Now that Saddam Hussein has replied to the UN Security Council's demand for complete disclosure of his weapons of mass destruction programs with stonewalling and obfuscation (and not very subtly at that), it's clear the march to war against the Iraqi regime has moved a step further along the way.

Outgoing chairman of the Senate Foreign Relations Committee Joseph Biden, a Democrat, and committee member Chuck Hagel, Republican, authored an opinion piece appearing last Friday in the Washington Post called “Iraq: the Decade After.”  Mostly sensibly written, I'd judge, their opinion is that we need to hang on for the long haul in Iraq after toppling Saddam Hussein.

As we ramp up to this war against Saddam's regime, no doubt the chorus of complaint from the antiwar left will become ever more shrill and strident, and we will hear, once again (as we did last year in the war against the Taliban), that this war is “illegal,” because “the U.S. hasn't declared war,” as stipulated by the U.S. Constitution.

Before that moment arrives, and while Joe Biden is still chairman of the Senate Foreign Relations Committee — representing the liberal wing of the Congressional viewpoint as to the constitutional need for and requisite accomplishment of a declaration of war — it's worth recalling what his position and that of other members (e.g., Representative Gephardt) of the Democratic Party leadership has been. 

Consider this emphatic statement by Senator Biden with regard to the Use of Force resolution passed nearly unanimously by Congress after 2001-09-11.  In response to a question from the floor following a speech (given 2001-10-22, shown on CSPAN), the interchange went as follows:

Question:  “My question is this, do you foresee the need or the expectation of a Congressional declaration of war, which the Constitution calls for, and if so, against whom?”

Senator Biden:  “The answer is yes, and we did it.  I happen to be a professor of Constitutional law.  I'm the guy that drafted the Use of Force proposal that we passed.  It was in conflict between the President and the House.  I was the guy who finally drafted what we did pass.  Under the Constitution, there is simply no distinction …  Louis Fisher(?) and others can tell you, there is no distinction between a formal declaration of war, and an authorization of use of force.  There is none for Constitutional purposes.  None whatsoever.  And we defined in that Use of Force Act that we passed, what … against whom we were moving, and what authority was granted to the President.”

Constitutional scholar Eugene Volokh, writing in the Volokh Conspiracy, summarizes Senator Biden's constitutional position as:  “Congressional authorization of the use of force is legally tantamount to a declaration of war.”  That's how I (not a constitutional expert) interpret Biden's words too.  (Note also discussion in Volokh's piece of why a war declaration is not required by the U.S. Constitution.  As Eugene points out, however, that's a separate issue.)

Thus, the chairman of the Senate Foreign Relations Committee, a Democrat, and author of the Use of Force resolution passed last year by Congress — roles which would appear to give him considerable credibility in this regard — categorically states that, for all practical constitutional purposes, the U.S. has declared war in this worldwide war (a real war, not a “metaphorical war” as some on the left allege) against terror round the globe.

Due to the recent resolution passed by Congress with regard to Iraq, via identical reasoning the United States has also now (legally, constitutionally) declared war against Saddam's Iraqi regime.  The antiwar left ought to be aware that the supposed lack of a declaration of war in this situation is not a valid argument for its panoply.  That will not keep many from falsely shouting it from the rooftops, but the rest of us can keep cognizant of the reality of the situation.

Whew!  The Taken series is finally over; what a relief!  Twenty hours, egad!  (Now my wife misses the program, though — and predicts a sequel.  She could be right; plus she's got all those tapes….  I predict I'll be seeing more of it.)

The biggest failing of Spielberg's Taken, as it turns out, is not a few stupid comments by the obligatory German scientist in cliched films picturing the late-40's and 50's, it's in the fundamental premise behind the entire series:  the idea that aliens from another world would want or need to conduct several generations of “selective breeding” of humans (or anything else) to produce some kind of master genetic superman.

Hello, this is the twenty-first century!  Selective breeding is how many millennia old?  Ten, fifteen thousand years?  Could there perhaps be a slightly more recent and advanced technology available (to us, much less sophisticated aliens from across the stars)?  Hm….  How about (pa-dum!) genetic engineering!

Read physicist Freeman Dyson's essay for imaginative yet entirely reasonable forecasting how such enormously powerful technology, once acquired, could be made use of.  Once we have mastered these new technologies (much less than a century away, I'd say), there will be no more need for breeding generation after generation to slowly approach some ideal phenotype.  Instead, one would simply program a “seed” or “egg” with the final genetic complement desired for the organism, then wait (pouring in energy and food to speed up the process) while it grows to adulthood.  Existing organisms can also be updated in place, rather than growing new ones.

