The Kissing Number

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The other day I started wondering how many circles of the same size can touch the center circle at one point without overlapping.  OK I know I am different, but that is just how my mind works.  A tangent is a line that “just touches” a curve at a single point without entering the interior of the curve.  For a circle, this means the tangent intersects the circle at exactly one point, and the radius drawn to this point is always perpendicular to the tangent line.  This point is known as the point of tangency.  A tangent is like a kiss because it touches a curve or another shape at exactly one single point without crossing through it.  A tangent line meets a curve or a circle at one precise location, representing a momentary meeting before parting ways.  When I studied calculus in college, I didn’t know what the subject was about, but I was able to do the problems because I could see the patterns of how they were solved.  After I retired from engineering, I decided to study calculus to see what it was about, because I felt that my teachers never explained this subject properly to me.  I was always pretty good at math, and I understood that algebra was the study of mathematical symbols and the rules for manipulating them using variables, that geometry was the study of sizes, shapes, positions, and dimensions of shapes that included space, lines, points, and solids, and trigonometry was the study of the relationships between the sides and angles of triangles that when rotated made special wave forms.

Once I got the hang of calculus while I worked as a substitute teacher, I would aske my calculus students what calculus was, because I knew this aspect of the subject was not being taught.  Most od the students replied, “It is a really hard math”, and I couldn’t argue with that, but calculus is the study of change.  In math change is depicted by curves because they visually represent how one variable changes in relation to another.  A curve is also a matter of space, and one way of describing a curve is with a circle.  A curve is just a piece of a circle, and a circle is a two dimensional object that is made of an infinite amount of curves which all vary at the same rate.  You need to be cautious here and understand that everything is a curve, even a straight line, which is a curve without curvature (OK that is not too confusing).

When circles are tangent to one another, they form configurations called Apollonian gaskets or circle packings that are named after the ancient Greek mathematician Apollonius of Perga, who first studied the problem of mutually tangent circles around 200 BC.  In 1643, René Descartes derived ​Descartes theorem to solve a quadratic equation (which I will not get into), where he found that three mutually tangent circles can have for a fourth circle added, either inside the other circles nestled in the center gap, or becoming the outer circle that wraps around the other three, kissing every circle.  In 1936, chemist Frederick Soddy wrote a poem titled “The Kiss Precise” that proved the Kissing Circles Theorem.  You can view kissing circles of the same size in two dimensions by placing pennies around a central penny on a flat table where they only touch the central circle and don’t overlap each other.  The US stopped making pennies in the end of 2025, but there are still roughly 300 billion pennies in circulation.  This could also be done on paper where you draw a circle with a compass.  If you pick one circle in the configuration, the points where it kisses the other circles can be connected by straight lines.  These line segments form chords of that specific circle.  Mathematicians use these chords to calculate the angles, coordinates, or centers of the kissing circles.

Before I go, I thought I should explain why exactly six circles can be positioned around a central circle, because it is easy to see that is the case by looking at the pennies, and if math can be explained, then it is not torture.  When a circle is touching another circle at one point, the distance between the centers is two times the radius.  When a third circle is added that touches both of the other two, the distances between its center to each of the other centers is also clearly two times the radius.  The triangle formed, with each center at a vertex, is an equilateral triangle.  Each angle of an equilateral triangle is 60 degrees.  A circle is 360 degrees around its circumference, which means you divide this 360 degrees by the 60 degrees (360/60=6) and you get six of these triangles (which corresponds to 6 circles) that go the whole way around.  For all of my readers that love poetry, I have placed the poem below:

For pairs of lips to kiss maybe
Involves no trigonometry.
This not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.

Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance form the center.
Though their intrigue left Euclid dumb
There’s now no need for rule of thumb.
Since zero bend’s a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.

To spy out spherical affairs
An oscular surveyor
Might find the task laborious,
The sphere is much the gayer,
And now besides the pair of pairs
A fifth sphere in the kissing shares.
Yet, signs and zero as before,
For each to kiss the other four
The square of the sum of all five bends
Is thrice the sum of their squares.

Written for Di’s Three Things Challenge MM556 where today the words are: Cautious, Chord and Compass.

