Random Thoughts from a Nonlinear Mind

The Package

This is a piece of Flash Fiction.  The topic: A person arrives home to find a package on their doorstep.

Simeon Langdon felt an unnaturally cold chill as he unbuckled his radiation suit and removed his propulsion pack.  Damn, the hairs on my arms are standing on end.  Why are they doing that?  What is going on with me?  He touched the proper sequence of buttons on the control panel, and the pad lifted him to his apartment.

He instantly saw the package as the platform rotated and then locked into place.  Huh, I don’t remember ordering anything.  I wonder what it could be…  He picked up the box and opened his door.  He set it down, injected himself with an aqua fluid, and went to the mandatory decontamination chamber.  He tried to relax as the toxins were slowly removed from his body.

After about 20 minutes, he made his way out of the chamber and examined the box.  He found perfectly symmetrical block letters on all six sides.

BROCKTON LANGDON
256 JOHNSTON COMPLEX
TUSCON, REPUBLIC OF ARIZONA
(TO BE DELIVERED ON FRIDAY, AUGUST THIRTEENTH IN THE YEAR 2652)

 Simeon took a deep breath, followed by a long pause.  Brockton was his grandfather, and he had been dead for at least 50 years.  How is this possible? I didn’t live at this address, there wasn’t a Republic of Arizona when he was alive, how and why did I get this package?  He closely examined the box and the material used to seal it.  No return address, no other clues, nothing.

Simeon cautiously opened the package.  He jumped back as an orb floated up out of the box and settled near the ceiling.    A flash of energy engulfed the room, and then a hologram of his grandfather appeared.  Not the grandfather he knew, not the aged, mysterious figure who showed no emotion and kept to himself.  The hologram seemed to be the 20-year-old version of a man he barely recognized.

Out of the eyes of the hologram came a shot of laser light targeting the data port in Simeon’s left shoulder.  He was overwhelmed by the encoded information, all ones and zeros, the binary language of computers.  Simeon heard the words the data stream was speaking to him, but he couldn’t understand how and why.

“The Langdon family is directly descended from the beings who seeded this planet with life billions of years ago.  The DNA animating this planet is ours.  It was me, in consultation with The Superiors, who set the wheels in motion all those years ago to destroy much of the life on Earth.  It is now your job to eliminate what is left of it in North America.  Your cousins will take care of the rest.  You will initially fight and struggle within yourself, but you will do your ancestor’s bidding.  Moreover, after you fully understand, you will want to do it, you will be compelled to do it.  The orb will deliver the devices, all you have to do is deploy them.  You will know where to go, what to do, and when to do it.”

The hologram disappeared into the orb, and then the orb disappeared into Simeon.  It felt warm and energizing.  He smiled as he basked in the epiphany that revealed his life’s true purpose.  As it was, gentleness and compassion never were words in his lexicon.  He now felt emboldened, fully realized, complete.  He put his head down and started to analyze the Orb-driven algorithms running through his matrix, his concentration only momentarily broken by the faint screams of “HELP!” coming from the kidnapped women he had locked in his bedroom closet.

A Most Curious Text

I have a bunch of relatives that live down South.  Many of them live in M i crooked letter crooked letter i crooked letter crooked letter i humpback humpback i. At least that is how I was taught to spell Mississippi by my cousin Christy when she was around 5 years old.

Christy’s sister Tammy is one of those Mississippians.  When she was young, she lived in Ohio, then moved to Mississippi.  She went to college in Georgia and…wait…what’s that?  Did I hear someone say “fascinating, tell me more ” (If you don’t recognize that little squiggle, check out my post from 1/14/20 ).

Well, I am going through Tammy’s history because I am trying to figure out where and when she learned French.  Have I heard her speak French? No.  Did she write me an email in French? She didn’t do that either.  So, what evidence do I have that she knows French?  I offer the following text she sent after she read the last post, the one about the mathematical exploits of her uncle.

 

 

Do you notice anything about her text?  Anything unusual at all?  I did.  It appears to be written by a French person or someone who knows how the French like to punctuate their sentences.  See the extra space between “that” and the question mark?  That is the giveaway.  It is one of those things that strikes Americans as unusual.  It just doesn’t look right.

Speaking of punctuation that does not sit well, I have a friend who insists on punctuating her texts in the British style.  Any and all quotation marks are inside of all punctuation.  She does this even though I am reasonably sure she has not been further east than Ohio.  It is just one of those things.  That said, I do believe that Tammy’s text is unique in my experience, I can not recall ever getting a message with French punctuation.

