The representation of an integer in base b
has some digits
. For example the
number 42 = 4×101
=2 in base b
It's sometimes convenient to switch to a different base, frequently
=2) or hexadecimal (b
=16). Is there ever a
reason to switch to noninteger b
? What pathologies would
a representation have?
2009-04-20 Monday 14:39:54
A black hole at the end of its Hawking evaporation radiates
with some very large power. But the high-power period
doesn't last very long, since the mass is so small.
Apparently the overall luminosity is small enough
that it'd be hard to see a radiating black hole outside
the solar system.
What limit can you set on the density of
very small black holes
knowing only that, say, there are none in the room right now?
2009-02-04 Wednesday 22:19:29
A jugful of water adds some thermal inertia and makes an empty
refrigerator cool more efficiently. A tubful of water ought to
do the same thing for drafty old house. How big is the effect?
2008-12-08 Monday 09:59:41
In quantum mechanics, the one-dimensional square well with periodic
boundary conditions has a solution with wavenumber zero. How does
this compare to the Goldstone boson in a very stiff "Mexican hat"
2008-11-03 Monday 23:06:09
Suppose I replace an incandescent light bulb with a more expensive,
more energy-efficient, longer-lived light — a CFL, an LED,
whatever — based on the expectation that it'll cost less over
its life. How old does my incandescent bulb have to be before I
actually save anything?
2008-10-28 Tuesday 21:42:08
Suppose I wanted to check the accuracy of an ensemble of weather
forecasts (e.g. "30% chance of rain tonight"). What's
the right metric for doing this?
2008-10-09 Thursday 10:35:34
Among the different Nobel prizes, there is a big spread between
when work is done and when it is rewarded. The physics prizes seem
to go to people whose work decades ago has shaped research since,
while the peace prizes seem to go to people who are actively doing
notable things right now. What's the distribution of times
between doing something noteworthy and winning a prize for it? What
about less famous prizes?
2008-10-08 Wednesday 10:54:38
Fresh Air interviewed
Katharine Jefferts Schori
, the primate of the US Episcopal
Church, who has a doctorate in oceanography. Are advanced degrees
in the sciences more common, or less common, in the clergy than in
other nontechnical fields? How does the frequency change across
2008-10-08 Wednesday 10:27:03
Suppose two stationary states in a nucleus differ only by their
(total) isospin. What's physically different between them?
2008-10-07 Tuesday 09:53:07
by Consumer Reports
, that breakfast cereals marketed to
children aren't terribly nutritious, has gotten some
evening-news press. The main contribution of the Consumer Reports
release seems to be that they bought a bunch of cereal and read the
nutrition labels. What's new here? Has the composition of
existing products been tweaked? Have some sweeter brands been
introduced to replace healthier ones? How do these sorts of news
blobs correlate with sales, or with marketing spending?
2008-10-06 Monday 12:29:26