RTNM – Page 18 – Random Thoughts from a Nonlinear Mind

Do Me a Solid…

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:

$\huge a^{2}+b^{2}=c^{2}$

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:

$\huge e^{i\pi }=-1$

If we do just a little manipulation we get this:

$\huge e^{i\pi }+1=0$

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:

$\huge WE'RE\; NUMBER\; -e^{i\pi}$

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…

$\huge i^{2}=-1\; or\; i=\sqrt{-1}$

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…

$\huge i^{i}=e^{\frac{-\pi }{2}}$

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

$\huge i^{i}=0.20787...$

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

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.

$\! \! \! \! \! \! a=b \; \; (easy\; enough)\\\\ a^{2}=ab \; \; (multiply\; both\; sides\; by \; a)\\\\ a^{2}+a^{2}-2ab=ab+a^{2}-2ab \; \; (add\; a^{2}-2ab\; to\; both\; sides)\\\\ 2(a^{2}-ab)=a^{2}-ab \; (simplify)\\\\ \frac{2(a^{2}-ab)}{a^{2}-ab}= \frac{a^{2}-ab}{a^{2}-ab}\\\\ \therefore 2=1$

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

$\! \! \! \! \! a=b \; \; (easy\; enough)\\\\ a^{2}=ab \; \; (multiply\; both\; sides\; by \; a)\\\\ a^{2}-ab=ab-b^{2}\; \; (ab=b^{2})\\\\ (a+b)(a-b)=b(a-b)\\\\ a+b=b\\\\ b+b=b\\\\ 2b=b\\\\ \therefore 2=1$

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.

A Problem with a Post

A few days ago, I published a short essay entitled Multiplicative Persistence. Now I want to tell the story behind the trouble I had trying to get the post, to well…post. It was an ordeal.

As you might imagine, I go through lots of drafts when I write these things. Actually, I go through a lot more than you might think. It is not unusual to have 20 or 30 of them. I am always tweaking a word here or there, and my good friend Grammarly always has something to add.

Usually, I am sitting at my computer pounding away on the keyboard, but that is not how all the posts originate. Lots of times, I am out at a bar or restaurant waiting for inspiration to strike. I always have an open notebook and a few working pens by my side. I have found that inspiration has its own timetable, and it doesn’t care much about what I want. That said, I always try to be ready in case The Inspiration Gods decide to shower me with booty. You will be learning much more about this process when I post the essays I wrote for a book called The Athena Chapters. Those will be up soon enough.

This post is about the problems I had trying to get my essay on Multiplicative Persistence to save and then show up on my website. The first few drafts were acting normal, but then the essay started to fight back. It didn’t want to post, it didn’t even want to save any new drafts. One moment I was typing and then, before I realized what was happening, I was engaged in battle. This is my story…

When I clicked on Save Draft, the computer gave me a 502 Bad Gateway error, then it did it again, and again, and again. I had never seen this error with WordPress or GoDaddy before, so I paused and tried to figure out what was going on. I assumed that the problem was on their end, seems reasonable, right? Nothing had changed on my system, and everything else I was working on seemed to be fine.

You know what I did, right? I hit Save Draft another dozen times. I got the 502 Bad Gateway error another dozen times. After that enjoyable experience, I decided to hit the Troubleshooting Chat Button on GoDaddy’s website. That is where the real fun began.

I can paraphrase the conversations…

Hello, what’s wrong?

502 Bad Gateway error when I try to save a draft of a post I am writing.

Ok, …give me a few minutes.

I went to your site, and I was able to log in, no problem.

I do not have a problem logging in, I am having a problem trying to save a draft of a post I am writing.

Hold on…I am transferring you to a specialized team.

Hello, you are having a problem logging into your site?

No, I am getting an error when I try to save a draft of a post I am writing.

OK…give me a few minutes…

We have put up a test post, and everything is fine. Are you some kind of moron? (They didn’t come out and say that, but it was strongly implied.)

Here is a screenshot of the 502 Bad Gateway error I am receiving when I try to SAVE A DRAFT OF A POST I AM TRYING TO WRITE!

OK…thank you very much. I am transferring you to a more specialized team.

All right. Is Batman part of this group? While he is not an actual superhero, he has world-class deductive skills. I am confident he could get me fixed up in no time.

No answer…

(I really love this next part.)

OK, sir, it is evident that you have no idea what you are doing.

Is this Batman?

No, sir, this is not Batman.

Can I speak to Batman?

There is no one here named Batman.

What should I do next? Hours are racing by, and my readers are clamoring for a new essay on multiplication. If I don’t get the post up soon, I can only imagine the level of rioting in the streets.

At this point, all I saw was a blinking cursor on the chat screen. I guess this person was trying to find Batman to tell him that I was out of my mind. This poor representative, with limited imagination, couldn’t understand why any person would want to read an essay on multiplication. The fact that he is pretty much right is beside the point.

Sir, please try another network and see what happens. We are thinking that the problem is on your end.

I don’t have another home computer network. My setup I not as sophisticated as that of someone like Batman. I am sure he has redundancies built-in, don’t you think?

I really don’t know. Again, there is no one here named Batman. Could you reset your router?

If I do that, I will lose you, and I will have to go through all this nonsense again, correct?

No answer…

I will reset, but can I have the direct line to Batman to save me some time after I reconnect?

No answer…

I tried the reset, lost the guy helping me, and still got the error message when I tried to save a draft. It was at this point that I started to utilize all those years of education I am rumored to have.