So, I had to do some research to get to the bottom of this.  It didn’t take me long to discover that autocorrect has been known to add an extra space before punctuation.  In fact, I read that many people have noticed this and are not fans of this quirk.  I have never been a fan of autocorrect, it sometimes has a mind of its own and that intelligence doesn’t necessarily mesh with mine.

There is another possibility, the predictive text function that shows up when texting.  If you choose a word from the available selections, the program puts a space after it.  It requires a little extra work to get rid of it, and I stand with those who can’t be bothered by such nonsense.

This is the end of this short post about a text Tammy sent me.  Do I think that she knows French, or is the extra space a function of her texting app?  The fiction writer in me wants to believe that she is a spy, planted here by the French government at a very young age for some nefarious purpose.  The scientist in me…well, who cares what that guy thinks, the spy theory makes for a much better story.

 

 

 

 

 

 

 

Do Me a Solid…and Read my Post about a Platonic Solid.

Something extraordinary happened a couple days ago.  I woke up and went upstairs to my library, sat down and turned on my computer; after that, I got some lunch and then went to the gym.  Nothing too exciting except for the fact that by the time I got out of the shower, my Dad solved a math problem that no one knew the answer to.  You read that right, at the age of 83, my Dad made an original contribution to mathematics by answering a question about a Platonic Solid.  How cool is that?

This is my story…

The other day I happened upon a Numberphile video about the mighty Dodecahedron, famous the world over for being one of the five Platonic Solids.  A Platonic Solid is a regular polygon, meaning that the same number of identical shapes meet at each vertex, or corner.  And that’s right, there are only five of them.  Try as you might, you won’t find another one.  Here is a fantastic video about Platonic Solids.  While this is not the video that inspired this sequence of events, I include it because we must have an understanding of these forms before I can get to the heart of my tale.

 

 

The solid we are interested in is the Dodecahedron, and yes, I still have a lot of trouble trying to spell it.  As I was doing some research on Platonic Solids, I came across this GIF.  I remember that scene from The Simpsons, and I am happy I found it.  It adds that little extra something to the post, don’t you think?  Anyway, I couldn’t possibly write a post about the Dodecahedron without including it.

 

 

As the Numberphile video demonstrates, the five Platonic Solids are the Tetrahedron, Cube, Octahedron, Dodecahedron, and Icosahedron.  The only thing we need to know about those shapes is that for four of the solids, it has been proven that you can not start at a vertex, head out in a straight line and return to your place of beginning without running into another vertex.  This has been proven for all the solids except for the Dodecahedron.  For that shape, the answer was unknown.  People had speculated that it was possible, but no one had found such a path or proven that such a trajectory would be impossible.  Until now.

In their impressively short paper, which I have included below, Jayadev S. Athreya and David Aulicino show such a path.  They took a Dodecahedron and unfolded it into the form of a net.  A net, in this case, is a flattened out two-dimensional version of the three-dimensional object in question.  In fact, their proof of the theorem is a little unusual and not mathematical at all. Grab some scissors, cut out the net, and then tape the Dodecahedron together.  You will see that the line is straight.

 

Download (PDF, 2.48MB)

 

After I watched the Numberphile video about the Dodecahedron, which I have included at the end of this post, I downloaded the paper.  After reading it, I remembered something that Professor Athreya said near the end of his presentation.  He stated that it wasn’t yet known if the special transecting line cut the Dodecahedron in half or not.  I looked at Figure 1 in their paper, said, “hmmm… to myself,” and then went to find my Dad at the office.

I handed him the paper, and he quickly read it.  After I told him that the areas of the shapes above and below the red trajectory line were unknown, he sat down at this computer.  It was apparent that he knew how to solve the problem.

 

 

Here is my Dad’s solution to the area problem. First, he had to compute the coordinates of every vertex for each of the 12 Pentagons shown in the figure.  He used Coordinate Geometry to do this.  Once this was done,  he was able to calculate the length and angle of the line transecting the Dodecahedron.  Then it was straightforward to calculate the areas above and below the red trajectory line.  How cool is that?

 

Download (PDF, 88KB)

 

I emailed my Dad’s solution to the professor.  He got back to me the same day.  He called my Dad’s approach to the problem “Awesome!” and thanked him for doing the calculation.  How cool is that?

