# Astounding Science Fiction/Volume 44/Number 05/Brass Tacks

From Astounding Science Fiction, vol. 44, no. 5 (January 1950)
BRASS TACKS
Dear Mr. Campbell:
I especially enjoyed your simple system of multiplication in the June issue. The only thing that ruined it was that "Why?" stuck on the end. It forced me to stay up half the night trying to figure the darn thing out. Finally out of sheer exhaustion, I came up with a fairly logical solution.
Here it is: the multiplication system is based on the binary system of numeration. (The numerical system using only two digits, 1 = 1 2 = 10 3 = 11 4 = 100 etc. See pp 94-95 May 1949 issue of ASF.)
Take a simple multiplication like 9 X 6 for instance. Now, set the problem up in the two columns and proceed according to directions, dividing the smaller by two and multiplying the larger by two the same number of times. The division of the smaller number really converts it to the binary system. The odd number = 1; the even = 0(1). Then converting the other column to the binary system, you have a form of binary multiplication. (2)
| (1) | ${\begin{matrix}6&\ &0\\3&=&1\\1&\ &1\end{matrix}}$$\qquad 6=110$$\qquad 9=1001$ |
| (2) | ${\begin{array}{lrr}&&&&1001\\&&&&{\mbox{X}}110\\0\,{\mbox{X}}&1001&&=&000000&=&0\\1\,{\mbox{X}}&1001&{\mbox{X}}\,10(2)&=&1001{\scriptstyle (0)}&=&18\\1\,{\mbox{X}}&10010&{\mbox{X}}\,10(2)&=&1001{\scriptstyle (00)}&=&36\\&&&&110110&=&54\\{\mbox{a}}&{\mbox{b}}&&&{\mbox{c}}\end{array}}$ |
​It can be seen that the multiplication of columns a and b results in the same addition as with the regular binary multiplication (c). Some way to multiply!— Frank Raasch Jr., Kearney, Nebraska.
Dear John:
Several readers have expressed a desire for some problems or puzzles. Here is one that may afford some entertainment, and the answer is startling indeed!
A rocket takes off with an initial horizontal velocity of 500 miles per hour and an initial rate of climb of 1,000 feet per minute. With each 1,000 feet of altitude its velocity increases 10 mph, and each 100 mph faster it goes the rate of climb increases 100 feet per minute. Where is the rocket in 200 minutes?—Douglas B. Netherwood, Capt., USAF, Electronics, Hq. SAC, Offutt Air Force Base, Omaha, Nebraska.
Dear Mr. Campbell:
John D. MacDonald’s story, "Trojan Horse Laugh", reminded me of an experience I had while in an army ordnance unit just outside Rosario, Luzon.
We had an outdoor arena for the projection of movies, the center portion of which was screened off with chicken wire to keep the civilians from occupying seats reserved for the troops. Around this barrier, the Filipinos would gather in hordes and stand quietly and patiently throughout the hour-long show.
One evening, something—we never knew what—startled a small knot of civilians at the extreme left of the inclosure and they started to run, encountering in their flight the larger body of Filipinos gathered about the projection booth. The air was soon filled with dust and the sound of hundreds of bare feet thudding into the earth.
Inside the inclosure, someone in the front row leaped up to join the exodus and, in a moment's time, the whole area became the scene of a wild retreat, soldiers and civilians mingling in their frenzied effort to get away from the spot. No words were spoken, no voices raised, but everywhere could be heard grunts and groans and the crash of falling bodies. Even the projectionists fled, leaving the projector running.
We were a bruised and sheepish lot when we finally straggled back to see the rest of the show. None of us had been frightened—it was just that everyone else had been running and we thought we had to run too—like sympathetic yawning.
Thus, when Alice and Joe were caught up in the hysteria of the city, even though they had had no injections, I was inclined to think the situation farfetched until I remembered that stampede in which I myself had taken part.
MacDonald's story was unusually good, as was the rest of the issue. Let's have more like it.— Joe E. Dean, ​315 West 33rd Street, New York, New York.
Dear Mr. Campbell:
Since you asked someone to check Art Kalaugher's figures, I accepted your challenge, and found that it was wrong. The correct value of π in the binary system is: 11.001001000011111101101010100010001000010110100011. If any of the readers of ASF have any use for it, I shall be glad to compute forty more places on it.
