Today I Learned:
1) During World War II, one of the effects of the wartime emergency plans in the US was wage controls, meaning that US companies were not allowed to pay more than a certain amount to their employees. This was part of a larger set of price controls to reign in inflation. This was a bit problematic for companies because it meant they couldn't compete for better workers by raising prices. What they *could* do was offer other benefits that weren't restricted by law, which is how employer-paid healthcare became standard.
After the war, Harry Truman proposed a national universal healthcare system, which was quite popular but opposed by doctors and hospitals, who had a lot of money in the private health insurance business, and labor unions, for whom employer-paid healthcare was a big trophy and bargaining chip. Truman lost.
2) ...how to frost glass! There are many ways to add a frosty finish to glass, but most of them are just variations on acid treatment (mostly using nasty fluoride-based acids of one form or another). You can also sand-blast glass, which is probably not as precise or nice as acid etching for, say, chemical glassware, but perhaps that's fine. If you're making many identical frosted glass pieces, you can also just etch the frosting into a glass mold.
3) A few abstract algebra terms:
Field: A field is a set of things on which "addition" and "multiplication" are defined (and their inverses, subtraction and division), such that the field is closed under both multiplcation and addition, and with some common sense properties satisfied for both operations (i.e., there is an addative and multiplicative identity, there are inverses for both operations for all elements of the field, both addition and subtraction are commutative and associative, and the distributive property holds). Some standard fields include the rational numbers, the real numbers, and the complex numbers. I tried really hard to come up with a good, instructive, non-numeric field, but I couldn't (the closest I could come up with was the set of lists of logical propositions, with addition being the set union of two lists of statements and multiplication being the list of all statements you could prove using two lists of statements, but it didn't really work out... for one thing, I'm not sure whether division is actually defined on such a "field"; for another, I couldn't come up with good addative and multiplicative identities that satisfied all of the properties of identities).
This is one of these terms that I keep learning and forgetting over and over again. Clearly I'm not using fields enough in my life.
Extension of a field: An extension of a field is basically a field that's a superset of another field. The most common example is the complex numbers, which are an extension of the real numbers -- it's the real numbers, "extended" with an extra element i and all the things you can get by adding and multiplying real numbers and i together. Another example would be the field consisting of all numbers of the form a + b*sqrt(2), where a and b are rational numbers -- this is the rational numbers extended with sqrt(2).
Automorphism: This is a mapping/function/rule that maps from a set onto itself and preserves some important property. Exactly what property is maintained depends on the kind of automorphism, but I think a good rule of thumb is that with an automorphism, if you add/multipy two elements together and apply the automorphism, it doesn't matter which one you do first (so for an automorphism A, you have A(x + y) = A(x) + A(y)).
Transcendental: This is a term I've heard all the time, but I never actually knew what it meant until today. A transcendental number (or element of a group) is one which cannot be defined as a root of an expression (usually a polynomial of some sort).
Also kind of learned about Galois groups, but at that point my comprehension dropped pretty precipitously. They may show up in a later TIL.
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