The problem with Taken, as is typical for the entire UFO mythos in fact, is not that the science of such hypothetical galaxy-spanning denizens is so advanced (civilizations millions or billions of years older than ours — as most extraterrestrial civilizations must be — have time to develop some pretty advanced technologies; however, see my earlier Taken post for a discussion of the real difficulties in traveling between the stars).  Rather, it is that the technologies the aliens are reportedly using here and now on Earth are primitive, even by standards of what we're learning to do today, much less what we'll be able to do by the time we learn to cross the great gulfs between the stars.

Where's just one of the millions of implants, for example, supposedly distributed among the estimated one-eighth (!) of Americans who, according to the scuttlebutt, have been “abducted”?  Where indeed is any verifiable alien artifact from any of the dozens of alien races reportedly buzzing round Earth like flies over a corpse?

It's worthwhile keeping the words of writer and visionary (inventor of the modern communications satellite) Arthur C. Clarke in mind:  “Any sufficiently advanced technology is indistinguishable from magic.”  Any civilization capable of reaching between the stars could easily build microscopic robots capable of studying us from wazoo to zilch, zenith to nadir — from the vantage point of particles of lint hiding in our navel!  There's no need for aliens to perform “abductions,” insert implants, or indeed act in any way that we can possibly observe.  We'd simply never see them at all.

As a result, the UFO mythos — as well as the Taken storyline — simply isn't credible.  That, not some imagined great conspiracy of all the governments of the world, is why the UFO paradigm has never gotten (nor deserves) “legs.”

Eugene Volokh and Stuart Banner do back to back postings on the 2002-12-20 Volokh Conspiracy regarding the fundamental nature of federalism in the American constitutional system.

Stuart Banner's posting, entitled “The Origins of Federalism,” considers the question of “Why does the United States have a federal structure?”  Banner answers the question he poses thusly:

Not because federalism is conducive to good government, not because the Framers thought it would be wise to have a country made up of sovereign states, and not because of racism.  We have federalism today because in the late 16th and early 17th centuries, when the English government began establishing colonies in North America, England set up a bunch of separate colonies rather than one big colony.  Distances were so great and technology so simple circa 1600 that North America would have been very hard to govern as a single colony.  By the time of independence it was too late to change.  Canada and Australia have a federal structure today for the same reason.  New Zealand does not, because it was small enough and colonized late enough to be run as a single colony.

Now, I have no idea whether on balance federalism is good or bad.  All I'm saying is that if it's good, we lucked into it, and if it's bad, we're stuck with a system intended for circumstances quite different from our own.

I agree with much of Stuart's reasoning, but I must note his explanation is insufficient to explain the existence much less prevalence of federalism among the British colonial successor states.  After all, the former Spanish empire is presently divided into a number of separate nations — not states or provinces of nations — for exactly the reason Banner points to above (separate colonial administrations), but without a whole lot of federalism, much less republicanism or democracy, resulting (at least until recently, and mostly under U.S. influence).

Thus, beyond a multiplicity of subject administrations created by the colonial power, there must be features in specifically British history, character, and culture that resulted not only in federalism in the subsequent development of the ex-colonial societies, but republicanism and democracy itself.

It was (Frenchman) Alexis de Tocqueville who, writing from the vantage point of a foreigner, observing America during the first half of the 19th century (he visited the U.S. during the 1830s), most perceptively saw and wrote about the kernels of the origins of the American system.

Because of his especially perspicacious view of American society and democracy during the 19th century, Alexis de Tocqueville's great work Democracy in America is so highly regarded here in the United States, in fact, that it is often considered to belong among America's “Crown Jewels.”  America's “Crown Jewels,” unlike the crown jewels of monarchies as they have existed round the world, consists of a small set of documents:  the Declaration of Independence, the Constitution, the Federalist Papers; that's about it — except for Alexis de Tocqueville's Democracy in America.

(This three-part article consists of three postings, the present, now coming to an end; next a moderately-lengthy quotation by Alexis de Tocqueville — presenting his analysis of the origins of Amerian republicanism, democracy, and federalism — which immediately follows this post; and lastly a follow-up post with acknowledgments and links.)

Quoting Alexis de Tocqueville's Democracy in America: ¹

Democracy more perfect than any of which antiquity had dared to dream sprang full-grown and fully armed from the midst of the old feudal society.

