Unfortunately, I don’t have any wonderful posts all ready for
our launch. At the moment, I’m the only administrator at Scientopia,
and I’ve been so busy working on just getting the site up and running
that I haven’t had any time to actually finish any posts.
But there’s stuff in progress! I’m working on two different series
of posts.
First, in my request for topics back at SB, a ton of you were interested
in topology. I’ve written about topology before, but it was four years ago
when GM/BM first moved to ScienceBlogs. So most of you guys probably
never got to read it. I’ll be taking those posts, updating them, and
reposting them.
The other series is on fuzzy logic. I really love logic – in particular,
I love what I call atypical logics – that is, logics that do something
different from basic propositional or predicate logic. Fuzzy logic is
particularly fun – it’s built around the fundamental idea of
vagueness. That is, what happens to concepts like “tallness”, where
there are some people who are clearly tall, and there are others
who are kind-of tall, and still others who clearly aren’t tall.
And yet, there’s absolutely no strict dividing line between those. But
capturing those in logic is difficult!
And, of course, if you’re doing fuzzy logic, you really need fuzzy set theory
underneath it. After all, in normal set theory, a predicate defines
a set. But if a predicate is completely true for some values, and it’s
only partly true for others, then what does a set mean? What does
membership mean?
We’ll find out soon!
Welcome back, Mark! Looking forward to seeing you back with your blogging hat on, rather than your sysadmin’s!
Probably not a good sign that pages are taking 30+ seconds to load at the moment. I hope you’ve provisioned your hosting for this influx of traffic!
Mark, can you tell yourself to install previewing software? Thanks!
Ha! If you want it done right, you’ve got to do it yourself.
Go Mark!
Mark:
Let me know if you need help.
It is good to see you back in action!
I look forward to reading lots more maths.
How do you do topology on fuzzy sets?
I’d imagine that you’d set up the fuzzy topos, using fuzzy functions between fuzzy sets. Then you’d mimic the definition of a topological space and a continuous map from their usual set-theoretic home in the new topos.
Of course, I expect Mark’s going to go into the details of how you do that.