Martin Gardner's Magic Numbers of Dr. Matrix

In 1993, I bought a book The Magic Numbers of Dr. Matrix authored by a Martin Gardner. He was an author I'd never heard of but some clever puzzles on the jacket caught my attention and I bought it. The jacket mentioned that Dr. Matrix was the greatest numerologist of all time. He had been the first person to reveal that the name HAL, the crazed computer in the film 2001 was obtained by shifting each letter of IBM back one letter. (Mr. Gardner asked Arthur C. Clarke if this was a deliberate choice but apparently it was not.)

When I began to read the book it was with the understanding that Dr. Matrix was a real person. He was diabolically shifty but I've known characters like him.. Until I'd read more than half the book I had no reason to doubt the book was about a real man but by then I had received a letter from Mr. Gardner, in response to one I'd written to him. Mr. Gardner’s home town was on the jacket of the book so after reading a certain vignette in the book, I called information to see if he had a listed number. He not only was listed but he answered when I called. The vignette was about pi and a curious reflection Dr. Matrix had noticed in the first 32 decimals of pi. When I asked if I could write to him about something I'd read in one of his books, he said he'd like to hear from me. I wrote a letter and sent it then read rest of the book.

At this point I will try to describe what Dr. Matrix had discovered in the first 32 decimals of pi:, using a form somewhat different than was in the book, but the relationships are the same. Dr. Matrix had noticed that 4 pairs of numbers appear twice in the first 32 decimals: 26, 79, 32, 38. Dr. Matrix makes several interesting comments about hidden symmetries in the repeating pairs of numbers,

He described how the pairs mirror in certain ways but it seemed to me nobody but the wily Dr. Matrix would ever notice such an odd pattern. They certainly didn't stand out when I read the page. Anyone can recognize there is a certain 'mirroring' pattern in the way I’ve illustrated them The number pairs 79, 32 and 38 are in the middle of the first pair, 26 for instance. He discussed many 'unlikely' but interesting relationships in the mirroring of 4 pairs of numbers in the first 32 decimals.

It was at that point that an experience I'd had with the first 10 decimals of pi in 1989 came to mind, which was also a reflection in those first 10 digits. But it was quite a different kind of mirroring pattern, I had thought of it as the 'moebius twist reflection'. I recognized a pattern and I knew the 'rules' to the pattern were familiar to me but I knew that nobody else would ever, ever have noticed it. I wanted to write to him about it because it seemed even more 'unlikely' than the pattern he'd written about. That's when I noticed his home town was on the jacket of the book, then I called him to ask if I could write to him. I was surprised that he answered the phone and more surprised when he told me he would like to read about my event.

After I’d sent the letter about my own ‘curious reflection' in 3.141592653... (that's the first 9 decimals plus the whole number 3) and explained it as best I could, as well as how I'd noticed the pattern, I resumed reading the book. I received a response to my letter to him very soon, but by then I'd read another vignette in the book and had a real shocking event happen. The copy of his response is at the end of this page, but I suggest reading further before reading his letter to me. He accurately assumed that I had believed Dr. Matrix was a real person when I wrote my letter to him!

(What I wrote about was only one level of the pattern beginning with this arrangement of pi's first 10 digits: 3 14 15 92 653 There were 'rules' for that arrangement, but they were certain habits of mine, that had formed from experiences that happened over decades, some when I was 9 years old. They arose from extremely personal habits and particular situations in my life. This is just the first level: The first 6 decimals, 14, 15, 92 are 'coded' in a certain pattern which I will explain. The next 3 digits, 653 are literal, explicit, they are what they are.

The pattern in 14, 15 92 is that they need to be 'cross summed'; 14 = 5, 15 = 6, 92 = 11 = 2. 92 is a reversed 'twisted pair' which means a double use is implied because 9 + 2 = 11 and 1 + 1 = 2 The result of this:

I saw 3 5 6 2 in the coded numbers and 2 6 5 3 in the literal numbers . Then a kind of slide show followed in the first block of decimals that were mirroring in a simple pattern but the numbers were 651 coded and literal . Those numbers were familiar to me . I had several events that had happened, one was an automobile that was licensed ETW 651 and Extra Terrestrial Woman 651 came into my mind automatically when I saw the license tabs. I laughed at the way my mind produced the association. I had noticed the car and wanted to buy it but my husband believed the mileage was wrong. He insisted the car had been owned by a salesman and the mileage was 150,000 not 50,000. The car didn't get sold and the salesman was puzzled that it didn't sell so he reduced theprice and I bought it. 651 was coded and uncoded in the first block of decimals.

The result was 356 2 653, the numbers mirror in two ways, matching first to last inwards, and from the center 2, outwards of course.

I was astonished to see this because I was not looking for anything, it was just 'suddenly there' but I saw much more that I would have to write a lot more about, more than most people would spend the time to read, then think about. It happened so rapidly but I've not forgotten how many relationships were made to numbers that were coded in the first 5 decimals and explicit in the last 5. 651 was a number that I had become very familiar with before 265 began to come to my attention in the few months prior to this event. I wrote more than this to Mr. Gardner because there are several levels of patterns. After sending the letter, I went back to reading the book. ((Another event happened about 2 years later that had this same pattern, where a 'coded' and a literal relationship to decimals in pi was revealed. That event also involved numbers that were specifically related to the first event which I'm going to describe now:)) I returned to reading the book:

In another chapter I read this vignette: “Dr. Matrix suggested: “Your readers might also enjoy searching for the unconsciously determined order behind THIS number:” Then he wrote 8,549,176,320 in a notebook as he said: “The first name of the woman who produced that arrangement of the 10 digits is named Betty. As another clue you can add that she suffers from a compulsion to put things in order….”

