Posts tagged Fibonacci
After my discovery of the graph – OneEye – 1i – I wasn’t all that interested anymore and left it aside for a little while, only to come back to it later as I had a lot of questions about the foundations of ‘numbers’ that govern our universe. But then a little more than two weeks later (on the 26th Nov), I was with my long-time friend (Fred Rouda – the guy that triggered my discovery) and we were going for a drive, when suddenly I felt this immense pressure on my chest. I thought I may be having a heart attack at first, but then the pain went into a weird flux of pressure, which made me feel almost depressed. It was hard for me to breathe and I was constantly grasping for air.
Fred was obviously concerned and asked if I was alright, since he’d never seen me like this before. I asked him to park to the side of the road so that I could get myself back to normal. I then took a minute to gain my composure, my breath and then something bizarre happened…
I started getting other mixed feelings, like anguish and hope at the same time, and along with this, a deep sense that something big was going to happen in exactly one month. Something massive and unlike anything we’ve seen before. It wasn’t like someone speaking to me, nor was I depressed (as I know what the symptoms of depression are – I have been through that and I know what it feels like). This was something totally different.
The ‘messaged-feelings’ soon started getting more clearer and I started to understand that this was something more than I could explain away. I mean, I’m a rational and very objective person that doesn’t accept wild theories without proper investigation, research and testing. After all, I’m a scientifically logical minded person and I don’t believe everything I read or hear very easily. However, the feelings soon started to get clearer and I was receiving these messages in some form or another, which even today I can’t explain, but the main message was that;
- something big was going to happen in exactly one month…
- something unlike anything we’ve seen before…
- I don’t know if it will be for good or bad.
That was all I was getting, but it was drumming into me the more I kept breathing heavily. This was on the 26th of November 2004 and even Fred was starting to worry. He asked along the lines of, “why are you saying these things Biz? Are you okay mate?” I just sat their breathing heavily, but still getting these weird messages louder and louder within the feelings inside me. Even today, I don’t know how to explain this and have sought professional help to try to explain what happened to me that night. None had valid explanations and didn’t diagnose me with anxiety, psychosis, nor depression. I even had all the relevant blood tests as a precaution and even a CAT (brain) scan, but all came up negative of any illnesses or signs of ill-health, thankfully!
Then came one month later and the world saw the horrors of the Indian Ocean Tsunami on Boxing Day 2004 (26th!). At first we didn’t make much of it as it seemed like just another awful tragedy, triggered by an earthquake that killed thousands of people (on the first few days of it occurring). But as time went along, like a week or two later, did we all understand and fathom the sheer intensity and fatality the Tsunami’s caused. As a consequence, over 220,000 people sadly died. This was by far, unlike anything the world had ever seen in its history and it definitely was a bad event.
However, there was good that came out of this. As we all saw, the people of the world stopped their squabbling and prejudices for a moment and came to the aid of the distressed survivors and the many that needed our help. Almost every nation on the planet came to the aid of these poor people and billions of dollars were raised in aid. Many doctors and volunteers from all over the globe came to do whatever they could to help.
Now that’s when I realised that the messages I was getting was spot on! This was a tragic event unlike any other we’ve seen or heard of in history (in terms of earthquakes at least) and I pray we never experience it again. It was bad yes, but the good came out in the form of Human unification and aid, to those in need no matter whether they were enemies or at the most distant parts of the world. Everyone either gave donations, aid (financial, medical, search & rescue, infrastructure etc) or even prayers for those left behind in despair.
It dawned upon me soon after that I had received some sort of message that night, in a deeply personal way. Unfortunately, the message wasn’t clear enough to tell me what exactly this “big event” was to be.
If that experience wasn’t perplexing enough for me, other weird things started to happen soon after. This was the beginning of the weirdest year of my life!
Let The Weirdness Begin!
