Tobi Lehman's blog

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Math has no god particle

mathematics economics
There is an interesting article from FiveThirtyEight about the Atlas of Lie Groups and Representations, and more generally about why mathematicians are reluctant to talk to the press. They explore the difference between physicists and mathematicians with respect to the press. This point came up: The asymmetry in storytelling between math and the other sciences may also be because the research has different start-up costs. You need billions of dollars to build an enormous tunnel to house a particle accelerator to discover evidence of the God particle, also known as the Higgs boson. Read more...

Fractals in Elm

fractals elm
Elm is a purely functional language, similar to Haskell. What makes it interesting is that it is built to compile to JavaScript. It also comes with libraries for generating HTML and SVG using ordinary functions. The architecture of Elm applications is also very simple and easy to reason about. Elm MVC Architecture An Elm application defines a Model type, an update function, and view function. The signatures of these two functions are instructive: Read more...

Seeing the bulk: a primer on dimensionality reduction

If you haven’t seen Interstellar, you might not get the reference in the title. Don’t sweat it, the bulk beings are some advanced civilization that is able to move outside the familiar 3D space that we are stuck in. A similar plot device was used in Edwin Abbott’s book Flatland. Outside of entertainment, there is a lot of value in attempting to understand high dimensional spaces. Physics, machine learning, and engineering control systems all make use of higher-dimensional spaces in one way or another. Read more...

Word embeddings and semantics

Can a machine understand what a word means? Right now machines routinely correct spelling and grammar, but are pretty useless when it comes to semantics. Search engines are an exception, they have a rudimentary understanding of what words mean. One of the ways this can work is explored in Tomas Mikolov’s 2013 paper on word embeddings. Word embeddings are mappings from sets of words to vectors, such that the distances between the vectors represent the semantic similarity of the words. Read more...
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Computer programmer and amateur mathematician. Lives in rainy Portland, Oregon, United States. Read more


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