I enjoy Brass Tacks very much, especially the mathematical problems that some readers have. My only suggestion is that I think most of the editor's comments would be a lot better after the letter than before. And incidentally, are you convinced that you have a very good magazine, or do I have to repeat it too?—Gary D. Gordon, Wesleyan Station, Middletown, Connecticut.
Dear Mr. Campbell:
I should like to call attention to a slight error in an otherwise excellent article: that entitled "Parboiled Pilots" in the August, 1949, issue. On page 5 is stated : "Any means of expanding compressed air cools it...". (The italics are yours.)
It is a little-known fact that any gas upon expanding may either heat up or cool down, or even do both in the same operation, depending upon the nature of the gas, the temperature at which the operation started, and the extent of the expansion. Below a certain temperature called the Joule-Thomson inversion temperature—different for each gas: -83° C for hydrogen; much higher for most gases—gases do indeed cool down upon expanding, as you state, but above this temperature, astonishingly enough, they heat up. The attainment of the extremely low temperatures around absolute zero is dependent on the fact that liquid air can cool hydrogen below its inversion temperature, whereupon expansion can cool it further; the resulting liquid is then used for cooling helium below its inversion temperature. If air liquefied at a temperature above Hydrogen's JTIT, cryogenics would be crying indeed.
Further information may be found in any book of thermodynamic or advanced physical chemistry, e. g., S. Glasstone, "Chemical Thermodynamics," (D. Van Nostrand).
It may be splitting hairs, but you did use italics on the word "any"! I just want to set the record straight. Please accept my congratulations on the remainder of the article. ​Popularizing technical data is not easy to do without making inaccurate simplifying generalizations or else becoming tedious. You have done an excellent job.—Crayton M. Crawford, 306 Russell Avenue, Greenville, South Carolina.
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Dear Sir:
Before I indulge in criticism, I would like to say that as a less than ardent fan of science fiction, I believe your magazine is of the best quality. Your stories seem to be much more logical and scientifically substantiated than the usual run of science fiction, which usual run usually runs into nausea. I am science editor for our local paper here at the University of Texas, have had a more than average amount of training in science and I think I may speak with some authority.
Now for the criticism. Happily, the criticism I have in mind does not refer to the logic used by your authors or the basis of your stories in science. Rather, it has to do with certain implications as regards the present controversy in the Armed Forces. Certain men in both the Navy and the Air Force are looking ​forward, rightly enough, to space travel. These men also seem to take it for granted that their own branch of service, viz. the Navy or the Air Force, will be the one to take over the military duties of patrolling the spaceways, or whatever might be required.
I have yet to read a story in your magazine, in which any particular branch of service now in existence is mentioned in connection with space patrolling, which gives the Air Force credit. All others of this 1 type either had the Navy, of all things, sailing through the waterways of space, or the job was assigned to an independently created unit specializing solely in space travel, which of course is more logical. It would seem to me, if it were a question of handing this future job over to the Navy or Air Force, the latter would be the most logical choice. The Navy traditionally steers its course on a two-dimensional plane, while the Air Force by its very nature must constantly operate in a three-dimensional plane. Of course, it is not necessary that any future space travel, if any, be assigned to any existing service. It would be more logical and a lot simpler to create a special, independent rocket force.
It seems to me, from the stories I have read recently, that either you or your writers are prejudiced in favor of the Navy. Even the rocket forces of alien peoples many light-years away have signed away their rocket forces to the local navies. I will admit the vast possibilities that I may be wrong in my assumptions, and I only hope I am. I did not start reading your magazine until the first of this summer of 1949.
Whether you wish to publish this in your letters to the editor column is of no import to me. What I would appreciate is a letter stating your policy on this subject, if you have made one.— Robert L. Smith, 200 E. 22, Austin, Texas.
Dear Campbell:
The September issue’s article "Cybernetics," by E. L. Locke tempts me to draw a few speculative conclusions in another direction from those he deemed mentionable. Perhaps the reason I've never thought of it before was that I hadn't quite suspected the possible relativity.
The single paragraph which hit the spark, however, occurred on P. 89 when Locke said that—as shown by Weiner—the number of cells go up as the cube of the brain dimension while the connectors go up only as the square. I'd heard before that the remote parts of the brain are affected first when there's a mental monkey-wrench loose in the works. Of course, Locke was considering primarily the functioning of feedback loops—but I was reading Astounding SCIENCE FICTION, wherein any mention of the brain is likely to be on the extreme view of developed ​Extra-Sensory Perception and/or Psycho-Kinesis!
