Radical Honesty is a kind of communication that is direct, complete, open and expressive. Radical Honesty means you tell the people in your life what you've done or plan to do, what you think, and what you feel. It's the kind of authentic sharing that creates the possibility of love and intimacy.

I came across this book at Borders and it really interested me.

Be sure to read the FAQ for some concrete examples.

What would happen if we told the whole truth all the time?

Caption this photo!



Source: Chicago Tribune, November 14, 2002

It used to be "pistols at dawn", but now we've got "tax plans at dawn".

Two blogs I follow have posted their thoughts on how to fix the US tax system in the last couple of days. First up is William Burton's tax plan, from a liberal perspective. He wants to keep the estate tax firmly in place, close up the corporate loopholes, restore the progressive brackets to something more like they used to be, and stop differentiating between payroll income and capital-gains income. Then we have Jane Galt's tax plan, from the libertarian perspective (at least, that's what I think her perspective is -- I read her blog sporadically, but her alias suggests a libertarian view). She wants to eliminate the corporate income tax, eliminate the estate tax, and end all deductions. The two agree that capital gains should not be treated any differently from other forms of income, they both agree that their respective views have zero chance of ever being enacted in the current political climate, and both concede that to tax Warren Buffett at twenty-five percent would not have nearly the same effect on his standard-of-living as the same percentage taxation would on, say, a family of three with a total income of $30,000 a year. (There are other points the authors discuss, but they are on tax details that I don't know anything about. I also don't get the impression, though I may be wrong, that the authors are aware of each others' proposals.)

So, what constitutes fairness in a tax system? And to what degree is "fairness" even desirable in a tax system, in the first place?

When I first heard the word palimpsest, it sounded to me like a nasty skin condition.


The death of Archimedes
taken from the article Proof, Amazement, and the Unexpected

Fellow Collaborators will recall that the word had been floated by Jason as a possible name for this blog. It means "twice-written" which when you think about it is a pretty cool name for a collaborative web log. In Latin it means literally means "scraped again" and this refers to the medieval practice of scraping clean old parchments so that they could be reused a second or more times. Parchments were generally made of animal skin, so I guess the nasty skin thing wasn't that far off.

Any way, we didn't go with the name but at the time I remembered hearing about the discovery of a palimpsest that contained a previously unknown work of Archimedes. It had been found as traces left on a 10th century parchment which had been roughly scraped clean, cut in half, bound into a book and overwritten with a 13th-century Greek prayer manual. The manuscript first came to light in 1906 in Constantinople but was almost immediately lost again (some say stolen) only to resurface on the block of a Christie's auction room in 1998. It sold for two million dollars.

Scholars have since had a chance to examine it and using ultraviolet photography and digital imaging have been able to read beneath the prayer book's lines and decipher Archimedes' text and diagrams. What they have found is was quite remarkable particularly in light of our current understanding of the development of mathematics. Copied and recopied by scribes over a thousand year period since the time when Archimedes lived, this is the largest existing tract of words by the man himself. He puts together in a treatise entitled the Method of Mechanical Theorems a series of proofs which, amongst other things, appears to anticipate the invention of calculus by more than eighteen centuries.

Calculus is an indispensable tool of modern mathematics and was invented by Leibniz (and independently by Newton) and, as you may recall from high school, is all about chopping things up into an infinite number of pieces that are themselves infinitely small. It's this kind of thinking about problems that is conventionally assumed to have been beyond the pale for the ancient Greeks who are said to have avoided dealing with infinities and always preferred to stay with the finite and the rational. Not so, apparently, when we come to Archimedes.

Modern scholarship always assumed that mathematics has undergone a fundamental conceptual shift during the Scientific Revolution in the 16th century. It has always been thought that modern mathematicians were the first to be able to handle infinitely large sets, and that this was something the Greek mathematicians never attempted to do. But in the palimpsest we found Archimedes doing just that. He compared two infinitely large sets and stated that they have an equal number of members. No other extant source for Greek mathematics has that.

The Origins of Mathematical Physics: New Light on an Old Question

See also:
Ancient Infinities
The Archimedes Palimpsest Exhibit at the Walters Art Gallery in Baltimore
Scholars decode ancient text, shake up pre-calculus history

You can find a full translation of the text and diagrams from the palimpsest here. As an example, this is an excerpt from Archimedes' Letter to Eratosthenes

Since I see, however, as I have previously said, that you are a capable scholar and a prominent teacher of philosophy, and also that you understand how to value a mathematical method of investigation when the opportunity is offered, I have thought it well to analyse and lay down for you in this same book a peculiar method by means of which it will be possible for you to derive instruction as to how certain mathematical questions may be investigated by means of mechanics. And I am convinced that this is equally profitable in demonstrating a proposition itself; for much that was made evident to me through the medium of mechanics was later proved by means of geometry because the treatment by the former method had not yet been established by way of a demonstration.

This is a game called "Landlord's Game", which was a precursor to the classic Monopoly. The classic game is the current feature of NPR's Present at the Creation series.