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  Sincerely,

  Isaac Barrow

  12 January 1667

  London

  Dear Mr. Newton:

  Thank you again for your rapid work in tabulating our results. It is most gratifying to find a young man with such zeal for his work.

  As I have said before, I am no mathematician, but I must confess that your explanation makes very little more sense to me than your original mathematical formulae.

  As I understand it, you are proposing a set of equations which will show the range of any weapon by computing the weight of the ball against the weight of the powder. (Perhaps I err here, but that is my understanding.) It seems to me that you are building a castle-in-Spain on rather insubstantial ground. Where is your data? What research have you done on cannon-fire? Without a considerable body of facts to work with, such broad generalisations as you propose are quite out of order.

  Even if such a thing could be done-which, pardon me, I take the liberty to doubt-1 fear it would be impractical. I realise that you know nothing of military problems, so I must point out to you that our cannoneers are enlisted men-untutored, rough soldiers, not educated gentlemen. Many of them cannot read, much less compute abtruse geometrical formulae. It will be difficult enough to teach them to use the range tables when we complete them.

  Indeed, I may say that this last point is one of the many stumbling-blocks in the path of our project. More than one of the staff at the War Office has considered it to be insurmountable, and many times I have fought for the continuance of research in the face of great opposition.

  I greatly fear that using any but methods known to be practicable would result in our appropriation being cut off in Parliament.

  Again, however, I thank you for your interest.

  Most sincerely,

  Ballister-ffoulkes

  24 January 1667

  Cambridge

  My dear Isaac,

  I am truly sorry I didn’t get around to looking over your second manuscript until now, but, to be perfectly truthful, I have been outlining our course of work on conic sections, and had little time for it.

  As it turns out, it was all for the best that I did so; it would have been sinful to take valuable time away from my work for such trivialities.

  You are still harping on your wine-barrel fluxions and your Army cannon balls. Am I to presume that the whole thing is a joke? Or are you seriously proposing that the path of a cannon ball is related to the moon? That is rank superstition! Sheer magic! One would think that even a lad as young as yourself would have grasped the basic concept of the Scientific Method by this time.

  How have you tested this absurd thing experimentally? Where are your measurements, your data? Your references?

  Do not think, my boy, that fame and fortune in the sciences can be achieved by pulling wild hypotheses out of your imagination. There is no short-cut to mastery of a difficult subject like mathematics; it requires years of hard work and study.

  As an example of what can happen when one has not learned enough of the subject, look at your own work. You appear to be handling Time as though it were a spatial dimension. You even end up, in several equations, with square seconds! Now, a yardstick will show that a foot up-and-down is the same as a foot East-and-West or a foot North-and-South. But where can you find a foot of time?

  Please, dear boy, use your time to study the things you have yet to learn; don’t waste it exploring a nonsensical cul-de-sac.

  I will send you the outline on conic sections within the week.

  Sincerely,

  Isaac Barrow

  1 February 1667

  London

  Dear Mr. Newton:

  In reference to your letter of 14 January 1667, on the simplified algebraic formulae for the prediction of the paths of cannon balls, our staff has considered the matter and found that not only is your mathematics incomprehensibly confusing, but the results are highly inaccurate. Where, may I ask, did you get such data as that? .On what experimental evidence do you base your deductions? The actual data we have on hand are not at all in agreement with your computations.

  Men with more experience than yours, sir, have been working on this problem for several years, and nothing in our results suggests anything like what you put forth. Finding data is a matter of hard work and observation, not of sitting back in one’s armchair and letting one’s mind wander.

  It would, indeed, be gratifying if our cannon would shoot as far as your equations say they should-but they do not. I am afraid we shall have to depend on our test results rather than on your theories. It is fact-not fancy-which is required in dealing with military operations.

  Sincerely,

  Edward Ballister-ffoulkes, Bart.

  General, Army Artillery

  3 February 1667

  Cambridge

  My dear Isaac:

  I feel it would clear the air all round if we came to an understanding on this thing. Your continued insistence that I pay attention to theories which have no corroboration in the literature and are based on, to say the least, insufficient confirmatory data, is becoming tedious. Permit me, as a friend, to show you where, in your youthful impetuosity, you err.

  In the first place, your contention that there is a similarity between the path of a cannon ball and the moon is patently ridiculous. I cannot imagine where you obtained such erroneous information. A cannon ball, when fired, strikes the earth within seconds; the moon, as anyone knows, has been in the sky since—according to Bishop Ussher—4004 B.C. Your contention that it remains held up by a force which pulls it down is verbal nonsense. Such a statement is semantically nothing but pure noise.

  You state that the path followed by a cannon ball is parabolic in nature. How do you know? Can you honestly say that you have measured the path of a cannon ball? Have you traced its path, measured it, and analysed it mathematically? Can you prove analytically that it is not an hyperbola or part of an ellipse? Have you any data whatsoever to back up your statements, or any authority to which you can refer?