What? 10 digits, a woman named Betty, suffering from a compulsion to "put things in order"?

The fact that my name is Betty and that I had just written a letter that had an arrangement of 10 digits (3141592653) caused me to feel more than a slight degree of surprise. The word 'coincidence' did not come to mind because obviously the 10 digits were not the same 10 digits that Dr. Matrix was writing about in this new vignette. It did seem at first glance to be a startling reference to what I'd just done however, every detail matched except the numbers were different. I felt somewhat vaguely that having a compulsion to put 'things' in order actually described me at that point so I recognized myself in that attribute also.

After a few minutes of considering this odd circumstance, I turned back to thinking about the numbers 8,549,176320 that he was writing about. I looked at the numbers but I couldn’t see any pattern. Then I saw an inner process at work in what I was looking at: those 10 numbers. What happened was a rapid shift of the numbers occurred, that I will try to describe although it occurred in a flash and it cannot be described as briefly as it happened. The rearrangement occurred so that I clearly read the numbers in this way:

With no space between the shifting, some part of me automatically read the result: 854 then read down beneath the 4 and read 719 backwards then above the 9 upwards to 8.

The result was 854 7198. Immediately, but most unexpectedly I recognized our family telephone number at the time. The shifting had revealed our phone number! We’d had that number for more than a decade. I had not until that moment noticed that the first number and the last number were the same, because as I’ve written, and I state this emphatically I don’t normally look for such relationships and I did not look for this one.

When I realized that my telephone number was in the first 6 digits, 854917(8) of Dr. Matrix' puzzle, it was not difficult with my particular personal data to recognize in the remaining numbers: 6320: My birth date was 1232, so numbers (1,2,3) in my birth date sum to the next number which is 6, (1+2 + 3). Then 3 2, the year I was born (1932) followed by 0 which was my personal point of origin, my beginning point.

I'd already had several experiences with 'zero' as a point of origin and even written a poem, in the same automatic kind of activity this 'shifting' operated.

However I still had not solved Dr. Matrix's puzzle so I had to look for the answer in the back of the book. The hidden ordering of the number 8,549,176,320 is that the numbers are arranged alphabetically according to how the word is spelled: eight, five, four, nine, one, seven, six, three, two, one, zero.

The entire series of numbers had specific identifying information about me! The way I think of it now, is that this event was more than a bundle of coincidence, these 10 numbers identified me by 'saying' my telephone number to me. It took many similar events for me to grasp that idea, of saying a detail about my life back to me, echoing it so to speak in this unexpected form; it was utterly a surprise.

I had not looked for those relationships. I would not have noticed them if the 'mental activity' that was so visible to me had not 'presented' this information automatically. It was a bundle of 'coincidence', so unexpected that I cannot describe the degree of shock that I felt, except that I'd already had one experience with pi that had been even more unexpected and much more shocking. It would require quite a lot more information but nothing I had ever thought about could have prepared me for that event!

I noticed The History of Pi in the library and because the pi symbol was everywhere at Boeing I decided to read the book that this event happened. I had named it a 'pi-mindquake' (it was a mental earthquake) because it linked back into my past to the very private memories of a few events that had happened as the result of an impulse when I was less than 10 years old.

This particular impulse and it's activities was laid very clearly in front of me in that which was the third big 'mindquake'. What it meant instantly was a kind of message given to me that gave me real evidence that I was to have faith in my own interpretations of experiences I'd been having since about 1984. A new kind of 'event' had begun to happen then, something in every day life that often made me feel confused, almost overwhelmed because I felt literally like the floor beneath my feet turned to wobbly.

After a few years I'd begun to grasp that there was a meaning to those new events, and I saw how content in my mind was at work helping me understand them, as it had 'worked' to create this display. It was in 1989 that I had the 'pi mindquake', the second of two mindquakes I had that year.

It happened when I had read most of Petr Beckmann's book, The History of Pi before noticing there were 2 pages at the back of the book that had 10,000 of pi's decimals neatly arranged in rows of 100, separated by a space between each 10 decimals. The result was neat rectangles on the page. I paused to read the copyright statement on the last page, and spent some moments wondering why 100,265 decimals were calculated rather that a nice round 100,000 or 100,250. It was unusual for me to think that way. Then I turned to the first page of decimals, noticed 265 in the first line and then.......

In a flash a much more complicated personal relationship in the decimals in the first rectangle occurred, that I knew nobody else would ever have noticed. I knew that I would not be able to explain those relationships or how they had been 'installed' very early in my life from an impulse that caused me to discover a pattern in the times tables after a thought occurred to 'add the double numbers across'. This was proof to me that I was not supposed to lose faith in my own interpretations and understanding of the flow of events that had begun in the few years prior to 1984 and continued even then.

That 1989 event had exposed a pattern in pi that would never have been possible to see excepting for the early life events marked by that impulse that had caused me to discover some seemingly trivial facts. The fact that I knew those memories were unique to me and not another person was unmistakable. That event had been a real shock to me, so utterly unexpected, but that was the memory that had caused me to want to write to Martin Gardener.

At that point I had also begun to figure out that Dr. Matrix was not a real person then within a few days I got the letter from Martin Gardener. This is a copy of it:: (It was before I had my maiden name restored. And he has misspelled my name.)

