
Information Geometry - clebio
http://math.ucr.edu/home/baez/information/
======
stared
It is a wonderful series.  For a bit simpler take on entropy (from the same
guy), there is a series on biodiversity (some of my faviourite:
[http://stats.stackexchange.com/a/144235/6552](http://stats.stackexchange.com/a/144235/6552)). 

E.g.:

[https://johncarlosbaez.wordpress.com/2012/06/21/the-
mathemat...](https://johncarlosbaez.wordpress.com/2012/06/21/the-mathematics-
of-biodiversity-part-1/)

[https://johncarlosbaez.wordpress.com/2012/07/02/the-
mathemat...](https://johncarlosbaez.wordpress.com/2012/07/02/the-mathematics-
of-biodiversity-part-4/)

[https://johncarlosbaez.wordpress.com/2012/07/12/the-
mathemat...](https://johncarlosbaez.wordpress.com/2012/07/12/the-mathematics-
of-biodiversity-part-7/)

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noobermin
Such cool sounding things make me wish I went to graduate school for
mathematics... I really wish one could learn such things on their own free
time, may be even publish in their free time separate from affiliation with a
university or educational institution. 

~~~
clebio
Well, you can (at least, learn).  I've been reading and practicing ever since
finishing college.  It is an enormous time effort, you have to practice (not
just read), and it _really_ helps to have people to share discussions and
ideas with (physics forums seems like a good place to go, for example).  But I
certainly think it's possible.  The alternative is not trying, which you know
won't succeed (though of course, it may be a conscious choice to do other
things). 

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PaulHoule
It's a lot like quantum mechanics but all real numbers. 

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happyscrappy
>Information geometry is the study of 'stochastic manifolds', which are spaces
where each point is a hypothesis about some state of affairs. 

First sentence and I am already lost. 

~~~
tel
In statistics you often think about having a "space of possible states of the
world" and then seeking the point in that space which is in best concordance
with the data you observe. 

[For instance, we might assume that a basketball player's score in a game is a
linear function of the number of shots they make.  The possible states of the
world are the multiplicative factors (points scored)/(shots made).  This space
is simple: it's just a line, probably even just a ray since negative points
are impossible.] 

One major trick is in the "seeking".  To do so we often assume that the space
is parameterizable like that it has latitude and longitude and then we scan
over all possible choices of parameters looking for the parameters of the
optimal point.  Depending on the kind of model of the world you're working
with, these parameterizations change. 

[In the running example, the space is a line and the actual assignment of
positive numbers along that line is a suitable parameterization.  Higher
dimensional models or curved models make parameterization tougher.] 

Information geometry uses the tools of differential geometry, the same ones
used to characterize general relativity in physics, to characterize this
"state of the world" space more completely.  It provides new tools for
parameterization and understanding when older parameterization tools failed. 

[In the running example we don't much need differential geometry to understand
the geometry of our ray.  In high dimensions, models with interactions,
curvature, with discrete and continuous parts, intuition breaks down.] 

It also provides a rich geometric vocabulary useful for visualizing the "state
of the world" space which can be instrumental in understanding statistics,
building new models, evaluating how models compare with one another. 

~~~
clebio
Thanks, tel.  It was your reply to my comment on the Tensor discussion the
other day that sent me searching for a general reference, and I found this
link this morning.  Cheers! 

~~~
tel
Hey, I'm glad!  This is a really good find.  I love Baez's writing so I'm pretty
eager to run through this as well. 

~~~
clebio
Papers-we-love G+ Hangouts?  Guess I just need to start my local Papers we love
Meetup. 

~~~
pjonesdotca
that's a fantastic idea.  Send me an email with link if you ever do launch
something like that. 

~~~
clebio
If I get around to organizing such a thing, I suppose I'll throw together a
quick single-page site, and share in on HN or something.