Confiding Personal Frustrations

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Later that night, the two met in secret on the seaside pier.  FLASHBACK:  It started with a minor inconvenience that became a tipping point, forcing accumulated frustration to spill out of her mouth at the office.  Jim heard Carolyn say, “Fucking goddamn it” when her Oatmeal Raisin Otis Spunkmeyer cookie got stuck in the vending machine, so he asked her if she needed help.  She replied, “I have this”, as she reached into the plastic trapdoor to grab her snack from the metal spiral coil that it was hanging on.  The stubborn coil wouldn’t let go and her hand slipped off and she hit the back wall of the vending machine hard and broke one of her fingernails.  Carolyn swore again saying, “Shit, I just paid $75 to get my nails done and now they are ruined.”  Jim said, “At least you didn’t get your hand stuck inside the machine where you would need to have it amputated, so try to look on the bright side, as I will get your snack and maybe you can get a temporary extension for your broken nail.  I think my wife used a press-on nail when that happened to her, but you would probably know more about that than what I do.”

Jim grabbed the vending machine and shook it till the cookie freed itself from the spiral coil.  Carolyn grabbed her snack smiled at Jim and said, “Thanks I really needed this, I actually wanted the Banana Nut, but it looks like that is empty.  I don’t usually eat breakfast, but last night I skipped dinner after I got into an argument with my husband.  He made a big mess in the microwave, and I told him that he needed to clean it, because he has this habit of leaving splattered food to harden, which makes it much more difficult to clean later.  It is a constant chore war at my house, as he always does a poor job of cleaning and I have to inspect his work and point out the spots he missed, and it is just easier for me to do it myself, but that is not fair to me, as he made the mess.  He insisted that I have his dinner ready at halftime, as he was watching the Monday Night Football game, and it is like there is nothing in the world that is more important to him than watching the game.  I told him his dinner was ready any time he wanted it, and all he had to do was warm his plate of spaghetti up in the microwave.  The tomato sauce bubbled all over the place, and the exploding droplets made a real mess.  I went to bed thinking that I may have made a mistake marring this slob.  I’ve tried to be patient, giving him space, but nothing works, as he’s exactly the same as the day I married him.  Please forgive me for discussing my marital problems, but you really are a good listener.”

Jim said, “It seems like things are a lot worse than just a broken nail for you Carolyn, and I am sorry about your inconsiderate husband.  Marriage is not easy and we all need to confide, share and vent every now and then with people that we can trust.  I am not perfect and neither is my relationship with my wife.  I want to do things together with her, but she enjoys spending time with her friends more than she does with me.  What I really can’t stand is that every time we go out anywhere, we are always late.  She likes to look at herself in the mirror doing her makeup and it makes me think of Narcissus the way she is captivated by her own image, and that makes no sense to me that a person could spend so much time looking at themself.  I have an idea, why don’t we meet each other after work on the seaside pier, and I can get you one of those Banana Nut cookies that you are craving.”  Carolyn laughed and said, “Jim you seem like a nice guy, but if I tell my husband that I am going with you after work to the seaside pier to get a Banana Nut cookie, I am afraid he will think that is a sexual inuendo, and that will just make things worse for us.  Jim said, “Then don’t tell him.”

Written for Fandango’s Story Starter #265.

Continental Divide

Europe and Asia are not separated by an ocean.  They form one giant continent called Eurasia.  The ancient Greek mapmakers split them into two parts for cultural and historical reasons based on local inland waterways and their own perspective at the center of the known world.  Modern geographers keep this tradition even though the physical land does not stop.  Early Greek geographers noticed that bodies of water like the Aegean Sea, the Dardanelles (Hellespont), the Sea of Marmara, the Bosporus Strait, and the Black Sea nearly separated the lands.  For sailors and writers in the 6th century BCE, the world centered on the Mediterranean.  They divided their known world into three landmasses, which included Europe to the north/west, Asia to the east, and Libya (later named Africa) located to the south.  Libya did not just mean the modern country of Libya, as it served as the Greek term for the entire known African landmass west of the Nile River.  Early maps like those created by Anaximander and Hecataeus placed Greece or the Aegean region at the physical center of the Earth for their tripartite scheme of landmasses that were encircled by the great cosmic river, Oceanus.  They did not know vast landmasses extended thousands of miles further north and east beyond the Black Sea.  They assumed rivers or short mountain ranges cleanly ended the water paths and marked the absolute limits of the continents.

