Skeptophilia (skep-to-fil-i-a) (n.) - the love of logical thought, skepticism, and thinking critically. Being an exploration of the applications of skeptical thinking to the world at large, with periodic excursions into linguistics, music, politics, cryptozoology, and why people keep seeing the face of Jesus on grilled cheese sandwiches.
Showing posts with label puzzles. Show all posts
Showing posts with label puzzles. Show all posts

Friday, September 17, 2021

Prolix proverbs

I thought I'd have a little fun with this week's Fiction Friday, and throw some word puzzles at you.  It may stretch the definition of Fiction Friday, but oh well.

It's my blog and I'll do what I like.

When I was in high school -- so, many years ago (how many is left as an exercise for the reader) -- my English teacher, Ms. Reinhardt, gave us a set of puzzles: familiar sayings, aphorisms, and clichés in unfamiliar guise.  Amazingly enough, I kept my copy all these years, and just ran across it this evening while searching for something else.

[Image licensed under the Creative Commons Wikimedia Foundation, Puzzly puzzled, CC BY-SA 3.0]

I don't know what their origin is -- I don't think she made them up -- but wherever they're from, they're cool brain-teasers.  (And if anyone does know the source, let me know so I can credit them properly.)  How many of them can you figure out?
1. A lithoid form, whose onward course
Is shaped by gravitational force
Can scarce enjoy the consolation
Of bryophytic aggregation.

2. To carry haulm of cereal growth
The tylopod is nothing loath;
But just one haulm too many means
That dorsal fracture supervenes.

3. When, nimbus-free, Sol marches by
Across the circumambient sky,
To graminiferous meads repair --
Your instant task awaits you there!

4. There is no use in exhortation
To practice equine flagellation,
If vital forces did depart
And still the breath, and cease the heart.

5. That unit of the avian tribe
Whose movements one can circumscribe
In manu, as a pair will rate
Subarborially situate.

6. For none who claims to represent
The Homo species sapient,
Will loiter Einstein's fourth dimension
Or sea's quotidian declension.

7. Faced with material esculent
As source of liquid nourishment
Avoid excess; 'twill but displease
Of culinary expertise.

8. Conducting to the watering place
A quadruped of equine race
Is simple; but he may not care
To practice imbibition there.

9. The coroner observed: "Perpend,
The death of this, our feline friend,
Reflects preoccupation shown
With business other than his own."

10. Of little value his compunctions
Who executes clavigerous functions,
When once from circumambient pen
Is snatched its equine denizen.
Have fun!  (And drop me an email if you want a hint or get stumped and are desperate for answers.)

 **************************************

London in the nineteenth century was a seriously disgusting place to live, especially for the lower classes.  Sewage was dumped into gutters along the street; it then ran down into the ground -- the same ground from which residents pumped their drinking water.  The smell can only be imagined, but the prevalence of infectious water-borne diseases is a matter of record.

In 1854 there was a horrible epidemic of cholera hit central London, ultimately killing over six hundred people.  Because the most obvious unsanitary thing about the place was the smell, the leading thinkers of the time thought that cholera came from bad air -- the "miasmal model" of contagion.  But a doctor named John Snow thought it was water-borne, and through his tireless work, he was able to trace the entire epidemic to one hand-pumped well.  Finally, after weeks and months of argument, the city planners agreed to remove the handle of the well, and the epidemic ended only a few days afterward.

The work of John Snow led to a complete change in attitude toward sanitation, sewers, and safe drinking water, and in only a few years completely changed the face of the city of London.  Snow, and the epidemic he halted, are the subject of the fantastic book The Ghost Map: The Story of London's Most Terrifying Epidemic -- and How It Changed Cities, Science, and the Modern World, by science historian Steven Johnson.  The detective work Snow undertook, and his tireless efforts to save the London poor from a horrible disease, make for fascinating reading, and shine a vivid light on what cities were like back when life for all but the wealthy was "solitary, poor, nasty, brutish, and short" (to swipe Edmund Burke's trenchant turn of phrase).

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]


Monday, September 14, 2020

Solution to the Census Taker Puzzle

A few days ago, I posted a puzzle, and challenged my readers to try to solve it.  (If you haven't seen it yet, it's in my post "Pieces of the Puzzle.")  I promised I'd post a solution, so here it is.  (If you're still working on it, read no further!  It's always more fun to work something out yourself than to have someone simply tell you the answer.)

