1. Don’t try to piss quietly. Nobody in a public restroom thinks you’re knitting in your stall. They came to piss, just like you. And if you have to take a dump, do it. Get over your fear of public toilets. It’ll make life a lot easier.
2. Masturbate. Masturbate a lot. Talk about it with your friends. You’ve got the right to make yourself feel good and brag about it just like all the boys with extra large kleenex packages on their desks.
3. If you want the large fries, get the large fries. Hunger and appetite are nothing to be ashamed of, just human. Don’t ever feel guilty for eating in front of others. You need to nourish your body to stay alive. We all do.
4. Laugh as loud as you have to, no matter if you snort or gasp or literally scream.
5. Fart when you have to.
6. Always remember you weren’t born to visually please others. Forget the phrase “what if they think it’s ugly”. If you think it’s lovely, it is lovely. You wanna wear it, wear it!
7. Speak your mind! You can learn to do so without insulting others or shoving your opinion down other people’s throats.
Anxious people can have a hard time staying motivated, period, because their intense focus on their worries distracts them from their goals
(click through the images to view in high-res)
Penrose tilings are an example of the non-periodic tilings discussed in the last post. Recall that these are tilings that cover the entire infinite plane leaving neither gaps nor overlaps. Whats nice about these tilings is that the set of tiles used to construct the Penrose tilings only consists of two different basic shapes consisting of quadrilaterals.
Whats even more remarkable about Penrose tilings is that using just these two shapes it is possible to construct infinitely many different tilings that cover the infinite plane. This infinity is infinitely bigger in size than the countable infinity of the whole numbers ( 1, 2, 3, 4, and so on), but rather equivalent to the uncountable infinity associated to the real numbers (which includes all whole numbers, fractions, and decimals with infinitely many digits).
Despite the existence of these infinitely many different Penrose tilings, there is one peculiar property they all exhibit. Consider any finite region, or patch, of one particular Penrose tiling. Then it is possible to find an exact copy of this patch in any other different Penrose tiling! Moreover, this patch occurs infinitely often in different spots in any given tiling! Note that this is true of any patch of any size no matter how big as long as its finite. This implies that if you were only able to examine a finite part of any Penrose tiling, you could never really distinguish that entire tiling from any other tiling. Thus, different Penrose tilings are only perfectly distinguishable in the infinite limit of the entire plane.
The images shown above display finite regions of Penrose tilings. They are constructed using an elegant "cut-and-project" method (also used here), which involves projecting the points of the integer lattice in 5-dimensional Euclidean space, onto a certain 2-dimensional plane. Connecting adjacent projected points in this plane by lines then yields a Penrose tiling.
- Penrose Tiles to Trapdoor Ciphers by Martin Gardner
- Algebraic Theory of Penrose’s Non-periodic Tiligns of the Plane by N.G. de Bruijn
- The Empire Problem in Penrose Tilings by Laura Effinger-Dean
Image Source: Wikipedia
Breaking Bad: Favorite moments → The Birth of Heisenberg (1x06)
“Have a seat, Heisenberg" "I don’t imagine I’ll be here very long.”
It’s hard not to let boys break your heart.