Engineers need to know physics in order to build things. The history of time keeping is called horology. Time keeping became more accurate over the years. A big breakthrough was pendulum clocks invented in the mid seventeenth century by Christiaan Huygens. His invention dramatically improved accuracy, reducing daily errors to under a minute.  Early longcase clocks are known today as grandfather clocks. The popular term “grandfather clock” comes from the 1876 song My Grandfather’s Clock by Henry Clay Work. The song, about a clock that “stopped, short, never to go again when the old man died,” was a big hit.      The grandfather clock uses a pendulum to keep time.  With this background, here’s this week’s Micro Softy.   Burt’s grandfather’s clock was running too fast, and he wasn’t sure how to fix it. Burt worked at NASA, and one evening during a gathering at his house, he cornered four scientists and asked for advice on how to slow the clock a bit. Here’s what they suggested:  “At the end of the pendulum, there’s a weight. Tape something to it to make it heavier. That should slow the clock.”  “The pendulum is too short. Lengthen it, and the clock will run slower.”  “Make the pendulum swing through a wider …

There are optical illusions and auditory illusions. This week’s Micro Softy concerns logical illusions.  Two optical illusions are shown in Figure 1.    On the left, the “Mad poiuyt” appeared on the cover of MAD Magazine in March 1965.   On the right, stairs repeat themselves in an impossible illusion. If you walk clockwise, you are always going downstairs forever. This staircase was used in the surreal art of M.C. Escher.  Figure 1: Two optical illusions. / WikipediaLeft, WikipediaRight.  The Shepard-Risset glissando is an auditory illusion where the pitch of a sound appears to continuously rise or fall indefinitely. Christopher Nolan’s films like Dunkirk and The Dark Knight used it to heighten the sense of dread or relentless motion. It can be used to create the illusion of an endless climb or descent, or to signify a special event, as in Super Mario 64’s endless staircase.  A tone that decreased in pitch forever is not possible. The Shepard-Risset glissando is an auditory illusion.    Logical Illusions  This week’s Micro Softy is about logical illusions. Here’s a classic example.  Epimenides, a 6th-century BC philosopher from Crete, reportedly said:  “All Cretans are liars.”  The Apostle Paul repeated this claim in the New Testament book of Titus.  “One of Crete’s own prophets has said it: `Cretans are always liars …’ ”  [Titus 1:12]   The logic illusion paradox arises when we consider that Epimenides himself is a Cretan. Suppose …

Computer engineers are required to study digital logic. This includes switching theory. Last week’s Micro Softy relates to this week’s puzzle, so let’s give last week’s solution first.  Solution to Micro Softy 68: An Overcrowded Prison   Frenchy was the 100th prisoner at the Pokey Nook Prison. Every day, each of the 100 prisoners here must flip a switch. Prisoner #1 goes first, then #2, etc up to prisoner #100. There are two switches next to each other. A prisoner can flip either switch but could only flip one. If Frenchy can tell the Warden with certainty when the 101st prisoner arrives, he’ll be released,     Frenchy and the other prisoners at Pokey Nook Prison flipped a switch each day for 101 days, On the 102nd day, Frenchy announced with certainty the 101st prisoner had arrived. How did he know?  The answer lies in 100 being an even number.   Suppose Frenchy starts with both switches in the up position. After 100 flips, including Frenchy’s flip, the switches will either both be up or both be down. If the initial configuration had one switch up and one down, then after 100 flips including Frenchy’s, they would still be in a one-up, one-down arrangement. Any other resulting configuration would signal to Frenchy that the 101st prisoner has arrived.  A Really Overcrowded Prison   This …

Good programmers have to be BFF’s with numbers. With this in mind, here’s this week’s Micro Softy. It’s tough and mathy. Choose any three-digit number, say 567, and repeat it: 567,567. Divide it by the prime numbers 13, then 11 and then 7. In each step, round to the nearest integer if necessary. The result will be the original three-digit number: 567. For example, · 567,567 divided by 13 is 43,659. · 43,659 divided by 11 is 3969, and · 3969 divided by 7 is 567 which is the original three-digit number. Wow. This works for any three-digit number. So this week’s (difficult) Micro Softy asks: Why? Solution to Micro Softy 65: Fathers and Sons Here’s the solution to last week’s relatively simple Micro Softy. Two fathers and their two sons walked into the Bass Pro Shop in Memphis, Tennessee. Each bought an AK47 rifle. But only three rifles were sold. How can this be? The men entering the Bass Pro Shop were a teenage boy, his father and the boy’s paternal grandfather. So there …

Great programmers must know when they are being phished. Here’s this week’s Micro Softy to test your detection ability. The presentation of this Micro Softy is a bit longer than usual, so grab a cup of coffee and prepare to think. It was 1948. Wealthy investment banker, Geardown Geko, received a short letter from an anonymous source in April, immediately before hockey’s Stanley Cup finals. It read: “I am gifted with powers to predict the future. Because of circumstances, I am not able to personally profit from this gift. But I can share my forecasts with those who can. I know that this seems too good to be true, so I will in future correspondence prove I have this gift. I’m sharing these predictions with a short list of investors who, I hope, will at some point pay a fee for my foresight. Here is my first forecast of the future. The Toronto Maple Leafs will defeat the Detroit Red Wings to win hockey’s 1948 Stanley Cup.” A few days later, a second note was …

The best computer programmers and engineers must be good at scheduling. This week’s Micro Softy tests this ability. Big Tony Mullins, known to his friends as Sisyphus Fats, exercises by pushing a giant bowling ball up a 100 foot hill. Every minute, he pushes the ball three feet closer to the top and then the bowling ball slides two feet back.  After regaining his breath, Sisyphus Fats pushes the ball another three feet up the hill and it slides back two. This happens every minute. How many minutes did it take for Sisyphus Fats to push the ball to the top of the 100 foot hill? Solution to Micro Softy 61: Take Five Last week’s Micro Softy asked what popular movie franchise theme is written in the unusual key signature 5/4? The answer is the theme for the Mission Impossible movie franchise starring Tom Cruz. Did the hint help? James Arness played Matt Dillon on Gunsmoke. Before the movies, on the television series Mission Impossible, the star was James Arness’ younger brother Peter Graves. Graves …