Yesterday Was Hard.

“they’re burning all the witches” 

ARTIST CREDIT

A 392 year-old shark found in the Arctic. This guy was wandering the oceans back in 1627.

“You ruin your life by desensitizing yourself. We are all afraid to say too much, to feel too deeply, to let people know what they mean to us. Caring is not synonymous with crazy. Expressing to someone how special they are to you will make you vulnerable. There is no denying that. However, that is nothing to be ashamed of. There is something breathtakingly beautiful in the moments of smaller magic that occur when you strip down and are honest with those who are important to you. Let that girl know that she inspires you. Tell your mother you love her in front of your friends. Express, express, express. Open yourself up, do not harden yourself to the world, and be bold in who, and how, you love. There is courage in that.”

— Biance Sparacino (How To Ruin Your Life Without Even Noticing That You Are)

The topologist’s sine curve.

Limts: f(x)=sin(1/x) is a rare example of a function with a non-existent one-sided limit. More technically, f(x)=sin(1/x) is defined for all numbers greater than zero, yet the limit as x approaches zero from the right of f(x)=sin(1/x) does not exist. This can be reasoned by considering the value of f at x-values near zero. Informally, f(near zero) could be 1 f(just a bit closer to zero) could be -1 so f(numbers near zero) does not seem to settle on a single y-value.

Continuity: Note that f is continuous for all numbers greater than zero but not continuous at x=0 since f is undefined there. Even if we were to “fill in the bad point” and let f(0)=0, the function would still not be continuous at zero! (note this is the natural choice as sin(0)=0). We can see that the adjusted f is still not continuous at zero since the sequence x_n=1/(pi/2+npi) converges but f(1/x_n) is the sequence (-1)^n which does not converge. This is similar to the argument above. In other words, closing in on x=0, we can keep finding x values such that f(x)=-1 and f(x)=1.

Topology: In topology, the topologist’s sine curve is a classic example of a space that is connected but not path connected. This space is formed in R^2 by taking the graph of f(x)=sin(1/x) together with its limit points (the line segment on the y-axis [-1,1], the red line on the second image). The graph of f is connected to this line segment as f and the segment cannot be sepearted by an open disc (no matter how small). This can be informally reasoned by the zooming illustration in the second image. But the space is not path connected by the sequence argument above (there is no path to the point (0,0)).

Image credits: http://mathworld.wolfram.com/TopologistsSineCurve.html and https://simomaths.wordpress.com/2013/03/10/topology-locally-connected-and-locally-path-connected-spaces/

And then use them for super and subindexes, of course

Raindrops, Flashcards, summaries, knitting and ginger tea.

Unexpected great discoveries. Calculating the cosmos: How mathematics unveils the universe. By Ian Stewart.

being a woman isn’t about the body you were born with or your feelings or your brain it’s about being haunted by this quote from margaret atwood for your entire life

Echoes

I made this painting for the Spellbinders gallery show at @gallerynucleus 💕✨ The opening is on 23rd, if you are in LA then come check it out. I’ll be there signing my new books and also holding a workshop ✨