I asked myself a question: Is there anything different about that post? Is there something unique about it? The answer was yes. It was those stupid right-pointing arrows that I included to show the progression of the numbers after the digits were multiplied together. Those were the culprit, and, of course, there is a story behind their use.

The first few drafts of that post were behaving normally. The Save Draft button was working fine. I finally realized that the problems started when I decided to put those arrows in. The arrows are specialized symbols, getting them into a program like WordPress is not the easiest thing to do. You don’t tap the keyboard, you have to have a specialized script for mathematical symbols, or you need an equation writer. For decades, scientists and mathematicians have used a program called LaTeX (pronounced lay-tech) to write their papers. It is not very user-friendly, I use it when I have to, and in WordPress, I have to.

I went back to my draft of the essay, and I removed all the arrows. I tried to save the draft, and it worked. I really wanted to use arrows, so I didn’t give up on them. I then inserted a different kind of arrow (this one from a Special Symbol Editor, not an Equation Editor), and everything was fine. I was instantly back on track, and the world is now a better place because a handful of people now know what Multiplicative Persistence is.

Isn’t it strange that a small piece of random code for a right-leaning arrow caused all these problems? That little symbol led to a lot of issues and cost me a bunch of time and aggravation. The mysterious ways in which some computer code can interact are not to be underestimated.

After I figured out what was going on I decided that it was best if I write the guy from the chat, I still had his email from when I sent the screenshot of the error message. I thought that maybe my story would help in the future when some other poor slob stumbled across something similar. I told him to let Batman know that I had solved the problem and that everything was fine. Neither of them wrote me back.

Multiplicative Persistence

277,777,788,888,899 is an unusual and special number. When it comes to Multiplicative Persistence, it is an unparalleled superstar.

Check out the following table. Can you figure out what is going on? The digits of any given number are multiplied together to get a new number, and then those digits are multiplied together, and so on. The Multiplicative Persistence of a number is equal to the number of steps required to get to a single digit. Really simple and pretty cool, isn’t it?

MP n

0 0

1 10→0

2 25→10→0

3 39→27→14→4

4 77→49→36→18→8

5 679→378→168→48→32→6

6 6788→2688→768→336→54→20→0

7 68889→27648→2688→…→0

8 2677889→338688→27648→…→0

9 26888999→4478976→338688→…→0

10 3778888999→438939648→4478976→…→0

11 277777788888899→4996238671872→438939648→…→0

So, 77 has a Multiplicative Persistence of 4 because it takes four steps to get to a single digit, in this case, 8. What about 11? Why did we stop there? Because 11 is the record, and 277777788888899 (commas aren’t necessary, right?) is the shortest number to share in that record. Other numbers, with many more digits, tie our special number, but none beat it. Did you get that? Do you fully understand the strength of that statement? The conjecture is that any number, any single one you can think of, has a Multiplicative Persistence of 11 or smaller. No number has been found that takes even 12 steps to get to a single digit.

This is quite extraordinary, don’t you think? If you like, take out a computer and start coding. Mathematical immortality awaits, but my guess is the search is futile, just like it is with the 10,958 problem I wrote about some time ago. I think that a series of digits with a Multiplicative Persistence of 12 or greater, if it exists, would have been found a long time ago.

I am happy that I get to mention the great Paul Erdos before I close out this short post. Erdos had a finger or two in this particular mathematical pie. He suggested that we ignore all zeroes and just multiply together all the other digits. After all, if you come across a zero, you are sunk. This makes for a tasty mathematical stew. There are people actively doing research in this area. If you ignore zeroes, I have seen a Multiplicative Persistence as high as 22. That said, I recently came across a paper on this very topic in French. I tried to understand it as best I could. The strange thing is that this is the first time I can remember that the specialized math did not lose me, I got lost in the language differences long before that could happen. Those French, it’s like they have a different word for everything. And yes, I tried to translate the page, but Google only decoded the numbers…

The Feynman Point

Richard Feynman was unusually intelligent. He earned a Nobel Prize in physics. He was one of those people who had a VIP pass to look at The Book virtually whenever he wanted. There are a bunch of biographies and autobiographies out there about him. It wouldn’t be a waste of time to pick them up and read them.

This short post is about a little known aspect of $\large \pi$ . There is a particular sequence in $\large \pi$ that starts at what has been named The Feynman Point. The Feynman Point starts at decimal digit 762 and runs for six consecutive 9’s before it takes off, once again, on its random journey. How cool is that?

…2113499999983729…

That is not the only instance of consecutive digits, either. One of the most interesting sequences starts at decimal digit 1,699,927. You are not going to believe what happens at that point. There are six consecutive zeroes before it takes off again. I find that genuinely extraordinary.

…5105800000059277…

Wait, there is more. How about 8 consecutive zeroes?

Starting at decimal digit 172,330,850 we get the first zero in this sequence:

…655810000000012202…

So, this brings up a question. Since $\large \pi$ is infinite, does that mean that, at some point in the sequence, we will get 1,000,000 zeroes in a row? How about 10,000,000? Furthermore, does $\large \pi$ contain every known, or possible, number string? Will my DNA sequence show up at some point? How about my Social Security number, that sequence is obviously a lot shorter. I did check, and my Social Security number does not appear in the first 200,000,000 digits. Neither does my phone number with area code.

The answer to the question I posed is unknown. Mathematicians do not yet know if the universe lies within $\large \pi$ . I don’t know what to think, the universe is a vast place but infinity is an awfully long “time.”