One such example was when I started seeing time in triplets or all the same numbers. Every time I looked at a clock or my watch, I would always see 2:22pm, or 5:55pm or 11:11am etc. Pardon the pun, but this happened every single time! I even tried it when I was aware of this at random moments, but it wouldn’t work. It would only work when I wasn’t aware of it. This went on for approximately one month and I was somewhat bemused by it, but then suddenly it stopped happening. And when it did stop, I was a bit sad because I was so used to it and quite enjoyed it really. But that has never happened again either.
Reflecting on the weird occurrences that had happened to me in the first few months after my discovery, I thought I’d go back to my graph and see what exactly this thing was and what the numbers in there could mean on a spiritual level, since this was getting too weird to explain scientifically. This was way beyond just numbers and graphs now. As time went on, I noticed that my inquisitiveness increased immensely during this time. As a lover of science, philosophy and religion, I was drawn to certain aspects of our lives in this grand universe and the questions that it instilled in me. Reflection and a lot of other weird occurrences saw me quickly asking questions about life, science and the essential questions that we all may have asked one time or another in our lives. However, what was about to happen to me was by far the most amazing journey that I have been on in my entire life. I soon realized that I was now on a journey of exponential learning curves and spiritual awareness.
Want Answers? Wait a second…
Every time that I had a question in mind and looked for an answer, there it was, right in front of me. The answers would pop up in many different mediums and forms, such as searching on the Internet, watching TV or even staring at a flower or a tree. What was happening? What ever it was, it was truly unbelievable! I confided in my Grand Creator – Allah (swt) – (being a Muslim) and quickly started asking Him many questions, followed by a very long prayer of thanks and praise as well as asking for forgiveness for anything that I may have done wrong. I kept thanking Him for blessing me with this increase in inquisitiveness and knowledge. I just couldn’t help stop saying His name every day and I loved talking to Him because I couldn’t really confide in any one else, as nobody that would be able to could make sense of how I was feeling nor what I was going through, except my close friend Fred, but he was an atheist at the time and I didn’t think he would take my views in the same way. Allah (swt) answered me in such ways that I felt overwhelmed with His love and mercy upon me. I felt truly blessed!
There was rarely a time when I didn’t find an answer to any of my questions. My curiosity was becoming almost obsessive because the amount of things that I was learning was perpetuating my insatiable thirst for knowledge. The more I learned, the more questions that I would ask and open up a new area of interest, with each like a chain of connecting links that led one fact to another. I would ask and the answer would come to me somehow and straight away too! The questioning eventually led me back to what I knew best, which is Science.
Something Common About Nature
As my knowledge increased I then noticed something perplexing about the way things were made and appeared in this universe. That is, I noticed a common trend in the way everything flowed and looked, including us. Everything seemed to be designed in such a way that there appeared to be a ‘common theme’ in the design. It was something that intrigued me immensely and I had to get to the bottom of it. I eventually did!
I eventually got to a stage where I was learning so much so fast, that I began to understand the deeper meaning of certain terms like infinity and eternity, with more clarity. Looking deeper and deeper into the meaning of life and the way we are created and appear, was very important to me. Never had it been more so than during that period because there seemed to be a fundamental similarity and flow in the way everything in this universe appeared and conformed within. This lingered in my mind for a while and eventually, I started getting some answers.
One day, another friend triggered the path for me to pursue this matter, when he mentioned of a ‘special ratio’ that appeared in nature and the makeup of the Human body. I asked him what this was, but he wasn’t exactly sure. He said he saw this in a documentary once and that was all. It struck a chord, a mighty big chord for me. I soon investigated and eventually found out this ratio to be what is called “The Golden Ratio,” or “The Divine Ratio” (to name just two) and for a good reason.
PHI – Φ – That Golden Answer!
Looking further into it I eventually found out that there is a special ‘irrational’ ratio called “PHI” – (Φ – a Greek symbol representation), much like other ‘irrational numbers’. It is a ratio of (1.6180339887…. onto infinity!).
PHI = (√5 + 1)/2 = 1.618 = (Φ).
Another interesting property of PHI is when we look at the reciprocal, it only reduces by EXACTLY 1:
1/PHI = (√5 – 1)/2 = 0.618 = (Φ-1). And… when we square PHI by itself, it increases by EXACTLY 1 also:
PHI x PHI or Φ2 = 2.618 = (Φ+1).