Immediately, I laid Locke’s article down for an instant and took off on my own speculations as to why we reputedly use only nine-tenths of the brain and why, as he says, the brain is apparently too large for efficiency already. I was considering a normally healthy brain, of course; psychotic brains are no more attractive to me than polio or cancer.
Now why, I mused, is the brain so darned inefficient? Well, maybe it isn't! I remembered how other parts of the human machine were considered inefficient until more was learned about their purposes and limitations, and the final conclusion seemed invariably that their only major inefficiency was man's ignorance. But here was, it seemed, undisputable physical evidence of the contrary, evidence that we're actually lugging around more brains than we could ever use!
Why should there be so few connectors? For engineering purposes, nature obviously had to accept some limitations—but Ol' Momma Nature is fiendishly adept at sidetracking limitations! Now, why couldn't it just happen to be that she had stuck in another entirely different system of communications when she made human brains, to compensate the necessarily few physical line-connectors? Something, say, so far out
​of this world that it involves a few entirely new frequency bands and a few centuries' development of subatomic research before its physical presence is even suspected? In other words, maybe a built-in equalizer? That suggested something else: anything that far "out of this world" would prove difficult for the brain itself to utilize! The communications received from such a system might conceivably be a tricky code that the brain would have trouble deciphering unless its physical structure was hitting peak efficiency! Good physical health and mental awareness.
Are you still with me? O.K., the next point was—in my chain of speculations—that here, perhaps, was the theoretical explanation of ESP and PK powers, the neutrinos of the mind. Rhine's experiments concluded that such powers were at their best when the subject was physically relaxed, mentally rested, and alert to the circumstances of the test. Ping—the conclusions dovetail!
Being Science Fiction enthusiasts, we next consider if and how these conclusions might point the way toward telepathy, tendrils, and the Gray Lensmen.
Obviously, we'll have to go a long way farther toward something resembling a good definition of the word "civilization" before: (A) the human race is physically in such good shape that we aren't bothered with such things as colds, rheumatism, fevers, chills, and whatnot, which are distracting; and (B) we're free of such pathological worries as keeping up with the Joneses, keeping our jobs, getting a home and making enough money to pay off loans, mortgages, installments, and the other little whatnots that form the structure of modern living, such as taxes. It is even too much worry, as yet, remaining compatible with the little woman so as to raise a fine, strong family of red-blooded young Americans. We'll have to get all these items off our neural patterns before we're mentally healthy enough to tackle ESP and PK code-messages with a vengeance!
A hit of supporting evidence, here, is that most cases of "mysticism" generally originate in the backwoods of this planet. There's something like a psychic accord between man and nature that considerably helps the subject attain mental accord, it seems. The extreme examples, of course, are the voodoo rites and Asiatic occult Mumbo Jumbo which, in successful cases such as a casual stroll upon hot coals, show that the subject must be jarred, shaken, or otherwise lulled into a semi-conscious or totally unconscious hypnotic trance. Otherwise, his neurons' are too occupied with everyday trivialities to concetnrate on ESP-PK code-messages. What the hypnotic trances do to his conscious rationalization is something for the psychologists to study.
But considering the present trend ​of social evolution, will such a civilization ever be realized? I think it will have to be realized if anything galaxy-wide is to be established. It seems possible that somewhere along the line a peak will be reached without benefit of political empires and ideological wars, a peak which will collapse from the weight of accumulated gimmicks of civilization rather than mass revolt against tyranny. O'Donnell came close to describing it in his novel, "Fury," and Williamson laid a possible background for it in his "The Equalizer," though the latter had a totalitarian-proletariat conflict. It might conceivably involve the attainment of immortality, or virtual immortality. But once it is realized, the pathological reaction to the collapse might be the thing which awakens the mental consciousness to the gimmick-free possibilities of ESP and PK practices. In other words, it might be effected in an historic moment when the impetus of mass-psychology fell in its direction. If Van Vogt's "Centaurus II" had led to the climax of Williamson's "The Equalizer"—that might suggest the required circumstances.—Joe Gibson, 24 Kensington Avenue, Jersey City 4, New Jersey.