Friday, September 29, 2006

Rene Descartes Has Doubts--Meditation I

1. SEVERAL years have now elapsed since I first became aware that I had accepted, even from my youth, many false opinions for true, and that consequently what I afterward based on such principles was highly doubtful; and from that time I was convinced of the necessity of undertaking once in my life to rid myself of all the opinions I had adopted, and of commencing anew the work of building from the foundation, if I desired to establish a firm and abiding superstructure in the sciences. But as this enterprise appeared to me to be one of great magnitude, I waited until I had attained an age so mature as to leave me no hope that at any stage of life more advanced I should be better able to execute my design. On this account, I have delayed so long that I should henceforth consider I was doing wrong were I still to consume in deliberation any of the time that now remains for action. To-day, then, since I have opportunely freed my mind from all cares [and am happily disturbed by no passions], and since I am in the secure possession of leisure in a peaceable retirement, I will at length apply myself earnestly and freely to the general overthrow of all my former opinions.[L][F]

2. But, to this end, it will not be necessary for me to show that the wholeof these are false--a point, perhaps, which I shall never reach; but as even now my reason convinces me that I ought not the less carefully to withhold belief from what is not entirely certain and indubitable, than from what is manifestly false, it will be sufficient to justify the rejection of the whole if I shall find in each some ground for doubt. Nor for this purpose will it be necessary even to deal with each belief individually, which would be truly an endless labor; but, as the removal from below of the foundation necessarily involves the downfall of the whole edifice, I will at once approach the criticism of the principles on which all my former beliefs rested.[L][F]

3. All that I have, up to this moment, accepted as possessed of the highest truth and certainty, I received either from or through the senses. I observed, however, that these sometimes misled us; and it is the part of prudence not to place absolute confidence in that by which we have even once been deceived.[L][F]

4. But it may be said, perhaps, that, although the senses occasionally mislead us respecting minute objects, and such as are so far removed from us as to be beyond the reach of close observation, there are yet many other of their informations (presentations), of the truth of which it is manifestly impossible to doubt; as for example, that I am in this place, seated by the fire, clothed in a winter dressing gown, that I hold in my hands this piece of paper, with other intimations of the same nature. But how could I deny that I possess these hands and this body, and withal escape being classed with persons in a state of insanity, whose brains are so disordered and clouded by dark bilious vapors as to cause them pertinaciously to assert that they are monarchs when they are in the greatest poverty; or clothed [in gold] and purple when destitute of any covering; or that their head is made of clay, their body of glass, or that they are gourds? I should certainly be not less insane than they, were I to regulate my procedure according to examples so extravagant.[L][F]

5. Though this be true, I must nevertheless here consider that I am a man, and that, consequently, I am in the habit of sleeping, and representing to myself in dreams those same things, or even sometimes others less probable, which the insane think are presented to them in their waking moments. How often have I dreamt that I was in these familiar circumstances, that I was dressed, and occupied this place by the fire, when I was lying undressed in bed? At the present moment, however, I certainly look upon this paper with eyes wide awake; the head which I now move is not asleep; I extend this hand consciously and with express purpose, and I perceive it; the occurrences in sleep are not so distinct as all this. But I cannot forget that, at other times I have been deceived in sleep by similar illusions; and, attentively considering those cases, I perceive so clearly that there exist no certain marks by which the state of waking can ever be distinguished from sleep, that I feel greatly astonished; and in amazement I almost persuade myself that I am now dreaming.[L][F]

6. Let us suppose, then, that we are dreaming, and that all these particulars--namely, the opening of the eyes, the motion of the head, the forth- putting of the hands--are merely illusions; and even that we really possess neither an entire body nor hands such as we see. Nevertheless it must be admitted at least that the objects which appear to us in sleep are, as it were, painted representations which could not have been formed unless in the likeness of realities; and, therefore, that those general objects, at all events, namely, eyes, a head, hands, and an entire body, are not simply imaginary, but really existent. For, in truth, painters themselves, even when they study to represent sirens and satyrs by forms the most fantastic and extraordinary, cannot bestow upon them natures absolutely new, but can only make a certain medley of the members of different animals; or if they chance to imagine something so novel that nothing at all similar has ever been seen before, and such as is, therefore, purely fictitious and absolutely false, it is at least certain that the colors of which this is composed are real. And on the same principle, although these general objects, viz. [a body], eyes, a head, hands, and the like, be imaginary, we are nevertheless absolutely necessitated to admit the reality at least of some other objects still more simple and universal than these, of which, just as of certain real colors, all those images of things, whether true and real, or false and fantastic, that are found in our consciousness (cogitatio) are formed.[L][F]

7. To this class of objects seem to belong corporeal nature in general and its extension; the figure of extended things, their quantity or magnitude, and their number, as also the place in, and the time during, which they exist, and other things of the same sort.[L][F]

8. We will not, therefore, perhaps reason illegitimately if we conclude from this that Physics, Astronomy, Medicine, and all the other sciences that have for their end the consideration of composite objects, are indeed of a doubtful character; but that Arithmetic, Geometry, and the other sciences of the same class, which regard merely the simplest and most general objects, and scarcely inquire whether or not these are really existent, contain somewhat that is certain and indubitable: for whether I am awake or dreaming, it remains true that two and three make five, and that a square has but four sides; nor does it seem possible that truths so apparent can ever fall under a suspicion of falsity [or incertitude].[L][F]

9. Nevertheless, the belief that there is a God who is all powerful, and who created me, such as I am, has, for a long time, obtained steady possession of my mind. How, then, do I know that he has not arranged that there should be neither earth, nor sky, nor any extended thing, nor figure, nor magnitude, nor place, providing at the same time, however, for [the rise in me of the perceptions of all these objects, and] the persuasion that these do not exist otherwise than as I perceive them ? And further, as I sometimes think that others are in error respecting matters of which they believe themselves to possess a perfect knowledge, how do I know that I am not also deceived each time I add together two and three, or number the sides of a square, or form some judgment still more simple, if more simple indeed can be imagined? But perhaps Deity has not been willing that I should be thus deceived, for he is said to be supremely good. If, however, it were repugnant to the goodness of Deity to have created me subject to constant deception, it would seem likewise to be contrary to his goodness to allow me to be occasionally deceived; and yet it is clear that this is permitted.[L][F]

10. Some, indeed, might perhaps be found who would be disposed rather to deny the existence of a Being so powerful than to believe that there is nothing certain. But let us for the present refrain from opposing this opinion, and grant that all which is here said of a Deity is fabulous: nevertheless, in whatever way it be supposed that I reach the state in which I exist, whether by fate, or chance, or by an endless series of antecedents and consequents, or by any other means, it is clear (since to be deceived and to err is a certain defect ) that the probability of my being so imperfect as to be the constant victim of deception, will be increased exactly in proportion as the power possessed by the cause, to which they assign my origin, is lessened. To these reasonings I have assuredly nothing to reply, but am constrained at last to avow that there is nothing of all that I formerly believed to be true of which it is impossible to doubt, and that not through thoughtlessness or levity, but from cogent and maturely considered reasons; so that henceforward, if I desire to discover anything certain, I ought not the less carefully to refrain from assenting to those same opinions than to what might be shown to be manifestly false.