It seems that in the ‘world of Phi’, powers of Phi are reduced to adding, and division are reduced to subtraction! Just adding and subtracting. Amazing hey? No other number/ratio seems to do this! Try it yourself on a calculator?
The Pentagram & Pentagon
After a bizarre dream sequence, which I will explain further down, I discovered that PHI is derived from the dimensions of a pentagram/pentagon (unlike Pi being derived from the circle) and I even analyzed it to see. This is what I got (more elaborations will be provided in my PHI pages):
As a previous student of science and mathematics, I had never heard of this before and it totally puzzled me. I was taught about all different kinds of irrational numbers such as “PI” and “e”, and were asked to work out Pi in angles of 15, 30, 45, 60, 75 degrees, but I never heard about PHI, let alone its trigonometry (angles of 9, 18, 27, 36, 45, 54, 63, 72, 81 degrees – note how the angles also relate to the number 9?).
What was this “PHI”? Where and when did this ratio come about in our worldly knowledge? Why wasn’t I taught about this at university? Did I miss something? All of these questions eventually became answered as my insatiable curiosity grew more and more. I was (admittedly) taught of the Fibonacci Sequence in my university studies, but this was very brief and seemed to just ‘skim’ the surface of what really is behind the sequence and where it derived from.
The Fibonacci Sequence is a simple series of numbers (discovered by Leonardo of Pisa – 1170-1250 – also known as Leonardo Pisano, Leonardo Bonacci and Leonardo Fibonacci):
The sequence starts with the numbers 0 and 1. When you add these numbers you obviously get 1, which is now the next number in the sequence. Then we add this 1 with the preceding number (1) and we get the next number again, which is 2. So the sequence then looks as follows: 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610… etc.
The amazing thing about this is that when we look at any number and divide it with the number preceding it, we get a figure which is very close to the PHI ratio of 1.6180339887… (the decimal numbers go on for infinity since it is an irrational number with no distinct pattern, just like Pi). For example, when we divide say, 55 by the preceding number 34 we get, 55/34=1.617647, which is … close to PHI. And again, let’s look at a higher number in the sequence: 233/144 = 1.6180556… (even closer to PHI – 1.6180339887).
Another example; 610/377=1.6180371… see how closer and closer it gets? The higher into the sequence you look, the closer you get to the magical number Φ, but will never be exact, as the decimals go on for infinity! It will only approach that amazing and unknown place in mathematics we call “PHI”.
There are other sequences such as the Lucas series, which starts with the numbers 2 and then 1, unlike 0 and 1 in the Fibo-series. You can make any sequence you want by starting with any two numbers and will get the same dividing result equaling PHI proportions/ratios. I will elaborate much more in the PHI pages.
As I pursued this marvelous new ratio, I delved deeper and deeper into a new way of looking at the universe, the galaxies, solar systems, living creatures, along with fauna, flora and ourselves. This amazing ratio seemed to be found in almost everything in nature. While I was investigating the mathematical background, I noticed that ancient races like the Mayans, Greeks and Egyptians already knew this ratio in their time and they even used this ratio to construct their buildings like the Parthenon and the Pyramids, for example. Even during the Renaissance, the great inventor/artist – Leonardo da Vinci – used PHI proportions in his works, with a few examples being; the “Vitruvian Man”, “Mona Lisa” and the “Last Supper”.
To quote Johannes Kepler – a German Mathematician, Scientist (1571-1630):
“Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.”
The golden ratio has fascinated intellectuals of diverse interests for at least 2,400 years:
Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa aka “Fibonacci” and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. — Mario Livio, The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number.
PHI is so amazing that it can be seen in the makeup of almost everything in this universe in one way or another. The most amazing is the makeup of the human body. PHI can be seen in our bodies and as such, is found in the:
Hand /Foot, Face, Body, Beauty (aesthetics), Teeth, Development, Heartbeat, Health and Body Temperatures.
