Tomorrow is the first day of the last summer art sessions! We're doing a pen and ink wave project inspired by Hokusai's 1830 woodcut masterpiece The Great Wave of Kanagawa. It's technically a mixed media project with watercolor for the sky. Above is my spin on the project. I'm expecting some amazing results from my students, because all of them were in my second session and I was blown away by their work and artistic abilities!
"The Great Wave of Kanagawa" Artist: Katsushika Hokusai |
So far, I've been most touched by a comment from Charlie Carey. He's a Facebook friend that I first met on an LDS-left Yahoo! e-mail group that has since evolved over to a Facebook page.
Keep in mind, I loved everything he had to say, even though the middle part of his comments had my head spinning a bit! (like the picture to the right - lol) However, where I got lost, I was back on track pretty quick!
I showed Charlie's comment to Chris and he laughed because he knows how my ADD mind works when it comes to mathematical concepts.
Charlie said:
OK, I seriously love this. The Great Wave is favorite anyway but this new treatment is at once both old and new.
And, from the math guy, this is a circle mapped to another domain. The equation of the golden spiral which The Great Wave uses as its wave shape is r=a exp(bθ), the logarithmic spiral or Archimedes Spiral. If you set b=0, the equation becomes r=a exp(0) =a(1) = a, a spiral which doesn't grow in radius, otherwise known as a circle. So the spiral is just a circle with the suppressed constant mapped to a monotonic exponential. Think of a circle as the shape a laser pointer makes as it rotates around the axis of a cylinder. If the pointer also moves down the axis as it rotates we get the helix. If the point moves axially and rotates while moving away from the vertex of a cone the shape traced on the cone is a linear spiral. If it does the same in a logarithmic come (like a trumpet bell) you get the Golden Spiral. Somehow you've moved in your explorations of space from a cylindrical space to a logarithmic space.
It's an amazing thing when I see the mathematically untrained mind make these associations. There's an underlying truth to the math that can be accessed by the mind without the formal tools that makes me think the truths are either an artifact of our minds or of reality itself. This is the quest that Escher spent his later life in exploring in profound ways.
And, from the math guy, this is a circle mapped to another domain. The equation of the golden spiral which The Great Wave uses as its wave shape is r=a exp(bθ), the logarithmic spiral or Archimedes Spiral. If you set b=0, the equation becomes r=a exp(0) =a(1) = a, a spiral which doesn't grow in radius, otherwise known as a circle. So the spiral is just a circle with the suppressed constant mapped to a monotonic exponential. Think of a circle as the shape a laser pointer makes as it rotates around the axis of a cylinder. If the pointer also moves down the axis as it rotates we get the helix. If the point moves axially and rotates while moving away from the vertex of a cone the shape traced on the cone is a linear spiral. If it does the same in a logarithmic come (like a trumpet bell) you get the Golden Spiral. Somehow you've moved in your explorations of space from a cylindrical space to a logarithmic space.
It's an amazing thing when I see the mathematically untrained mind make these associations. There's an underlying truth to the math that can be accessed by the mind without the formal tools that makes me think the truths are either an artifact of our minds or of reality itself. This is the quest that Escher spent his later life in exploring in profound ways.
Independence Day 2012
I should have updated with the 4th of July a few days ago. Oh well. It didn't happen, so this is kind of a "super-post". We also went camping and back to Flagstaff over the weekend. If I don't get to that in this entry, I will follow up with that tomorrow!
Anyone that knows me knows that I'm not a fan of Independence Day. It has nothing to do with America, patriotism, American History, hot dogs or fireworks. Nope. It has to do with it being JULY.
July here in hell.
Well, this year was a gift.
We came close to setting a record. Usually when we talk about "records" in the summer, it usually means record high hot temperatures. For example, in 1989 the July 4th high was 118F. At the time, that was a record all-time high. It didn't last very long. We hit the 122F high the following year on June 26th. Oh yeah. This is where I live, people. And I'm still here.
But nope - this was the best kind of record "high". I'm not sure what the all time record is, but this year's 4th of July we had a record low temperature as that day's high temperature. Those are my favorites! (as a side-note, I especially love when it happens in the winter and we have crazy cold temperatures. It upsets all the transplants who moved here to escape the cold. Haha on them!)
One article said: Strange weather, Phoenix records the coolest fourth of July in 100 years and flooding south of the city. One of the comments on that article took the words out of my mouth: "It was so nice yesterday, I don't ever remember a July fourth having rain and being this pleasant." The official record is in 1912 by one degree. You know what, I'll consider this year's Independence Day a record! Close enough for me!
Usually on the 4th, I don't want to see fireworks. I'll be okay going out to dinner, but that's it. However, we headed to the Crosby's and sitting outside wasn't something to dread.
Dad and X-man! |
Mom and crazy X-man! |
Alexander doesn't like being held still for anything. But he was happy being squirmy. |
When Christian first saw me with the camera, he did a backflip thing. |
Re-surfaced! |
Mikelle and Ryann Kreps |
Ryann, Katie Crosby and Mikelle |
Bruce's way to be patriotic. A Charlton Heston Planet of the Apres Centerpiece. God Bless America. |
Alexander - waiting for fireworks. He was running all over the place. This was a rare second of stationary activity. |
Ryann, Mikelle and Katie |
Joshua Kreps, Ryann Kreps and Mikelle |
Christian and Alexander (note Alexander is in a different chair. I think he hit them all) |
Ryann, Katie, Mikelle and Alexander |
Christian |
Alexander being held by some weirdo. (Tev Kreps) |
We went to the ward campout and then hit Flagstaff for the second weekend in a row. The cool 4th was gone as quick as it came and it was time to get out of here again! But sadly, we got back late last night. And tomorrow's high? 112. At least we had that gift on Independence Day!
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