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605

On a Clear Day .

Doris Glass

-^r ^ ’ On a clear day, the noon November,^’-^S^-sun warms your back. You can see

<^- 1l Mount Mitchell, elevation 6684 feet,

A I°

t^e highest point in North Carolina,

J^^^l^^ miles away. Or is it really 50

^f^%^^^^ away�past Chimney Rock,^|gfc;;^; through Bat Cove, Old Fort, and

^|^ Pleasant Gardens? That depends onthe meaning of away.We are standing in front of Carl

Sandburg’s home. We can no longerask him the meaning of words.What would he say? Perhaps, "Areyou a bicycle or a crow?"

r johr’ Tennie;

AfUSt

Is distance an exact word? Does itmean separation of points on a line,or on a path"! No longer a straightline, now, all lines are straight? Nolonger a curved line, no line iscurved? Or does it mean pathlength? For example, from NewYork to Boston, back to New York,and then to Philadelphia is our dis-tance positive 90, negative 90, orjust plain 90 miles? If you read the

’The time has come,’the Walrus said,

’To talk of many things:

Of shoes�and ships�and sealing wax�Of cabbages�and kings-

Through th-? l.oo;\in,3 GIBS’.

odometer, is the distance about 550? Does a crow fly a line, a curve, oran arc, (radius about 4000 miles)? Is the distance to the moon ever nega-tive?

Lewis Carroll, speaking through the broad mouth of Humpty Dumptyin Through The Looking Glass, said:

School Science and MathematicsVolume 84 (7) November 1984

606 On a Clear Day . . .

The writers, and editors, of the Logical text-books which run in the ordinarygrooves�to whom I shall hereafter refer by the (I hope inoffensive title)"The Logicians"�take, on this subject, what seems to me to be a more hum-ble position than is at all necessary. They speak of a Copula of a Proposition"with bated breath"; almost as if it were a living conscious Entity, capable ofdeclaring for itself what it chose to mean, and that we, poor human creatures,had nothing to do but to ascertain what was its soveriegn will and pleasure,and submit to it.In opposition to this view, I maintain that any writer of a book is fully au-thorized in attaching any meaning he likes to any word or phrase he intends touse. If I find an author saying, at the beginning of his book, "Let it be under-stood that by the word black, I shall always mean white, and that by the wordwhite I shall always mean black." I meekly accept this ruling, however injudi-cious I may think it.And so, with regard to the question whether a Proposition is or is not to beunderstood as asserting the existence of its Subject, I maintain that everywriter may adopt his own rule, provided of course that it is consistent with it-self and with the accepted rules of Logic.Let us consider views that may logically be held, and thus settle which of themmay conveniently be held; after which I shall hold myself free to declarewhich of them / intend to hold.

Do we, in both science and mathematics classrooms and textbooks,distinguish clearly enough between distance and displacement^ Do we, inlinear movement when the first point is at the origin, usex for three con-cepts: 1) place, 2) path distance, and 3) displacement?

((. . . we, poor human creatures, had nothing to do but toascertain what was its sovereign will and pleasure, and sub-mit to it."

In this special case, x and Ax (delta x, change in x) are often used inter-changeably. On a trip to New York to Boston to Philadelphia ourrecord can show 220+220+90=530 or 220-220+90=90 or220-220-90= -90. And what if we back up a bit during each of thethree parts of the trip? Similar difficulties often occur from interchang-ing t and A/. Times comes in two varieties: clock time (corresponding toplace) and duration (corresponding to displacement). Einstein said thatthings should be made as simple as possible,�but no simpler. HumptyDumpty said, in a rather scornful tone, ’ ’When / use a word it means justwhat I choose it to mean�neither more nor less." Humpty Dumpty hada great fall! Are we looking for trouble when we mix colloquial idiomand exact usage?


On a Clear Day ... 607

We are as close to the top of Mount Mitchell as we are going to get. Wecannot see Carl Sandberg’s home. Sometimes what started as a clear dayends as a foggy dusk in the Great Smokies. Carl Sandburg wrote:

The fog comeson little cat feetIt sits lookingover harbor and cityon silent haunchesand then moves on.

What do you think?

Doris Glassc/o Editors,School Science and Mathematics

NATURAL IMMUNITY TO CANCER BOOSTED

Scientists at Duke University Medical Center have been able to stimulate theimmune system of mice to kill cancer cells, and hope eventually to accomplishthe same in humans.

"We’re trying to gain better understanding of the role of macrophages in de-stroying a tumor, with the long range goal of improving immunotherapy," saidDr. Dolph Adams, professor of pathology.Macrophages are large white blood cells that defend the body against bacteria

and other invaders.Duke scientists recently reported discovery of a protein produced by tumor

cells that protects them from macrophages. Drs. Ralph Snyderman and GeorgeCianciolo are attempting to develop ways of breaking down this biochemicalshield, leaving tumor cells vulnerable to the immune system.Adams’ lab is taking a different tack by attempting to define the biochemical

signals the body uses to activate macrophages, in hopes that alternate or bettersignals can be developed to override any block in the system."We know that macrophages in mice go through four distinct stages, activated

by at least three signals sent in a precisely defined order," Adams said."In one instance, we found that macrophages weren’t killing tumor cells be-

cause they weren’t picking up signal three. We found a different way of sendingthat signal and were then able to stimulate them to kill the cancer cells."The third signal apparently induces macrophages to release a killer enzyme

that aids in the destruction of tumor cells or bacteria, Adams said. The enzymewas discovered by Dr. Salvatore Pizzo, a member of the Duke research team.
