Confessions of an Eccentric James A. Foster IBEST, UI, etc. 27 March 2003 

27 March 2003  Confessions of Eccentric The Theme Contemplation of the wonderful is not passive or discipline specific. It is eccentric. And eccentrics make great friends.

27 March 2003  Confessions of Eccentric First Turning: Exploration When human life, all too conspicuous Lay foully grovelling on earth, weighted down By grim superstition looking from the skies Horribly threatening mortal men, a man A Greek, first raised his mortal eyes Bravely against this menace. No report Of gods, no lightning-flash, no thunder-peal Made this man cower, but drove him all the more With passionate manliness of mind and will To be the first to spring the tight- barred gates Of Nature ’ s hold asunder. So his force, His vital force of mind, a conqueror Beyond the flaming ramparts of the world Explored the vast immensities of space With wit and wisdom, and came back to us Triumphant, bringing news of what can be And what cannot, limits and boundaries, The borderline, the bench mark, set forever. Superstition, so, is trampled underfoot, And by his victory we reach the stars. (Lucretius, De Rerum Natura I.62-79)

27 March 2003  Confessions of Eccentric Exploring Infinities There are as many fractions as counting numbers (some infinities are smaller than you think)

27 March 2003  Confessions of Eccentric Exploring Infinities There are as many fractions as counting numbers 1/11/21/31/4 … 2/12/22/32/4 … 3/13/23/33/4 … 4/14/24/34/4 … ………… Etc.

27 March 2003  Confessions of Eccentric Exploring Infinities There are as many fractions as counting numbers 1/11/21/31/4 … 2/12/22/32/4 … 3/13/23/33/4 … 4/14/24/34/4 … ………… Etc. 1

27 March 2003  Confessions of Eccentric Exploring Infinities There are as many fractions as counting numbers 1/11/21/31/4 … 2/12/22/32/4 … 3/13/23/33/4 … 4/14/24/34/4 … ………… Etc

27 March 2003  Confessions of Eccentric Exploring Infinities There are as many fractions as counting numbers 1/11/21/31/4 … 2/12/22/32/4 … 3/13/23/33/4 … 4/14/24/34/4 … ………… Etc

27 March 2003  Confessions of Eccentric Exploring Infinities There are as many fractions as counting numbers 1/11/21/31/4 … 2/12/22/32/4 … 3/13/23/33/4 … 4/14/24/34/4 … ………… Etc

27 March 2003  Confessions of Eccentric Exploring Infinities There are more real numbers than fractions (some infinities are larger than others) Think of real numbers (between 0 and 1) as infinite fractions of the form: 0.d 1 d 2 d 3 d 4 d 5 d 6 d 7

27 March 2003  Confessions of Eccentric Exploring Infinities Suppose you can count the reals, like this: 1 0.d 1,1 d 1,2 d 1,3 d 1,4 … 2 0.d 2,1 d 2,2 d 2,3 d 2,4 … 3 0.d 3,1 d 3,2 d 3,3 d 3,4 … 4 0.d 4,1 d 4,2 d 4,3 d 4,4 … …

27 March 2003  Confessions of Eccentric Exploring Infinities Then you missed at least one! Let m i be any digit other than d i,i. Consider: Oops! 0.m 1 m 2 m 3 m 4 … 1 0.d 1,1 d 1,2 d 1,3 d 1,4 … 2 0.d 2,1 d 2,2 d 2,3 d 2,4 … 3 0.d 3,1 d 3,2 d 3,3 d 3,4 … 4 0.d 4,1 d 4,2 d 4,3 d 4,4 … …

27 March 2003  Confessions of Eccentric Exploring Infinities So, no matter how you try to line up counting numbers and reals, you will miss at least one. Hence, there are more real numbers than fractions and some infinities are larger than others

27 March 2003  Confessions of Eccentric Exploring Infinities Implications:  Speaking of “ infinity ” is imprecise. There are many “ sizes ”  Reason alone suffices to show this  Since one can count all possible computer programs, and there are as many yes/no questions as reals: most decision questions cannot be answered algorithmically Questions:  What are unsolvable problems like?  Are there “ intermediate ” infinities?

27 March 2003  Confessions of Eccentric Second Turning: Poetry & Desire The Muses ’ grace is on me, as I write Clear verse about dark matters. This is not A senseless affectation; there ’ s reason to it. Just as when doctors try to give to children A bitter medicine, they rim the cup With honey ’ s sweetness, honey ’ s golden flavor, To fool the silly little things, as far As the lips at least, so that they ’ ll take the bitter Dosage, and swallow it down, fooled, but not swindled, But brought to health again through double-dealing, So now do I, because this doctrine seems Too grim for those who never yet have tried it, So grim that people shrink from it, I ’ ve meant To explain the system in a sweeter music, To rim the lesson, as it were, with honey, Hoping, this way, to hold your mind with verses While you are learning all that form, that pattern Of the way things are. (Lucretius, De Rerum Natura I )

27 March 2003  Confessions of Eccentric Evolution  We can evolve programs and computers  We can evolve teams  Evolved artifacts are robust  Some of our DNA evolves independently of us  We can watch evolution in the lab  We can discover evolutionary history  We can evolve explanations of natural evolution

27 March 2003  Confessions of Eccentric Third Turning: Friendship For what ensues, my friend, Listen with ears attentive and a mind Cleared of anxiety; hear the reasoned truth And do not without understanding treat My gifts with scorn, my gifts, disposed for you With loyal industry. (Lucretius, De Rerum Natura 50-53

27 March 2003  Confessions of Eccentric Initiative for Bioinformatics & Evolutionary STudies (IBEST) IBEST  Mission: have fun by doing good science  MO: hobnob with eccentric friends History  General faculty meeting (1993)  Lunches with eccentrics (1993-now)  Computer Scientist growing viruses (1999)  Formation, lunches, name (2000)  $26M in competitive funding to date, dozens of papers, many grad students, new BCB degrees, model for interdisciplinary studies, new friends

27 March 2003  Confessions of Eccentric Fourth Turning: Wonder Look up at the pure bright color of the sky, The wheeling stars, the moon, the shining sun! If all these, all of a sudden, should arise For the first time before our mortal sight, What could be called more wonderful, more beyond The heights to which aspiring mind might dare? Nothing, I think. And yet, a sight like this, Marvelous as it is, now draws no man To lift his gaze to heaven ’ s bright areas. We are a jaded lot. … The sum of space is infinite, reaching far Beyond the ramparts of the world; the mind Persists in questioning: what can be there? What is there so far off, toward which the urge Of the free spirit flies? (Lucretius, De Rerum Natura II