Here's the puzzle:
A census taker goes to a man's house, and asks for the ages of the man's three daughters.  
The man says, "The product of their ages is 36."  
The census taker says, "That's not enough information to figure it out." 
The man says, "Okay. The sum of their ages is equal to the house number across the street."  
The census taker looks out of the window at the house across the street, and says, "That's still not enough information to figure it out."  
The man says, "Okay.  My oldest daughter has red hair."  
The census taker says thank you and writes down the ages of the three daughters.  
How old are they?
Clue #1 -- that the product of the three girls' ages is equal to 36 -- gives us eight possible combinations of ages:
1, 1, 36
1, 2, 18
1, 3, 12
1, 4, 9
1, 6, 6
2, 3, 6
2, 2, 9
3, 3, 4
So the census taker is quite right that this is insufficient information.

The second clue is that the sum of their ages is equal to the house number across the street. So let's see what the house number could be:
1 + 1 + 36 = 38
1 + 2 + 18 = 21
1 + 3 + 12 = 16
1 + 4 + 9 = 14
1 + 6 + 6 = 13
2 + 3 + 6 = 11
2 + 2 + 9 = 13
3 + 3 + 4 = 10
The census taker looks at the house number through the window, and still can't figure it out.  This is the key to the puzzle. 

Suppose the house number had been 21.  Then looking at the house number would have been sufficient information for solving it; the children would be 1, 2, and 18.  The only way that looking at the house number would be insufficient is if there were two sets of ages that added to the same thing -- which is only true for 1, 6, and 6, and 2, 2, and 9, both which add to 13.

The third clue is that the oldest daughter has red hair.  In the first of our remaining possibilities, 1, 6, and 6, there is no oldest daughter -- the eldest children are twins.  Therefore the daughters are 2, 2, and 9.

I hope you enjoyed this puzzle -- I think it's one of the cleverest ones I've ever seen!

Thursday, September 10, 2020

Pieces of the puzzle

I'm curious about where the human drive to solve puzzles comes from.

It's a cool thing, don't get me wrong.  But you have to wonder why it's something so many of us share.  We are driven to know things, even things that don't seem to serve any particular purpose in our lives.   The process is what's compelling; many times, the answer itself is trivial, once you find it.  But still we're pushed onward by an almost physical craving to figure stuff out.

When I taught Critical Thinking, every few weeks I devoted a day to solving divergent thinking puzzles.  My rationale is that puzzle-solving is like mental calisthenics; if you want to grow your muscles, you exercise, and if you want to sharpen your intellect, you make it work.  I told the students at the outset that they were not graded and that I didn't care if they didn't get to all of them by the end of the period.  You'd think that this would be license for high school students to blow it off, to spend the period chatting, but I found that this activity was one of the ones for which I almost never had to work hard to keep them engaged, despite more than once hearing kids saying things like, "This is making my brain hurt."

Here's a sample -- one of the most elegant puzzles I've ever seen:
A census taker goes to a man's house, and asks for the ages of the man's three daughters. 
The man says, "The product of their ages is 36." 
The census taker says, "That's not enough information to figure it out." 
The man says, "Okay. The sum of their ages is equal to the house number across the street." 
The census taker looks out of the window at the house across the street, and says, "That's still not enough information to figure it out." 
The man says, "Okay. My oldest daughter has red hair." 
The census taker says thank you and writes down the ages of the three daughters. 
How old are they?
And yes, I just re-read this, and I didn't leave anything out.  It's solvable from what I've given you.  Give it a try!  (I'll post a solution in a few days.)

This drive to figure things out, even things with no immediate application, reaches its apogee in two fields that are near and dear to me: science and linguistics.  In science, it takes the form of pure research, which, as a scientist friend of mine put it, is "trying to make sense of one cubic centimeter of the universe."  To be sure, a lot of pure research results in applications afterwards, but that's not usually why scientists pursue such knowledge.  The thrill of pursuit, and the satisfaction of knowing, are motivations in and of themselves.

In linguistics, it has to do with deepening our understanding of how humans communicate, with figuring out the connections between different modes of communication, and with deciphering the languages of our ancestors.  It's this last one that spurred me to write this post; just yesterday, I finished re-reading the phenomenal book The Riddle of the Labyrinth by Margalit Fox, which is the story of how three people set out, one after the other, to crack the code of Linear B.

Linear B was a writing system used in Crete 4,500 years ago, and for which neither the sound values of the characters, nor the language they encoded, was known.  This is the most difficult possible problem for a linguist; in fact, most of the time, such scripts (of which there are a handful of other examples) remain closed doors permanently.  If you neither know what sounds the letters represent, nor what language was spoken by the people who wrote them, how could you ever decipher it?