The English government watched untroubled the departure of so many emigrants, glad to see the seeds of discord and of fresh revolutions dispersed afar.  Indeed it did everything to encourage it and seemed to have no anxiety about the fate of those who sought refuge from its harsh laws on American soil.  It seemed to consider New England as a land given over to the fantasy of dreamers, where innovators should be allowed to try out experiments in freedom.

The English colonies — and that was one of the main reasons for their prosperity — have always enjoyed more internal freedom and political independence than those of other nations; nowhere was this principle of liberty applied more completely than in the states of New England.

It was at that time generally recognized that the lands of the New World belonged to that nation who first discovered them.

In that way almost the whole of the North American coast became an English possession toward the end of the sixteenth century.  The means used by the British government to people these new domains were of various sorts; in some cases the king chose a governor to rule some part of the New World, administering the land in his name and under his direct orders [Footnote: This was the case in the state of New York]; that was the colonial system adopted in the rest of Europe.  In others he granted ownership of some portion of the land to an individual or to a company.  [Footnote: Maryland, the Carolinas, Pennsylvania, and New Jersey were in this category.]  In those cases all civil and political powers were concentrated in the hands of one man or a few individuals, who, subject to the supervision and regulation of the Crown, sold the land and ruled the inhabitants.  Under the third system a number of immigrants were given the right to form a political society under the patronage of the motherland and allowed to govern themselves in any way not contrary to her laws.  This mode of colonization, so favorable to liberty, was put into practice only in New England.

In 1628 a charter of that sort was granted by Charles I to the emigrants who were going to found the colony of Massachusetts.

But generally charters were only granted to the New England colonies long after their existence had become an established fact.  Plymouth, Providence, New Haven, and the states of Connecticut and Rhode Island were founded without the help and, in a sense, without the knowledge of the motherland.  The new settlers, without denying the supremacy of the homeland, did not derive from thence the source of their powers, and it was only thirty or forty years afterward, under Charles II, that a royal charter legalized their existence.  [Footnote: In shaping their criminal and civil laws and their procedures and courts of justice, the inhabitants of Massachusetts diverged from English usages; in 1650 the king's name no longer headed judicial orders.]

For this reason it is often difficult, when studying the earliest historical and legislative records of New England, to detect the link connecting the immigrants with the land of their forefathers.  One continually finds them exercising rights of sovereignty; they appointed magistrates, made peace and war, promulgated police regulations, and enacted laws as if they were dependent on God alone.

Nothing is more peculiar or more instructive than the legislation of this time; there, if anywhere, is the key to the social enigma presented to the world by the United States now.

Among these records one may choose as particularly characteristic the code of laws enacted by the little state of Connecticut in 1650.

The Connecticut lawgivers turned their attention first to the criminal code and, in composing it, conceived the strange idea of borrowing their provisions from the text of Holy Writ:  “If any man after legal conviction shall have or worship any other God but the Lord God, he shall be put to death.”

There follow ten or twelve provisions of the same sort taken word for word from Deuteronomy, Exodus, or Leviticus.

Blasphemy, sorcery, adultery, and rape are punished by death; a son who outrages his parents is subject to the same penalty.  [Footnote: The laws of Massachusetts also imposed the death penalty for adultery, and Hutchinson (Vol. I, p. 441) says that several people were actually executed for that crime; in this context he quotes a strange story of something which happened in 1663.  A married woman had a love affair with a young man; her husband died and she married him; several years passed; at length the public came to suspect the intimacy which had earlier existed between the spouses, and criminal proceedings were brought against them; they were thrown into prison, and both were very near being condemned to death.]  Thus the legislation of a rough, half-civilized people was transported into the midst of an educated society with gentle mores; as a result the death penalty has never been more frequently prescribed by the laws or more seldom carried out.

The framers of these penal codes were especially concerned with the maintenance of good behavior and sound mores in society, so they constantly invaded the sphere of conscience, and there was hardly a sin not subject to the magistrate's censure.  The reader will have noticed the severity of the penalties for adultery and rape.  Simple intercourse between unmarried persons was likewise harshly repressed.  The judge had discretion to impose a fine or a whipping or to order the offenders to marry.  [Footnote: Code of 1650, p. 48.  It would seem that sometimes the judges would impose more than one of these penalties, as is seen in a judicial sentence of 1643 {…} which directs that Margaret Bedford, convicted of loose conduct, be whipped and afterward compelled to marry her accomplice, Nicholas Jemmings.]  If the records of the old courts of New Haven are to be trusted, prosecutions of this sort were not uncommon; under the date May 1, 1660, we find a sentence imposing a fine and reprimand on a girl accused of uttering some indiscreet words and letting herself be kissed.