11. But it is not sufficient to have made these observations; care must be taken likewise to keep them in remembrance. For those old and customary opinions perpetually recur-- long and familiar usage giving them the right of occupying my mind, even almost against my will, and subduing my belief; nor will I lose the habit of deferring to them and confiding in them so long as I shall consider them to be what in truth they are, viz., opinions to some extent doubtful, as I have already shown, but still highly probable, and such as it is much more reasonable to believe than deny. It is for this reason I am persuaded that I shall not be doing wrong, if, taking an opposite judgment of deliberate design, I become my own deceiver, by supposing, for a time, that all those opinions are entirely false and imaginary, until at length, having thus balanced my old by my new prejudices, my judgment shall no longer be turned aside by perverted usage from the path that may conduct to the perception of truth. For I am assured that, meanwhile, there will arise neither peril nor error from this course, and that I cannot for the present yield too much to distrust, since the end I now seek is not action but knowledge.[L][F]

12. I will suppose, then, not that Deity, who is sovereignly good and the fountain of truth, but that some malignant demon, who is at once exceedingly potent and deceitful, has employed all his artifice to deceive me; t will suppose that the sky, the air, the earth, colors, figures, sounds, and all external things, are nothing better than the illusions of dreams, by means of which this being has laid snares for my credulity; I will consider myself as without hands, eyes, flesh, blood, or any of the senses, and as falsely believing that I am possessed of these; I will continue resolutely fixed in this belief, and if indeed by this means it be not in my power to arrive at the knowledge of truth, I shall at least do what is in my power, viz., [ suspend my judgment ], and guard with settled purpose against giving my assent to what is false, and being imposed upon by this deceiver, whatever be his power and artifice. But this undertaking is arduous, and a certain indolence insensibly leads me back to my ordinary course of life; and just as the captive, who, perchance, was enjoying in his dreams an imaginary liberty, when he begins to suspect that it is but a vision, dreads awakening, and conspires with the agreeable illusions that the deception may be prolonged; so I, of my own accord, fall back into the train of my former beliefs, and fear to arouse myself from my slumber, lest the time of laborious wakefulness that would succeed this quiet rest, in place of bringing any light of day, should prove inadequate to dispel the darkness that will arise from the difficulties that have now been raised.[L][F]

Tuesday, September 26, 2006

Francis Bacon, Idols of the Mind

Idols Which Beset Man's Mind
by Francis Bacon

Man, being the servant and interpreter of nature, can do and understand so much and so much only as he has observed in fact or in thought of the course of nature: beyond this he neither knows anything nor can do anything.
Human knowledge and human power meet in one; for where the cause is not known the effect cannot be produced. Nature to be commanded must be obeyed; and that which in contemplation is as the cause is in operation as the rule.
There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable proceeds to judgment and to the discovery of middle axioms! And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried.

The understanding left to itself takes the same course (namely, the former) which it takes in accordance with logical order. For the mind longs to spring up to positions of higher generality, that it may find rest there; and so after a little while wearies of experiment. But this evil is increased by logic, because of the order and solemnity of its disputations.

The understanding left to itself, in a sober, patient, and grave mind, especially if it be not hindered by received doctrines, tries a little that other way, which is the right one, but with little progress; since the understanding, unless directed and assisted, is a thing unequal, and quite unfit to contend with the obscurity of things.

Both ways set out from the senses and particulars, and rest in the highest generalities; but the difference between them is infinite. For the one just glances at experiment and particulars in passing, the other dwells duly and orderly among them. The one, again, begins at once by establishing certain abstract and useless generalities, the other rises by gradual steps to that which is prior and better known in the order of nature.
The axioms now in use, having been suggested by a scanty and manipular experience and a few particulars of most general occurrence, are made for the most part just large enough to fit and take these in: and therefore it is no wonder if they do not lead to new particulars. And if some opposite instance, not observed or not known before, chance to come in the way, the axiom is rescued and preserved by some frivolous distinction; whereas the truer course would be to correct the axiom itself.

The conclusions of human reason as ordinarily applied in matter of nature, I call for the sake of distinction Anticipations of Nature (as a thing rash or premature). That reason which is elicited from facts by a just and methodical process, I call Interpretation of Nature.

Anticipations are a ground sufficiently firm for consent; for even if men went mad all after the same fashion, they might agree one with another well enough.

For the winning of assent, indeed, anticipations are far more powerful than interpretations; because being collected from a few instances, and those for the most part of familiar occurrence, they straightway touch the understanding and fill the imagination; whereas interpretations on the other hand, being gathered here and there from very various and widely dispersed facts, cannot suddenly strike the understanding; and therefore they must needs, in respect of the opinions of the time, seem harsh and out of tune; much as the mysteries of faith do.

In sciences founded on opinions and dogmas, the use of anticipations and logic is good; for in them the object is to command assent to the proposition, not to master the thing.

Though all the wits of all the ages should meet together and combine and transmit their labours, yet will no great progress ever be made in science by means of anticipations; because radical errors in the first concoction of the mind are not to be cured by the excellence of functions and remedies subsequent.

It is idle to expect any great advancement in science from the superinducing and engrafting of new things upon old. We must begin anew from the very foundations, unless we would revolve forever in a circle with mean and contemptible progress.

The honour of the ancient authors, and indeed of all, remains untouched; since the comparison I challenge is not of wits or faculties, but of ways and methods, and the part I take upon myself is not that of a judge, but of a guide.

This must be plainly avowed: no judgment can be rightly formed either of my method or of the discoveries to which it leads, by means of anticipations (that is to say, of the reasoning which is now in use); since I cannot be called on to abide by the sentence of a tribunal which is itself on its trial.

Even to deliver and explain what I bring forward is no easy matter; for things in themselves new will yet be apprehended with reference to what is old.

It was said by Borgia of the expedition of the French into Italy, that they came with chalk in their hands to mark out their lodgings, not with arms to force their way in. I in like manner would have my doctrine 'enter quietly into the minds that are fit and capable of receiving it; for confutations cannot be employed, when the difference is upon first principles and very notions and even upon forms of demonstration.