One final thought, my Dad was most likely the first human being to ever calculate the areas created by the special transecting line.  He was the first person to know that the area above the line gets 47.7% of the original total while the bottom gets 52.3%.  All I have to say is…How cool is that?

 

NOTES:

Here is the Numberphile video about Platonic Solids.  Professor Athreya talks about the problem my Dad solved at the 18:00 mark.  The video is very good, it is worth the investment of time to watch the whole thing.

My Dad’s name is Jerry Slay.  His email address is [email protected].  If you wish, send him a message letting him know how cool this story is.

 

 

 

 

 

 

 

 

We’re Number…Huh?

If I gave you five guesses, could you identify the most famous equation in mathematics?  Perhaps this would be your first guess:

I must admit that is not a bad choice.  I think that one might be my personal favorite, but I do believe there is a general consensus about the most beautiful and elegant equation math has to offer.  It is known as Euler’s Identity, it looks like this:

If we do just a little manipulation we get this:

That is the version I prefer.  Within one simple equation, we get the five most important numbers in mathematics.  And as an added bonus, we get to see exponents.  Pretty cool.

There are lots of excellent videos on the internet on the topic of Euler’s Identity.  The equation can be derived in lots of different ways, each more fascinating than the next.  There is no need for me to include even a single derivation here.  I am going to do something much more interesting.

If there are any sports fans out there, I have a suggestion for you.  I don’t believe I have ever seen such a sign, but the world is undoubtedly in need of one.  The next time you head out to a game, you might want to take the time to get some poster board and markers, clear off a desktop, and get to work.  It won’t take long.

I suggest the following text:

If you really are proud and excited about your sign, feel free to add an exclamation point at the end, after all, 1! does indeed equal 1.  If a cameraman catches you, you just might make it onto ESPN.  If that happens, you can bask in the thought that 5 or 10 people across the nation chuckled when they saw your handiwork.

 

 

0.20787…

Check this out…

That looks familiar, right?  I think most of us have come across both of those definitions at some point.  What you probably didn’t learn is this…

Take a close look at that…and then look at this…

Truly astonishing, an imaginary number raised to the power of an imaginary number gives us a never-ending decimal.  As always, if you are interested in deriving the answer, do a Google search.  You will be amazed at what you will find.

 

 

How About a New Punctuation Mark?

Do you have any idea what this is?

How about a hint?  Oh yeah, that is a really good idea  

Can I have another one, that last one was so helpful  

OK, you can have a couple more.

You look great   Where are you going, gravedigging  

Nice ketchup stain, it really pulls your entire ensemble together  

Yes, I present the mighty Sarcmark.  Douglas Sak, a man in need of a punctuation mark to better denote sarcasm in his emails, founded Sarcasm, Inc. in 2006.  Shortly thereafter, the Sarcmark was offered for sale.  Not really a bad idea, is it?

I am always on board when someone is offering up ways to better clarify ideas, especially those of the written variety.  The website claims that the symbol is gaining traction but I must admit I have not seen it being used anywhere.  Except here.  Except now.  Where else on the entire internet could you get such valuable information this easily?  

If you really feel you need this Punctuation Mark in your grammatical arsenal, then I urge you to get over to the Sarcmark website ASAP.  When I came across the site years ago, the Sarcmark cost real money, now it is free.  I suggest you head on over, I would hate for you to send an email to a friend only to have them not realize you were insulting them.  

Inspired by a Yahoo: Inspiration is in Short Supply, we all need to take it Wherever and Whenever we can get it.

I am bursting at the seams.  Writing about Edwin Goodwin (the clown who “discovered” that π = 3.2) has elevated me; my ambitions now include worldwide fame.  I want riches, texts from supermodels (OK, Danica Patrick would do just fine), and a driver named Jeeves.  How am I going to get all these things?  Easy, I stayed up late last night and came up with the following rock-solid mathematical proof that 2 = 1.  Read on.

Why would I give you only one proof when I have two in the bag?  Behold the following:

I am basking in my own genius.  I am going to call my congressman and get this thing written into law ASAP.  I wonder which supermodel will text me first?  My mind is racing, good grief I might even hear from Athena (you will be hearing much more about her later this year).  Wow, I’ll probably have to set up some kind of a rotating schedule so that all these women don’t show up at my house at the same time.  I don’t want them fighting over little old me.  So, do you think this will be a big problem or have I missed something?  Do I need to buy some new socks and shirts or should I just chill?

