
The mathematics of discovering new things - ColinWright
http://www.washingtonpost.com/news/speaking-of-science/wp/2014/08/01/the-mathematics-of-discovering-new-things/
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mojuba
So if I get it right:

Say you have elementary concepts A, B and C. Combinations of these concepts
also give something, e.g. AB, AC, etc. You have tried and exhausted all
possible (and sensible) duplets, triples, etc. and now you are bored.

Then something new comes along, D. Now you not only have a new elementary
concept, but a whole lot of new possible combinations with previously known
elementary concepts: AD, BD, etc.

~~~
jimmaswell
I've observed this with fandom crossovers.

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MrQuincle
Huh? A common representation of the Polya urn which results in a Dirichlet
process corresponds to "novel" colors as well. If you pick a normal color you
put it back with another ball of that color, but if you pick the black ball,
you can pick an entire new color, hence discovery of a new thing. You can read
it on Wikipedia, the source of all knowledge. :-)
[https://en.wikipedia.org/wiki/Dirichlet_process](https://en.wikipedia.org/wiki/Dirichlet_process)

Original link is by the way:
[http://www.nature.com/srep/2014/140731/srep05890/full/srep05...](http://www.nature.com/srep/2014/140731/srep05890/full/srep05890.html#affil-
auth)

Shameless plug: if anyone wants to work with me on application of
nonparametric Bayesian methods to 3D navigation and scene reconstruction,
please do so. [https://github.com/mrquincle/octave-
scripts/tree/master/thes...](https://github.com/mrquincle/octave-
scripts/tree/master/thesis).

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noelwelsh
You can click through the full Nature article, which is nice. I haven't read
the article in depth, but it looks like interesting stuff. A bunch of models
in Bayesian non-parametrics are, like the described model, based on Polya
urns. It should be a simple matter to use this model for some interesting
clustering tasks, perhaps as an alternative to the CRP.

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ccvannorman
I love how after I cofounded a math game company, there seems to be more and
more math everywhere I look. "Blue car syndrome" at its finest!

For me this article especially rings true with self identity / confidence.
Since four years ago I started learning how to program video games, I
recognized that internally, "Well if I could totally change my career
overnight, and open up a plethora of new possibilities, then I wonder how many
additional choices I will now start to see over time?"

I saw it as a graph of my life possibilities, with the first 25 years of my
life bumping along in the 1-10 range, then a sudden inflection point to 100.
Looking at this graph objectively, one can imagine a second inflection point
that goes to 1000, etc.. maybe leading to an asymptote! But I digress.

~~~
ColinWright
> "Blue car syndrome"

There's a Name for That: The Baader-Meinhof Phenomenon[0], also known as the
"Frequency Illusion."[1]

[0] [http://www.damninteresting.com/the-baader-meinhof-
phenomenon...](http://www.damninteresting.com/the-baader-meinhof-phenomenon/)

[1] [http://en.wikipedia.org/wiki/Baader-
Meinhof_phenomenon#Frequ...](http://en.wikipedia.org/wiki/Baader-
Meinhof_phenomenon#Frequency_illusion)

~~~
judk
"Blue car syndrome" is also a name for that, and an older one than "B-M".

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hebbarp
Very interesting. Is there a corollary to this? Say, if a person or a bunch of
people are curating articles then they will select only those which are _most_
novel and all other related things will get dropped. In that sense, we should
not see similar stuff on the front page of HN. Yet, I recall, seeing at least
3 news items about Microsoft retrencing people, on the front page of HN. So
should HN consider applying the corollary "correlated novelty".