  You make broad generalisations on the assumption that “every body is attracted equally to every other body;” that the earth attracts the moon in the same way that it attracts an apple or a cannon ball. Where is your data? You have not, I dare say, measured the attraction between every body in the universe. Have you checked the variations in apples according to sugar content or the variations in cannon balls with reference to their diameters? If not, have you checked with any reliable authority to see if such work has already been done?

  And where did you learn that anyone can just sit down and make up one’s own mathematical systems? I am certain that I taught you no such thing. Mathematics, my boy, is based on logical interpretation of known facts. One cannot just go off halfcocked and make up one’s own system. What would happen to mathematics as a science if anyone should just arbitrarily decide that two added to two yields five or that two multiplied by two equals one hundred?

  You said that the whole thing came to you loin a flash” last summer when you were sitting under an apple tree and one of the fruit fell and struck you on the head. I suggest that you see a good physician; blows on the head often have queer effects.

  If you have the data to prove your contentions, and can show how your postulates were logically deduced; then I will be very happy to discuss the problem with you.

  As soon as you feel better, and are in a more reasonable frame of mind, I hope you will return to Cambridge and continue with the studies which you so badly need.

  Sincerely,

  Dr. Isaac Barrow

  P.S.: It occurs to me that you may have meant your whole scheme as some sort of straight-faced pseudo-scientific joke, similar to that of another gentleman who bears our common Christian name.* If so, I fail to comprehend it, but if you would be so kind as to explain it to me, I will be only too happy to apologise for anything I have said.

  Is. Barrow

  *I have no idea who this might be. The reference is as obscure as
the joke.-S.H.

  8 February 1667

  London

  Dear Mr. Newton:

  I have tried to be patient with you, but your last letter was sulphurous beyond all reason. I may not, as you intimate, be qualified to judge the mathematical worth of your theories, but I can and do feel qualified to judge their practical worth.

  For instance, you claim that the reason your computations did not tally with the data obtained from actual tests was that the cannon ball was flying through the air instead of a vacuum. By whose authority do you claim it would act thus-and-so in a vacuum? Do you have any data to substantiate your claim? Have you ever fired a cannon in a vacuum? For that matter have you ever fired a cannon?

  What would you have our cannoneers do-use a giant-sized Von Guericke Air Pump to evacuate the space between the cannon and the target? I fear this would be, to say the very least, somewhat impractical and even dangerous under battle conditions. I presume a tube of some kind would have to be built between the enemy target and the gun emplacement, and I dare say that by that time the enemy would become suspicious and move the target.

  You speak of “ideal conditions.” My dear Newton, kindly keep it in mind that battles are never fought under ideal conditions; if they were, we should always win them.

  If you wish to spend your time playing with airy-fairy mathematical abstrusities which have no basis in fact, that is perfectly all right with me. This is a free country, and no one proposes to dictate one’s private life. However, I would appreciate it if you would do me the honor of not burdening my already overtaxed mind with such patent nonsense.

  Otherwise, your work with the tabulations has been most excellent; I am enclosing a cheque for £ 20 to cover your work so far.

  Sincerely,

  Edward Ballister-ffoulkes, Bart..

  12 February 1667

  Cambridge

  My dear Newton:

  You have stretched the bonds of friendship too far. You have presumed upon me as a friend, and have quite evidently forgotten my position as head of the Department of Mathematics at this College.

  The harsh language in which you have presumed to address me is too shocking for any self-respecting man to bear, and I, for one, refuse to accept such language from my social inferiors. As a Professor of Mathematics in one of the most ancient of universities. I will not allow myself or my position to be ridiculed by a young jackanapes who has no respect for those in authority or for his elders.

  Your childish twaddle about glass prisms producing rainbows—a fact which any schoolboy knows—is bad enough; but to say that I am such a fool that I would refuse to recognize “one of the most important advances in mathematics” is beyond the pale of social intercourse.

  Repeatedly during the last few months, you have attempted to foist off on me and others implausible and unscientific theories which have no basis whatever in fact and which no reputable scientist would be foolish enough to endorse. You are not a mathematician, sir; you are a charlatan and a mountebank!

  You have no data; you admit working from “intuition” and hypotheses cut out of whole cloth; you cannot and will not give any reliable authority for ay of your statements, nor will you accept the reliable statements of better men than yourself.

  This unseemly behavior forces me to exercise my prerogative and my authority in defence of the college and the university. I shall recommend to the authorities that you be effused readmission.

  Isaac Barrow, Ph.D.

  Department of

  Mathematics

  Trinity College

  16 February 1667

  FROM: Ballistics Research Department, Army Artillery

  TO: Mr. Isaac Newton, A.B., Woolsthorpe

  SUBJECT: Reduction in personnel

  ENCLOSURE: Cheque for 2/10s/6d

  1. In view of the increased personality friction between yourself and certain members of this department, this department feels that it would be to our mutual disadvantage to continue retaining your services as mathematical consultant.

