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Confessions of an Eccentric
James A. FosterIBEST, 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: ExplorationWhen human life, all too
conspicuousLay foully grovelling on
earth, weighted downBy grim superstition
looking from the skiesHorribly threatening
mortal men, a manA Greek, first raised his
mortal eyes Bravely against this
menace. No reportOf gods, no lightning-
flash, no thunder-pealMade this man cower, but
drove him all the moreWith passionate manliness
of mind and willTo be the first to spring
the tight-barred gatesOf 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 InfinitiesThere are as many fractions as counting
numbers (some infinities are smaller than you think)
27 March 2003 Confessions of Eccentric
Exploring InfinitiesThere are as many fractions as counting numbers
1/1 1/2 1/3 1/4 …2/1 2/2 2/3 2/4 …3/1 3/2 3/3 3/4 …4/1 4/2 4/3 4/4 …… … … …
Etc.
27 March 2003 Confessions of Eccentric
Exploring InfinitiesThere are as many fractions as counting numbers
1/1 1/2 1/3 1/4 …2/1 2/2 2/3 2/4 …3/1 3/2 3/3 3/4 …4/1 4/2 4/3 4/4 …… … … …
Etc.
1
27 March 2003 Confessions of Eccentric
Exploring InfinitiesThere are as many fractions as counting numbers
1/1 1/2 1/3 1/4 …2/1 2/2 2/3 2/4 …3/1 3/2 3/3 3/4 …4/1 4/2 4/3 4/4 …… … … …
Etc.
12
3
27 March 2003 Confessions of Eccentric
Exploring InfinitiesThere are as many fractions as counting numbers
1/1 1/2 1/3 1/4 …2/1 2/2 2/3 2/4 …3/1 3/2 3/3 3/4 …4/1 4/2 4/3 4/4 …… … … …
Etc.
12
3 6
5
4
27 March 2003 Confessions of Eccentric
Exploring InfinitiesThere are as many fractions as counting numbers
1/1 1/2 1/3 1/4 …2/1 2/2 2/3 2/4 …3/1 3/2 3/3 3/4 …4/1 4/2 4/3 4/4 …… … … …
Etc.
12
3
7
6
5
4 8
9
10
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.d1d2d3d4d5d6d7
27 March 2003 Confessions of Eccentric
Exploring InfinitiesSuppose you can count the reals, like this:
1 0.d1,1d1,2d1,3d1,4…
2 0.d2,1d2,2d2,3d2,4…
3 0.d3,1d3,2d3,3d3,4…
4 0.d4,1d4,2d4,3d4,4……
27 March 2003 Confessions of Eccentric
Exploring InfinitiesThen you missed at least one! Let mi
be any digit other than di,i. Consider:
Oops!0.m1 m2 m3
m4…
1 0.d1,1d1,2d1,3d1,4…
2 0.d2,1d2,2d2,3d2,4…
3 0.d3,1d3,2d3,3d3,4…
4 0.d4,1d4,2d4,3d4,4……
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 & DesireThe Muses’ grace is on me,
as I writeClear verse about dark
matters. This is notA senseless affectation;
there’s reason to it.Just as when doctors try to
give to children A bitter medicine, they rim
the cupWith honey’s sweetness,
honey’s golden flavor,To fool the silly little things,
as farAs the lips at least, so that
they’ll take the bitterDosage, 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.935-950)
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: FriendshipFor what ensues, my friend,Listen with ears attentive and a
mind Cleared of anxiety; hear the
reasoned truthAnd do not without understanding
treatMy gifts with scorn, my gifts,
disposed for youWith 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: WonderLook 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 ariseFor 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 mindPersists in questioning:
what can be there?What is there so far off,
toward which the urgeOf the free spirit flies?
(Lucretius, De Rerum Natura II 1030-1047