 

Bill #246: Strange Doings in Indiana

‘we think it something on which the members of both houses can unite without distinction of party.'”

James Garfield, commenting on his proof of The Pythagorean Theorem (as discussed in a previous essay).

Does it strike you at all as strange that then-Congressman James Garfield would make such a comment? My initial thought was that he was having a little fun, that his tongue was firmly planted in his cheek as he made that statement about his neat little proof. Then I remembered something I learned years ago, I recalled an attempt to legislate mathematical truth by what can only be described as a group of yahoos in Indiana. Hold your breath and take a look at this.

In the late 1800’s something happened in the state legislature of Indiana that is inconceivable. Let me begin by telling you that I keep an unofficial list of the dumbest, most inexplicable things I have ever heard. The following short story is always at or near the top of that fluid archive.

In 1897 the Indiana General Assembly took up Bill #246, generally known today as The Indiana π Bill. It is going to be hard for me to finish off this essay because I have trouble typing while my head is shaking violently back and forth. You see, every time I am reminded of this story, I lose a little more faith in humanity. The story of what happened in Indiana is easily one of the dumbest things that have ever occurred in the legislative history of this country. You know what? Let me qualify that last statement and say that it is one of the dumbest things that has ever happened anywhere at any time in the history of humanity.

Our road to perdition begins with Edwin Goodwin, a physician and amateur mathematician (let me stress amateur) who decided he had figured out how to square a circle using only a compass and a straightedge. The big problem with that is that in 1882 a real mathematician named Lindemann had proved that such a thing was impossible. Such nasty little facts never, ever get in the way of a crackpot on a mission, and Goodwin certainly was a goofball with an agenda. As unbelievable as it may sound, he found many willing accomplices in the representatives of the people of Indiana.

The details of the mathematics are not necessary, his paper is so bad that I would not feel right telling you about it. Sometimes it is good to set up a straw man just to show how bad an argument is but not in this case. I think the story of what happened with this atrocious bit of mathematics is the interesting part. For our purposes, there is only one thing you need to know, namely that Goodwin came up with 3.2 as the value of π. As you probably know, the real value is 3.1415927… The decimal just keeps going, never repeating on its way to infinity and beyond.

Goodwin actually had his paper published by the American Mathematical Monthly, a journal founded in 1894 and still around today. The thing is, the people responsible for publishing the journal let Goodwin pay for the privilege of having his “genius” exposed to the world at large. The paper was printed with a disclaimer indicating that it had not been peer-reviewed and that it was published at the request of the author. Do you think anyone took note of these facts? Nope.

Goodwin took his paper to a state representative named Taylor Record, and in one of the worst decisions ever made by any person anywhere at any time, Record introduced a bill, Bill #246, to have Goodwin’s claims written into law. The bill was put to the vote, and as you might have guessed, the vote was unanimous. What you might not have supposed is that the bill passed!

Goodwin had figured the value of π to be 3.2 and the Indiana General Assembly readily agreed. Can you believe that? They all agreed, without a single dissenting vote, that the value of π was to be 3.2 and that would be the law of the land. What were they thinking? It is my contention that they were not thinking at all. They were apparently charmed by Goodwin and stood in awe of his “genius.”  It didn’t help that Goodwin told the politicians that the people of Indiana could use his result without paying royalties.  Of course, the rest of the world would have to pay up.

Fortunately, the bill had to then go on to the Indiana Senate. It failed in a close vote, a very close vote. Even though it was apparent to everyone but the politicians that they all had lost their minds, they still nearly passed a law indicating that anyone using a value of π different than 3.2 was guilty of somehow breaking the law. Not only that, but in 1985, a scholar went through Goodwin’s paper and found that there were seven different values of π implied by Goodwin’s ridiculous mathematics. Can you actually believe any of this nonsense?

This story is relevant today as the purveyors of Intelligent Design try, time, and time again, to discount evolution by attempting to legislate what science is and what it is not. It is also a remarkable story as the science of Climate Change has become politicized to the point where the actual science, and the rock-solid mathematics that is its foundation, doesn’t seem to matter at all. The story of The Indiana π Bill is a cautionary tale, a spook story, one where the stakes are as high as you and I can imagine. We all must remain vigilant to ensure that the crackpots and the self-described geniuses remain hidden in the dark underbrush where they indeed belong.

