All posts tagged: Softy

Monday Micro Softy 84: Meet the Followers

Monday Micro Softy 84: Meet the Followers

Published by Jenni Sidey

Over the past two weeks, we’ve tested our puzzlers’ ability to think deeply outside the box. We explored how swarms of dumb bugs can follow very simple rules yet produce surprising, emergent behaviors. This week continues our Micro Softy series on swarm intelligence, (that’s the technical term). Our new swarm is called The Followers. This time, the rules they follow are even simpler. Each bug in the swarm randomly picks another bug and begins to move toward it. What happens in the long run? For this week’s Micro Softy challenge, your task is to describe the emergent behaviors that result from this kind of swarm. Hint: At least two distinct emergent behaviors can occur. One emerges when a bug happens to choose itself to follow. Since it can’t get any closer to itself, it remains still.  The other emerges when a group of bugs contains no bug that has chosen itself. Figure 1: The green coward tries to placeitself between the blue protector and thered bully. Each bug in the swarm is trying todo the …

Monday Micro Softy 83: A Swarm of Cowards?

Monday Micro Softy 83: A Swarm of Cowards?

Published by Jenni Sidey

Figure 1: In this swarm of Cowards,each bug moves to position itselfin this way. What happens if every bug in the swarm randomly choosestwo other bugs and does this? Last week’s Micro Softy challenged our puzzlers ability to think abstractly. We explored how simple rules can lead to complex behavior when the rules are followed by unintelligent agents — in that case it was dumb bugs. We continue that theme this week but instead of looking at “Peacemaker” bugs, we’re going to focus on the “Cowards.” We’ll return to the Peacemakers shortly when we reveal the answer to last week’s Micro Softy. But first, the Cowards. Imagine a swarm of bugs again. Each one randomly chooses two others from the group. One of them —shown in red in the figure — is an aggressive bully that wants to attack the green bug. The other —shown in blue — is a protector. The timid green bug moves so that the blue protector stands between itself and the red bully. Now imagine that every bug in the …

Monday Micro Softy 82: When Bugs Break Up Fights…

Monday Micro Softy 82: When Bugs Break Up Fights…

Published by Jenni Sidey

Figure 1: In the Peacemaker Swarm, a peacemaker, shown in green, pickstwo warring bugs shown in red andmoves to place itself between them. A fascinating branch of computational intelligence is swarm intelligence — inspired by how simple creatures in nature achieve complex goals together. Individually, these “dumb bugs” perform only basic tasks. Yet collectively they create intricate structures like beehives, hornet nests, and termite mounds. Their coordinated activity gives rise to what’s known as emergent behavior — complex outcomes arising from simple individual actions. Last Monday’s Micro Softy was about termites. The solution is below. Today’s puzzle is about how bugs can break up fights. Picture a large swarm of crawling insects, represented by the dots in Figure 1. Each bug eyes two other bugs that he thinks are going to fight. As a peacemaker, he moves to place himself between these two.  Meanwhile, every bug in the swarm eyes two different bugs and does the same thing. Each bug is moving trying to place itself between two other bugs chosen at random. So the …

Monday Micro Softy 81: Termites Are Surprisingly Smart

Monday Micro Softy 81: Termites Are Surprisingly Smart

Published by Jenni Sidey

Artificial intelligence isn’t just large language models or image-generating transformers. Another rich vein of AI is swarm intelligence — lessons from nature on how dumb bugs do smart things collectively. Dumb bugs, each doing a simple task, work together to build bee hives, hornet nests and termite villages. Their collective effort is called the emergent behavior of simple actions. Ants, for example, use chemical communication to find the shortest path between food and their nest. When a scout ant discovers something desirable — say, a Snickers bar — it heads back home, all the while laying down a trail of pheromones, chemicals that trigger behavior in other ants. The other ants pick up this scent and follow it. They reinforce the trail with their own pheromones if they reach the food successfully. At first, ants may explore multiple routes, but shorter paths allow them to make more trips in less time, which means those trails receive pheromone reinforcement more frequently. Over time, the shorter route becomes much stronger in scent and more heavily trafficked, while …