One method of delivery alone remains to us; which is simply this: we must lead men to the particulars themselves, and their series and order; while men on their side must force themselves for awhile to lay their notions by and begin to familiarise themselves with facts.
The doctrine of those who have denied that certainty could be attained at all, has some agreement with my way of proceeding at the first setting out; but they end in being infinitely separated and opposed. For the holders of that doctrine assert simply that nothing can be known; I also assert that not much can be known in nature by the way which is now in use. But then they go on to destroy the authority of the senses and understanding; whereas I proceed to devise and supply helps for the same.

The idols and false notions which are now in possession of the human understanding, and have taken deep root therein, not only so beset men's minds that truth can hardly find entrance, but even after entrance obtained, they will again in the very instauration of the sciences meet and trouble us, unless men being forewarned of the danger fortify themselves as far as may be against their assaults.

There are four classes of Idols which beset men's minds. To these for distinction's sake I have assigned names, -- calling the first class Idols of the Tribe; the second, Idols of the Cave; the third, Idols of the Market-place; the fourth, Idols of the Theatre.

The formation of ideas and axioms by true induction is no doubt the proper remedy to be applied for the keeping off and clearing away of idols. To point them out, however, is of great use; for the doctrine of Idols is to the Interpretation of Nature what the doctrine of the refutation of Sophisms is to common Logic.

The Idols of the Tribe have their foundation in human nature itself, and in the tribe or race of men. For it is a false assertion that the sense of man is the measure of things. On the contrary, all perceptions as well of the sense as of the mind are according to the measure of the individual and not according to the measure of the universe. And the human understanding is like a false mirror, which, receiving rays irregularly, distorts and discolours the nature of things by mingling its own nature with it.

The Idols of the Cave are the idols of the individual man. For every one (besides the errors common to human nature in general) has a cave or den of his own, which refracts and discolours the light of nature; owing either to his own proper and peculiar nature; or to his education and conversation with others; or to the reading of books, and the authority of those whom he esteems and admires; or to the differences of impressions, accordingly as they take place in a mind preoccupied and predisposed or in a mind indifferent and settled; or the like. So that the spirit of man (according as it is meted out to different individuals) is in fact a thing variable and full of perturbation, and governed as it were by chance. Whence it was well observed by Heraclitus that men look for sciences in their own lesser worlds, and not in the greater or common world.

There are also Idols formed by the intercourse and association of men with each other, which I call Idols of the Market-place, on account of the commerce and consort of men there. For it is by discourse that men associate; and words are imposed according to the apprehension of the vulgar. And therefore the ill and unfit choice of words wonderfully obstructs the understanding. Nor do the definitions or explanations wherewith in some things learned men are wont to guard and defend themselves, by any means set the matter right. But words plainly force and overrule the understanding, and throw all into confusion, and lead men away into numberless empty controversies and idle fancies.

Lastly, there are Idols which have immigrated into men's minds from the various dogmas of philosophies, and also from wrong laws of demonstration. These I call Idols of the Theatre; because in my judgment all the received systems are but so many stage-plays, representing worlds of their own creation after an unreal and scenic fashion. Nor is it only of the systems now in vogue, or only of the ancient sects and philosophies, that I speak; for many more plays of the same kind may yet be composed and in like artificial manner set forth; seeing that errors the most widely different have nevertheless causes for the most part alike. Neither again do I mean this only of entire systems, but also of many principles and axioms in science, which by tradition, credulity, and negligence have come to be received.

Saturday, September 23, 2006

Prospero's Daughter

Channeling Shakespeare: Prospero's daughter turns a classic plot inside out to examine questions about colonization, race and rape

IMAGINE ME, A 14-YEAR-OLD BROWN-skinned girl, fixing on the island of Trinidad, a colony of England. I am lucky enough to have won a scholarship to one of the premier secondary schools that the British colonial government had helped to establish for the children of the plantation owners and the British colonial masters. Imagine I am sitting in Mother Perpetua's class (not her real name). We are reading The Tempest, a play by William Shakespeare. In that play, a European, Prospero, and his daughter, Miranda, have been set adrift on the ocean by Prospero's envious, evil brother. Prospero and Miranda end up on an isolated, tropical island. There are two creatures on the island, one a deformed, freckled male savage called Caliban, and the other an airy spirit, Ariel.

When the play begins, Prospero and Miranda have been on the island for 12 years. We learn that it is only recent that Prospero has imprisoned Caliban. Prospero tells us why. He says Caliban "didst seek to violate the honor of my child." In other words, Caliban had attempted to rape Miranda.

Mother Perpetua does not hide her revulsion. I think it is not our hot, tropical climate that makes her face turn beet red. I think it is this talk of sex, the picture she has formed in her head of a black man raping a young white woman. Her voice rises and perspiration pearls on her top lip as she reads lines from the play where Prospero calls Caliban a savage, a lying slave, a misshapen knave whose body grows uglier with age, "a born devil, on whose nature / Nurture can never stick."

Mother Perpetua takes out her handkerchief and wipes her brow. Caliban is an ungrateful brute, she tells us, unappreciative of the kindness Prospero has extended to him. Her indignation is as righteous as Prospero's when Prospero lashes out at Caliban for his ingratitude: "I have us'd thee / (Filth as thou art) with humane care, and lodg'd thee / In mine own cell...."

On Being Colonized

I cringe in my seat because, even at 14, I cannot miss the parallels between my situation in a British colony and Caliban's. In both our cases, Europeans have come to our islands, and though surely they have laid claim to our land, they have given us much in return. I am proof of their beneficence, siring in a classroom, getting an education they have been kind enough to provide for me. Prospero, too, makes it clear that his stinging condemnation is directed not only at Caliban. Caliban is "a lying slave / Whom stripes may move, not kindness" He later says Caliban belongs to a "vile race."

But Caliban does not cringe. He strikes out at Prospero. He taunts him: "You taught me language; and my profit on't / Is, I know how to curse. / The red plague rid you / For learning me your language!"

Imagine me now an older teenager, giddy with the pride that has overtaken my island, now that Trinidad has gained its independence from England. The Barbadian writer George Lamming publishes The Pleasures of Exile. He proclaims Caliban a hero, a Caribbean man who defies the colonizer and claims his rightful ownership of his island. I reread The Tempest. I commit to memory Caliban's audacious assertion: "This island's mine by Sycorax my mother / Which thou tak'st from me."