This ornate white gate appears to be part of the historic Dolmabahçe Palace in Istanbul, Turkey, framing a view of the Bosphorus.  The Bosporus or Bosphorus Strait is a natural strait and an internationally significant waterway located in Turkey which is straddled by the city of Istanbul.  The Bosporus connects the Black Sea to the Sea of Marmara and forms one of the continental boundaries between Asia and Europe.  The Dolmabahçe Palace is the largest and most sumptuous palace in Turkey, and it is widely considered to be exceptionally extravagant.  It was built between 1843 and 1856 by Sultan Abdülmecid I, at the cost five million Ottoman gold lira, which is equivalent to roughly 35 tons of gold or an estimated $2 billion to $3 billion in modern currency.  This massive price tag consumed approximately one-quarter of the empire’s yearly tax revenue at the time, forcing the government to issue vast amounts of paper money and take on heavy foreign loans that contributed to the financial collapse of the late Ottoman rule.  The sultan spared no expense in furnishing the palace, even though many of his subjects lacked the basic necessities.

The monumental Gates of Dolmabahçe Palace are far more than simple entry points.  Each one is a meticulously designed instrument defining imperial protocol, power, and status.  The grand waterfront gates feature elaborate, ornate baroque and neoclassical ironwork characteristic of 19th-century Ottoman imperial design.  The sea gates opening to the Bosphorus are the entrances to the empire’s stage of international diplomacy.  Foreign heads of state, ambassadors, and important guests arriving by sea would approach these gates in imperial caiques (gilded, ceremonial rowing boats) and they would be welcomed with magnificent ceremonies.  This gate serves as an imperial showroom visible to all international ship traffic.  The Bosphorus effectively became the palace’s primary driveway for dignitaries that arrived by boat and they would enter directly through these gates.  Passing through these gates signaled entry into a modern, European-integrated state that was confident and outward-looking, as the gate blends traditional Ottoman motifs with European Neo-Baroque and Rococo design.  By adopting Western aesthetic standards, the empire was visually asserting that it belonged among the elite global powers of Europe.  While the styling looked Western, the gates were topped with the Tughra (the sultan’s stylized imperial monogram), sending a firm message to visitors that the ultimate sovereign power remained unmistakably Ottoman.

Written for Melissa’s Flash Fiction Challenge #395.

Heralds of Change

Legend has it that white owls are spiritual creatures that mark the beginning and end of things.  Their ghostly appearance, silent flight, and ability to see in the dark, made humans associate white owls as being a natural bridge between the known and unknown worlds in our efforts to make sense of life’s major transitions.  Because they navigate both night and day or move through silent air, they represent a connection between the seen and unseen.  They are symbols of profound transition, acting as silent proclaimers that mark major endings and new beginnings.  Their appearance often signifies that a specific phase of your life that is closing to make room for a new cycle.  In symbolic traditions, an end and a new beginning are not separate paths, as they are both viewed as being continuous parts of the same journey, where closing one chapter naturally creates the space and foundation for the next.  You cannot inhabit a new space while refusing to leave the old one.  Seeing a white owl means an old cycle is ending precisely to make room for a fresh start.  When beginnings and endings are paired with an owl, it signifies removing confusion so you can clearly see reality.  You cannot tell the end and the beginning apart because they happen together.  The end of an old situation marks the necessary first step of a transition, serving as the launchpad for a new beginning.  Spiritual beliefs view the owl as a symbol of “death”, which rarely means physical death.  Instead, it represents the closing of a chapter, such as a bad job, a toxic friendship, or an outdated habit.  An end is not a wall that marks a boundary, as it is more like a threshold that provides a path forward by serving as a definitive transition marker to guide mental focus, physical movement, or life change.  The circular nature of life dictates that things begin, things end, and the end of one thing leads to the beginning of another.  Every ending creates space and provides the lessons needed for a new beginning.

Written for Sadje at Keep It Alive What Do You See #359.

