I know I haven't posted in a while. I haven't had much interesting to post about. But there have been enough little things that I guess I'll post them now.
- For one, shame on the math-blog-o-sphere for not rushing to my aid over my pi problem from my previous post. I'm still looking for any convincing arguement one way or the other. The future of pi is at stake here, folks, I expect a little bit more thought. Which is my way of saying...I'm not smart enough to figure out the answer myself.
- A guy came to speak at my school about politics in my state. He wasn't the greatest or most coherent speaker, but he made some good points. One of them was the distinction between 'technical' and 'adaptive' as adjectives to describe problems and solutions. I don't remember the source he cited as the origin of these terms. In the medical world, a technical problem is something like "you have a bacterial infection", and it requires a technical solution like "take these antibiotics". An adaptive problem is more like "you're in very bad shape", and it requires an adaptive solution like "change your outlook on food and exercise". In politics, he says, legislatures are very good at coming up with technical solutions to technical problems. People are dying from car accidents? Require seat belts and air bags. That works, demonstrably. But they also offer technical solutions to adaptive problems like race relations or energy consumption. These require solutions like "learn to see structural racism instead of merely individual racism" and "give up your idea of the ideal house so you can live closer to work". He cited Lyndon Johnson's approach to the civil rights movement (don't act impulsively, let the country internalize how awful the status quo is via watching Black people get beaten up for sitting at a lunch counter) as a good example of an adaptive solution. We have to find a way to make the entire country have more of a stake in racism. This is essentially what Ampersand says in this blog post (on a blog I've been spending rather a lot of time reading).
- I'm not looking forward to grading for hours this weekend, but I do suspect that these tests went well. I've found myself thinking more and more that it's good to trade speed for depth of understanding in my classes. That is, I'd rather go slow and have the top kids understand the very minute subtleties and the middle kids really get the basics. I find it makes things much easier when we get to more advanced topics, although it means we may not get to as many. Maybe I'm just getting soft in my old (hah!) age.
- It now looks like it will be a good 6 months longer than we thought before we can go to China to pick up the baby we have been in the process of adopting for about a year now. October or November of next year seems most probably. My wife is not good at waiting. I tend to take life one day at a time more than she does, so the wait doesn't seem as daunting for me. But I've been regretting my undauntedness because it makes me seem callous to my wife's difficulty with the wait. I don't doubt that my reaction appears cool and uncaring to her, even when I'm caring for her. I guess this is exactly the kind of manner in which life stresses cause marital stresses. Our marriage is thankfully strong enough to handle this, but I could easily see how poorer communication in a relationship could cause it to be torn apart for much smaller reasons.
- Oh, and being sick really sucks. Could someone please get rid of this cough for me?
i stand duly chastised.
only now have i come to
figure out what your pi
conjecture even is:
does some *first* block
of n digits (1st, 2nd, ...
n^th) repeat *right away*
in digits n+1, n+2, ... 2n ?
gee. seems very unlikely.
i have no idea how one would
go about *proving* anything
like this, though ...
i think your reasoning's
a little shady on the
infinite product: it *is*
possible for an infinite
product of nonzero factors
(not "terms") to be zero.
e.g. (1/2)*(1/2)*(1/2) ...
is clearly smaller than any
positive number. your
product has the n^th factor
approaching 1 as n->\infty,
though (the condition for
an infitite product to be
interesting), so, again,
i'm with you: i don't know
how to compute its value.
anyhow, the probability that
a random normal number will
repeat its first n blocks
in positions n+1 through 2n
doesn't tell us anything
about pi itself even if
we knew pi to be normal
(which, anyway, *i* don't).
you might very well have hit
on a problem for which math
just isn't ready ...
Posted by: vlorbik | December 07, 2005 at 11:18 AM
ah yes, factors...of course. my students would laugh me out of the school if they saw that i misused the words, since i insist they use them right.
see the post for an update.
Posted by: Polymath | December 07, 2005 at 11:22 PM
stag
Posted by: göğüs büyütücü | May 18, 2012 at 05:46 AM
geciktirici stag
Posted by: geciktirici stag | May 18, 2012 at 05:46 AM
sperm hapı
Posted by: sperm hapı | May 18, 2012 at 05:48 AM