Mysteries of Man and Nature

I've been contemplating three mysteries.  The first is a simple one of human nature and unbounded greed, amplified by the normal tendency of people to not pay attention.  The second seems to be in the same category, but it may also have subtleties of which I'm unaware, and about which I call on my thousands of millireaders for elucidation.  It presents an opportunity for people everywhere to save a trivial amount of money with excessive effort, but in a feel-good way.  The final mystery pits this blogger against the mysteries of the cosmos. 

Mystery 1:  American Express Reward Points

When you spend money using an AmEx card after signing up for their "Rewards" program, you get a point for ever dollar you spend. These points are, in effect, a rebate on the money you spend using the card, or you can think of it as a discount on the merchandise you buy.  (This discount, of course comes out of the seller's pocket, along with the card fees.  The recent change in the credit card laws did nothing to make it easier to allow merchants to offer discounts for cash or to charge extra for card usage.)

These "points" can be used to buy merchandise and, depending on what you buy, are worth from a fraction of a penny to a penny each.  For example, I recently redeemed 20,000 points for a $200 certificate to purchase a $300 Dell netbook computer.  So far so good, or at least so far somewhat rational.  But what if you're short of points?  AmEx, which redeems points at 100 for a dollar, will also sell them to you at 250 points for a dollar.  The mystery, of course, is not why AmEx does this, but why anyone anywhere would be stupid enough to buy extra points.  If there were such a thing as felony arbitrage, this would be the prime example.  It's comforting that nobody I know, and certainly nobody with the sagacity to read this blog, would ever consider doing such a thing.

Mystery 2:  The Price of Gas

This trick seems to work.  Note that the prices for full service, regular gas are only a few pennies apart.  Even majestic Exxon, the most valuable company on earth, sells the hoi polloi a gallon of gas for only four cents per gallon more than does First, whoever they might be.  But look at the prices for "PLUS" grade!

I had always understood that the "plus" grade was created by blending the regular and the premium, in more or less equal proportions, to achieve an intermediate octane rating.  In the old days this was carried to extremes by Amoco, which had five blended grades, if memory serves.  One would assume that, if there is a price for premium and a price for "regular," then the blended gas would have an intermediate price in proportion to the percentage of each in the final mix.  This seems to be the case in the left photo, almost the case in the center one, and bizarrely out of whack at the Exxon pump.  Assuming that the Exxon "plus" grade isn't almost all premium, but rather a 50-50 mix, why wouldn't anyone using "plus" not just fill half his tank with full premium and the other half with regular, thus pumping himself a $.10/gallon discount?  Why not indeed?

I can think of several reasons.  One is that I'm wrong about how the mixing works.  One is that it doesn't occur to them and that they didn't read this blogitem.  One is that they're not as cheap as I am.  Of course it could be all three.

Mystery 3: Big G

A few weeks ago I speculated that the reason for the anomalous results of "cold fusion" experiments might lie in the possibility that "dark matter" is somehow responsible.  I was careful to point out that I have no factual basis for this guess; it's just something that occurred to me that "explained" the results and that wasn't, prima facie, impossible or illogical.  Subsequent to that blogitem, I have spent a number of commutes just thinking about ways to "falsify" the guess and thus save myself the necessity of actually doing the experiment I outlined.  One thing I considered was that ordinary measurements of gravity might provide enough information to show that I was wrong or "not even wrong" as Pauli put it.

"Big G" is the colloquial name for the universal gravitational constant.  Most physical constants can be measured to great accuracy.  Time or frequency, for example, can be compared (with great difficulty) to about 18 decimal places!  There's no difficulty in measuring time to about 11 decimal places for $100 worth of hardware.  Contrast this with the careful, exquisite experiments needed to measure the gravitational constant to a paltry 4 decimal places.

My guess about dark matter requires it to have certain characteristics. 

• It cannot be completely diffuse throughout the universe.  If it were, it would have no gravitational effects at all, and the galaxies would look very different according to current theory.

• It cannot be very strongly clumped as ordinary matter is.  Otherwise it would be easily observable by gravitational effects, e.g., if a dark matter stars or dark matter planets existed, they would stand out in astronomical studies.

• Therefore it must have some variable density structure, but the nature of that structure is poorly bounded.

The first two are ruled out by observation, so it would seem that the third is correct.  It would be nice to be able to say "Let's measure gravity at a certain location and see how it varies" and then ascribe that to the presence of shifting dark matter "clouds" (or whatever).  But that is difficult to do to any great precision since gravity is so hard to measure, varies slightly for other reasons (the earth isn't solid, lunar motion, etc.), and unless the dark matter effect on gravity were extremely strong, it might not even be above the noise level. 

One interesting addendum, which neither those who did the measurements nor anyone else has yet figured out, is that some recent precision measurements of Big G differ by more than the error margins of the experiments.  Does this have anything to do with dark matter, as I speculate cold fusion might?  I have no idea, but so far, as you can see above, there doesn't seem to be any known information about dark matter that immediately falsifies my speculation about its effect.  With regard to its effect on Big G, one wacky guess at a time...

NP: "Visions" The Looking Glasses

TotD From the Bungonia Optical SETI site in Australia.  I don't remember the circumstances by which this shirt fell into my collection.

Yesterday  |  Tomorrow