1. Biology How Does Information/Entropy/ Complexity fit in?

2. The Mad Dash Shannon Information Theory –Ensembles, Information and Entropy –Applications to Symmetry –Limitations Kolmogorov Complexity Extension –Measuring Redundancy in a Single Microstate –A Distance Metric –Applications: Ant Language and Phylogeny

3. Shannon Information is the potential to transmit bits A book of n characters is a single microstate, s Every possible book of n characters is the ensemble of books, S

4. Formulae Information, I, encapsulated in the sth state of S is Entropy is the expected value of the information

5. Symmetry The more the symmetry, the more the redundancy The more redundant, the less room for information Math Symmetry -> Loss of microstates -> All microstates become more probable -> Each microstate transmits less information

6. Biological Ensembles? How big is an ensemble? DNA How do we set bounds? Evolution & Ecology XHow do we compare information content of two microstates?

7. Binarify Any object can be represented as a binary sequence, e.g. 11010011101000101100001011011 or 1010101010101010101010101010 or 11001101100000110010101100110 Some are more complex and contain more information; some are more redundant and contain less info

8. Kolmogorov Complexity Denote the Kolmogorov Complexity of the string s as K(s) Denote the shortest binary program run on a Turing Machine which can reproduce s as d(s) Then K(s)=d(s) Upper Bound is the program –return s Whose length is of order |s|  Uncomputable! (Bummer)

9. What to do? The amount of compression is a good way to approximate K(s) –Compression of Human Genome ~ 12% Conditional Kolmogorov Complexity: –K(x|y) the shortest program which spits out x given y –Not Symmetric, so still need to find a good distance metric between two sequences

10. Phylogeny! One possible metric: Phylogeny trees determined with this and other metrics applied to unaligned mitochondrial genomes compressed by any of 20some algorithms

11. Phylogeny Trees Mammalian Trees automatically computed using KC.

12. Intelligent Social Ants Communication via compressed messages Regular messages are communicated more quickly and apparently more efficiently

13. Conclusions Shannon Information Theory deals with ensembles and microstates –Most useful for ennumerable sets –More symmetry, more entropy, less information Kolmogorov Complexity –Defines an information measure for every microstate independent of the ensemble –“Clear” way to compare information content and patterns between two objects

14. Warning: Do not calculate Pi in binary. It is conjectured that this number is normal, meaning that it contains all finite bit strings. If you compute it, you will be guilty of: –Copyright infringement (of all books, all short stories, all newspapers, all magazines, all web sites, all music, all movies, and all software, including the complete Windows source code) –Trademark infringement –Possession of child pornography –Espionage (unauthorized possession of top secret information) –Possession of DVD-cracking software –Possession of threats to the President –Possession of everyone's SSN, everyone's credit card numbers, everyone's PIN numbers, everyone's unlisted phone numbers, and everyone's passwords –Defaming Islam. Not technically illegal, but you'll have to go into hiding along with Salman Rushdie. –Defaming Scientology. Which is illegal -- just ask Keith Henson.