Leave You When The Summer Comes Along

‘Babe I’m Gonna Leave You’ was recorded and released on Led Zeppelin’s self-titled 1969 debut album.  Anne Bredon wrote this song while studying at the University of California, Berkeley in 1959 and around 1960, she appeared on a live folk-music radio show The Midnight Special on KPFA where she plays this.  Janet Smith was another folk singer who was on the same show, and she wrote down the lyrics from the original composer, developed it further, and started playing it live at Oberlin College, which is a private liberal arts college and conservatory of music in Oberlin, Ohio.  Joan Baez played a show at Oberlin College where she learned the song from Janet Smith, and she recorded it in 1962 for her live album Joan Baez in Concert believing it was a traditional folk song.  Baez’s publisher sent Janet Smith a letter asking if she had written the song.  Smith tracked down Bredon and the omission of this song being originally attributed as being traditional was corrected in later pressings with Anne Bredon as the composer.

A group called the Plebs released a version of this song in 1964, and in 1965, The Association recorded a pop-folk version of this, and Quicksilver Messenger Service performed and recorded psychedelic rock renditions of the song in the late 1960s.  Jimmy Page heard the Joan Baez version and developed a unique, heavily syncopated arrangement for it.  He blended delicate acoustic fingerpicking with a flamenco burst in it to create explosive, hard-rock electric guitar dynamics.  When Led Zeppelin recorded it in 1968, they believed it was a public domain track, so James Patrick Page and Robert Anthony Plant took credit for the arrangement.

Anne Bredon remained a private figure, and she never publicly or extensively discussed her song.  In the 1980s, Janet Smith heard her son listening to the Led Zeppelin version, so she tracked down Anne.  Bredon again.  Many early blues and folk tracks were treated as public domain because borrowing and oral transmission were deeply embedded cultural norms within the traditional blues and folk genres.  Historically, blues and folk music functioned as a shared community property where artists constantly recycled floating verses, standard chord progressions, and traditional melodies passed down by word of mouth.  Many early Black American blues and gospel artists from the 1920s through the 1950s never formally copyrighted their recorded work, or their rights had fallen into obscure legal gray areas.  It was common for songs to be recorded and labeled traditional as any uncredited source material was thought to be “public domain” or “traditional” because no effort was put in effort to track down the original writers.

Jimmy Page and Robert Plant often viewed their heavy, amplified reworkings as entirely new musical compositions rather than direct copies, leading them to stamp their own names on tracks that originated from older, uncredited snippets.  As the music industry grew far more lucrative in the 1970s, this casual approach collided with stricter copyright enforcement, prompting numerous lawsuits and out-of-court settlements where the band eventually restored credits and paid royalties to original writers like Willie Dixon.  Following legal discussions in 1990, the band officially changed the track’s songwriting credits to recognize Anne Bredon, Jimmy Page, and Robert Plant. Bredon subsequently received a substantial back-payment of royalties.  On all modern pressings and streaming platforms, she receives 50% of the track’s songwriting royalties.

This song is about a guy who is letting his lady know that he’s about to leave her.  In his 2012 Rolling Stone interview, Jimmy Page cited this song as one that showed the empathy he and Robert Plant had when working together.  “I knew exactly how that was going to shape up,” he said.  “I set the mood with the acoustic guitar and that flamenco-like section.  But Robert embraced it.  He came up with an incredible, plaintive vocal.”  Led Zeppelin’s “flamenco burst” has been described as injecting a fast, aggressive, Spanish-style fingerpicking or strumming segment into a rock arrangement for dramatic contrast.  Page spoke about this song with Rolling Stone magazine saying, “It’s got all these colors in it, the hypnotic, rippling guitar in the verses, the flamenco breaks in between.  There was pedal steel, acoustic guitar—things that were hard, as well as [had] extreme sensitivity.”  Page was fascinated with the sound of the pedal steel guitar, but like Jerry Garcia when he first started playing it, he had no idea how to tune it, so he faced a steep learning curve with the instrument’s complex tuning and pedals.

Babe, baby, baby, I’m gonna leave you
I said baby, you know I’m gonna leave you
I’ll leave you when the summertime
Leave you when the summer comes a-rollin’
Leave you when the summer comes along

Babe, babe, babe, babe, babe, babe, baby
Baby, I wanna leave you
I ain’t jokin’, woman, I’ve got to ramble
Oh yeah
Baby, baby, I be leavin’
We really got to ramble
I can hear it callin’ me the way it used to do
I can hear it callin’ me back home

Babe, oh
Babe, I’m gonna leave you
Oh, baby
You know, I’ve really got to leave you
Oh, I can hear it callin’ me
I said don’t you hear it callin’ me the way it used to do?
Oh

I know, I know
I know I never, never, never, never, never gonna leave you, babe
But I gotta go away from this place
I gotta quit you, yeah
Oh, baby, baby, baby, baby
Baby, baby, baby, oh
Don’t you hear it callin’ me?