Monday Micro Softy 80: The Digits of Least Significance

Monday Micro Softy 80: The Digits of Least Significance

Published by Jenni Sidey

Engineers, mathematicians, and computer scientists need to know some number theory, the branch of mathematics that studies the way numbers behave. Number theory is needed to understand modern data encryption, for example. This week’s Micro Softy is about number theory and least significant digits (the last digit of a large number is its least significant one). It builds on the solution of last week’s puzzle. So let’s reveal that solution first. Solution to Micro Softy 80: The Last Digits in Fermat’s Last Theorem It’s a tough puzzle. My mathematics friend Professor Dave Johns texted me that he believed Wiles’ celebrated proof of Fermat’s Last Theorem was incorrect. Here’s the math behind the theorem again: Remember, one counter example is all that is needed to disprove Fermat’s theorem. Johns said he had found a counter example. He provided three numbers. (All math variables should be in italics) x = 321,232,430,786,123,860 y = 487,367,975,876,123,125 z = 4,534,432,154,871,543,981 But poor Professor Jones lost his memory before he announced the value of n in the equation above, where n>2 …

Micro Softy 77: Two Proud Texans

Micro Softy 77: Two Proud Texans

Published by Jenni Sidey

I’m a proud resident of the lone star state of Texas. Texas’s shape on the map is arguably the most recognizable of all the states. And I’m aware of no other state where businesses and citizens proudly fly their state flag. I pass two enormous Texas flags on my daily commute. Dr Pepper, HEB stores, Whataburger and Buc-ee’s all had their genesis in Texas. (Fun fact: There is no period after Dr in Dr Pepper.)  I live in McGregor, Texas, where Elon Musk’s Space X has a testing center. Occasionally, the testing of their rocket engines gently rattles the dishes on the shelves in my home.  So, here’s this week’s Texas Micro Softy:   The Glenn Beck radio program originates from the Mercury Studios in Irving, Texas (Dallas–Fort Worth area).  Two Texans were guests on his show.   One of them was the father of the other one’s son.   How can this be? There are no adoptions, divorces or sperm banks involved in the answer.  We’ll give the answer next week here at MindMatters.ai.  Solution to Micro Softy 76: The Smoking Gun  Here’s last week’s puzzle.  After a 911 call about a heated argument, officers entered an unlocked apartment. From the bedroom they heard, “Don’t shoot, Frank!” then two shots. Inside, a physician and a clergyman stood side by …

Micro Softy 76: The Smoking Gun

Micro Softy 76: The Smoking Gun

Published by Jenni Sidey

Like a computer scientist or engineer, a law enforcement officer often relies on abductive reasoning to crack a case. Here’s an example:  After a 911 call about a heated argument, officers rushed to an apartment. When no one answers their knock, they enter through the unlocked door. From the bedroom came chatter; one officer clearly heard a voice say, “Don’t shoot, Frank, don’t shoot,” followed by two loud shots. The police ran and opened the door to a bedroom.  Inside the room were a physician, a mechanic, and a clergyman. When the policeman entered the room, a smoking gun lay at equal distance from the clergyman and the physician who were standing next to each other. The mechanic lay dead on the floor. Immediately, without touching anything in the room or a word being spoken, the police office arrested the clergyman.  What obviously observed circumstances would justify this immediate arrest? That’s this week’s Micro Softy puzzle.  Hint: Review Micro Softies 22 and 52. Solution to Micro Softy 75: Horology: Not What you Think  Last week’s Micro Softy concerned the slowing of a pendulum’s period in order to slow down a grandfather clock that was running too fast.  Here are the four suggestions and whether they are true or not. For fellow nerds, below the answers, is the supporting …

Micro Softy 75: Horology: Not What You Think

Micro Softy 75: Horology: Not What You Think

Published by Jenni Sidey

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 …

Micro Softy 74: The Cretan Paradox & Logical Illusions

Micro Softy 74: The Cretan Paradox & Logical Illusions

Published by Jenni Sidey

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 …

Micro Softy 73: The Ups & Downs of Escalator Design

Micro Softy 73: The Ups & Downs of Escalator Design

Published by Jenni Sidey

Civil engineers need to design around people. This is a hint for this week’s Micro Softy.  At the Dallas-Fort Worth (DFW) airport, the train Skylink seamlessly transports you from terminal to terminal. Trains depart every 2 minutes, with a maximum travel time of 9 minutes between the farthest points, making it highly efficient. The train operates from Level 3. An up escalator takes you there.  Here is something interesting. There is a single escalator that takes you up to the Skylink train. There are two down escalators for those exiting the train. That’s this week’s Micro Softy. Why are there two down escalators but only a single up escalator for Skylink?   See next week’s Micro Softy for the obvious answer.  Solution to Micro Softy 73: Necklace Cutting   Here’s last week’s Micro Softy concerning a girl named Sally with money flow problems.   Sally needs to pay her rent daily for 30 days using individual gold beads from a 31-bead necklace. However, each time she cuts the necklace to separate beads, she must pay a jeweler to reconnect it. To minimize these jeweler fees, she must find a strategy that allows her to give the landlord exactly one bead per day using the fewest possible cuts. …