An uplifting news item, poem, thought or quotation each day.
Archive of past entries

7 August 2005

            Disengagement

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.

-Josh Mitteldorf

6 August 2005

On essentialness and usefulness

Thirty spokes share the wheel’s hub;
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

Physics, like 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 accuracy.

Twenty-first century 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.

Some 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.

Humbling.

New Scientist article

4 August 2005

For every true mathematical theorem, there is a proof.
- Bertrand Russell

Not so.  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 two tricks:

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 one.

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.

Humbling.

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 giants."

-Maggie 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

Swarm Intelligence

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 efficiency.

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.

Large corporations 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."

- Moby Dick by Herman Melville, born this day in 1819