The code of 1650 is full of preventive regulations.  Idleness and drunkenness are severely punished.  Innkeepers may give each customer only a certain quantity of wine; simply lying, if it could do harm, is subject to a fine or a whipping.  In other places the lawgivers, completely forgetting the great principle of religious liberty which they themselves claimed in Europe, enforced attendance at divine service by threat of fines and went so far as to impose severe penalties, and often the death penalty, on Christians who chose to worship God with a ritual other than their own.  [Footnote: Under the penal law of Massachusetts a Catholic priest who sets foot in the state after he has been driven out therefrom is subject to the death penalty.]

Finally, sometimes the passion for regulation which possessed them led them to interfere in matters completely unworthy of such attention.  Hence there is a clause in the same code forbidding the use of tobacco.  We must not forget that these ridiculous and tyrannical laws were not imposed from outside — they were voted by the free agreement of all the interested parties themselves — and that their mores were even more austere and puritanical than their laws.  In 1649 an association was solemnly formed in Boston to check the worldly luxury of long hair.  {…}

Such deviations undoubtedly bring shame on the spirit of man; they attest the inferiority of our nature, which, unable to hold firmly to what is true and just, is generally reduced to choosing between two excesses.

Alongside this criminal code so strongly marked by narrow sectarian spirit and all the religious passions, stimulated by persecution and still seething in the depths of men's souls, was a body of political laws, closely bound up with the penal law, which, though drafted two hundred years ago, still seems very far in advance of the spirit of freedom of our own age.

All the general principles on which modern constitutions rest, principles which most Europeans in the seventeenth century scarcely understood and whose dominance in Great Britain was then far from complete, are recognized and given authority by the laws of New England; the participation of the people in public affairs, the free voting of taxes, the responsibility of government officials, individual freedom, and trial by jury — all these things were established without question and with practical effect.

These pregnant principles were there applied and developed in a way that no European nation has yet dared to attempt.

In Connecticut the electoral body consisted, from the beginning, of all the citizens, and that is readily understood.  [Footnote: Constitution of 1638 {…}.]  In that nascent community there prevailed an almost perfect equality of wealth and even greater intellectual equality.  [Footnote: In 1641 the general assembly of Rhode Island declared unanimously that the government of the state was a democracy and that power resided in the body of free men, who alone had the right to make the laws and provide for their enforcement.  Code of 1650 {…}.]

At that time in Connecticut all executive officials were elected, including the governor of the state.

Citizens over sixteen years of age were obliged to bear arms; they formed a national militia which appointed its officers and was bound to be ready to march at any time to the country's defense.

In the laws of Connecticut and of all the other states of New England we see the birth and growth of that local independence which is still the mainspring and lifeblood of American freedom.

In most European nations political existence started in the higher ranks of society and has been gradually, but always incompletely, communicated to the various members of the body social.

Contrariwise, in America one may say that the local community was organized before the county, the county before the state, and the state before the Union.

In New England, local communities had taken complete and definite shape as early as 1650.  Interests, passions, duties, and rights took shape around each individual locality and were firmly attached thereto.  Inside the locality there was a real, active political life which was completely democratic and republican.  The colonies still recognized the mother country's supremacy; legally the state was a monarchy, but each locality was already a lively republic.

The towns appointed their own magistrates of all sorts, assessed themselves, and imposed their own taxes.  The New England towns adopted no representative institutions.  As at Athens, matters of common concern were dealt with in the marketplace and in the general assembly of the citizens.
 
 

¹ Alexis de Tocqueville, Democracy in America, 12th Edition, 1848, edited by J. P. Mayer, translated by George Lawrence, Anchor Books, Doubleday and Co., Inc., New York, 1969; pp. 39-44.

I decided to excerpt the above quote from the Mayer/Lawrence edition described above — fully crediting J. P. Mayer and George Lawrence's work — instead of obtaining the text from the on-line version pointed-to below, in the hope this will encourage readers to buy or check out the foregoing fine translation of Alexis de Tocqueville's Democracy in America.

Tocqueville's travel diary from his years-long visit to America has also been published.  See:  Alexis de Tocqueville, Journey to America, edited by J. P. Mayer, Yale paperback series, New Haven, 1962.

An on-line version of the entirety of Tocqueville's Democracy in America is available on the Internet here. 