 

 

1,000,000 Digits Isn’t Nearly Enough: A Few Thoughts on π

A few years ago, I sat down at my computer intending to write a short essay on one of my favorite subjects, π.  I thought I would start by computing π to as many digits as possible.  It was at that point that I realized that I had never computed π, and I had no idea how to do it.  I knew about the old methods, like those of people like Archimedes, but I had no idea how to compute the digits using modern methods and a computer.  As odd as it sounds, it simply had never come up.  I was truly stunned as I sat motionless in my chair, unsure of what I was supposed to do.  It never occurred to me that if I were tasked with computing π, I would have no idea where to start.  It really was a strange and confusing feeling.

After I stopped rolling around on the floor (I couldn’t quite get into the fetal position), I started my research into how to compute π.  I quickly found that the process is not straightforward, and it certainly is not trivial.  I eventually found a freeware program called y-cruncher, which will compute π to n digits, depending entirely on the amount of RAM in your computer.  This was also a surprise to me.  I wasn’t quite sure what RAM had to do with the calculation then, but I have a better idea now.  All the previous numbers in π must be loaded into memory because they are used to derive the next digit, and the next, and the next.  Who knew?  I suspected that something like this might be the case, but I was surprised that hard drive space wasn’t used instead of RAM.

I loaded up the y-cruncher program on the killer computer I built a few weeks ago and looked over the settings.  After it scanned my system, the clever code told me that I could compute 5 billion digits of π with no problem.  Of course, I took the program up on its offer.  Before I knew what had happened, I had a file on my hard drive that contained 5 billion digits of π.  Amazing.  As I tried to load the 4.8GB file into a text editor, I ran into another unexpected problem.

Have you ever tried to open a large text document?  I mean a very large text document, say one with 5 billion digits?  It is not a simple thing.  Notepad won’t do it; Word can’t handle it, and on and on and on.  A developer wrote a program for Windows specifically for large files called Notepad++, but it wouldn’t open it either.  Fortunately, I am very familiar with a suite of programs called LibreOffice.  It mimics Microsoft Office and, best of all, the programs are free.  LibreOffice Writer has been my preferred text editor for years.  For now, the critical point is that LibreOffice claims not to have a file size limit.

I opened LibreOffice 6.2 and had a go at loading my giant file.  The file is so large that it crashed my computer, I mean the whole thing.  The program ran for hours, chugging along, trying its best to load the entire file.  It was taking so long that I went to the gym.  When I came back, the file was still loading.  I got something to eat, and when I came back to my computer room, I found that the system had crashed.

Not one to give up that easily, I tried loading it again.  This time it just crashed the LibreOffice program.  Progress!  Then it crashed again.  As of now, the file has processed about 140,000,000 characters out of the 5 billion total.  Will the file open?  I am not sure, but even if it does fully open, I doubt I will be able to search through it.  It is just too big.

At this moment, LibreOffice is using over 18 GBs of the 32 GBs of spiffy new RAM I installed in my new system.  The program is plugging along.  It has processed over 250,000,000 characters.  Sure, that is a lot of numbers, but it is only a small fraction of the total.

The program has been trying to open the file for about a day now.  After numerous crashes, it still has a long way to go.  I am writing this post while LibreOffice is working hard to fulfill my request.   It has over 625,000,000 characters open, we have reached a milestone, it is over 10% of the total.  The font is 10 point Liberation Mono, the page count is about 11,000.

Strangely, LibreOffice is splitting the digits into words.  Every 10,000 digits of π are counted as one word.  How odd.  I have no idea why it is doing that.  Apparently, no one else does either.  I have been doing some searching, and it appears I am the first person to ask such a question.  Everyone else probably instantly went to the proper program, the one known by scientists and mathematicians to be the go-to program for such nonsense.  I have been out of that loop for a long time, I stopped getting the flyers and emails years ago…

After a bunch of time and effort, I managed to get over 1 billion of the digits to appear in LibreOffice.  That was the limit, my system would not allow it to load more. Why?  Once again, we are back to the limitations my new computer has due to the amount of RAM I installed.  32 GBs, which is overkill for almost any system, simply falls short in this instance.  LibreOffice used it all up and wanted more.  The program crashed one final time, and then I gave up.

In the future, I will load a file with hundreds of millions of digits, or maybe even a billion, and see what I can find.  I am sure there is some interesting stuff in there.  Do we get 20 consecutive zeroes?  How about forty 9s in a row?  Is my phone number with area code in there?  How about my social security number?  In due time, we should have answers to these questions and more.