Micro Softy 74: The Cretan Paradox & Logical Illusions
Around and around we go in a cyclic logical illusion.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.
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 he had gone a step further and claimed.
“Everything I say is a lie.”
If you apply the statement to itself, Epimenides just lied which means he always tells the truth. But if he is telling the truth, he is lying. But if he always lies, he is telling the truth. But if he is telling the truth, …
Around and around we go in a cyclic logical illusion. Optical illusions and audio illusions have no place in reality. Neither do logical illusions even though they are used a lot in math proofs.
Kurt Gödel used a logical illusion to prove his “Incompleteness Theorems.” His fundamental results showed that assuming a consistent axiomatic mathematical system led to a logical illusions. The assumption of a consistent axiomatic mathematical system can therefore not be true. Smart people use Latin and call this use of reductio ad absurdum.
The Road to Corinth
Gödel showed that logical illusions can be useful. This week’s Micro Softy shows this another way.
On the road to Corinth, Paul came to a fork in the road and met twin brothers Epimenides the Liar and his twin brother Honest Thomas. Epimenides the Liar always told lies. So he was lying when he held up the sign “I Never Lie.” Honest Thomas, who always told the truth, also held up a sign that said “I Never Lie.” He was telling the truth.
Paul wanted to know which fork in the road to take. Epimenides the Liar and Honest Thomas both knew which road to take. Before asking the twins, Timothy, who was traveling with Paul, whispered to Paul.
“I’ve heard of these twins. The first question is free, but you’re charged a lot to ask more questions. Also, one always lies and the other always tells the truth. But it’s impossible to tell them apart.”
But, known to those who have read his writings, Paul was a clever man. He was also short on denarii.
Paul chose one of the brothers and took him aside. He had no idea whether it was Epimenides the Liar or Honest Thomas.
Paul asked his single free question that told him which road to take.
Here is this week’s Micro Softy. What single question did Paul ask that told him which road to take?
Solution to Micro Softy 73: The Ups & Downs of Escalator Design
Here’s the solution to last week’s Micro Softy.
At DFW Airport, the Skylink train efficiently connects all terminals. It operates on Level 3, accessible via a single up escalator—while two down escalators serve passengers exiting the train.
Why are there two exit escalators and one up escalator?
Here’s the answer.
Passengers going to the train arrive sporadically and are spread out over time. But when the train arrives, a large number of travelers exit the train at the same time. To handle this crowd spurt, there are two down escalators.
The Monday Micro Softy is a weekly feature of Mind Matters News. Here are the links to all the puzzles and answers to date:
Monday Micro Softy 73: The ups and downs of escalator design was about a single escalator that takes you up to the Skylink train. There are two down escalators for those exiting the train. So, why are there two down escalators but only a single up escalator for Skylink? You can find puzzles 55 through 73 here as well
Monday Micro Softy 72: Necklace Cutting required knowledge of binary numbers. Keep this in mind to work out the minimum number of cuts that allows Sally to give the landlord one bead a day for a month. You can find puzzles 55 through 72 here as well.
Monday Micro Softy 71: Strange Economics required you to grasp the deeper meaning of overheard conversations between a customer named Bill and a store clerk in a hardware depot. The question is: What was Bill buying? You can find puzzles 55 through 71 here as well.
Monday Micro Softy 70: The light above your stairs involved the Switching Theory and how a two-way switch works. If the stair light is on, flip the downstairs switch and the light goes on/off. A flip of the upstairs switch does the same thing. If the light is off, flipping either switch turns the light on. What’s a simple circuit that does this? You can find puzzles 55 through 70 here as well.
Monday Micro Softy 69: A Bunch of Switches involved knowledge of Switching Theory. Last week, 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? You can find puzzles 55 through 69 here as well.
Monday Micro Softy 68: An Overcrowded Prison featured Frenchy and the other prisoners at Pokey Nook Prison, who 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? You can find puzzles 55 through 68 here as well.
