and if you want I can explain to those who are interested. The third one is medium difficulty. How about using the patterns from last time also?
Canibus Songs
Sunday, November 4, 2007
Canibus Post 1 - For Everyone - Before the Discussion
Hello WhIM Class!
I hope you are having a good weekend. I am at Power Shift 2007 and it is very exciting to be here. I wanted to give you all a little bit more to think about before we talk about my project this Friday and then after Friday I think I will put up another blog if people want to share their thoughts again. I am going to give you some more Canibus lyrics and ask some specific questions. This post asks general questions about the songs and gives general information. I will make other posts that will give specific information on the specific songs.
*******IMPORTANT*******
I ask you to please listen to your song once before reading this post, then resopond to the questions and read the post. Do this before Friday. After Friday I will ask you to listen to the song again, to write your response this time around, and put them in the post specifically about your song.
*******QUESTIONS*******
Please refer to the song that you listened to.
1. Do you normally listen to hip-hop music? Specifically underground hip-hop?
2. Would you listen to this song again/not for the assignment?
3. When you were listening to the song, describe what you imagined? Did you visually see the thing that Canibus was talking about - give a specific example? Did you think about the things he was talking about and try to connect them and unpack them, or just keep up with the song - give an example?
4. When you were listening to the song, how did you relate to it? Did you empathize with Canibus, i.e. try to imagine things from his perspective? Did you listen to the song from the perspective of the "you" that Canibus speaks to, whether this is an enemy emcee, or fans of hip-hop, or just people in general? Can you think of a specific time that Canibus was speaking to "you" in the song and if you felt like he was really speaking to you or to someone else?
5. Did you notice any mathematical elements in the songs? Were you impressed by Canibus's knowledge of places, people, theories etc.? Did this make you think differently about the potential of hip-hop music? Did these various references mean anything to you? Pick a specific one that did and explain how you reacted when hearing it or perhaps when finding out later what it meant. Do you think that the complexity of Canibus's lyrics helped get his message across?
6. What part of Canibus's song did you really dislike? Describe why and how it made you feel to hear him saying something that you thought was wrong.
7. From my first presentation, your first reactions, and your answers to these questions describe Canibus as an emcee to someone who has never listened to him. Do you think Canibus has a stronger sense of Ego or Self? How does he express elements of each in his lyrics (give an example). What do you think the relationship is between reality and fantasy in the songs? Do you think Canibus could be a leader, a teacher or a hero in the hip-hop world, in real life? Describe what kind of person you think Canibus is.
Thank you! Please read the background info, there are a few more questions in the last part of this post.
*******Background Info*******
The Law of Three - States that everything consists of three basic parts. For instance mind/body/soul or mind/body/emotion. The Holy Trinity or the executive/judiciary/legislative branches.Canibus assumes three main personas in his songs.
I. 'Bis - Bis is short for Cannabis, which is the origin of Canibus's name. Bis was the name Canibus used before the fallout with LL Cool J.
II. Rip the Jacker - Rip the Jacker became another one of aliases during his battle with LL. Jack the Ripper (the infamous serial killer who murdered prostitutes) was the title of a song on one of LL's previous albums. Rip the Jacker was Canibus's idea of a clever play on that name. It first appeared on Canibus's song "Rip the Jacker" the song starts out - Calling all dogs, calling all dogs, be on the lookout for a big homo nigga with dimples and I'ma let ya'll know something, it ain't just start here we've been playing on that ass since Jack The Ripper and now it's time to Rip the Jacker. This is saying that 'Bis had been better than LL since he was making his earlier, more simplistic music, like the album on which Jack the Ripper appears, but now he's going to take LL to war.
III. Germaine Williams - Canibus's real name. The importance of this name to him is that once he joined the military he was no longer 'Bis or Rip the Jacker or Canibus. He was referred to by his government name, as Private Williams, just like all of the other soldiers. Canibus has always prided himself on being more connected to his fans than other rappers and he talked about this being part of the reason he joined the military. He also sometimes calls himself St. Germain - see this article http://religiousmovements.lib.virginia.edu/nrms/iam.html.
