Threads: Science and Computers Letters written by me, updated March 2003 to include the period 1974-1981 Background:  In March of 1974, I moved into my first apartment (in Washington, Pennsylvania).  I continued to be fascinated by science and technology.  Eventually, I even added an early Radio Shack computer to the apartment.   Sunday, April 14, 1974 Washing the dishes still takes more time than I think it should.  This is really no surprise.  In the lab in Chemistry 2, where we did qualitative analysis on inorganic unknowns, I did fairly well except that I was very slow, taking plenty of time to make sure I did each step of the procedure correctly.  It's the same problem now in the kitchen.  I'm learning how to get the dishes clean, but I have a feeling I work too carefully.  Rinsing and drying takes me about 20 minutes.  The whole process, including mopping up the counter-top afterwards, takes about 40 minutes.  I think I'm going to have to learn to zip through the process and ignore the possibility that I might fail to rinse off every bit of suds before applying the towel. Before leaving this subject, I'd like to pass along a discovery I made yesterday noon.  We physics majors were taught in our advanced math courses about "saddle-shaped surfaces."  If one takes a cross section of such a surface in the x-z plane, it looks like a parabola opening in the +z direction, but a cross section in the y-z plane looks like a parabola opening in the -z direction.  The name "saddle shaped" didn't help me much, however.  Never having spent any time around horses, I didn't realize that a saddle was, in fact, shaped like that.  But now, after all these years, I've found something in my daily experience that is an example of such a surface.  It's a Pringle's Newfangled Potato Chip.  In today's mechanized society, many more of us are acquainted with Pringle's than with saddles.  So I think all the analytical geometry texts should be written to call the concepts in question "pringle-shaped surfaces." CONCURRING OPINION, 50 YEARS LATER: "There's something highly unusual about the new 2024 Olympic Aquatics Center on the outskirts of Paris," Feargus O'Sullivan and Jenny Che write for Bloomberg.  They cite "the building's striking form, with its massive, Pringle-shaped solar roof." Saturday, January 18, 1975 Yes, I have seen "The Ascent of Man," with your fellow mathematician, the late Dr. Bronowski.  The Australopithecus-skull episode covered some rather familiar ground, since a couple of years ago I started receiving the Time-Life Books series "The Emergence of Man."  That series of books, at a new volume every two months, has continued a lot longer than I suspected when I signed up for it.  I'm currently reading Volume 16, about the archaeological evidence on the Celtic tribes who inhabited Caesar's Gaul and later Ireland.  And it could go on for several years more, since there are many ancient tribes and civilizations that they haven't gotten around to yet.  Maybe someday I'll cancel. A strange thing has been happening on Saturday mornings.  Many nights I'll go to sleep with my radio on, and it stays on all night, apparently without disturbing my sleep or the dreaming process.  I don't feel tired or dream-deprived the next morning. But often on Saturday mornings, I'll wake up about 6:35, apparently wakened by the radio.  There's a show that comes on at 6:30, one of those public-service things that radio stations run when they know not many people are listening anyway; it seems as though I'm hearing it while I'm still asleep, deciding that it sounds interesting, and then waking up in order to listen to it. One morning I woke up to an interview about the Devil's Triangle near Bermuda.  Another morning, Walter Cronkite was describing the JFK assassination in the present tense, which turned out to be part of a record of audio news highlights of the 1960's. Am I being awakened by the subject matter at 6:35, even though I've slept through many records and several newscasts during the night? Probably not.  My alarm goes off on other days of the week at 7:15, so I'm probably simply being awakened by my internal clock.  Internal clocks don't know about days off.   Sunday, April 3, 1977 In my non-working hours this past week, the theme has turned out to be cosmology. You may have heard that the leading scientific theory on the origin of the universe is now the "Big Bang" idea.  The universe is still expanding.  The question is whether this expansion will ever stop.  Will gravitational attraction among the galaxies slow them down, stop the expansion, and then pull them back together again in a "Big Crunch"? I've kind of been rooting for the Big Crunch.  To me, it's more satisfying to think of an oscillating universe that crunches and bangs every 20 billion years or so, thus always renewing itself.  But in the April Smithsonian magazine, the director of the Hale Observatories is quoted:  "If the deceleration has been so mild, then the expansion is irreversible and the universe has apparently happened only once."  Too bad.  But fortunately, the astronomers aren't certain.   Sunday, November 13, 1977 These past four months have seen two new calculators added to my collection, which now stands at four.  I'm still fascinated by what these little machines can do, and by how inexpensive they are by the standards of five or ten years ago.  Each of the new marvels cost $60, which I consider a reasonable amount for a 30-year-old man to spend on a toy. The first is a programmable calculator.  