  2. As of 16 February 1667 your employment is hereby terminated.

  3. Enclosed is a cheque covering your services from 8 February 1667 to date.

  By order of the Commanding General

  Major Rupert Knowles,

  Adjutant for General Sir Edward Ballister-ffoulkes

  12 March 1667

  Whitehall

  My dear fellow,

  I am making this communication quite informal because of your equally informal method of—shall we say—getting my ear.

  I have been nagged at day and night for the past three weeks by a certain lady of our mutual acquaintance; she wants me to “do something for that nice young Mr. Newton.” She seems to think you are a man of some intelligence, so, more in order to stop her nagging tongue than anything else, I have personally investigated the circumstances of your set-to with the Ballistics Research Department.

  I have spoken with General B-f, and looked over all the correspondence. Can’t make head or tail of what you’re talking about, myself, but that’s beside the point. I did notice that your language toward the general became somewhat acid toward the last. Can’t actually say I blame you; the military mind can get a bit stiff at times.

  And I’m afraid it’s for that very reason that my hands are tied. You can’t expect a man to run a kingdom if he doesn’t back up his general officers, now, can you? Political history and the history of my own family show that the monarch is much better off if the Army and Navy are behind him.

  So I’m afraid that, our little lady notwithstanding, I must refuse to interfere in this matter.

  CAROLUS II REX

  19 March 1667

  Whitehall

  Newton:

  No! That is my final word!

  C II R

  21 May 1667

  Cambridge

  My dear Isaac,

  Please accept the humble apologies of an old friend; I have erred, and I beg you, in your Christian charity, to forgive me. I did not realise at the time I wrote my last letter that you were ill and overwrought, and I have not written since then because of your condition.

  As a matter of fact, when your dear mother wrote and told me of your unbalanced state of mind, I wanted desperately to say something to you, but the blessed woman assured me that you were in no condition for communication.

  Believe me, my dear boy, had I had any inkling at all of how ill you really were, I would have shown greater forbearance than to address you in such an uncharitable manner. Forgive me for an ungoverned tongue and a hasty pen.

  I see now that the error was mine, and it has preyed on my mind for these many weeks. I should have recognised instantly that your letters to me were the work of a feverish mind and a disordered imagination. I shall never forgive myself for not understanding it at the time.

  As to your returning to the College for further study, please rest assured that you are most certainly welcome to return. I have spoken to the proper authorities, and, after an explanation of the nature of your illness, all barriers to your re-entrance have been dropped. Let me assure you that they are well aware of what such an unhappy affliction can do to unsettle a man temporarily, and they understand and sympathise.

  I can well understand your decision not to continue your studies in mathematics; I feel that overwork in attempting something that was a bit beyond one of your tender years was as much responsible for your condition as that blow on the head from that apple. 11 is probably that which accounts for the fact that serious symptoms did not appear until late in March.

  I feel that you will do well in whatever new field you may choose, but please do not work so hard at it.

  Again, my apologies.

  Isaac Barrow

  3 April 1687

  York

  To His Grace,

  The Most Reverend Dr. Isaac Newton,

  By Divine Providence the Lord Archbishop of Canterbury

  My Lord Archbishop,

  May I take this
opportunity to give you my earnest and heartfelt thanks for the copy of your great work which you so graciously sent; I shall treasure it always.

  May I say, your Grace, that, once I had begun the book, I found it almost impossible to lay it down again. In truth, I could not rest until I had completed it, and now I feel that I shall have to read it again and again.

  In my humble opinion, your Grace is the greatest theological logician since the Angelic Doctor, St. Thomas Aquinas. And as for beauty and lucidity of writing, it ranks easily with “De Civitate Deo” of St. Augustine of Hippo, and “De Imitatione Christi” of St. Thomas a Kempis.

  I was most especially impressed by your reasoning on the mystical levitation of the soul, in which you show clearly that the closer a human soul approaches the perfection of God, the greater the attraction between that soul and the Spirit of God,

  Surely it must be clear to anyone that the more saintly a man becomes, the greater his love for God, and the greater God’s love for His servant; and yet, you have put it so clearly and concisely, with such beautifully worded theological reasoning, that it becomes infinitely more clear. It is almost as though one could, in some mystical way, measure the distance between an individual soul and the Holy Presence of God by the measure of the mutual love and attraction between the soul and the Blessed Trinity.

  Your masterful analysis of the relative worthiness of those who have come to the Kingdom of Heaven on the Day of Judgement is almost awe-inspiring in its beauty. Even those souls which have been cleansed as white as snow by the forgiving Grace of God differ, one from another, and your comparison between those souls and a ray of pure white light striking a prism of clearest crystal is magnificent.