As an erstwhile math major (I couldn't hack the honors basic algebra class - the difference between a euclidean domain and a principal ideal domain got too confusing; but I rocked proofs in analysis) I have to say that the author is confusing Mathematics (which is an art) and Arithmetic (which is a skill). Part of what make the opening farce absurd is that musical skills and painting are not terribly necessary as a matter of life and death, or even to a certain degree, quality of life or death; whereas understanding sums and compounding processes ARE.
While SALVIATI is completely correct in his analysis of the situation, he offers no solution, and I identify with SIMPLICIO more.
Perhaps the problem is that in our schools we conflate arithmetic with mathematics. Surely, they are related, but perhaps they need to be delineated and the difference understood.
> whereas understanding sums and compounding processes ARE [terribly necessary as a matter of life and death, or even to a certain degree, quality of life or death].
Please give one example applicable to a reasonable majority of human beings on the planet at this current time where "understanding sums and compounding processes" are a matter of life and death.
It seems probable that the subprime mortgage crisis was a contributing factor in a number of deaths, via suicide, stress-induced illness, or, with the help of alcohol, violent or vehicular incidents.
(1) The subprime mortgage crisis could not have been averted by a larger percentage of the population understanding sums and compounding processes.
(2) The advent of civilization was a contributing factor to everything that's happened in the last several thousand years, including the paper cut I just got.
you understand that interest-bearing loans are a compound process, right - and that an understanding thereof might be of relevance to someone entering into a loan agreement which they probably, if they really understood it, were not going to be able to repay...
But let's not only blame the borrowers of subprime loans, let's also ask whether the banks didn't entirely understand the risk models of the derivatives they were compiling out of subprime mortgages because many of their senior managers also didn't understand compounding processes, or, possibly, sums...
> an understanding thereof might be of relevance to someone entering into a loan agreement which they probably, if they really understood it, were not going to be able to repay...
Oh, it's relevant. It's sort of like how being able to load and fire a gun is relevant to the decision whether or not to commit suicide. Sure, it can modify one of the many, many details, but some people just make a noose and hang themselves.
Keep in mind, this is your argument: if more people in the world understood sums and compounding processes, this would have prevented the subprime mortgage crisis and thus the many deaths that were inspired by the resultant fallout. There is no possibility that anything else caused the crisis, and no possibility that anyone is at fault for these deaths other than parents and teachers.
This claim, if true, actually absolves the lenders that you talk about below, because they can be held responsible only for their own understanding of sums and compounding processes.
Amusingly, if you accept your argument, you can also make an interesting inverse version. The fact that lenders understood sums and compounding processes led to their employment at unscrupulous institutions which then mandated their sign-off on high-risk mortgages, which then caused the deaths of all those people.
did you not read what I wrote? "or quality of life [or quality of death]". Nor did I proclaim that the life-or-death situation was applicable to a majority of people.
Your point is lost if it's not applicable to a significant majority. If it's only applicable to a minority, then that minority ought to be identified and specially trained, like we do with peanut allergies.
> The difference between a euclidean domain and a principal ideal domain
A Euclidean domain is an integral domain where the Euclidean algorithm works. For the Euclidean algorithm to work, you need to be able to divide two elements and produce a remainder that's smaller than the divisor.
So an ED requires a notion of "smallness" (the Euclidean norm) which interacts with division in a way that makes the Euclidean algorithm work (remainder is always smaller than divisor).
A principal ideal domain is an integral domain where every ideal is principal (can be generated by one element). It can be useful for you to know that certain situations cannot happen, e.g. in a PID you can say, "Let I be an ideal of D, then I = <g>..." and do something with the generating element g. It lets you pass from an ideal to a single generating element in a proof, which may be a useful capability. The PID concept is also part of a taxonomy, since Euclidean domains ⊆ principal ideal domains.
yes, I know what the technical definition is, but I never felt like I understood in a deep, mechanistic way, why all EDs are PIDs, beyond the constructive proof, and while I could prove that some wierd Q[some element] was a PID, but !ED, I never felt like I truly understood why. Mathematical taxonomy always wierded me out, maybe I took the Rutherford quote "all science is either physics or stamp collecting" too seriously.
While SALVIATI is completely correct in his analysis of the situation, he offers no solution, and I identify with SIMPLICIO more.
Perhaps the problem is that in our schools we conflate arithmetic with mathematics. Surely, they are related, but perhaps they need to be delineated and the difference understood.