Imagine me now in graduate school in the United States, working on a dissertation for a Ph.D. in English literature. I ask my professor to explain what Prospero means when he says Caliban's mother was "a blue-eyed hag." Was Caliban's mother a white woman? I ask. Oh surely not, my professor says. Caliban is meant to be a sort of savage, a colored man, his name a derivative of cannibal. Hag is the operative word. Caliban's mother was an old black woman whose eyes had turned blue because of cataracts, he explains. Tricky Shakespeare! Let's say Caliban's mother had Caliban at 20 (which is old, given that she slept around), she would have had to be at least 75 for the cataracts to thicken so her eyes would appear blue.

Which means Caliban was a dirty old man around age 55 when he attempted to rape a 15-year-old virgin. Must one add lecherous old man to the names Prospero calls Caliban? To what degree must one suspend logic to avoid identification with Caliban?

In Killens Class

Imagine me now a professor at Medgar Evers College. I am chairperson of the Humanities Division. The extraordinary African American writer John Oliver Killens joins our faculty as writer-in-residence. He asks me if I have ever been interested in becoming a writer. I have been waiting years for someone to ask me that question.

Encouraged by his genuine interest and his kindly manner, I dare to show him some scraps of paper on which I have scribbled the beginnings of a novel. The next week, I am in his Saturday writing workshop. In it are Terry McMillan, who is working on Mama; Doris Jean Austin, who is writing After the Garden; and Arthur Flowers, who has started De Mojo Blues.

Killens inspires us. He tells us that every time he picks up his pen or strikes a key on the keyboard, his intent is to change the world. He tells us that writers of color have a responsibility to use their talents to change the negative ways in which people of color see themselves, and the negative ways in which they are portrayed by others. He makes me think of the days I hung my head in shame as Mother Perpetua castigated Caliban. He makes me think of my outrage later on, after I read Lamming. He makes me try to examine my attitude toward the British, why in spite of my anger for their colonization of my island, I continue to admire them and find it impossible to summon up a rage similar to the rage that many of my African American friends have toward white America.

Killens dies too soon, four short years after I met him, one short year after he and I worked together to organize the first National Black Writers Conference at which the venerable Maya Angelou spoke, and which I continued to direct for 17 more years, drawing on the capital Killens left behind, which brought distinguished writers to our college who had not forgotten how generously he had shared his talent and knowledge with them. I write five novels, but I continue to be haunted by Killens's charge to writers of color; I continue to be haunted by my discomfort with scholarly interpretations of The Tempest. I ask myself questions I had not asked in my doctoral dissertation. I ask why, after 12 years of an apparently amicable relationship with Caliban, does Prospero turn on him? What actually happened between Miranda and Caliban? What connection is there in the coincidental timing of Prospero's desperation to find a husband for Miranda and his accusation that Caliban attempted to rape her?

I write a novel to find the answers. I write Prospero's Daughter. It is a contemporary novel about an English doctor, Philip Gardner, who, with his daughter, Virginia, is stranded on a former leper colony off the coast of Trinidad. Living on the island is a boy, Carlos, whose eyes, like his mother's, are blue, and a girl, Ariana. Twelve years later, Gardner accuses Carlos of attempting to rape Virginia. Why? What really happened on the island between Carlos and Virginia? What part does Gardner play in the events that lead up to this accusation? Is Ariana, as Caribbean scholars have said of Shakespeare's Ariel, a wilting lackey to Gardner? Is she, like Ariel, a spy for the European? What hold does Gardner have on her?

It takes me four years, writing and rewriting, destroying page after page--at one time, almost a hundred pages--to discover the answers to these questions. Prospero's Daughter, of course, was many more years in the making.

Elizabeth Nunez, City University of New York Distinguished Professor at Medgar Evers College, is the author of five other novel, including Bruised Hibiscus

Sunday, September 10, 2006

Galileo, Astronomy, and Physics

Galileo Galilei
There was another man, working at around the same time as Kepler, who made an even greater contribution to the dawn of modern astronomy and single-handedly pioneered modern mathematical physics. This was a man who laid down virtually all the groundwork for Newton and his name was Galileo Galilei (usually referred to only as Galileo). He has been called by some as the father of both modern astronomy and modern physics and certainly his role as a pivotal figure in the development of both these sciences is beyond question.

On top of this he was also the pioneer of modern experimental scientific method.

It was Galileo that finally provided proof of the Copernican theory, and thus confirming Kepler's work to be correct.

He also had time to lay down the foundations of correct understanding of dynamics and of gravity.But we are getting ahead of ourselves here.

Galileo's Telescope
Before Galileo began so much of his ground breaking work in astronomy an invention was to come along and help him out, that invention was the telescope and in the arms of Galileo it was the instrument that was to revolutionise the science of astronomy, allowing Galileo to peer into the heavens and see at a magnification many times what any human had seen before.

The discovery of the telescope is usually credited to Hans Lippershey in 1608, although there is some evidence that there was one or possibly even two people before him to invent a telescope, but this evidence remains very much inconclusive, so we shall not break from tradition here!

Galileo and Astronomy
So back to Galileo, in 1609 (about the same time as Kepler was about to publish his first two laws) from only simple reports of this new invention, Galileo, using his skills, was able to construct a vastly superior model to Lippershey's telescope and is said to be the first to use the refracting telescope. Some of his early observations included:

The Moon was not smooth but actually covered in mountains and craters.
The planets were discs not points of light.
The Milky Way was composed of an enormous number of stars (agreeing with Copernicus' idea of the universe being much vaster than previously thought, also destroying the only argument for the Taychoic system, by providing reason for why, in a heliocentric system there would appear to be no stellar parallax).

As a collective what these observations did was to raise the issue of the credibility of the Ptolemaic system, how could Aristotle and Ptolemy's work be trusted to be correct when there was so much of the universe they didn't know?

Galileo's early observations convinced him of the accuracy of the Copernican system and he began to argue strongly for it, basing his arguments on his observations with his telescope.

In this work there are 3 further observations in particular that deserve special mention:
His observations of the Moons of JupiterGalileo used the so called Galilean moons to prove a major argument against the Copernican system was incorrect.

The argument suggested that given the moon orbited the Earth, if the Earth then orbited the Sun, the Moon would be left behind. With the discovery of the moons around Jupiter it was clear that a planet could orbit a body without leaving behind any moons that were in turn orbiting it.

Observations of Sunspots

With the observation of Sunspots not only did Galileo prove that the Sun was not perfect (remember at the time the held ideas continued to be Aristotle's theory that God made all the celestial bodies and so they must be perfect) but he also observed that these imperfections were moving. This implied that the Sun was rotating on an axis which meant it was more feasible for the earth to be rotating (the idea of the Earth rotating in the Copernican model was one of the greatest arguments against it as such rotation could not be felt).