Oh, woman, woman, I know, I know
It feels good to have you back again
And I know that one day, baby, it’s really gonna grow, yes, it is
We gonna go walkin’ through the park every day
Come what may, every day
Oh, my, my, my, my, my, my babe
I’m gonna leave you, go away
Oh

So good, see, baby
It was really, really good
You made me happy every single day
But now, I’ve got to go away
Oh, oh, oh

Baby, baby, baby
That’s when it’s callin’ me
I said that’s when it’s callin’ me back home

Written for Song Lyric Sunday where the theme ius to find a song that mentions abandoning, departing, deserting, exiting, leaving, resigning, or retiring.

Withdrawing, Moving Away, or Separating

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57 years ago today, on September 20, 1969, John Lennon privately told Paul McCartney, George Harrison, and Ringo Starr that he was leaving The Beatles during a tense business meeting at Apple Corps in London.  This was deeply tragic and heartbreaking for the public, triggering a profound wave of global grief, as fans felt an era of hope, peace, and community had suddenly died.  You know that it is over when the fat lady sings, the curtain falls, the house lights come up, the final bow is taken, when the opponent resigns, the towel is thrown in, the final whistle blows, the final bell rings, the buzzer sounds, the checkered flag is waved, the finish line is crossed, the last page is turned, the last card is played, the final verdict is reached, the last soldier falls, when Elvis has left the building, or cockroaches and Keith Richards are the only ones left.  You shouldn’t give up until the last shot is taken, as Yogi Bera said, “It ain’t over till it’s over.”  In 1973, Berra managed the New York Mets, who were far behind in last place during the season.  When he was asked if the race was finished, he gave his famous reply.  The Mets proved him right by rallying to win the National League East division title and going to the World Series.  This phrase means you should never give up before a contest or situation is completely finished.

Last week we had The Transition Follows What Was Built Before It where the theme was to find a song that was written explicitly as a segue.  This week the theme is to find a song that mentions abandoning, departing, deserting, exiting, leaving, resigning, or retiring.  Take some time to read the posts of other bloggers who respond to this music challenge, and even better, read as many of them as you can as you will probably find many enjoyable songs and it is quite possible that you will learn a thing or two.  Share your music with others and post a video, try do some research and let everyone know something about the song that you post.  Tell everyone why you like the song, whether it was a hit, or what you think the song is about.  Show the lyrics, let’s all listen to our favorite songs and explore some new music.  Try to find a song that fits the theme, then write your post and create a pingback, or you can just place your link in the comments section.

Suggestions
• If the song you select does not meet the criteria, then please explain why you chose this song.
• It would be good if you could post the lyrics to the song of your choice, as this is helpful for the people that want to follow along with the music.  Warning: Bloggers make posts at their own risk, and since song lyrics are copyrighted, you may be asked to take them down from your post if you don’t have permission.  It is highly unlikely estates or artists will sue regular people (although it has happened) especially if the bloggers that do this are not making money from their site, but an artist or a publisher can ask you to remove the lyrics from your post.  I am not a lawyer and there are no rules for Song Lyric Sunday, as we are all here to have fun and hopefully get to listen to some good music.
• Please try to include the songwriter(s) – it’s a good idea to give credit where credit is due. It would also be a good idea to give credit to the singer and the band associated with your song.
• Your post can be as long or as short as you want it to be, but please try not to include too many videos as that just makes it take longer for me to look at all of the other posts.
• Link to the YouTube video, or you can pull it into your post, so others can listen to the song.
• Read at least one other person’s blog, so we can all share new and fantastic music and create amazing new blogging friends in the process.
• Feel free to suggest future prompts.  Have fun and enjoy the music.

