7 August 2005
I know best what's best for thee
And what thou wilst - it cannot be.
Heed my words and thou shalt thrive
And prosper and be more alive.
Though thy wisdom knew no bound,
I'd choose my own, my humble ground
To sow my seed and reap my hay -
'Tis not a boon I'll trade away.
Without thy heed, how can I live?
Who am I, if I've nought to give?
My counsel I beseech thee take
For me, if not for thine own sake.
In homely garb myself to rule,
I'll be for no fine king his fool,
Nor e'en in heav'n to be a pawn:
Take thy wisdom and be gone.
6 August 2005
On essentialness and
Thirty spokes share the
It is the center hole that makes it useful.
Shape clay into a vessel;
It is the space within that is of use.
Build a room for shelter, with door for entry;
It is the holes which make them useful.
Thus does benefit derive from what is there;
Usefulness from what is not there.
- Lao Tse
5 August 2005
mathematics (see yesterday's entry, below), may be a marvelously
powerful, predictive discipline built on shaky logical ground.
First there was Newtonian
mechanics, based on real, solid particles that exist in an objective world,
and which we may observe or not - the particles don't much care.
In the early years of the
twentieth century, that view became untenable, and Newtonian mechanics gave
way to quantum mechanics. Quantum physics deals with the results of
measurements of physical quantities. While the world is not being
"watched", it evolves according to probabilistic laws that
determine the chances concerning where we will find it in a subsequent
measurement. This is a theory deriving from a strange view of the world, which
most everyone (beginning with Einstein) found disturbing; but it worked, in
the sense that it predicts what it claims to predict with impressive
physicists are seeking explanations for the universe as a whole, combining
quantum physics with cosmology. Most recently, the cosmological
analysis points to a world in which all matter will ultimately fly apart,
every particle scattering separately, until it is beyond all reach and
beyond all contact with other matter.
physicists are starting to notice that such a world doesn't satisfy the
postulates of quantum mechanics. QM can calculate the probabilities
for a particle's behavior as it evolves between one observation and the
next. But suppose a particle is interacting for the last time,
destined never to influence any other particle again, let alone subject
itself to a "measurement"? We have no experience with such
circumstances, and quantum mechanics can say nothing about what such a
particle is likely to do.
4 August 2005
For every true
mathematical theorem, there is a proof.
- Bertrand Russell
There is an infinity of mathematical statements of which it is impossible to
know, even in principle, whether they are true or false.
- Kurt Gödel
Bertrand Russell and
Alfred North Whitehead were spearheading a project of the
ultimate rationalists. Their idea was to create a branch of mathematics that
described how mathematical reasoning worked. They hoped to put
mathematical logic on a sound foundation, by demonstrating that every
statement that was true was provably true, and every statement that was
false was provably false, and so long as we mathematicians work sufficiently
hard, eventually we shall be able to know of any mathematical statement
whether it be true or false.
In 1931, Gödel demonstrated a surprising fact about mathematics. There
are an infinite number of mathematical statements that are true, but we’ll
never know for sure that they’re true, because no proof is possible.
In order to show this, here’s what Gödel did: He devised a numbering
system for all possible mathematical statements, both true and false. 1st
statement, 2nd statement, 3rd statement... just like that. Then he numbered
all logical sequences of statements that could constitute a proof. Now his
He showed that there is a mathematical formula – something like x2
+ 2x – 17, but considerably more complicated – that connects the
number for each statement with the number for its proof, if there is
Then he found the number for a formula that corresponds to a
statement that says "there is no proof for me."
The statement that has this number, then, is true if and only if it
cannot be proved. What’s worse, there is not just one such statement but
an infinite number with this property.
Mathematics contains an infinite number of statements that are true, but
can never be proved; or, even worse, some of these statements can be proved,
even though they are false. And we’ll never know which is the case. We can
never know which is the case.
3 August 2005
"Go to the people at the
top—that is my advice to anyone who wants to change the system, any
system. Don’t moan and groan with like-minded souls. Don’t write letters
or place a few phone calls and then sit back and wait. Leave safety behind.
Put your body on the line. Stand before the people you fear and speak your
mind—even if your voice shakes. When you least expect it, someone may
actually listen to what you have to say. Well-aimed slingshots can topple
Kuhn, born one hundred years ago this day.
With the slogan "Do something outrageous every day," Kuhn organized and founded the
Gray Panthers in 1970 to advocate the rights of the elderly. The National organization continues to be dedicated to social change with both "age and youth in action."
2 August 2005
Certain mathematical problems
are susceptible to solution, not by insightful understanding of the whole,
but by a kind of distributed intelligence. Swarms of ‘virtual agents’
are programmed to follow simple rules, and the result is that collectively a
problem is solved. Where is the intelligence that ‘figured out’ how to
solve it? It is everywhere and nowhere, distributed through the system.
It is thought that ant hills
are able to accomplish what they do because each ant operates according to
simple rules that work together in a globally effective way.
For example, the ‘Cinderella
problem’: A pot of dry lentils is thrown into the ashes. How can the
lentils be gathered into one pile again? Solution: A swarm of ants is
released. Each ant walks in a straight line until she encounters a lentil.
She picks it up and makes a random turn, then walks with her lentil in a
straight line until she encounters another lentil. Then she puts down her
load, makes a random turn, and begins again. With these simple behaviors,
the pile of lentils is reconstituted from the ashes with remarkable
Ant colonies are also able to
find a direct
route to a food source, though each ant is foraging randomly. One
of the benefits of this kind of solution is ‘fault tolerance’: If
individual ants make mistakes, their effect on the efficiency of the global
process is minimal.
are learning from the ants, and adopting procedures that require little
of each worker, yet produce a robust and efficient cooperation globally.
1 August 2005
"There are some enterprises in which a careful disorderliness is the true method."
Dick by Herman
Melville, born this day in 1819