On the Third Hand

Part of a student's difficulty with simplifying expressions is the blurry extension of real number operations beyond the dyadic operators of add and multiply in the field properties. For conciseness, an "agreed-to" order of operations must then include non-field operators (dyadic and monadic) and semi-logical operators. The field properties do not specify that multiplication comes before addition, and most certainly does not demand that exponents be done before multiplication. Indeed, radicals, division, and subtraction operations are usually defined at the elementary level in terms of conversion to their inverse operation: radicals to exponents, division to multiplication, and subtraction to addition. Indeed, any algebraic expression with mixed operators requires punctuation in the form of grouping symbols to specify the priority of operations UNLESS the writer and reader agree to an order of operations for incompletely punctuated expressions. Even the simplest mixed...

John talks to Clem about skydiving. Clem is hesitant because jumping out of plane just for the sake of falling doesn't make a lot of sense, but John insists that such a stunt will make a big difference in Clem's life. Clem says, "You wouldn't lie to me would you, John."  John says, "No way. I guarantee your life will be better, and jumping will be the greatest experience of your life. And better yet, all those people who made fun of you over the years will look at you in awe and Tweet 'OMG, he jumped out of a plane. LOL." So Clem says, "Well, maybe ... How does it work?" "First," John says, "we go up in a plane--" "What kind of plane?" "Why the very best of planes. Big luxurious seats. Drinks served. It will be the greatest experience of your life. Then the instructor will give you a parachute--" "What kind of parachute?" Clem asks. "The very best kind of parachute. ...

Rant for the Day: I prefer buying a car by comparison shopping and then selecting the dealer who gives me the best price. But a classic dealer tactic is high-pressure negotiation in which they push the buy-now special to keep me from comparing prices and included accessories elsewhere. How frustrating to buy a car and then find your neighbor bought the same car from the same dealer the next day for $500 less. Dealer invoices don't help, because they don't show dealer incentives and rebates. Neither do they show the influence of the bank that actually owns the dealer's stock. If you think that buying a car is complicated, consider buying healthcare. Despite claims to the contrary, IMHO, you can't reliably comparison shop hospitals and doctors. You may put off buying a car for a week while you compare prices, but that emergency bypass is not likely to wait. Moreover, surgeons and hospitals don't have the brand-name consistency of Ford or Toyota. I've yet to ...

I e-filed my income tax this year. The process was relatively painless compared to previous years where they wanted to charge you a premium to make the data entry for the government easier. I refuse to pay $20 for the privilege of filing on line. It was free with my tax software this year, so I was happy to use it. I hope my meager refund is deposited to my checking account without additional excitement. Not that I am enthusiastic about paying income tax. I am not enthusiastic about paying taxes in general. But I realize that taxes are necessary to fund essential services from the government. That creates a debate on two ends: the paying end and the spending (budget) end. Consider the paying end first. My main concern about paying taxes is that I pay my fair share. This is not the day for me to argue about government waste and frivolous spending. The overhead in a democracy is that I end up paying for a service that someone else claims is essential, but that I believe is frivol...

In 1812  Governor Gerry of Massacusettes redistricted his state to give his party a political advantage. The resulting boundary lines altered the shape about Essex county until it resembled a salamander. Governor Gerry inaugurated the time-honored political tradition of the gerrymander. There are two views of representation for nationwide offices. The view on the one hand is that a representative should be attached to a geographical locale. So it is that we have Senators who represent a state without regard to the population of the state. On the other hand, there is a  view that representation should be based on people rather than on geography. That is one reason for the national census, constitutionally mandated to be taken at regular intervals. Population defines the allocation of Congressmen assigned to a state. Notice that there is still a strong geographical content to congressional representation, and the redrawing of political boundaries within a state are an effort...

Well, we sprang forward again to enjoy the benefits of a longer daylight afternoon. I don't mind Ben Franklin's conceit all that much, it's the execution I find flawed. First, two arbitrary, early Sunday morning dates are chosen by those in charge for the translation of temporal axes. Few people change their clocks at 2:00 AM, and the surprise the next morning is punctuated by "What time is it?" or groans from revisionistic sleep. [ Congress in the  Energy Policy Act of 2005  established that in 2009, daylight time begins on March 8 and ends on November 1] I wear an "atomic" wristwatch synchronized to standard time in Colorado. My watch really isn't atomic, but it is radio linked to the time given by the cesium fountain atomic clock in Boulder. Several clocks in my house have the same feature. My computers get corrected time on-line. I like the automatic adjustment feature. When I wake up Sunday morning in March, the only surprise for me ...

ayo - loose and flying away, describing a kite when the string is cut and it flies away. masala - gossipy embellishments in repeating a story.   You can imagine the tiny snap, followed by a sorrowful gasp as the kite's string breaks: Adios ayo.  On second thought, you can imagine the horrific thud to chop the kite line, followed by a scream of agony at the loss. For a quite a few years, breaking into book fiction has been difficult. As publishers, with rare exception, refused to accept unsolicited manuscripts, authors were forced to find an agent to represent them. The publisher had a buyers market: more good submissions than they could wade through. Of course, there was an even larger supply of illiterates who were writing the great American novel, and so the cost of sifting through submissions became very expensive. By shifting the burden to agents, the publisher achieved a way to control the avalanche of manuscripts, particularly those that were less than good, and  some of th...