Not only this, but PHI is also found in many other things like:
Animals, Plants, DNA, Population Growth, Life, Acoustics, Architecture, Art, Color, Credit Cards, Marketing, Music, Poetry, Stock Markets, Energy, Solar System, Quantum Time and The Universe itself!
I will discuss and thoroughly elaborate all of these and more in my PHI pages, since it has a major impact on the way I view the universe and ourselves.
As you can see, PHI has simply amazed me and still does to this day. To me, PHI is the Divine Ratio in which Allah (swt) has fashioned this universe in such a beautiful way that it has an aesthetic and pleasing effect on our psyche. But how did I learn so much about this in such a short time? Well, it goes back to those bizarre moments when the answers would come to me in almost an instant via many different mediums. For example, when I was first perplexed by this ratio, I wanted to know where it derived from, much like how PI is derived from the circle. I pondered deeply and asked Allah to help me in this and surely enough something weird happened. I was alone in my car parked and doing some number crunching (as I was doing a lot of this after the discovery of “OneEye”). Then all of a sudden, a small bud fell from a tree and onto the hood of my car. It was quite a loud sound for something so small to make. I went outside and picked up this bud from the top of my hood and looked at it and noticed that the inside of the bud there was a star. It looked perfect in all its dimensions! But I wondered what did this have to do with PHI? I pondered yet again and wondered what this meant?
Answers From Dreams
On that night, when I went to sleep, I had a weird dream. I went into a deep sleep and had this dream where it only lasted for about 5-10 seconds (in the actual dream-state). Normally dreams seem to go on for hours on end in this state, but in reality we already know that dreams actually last for only 5 seconds in the ‘real world’. Nevertheless, the dream was very short. The dream was very simple and what appeared was a circle with different geometrical shapes taking place inside it, then disappearing, and then I woke up. I couldn’t make anything of it.
Surprisingly, the next night I had the same dream again, but this time the circle appeared with colours inside of it along with the changing shapes and lines. Again, I couldn’t make sense of it and this dream lasted for 5-10 seconds as well. Then, for a third night I had the same dream again, but this time something amazing happened. The circle appeared, as usual, and then the shapes and colours and everything in the circle converged into a dot, right in the middle of the circle. It then started spreading outward towards the border of the circle and what started appearing was a star (the pentagram), but this time whilst it was happening, a feeling with ‘another message’ overcame me again, much like that night I had the messages about the Tsunamis. This time, there were no overwhelming feelings at all, or any message that ‘something BIG’ was going to happen either. It was a simple message and it was hinting that, “this is the right way”, while the star took shape from the center of the circle all the way to the boundary of the circle. The feeling was saying along the lines that “this is the correct way to do it.” … and that was it! I woke up and was in such a state that it all made perfect sense this time. The formation itself made me realize that this was how PHI is constructed as a mathematical construct. The star (pentagram) was the answer! I immediately investigated the star (the pentagram/pentagon) and that’s when I came up with the figures you saw above in the dimensions of the pentagram and how they relate to PHI. The answer was given again!
Then there was another time later on when I wanted to learn how Bloomberg rose to prominence in the financial world, as this also had a relation to PHI and the stock-market. I searched on the internet and couldn’t find anything and then sat back and pondered once again. I almost gave up on this until I turned on the TV and all of a sudden, there it was! A documentary was coincidentally talking about Bloomberg’s influence on the financial world during his time. This was no surprise to me and I simply laughed, but I watched it and got my answers as usual. This was truly an amazing time that I was going through.
During the year following my discovery of “OneEye” I learned a lot more and investigated into other areas such as; crop-circles, sacred geometry, esoteric beliefs and ancient civilizations. What I learned was simply astonishing and correlated to everything I was learning, as well as what I had been taught already (both scientifically and spiritually).
So where is all this leading to?
After a whole year since that simple question Fred asked about the number 9 and the consequent discovery of OneEye, I had learned so much and a lot of things started to make sense to me. The graph I discovered was, to me, a message on its own! What it means to me is another thing entirely!
Read the next article: My Thoughts On OneEye to see how it all connects.