For example, I was trying to solve a mathematical puzzle that led me to the equation 39 cos T – 84 sin T + 46 = 0, so I entered this program in the calculator: M1 cos x 39 + 46 = M2 MR1 sin x 84 – MR2 = m3 x = – .00000001 = skip goto40 R/S MR1 – MR3 = pause goto00 This is a trial-and error method.  It stores a tentative value of T as M1, calculates 39 cos T – 84 sin T + 46 as M3 (which should turn out to be zero if the correct M1 is used), compares the square of M3 to a very small number, and ends the program if the very small number .00000001 is larger.  But if not, the program subtracts M3 from M1 and starts over again.  The calculator came up with the answer of 54.6864º in about two minutes. This was a notable improvement over my first attempt, when I had changed the trial value of M1 not by M3 but rather by the arbitrary figure of .0001º.  I started the calculator grinding away on this program.  In theory, when it reached 54.6864º it would stop, and I'd have my answer.  So it tried numbers as follows: 54.0000, 54.0001, 54.0002, 54.0003, 54.0004, 54.0005, 54.0006, 54.0007, 54.0008, 54.0009, 54.0010, et cetera I began to realize that it would take two hours to reach the correct value.  This would never do. What I needed was a smarter program that would make a big change in the trial M1 if the error M3 was large, and only a small change if the error was small.  So I decided to change M1 not by .0001º but by M3, as shown in the program above.  This time, the calculator didn't need to grind so long: 54.0000, 54.9662, 54.5742, 54.7317, 54.6681, 54.6937, 54.6876, 54.6859, 54.6866, 54.6863, 54.6864, and stop   [My first attempt is shown by the almost imperceptibly rising red line on this graph. The blue line shows my second attempt, which zeroed in on the result in only 11 steps.]   I go into all this detail to point out that programmable calculators might be of great use in helping students to understand computer programming.  I recall that there was a problem in an Oberlin physics class when a class computer problem that was supposed to take less than two minutes to run was averaging more like ten minutes.  Probably we were doing something inefficient like adding .0001 each time.  Learning not to make that kind of mistake could be accomplished on a programmable calculator, without tying up the valuable time of the main computer. My other new electronic marvel is a bit less of a toy, because I actually use it in my daily work.  It's a Casio MQ-1, not only a calculator but also a clock, calendar, and stopwatch, all in a case the size of a pocket comb, one centimeter thick and weighing only 40 grams. This little thing still amazes me. It's the equivalent of a digital wristwatch, but better than most because it displays not only the hour and the minute but also the second.  And rather than using power-hungry LEDs, the display is liquid-crystal, meaning that it's visible all the time.  So when I'm broadcasting a football game, I slide the Casio under the clip on my clipboard, and when I need to log the time when we go to a commercial, there's the exact time right in front of me.  I don't have to reach around to my wrist and hit buttons to get hour, minute, and seconds. It's a stopwatch with a digital readout.  And an additional feature makes it handy for TV work:  the stopwatch can count either up or down.  It's capable of adding and subtracting sexagesimally; for example, 0:43:30 + 0:29:45 = 1:13:15. And it's a 200-year calendar.  If you want to know what date it is today, a push of the button tells you 1977 Nov.13, Sunday.  If you want to know what date it will be 90 days from now, press DT+90= and the answer is 1978 Feb.11, Saturday.  If you want to know on what day of the week you were born, enter 1947 June 8 and the Casio tells you it was Sunday.  If you want to know how long you have lived, press –DT= and the Casio subtracts today's date for the answer of 11,116 days. This last answer can be useful for biorhythm calculations, if you believe in that sort of thing.  To find where you are in your 23-day physical cycle, for example, divide 11,116 by 23.  The answer, 483.30, shows that you're 30% of the way through your 484th cycle, which means you've just passed the high point of it (25%). With the Casio, I've worked out my biorhythmic highs, lows, and critical days for November and December, and so far I haven't found much correlation between the biorhythm theory and reality.  That doesn't surprise me.   Sunday, June 4, 1978 There have been experiments made, I understand, in which volunteers lived for a month or so in a closed environment.  They couldn't tell whether the sun was shining, and they had no clocks or radios or watches or TVs.  Eventually they lost track of the earth's rotation and had to decide for themselves when it was "day" and when it was "night."  As I recall, most of the volunteers ended up with a circadian day of about 25 hours. I wonder:  Is this perhaps why we humans tend to remain active after sundown, and not arise until after the sun is up?  Our natural rhythms are running more slowly than the sun, so we're always lagging behind. If that speculation is true, I'd like to see the experiment run on birds.  I bet their internal clocks would turn out to be set for a day of about 22 hours.  In the morning, they're active before dawn; and as I was walking home from work yesterday evening, at least an hour before sunset, the pigeons were already gathered on the roof of a building, picking out their roosting spots for the night. ----- Carl Sagan, the astronomer, appeared at the end of a recent Nova program that debunked the Erich von Däniken "ancient astronauts" books.  