Randall Garrett

“ Surely you are not thinking of becoming a wine merchant? If so, what need is there to waste your time studying mathematics? On the other hand, if you intend to become a mathematician, why should you debase a noble and lofty study by applying it to wine barrels? ”

“ 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. ”

“ Or are you seriously proposing that the path of a cannon ball is related to the phases of 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 ”

“ 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? ”

“ Newton:
Thank you for your tabulations on the seven-pounder. I must say you were very prompt in your work; there was no need to work over the holidays.
Your questions show that you are unacquainted with the difficulties of manufacturing military arms; I am not at all surprised at this, because it takes years of training and practical experience in order to learn how to handle the various problems that come up. It is something that no university or college can teach, nor can it be learned from books; only experience in the field can teach it, and you have had none of that. ”

“ I do not say that such work is menial, either. I would not have you think that I deplore your choice of work in any way; it is necessary work, and money is certainly necessary for life.
However, let me warn you: a simple task like this, which pays rather well, can become soporific in its effect. Many men of talent, finding themselves comfortably fixed in a mediocre position, have found their minds have become stultified through long disuse. Please, dear boy, don't fall into that trap; don't throw away a fine career in mathematics for the sake of a few paltry pounds. ”

“ It has come to my attention that you are—shall we say—prostituting your talents. A friend of mine who works at the War Office tells me that you are doing some mathematical work by correspondence—something to do with cannon, I believe.
Now, I quite understand that you are in a somewhat precarious financial position, and believe me, I deeply sympathise with you. I know that the earning of a few pounds can mean a great deal to you in furthering your education. ”

“ 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 motion of the moon is patently ridiculous. I cannot imagine where you obtained such erroneous information. A cannon ball, when fired, strikes the earth within seconds ”

“ Mathematics, my boy, is based on logical interpretation of known facts. One cannot just go off half-cocked 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? ”

“ The Church has always held that those whose entire lives have been lived in holy purity and in the Grace of God would hold a higher place in Heaven than those whose lives have been sinful, even though God, in His graciousness, has forgiven them their sins. ”

“ 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 ”

“ Reading these letters is somewhat like listening to a conversation when only one of the speakers is audible, but they seem to indicate another side to the man, one which has not heretofore been brought to light. ”

“ 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. ”

“ Each cannon to be tested is fired with several balls—some of iron, some of lead, some of brass, and some which have been hollowed out to make room for a charge of gunpowder in order that they may explode upon reaching the target. With each type of ball, we find the amount of powder required to drive the ball five yards from the muzzle of the piece; this is considered the minimum range. ”

“ 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. ”

“ 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! ”

“ As I told you, I have no objection to your making a few pounds by doing minor calculations for the Army, but this is foolishness. You have gone to a great deal of trouble for nothing; as you gain more experience, you will realize the folly of such things. ”

“ 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. ”

“ The first two factors are obvious; the heavier the cannon ball, the more powder it will take to blow it a certain distance, and contrariwise.
The third is somewhat unwieldy to work with and definitely problematical in its effects. Up to a certain point, increasing the angle seems to increase the range, but after that point is reached, an increase in elevation decreases the range of the weapon. In view of this, it has been decided that all cannon will be fixed at the best angle for maximum range and the other factors varied to change the actual distance the cannon ball is fired. ”

“ Many of them cannot read, much less compute abstruse 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 the research in the face of great opposition. ”