It was a bit of a surprise to realize he used a typewriter but I was more surprised that he'd taken the time to find my address. He had made many corrections in the letter, unashamed and not apologetic. It would have been impossible for me to link the author of the letter to the man who wrote that book! I know other people who do not really care for learning to use software and computers for reasons of their own, one of whom is even more wily and diabolical than Dr. Matrix.

It was very remarkable to me that in the letter he mentioned that I apparently didn’t know Dr. Matrix was not a real person. That indicates he certainly is able to pick up on how I did feel when I wrote to him. He also told me that the book was a ‘spoof’ on numerology, so that is how I became aware of ‘numerology’. I knew nothing about what he named as ‘numerology’. It was only then that I realized his ‘pre-assumption’ that I was 'into numerology' put a big barrier between us. I knew nothing about the history of numbers then either.

He pre-assumed I knew something he knew, but I did not know. It was news to me that 'numerology' meant seeing the kind of relationships that had happened to me. But I realized he could do the same thing but it was a 'spoof' to him!. But worse yet I thought he'd ignored what I'd written that seemed most important. It did not occur to me that he didn't remember the entire book , until later. That's why I thought he had not noticed or given any significance to the utterly precise timing of events that I could not have arranged myself. The precise timing of certain events had begun to seem unlikely to happen, but this bundle seemed impossible even once.

At this point I realize that in my original letter I had not written to him about the 'coincidences' because I had not read the vignette about 8,549,176, 320 when I wrote the letter to him. And it didn't occur to me he wouldn't make the association I did. I believe I wrote about that in another letter, but I also mentioned Emanuel Swedenborg's name as well as Carl G. Jung's and mentioned 'synchronicity but he certainly did not like that.

The way it seemed to me after so many experiences was a shift in perception and understanding that was so drastic I almost fainted, literally. It seemed to me that a hidden from anyone else detail about my very real physical life had been 'told' to me, 'given' to me to see, revealed but it spoke something. It 'echoed' back to me by this strange form of conversation, a detail that identified me in my 'now'.

It's a strange kind of event, one I've had to try to understand over the last years, since 1984. I think of these events as 'identifying' me, describing a detail about my life, to me. It's a form of 'speaking' to me, about the details of my life.

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1982, 1984, 1989, 1989, and 1993 were years when I had 'mindquakes'. The big one was in 1984. It took 5 years to even reach a point where I could relate to it, and that's when the first 1989 event happened. It linked back to a smaller event that had happened in 1982, and it caused me to understand that I was not creating them, they were happening to me, and that they were being explained in detail, to me through the events in my life.

I have not always noticed number patterns the way I do now, nor have I ever noticed the hidden vein of events that become evident only when they are retrieved then replayed so unexpectedly in 1989.

This 'event' involving Martin Gardner was connected to a prior event, and would not have happened if I'd not chanced to spot Petr Beckmanns’ book, The History Of Pi then decided to read it. I would never have read it except that I worked with a company that uses the symbol as their Pride In Excellence logo. It was the first visible mental event of this kind that had exposed the hidden pattern in the first block of decimals in pi the particular way they are arranged. Any other arrangement would not bring numbers into neighborhood that was obvious. This second similar event with Dr. Matrix was trivial in comparison, but then about 2 years later a third event happened that was equally precisely timed, and it revealed instantly information that was personal and significant to me, about me.

It is not possible to understand the kind of event I'm trying to describe without knowing many details about me and certain actual real world events that happened in my past. The information that sets a context for what I saw in a first glimpse of the first rectangle of decimals at the back of the book are:

1. My birthdate 1232 . I had noticed when I was much younger the numbers forms a ‘circle’ when the end is joined to the beginning: 1,2,3,2,1,2,3. The numbers repeat forever. That was 'nice' I thought to myself. Throughout the years other incidents caused me to experience #32 quite frequently, for a time it was everywhere. Remember OJ Simpson's number? Question #32 on the MMPI is "I experience very peculiar and strange events." True or False (I had answered 'False' because at that point I did not know what a 'very peculiar and strange event' was.)

The number 32 was everywhere for several years but the number had no significance to me, until it showed up so often in unexpected ways. Once on New Years Eve my daughter had treated me to a birthday gift, we went to a concert at the Kingdome. Two giant T-shirts hung from the rafters: one was number 19 the other was 32. We laughed at the apparent recognition of my birth year, although I knew the numbers had belonged to retired Gus Williams and Lenny Wilkins. Then many 'events' happened that would require that I write many details about them because each event was significant only afterwards when they were used in the pi quake.

A string of events happened prior to the 'pi quake' that caused me to also notice the numbers 651/156, then later 256 and 265. This string of events were just ordinary every day situations until 1989 when I glanced briefly at the first rectangle of decimals on two pages at the back of Petr Beckmann's History of Pi. Many events happened that were unrelated to each other until that day linked them together.

These events were somewhat humorous when they happened and I recognized the 'coincidental' attribute, because I had become aware of 'coincidences' already, over a period of 4 years between 1984 and 1988. It had been an arduous 'trip' through nearly 4 years, filled with new to me experiences that actually made my body feel 'dizzy' and my head literally felt as though it would burst at times. Everything seemed changed subtly but I couldn't really see any difference, and I was trying to understand what was going on. I realize now I had become inflamed with a high degree of curiosity and determination that I'd not had before, but there was a reason that drove me. A certain situation in my life demanded of me that I try to prove I was not 'mentally ill', or worse, 'crazy'. Real world situations always were the 'first cause', but I became aware by 1989 the real causes were not what I had assumed were the causes of this great change.

It became obvious, but not too quickly, that the change outside was the result of a change in my mind.