The U.S. public affairs television network C-SPAN has done a tremendous amount of programming on Alexis de Tocqueville.  Do a search for “Toc” on the index for the C-SPAN on-line store to review all the programming on him that is available.  C-SPAN also has a nice map showing Tocqueville's travels in America.

Then there's the web page “Tocqueville.org” containing numerous links to information about Alexis de Tocqueville and his writings.

Dominican friar Felix Faber from the German city of Ulm twice traveled as a pilgrim to the Holy Land during the latter part of the 15th century.  Faber offered up this dry advice for travelers on long Mediterranean boat voyages of his day: ¹

As the poet says, “A ripe turd is an unbearable burden” [ut dicitur metrice: maturum stercus est importabile pondus].  A few words on the manner of urinating and shitting on a boat.

Each pilgrim has near his bed a urinal — a vessel of terracotta, a small bottle — into which he urinates and vomits.  But since the quarters are cramped for the number of people, and dark besides, and since there is much coming and going, it is seldom that these vessels are not overturned before dawn.  Quite regularly in fact, driven by a pressing urge that obliges him to get up, some clumsy fellow will knock over five or six urinals in passing, giving rise to an intolerable stench.

In the morning, when the pilgrims get up and their stomachs ask for grace, they climb the bridge and head for the prow, where on either side of the spit privies have been provided.  Sometimes as many as thirteen people or more will line up for a turn at the seat, and when someone takes too long it is not embarrassment but irritation that is expressed [nec est ibi verecundia sed potius iracundia].  I would compare the wait to that which people must endure when they confess during Lent, when they are forced to stand and become irritated at the interminable confessions and await their turn in a foul mood.

At night, it is a difficult business to approach the privies owing to the huge number of people lying or sleeping on the decks from one end of the galley to the other.  Anyone who wants to go must climb over more than forty people, stepping on them as he goes; with every step he risks kicking a fellow passenger or falling on top of a sleeping body.  If he bumps into someone along the way, insults fly.  Those without fear or vertigo can climb up to the prow along the ship's gunwales, pushing themselves along from rope to rope, which I often did despite the risk and the danger.  By climbing out the hatches to the oars, one can slide along in a sitting position from oar to oar, but this is not for the faint of heart, for straddling the oars is dangerous, and even the sailors do not like it.

But the difficulties become really serious in bad weather, when the privies are constantly inundated by waves and the oars are shipped and laid across the benches.  To go to the seat in the middle of a storm is thus to risk being completely soaked, so that many passengers remove their clothing and go stark naked.  But in this, modesty [verecundia] suffers greatly, which only stirs the shameful [verecunda] parts even more.  Those who do not wish to be seen this way go squat in other places, which they soil, causing tempers to flare and fights to break out, discrediting even honorable people.  Some even fill their vessels near their beds, which is disgusting and poisons the neighbors and can be tolerated only in invalids, who cannot be blamed: a few words are not enough to recount what I was forced to endure on account of a sick bedmate.

The pilgrim must be careful not to hold back on account of false modesty and not relieve the stomach; to do so is most harmful to the traveler.  At sea it is easy to become constipated.  Here is good advice for the pilgrim: go to the privies three or four times every day, even when there is no natural urge, in order to promote evacuation by discreet efforts; and do not lose hope if nothing comes on the third or fourth try.  Go often, loosen your belt, untie all the knots of your clothes over chest and stomach, and evacuation will occur even if your intestines are filled with stones.  This advice was given me by an old sailor once when I had been terribly constipated for several days.  At sea, moreover, it is not safe to use pills or suppositories [pilulas aut suppositoria accipere], because to purge oneself too much can cause worse trouble than constipation.

Probably good advice for any time and place.

¹ Quoted from A History of Private Life: Vol. II – Revelations of the Medieval World, edited by Georges Duby, translated by Arthur Goldhammer, the Belknap Press of Harvard University Press, Cambridge, Massachusetts, 1988; pp. 587-588.

Quote of the day, from the same volume (p. 589):

Felix conjunctio!  (“Happy coupling”)  —Carmina Burana (10th to 13th century)

Images have been added to the Roaring Camp piece.  Enjoy!

“To see the world in a grain of sand,
Heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour.”
William Blake

To paraphrase Yoda in George Lucas's Star Wars:  “Always in motion is the past.”

It might be thought that our knowledge of the ancient world (at least the better known periods and aspects of it) would have mostly shaken into a settled shape by now.  It's true that much information about the past is well and reliably known; in vast areas of concern, however (intellectual history, as an example), there remain crucial gaps, some of which are only now being partially filled in, with details sometimes importantly different from what had been presumed to be there before.