The Law of Seven - http://www.rahul.net/raithel/otfw/93article.html From what I've read the law of seven states that things do not happen in a strictly linear progressive manner as we assume they do, when dealing with chronological history, for example. I haven't delved very deep into this subject, however. Seven has always been a sacred number for humanity - as with the seven day week, in Jewish mysticism etc.
Canibus's writing style may seem abstract, and without any traditional form. He talks about this in a few songs, for instance in the outro of Poet Laureate II James Dickey says "Usually I go with the given, with what comes to you over the celestial wireless, you're lucky when you get it" and in that song he says "In the words of Joseph Heller, I learned how to write better/ Even though it sorta irked me, he said he didn't understand the process / of the imagination but he felt he was at its mercy".
8. How do you think that this writing process effects the finished product? What do you like about this style and what do you think it lacks?
I was reading a book about superheroes and philosophy and it talks about how as a young boy Clark Kent (secret identity of Superman) feels that he lacks a sense of community and that this is why he becomes Superman. I will share a few quotes that outline this idea.
"It is fair to presume that despite his extraterrestrial origins, Superman feels the same basic need for community that is shared by all the human beings around him; it not, he most likely wouldn't bother being Clark Kent at all and would just as soon soar off to explore the greater solar system and galaxies beyond than work a nine-to-five in metropolis"
"Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure."
"How does Superman connect with the world around him? Not by turning his back on his alien heritage, though that was certainly his instinct while he was growing up in a small town. NO, he ultimately connects by embracing that heritage-by creating as an adult a new identity for himself that is as Kryptonian as Clark Kent is human. Superman knowns instinctively that it is only when he puts his gifts to use that he truly feels alive and engaged."
"Only by being openly Kryptonian can he also be an Earthman with exuberance and excellence. When he lives as who he really is, in full authenticity to his nature and gifts, and then brings his distinctive strengths into the service of others, he takes his rightful place in the larger community, in which he now genuinely belongs to and can feel fulfilled."
"Superman has...been a shining example...of the virtue of selfless heroism-but he has accomplished this by acting in his own self interest."
9. What connections do you see between the Sueprman paradox described in these quotes and Canibus? Does this change the way you would answer question 7?
I hope you are having a good weekend. I am at Power Shift 2007 and it is very exciting to be here. I wanted to give you all a little bit more to think about before we talk about my project this Friday and then after Friday I think I will put up another blog if people want to share their thoughts again. I am going to give you some more Canibus lyrics and ask some specific questions. This post asks general questions about the songs and gives general information. I will make other posts that will give specific information on the specific songs.
*******IMPORTANT*******
I ask you to please listen to your song once before reading this post, then resopond to the questions and read the post. Do this before Friday. After Friday I will ask you to listen to the song again, to write your response this time around, and put them in the post specifically about your song.
*******QUESTIONS*******
Please refer to the song that you listened to.
1. Do you normally listen to hip-hop music? Specifically underground hip-hop?
2. Would you listen to this song again/not for the assignment?
3. When you were listening to the song, describe what you imagined? Did you visually see the thing that Canibus was talking about - give a specific example? Did you think about the things he was talking about and try to connect them and unpack them, or just keep up with the song - give an example?
4. When you were listening to the song, how did you relate to it? Did you empathize with Canibus, i.e. try to imagine things from his perspective? Did you listen to the song from the perspective of the "you" that Canibus speaks to, whether this is an enemy emcee, or fans of hip-hop, or just people in general? Can you think of a specific time that Canibus was speaking to "you" in the song and if you felt like he was really speaking to you or to someone else?
5. Did you notice any mathematical elements in the songs? Were you impressed by Canibus's knowledge of places, people, theories etc.? Did this make you think differently about the potential of hip-hop music? Did these various references mean anything to you? Pick a specific one that did and explain how you reacted when hearing it or perhaps when finding out later what it meant. Do you think that the complexity of Canibus's lyrics helped get his message across?
6. What part of Canibus's song did you really dislike? Describe why and how it made you feel to hear him saying something that you thought was wrong.
