Hi everyone! I’m moving my blog to @chaoticaldynamics
Long story, but tumblr is a chaotic website. Follow me there if you are interested!
Don’t worry. Start now. Get up, take a few deep breaths, stretch, count to ten with your eyes closed. Then take out your books and a notebook and a pen. Get on with it. Start reading, annotating, take down your notes. If you feel your focus faltering, sit back, take a few deep breaths, walk around a bit, get back to your books. It’s never too late.
Mr. Hozier, ladies and gentlemen
Littlewood polynomials are polynomials all of whose coefficients are either +1 or −1 (so even 0 is not allowed). If you take all Littlewood polynomials up to a certain degree, calculate all their (complex) roots, and plot those roots in the complex plane, then you get a beautiful fractal-like structure above.
The image is slightly misleading, because the “holes” on the unit circle tend to completely fill in if the degree goes up. Intuitively, the holes mean that complex numbers on the unit circle that are close to low-degree roots of unity are hard to approximate by low-degree Littlewood polynomials (unless they already are roots of unity).
In particular the structure at the edge of the ring is deeply interesting. Notice the familiarity with the dragon curve?
I’m a “late” PhD student and it’s the best decision I’ve ever taken.
Yes, everyone is younger than me. But this is my place, my time and my moment. Everyone has their speed and this is mine.
you’re not falling behind. you are still young and have a whole life ahead of you. you have enough time to explore things u love and experience your life and make your goals come true and find reasons to live. take things one day at a time and don’t let the fear of falling behind stop you because life isn’t a race.
Small and angry.PhD student. Mathematics. Slow person. Side blog, follow with @talrg.
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