Galileo's view of SunspotsFrom Galileo's own sketches
A 2001 view of SunspotsCourtesy of SOHO/MDI

Observations of the Phases of Venus
Galileo's most important achievement in astronomy was demonstrating that the planet Venus, as seen from the Earth, went through a complete set of phases just like the Moon, which he first noticed in 1610.This wasn't just ground breaking it was earth shattering, it provided conclusive evidence that was consistent with the Copernican model but not with the Ptolemaic model.How? Well if the Earth was the centre of the Universe then due to the position of the Earth, Venus and the Sun, we would only ever see Venus in crescent phases because Venus would always be between the Earth and the Sun (see Ptolemaic system below).

The Ptolemaic System

The Copernican SystemGalileo identified that Venus went through a full cycle of phases, as viewed from the Earth, which meant that sometimes Venus must be on the opposite side of the Sun from Earth (see the Copernican system above), thus disproving the Geocentric theory of the Universe. So long after Copernicus' discovery finally there was empirical evidence to allow a definitive test, which proved Copernicus' and Kepler's work to be correct and the Ptolemaic model that had been held to be correct for 1500 years to be wrong!

Galileo Publishes His Work
In 1632 Galileo published his work Dialogue Concerning The Two Greatest World Systems. This latest work, supporting the Copernican model and proving the geocentric system wrong was not received well by the Roman Catholic Church! Indeed they were incensed by this work as it was contrary to scripture, contrary to the very foundations of religion. Of course a century before Copernicus himself and delayed the publication of his work for fear of the reprisal of the church, and it appears that his fear was justified.

In 1633 Galileo was summoned to Rome and quickly convicted of heresy, he was forced to make a public confession of his error in judgement and withdraw his support for the Copernican model, he was also forbidden to publish any further work and sentenced to life imprisonment. Due to his age, however, he was permitted to serve his sentence under house arrest.

Galileo's 'Ears of Saturn'
As a point of interest Galileo also discovered what he called the 'ears' of Saturn (of course we now know these to be rings but Galileo's telescope was not powerful enough to determine this).

Galileo and Physics
After Galileo's conviction in Rome, publicly at least, he lost interest in astronomy and he concentrated his efforts on his other life long work in the pioneering field of mathematical physics. In 1638, he managed to have his final work, Discourse on Two New Sciences smuggled out of Italy and published in the Netherlands. This work detailed his findings on the correct understanding of dynamics, gravity and, putting the two together, of projectiles.

Yet again Galileo was to challenge the long held theories of Aristotle.

In his early work in this field he performed inclined plane experiments, in which he studied both gravity and inertia.

He was studying the Law of Fall from as early as 1604 and was using inclined planes because in his initial experiments he found that objects in free fall accelerate too quickly for accurate measurement so he began using these planes to effectively slow down the rate of fall, therefore allowing him to make accurate time and distance measurements.

Aristotle had previously said that bodies falling in the same medium will fall at a speed proportional to their weight. Galileo believed this to be incorrect he suggested that all objects in a medium without resistance (e.g. on the Earth's surface but ignoring the effects of air resistance) will all gain equal amounts of velocity in equal intervals of time (uniform acceleration), regardless of weight (in other words all objects will fall at a constant rate and further to this, this rate will be the same for all objects no matter their weight).

After long experimentation he found that as the seconds past the distance the object would travel would increase in ascending odd numbers i.e. 1, 3, 5 ,7 ,9 etc (in other words in the third second the object will travel a distance of 5 units, but the total distance travelled in all 3 seconds of the experiment is 5+3+1=9units) from this he realised that the distance covered is directly proportional to the square of time taken (see table).This was one of his startling discoveries, that laid down the groundwork for some famous work to be done in the not too distant future.

Galileo's Law of Inertia
On inertia Aristotle had formulated the principle of impetus from his observations that most objects do not remain in motion after a force that is acting upon them is moved is removed. So he suggested that any object in motion will not remain so unless the force that is acting upon it does so constantly, if a force was removed the impetus would run out. What Aristotle actually believed was that the natural state of any object is at rest and so any object at rest will remain so unless acted upon by a force. Using just observation it is clear why Aristotle would think this
way, although this concept clearly has shortcomings.

Take, for example, an arrow travelling through the air, how could this arrow continue on its path after the force (the bow string) was removed?Aristotle's principle should mean that the arrow would not remain in motion after the force acting on it was removed. This is an often quoted example because it this was particularly troublesome to the Greeks (their actual reasoning for why it remained in motion had something to do with the arrow creating a vacuum behind it and air rushed into the vacuum to push the arrow along!).

With use of inclined planes Galileo realised that this was wrong because Aristotle had failed to take into account a hidden force (of course frictional force). He worked out that this force was acting in the opposite direction to motion and that if this force was decreased (by using oil, grease etc) then the object in motion would move further before stopping.

From this Galileo was to formulate his Law of Inertia:
An object in a state of motion possesses an inertia causing it to remain in a state of motion unless acted on by an external force.

Another way to state this is: if the frictional force is reduced to zero and a force is applied to an object so that it is pushed at a constant velocity after that force is removed the object will continue at that velocity forever, unless of course a new force acts on it at a later time.Clearly then Galileo demonstrated that a object's natural state was not at rest, as Aristotle had believed, but in fact in motion, and rest was just a special case where velocity was zero, though there was still forces acting on it.

These principles are simply taken for granted now, just as many of Galileo's achievements are, but it must be remembered at the time, as foolish as it seems to us now, everyone believed Aristotle's principles and Galileo's work was totally revolutionary. Clearly his work laid down the principles of the modern day understanding of dynamics.Galileo and Projectiles

Then Galileo went on to study projectiles, where he brought together his work on falling bodies and inertia and added the principle of Superposition. This stated that if a body is subject to two influences, each producing a characteristic type of motion, the object will respond to each, without modifying its response to the other. Or in simpler terms, referring to the diagram (right), a diagonal motion (V) may be spilt into its vertical (Vy) and horizontal (Vx) vectors and these two vectors can be treated separately.Before Galileo it was believed that when a projectile was launched it would continue until its impetus (horizontal motion) was lost and then fall towards ground. (Aristotle believed that the projectiles were pushed along (horizontally) by an external force transmitted through the air, see the example of the arrow above).For Galileo though projectiles move both horizontally and vertically at the same time, and that the motion can be separated into these two components (principle of Superposition). So what Galileo achieved here was to realise that the object was subject not only to horizontal force that caused acceleration but also to a vertical acceleration.