7. From my first presentation, your first reactions, and your answers to these questions describe Canibus as an emcee to someone who has never listened to him. Do you think Canibus has a stronger sense of Ego or Self? How does he express elements of each in his lyrics (give an example). What do you think the relationship is between reality and fantasy in the songs? Do you think Canibus could be a leader, a teacher or a hero in the hip-hop world, in real life? Describe what kind of person you think Canibus is.
Thank you! Please read the background info, there are a few more questions in the last part of this post.
*******Background Info*******
The Law of Three - States that everything consists of three basic parts. For instance mind/body/soul or mind/body/emotion. The Holy Trinity or the executive/judiciary/legislative branches.Canibus assumes three main personas in his songs.
I. 'Bis - Bis is short for Cannabis, which is the origin of Canibus's name. Bis was the name Canibus used before the fallout with LL Cool J.
II. Rip the Jacker - Rip the Jacker became another one of aliases during his battle with LL. Jack the Ripper (the infamous serial killer who murdered prostitutes) was the title of a song on one of LL's previous albums. Rip the Jacker was Canibus's idea of a clever play on that name. It first appeared on Canibus's song "Rip the Jacker" the song starts out - Calling all dogs, calling all dogs, be on the lookout for a big homo nigga with dimples and I'ma let ya'll know something, it ain't just start here we've been playing on that ass since Jack The Ripper and now it's time to Rip the Jacker. This is saying that 'Bis had been better than LL since he was making his earlier, more simplistic music, like the album on which Jack the Ripper appears, but now he's going to take LL to war.
III. Germaine Williams - Canibus's real name. The importance of this name to him is that once he joined the military he was no longer 'Bis or Rip the Jacker or Canibus. He was referred to by his government name, as Private Williams, just like all of the other soldiers. Canibus has always prided himself on being more connected to his fans than other rappers and he talked about this being part of the reason he joined the military. He also sometimes calls himself St. Germain - see this article http://religiousmovements.lib.virginia.edu/nrms/iam.html.
The Law of Seven - http://www.rahul.net/raithel/otfw/93article.html From what I've read the law of seven states that things do not happen in a strictly linear progressive manner as we assume they do, when dealing with chronological history, for example. I haven't delved very deep into this subject, however. Seven has always been a sacred number for humanity - as with the seven day week, in Jewish mysticism etc.
Canibus's writing style may seem abstract, and without any traditional form. He talks about this in a few songs, for instance in the outro of Poet Laureate II James Dickey says "Usually I go with the given, with what comes to you over the celestial wireless, you're lucky when you get it" and in that song he says "In the words of Joseph Heller, I learned how to write better/ Even though it sorta irked me, he said he didn't understand the process / of the imagination but he felt he was at its mercy".
8. How do you think that this writing process effects the finished product? What do you like about this style and what do you think it lacks?
I was reading a book about superheroes and philosophy and it talks about how as a young boy Clark Kent (secret identity of Superman) feels that he lacks a sense of community and that this is why he becomes Superman. I will share a few quotes that outline this idea.
"It is fair to presume that despite his extraterrestrial origins, Superman feels the same basic need for community that is shared by all the human beings around him; it not, he most likely wouldn't bother being Clark Kent at all and would just as soon soar off to explore the greater solar system and galaxies beyond than work a nine-to-five in metropolis"
"Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure."
"How does Superman connect with the world around him? Not by turning his back on his alien heritage, though that was certainly his instinct while he was growing up in a small town. NO, he ultimately connects by embracing that heritage-by creating as an adult a new identity for himself that is as Kryptonian as Clark Kent is human. Superman knowns instinctively that it is only when he puts his gifts to use that he truly feels alive and engaged."
"Only by being openly Kryptonian can he also be an Earthman with exuberance and excellence. When he lives as who he really is, in full authenticity to his nature and gifts, and then brings his distinctive strengths into the service of others, he takes his rightful place in the larger community, in which he now genuinely belongs to and can feel fulfilled."
"Superman has...been a shining example...of the virtue of selfless heroism-but he has accomplished this by acting in his own self interest."
9. What connections do you see between the Sueprman paradox described in these quotes and Canibus? Does this change the way you would answer question 7?
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