The Straight Dope 07/01/2005

The Straight Dope -- By Cecil Adams
http://www.straightdope.com

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THE STRAIGHT DOPE 07/01/2005

Dear Cecil:

Several months ago I posed a question concerning the
confusing (and potentially misleading) statistics placed
on toothpastes, which my paranoid mind attributes to
advertising spin and possibly outright lies by toothpaste
makers. Wanting to get the most fluoride bang for my
buck, I trusted only your answer because I know firsthand
just how expensive it is to maintain (and replace) my
teeth. I consistently check your column and understand
that not all questions are answered, and that some
questions are follow-ups on previous material. But today
I see a brand new article on coprophagia, of all things.
I am hoping that a serious question didn't fall on ears
deaf to all but the sensational or shocking. --Johnny
Henson, via e-mail

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Cecil replies:

Patience, chief. We get to everything (of consequence)
eventually. Besides, after a column on coprophagia, what
could be more fitting than one on the best way to clean
your teeth?

Your original letter made a number of observations: (1)
The price range for toothpaste is surprisingly wide. Sure
enough, during a recent casual survey at the supermarket
I noticed that the price per ounce ranged from 17 cents
for Ultra Brite on sale to $3.00 for Rembrandt Plus
"premium whitening toothpaste with fluoride." (2) Most
toothpastes contain pretty much the same proportions of
the same active ingredients. (3) However, not all do.
Presumably you refer to the fact that most toothpastes
use sodium fluoride (NaF) for cavity control while some
use sodium monofluorophosphate (SMFP). A few also include
ingredients to control gingivitis (inflamed gums) and
tooth sensitivity, but, oddly, none lists an active
ingredient to make teeth whiter, a common toothpaste
claim. Your unsurprising questions: What gives, and which
toothpaste is best?

Fluoride first. 

For more, see:
http://www.straightdope.com/columns/050701.html

STAFF REPORT

Dear Straight Dope:

What exactly is the deal with perfect numbers and why are
only 38 recognized? Is there some sort of math mafia that
limits this sort of thing or what? --Mac McCartney

Guest contributor Mathochist replies:

Perfect numbers are one of those holdovers from the days
of the Pythagoreans, when mathematicians were mystics as
much as anything else and put a lot more stock in
coincidence. 

Start with a number. Find all the numbers that divide it
evenly. Add them all up (other than the number itself),
and sometimes you'll get your original number back again.
These are the perfect numbers. For example, 6 is evenly
divisible by 1, 2, and 3. 1+2+3 = 6. Others are [see
reference 1]: 

28
496
8,128
33,550,336
137,438,691,328
2,305,843,008,139,952,128
2,658,455,991,569,831,744,654,692,615,953,842,176
191,561,942,608,236,107,294,793,378,084,303,638,130,997,321,548,169,216

These are the first 9 of the 38 known perfect numbers.
Luckily, we don't have to factor and add up the divisors
to check these. Euler proved in 1747 that even perfect
numbers all have the form 2n-1(2n-1), where 2n-1 is a
kind of prime number called a Mersenne prime. Also, given
a Mersenne prime, applying the formula will always give a
perfect number. That is, Mersenne primes and even perfect
numbers go hand in hand. 

For more, see: 
http://www.straightdope.com/mailbag/mperfectnumbers.html

STRAIGHT DOPE CLASSIC - 04/17/1987

Dear Cecil: 

A couple years ago a friend of mine who owns a small
recording studio mentioned that a client wanted to record
a bunch of different subliminal messages on separate
tracks and then mix them all down into one hodgepodge
under ocean waves or some other masking sound. The idea
was that the unconscious mind could sort out and soak up
all this knowledge, reprogramming your brain for better
golf scores, better relationships, an end to smoking or
procrastination, financial independence, enhanced sex,
and anything else they felt like including.  More
recently, while flipping through the UHF channels, I
discovered some success motivation lecturer types
offering their own subliminal tapes with hundreds of
multilayered, multitracked affirmations to improve every
aspect of your life. It all smacks of snake-oil salesmen
selling rose-colored water from the back of a medicine
wagon to me. What's the straight dope on the unconscious
mind's ability to absorb even one subliminal message,
much less hundreds at one time? Is it really possible to
reprogram my head? --Ken, Panorama City, California

Dear Ken:  

Having once participated in a four-year study of
the unconscious mind's ability to absorb subliminal
messages (in those days it was called "going to
college"), I can assure you the technology ain't what
it's cracked up to be. However, things have come a long
way in the last few years. While it's doubtful that
subliminal cassette tapes do much besides lighten your
wallet, there's a considerable body of evidence to
suggest that subliminal messages can improve performance
under some conditions. A couple years ago researchers
Lloyd Silverman and Joel Weinberger published a paper
summarizing numerous experiments, the gist of which was
that if you flashed a certain message before and after
some other, more conventional training technique (e.g.,
antismoking therapy), you greatly enhanced the therapy's
effectiveness.  

Now things start to get weird. 

For more, see:
http://www.straightdope.com/classics/a2_324.html

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