One of the Linear B tablets found at Knossos by Arthur Evans [Image licensed under the Creative Commons vintagedept, Clay Tablet inscribed with Linear B script, CC BY 2.0]

I'd known about this amazing triumph of human perseverance and intelligence ever since I read John Chadwick's The Decipherment of Linear B when I was in college.  I was blown away by the difficulty of the task these people undertook, and their doggedness in pursuing the quest to its end.  Chadwick's book is fascinating, but Fox's is a triumph; and you're left with the dual sense of admiration at minds that could pierce such a puzzle, and wonderment at why they felt so driven.

Because once the Linear B scripts were decoded, the tablets and inscriptions turned out to be...

... inventories.  Lists of how many jugs of olive oil and bottles of wine they had, how many arrows and spears, how many horses and cattle and sheep.  No wisdom of the ancients; no gripping sagas of heroes doing heroic things; no new insights into history.

But none of that mattered.  Because of the form that the inscriptions took, Arthur Evans, Alice Kober, and Michael Ventris realized pretty quickly that this was the sort of thing that the Linear B tablets were about.  The scholars who deciphered this mysterious script weren't after a solution because they thought the inscriptions said something profound or worth knowing; they devoted their lives to the puzzle because it was one cubic centimeter of the universe that no one had yet made sense of.

That they succeeded is a testimony to this peculiar drive we have to understand the world around us, even when it seems to fall under the heading of "who cares?"   We need to know, we humans.  Wherever that urge comes from, it becomes an almost physical craving.  All three of the people whose work cracked the code were united by one trait; a desperate desire to figure things out.  Only one, in fact, had a particularly good formal background in linguistics.  The other two were an architect and a wealthy amateur historian and archaeologist.  Training wasn't the issue.  What allowed them to succeed was persistence, and methodical minds that refused to admit that a solution was out of reach.

The story is fascinating, and by turns tragic and inspirational, but by the time I was done reading it I was left with my original question; why are we driven to know stuff that seems to have no practical application whatsoever?  I completely understood how Evans, Kober, and Ventris felt, and in their place I no doubt would have felt the same way, but I'm still at a loss to explain why.  It's one of those mysterious filigrees of the human mind, which perhaps is selected for because curiosity and inquisitiveness have high survival value in the big picture, even if they sometimes push us to spend our lives bringing light to some little dark cul-de-sac of human knowledge that no one outside of the field cares, or will even hear, about.

But as the brilliant geneticist Barbara McClintock, about whom I wrote last week and whose decades-long persistence in solving the mystery of transposable elements ("jumping genes") eventually resulted in a Nobel Prize, put it: "It is a tremendous joy, the whole process of finding the answer.  Just pure joy."

**************************************

Humans have always looked up to the skies.  Art from millennia ago record the positions of the stars and planets -- and one-off astronomical events like comets, eclipses, and supernovas.

And our livelihoods were once tied to those observations.  Calendars based on star positions gave the ancient Egyptians the knowledge of when to expect the Nile River to flood, allowing them to prepare to utilize every drop of that precious water in a climate where rain was rare indeed.  When to plant, when to harvest, when to start storing food -- all were directed from above.

As Carl Sagan so evocatively put it, "It is no wonder that our ancestors worshiped the stars.  For we are their children."

In her new book The Human Cosmos: Civilization and the Stars, scientist and author Jo Marchant looks at this connection through history, from the time of the Lascaux Cave Paintings to the building of Stonehenge to the medieval attempts to impose a "perfect" mathematics on the movement of heavenly objects to today's cutting edge astronomy and astrophysics.  In a journey through history and prehistory, she tells the very human story of our attempts to comprehend what is happening in the skies over our heads -- and how our mechanized lives today have disconnected us from this deep and fundamental understanding.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]



Thursday, March 5, 2015

Piecing together the puzzle

I'm curious about where the human drive to solve puzzles comes from.

It's a cool thing, don't get me wrong.  But you have to wonder why it's something so many of us share.  We are driven to know things, even things that don't seem to serve any particular purpose in our lives.  The process is what's compelling; many times, the answer itself is trivial, once you find it.  But still we're pushed onward by an almost physical craving to figure stuff out.

Every few weeks I devote a day in my Critical Thinking classes to solving divergent thinking puzzles.  My rationale is that puzzle-solving is like mental calisthenics; if you want to grow your muscles, you exercise, and if you want to sharpen your intellect, you make it work.  I tell the students at the outset that they're not graded and that I don't care if they don't get to all of them by the end of the period.  You'd think that this would be license for high school students to blow it off, to spend the period chatting, but I find that this activity is one of the ones for which I almost never have to work hard to keep them engaged, despite more than once hearing kids saying things like, "This is making my brain hurt."