Mathematician and philosopher of science Jacob Bronowski put it like this: ¹

It is absurd to ask why the future should turn out to chime with our knowledge of the past.  This puts the question upside down and makes nonsense of it.  What we have learnt from the past is knowledge only because the future proves it to be true.

This principle is exemplified in the appreciation of one of antiquity's most brilliant minds, Archimedes (one of a handful through history whose achievements may be said to lie on a par with those of modern giants Newton and Einstein).  The story of the recovery of Archimedes' great work Method of Mechanical Theorems in 1906 after more than 2,000 years is remarkable enough, but the tale is not yet ended!  Now after nearly another 100 years further progress has recently been made, and the results are illuminating.
 

Born circa 290-280 B.C. in the Greek city of Syracuse in Sicily, dying in the Roman sack of that city in 212-211 B.C. during the Second Punic War, Archimedes is most famous today as the great ancient Greek inventor and mathematician.  In antiquity, Archimedes was also well known as a superb astronomer.

In a recent piece, “Proof, Amazement, and the Unexpected” in the journal Science, Stanford professor Reviel Netz characterizes Archimedes' mathematical contributions. ²

The bath anecdote does not give us the true measure of the man.  In On Floating Bodies, Archimedes made the following, astonishingly subtle deduction:  In a stable body of liquid, each column of equal volume must have equal weight; otherwise, liquid would flow from the heavier to the lighter.  The same must hold true even if some solid body is immersed in such a column of liquid.  In other words, if we have a column of liquid with a solid body immersed in it, the aggregate weight of the liquid and the body must be equal to that of a column of liquid of the same total volume.  It follows that the immersed body must lose weight: it must lose a weight equal to the weight of the volume of water it has displaced.  (This is why we feel lighter in the bath.)  This fundamental theorem was proved by Archimedes, with perfect rigor, in On Floating Bodies, Proposition 7.  Now that's something to cry “eureka” about.

Austere and technical as they are, Archimedes' treatises are just as striking as the anecdotes about him.  In the treatises three motives run together: proof, amazement, and the juxtaposition of the unexpected.  Proof and amazement are related, because Archimedes amazes us by proving that something very surprising is in fact true.  Amazement and the juxtaposition of the unexpected are related, because the amazing result is usually seen in the equality or equivalence of two seemingly separate domains.

Archimedes very rarely makes arguments that merely appear intuitive — and, crucially, when he does, he says so explicitly.  He sets out as postulates some very subtle assumptions.  For instance, in the introduction to the First Book on Sphere and Cylinder, Archimedes asserts that if two lines are concave to the same direction, and one encloses the other, the enclosing line is greater than the enclosed and so, for instance, the line is the shortest distance between two points.  He took enormous care to distinguish what can be proved from what cannot.  By turning seemingly obvious observations into explicit postulates, Archimedes was able to set out truly incontrovertible proofs.

Books such as Euclid's Elements have come down to us by way of numerous Greek and Arabic manuscripts, but, as Carl Boyer points out in his excellent History of Mathematics, the connecting link to Archimedes' works is thin.  Boyer writes: ³

Almost all copies are from a single Greek original which was in existence in the early sixteenth century and itself was copied from an original of about the ninth or tenth century. … There have been times when few or even none of Archimedes' works were known.  In the days of Eutocius, a first-rate scholar and skillful commentator of the sixth century, only three of the many Archimedean works were generally known….
 

The dearth in availability of Archimedes' works over much of the past two millennia has, as one might expect, led to errors in the appreciation of the body of his work.  Boyer writes:

His other treatises are gems of logical precision, with little hint of the preliminary analysis that may have led to the definitive formulations.  So thoroughly without motivation did his proofs appear to some writers of the seventeenth century that they suspected Archimedes of having concealed his method of approach in order that his work might be admired the more.

How unwarranted such an ungenerous estimate of the great Syracusan was became clear in 1906 with the discovery of the manuscript containing The Method.  Here Archimedes had published, for all the world to read, a description of the preliminary “mechanical” investigations that had led to many of his chief mathematical discoveries.  He thought that his “method” in these cases lacked rigor, since it assumed an area, for example, to be a sum of line segments.

The Method, as we have it, contains most of the text of some fifteen propositions sent in the form of a letter of Eratosthenes, mathematician and librarian at the university of Alexandria.  The author opened by saying that it is easier to supply a proof of a theorem if we first have some knowledge of what is involved; as an example he cites the proofs of Eudoxus of the cone and pyramid, which had been facilitated by the preliminary assertions, without proof, made by Democritus.  Then, Archimedes announced that he himself had a “mechanical” approach that paved the way for some of his proofs.  The very first theorem that he discovered by this approach was the one on the area of a parabolic segment; in Proposition 1 of The Method the author describes how he arrived at this theorem by balancing lines as one balances weights in mechanics.