The horizontal component is described by Galileo's principle of inertia (contrast to impetus) so, providing no force acts on it after launch (in this case no air resistance) the horizontal velocity will remain constant (i.e. horizontal acceleration is zero), so the horizontal distance is clearly proportionate to the time taken to cover it.The vertical component causes constantly accelerated motion (don't forgot it is a vector so the direction is important, in this case downwards towards the Earth) so the vertical distance is proportional to the square of time taken (from his law of fall).

By treating the components separately when Galileo combined the calculations for the components he predicted that the path of a projectile would be a gently curving arc called a parabola and he proved this by experimentation. He showed that the projectile would always follow this path regardless of launch angle and launch velocity. (Obviously there is resistance in real world experiments, but the effect of air resistance is not that great and experimentation results are very similar to what would be predicted using the mathematics).

Galileo's Projectile work
Galileo stands as one of the all time great scientists, not only for his discoveries and his pioneering techniques but also for the fact that he had the courage to stand up and fight against tradition, public opinion and the church for what he believed in.

Science truly owes Galileo Galilei a debt of incredible gratitude.

Wednesday, September 06, 2006

Galileo and the Ptolemaic System

The Galileo Project

Ptolemaic System

In his Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican of 1632, Galileo attacked the world system based on the cosmology of Aristotle (384-322 BCE) and the technical astronomy of Ptolemy (ca. 150 CE).

In his books On the Heavens, and Physics, Aristotle put forward his notion of an ordered universe or cosmos. It was governed by the concept of place , as opposed to space, and was divided into two distinct parts, the earthly or sublunary region, and the heavens. The former was the abode of change and corruption, where things came into being, grew, matured, decayed, and died; the latter was the region of perfection, where there was no change. In the sublunary region, substances were made up of the four elements, earth, water, air, and fire. Earth was the heaviest, and its natural place was the center of the cosmos; for that reason the Earth was situated in the center of the cosmos. The natural places of water, air, and fire, were concentric spherical shells around the sphere of earth. Things were not arranged perfectly, and therefore areas of land protruded above the water. Objects sought the natural place of the element that predominated in them. Thus stones, in which earth predominated, move down to the center of the cosmos, and fire moves straight up. Natural motions were, then, radial, either down or up. The four elements differed from each other only in their qualities. Thus, earth was cold and dry while air was warm and moist. Changing one or both of its qualities, transmuted one element into another. Such transmutations were going on constantly, adding to the constant change in this sublunary region.

The heavens, on the other hand, were made up of an entirely different substance, the aether [1] or quintessence (fifth element), an immutable substance. Heavenly bodies were part of spherical shells of aether. These spherical shells fit tightly around each other, without any spaces between them, in the following order: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, fixed stars. Each spherical shell (hereafter, simply, sphere) had its particular rotation, that accounted for the motion of the heavenly body contained in it. Outside the sphere of the fixed stars, there was the prime mover (himself unmoved), who imparted motion from the outside inward. All motions in the cosmos came ultimately from this prime mover. The natural motions of heavenly bodies and their spheres was perfectly circular, that is, circular and neither speeding up nor slowing down.

It is to be noted about this universe that everything had its natural place, a privileged location for bodies with a particular makeup, and that the laws of nature were not the same in the heavenly and the earthly regions. Further, there were no empty places or vacua anywhere. Finally, it was finite: beyond the sphere of the fixed stars and the prime mover, there was nothing, not even space. The cosmos encompassed all existence.

Christian Aristotelian Cosmos. From Peter Apian, Cosmographia [click for larger image]
Now, ingenious as this cosmology was, it turned out to be unsatisfactory for astronomy. Heavenly bodies did, in fact, not move with perfect circular motions: they speeded up, slowed down, and in the cases of the planets even stopped and reversed their motions. Although Aristotle and his contemporaries tried to account for these variations by splitting individual planetary spheres into component spheres, each with a component of the composite motion, these constructions were very complex and ultimately doomed to failure. Furthermore, no matter how complex a system of spheres for an individual planet became, these spheres were still centered on the Earth. The distance of a planet from the Earth could therefore not be varied in this system, but planets vary in brightness, a variation especially noticeable for Venus, Mars, and Jupiter. Since in an unchangeable heaven variations in intrinsic brightness were ruled out, and since spheres did not allow for a variation in planetary distances from the Earth, variations in brightness could not be accounted for in this system.

Thus, although Aristotle's spherical cosmology had a very long life, mathematicians who wished to make geometrical models to account for the actual motions of heavenly bodies began using different constructions within a century of Aristotle's death. These constructions violated Aristotle's physical and cosmological principles somewhat, but they were ultimately successful in accounting for the motions of heavenly bodies. It is in the work of Claudius Ptolemy, who lived in the second century CE, that we see the culmination of these efforts. In his great astronomical work, Almagest, [2] Ptolemy presented a complete system of mathematical constructions that accounted successfully for the observed motion of each heavenly body.

Ptolemy used three basic constructions, the eccentric, the epicycle, and the equant. An eccentric construction is one in which the Earth is placed outside the center of the geometrical construction. Here, the Earth, E, is displaced slightly from the center, C, of the path of the planet. Although this construction violated the rule that the Earth was the center of the cosmos and all planetary motions, the displacement was minimal and was considered a slight bending of the rule rather than a violation. The eccentric in the figure below is fixed; it could also be made movable. In this case the center of the large circle was a point that rotated around the Earth in a small circle centered on the Earth. In some constructions this little circle was not centered in the Earth.

The second construction, the epicycle, is geometrically equivalent to the simple movable eccentric. In this case, the planet moved on a little circle the center of which rotated on the circumference of the large circle centered on the on theEarth. When the directions and speeds of rotation of the epicycle and large circle were chosen appropriately, the planet, as seen from the Earth, would stop, reverse its course, and then move forward again. Thus the annual retrograde motion of the planets (caused, in heliocentric terms by the addition of the Earth's annual motion to the motion of the planet) could roughly be accounted for.

But these two constructions did not quite bring the resulting planetary motions within close agreement with the observed motions. Ptolemy therefore added yet a third construction, the equant. In this case, the center of construction of the large circle was separated from the center of motion of a point on its circumference, as shown below, where C is the geometrical center of the large circle (usually called in these constructions the excentric circle) but the motion of the center of the epicycle, P (middle figure), is uniform about Q, the equant point.

Ptolemy combined all three constructions in the models of the planets, Sun, and Moon. A typical construction might thus be as in the picture below, where E is the Earth, C the geometric center of the eccentric circle, Q the equant point, F the center of the epicycle, and P the planet. As mentioned before, the eccentric was often not fixed but moved in a circle about the Earth or another point between the Earth and the equant point.