Here's a sample -- one of the most elegant puzzles I've ever seen:
A census taker goes to a man's house, and asks for the ages of the man's three daughters. 
The man says, "The product of their ages is 36." 
The census taker says, "That's not enough information to figure it out." 
The man says, "Okay.  The sum of their ages is equal to the house number across the street." 
The census taker looks out of the window at the house across the street, and says, "That's still not enough information to figure it out." 
The man says, "Okay.  My oldest daughter has red hair." 
The census taker says thank you and writes down the ages of the three daughters. 
How old are they?
And yes, I just re-read this, and I didn't leave anything out.  It's solvable from what I've given you.  Give it a try!

This drive to figure things out, even things with no immediate application, reaches its apogee in two fields that are near and dear to me: science and linguistics.  In science, it takes the form of pure research, which, as a scientist friend of mine put it, is "trying to make sense of one cubic centimeter of the universe."  To be sure, a lot of pure research results in applications afterwards, but that's not usually why scientists pursue such knowledge.  The thrill of pursuit, and the satisfaction of knowing, are motivations in and of themselves.

In linguistics, it has to do with deepening our understanding of how humans communicate, with figuring out the connections between different modes of communication, and with deciphering the languages of our ancestors.  It's this last one that spurred me to write this post; just yesterday, I finished reading the phenomenal book The Riddle of the Labyrinth by Margalit Fox, which is the story of how three people set out, one after the other, to crack the code of Linear B.

Linear B was a writing system used in Crete 4,500 years ago, and for which neither the sound values of the characters, nor the language they encoded, was known.  This is the most difficult possible problem for a linguist; in fact, most of the time, such scripts (of which there are a handful of other examples) remain closed doors permanently.  If you neither know what sounds the letters represent, nor what language was spoken by the people who wrote them, how could you ever decipher it?

One of the Linear B tablets found at Knossos by Arthur Evans [image courtesy of the Wikimedia Commons]

I'd known about this amazing triumph of human perseverance and intelligence ever since I read John Chadwick's The Decipherment of Linear B when I was in college.  I was blown away by the difficulty of the task these people undertook, and their doggedness in pursuing the quest to its end.  Chadwick's book is fascinating, but Fox's is a triumph; and you're left with the dual sense of admiration at minds that could pierce such a puzzle, and wonderment at why they felt so driven.

Because once the Linear B scripts were decoded, the tablets and inscriptions turned out to be...

... inventories.  Lists of how many jugs of olive oil and bottles of wine they had, how many arrows and spears, how many horses and cattle and sheep.  No wisdom of the ancients; no gripping sagas of heroes doing heroic things; no new insights into history.

But none of that mattered.  Because of the form that the inscriptions took, Arthur Evans, Alice Kober, and Michael Ventris realized pretty quickly that this was the sort of thing that the Linear B tablets were about.  The scholars who deciphered this mysterious script weren't after a solution because they thought the inscriptions said something profound or worth knowing; they devoted their lives to the puzzle because it was one cubic centimeter of the universe that no one had yet made sense of.

That they succeeded is a testimony to this peculiar drive we have to understand the world around us, even when it seems to fall under the heading of "who cares?"  We need to know, we humans.  Wherever that urge comes from, it becomes an almost physical craving.  All three of the people whose work cracked the code were united by one trait; a desperate desire to figure things out.  Only one, in fact, had a particularly good formal background in linguistics.  The other two were an architect and a wealthy amateur historian and archaeologist.  Training wasn't the issue.  What allowed them to succeed was persistence, and methodical minds that refused to admit that a solution was out of reach.

The story is fascinating, and by turns tragic and inspirational, but by the time I was done reading it I was left with my original question; why are we driven to know stuff that seems to have no practical application whatsoever?  I completely understood how Evans, Kober, and Ventris felt, and in their place I no doubt would have felt the same way, but I'm still at a loss to explain why.  It's one of those mysterious filigrees of the human mind, which perhaps is selected for because curiosity and inquisitiveness have high survival value in the big picture, even if they sometimes push us to spend our lives bringing light to some little dark cul-de-sac of human knowledge that no one outside of the field cares, or will even hear, about.

But as the brilliant geneticist Barbara McClintock, whose decades-long persistence in solving the mystery of transposable elements ("jumping genes") eventually resulted in a Nobel Prize, put it:  "It is a tremendous joy, the whole process of finding the answer.  Just pure joy."