. A coworker showed me a cartoon in the newspaper, and told me how it related to an astonishing coincidence he's had the prior weekend. He'd gone to the PX to shop for a birthday present for his wife with his three children. The checkout clerk turned out to be his first love. They'd talked and arranged to meet one evening, and in that evening the flame of their love returned, so that they each immediately planned to leave their spouses and children !! They could not think of anything but being together, and even his parents had told him to do whatever made him happy. He was aflame with happiness, utterly joyous as he told me what had happened!!!

Then we got to talking about birthdays. I told him I had just noticed that the license plate on my automobile, ETW 651 was a pattern:. I had owned the car for 4 years when I glanced out of my window and had what I now realize was a 'bundle' of 'influx' about what was in front of me, which in this event was the license tab ETW 651. I saw that the second two numbers were the sum of the first one, 6 = 5 + 1. That's obvious but I'd not thought about that before and I'd seen that tab hundreds of times. I had noticed the ETW when I applied for registration and had been astonished as well as amused when an automatic activity generated Extra Terrestrial Woman from the ETW. That was not a vanity plate, this was an instantaneous thing. (I had some unusual experiences with ETW 651, such that one day I thought the 'Extra Terrestrial Woman' was somehow related to my sense of being 'manipulated from afar' as though I were a satellite out in space. I felt 'spaced out', but I had not chosen to think Extra Terrestrial Woman 651, it had just 'bloomed' in my thought the first time I'd looked at it. I'd had some unusual experiences with the red Datsun 210 Station Wagon by the time this happened.)

In the same 'vision' I noticed that the numbers in my birthdate, 1232 had a relationship to 651. This is the way it came out, and it will take much longer to write it than the time in which it happened: 6 = 1 + 2 + 3. The car which I'd owned for 4 years had other numbers that suddenly loomed into being very significant, the reverse of 651, i.e. 156 was the address of an attorney that was sending me papers regularly, and I had noticed that if I chanced to look at a street sign or a house number it was 156.

As we talked he noticed a lottery report on the same page and told me that if I'd added '1' to the first number and bought a lottery ticket on 256, I would have been a winner in the lottery because 256 was the winner of the daily game. This may read as ludicrously irrelevant in any known logic, but this report of the lottery numbers seemed alive in a single glance.

I don't usually read that page and would not have read it that day if he'd not wanted to show me something on the page. It just happened that all the lottery results of the prior week were on the page. After I saw 256, in a flash I 'saw' quite a lot in that report. The cards in the Quinto Game were the Queen of hearts, 2 of spades, 4 of clubs, 5 of diamonds and 3 of clubs. What emerged was the 'difference' between the 2 and 4, . between 4 and, 9 and between 9 and 3 which was 2 5, 6. The same numbers drawn in the daily game. This was not something I looked for, it just 'bloomed' out of a glance at the report.

Then the Lotto drawing numbers, 11, 14, 15, 16 23, 44 suddenly took the form of 'sum of digits addition, (which I'd learned from an impulse when I was 9 years old): 11 = 2, 14 = 5; 15 = 6 and there was 256 again.. In the same glance the August 3 Lotto drawing numbers, 3, 4, 6, 16,28, 30 contained the same 256 in the difference between 4 and 6, and between the 1 and 6 in 16, and between the 2 and 8 in 28.

I realized how those events had gradually brought '256/265' into prominence in the few months before I read The History of Pi only when the 'batch of events' was complete and it was used in what I thought of as my 'pi quake'. It built upon much that had happened in my life, as well as many purely mental events beginning (I believed) with the first 'mindquake' in 1984 another in 1989 which occurred in a location I thought I could never tell anyone about. This event had made me aware that I'd really learned to understand what was going on in the painful flow of circumstances in my real life, as well as in the almost overwhelmingly confusing mental world that had become so visible to me. But I'd had some therapy, read quite a lot and been validated by a Jungian therapist that I had come to understand how this inner change had happened, as a result of a marital relationship. I could see my mind at work, and realized how a mechanism altered how I heard and saw what was outside of my body. .

I had by then noticed that the numbers 156/651 had been occurring for years in certain a ways which had no significance to me other than that I noticed them. How could I just happen to glance at a street sign when it was 156th Street or Ave? That happened so regularly I was puzzled, after I noticed it.

This reads as trivial but that moment had enormous content in it of memories abstracted from my past that formed instantaneous recognition, without any understanding then of what it meant because the 'last event' was being built up from these every day events.

A period of time was somehow 'marked off', I could recognize that in retrospect, when I realized that the numbers 156 had been coming 'at' me for several years before I bought ETW 651.That was NOT a vanity license tab. The progression of a span of time when events marked by 156 moved forward and changed into 256 (a new stage) had passed without my noticing it until I had read most of Petr Beckmann's book. Then I looked in the index and noticed 2 pages of decimals, after reading the copy write statement. "The first 10,000 decimals of 100, 265 decimals calculated in July 1961."

With hindsight, I suddenly recognized long strings of related situations marked by those numbers. (my husband's attorney's address was 156th Ave. and his mail had angered me very much for several years between 1983 and 1989.)

The impact of the 'pi quake' immediately formed a link back into my past beginning with certain specific events that happened at about the time I was 9 years old. It revealed immediately a hidden 'vein of activity' that had been carried forwards in my life, leading exactly to that precise moment. They were all assembled on a string. Two of them are especially significant because they were linked then to an impulse. It was a specific impulse that I experienced as a kind of 'thought voice' that caused me to do something specific without hesitation. I'd learned something from the impulsive activity that later I read about or heard about in a different way. Having learned from the impulse was brought into memory by a childish thought that I experienced whenever I 'met' in some form, named differently what I'd learned privately from the impulse: I thought: "I can learn new things on my own." A description of those two events follows after the next three paragraphs.