With such combinations of constructions, Ptolemy was able to account for the motions of heavenly bodies within the standards of observational accuracy of his day. The idea was to break down the complex observed planetary motion into components with perfect circular motions. In doing so, however, Ptolemy violated the cosmological and physical rules of Aristotle. The excentric and epicycle meant that planetary motions were not exactly centered on the Earth, the center of the cosmos. This was, however, a "fudge" that few objected to. The equant violated the stricture of perfect circular motion, and this violation bothered thinkers a good deal more. Thus, in De Revolutionibus (see Copernican System), Copernicus tells the reader that it was his aim to rid the models of heavenly motions of this monstrous construction.

Aristotelian cosmology and Ptolemaic astronomy entered the West, in the twelfth and thirteenth centuries, as distinct textual traditions. The former in Aristotle's Physics and On the Heavens and the many commentaries on these works; the latter in the Almagest and the technical astronomical literature that had grown around it, especially the work of Islamic astronomers working in the Ptolemaic paradigm. In the world of learning in the Christian West (settled in the universities founded around 1200 CE), Aristotle's cosmology figured in all questions concerned with the nature of the universe and impinged on many philosophical and theological questions. Ptolemy's astronomy was taught as part of the undergraduate mathematical curriculum only and impinged only on technical questions of calendrics, positional predictions, and astrology.
Copernicus's innovations was therefore not only putting the Sun in the center of the universe and working out a complete astronomical system on this basis of this premise, but also trying to erase the disciplinary boundary between the textual traditions of physical cosmology and technical astronomy.

Notes:[1] The traditional English spelling, aether, is used here to distinguish Aristotle's heavenly substance from the modern chemical substance, ether.[2] The title is one given to this book by Islamic translators in the ninth century. Its original Greek title is Mathematical Syntaxis.
Sources: The Aristotelian cosmos is described in his Physics and On the Heavens, see The Complete Works of Aristotle: The Revised Oxford Translation, ed. Jonathan Barnes, 2 vols. (Princeton: Princeton University Press, 1984). On the relationship between Greek cosmology and astronomy, see B. R. Goldstein and A. C. Bowen, "A New View of Early Greek Astronomy," Isis 74 (1983):330-40, and Thomas S. Kuhn, The Copernican Revolution (Cambridge: HArvard University Press, 1957. The best translation of the Almagest is Ptolemy's Almagest, tr. G. J. Toomer (London: Duckworth; New York: Springer Verlag, 1984). Godd expositions of the technical details of the Ptolemaic System can be found in Olaf Pedersen, A Survey of the Almagest (Odense: Odense University Press, 1974); Michael J. Crowe, Theories of the World from Antiquity to the Copernican Revolution (New York: Dover, 1990); and Olaf Pedersen and Mogens Pihl, Early physics and astronomy : a historical introduction (London : MacDonald and Janes ; New York : American Elsevier, 1974; 2nd ed. Cambridge: Cambridge University Press, 1993). On Medieval cosmology and astronomy, see Edward Grant, "Cosmology," in Science in the Middle Ages, ed. David C. Lindberg (Chicago: University of Chicago Press, 1984), pp. 265-302; and Olaf Pedersen, "Astronomy," ibid, pp. 303-37. For an account of Aristotelian cosmology and Ptolemaic astronomy in the period leading up to Galileo's discoveries, see James M. Lattis, Between Copernicus and Galileo: Christoph Clavius and the Collapse of Ptolemaic Cosmology (Chicago: University of Chicago Press, 1994).

Tuesday, September 05, 2006

John of Leyden


Raised a "bastard" and dogged by poverty, young John became a charismatic leader who was widely revered by his followers. According to his own testimony, he went to the German city of Münster, arriving in 1533, because he had heard there were inspired preachers there. He sent for Jan Matthys, who had baptized him, to come. After his arrival Matthys - recognized as a prophet - became the principal leader in the city. Following a failed military attempt on Easter Sunday 1534, in which Matthys died, John of Leiden became King of Münster until its fall in June of 1535. He set up a theocracy in Münster and led a communalistic and polygamous state. Some sources report that John of Leiden took sixteen wives. He publicly beheaded one of his wives after she rebelled against his authority.

The army of Münster was defeated in 1535 by the prince bishop Franz von Waldeck, and John of Leiden was captured. He was first taken to a dungeon in Dülmen, then brought back to Münster. On January 22, 1536, along with Bernhard Krechting and Bernhard Knipperdolling, he was tortured and then executed. Each attached to a pole by an iron spiked collar, their bodies were ripped with red-hot tongs for the space of an hour, then each was killed with a dagger thrust through the heart. Their bodies were raised in three cages above St. Lambert's Church, the remains left to rot. Their bones were removed about 50 years later, but the cages have remained into the 21st century.


The Kingdom through progress or crisis?
Jeffrey Fletcher

IV. Historical Examples of Catastrophic and Progressive Millennialism
We have explored some of the fundamental elements of both catastrophic and progressive millennialism in conceptual and theological ways. To use our millennial dance metaphor, we’ve learned some of the basic steps to the dance, but to get a better feel for what it looks like, we need to see some examples of the dance. We now turn to three distinct historical periods and see how the community of faith lived out these millennial views.

Sixteenth Century
Catastrophic Millennialism
— From the first century to the reformation, culminating in the radical anabaptist Thomas Muntzer/the city of Munster

The first Christians were catastrophic millennialists. From the apostles who asked the question "Lord, is this the time when you will restore the kingdom to Israel?" to the time of Augustine and the fall of Rome, catastrophic millennialism was predominant in the Church. From the time of Constantine until the Protestant Reformation a thousand years later, the doctrine of the Church as the Kingdom was the official position of the Church — and yet, this did not prohibit the common folk in Christendom from embracing catastrophic millennialism.

Abanes chronicles a number of occasions when apocalyptic fervor held sway:

c. 950 the monk Adso writes Letter on the Antichrist . . . the letter was copied and circulated throughout Europe. Adso declared that the Antichrist would rise when the rule of the Frankish kings ended.

c. 950-980: A letter about the Hungarians from the Bishop of Auxerre to the Bishop of Verdun "speaks of widespread apocalyptic reactions among the population."

968: Soldiers in Otto’s army panic at an eclipse, which they see as a sign of the end.

994/996: Abbo of Fleury, an influential French abbot, in his apologetic works relates: "When I was a young man I heard a sermon about the end of the world preached before people in the cathedral of Paris. According to this, as soon as the number of a thousand years was completed, the Antichrist would come and the Last Judgment would follow in a brief time. I opposed this sermon with what force I could from passages in the Gospels, the Apocalypse and the Book of Daniel."

