James Tauber's Blog 2005/06/08
Apple on Intel and the Osborne Effect
A number of people (such as Jeff Nolan) have suggested that Steve Jobs's announcement of the move to Intel will hurt Apple due to the Osborne Effect.
If Steve had announced that a G6 PowerMac or G5 PowerBook was going to ship in 2006, wouldn't that be just as likely to cause an Osborne Effect?
So even if there is an Osborne Effect, I don't think see why it should be attributed to the switch per se.
Mind you, given there are always new technological innovations, holding off on something you were planning to do now because of an announcement about a release a year away doesn't make that much sense to me. A quarter or two maybe. But not a year.
But then again, no one said the Osborne Effect was rational. Just that (some) humans think that way.
by jtauber : Created on June 8, 2005 : Last modified June 8, 2005 : 2 comments (permalink)
Continuous Functions are between Topological Spaces not Sets
In the Poincare Project, I've said things of the form "a continuous function from (some subset of the real numbers)".
There's an assumption in that phrase that's worth pointing out.
Whenever someone talks about a continuous function, they are actually talking about a mapping between topological spaces rather than just between two sets. This is because the definition of "continuous" requires a topology.
So, in this context, whenever I say "the reals", I mean "the topological space consisting of the set of real numbers with the standard order topology". Recall that any totally ordered set has a particular topology that can be derived from the ordering relation.
Mathematicians frequently take this kind of shortcut and it should always be clear from the context what is being referred to. But I think it's useful to point out because I think it's something that needs to be understood explicitly.
UPDATE: next post
by jtauber : Created on June 8, 2005 : Last modified Aug. 9, 2007 : Categories poincare_project : 0 comments (permalink)