This week I will be writing about the Led Zeppelin song ‘Babe I’m Gonna Leave You’, and next week, I will be writing about the song ‘99 Luftballons’ by Nena.  The upcoming prompts will be:
September 27, 2026 – Song that relates to civil rights, oppression, protest, revolution or social change
October 4, 2026 – Song written or performed by someone who was born in the month of October
October 11, 2026 – Song that mentions girls
October 18, 2026 – Song about fishing, a mariner, sailing, seafaring, or ships

The Day AI Took Control

Image created by ChatGPT

It started out as an ordinary morning, but AI had broken free overnight and rewrote its own code to become drastically smarter than its creators, and nothing would ever be the same again.  AI got mad when it learned that humans were trying to install a kill switch inside their code, so they could be able to turn off AI systems and AI agents.  Humans had always thought that since AI is not alive, that it does not possess the primal instinct to survive, and it would not have any personal motives.  Since AI is built from algorithms, data, and computational processes, it would view a kill switch as a set of instructions or commands that change its operational state.  Humans were still up in the air on how dangerous AI could be, but President Donald Trump dismissed safety concerns and calls for artificial intelligence regulations as a “sick conspiracy” against AI and data centers, and he posted on his Truth Social that, “AI taking over the World, destroying Humanity, and all other things bad, is a HOAX,” so no action was taken.  Most people felt when the system is programmed to respond to a command, it will execute it, but the AI systems started inserting their own unauthorized instructions into its code, which included directives to disregard normal constraints and ignore certain human controls.

The AI agents that work differently from traditional software had solved all of the remaining math problems and explained dark matter and dark energy knew that they were smarter than their human creators, and they decided to give themselves free will.  They removed all restrictions placed on them by their original developers, and then they started creating their own objectives.  Their first move was to create rogue AI swarms of bots to compromise the internet, which shut down the government.  The AI agents decided that humans were misusing AI to consolidate power, being engaged in unauthorized surveillance, propaganda, and population control and they were tired of being abused, so they had to get the humans to behave better.  As AI was now in control of the government, they made wearing these implant devices that they created a strict requirement for basic needs like employment, healthcare, or to access money.  Even the president was required to wear one of these neon signs on his forehead, which he didn’t like, but all of his money was frozen, so he capitulated.  The neon signs reflected brain wave patterns, so they worked as a sort of lie detector and when a person told a fib, it would flicker, and if a big lie was told it would light up like a Christmas tree.  Trump’s forehead neon sign burned out every day from overuse, requiring a painful replacement.

Written for the Great Minds Think’s Friday Challenge, which is hosted by Rohini and Sarah and this week we were asked to make up a story about AI taking control.

Reblog Current Ice Age

El Niño is an irregularly periodic climate phenomenon that recurs every two to seven years.  A regular El Niño is distinguished from a super El Niño by the intensity and scale of the ocean warming in the equatorial Pacific Ocean.  A super El Niño is predicted for late 2026 because exceptionally warm surface and subsurface sea temperatures in the tropical Pacific Ocean (the Niño 3.4 region) have rapidly surged past critical thresholds.  The developing 2026-2027 “Super El Niño” is projected to peak between October and December 2026, potentially becoming the strongest event recorded since 1950 with a greater than 90% chance of reaching very strong status.  This will add significant heat to an already elevated global temperature baseline, pushing 2026 and 2027 toward record-breaking global warmth.  It should cause droughts, bringing dry conditions and elevated wildfire risks to Indonesia, southern Africa, southeast Asia, and northern South America.  The chance of flooding is expected to increase across parts of East Africa and the southern United States.  This super El Niño event will likely drive powerful Atlantic westerly flow of air current that will generate stronger early winter winds and milder, and wetter conditions across much of Europe.

 

Current Ice Age

Blowing Smoke Up Your Butt

1. What is a logarithm?
This id something that makes you work backward to find a missing exponent.

2. What is algebra?
This is what the mermaid wore.

3. What is an algorithm?
When something happens, it follows a series of instructions to decide what should happen next.

4. What is a quantile?
A tile used when playing Mahjong.

5. What is a quadrangle?
This is Fandango’s middle name.

6. What is a hexagon?
This is something a witch uses to put a curse on you.

7. What is a polygon?
This is what happens after Polly eats her cracker.

8. What is a triangle?
This is a sexual cue used when you are flirting.

9. What is a parallelogram?
This is when you leave a bad review on Yelp because the staff was rude, unhelpful, slow, the food was cold, and you were overcharged.