Monday Micro Softy 67: Three Switches and a Song was about switching theory. Wide Clyde wants to go upstairs to cook some Top Raman noodles. To do that, he needs to identify which of three switches controls the hot plate upstairs. The hot plate is plugged in but currently off. The other two switches turn outside lights off and on. Wide Clyde can’t see outside, so he can’t determine which switches control the lights. How can Wide Clyde determine which switch controls the hot plate with just one trip upstairs? You can find puzzles 55 through 67 here as well.
Monday Micro Softy 66: Reducing Repetitive Repetition requires being BFF’s with numbers, and last week’s Micro Softy was tough and mathy. You can find puzzles 55 through 66 here as well.
Monday Micro Softy 65: Fathers and sons was about two fathers and their two sons who walked into a Bass Pro Shop in Memphis, Tennessee. Each man bought an AK47 rifle with ammunition and a 75-round drum magazine. But all together, only three AK47’s were sold. How could this be? You can find puzzles 55 through 65 here as well.
Monday Micro Softy 64: Old Time Phishing was about an investment banker, Geardown Geko, who received anonymous tips forecasting the outcome of future events starting in 1948. You can find puzzles 55 through 64 here as well.
Monday Micro Softy 63: A Beggar’s Tale. Exceptional nerds are psychologists who see through surface actions. Such a skill is required to solve this Micro Softy. You can find puzzles 55 through 63 here as well.
Monday Micro Softy 62: The Ordeal of Sisyphus Fats. The best computer programmers and engineers must be good at scheduling. You can find puzzles 55 through 62 here as well.
Monday Micro Softy 61: Micro Softy Take Five was more of a trivia question than it was a puzzle. To solve Micro Softy 61, the answer is the theme for the Mission Impossible movie franchise starring Tom Cruz. You can find puzzles 55 through 61 here as well.
Monday Micro Softy 60: Here’s a puzzle from Gunsmoke Told to “get out of Dodge”after a shooting, a gunslinger does so at a nearly inexplicable time. Can you solve the puzzle?
To solve Microsofty 59, recall that direction of air flow is due to pressure — not size. Which tire is under more pressure? You can find puzzles 56 through 59 here as well.
Monday Micro Softy 55: “It happens every spring.” Baseball, that is. Here’s a puzzle that takes in baseball’s summer. To solve last week’s puzzle, you don’t need to know the distance. Check the problem again for the number you do need to know. You can find puzzles 51 through 54 here as well.
Monday Micro Softy 50: Cutting through the cornbread. How did Yuri Senior cut the cornbread into eight identical portions using only three straight cuts? You can guess the answer to Microsofty 49 if you try the test question yourself at home, using a small mirror. Links to Microsofties 46 through 49 are here as well.
Monday Micro Softy 45: Can Tony beat the fast-food curfew? An early curfew on fast food service motivated a boy to exercise more vigorously. But how fast was he pedalling? To solve Micro Softy 44, recall that Tony doesn’t need to take the individual pills each day, only the prescribed amount of each. You will find links here to Micros Softies 41 through 44 as well.
Monday Micro Softy 40: The fate of a false prophet. He wasn’t actually fired for being a false prophet but for something that his prophecy unintentionally revealed. The solution to Micro Softy 39 lies in considering an alternative possible meaning of a word commonly used in sports. You will also find links to Micro Softies 30 through 39 and their answers here as well.
Monday Micro Softy 29: A funeral lament in four lines. The funeral director was puzzled by Dan’s description of his relationship to the deceased but there was no question that his grief was sincere Here, you will also find links to Micro Softies 22 through 29.
Monday Micro Softy 21: Finding More of the Deadly Fentanyl Pills. Here, you will also find links to Micro Softies 11 through 20 as well.
Monday Micro Softy 11: What Happened to That Other Dollar? Here you will find links to the first ten Micro Softies. Have fun!