Gerald Toomer of Brown University assesses Archimedes' Method, as it was known during the twentieth century. ⁴

Method Concerning Mechanical Theorems describes the process of discovery in mathematics.  It is the sole surviving work from antiquity and one of the few from any period that deals with this topic.  In it Archimedes recounts how he used a “mechanical” method to arrive at some of his key discoveries, including the area of a parabolic segment and the surface area and volume of a sphere.  The technique consists of dividing each of two figures, one bounded by straight lines and the other by a curve, into an infinite but equal number of infinitesimally thin strips, then “weighing” each corresponding pair of these strips against each other on a notional balance, and summing them to find the ratio of the two whole figures.  Archimedes emphasizes that, though useful as a heuristic method, this procedure does not constitute a rigorous proof.
 

The story of the recovery of Archimedes' Method of Mechanical Theorems is a terrific example, in my view, of how our comprehension of the past can even at this late date be dramatically changed by new discoveries, which may hinge on the merest chance.  Quoting Boyer again:

The work containing such marvelous results of more than 2000 years ago was recovered almost by accident in 1906.  The indefatigable Danish scholar J. L. Heiberg had read that at Constantinople there was a palimpsest of mathematical content.  (A palimpsest is a parchment the original writing on which as been only imperfectly washed off and replaced with a new and different text.)  Close inspection showed him that the original manuscript had contained something by Archimedes, and through photographs he was able to read most of the Archimedean text.  The manuscript consisted of 185 leaves, mostly of parchment but a few of paper, with the Archimedean text copied in a tenth-century hand.  An attempt — fortunately, none too successful — had been made to expunge this text in order to use the parchment for a Euchologion (a collection of prayers and liturgies used in the Eastern Orthodox Church) written in about the thirteenth century.  The mathematical text contained On the Sphere and Cylinder, most of the work On Spirals, part of the Measurement of a Circle and of On the Equilibrium of Planes, and On Floating Bodies, all of which have been preserved in other manuscripts; most important of all, the palimpsest gives us the only surviving copy of The Method.

In a sense, the palimpsest is symbolic of the contribution of the Medieval Age.  Intense preoccupation with religious concerns very nearly wiped out one of the most important works of the greatest mathematician of antiquity; yet in the end it was medieval scholarship that inadvertently preserved this, and much besides, which might otherwise have been lost.

No sooner had Archimedes' Method been almost miraculously recovered in 1906, but it was lost again (or stolen), disappearing for most of the rest of the century.  Fortunately for Archimedean scholarship of the twentieth century, the palimpsest had been photographed before being lost, allowing Heiberg to perform his remarkable feat. 

In 1998 (!) the nearly priceless document reappeared at a New York auction house.  Netz chronicles the manuscript's recent history:

Archimedes' treatise on the Method of Mechanical Theorems, which itself tends to turn up in unexpected places, was his most remarkable work.  It was lost until the great philologist Heiberg discovered it in a palimpsest (a scraped and overwritten parchment) in Istanbul in 1906.  Heiberg had discovered a 10th-century copy of the treatise, which had been used as the fabric for a 13th-century prayer-book.  Heiberg was able to read much, but not all of the faint traces.  Shortly after this astonishing discovery, the manuscript was lost or stolen, but in 1998 it resurfaced at a Christie's auction sale at New York.  It sold for two million dollars.  The anonymous owner generously supports the conservation and imaging now taking place at the Walters Art Museum, Baltimore. ⁵
 

Netz proceeds to the heart of the matter: the remarkable results recently obtaining from the re-recovery of the original manuscript in 1998.

As we should expect of Archimedes, the results of our recent research on the palimpsest are indeed unexpected.

Since 1906, it has been known that in the Method of Mechanical Theorems, Archimedes combined concepts of straight, curved, physical, and geometrical.  Above all, anticipating the calculus, he combined finite and infinite….

So much we have known for a century.  In a visit to Baltimore in 2001, Ken Saito from Osaka Prefecture University and I examined a hitherto unread piece of the Method of Mechanical Theorems.  We could hardly believe our eyes:  It turned out that Archimedes was looking for rigorous ways of establishing the calculus.

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.
 