The program showed that most of the "evidence" of visitations in ancient times, from representatives of a more advanced civilization, can be better accounted for by more conventional explanations. Sagan then commented that perhaps all this interest in ancient astronauts or Close Encounters of the Third Kind is really a manifestation of a need for religion.  People seem to want to believe in benevolent beings, wiser and more powerful than ourselves, who come down from the sky to show mankind a better way to live.  For those people to whom Christianity is no longer in favor, it's natural to turn for a substitute to the stars.  Instead of reading Bibles and singing hymns, we find folks reading horoscopes and listening to the Carpenters sing "Calling occupants of interplanetary craft." Sagan concluded that the danger is that we will hope too strongly for a visit from the heavens to solve the earth's problems, and thereby do nothing to solve them ourselves.   Sunday, April 8, 1979 Hidden in the back of last month's Smithsonian was an article by a Harvard graduate student, Thomas Ray Jr., which describes the behavior of vines in the jungles of Costa Rica.  The aroid vines he's talking about have no roots; they grow at one end and die off at the other, and thus they can move from place to place.  May I anthropomorphize them?  Good; thank you. It seems that the seedlings look around to find the nearest dark vertical stripe, which corresponds to the trunk of a tree.  (A high school junior has demonstrated this behavior in a science fair project.  Ray calls this growing toward darkness "skototropism.")  Once a seedling has found a tree to climb, it switches to the more familiar phototropism and begins growing toward the light, which in this case means up the tree towards the sky. As it climbs, the new sections of stem are long and skinny, without large leaves.  The vine is trying to get up the tree as quickly as possible, so why waste resources in making big leaves, which wouldn't do much good anyway in the comparative darkness of the jungle undergrowth? Once the vine arrives in the sunlight at the top of the tree, the added sections of stem become much shorter, which slows its motion almost to a stop.  It puts out huge leaves that photosynthesize enthusiastically, and it begins bearing fruit.  [See also this example.] But suppose the vine has unfortunately chosen to climb a tree that's only half as tall as its neighbors?  When the vine reaches the top of this tree and discovers it can go no further, it branches.  One half stays in the top of the short tree, putting out big leaves and photosynthesizing as much as it can.  The other half turns around and heads back down the tree, using long, skinny stem sections without leaves.  The half that's still in the treetop is feeding the searching half. The searcher goes all the way back down to the jungle floor and sets out across it again, looking for another tree which hopefully will be taller.  If it's broken off from the half that's still in the short treetop, the searcher will begin producing some leafy segments to take advantage of what sunlight there is.  Eventually, some part of the vine will succeed in climbing a tall tree where there's enough light to bear fruit. And some people say that plants lack intelligence! These vines are smarter than many people.  In a confused tangle of undergrowth, they can look around for a worthy goal.  It's only when they've reached the top that they slow down and enjoy the sunshine.  And if they find they've reached a dead end, they immediately turn around and return to square one to begin again.   Sunday, March 9, 1980 In order to write you, I first had to tear myself away from my computer.  So I came down here to the studio on a Sunday afternoon.  I had some other things to do here anyway, and now that they're done, I'll use the office typewriter to send a message your way. The computer is a new addition to my apartment.  At the first of the year, I had eight hundred dollars or so I could part with, so I decided to go ahead and splurge on a Radio Shack TRS-80 Level II 16K microcomputer.  The device consists of a video monitor (which looks like a 12" black-and-white TV set), a separate typewriter-like keyboard (which also contains the electronics), and an ordinary audiocassette recorder (to save programs and data). I bought it mainly as a hobby, for entertainment.  There's nothing practical for it to do at home, since income tax preparing and checkbook balancing are sufficiently simple to be easier done by hand.  There are some ways in which the computer could be useful here at the studio:  election returns, budget preparation, and special graphics for commercials, to name a few.  But I'm reluctant to pack it up and carry it down here.  Besides, I'm having too much fun with it at home. The Tandy "Model 1" did not have a disk drive or a printer.  It also lacked a modem, although that didn't matter much in 1980 because there was no Internet.  This machine was a good introduction to computing.  But several years later, when I bought a later model that did have a disk drive, printer, and modem, I retired the Model 1 to the basement. Mostly what I've been doing is adapting games to the TRS-80.  For example, in a book I found a program that allows one to play checkers against the computer.  But the human has to keep track of the moves on an actual checkerboard, and moves are communicated in the form FROM 3,5 TO 4,4. I used the same algorithm by which the computer decides its moves, but I changed the interaction between the computer and the human.  The checkerboard and the checkers (X's and O's) are displayed on the screen, with a letter beside each square.  Moves can be entered in the form FROM G TO L.  