I had experienced the same impulse afterwards a few times, but very rarely. I'd not considered it in relation to those two events that had happened when I was 9 years old until the pi quake exposed the entire line of hidden endeavor that had lead towards that specific moment. The fact that this impulse and no physical person had brought forth this hidden vein of activities was made quite distinct by a retrieval of memories from the past, batched as a unit so unexpectedly that I nearly lost consciousness... Literally I almost swooned at the undeniable validation of the hidden 'vein of activity' that had been events that were abstracted from their embeddedness in all the events in my life and displayed in a fraction of a second.

I believe Emanuel Swedenborg's idea about 'remains' explains this kind of event. There were a few events that happened only once really, but which afterwards flashed into my mind for no apparent reason. I was in my mid forties before I even wondered to myself about them, having barely noticed them with some level of awareness by then! P. D. Ouspensky also mentions certain 'reoccurring memories' in the first paragraph of the introduction to A New Model Of The Universe. In addition he makes reference to experiences that must be similar to what I named 'mind quakes' in that book, when he experiences 'time slowed down' such that the distance between one word and another was so great it was impossible to connect words together. .

One event was this: (1). Trying to memorize the 'times tables', I wrote them down on my Golden Rod Tablet. As I looked at them a thought occurred to me: "Add the double numbers in each product across." so without hesitation I added the numbers in each product across. When I finished I noticed a different repeating pattern in each table. That's nice, I thought to myself.

(2) I read dictionaries and encyclopedias that we had in our grade school library when I got through with assignments. One day I read a definition for a moebius band: "Take a strip of paper of any length, twist it one half and join the ends." I cut a strip of paper, pasted the ends together then looked at the result. (This was not easy to do with the 'paste' I made out of flour and water.) "What can the use of such a thing be?" occurred to me. Then a thought followed it: "Cut it around it's center length." which I did without hesitation. The surprising result was a single band twice as long, half as wide. The thought repeated: "Cut it around it's center length." and again I responded without hesitation. This cut produced another surprising result: two completely separate bands but knotted together in a way that probably could not be separated without cutting them apart. They were together forever but also forever apart. This idea linked up in my mind later to a real world circumstance in which the past with its present day effects as Carl G. Jung wrote of them, could be 'cut off', but that's a very complex idea.

Four decades later when I was 53 years old, I was a passionate challenge level square dancer, struggling with what I had been told were the effects of a complete hysterectomy, then a terrible blow on my head a year later. Nothing was easy to do, everything looked subtly different to me and I believed the effects of those two events had caused all the changes I was experiencing. After 3 years of prolonged effort at trying to regain some of the skills I'd lost I stopped in one day to ask for an application to work for Boeing.

During that period of time I had felt, or sensed words formed within my mind, that I was getting ready for my job at Boeing.

On the first day that I walked through the corporate security gates, 2-11-85, I saw the pi symbol for the first time. A fellow square-dancer whom I knew had worked for Boeing had formed what he hoped would be an elite challenge level square dance club using the Pride In Excellence logo. Only then was I aware of where he’d gotten the slogan. The connection was surprising because this man had said something important to me that I wouldn’t have thought about otherwise. He had remarked one night, that a certain club my husband and I belonged to would never achieve his goal or ours, which was to learn advanced and challenge levels of square-dancing. He mentioned a group that he believed had the potential to reach his goal: go right through the levels, Mainstream Plus, Advanced, Challenge 1,2,3,4.

As a result of what he said that night my husband and I eventually joined him in that club. It was the exact opposite in many ways to the one we belonged to at that point. The men who operated each club were passionate about their love of challenge level square-dancing but as to their personalities and relationships to their respective clubs they were exact opposites. One man had a reputation for being hard, even mean to his dancers so we didn't attend any of his dances until we moved close to him.

There I met the one man who generated the dream I had, that initiated the stream of 'nonstop thinking' that was so troubling to me that I didn't sleep normally afterwards for years. But that's a long story and not related to the pi quake directly.

When I saw the pi symbol in the Boeing plaza I realized then that the man who had worked for Boeing had gotten his idea of Pride In Excellence from that model. I saw it without thinking much about what the pi symbol meant, other than as a logo for a high level square-dance group. Later several incidents happened that could not have occurred randomly or by chance but they were directly connected to that model of the pi symbol. See the picture of David Blatner standing by the pi model, it's a link, click on it.

The group we had joined was using a new concept: there were no gender roles in the set. This was a radical change and it angered mainstream clubs very, very much. It was known then only as All Position Dancing, or APD but to the mainstream dancers this was their 'f' word. They were not just angered very much by such an idea, they were outraged and very expressive of how they felt. . The removal of gender roles required the females and males to learn each other’s positions. This 'role reversal' made an already complicated 'dance' more difficult. It was the first time in my life that I ever experienced being discriminated against, which is not to say I had never been discriminated against.

Think about that a minute or two: in the early 1980’s a small group of people were really ‘leaving the mainstream level’ and really entering into ‘higher levels’ where the rules changed radically by deleting ‘gender’, thus adding role reversal into the definitions of a square-dance movement.

4. On 2-11-85 I drove an automobile ETW 651 to my orientation to my new job. The car was already tabbed when I bought it. Although an automatic association had formed in my mind when I looked at ETW, Extra Terrestrial Woman 651, this had only made me smile somewhat to myself. THIS HAD NEVER HAPPENED BEFORE. One reads FYI and the words 'for your information' magically appear, but ETW forming Extra Terrestrial Woman? Nothing like that had ever happened to me.