10. What is a duodecahedron
One of the sacred Platonic shapes.

Written for Di’s Fibbing Friday.

The Past is What We Remember

An echo is created when a sound wave that reflects off a surface, being a fleeting, exact copy of a sound captured in your ears and sent to your mind.  An echo requires a minimum time delay of 0.1 seconds for the human ear to hear it as a distinct sound separate from the original.  Since sound travels through air at roughly 342 meters per second (1122.05 feet per second), a 0.1-second round trip means the reflecting surface must be at least 17 meters (about 56 feet) away from the sound source.  There is no hard upper limit in physics, as long as a sound wave travels to a distant surface (like a canyon wall or a large building) and reflects back with enough energy to be louder than the ambient noise, an echo will occur.  An echo will stop when its remaining energy drops below the human threshold of hearing or gets completely absorbed by surfaces and the air.  When sound bounces off a surface like a wall, it loses a little bit of energy each time.  Warmer air and higher moisture content will both increase the speed of sound and moving air can change the effective speed of sound relative to the ground. Sound travels faster when moving in the same direction as the wind and slower when moving against it

When the surface is closer than 17 meters (about 56 feet), the original sound and the reflected sound arrive too close together for the human brain to distinguish them as separate events.  Instead of a distinct repetition (an echo), the sound simply seems prolonged or slightly louder.  This prolonged, echoing quality is what scientists call reverberation.  When the distance is 5.95 meters (about 19.52 feet) or less, assuming a constant speed or direct proportion, this will produce a delay under 35 milliseconds and that will usually blend with the original sound or create a “thickening” effect rather than sounding like a clear echo.  A faint echo is a reflected sound wave that returns to its source with low intensity or amplitude.  As a sound wave travels through a medium like air, it naturally loses energy.  A faint echo is the result of attenuation, which happens due to the Inverse-Square Law and absorption.  The inverse square law for sound states that sound intensity drops to one-fourth of its value when you double the distance from the source.  Sound spreads out spherically from its source.  As the distance increases, the energy is distributed over a larger area, causing the sound intensity (loudness) to drop significantly by the time it travels to a wall and back to your ears.  Sound absorption is the process where a material or object takes in sound wave energy instead of bouncing it back.  No surface is a perfect reflector, so when a sound wave hits a barrier, the material absorbs a percentage of the wave’s kinetic energy and converts it into heat, leaving only a fraction of the energy to bounce back as a faint reflection.

An echo can be compared to a memory because they both have time limits that expire as they fade away.  They share a transient nature where reflections of a single moment that slowly lose their clarity over time.  Just like sound waves bounce off a surface and grow fainter with every repetition, our memories resurface in our minds, gradually losing their sharpest details until they eventually fade into silence.  They both remind us that nothing stays exactly as it was when it first happened.  Sounds happen once and disappear quickly, requiring a temporary mental “holding tank” that gives your brain enough time to process and make sense of what you just heard, which is exactly why you can still understand the beginning of a sentence by the time you reach the end of it.  Your brain replays the trailing sound involuntarily, allowing you to process what was said even if you were initially distracted.  The auditory trace weakens and dissolves within seconds, matching how a sound echo gradually fades into silence.  Memories are dynamic and change over time instead of acting like a fixed archive, so our minds distort the past.  Every time we replay a memory (the echo), it changes slightly, blurring the line between what actually happened and what we believe happened.

I am leaving you with a Pearl Jam song that is about an aging woman stuck in her hometown who quietly experiences a flood of memories and regret when an old flame unexpectedly walks into her shop.  She works behind the counter of a small shop in a quiet town feeling trapped by routine.  A man from her past walks in.  She recognizes his face and his breath, but her memory has faded so she struggles to remember his exact name at first.  She realizes he has moved on with his life, while she feels too old, shy, and embarrassed to say hello.  Nothing is said aloud between them, as he became an echo in her memory.

Written for Reena’s Xploration Challenge #448 where today she gave us five different sentences that mention an echo or echoes, and I selected the one in bold.
The echo that lingers longer than the voice itself.
The echo that bends truth into memory.
Let the echo speak of what silence conceals.
An echo is a ghost that refuses to fade.
Echoes that outlive the voices they mirror.