Confessions of an Eccentric
James A. Foster
IBEST, UI, etc.
27 March 2003

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 tightbarred gates
Of Nature’s hold asunder.
27 March 2003
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)
 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
1/1 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
…
…
…
…
27 March 2003
 Confessions of Eccentric
…
…
…
…
Etc.
Exploring Infinities
There are as many fractions as counting numbers
1/1
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
…
…
…
…
27 March 2003
 Confessions of Eccentric
…
…
…
…
Etc.
Exploring Infinities
There are as many fractions as counting numbers
1/1
1 1/2
3 1/3 1/4
2/1
2 2/2 2/3 2/4
3/1 3/2 3/3 3/4
4/1 4/2 4/3 4/4
…
…
…
…
27 March 2003
 Confessions of Eccentric
…
…
…
…
Etc.
Exploring Infinities
There are as many fractions as counting numbers
1/1
1 1/2
3 1/3
6 1/4
2/1
2 2/2
5 2/3 2/4
3/1
4 3/2 3/3 3/4
4/1 4/2 4/3 4/4
…
…
…
…
27 March 2003
 Confessions of Eccentric
…
…
…
…
Etc.
Exploring Infinities
There are as many fractions as counting numbers
1/1
1/4
1 1/2
3 1/3
6 10
2/1
2 2/2
5 2/3
9 2/4
3/1
4 3/2
8 3/3 3/4
4/1
7 4/2 4/3 4/4
…
…
…
…
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 Confessions of Eccentric
…
…
…
…
Etc.
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 Infinities
Suppose 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…
…
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 Confessions of Eccentric
Exploring Infinities
Then you missed at least one! Let mi be any
digit other than di,i. Consider:
Oops!
1
2
3
4
0.m1 m2 m3 m4…
0.d1,1d1,2d1,3d1,4…
0.d2,1d2,2d2,3d2,4…
0.d3,1d3,2d3,3d3,4…
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?
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 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.935950)
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


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 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 10301047
27 March 2003
 Confessions of Eccentric