(Years later I realized that my attention had already been focused on 'small details' in front of me, such as the numbers and letters on license tabs. I had noticed that my mind seemed to dwell on making some kind of 'sense' out of them. This had been irritating but I had not connected it to the one incident where the letters ETW did generate meaningful set of words: Extra Terrestrial Woman. It was not a use of attention that made sense to me, and I had not realized a 'non voluntary activity' had been initiated. I had basically been 'looking for meaningful combinations' already. This 'non-volitional activity' had occurred periodically for a couple of years before it became 'a new normal for me' loss of control. A part of me watched and listened, without knowing why or what was being watched as well as listened to.

5. That day during orientation for my new job, I was told that if I wanted the job I had to join a union: IAM 751. So by the end of the day I belonged to a union IAM 751. Those numbers had no significance to me , they did not in any way relate to ETW 651 until almost 5 years later. That's when a glance at the first rectangle of decimals on a page in the New Yorker Magazine in a n article about pi that an arrangement of the most recent calculation of decimals on it revealed another amazing relationship. That's another part of this story.

In a flash a pattern I knew very well by then suddenly exposed.651 and also 751but only in a glimmer of relatedness. Until that incident which I named a 'pi quake' after I could think about it, ETW 651 and IAM 751 were just isolated numbers, there was no connection between them on that date.: 2-11-85

When the ‘hidden relationships’ to my personal past had been exposed in a surprising flurry of mental activity it was so unexpected that I nearly fainted because of the implications: a purpose filled endeavor had been building towards this moment, beginning with my painful struggle to memorize the 'times tables', and a habit I had of reading dictionaries and encyclopedias.

I don’t believe I consciously had any part of generating the relationships. Certainly I did not have any idea about ‘numerology’ the way Mr. Gardener thought about it. I just watched and remembered afterwards what happened, then later I named this my pi mindquake.

It was a truly astonishing event, linked to my earliest years and I want to write about it, to try to describe at least enough to make my point about what happened when I wrote to Mr. Gardener, unawares that he was well known, even a genius with the kind of stuff that in another mind would be ‘irrational’.

I had just read the copyright statement that the first 10,000 of 100,265 decimals calculated in 1961 were on the two pages at the back of the book. This number 100, 265 seemed an odd choice. I remember thinking about why it was not a round number like 100, 000 or 100,250 or 100,500. When I turned back to the first page the number 265 was in my mind as a result of the thought about it, so right away I noticed 265 was in the first row of the first rectangle of decimals: 1415926535…

It is impossible to describe how suddenly in rapid succession, incredibly rapidly I saw the numbers grouped this way: 3. 14 15 92 6535 8...

I recognized the first Fibonacci numbers:: 1 . 1. .2. .3 . 5 8... (I had just read about them in History of Pi. The 11^th decimal is 8, the next Fibonacci number.)

Almost simultaneously it occurred into my mind that these numbers were also my father’s birth date in reverse (He was born 52311) except that the 32 was a ‘twisted pair’, reversed. ) The numbers also contained my birth date, 1232 which I’ve always thought was nice because it forms a circle when the end is joined to the beginning: 1,2,3, 2,1,2,3,… ( I have a daughter born 4563 which is a related pattern to mine, (45634563…) although I didn’t notice it until she was into her twenties)

Then I saw the result of this grouping, but in a different form, arranged with the paired numbers 'cross summed' in my old familiar way: From 3.14 15 92 65 35, I saw 3 5 6 2 653 5… Explanation: 3, then (1 + 4 = 5) then (1 + 5 = 6) then (9 + 2 = 11 = 2). The first 6 decimals were ‘cross summed’ but the numbers after 9 were not.

The result was that the first 10 numbers in pi, ignoring the decimal, mirrored from the center out. 3 5 6 2 653 There was a 'mini mirroring' in the 5 3 5, which also mirrored from the center outwards.)

3. 14 15 92 65 35 … another perception generated: 3 5 6 11 11 8 the result of 'cross summing' pairs after the decimal point: 14 15 92 65 35

3 11 11 11 8 3 + 8 = 11 the next level

11 11 11 11

2 2 2 2 which equals the next decimal 8, which is 2³

Because what I saw so suddenly that day involved the first block of decimals, I wrote more to him than what I’ve written above, but this is sufficient to get on with my recitation, in case anyone is still reading.

The 'moebius twist' refers to an idea that had emerged over a period of years (1975 to 1989) while I learned challenge level square dancing. This pattern is the basis of the square dance set, but I was unawares of it when I began learning this seemingly simple ‘dance’.)

Many long strings of real world events brought this one event into ‘being’ and nobody could have been more surprised than I was.

The habit of adding numbers across was one I'd used for many years as a bookkeeper because the difference between transposed numbers are always divisible by 9. I'd learned this to find errors when I was a bookkeeper at Sears, my first real employer after I graduated..

99999999992 = 2; 293 = 5; 1234 = 10 = 1 since 9’s don’t change anything. Any number that is 9 or sums to 9 can be ignored. It was interesting to me when I was a young girl struggling with memorizing the 'times tables' that the products in the table of 9’s summed to 9 and that in the middle, 45 twisted around to 54. Then every product repeated, but twisted around.

Later I learned other names for this kind of addition (casting out 9’s, modulo 9) but I always remembered that it was a personal discovery. At age 9 one takes pride in such seemingly trivial incidents.