Erdoes has devoted an entire book to the cataclysmic millennial expectations that occurred around the first millennial shift at the year 1000:

Some were certain that the Second Coming of Christ would fall on the last day of the year 999, at the very stroke of midnight. Others were equally convinced that Armageddon would happen a little earlier, on the eve of the nativity when "the Children of Light would join in battle with Gog’s army of hellish fiends." Some fixed the date on the day of the summer or winter solstice in the thousandth year after our Lord’s passion.

Mackey writes:

An epidemic terror of the end of the world has several times spread over the nations. The most remarkable was that which seized Christendom about the middle of the tenth century . . . the delusion appears to have been discouraged by the Church, but it nevertheless spread rapidly among the people. The scene of the last judgment was expected to be at Jerusalem. In the year 999, the number of pilgrims proceeding eastward, to await the coming of the Lord in that city, was so great that they were compared to a desolating army. Most of them sold their goods and possessions before they quitted Europe, and lived upon the proceeds in the Holy Land.3

Apocalyptic terrors in catastrophic millennialism were not limited to the continent. According to Russell, in 1656 a Quaker named James Naylor was believed by some to be an earthly incarnation of Christ. Certain members of the Quaker community in England began to worship Naylor. On October 24 Naylor and his community entered the city of Bristol "imitating the triumphal entry of Jesus into Jerusalem." Naylor was promptly arrested, convicted and given a nasty sentence which included having his tongue bored through with a hot iron and the letter "B" emblazoned on his forehead, along with public flogging and other forms of humiliation.4

However, all of these examples of catastrophic millennialism pale in comparison to Thomas Muntzer. The story of Muntzer is well documented.

Muntzer was a parish priest near Wittenburg when Luther tacked his 95 theses to the church door. Muntzer came to Wittenburg and pursued his degree in theology. He disagreed with Luther’s "sola scriptura," believing that divine revelation did not end with the apostles. He believed in ongoing revelation. Muntzer taught a doctrine of social revolution. He took an active role in introducing the end time: he thought of himself as God’s scythe for His harvest. Muntzer promoted a communist view of community and is still honored today by the communist world. Muntzer came to Mulhausen in the midst of the German peasants’ revolt. He seized upon the civil unrest among the poor and dispossessed who were ready and willing to invest him with prophetic religious authority. They removed the city council and formed their own "eternal council." Muntzer designed banners for the peasants, consisting of a white flag with a sword and a great white banner with a rainbow, symbolic of the new covenant. Some of the German princes began to attack Muntzer and his people. The people were encouraged into battle by Muntzer, who repeatedly promised to catch the cannonballs in his sleeves and hurl them back. A rainbow appeared in the sky, which the peasants took to be a good omen, but it was not: the peasants were slaughtered; Muntzer was captured and beheaded.

In summarizing the story of Muntzer, Cohn writes: "Muntzer was a prophet obsessed by eschatological phantasies which he attempted to translate into reality by exploiting social discontent."

Muntzer used catastrophic millennialism to lead the poor and marginalized into warfare against the dominant culture. In 1534 leaders in the city of Munster would attempt to establish the apocalyptic Kingdom of God on the earth. They would become the New Jerusalem and their leader John of Leyden, a tailor, set himself up as the "king of the world." The entire population of Munster assembled to worship their "messiah." According to Meissner, "While the population starved to death, he and his entourage lived richly and enjoyed lavish feasts and entertainments."

Eventually, a siege was brought against the city, many starved to death, and Leyden was captured and tortured to death.

These examples should not be seen as in any way normative behavior, but they do illustrate rather vividly the effects of catastrophic millennial beliefs gone out of control. There is the potential for great violence as the oppressed and marginalized target their frustration at the dominant culture under the prophetic leadership of militant catastrophic millennialists.

Progressive Millennialism — Calvinism in Geneva
Was John Calvin a progressive millennialist? According to Erickson, John Calvin’s eschatological teachings aren’t always easy to pin down. Both amillennialists (realized millennialists) and post-millennialists (progressive millennialists) have attempted to claim Calvin as one of their own. However, I believe Calvin’s actions and theology clearly fit the definition of progressive millennialism. And so, just as Thomas Muntzer provides an excellent example of cataclysmic millennialism run rampant, John Calvin shows where progressive millennialism in its extreme form can lead.

Calvin’s life and theology have been well documented and his relationship and interactions with the radical reformers are chronicled superbly by Williams.

Calvin published his Institutes of Christian Religion at about the same time that the radical catastrophic militant community at Munster was collapsing. Calvin dedicated his Institutes to Francis I of France, and warned the monarch not to confuse the kind of restitution movement that happened in Munster with his own vision of reformed Christianity, which he considered to be far more politically responsible. This serves to illustrate a key point: in Munster, radical catastrophic millennialists confronted the political powers and took over; in Geneva, Calvin and the reformed leaders sought to bring the rule of God into the life and leadership of the community. Shelley observes, "The consequence of faith to Calvin . . . is strenuous effort to introduce the kingdom of God on earth."

Tillich writes:

Calvin was a humanist and, therefore, gave to the state many . . . functions . . . Calvin used the humanistic ideas of good government, of helping the people, etc. But Calvin never went so far as to say, with the sectarian movements, that the state could be the kingdom of God itself. He called this a Jewish folly. What he said . . . is that a theocracy has to be established, the rule of God through the application of evangelical laws in the political situation. Calvin worked hard for this. He demanded that the magistrates of Geneva care not only for legal problems, the problems of order in the general sense, but also for the most important content of daily life, namely, for the church. Not that they shall teach in the church or render decisions as to what shall be taught, but they shall supervise the church and punish those who are blasphemers and heretics. So Calvin, with the help of the magistrates of Geneva created the kind of community in which the law of God would govern the entire life. Priests and ministers are not necessarily involved in it. Theocratic rulers are usually not priests, otherwise theocracy becomes hierocracy; rather, they are usually laymen. Calvin said that the state must punish the impious. They are criminals because they are against the law of God.

It was under this Calvinist progressive millennial system that the magistrates of Geneva, with the approval of Calvin, convicted Michael Servetus of heresy for his anti-trinitarian views and had him executed.

The legacy of Calvinism goes far beyond the Reformed tradition in the Church. Calvin’s view of the relationship between the Church and the State and the Kingdom of God, of the ability of lower magistrates to revolt under certain circumstances, made it possible for our modern forms of democracy to exist. Were it not for Calvin’s progressive millennial views, the United States may never have had an opportunity to come into existence.

In contrasting catastrophic and progressive millennialism in the 16th century one thing is clear: catastrophic millennialists who oppose the culture or try to create an apocalyptic Kingdom of God tend to get killed by the state, while progressive millennialists tend to achieve positions of power and influence and lead to the creation of new governments on earth.