Thank you goobster! Stop by any time for a beer, or an akvavit. Or better yet we can drink karsk, the local drink: put a one crown coin in the bottom of a coffee cup. Fill with coffee until you cannot see the coin any longer. Then add moonshine until you can see the coin again. Skål!
OK! I think it's a difficult question because it's really quite meaningless. All of our logic, all of the way we think, is developed from our interaction with the universe, in very fundamental ways. I am in my bed. My bed is in my room. Therefore I am in my room. In this way our logic develops. Mathematics is the body of knowledge that grows from this logic. It is a human construct and it does such an amazingly good job of describing the universe because it grew from the structure of the universe. So when we find a surprising result and then find an example of that result in nature, we are even more surprised and get a feeling of being small surrounded by The Big Mystery. "Was the math there or did we make it?" ignores the fact that we ourselves are a part of the mechanisms of the universe. To me, creating and discovering are the same. I am just happy I can take pleasure in the process! (I suspect that the universe itself is an emergent phenomenum that comes from the simplest of rules, "1+1=2" or even simpler, like "1". It only really makes sense to me to think that the universe is just one particle.)
Oooh! I might get a prize for this one! Thought I had a pneumothorax, a small hole in the lining of my lung. Just takes some antibiotics to fix, or so the google-machine told me. I was on my way to Paris for vacation and didn't want to bother until I got home. Got home and made an appointment to see the doctor after the weekend. I saw the doctor 11 days after the first indication of trouble. Turns out if I had waited a few more days I'd have been dead. They drained 3 liters of fluid out my lung in 24 hours, and continued to drain a liter a day for a month. Lymphoma. 3 years chemo, radiotherapy, surgery, the works. Moral: when it hurts to breathe, it's probably not nothing!
Inspired by veen, here is a fractal hubski animation. I know it would have to be a tricky sticker to animate. This has recursion level 4: And here's one with recursion level 6: Each group of 8 "satellites" has a total area equal to its "planet". The initial orbital distance of the first ring of 8 satellites varies in this animation (in the Hubski logo, they are spaced one satellite diameter away from the planet). Subsequent orbits are of the ratio of sqrt(2)-1, or approximately 0.4142. This makes the satellites of neighbors overlap precisely. I was pleased to find the ratio of sqrt(2)-1. I've done a lot of cool math with sqrt(2)+1, and so this is a new direction to explore!
Dude you are a genius. I love these. I make a lot of fractals myself. I love the first and the "pushing back the dark" one. Brilliant work!
I made a new necklace with 5 fives, but I'm away at a convention and don't have a picture of it today. So instead I will post one of my pictures that I really like. It seems to mostly elicit shrugs, but some folks have really loved it. It got gallery time and a tiny bit of press. It's called Pisces and it's based on binary counting numbers.
Congratulations! This will be fascinating to watch develop. Good luck TC!