If you try to move to L but that square is already occupied, the computer doesn't print the letter L that you typed; it does nothing until you enter a valid move.  Once a move is made, the computer erases from the screen the checker at the old location (as well as any jumped checkers) and adds to the screen the checker at its new location. Getting all this to work properly was more fun, actually, than using the finished program to play checkers against the machine.  But that's kind of enjoyable, too. I've also developed some programs completely from scratch.  One of the early ones will serve as the scorekeeper for a rally. As each team arrives at the finish, they turn their log over the computer operator, who enters into the computer such data as car number, time of arrival at checkpoint 1, time of departure from checkpoint 1, time of arrival at checkpoint 2, special penalty points, and so on.  Already entered are other data such as the time it should have taken to get from checkpoint 1 to checkpoint 2, along with scoring rules.  So once all the data on the team's performance have been entered, the computer can calculate the team's score in a second or two. It then sorts all the scores it has calculated so far into increasing order.  On the screen these scores are listed, the leader at the top, along with the previously entered names of the driver and navigator to whom those scores belong, their car number, their class of competition, and their scores on each of the half-dozen legs that make up the rally. This complete scoreboard remains on the screen while the computer operator is entering the data on the next team, so that rallyists waiting around for the awarding of the trophies can look over the operator's shoulder and see exactly where they stand.  If necessary, the operator can call up other displays that show the scoring of a particular team in greater detail, or the minute-by-minute chronicle of what happened at checkpoint 2. This program would be completely practical, but I probably won't have cause to use it since I'm no longer a member of that rally club in Columbus, Ohio.  Columbus is just too far away. Well, anyway, you can see that I've been spending long hours at the keyboard and display.  Formerly I would watch TV in the evenings and go to bed at 10 pm; now I hardly turn the TV on, and I don't get to bed until 1 am or so.  So far, the novelty hasn't worn off, and there are a lot of ideas I still want to try.   Thursday, June 4, 1981 At home, I'm still playing with my computer when I get the chance.  One program that I wrote myself puts a dot in orbit around a little "planet," taking about a minute for each revolution.  The dot traces out an ellipse on the screen.  Every second, it sounds a beep that changes pitch according to its velocity.  Also, in the corners of the screen are displayed the numbers representing the velocity, altitude, perigee, apogee, and period.  You can observe how the orbiting dot speeds up as it falls toward its perigee, and so forth.  Pressing buttons on the computer keyboard allows you to increase or decrease the velocity (with appropriate rocket-burn sound effects), thus changing the orbital parameters.  I've obtained a very eccentric orbit with a period of more than five minutes, almost all of which is spent invisibly off the left side of the screen.  Another feature is a blinking dot in another orbit, which serves as a target for rendezvous.  This whole simulation is fun to watch and ought to be a good teaching tool. A second program, which I got from a magazine article, is remarkable for the sophistication of its graphics.  Eighteen two-inch-tall "androids" play a game of Nim with you.  The androids all move independently and at random while they're waiting for your commands.  These moves include changing the positions of their arms, looking up, looking down, looking left, looking right, and even blinking their tiny eyes!  In response to your instructions, they'll either nod yes or shake their heads no.  Seeing eighteen of these little guys looking around and blinking with apparent curiosity is of equal entertainment value with watching fish in an aquarium. Finally, I've also been using the computer to help me decipher a 16-year-old code.  During my final semester of high school, I had extra time in study halls and wanted to write down some diary-type comments.  But study halls aren't very private.  Someone could have come along and read over my shoulder.  Therefore, I decided to write in a simple code, which involved merely writing the letters in a peculiar sequence.  For example: RHI NHN RTA EED PTH ATO BPY LYE FIY LSX TOR JAO THU NAI Of course, once you figure out the sequence you can read these things without the aid of a computer.  But that requires concentration.  So much of it, in fact, that I found myself writing things which I don't think I could have written had I been able to re-read the sentence easily afterwards.  The computer makes the translation a mechanical process:  just type in the code and read the decoded message right off the screen.  I had no idea when I wrote these codes that I would later decipher them with the aid of a computer; who would have thought that in 1965? Anyway, these surprisingly uninhibited writings gave me some insight into what I was like in my late adolescence.  I am a different person now in many respects.  The thought processes evident in these codes have not operated that way in the last five years or more.  And I recall that when I was in high school, I winced when I recalled some of the childish things I had done in junior high.  As time goes on, our personalities do evolve.