¹ J. Bronowski, The Common Sense of Science, Harvard University Press, Cambridge, Massachusetts, 1963; pp. 117-118.

² Reviel Netz (Assistant Professor of Classics, Stanford University), “Proof, Amazement, and the Unexpected” (link requires subscription or pay per view), Science (1 Nov 2002), Vol. 298, No. 5595, pp. 967-968.

³ Carl B. Boyer (Professor of Mathematics, Brooklyn College), A History of Mathematics, Second Edition, revised by Uta C. Merzbach, John Wiley & Sons, Inc., New York, 1991, ISBN 0-471-09763-2 or 0-471-54397-7 (pbk); pp. 136-137, 139.

⁴ Gerald J. Toomer (Professor of the History of Mathematics, Brown University, Providence, Rhode Island), “Archimedes,” Encyclopædia Britannica, CD 1997, Encyclopaedia Britannica, Inc.

⁵ See “Eureka! Archimedes Palimpsest at the Walters Art Gallery.”

U.S. government black project's captive German scientist, in Steven Spielberg's Taken episode 2:

These are beings of unimaginable power of mind.  The ability to reach inside a man's mind and give him the images that are lurking there, surely that requires more energy than what is needed to guide a ship among the stars.

Anyone who's glanced at a few of the books entertaining the possibility of interstellar travel (covering such topics as the amount of fuel vs. payload needed to get a vessel to the stars) can see what a terrific boner is being pulled here.  In brief, if you have to carry your fuel along with you (as in ordinary rockets), even using nuclear or antimatter powered spaceships, the payload achievable is an extremely tiny fraction of the size of the entire ship, with required fuel occupying almost all of it.  Needless to say, a vast ship full of antimatter (and normal matter) fuel equals a stupendous amount of energy. 

Ramscoops or ground-laser illuminated lightsails offer significant escape from these limitations, because you don't have to carry (most of) the fuel along with you.  Even using these approaches, however, the amount of portable energy that must be carried on an interstellar ship is immense.

Beyond straightforward acceleration-deceleration means of getting to the stars, even if suggested approaches for bypassing the great distances between the stars turn out to be feasible (hypotheticals such as wormholes or “hyperspace”), who says the amount of energy needed to make use of such methods would be small?  If opening up a wormhole requires, say, artificial creation of a black hole massive enough not to crush “passengers” passing through its event horizon (i.e., much-much larger than a stellar-mass black hole), then the physical energy requirements for interstellar travel via wormholes would be truly gigantic!

Coming at it from the other direction, one must consider the question of how much “energy,” if that's the right term, is needed in principle to “reach inside a man's mind and give him the images that are lurking there.”  The “scientist” providing the Taken quote tosses it off as if of course! the energy required would be huge.  How much energy, though, did it take for the Voyager spacecraft to send images into the minds of Earthlings across billions of miles of space from the planet Neptune?  A few watts of power in Voyager's transmitter?

In the scene in Taken to which the above quote refers, the alien stood only a few feet from a human into whose brain he fed “the images that are lurking there.”  How much “energy” would that take?  How much energy under optimum conditions would it take to send a TV signal across a few feet?  Microwatts, at a guess?

Whether any signal transmitted could be received is another matter.  If a reception mechanism is already present in the human brain (which if telepathy exists — a big if — there must be; or if “synchronicity” is the way that telepathy works, that too will do for an explanation), in either case, once again, watts or microwatts (or even less, in the case of synchronicity) should suffice.  If there is no reception mechanism already present in the brain, however (or no synchronicity), then even an infinitude of power might not do.

In the situation where humans do not already come equipped with a “transmission image receptor” mechanism, the easiest way to get such a reception system implanted, in my view, would simply be to waft a “designer virus” across the intervening space (once again, a few feet, given the premise of the story), which infecting the intended individual, would cause a suitable receptor system to be grown, perhaps in his or her brain.  How much “energy” does it take to waft a tiny virus (far smaller than anthrax spores) across a few feet of space?

Once a suitable reception mechanism is present in the intended recipient, images should, once again, be transmittable using minimal energy.  Of course, if a continuing transmission link isn't needed, the viruses themselves could carry all the images or other data desired without any subsequent energy requirements.

However, the words Spielberg later in that same episode of Taken also places in the mouth of that “German scientist,” are if anything even stupider than the above quote!

We lost the war [WWII] because the Russians betrayed our trust.  There was never a question of our attitude.

I don't know about Spielberg.
 

UPDATE:  2002-12-22 01:30 UT:  More fundamental Taken stupidity.