The bull case is that everyone losing their jobs will accelerate and bring about the socialist revolution, giving us universal basic income and universal healthcare.
The first app that lets you type in an implicit curve and get a graph of its level set is a very different claim from "For all the history of computational mathematical visualization, graphing equations has been done in binary mode".
The millions of brightly-colored fractal posters adorning walls in the 80s are a very clear counter-example to your claim.
Your app is cool and the visualization is neat. The hyperbolic claims of originality really detract from that.
To be fair, yes, there are some places where non-binary graphing has been done (like error gradient graphs in AI), but as far as I know, this is the first app where you can type in a basic x/y equation and get a non-binary graph.
Lee taught Intro to Topological Manifolds for one quarter, and then the next two quarters where Intro to Smooth Manifolds. Then Riemannian, then vector bundles, and then complex manifolds.
Yesterday there was an article about how the ear works more like a Gabor transform or a wavelet transform than a Fourier transform, both of which are Short Time Fourier Transforms, so yes!
A function (which is an isomorphism) from complex numbers a+bi to matrices is a+bi |-> [[a,-b],[b,a]] where the matrix is listed by rows. So i is sent to the matrix R with a 0 in the top left, 1 in the bottom left, 0 in the bottom right and a -1 in the top right. R is a 90 degree rotation, you can check that it sends the unit vector [1,0] on the x-axis to [0,1], and the unit vector [0,1] on the y-axis to [-1,0].
reply