If you are still reading: the first part of this pattern that I wrote to Mr. Gardener about concerned the whole number 3 and the first 10 decimals: 3.1415926535…

The black and white book with the large pi symbol on it’s jacket caught my attention as I passed through the library and almost without thinking I picked the book and checked it out. I

This links with copies of 2 letters I got from Mr. Gardener after I read The Magic Numbers of Dr. Matrix. Two Letters from Martin Gardener

(There is a scene in the movie Mercury Rising that has an incident in which an autistic boy opened a new book of puzzles he'd been given. On one page he gazes at the numbers, letters and symbols on the page which seem to shift about. He goes to the telephone, dials a number and says: "I am a stranger." He has made a call that was supposed to be impossible to make because the message was concealed in an unbreakable code. This autistic boy has decoded it in a glance.)

It's not possible to describe how quite suddenly in rapid succession, incredibly rapidly I saw the numbers grouped this way: 3. 14 159 265 35… Then the Fibonacci numbers loomed into prominence: 1 . 1. .2. .3 . 5 There was a pattern marked by 1 1 2 3 5 (I had just read about them in History of Pi. The 11^th decimal is 8, the next Fibonacci number. Almost simultaneously it occurred into my mind that these numbers were also my father’s birth date in reverse (He was born 52311) except that the 32 was a ‘twisted pair’, reversed. ) The numbers also contained my birth date, 1232 which I’ve always thought was nice because it forms a circle when the end is joined to the beginning: 1,2,3, 2,1,2,3,… (Another of those child hood discoveries. I have a daughter born 4563 which is a related pattern to mine, (45634563…) although I didn’t notice it until she was into her twenties.) I just noticed it one day in the same kind of 'event' that seems to have 'just happened' to bring a detail to my attention.

3. 14 15 was 3. 5 6 automatically as quickly as I saw the result of this grouping this way: 3 5 6 2 653 5… and noticed the 'reflection' of 356 2 653 in the first 10 numbers, ignoring the decimal point. The same numbers mirrored from the center outwards. I saw this in two ways: 3562 (2)653 and this was because 9 + 2 = 11; 1 + 1 = 2 thus a 'double use' of the number 2. (Really, this reasoning just came into my thought without any work from me. I felt like I was watching something happen, not making it happen.) The pattern was that the numbers before 9 were ‘cross summed’; the numbers after 9 were not and the resulting numbers mirrored from the center out. (The first 10 numbers included the whole number 3, excluding the last 5. I saw that 535 also mirrored from the center outwards, a very small reflection, but the pattern was there.)

This is the first rectangle of decimals; the first ten of each of the first hundred decimals.

1415926535 8… The first 6 Fibonacci numbers are in the first 11 decimals. A pattern is marked:

651 and 156 ETW 651 was my license tab, it was not a vanity plate. 156 was also familiar.

The number 651 stood out in many arrangements in the first rectangle, immediately:

There are other mirroring relationships, in this particular arrangement also: #3 can be #1 on the second level.

Modulo 9 is a mathematical term, meaning ‘divide a number by 9 and consider the remainder. It’s used to test whether a number is divisible evenly by any number, and I’m using ‘modulo 9’ in this case, because 9 is the number I’m testing. I could ‘test’ modulo 5, or ‘mod 5’ or I could test ‘mod 6’ if 5 or 6 were the number I wanted to test for divisibility.

Notice 5,6,1 in several forms in the first five lines, after transforming according to the rules of modulo 9. (or casting out 9's or sum of digits)

The numbers are coded in the same way then repeated uncoded in the same block of decimals. I am still working on this page.

There is more, much more. 6,5,1 ends the 2nd, 3rd,4th row, and is encoded in several ways in the rectangle.

3. 14 15 92 65 35 … another perception generated: 3 5 6 11 11 8 The pairs were 'cross summed'

11 11 11 11 3 and 8, the single numbers were joined and cross summed. Then 'cross sums' formed:

^{The result was 8, which is 2 cubed:}2^{3 Oddly, I also 'saw' 8:32' emerge in
another paper. the news of my birthdate that I got in Chicago in 1989, along with a memory
of Mt. St. Helens Eruption May 18, 8:32. The number 8 and the 'twisted
around' 2,3' were related to another event, which happened May 18, 1989,
but that's another part of the 'story'.}

It is not my habit to write to authors or to call them although I had done this once before in 1989, after reading The History of Pi by Petr Beckmann in 1990. His home town was on the books' jacket also. I had called information, got his phone number, dialed it and he answered the phone. He was very ill then and we talked about his illness for some time. He did not want to die, he was very sad so I didn't talk to him about what I wanted most to talk about. the pattern in pi. I asked if I could use the decimals to make a T- shirt I had in mind to make and he told me I could use the Dover edition. I told him I'd send him a T-shirt which I did do. When I called a few months later, his wife answered to tell me he had passed away.

It is important to understand that until I read about 'squaring the circle' in his book I had not heard of 'quadrature of the circle' or 'squaring the circle'. I had been a challenge level square-dancer for several years when this 'pi' quake happened so the thought occurred to me that there was one place where 'squaring the circle' or 'circling the square' could easily be done: in the square dance. The pattern of the moebius twist and the 'twisted pair' had become evident slowly as two small groups of people worked to learn the very challenging levels of square-dancing.

In the normal square there are two subsets of 4 dancers. The 'odds numbers' (1 and 3) and the 'even numbers' (2 and 4) work against each other to form a single unit of 8. The 'head couples' are the 'odd number 1 and 3. They face each other across the square and the 'side couples', 2 and 4, face each other. The binariness of the set has many levels. There are times when two dancers are a unit, working as a single body, so 1 + 1 = 1. . There are certain movements that require learning to dance with 'phantoms', they are imaginary people whose position one must know in order to make the dance succeed.

