660 karma · joined March 26, 2010
In our experiments, we need to know how the frequency of an electromagnetic resonator will change when we couple it to a quantum system. We calculate these frequency shifts with integrals. Being able to calculate these integrals analytically for some limiting cases helps us understand the dependence on the parameters. And usually you can patch the limiting cases together and not even have to compute the integrals numerically.
"A coffee cup and a doughnut are homeomorphic because a coffee cup can be stretched into a doughnut. A doughnut cannot be a sphere because a sphere does not have any holes. Cutting is not allowed in topology but Homer finds a workaround by biting the doughnut, because if you bite the top off of an A and eat it, then the top no longer exists. Homer makes the doughnut and the sphere homeomorphic. And maybe that’s why he’s also called Homer."
"Imaginary numbers are not real—The geometric algebra of spacetime"
https://link.springer.com/article/10.1007/BF01883676
(http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/Im...)
https://theconversation.com/is-the-covid-19-pandemic-cure-re...
Although intermittent calorie restriction (CR) has been shown to lower IGF-1, this article shows that prolonged CR does not affect IGF-1 levels. However prolonged protein restriction, especially animal protein, _is_ shown to reduce IGF-1 levels.