I'm not very sure about the vinegar + steal wool part... that makes ferrous acetate pretty quickly, and what we want here is a ferro-gallate. I think there are ways of producing ferro-gallate inks without using sulfates, but historically ferrous sulfate was commonly used ( and leads to paper being eaten away over time )
Excellent comment. I'm one of those people who always thought: "I can't draw". Now I understand that for me it is a matter of practice. I started with Drawing on the Right Side of the Brain.
This book is not really addressing the more common "is math real" question of it being empirical or invented. For an interesting take on that question, see the 1st section of the 2nd part of Daniel Shanks' Solved and Unsolved Problems in Number Theory. He makes some interesting points about the old Pythagorean views
I don't disagree with you, but this is a horribly sad comment. I worry that the text of papers often gives short shrift to nuance and subtlety that is necessary for reasonable interpretation.
I've also been roasting coffee from Sweet Maria's for many years, and the thing that's useful is that I learned how Tom will describe flavors that I like. So, whether he calls it "hazelnut" or "almond" doesn't matter, but when he says "hazelnut" there is a flavor I enjoy that isn't there when he writes "almond"... and some other things like when he writes 'crowd pleasing" there is likely to be a lot of balance... over time the descriptions have become more and more useful to me!
good comment. This seems to come up more in number theory than in foundations/philosophy of mathematics, but I agree is has an important place. Not just triangles, but natural numbers having a fundamental place in reality ( e.g. integral numbers of dimensions, degrees of equations at the foundations of physics, etc., etc. Daniel Shanks has a list of about 60 of these "arguments" for Pythagorean interpretation of numbers )
There was a paper a few years ago in the American Mathematical Monthly ( sorry... can't remember the author, I think it was a Russian mathematician ) that gave some interesting heuristics for why this form is natural to consider, where the 1/30 comes from ( and considerations of a couple of alternatives to the "30" ), and the kind of intuition/thinking that Ramanujan may have used. When you only see the final form of the equation like this, it looks very mysterious and impossible that someone could find it ( and to be fair, there are other results from Ramanujan that are definitely in that class! ). Probably a google search could find the paper, it was delightful to read.
Agreed, and current estimates are more on the order of 4 to 5 per million. A high proportion of these cases are among people with a history of anaphylactic reactions to drugs, needle sticks or food/tree nuts ( many were already carrying their own epi pens! ) so it includes people who probably would skip an annual flu vaccine but of course do not want to skip this one. I'm not trying to suggest that the rate isn't higher than other vaccines, but it may not be as much higher as it first appeared. ( Also, to be fair, now that there is so much vigilance, it's possible that a number of pre-anaphylaxis are being caught early and treated with epi or benadryl before they could become full-blown anaphylaxis. So, this could make the rate appear lower. These things always need to be considered thoughtfully! )
As others have pointed out, the risk/benefit calculation here is extreme: a few bad reactions per million vs. a disease that has already killed more than 1000 people per million population in the US.
If you've got enough math background to follow it, Harold Edwards' Riemann's Zeta Function is a gem of a book and available inexpensively from Dover. There is an English translation of Riemann's paper at the end of the book. I spent a worthwhile few weeks of spare time working my way through the paper ( and a lot of pencil & paper to work "between" the steps in the paper -- math is not a spectator sport ) with a longish diversion diving into the gamma function along the way.
Interesting point about Bayesian methods, whenever there are potential flaws or additional uncertainty, it's better if they are more explicit to prompt thoughtful interpretation.