When phantoms are added to the 8 real people, the chess board is a good representation of the positions that can be used on many movements.

The set requires 8 real people but at higher levels 'phantom' people can be added to the set, as few as 2 depending on the movement the caller chants. This is where I almost 'lost it', literally because I could not 'imagine' the position of a 'phantom', or myself for that matter. These 'phantoms' have to be tracked as though they were real and every step changes their location.

I had thought quite a lot about the way people talked about 'mirror image' in the square dance set. In a real mirror image I could look across the set and see my counterpart, my opposite. But in the set my opposite was standing beside the person across from me. That puzzled me for some time, until I really understood the 'binary unit' i.e 1 + 1 = 1. The couple across from me was a binary unit, one body was the right hand, the other body the left hand although they separated at the beginning of a set and had to be restored to the proper position and partner at the end of the set. I could not see how the term 'mirror image' applied.

Then one day an impulse occurred to me to draw half of a square dance formation on the end of a transparent strip and draw the other half on the opposite end of the same strip. When I joined the ends, this was a normal mirroring but it did not represent the way the dancers actually look. I twisted one end of the strip half a turn and then joined the ends. The result was a legitimate formation, and any formation could be used. This was the first incident in which the 'twisted pair' that I later named the 'moebius twist' first became evident to me.

I had always been puzzled by the fact that my opposite, my counterpart in the set was not directly across from me, but was beside the person across from me, and this explained it although I had recently read Anatomy Of Reality by Jonas Salk. In that book he wrote that nothing occurs in nature that is not binary.

Keep in mind that this was my first acquaintance with Martin Gardner when I bought the book, The Magic Numbers of Dr. Matrix. I noticed it only because the jacket had several interesting (to me) puzzles. There was a background of experience behind what happened when my telephone number was suddenly exposed in the vignette about 8549176320. I was not looking for it, but I saw clearly how the 'display' happened because I'd had the even more astonishing event happen when I'd read Petr Beckman's History Of Pi a year or so prior .

This was a pattern I'd had to learn from a state of ignorance (or innocence), and it built itself, and even named itself as the 'moebius twist' reflection'. I had recognized detail by detail while I tried to learn challenge level square-dancing between 1979 and 1989 the information necessary to understand it and recognize it later in The History Of Pi. I had to discover that this 'moebius relationship' was the basic form of not only the square dance set, but the chess board, the I Ching, the structure of quantum level physics and believe it or not, a psychiatric idea about projection and the interaction of opposites.

The 'pi quake' was an amazing event, because it retrieved an enormous assembly of memories and experiences from my past, beginning with my first memory and including certain memories that had made themselves quite distinct because they reoccurred into my mind, as thought, for no reason I could understand. P. D. Ouspensky mentioned them accurately as 'recurring memories'. I believe Emanuel Swedenborg named them also accurately, as 'remains'. They were memories of a real event that had happened only once, they certainly do remain and one becomes familiar with them unconsciously before a more conscious level of mind really wonders why they do regenerate for no reason. The fact that they reoccurred spontaneously into my mind for almost 3 decades before I really was aware enough of them to ask myself why they flashed into my mind made them distinctly different.

The level of mind that could 'see' them and 'wonder' about them became distinct also.

The content of each memory is quite important and it is not possible to understand their real relationship to this 'pi quake' without knowing that content. The display occurred to an unsuspecting individual and it happened in a flash of time, although I remembered afterwards everything that had been exposed. This 'movie in a flash of time' exposed a previously hidden line of endeavor that extended back from that moment to the first memory I had on this planet. This was a link with my past that I would never have been able to trace myself.

A ‘ strange event’ relating to pi and I. happened two years later as a result of my being transferred to another job site. It relates to the Martin Gardener incident and it was further validation that irregardless of how absurd it seems to 'trust' in this kind of experience, one can in fact consider them to be 'identification' processes, similar to road signs. "I know thee...." is being 'said' to the person who 'gets the message' from them.

I can cite a scene in a movie that is somewhat close to representing what happened in this event. Mercury Rising has a scene in which an autistic boy opens a new puzzle book he’s been given. He turns to a page, which is shown on the screen and as he looks the numbers, letters and symbols they seem to shift about. He goes to the telephone, dials a number and says: “You are a Stranger.” He had somehow uncoded a hidden message on the page and it was supposed to be an unbreakable code.

The ‘event’ that I experienced had the effect of exposing something hidden, although the process of ‘exposing’ what was hidden was familiar to me. It was unexpected and I felt a real shock, not a symbolic shock when it happened.

An aside: I looked for the meaning of my birth name and was more than interested to read that ‘Eldritch’, a form of my name means ‘strange’. I could relate to what the boy said: “You are a Stranger.” Because I have become aware of my ‘strangeness’. That is the name of a quark also, if I remember correctly. The most surprising attribute of this kind of ‘event’ is that they identify the one that ‘gets’ them.

In 1992 I was transferred to Everett, Washington. After a few weeks I had to go to medical because I was affected by a chemical. While I waited I read one of two books I had with me. The doctor passed me and made a comment about the books: “We read the same books.” The one I was reading was History of Pi by Petr Beckmann, the other was Godel, Escher and Bach by Douglas Hofstadter. He asked me if I’d read the recent article in The New Yorker Magazine about two brothers who had calculated pi to 2 billion places. I had not but that evening I went to the library and checked out the magazine. The Chudnovski incident