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Why would a company like Twitter be interest in algebraic concepts like groups, monoids and rings. https://github.com/twitter/algebird

All I could find is:

Implementations of Monoids for interesting approximation algorithms, such as Bloom filter, HyperLogLog and CountMinSketch. These allow you to think of these sophisticated operations like you might numbers, and add them up in hadoop or online to produce powerful statistics and analytics.

and in another part of the GitHub page:

It was originally developed as part of Scalding's Matrix API, where Matrices had values which are elements of Monoids, Groups, or Rings. Subsequently, it was clear that the code had broader application within Scalding and on other projects within Twitter.

What could this broader application be? within Twitter and for general interest?

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john mangual
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    Asking for speculation doesn't make for a good question. But note that group theory underpins *almost all of of applied mathematics* so if you want to do anything with statistics or prediction or whatnot, it doesn't hurt to have the appropriate algebraic structures in your pocket. – Rex Kerr Feb 09 '13 at 19:32
  • What groups are used in computer science besides integers, reals and direct sums thereof? My hope is that someone twitter would have had an answer to my question - then it would not be speculative. – john mangual Feb 09 '13 at 20:01
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    There are all sorts of applications of matrices in statistics, machine learning, etc.; quaternions and other odd beasts get used in computer graphics; and there are all sorts of things that actually are (probably infinite, theoretically) groups that we don't normally think of as such. (Strings? Boolean?--really, it's hard to find something that _doesn't_ have the structure of at least a semigroup or somesuch.) – Rex Kerr Feb 09 '13 at 20:10
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    I do not believe this is off-topic. Discrete mathematics _is_ the foundation of computing. We ignore these theoretical underpinnings at our peril. It boggles my mind that software practitioners eschew formalism while still wishing to be called engineers and thought of as professionals. Do practitioners of _any_ other engineering field reject formal mathematical foundations? No! They've learned from failures and catastrophes. But, inexplicably, people who create software systems insist on a purely intuitive approach. Until that changes, we will continue to be "hobbyist professionals." – Randall Schulz Feb 09 '13 at 22:13
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    @johnmangual, repost this question in quora. – pedrofurla Feb 09 '13 at 22:16
  • @RandallSchulz - I don't disagree except that asking _why is Twitter interested_ is asking for speculation about their motives. If the question were instead _what use are groups, monoids, and rings in computation_ then it would be definitively answerable. – Rex Kerr Feb 09 '13 at 23:08
  • @RandallShultz quora seems like a better place for open-ended questions. There should be a finite answer to my question about Twitter's motives. On Twitter (at)posco (author of scalding) says they needed it for aggregations. So those aggregations being composed form a monoid. – john mangual Feb 10 '13 at 20:57
  • @RexKerr Where is the most appropriate place to post a question like *"what use are groups, monoids, and rings in computation"* ? I could post it here on StackOverflow but also cs.stackexchange.com Yet, it seems more open-ended then the one I have asked. As a mathematician, I'd be glad to see explicit examples of groups and semigroups in computer science for my algebra class. – john mangual Feb 10 '13 at 21:02
  • @johnmangual - I would try cs.stackexchange. You can use the above as an example. Probably a good idea to mention that you have some background in maths but don't see the connection to CS, and also that you are interested not just in theory but also application (since apparently Twitter found it useful enough in application to write a library). – Rex Kerr Feb 10 '13 at 21:09
  • Twitter: https://twitter.com/posco/status/300692719561482240 Quora: http://www.quora.com/Twitter-1/What-is-Twitters-interest-in-abstract-algebra-with-algebird – john mangual Feb 10 '13 at 21:10

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