# Fibonacci 60 Repeating Pattern (and other natural mathematical wonders!)



## Silent Bob (Nov 26, 2020)

So, as promised on the logarithm thread here is one on the Fibonacci sequence. Many of you will already be familiar with this sequence, but for those who aren't here is a quick summary.

It is a number sequence with 1 simple rule to find the next number - just add the previous two numbers together. You start with 1.

So, first number is 1. The next is also 1, as there is only one previous number at this point. Then we get 2 (1+1) then 3 (1+2) then 5(2+3) then 8(3+5) etc.

so the sequence goes: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 etc

There are all sorts of patterns in nature formed by this sequence, but that is fairly standard stuff you see all over. This next pattern is particularly interesting.

The last digit of the numbers in the Fibonacci Sequence form a pattern that repeats after every 60th number:

0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3, 0, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1

This pattern can be seen in the following list of the first 72 Fibonacci numbers at this link Fibonacci 60 Repeating Pattern - The Golden Ratio: Phi, 1.618

If you write these 60 numbers around a circle (or clockface....) you get this:






The first thing to notice is how the number zero occurs 4 times, at 3, 6, 9, and 12 o'clock or N, E , S, W on a compass. What are the odds?

The second point is that the number 5 occurs where each hour mark would be on a clock (except for 3, 6, 9 and 12 which are zeros), which also represents 5 minutes..... Coincidence?

Also all the numbers opposite each add together to equal 10, except for the zeros.

So, is this where our measurement of time comes from? A clock built into nature itself, all from adding two numbers to get the next one!

When I first stumbled across this I realised that this must be where our measurement systems using base 60 come from. This also strengthens Velokovski's claim that we had 360 days in the year in ancient times, especially when we also have 360 degrees in a circle aswell. I was teaching maths at the time and included this in my lessons. I also discussed it with the head of maths, who was a real maths geek - he had never heard about it. He kept looking at me puzzled and saying 'are you sure?' - completely blew his mind 

More here:

https://www.jain108.com/fibonacci-60-code/
As a brief aside and a chuckle, here is Dave Allen trying to teach his son how to tell the time - makes you realise it's trickier thatn you think 


_View: https://www.youtube.com/watch?v=0QVPUIRGthI_


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## Silveryou (Nov 26, 2020)

On the clock there are:
4 zeros
8 ones
4 twos
8 threes
4 fours
8 fives
4 sixes
8 sevens
4 eights
8 nines

The complete sequence around the clock:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1.597, 2.584, 4.181, 6.765, 10.946, 17.711, 28.657, 46.368, 75.025, 121.393, 196.418, 317.811, 514.229, 832.040, 1.346.269, 2.178.309, 3.524.578, 5.702.887, 9.227.465, 14.930.352, 24.151.817, 39.082.169, 63.233.986, 102.316.155, 165.550.141, 267.866.296, 433.416.437, 701.282.733, 1.134.699.170

Some divisions:
3/2 = 1,5
5/3 = 1,666666666666667
8/5 = 1,6
13/8 = 1,625
21/13 = 1,615384615384615
34/21 = 1,619047619047619
55/34 = 1,617647058823529
89/55 = 1,618181818181818

34/3 = 11,33333333333333
377/34 = 11,08823529411765
4.181/377 = 11,09018567639257
46.368/4.181 = 11,09016981583353
514.229/46.368 = 11,09016994478951
5.702.887/514.229 = 11,09016994374102
63.233.986/5.702.887 = 11,08806574634917
701.282.733/63.233.986 = 11,0902819411068

55/5 = 11
610/55 = 11,09090909090909
6.765/610 = 11,09016393442623
75.025/6.765 = 11,09016999260902
832.040/75.025 = 11,09016994335222
9.227.465/832.040 = 11,0901699437527
102.316.155/9.227.465 = 11,08821924548075
1.134.699.170/102.316.155 = 11,09012716515784


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## Silent Bob (Nov 27, 2020)

Silveryou said:


> On the clock there are:
> 4 zeros
> 8 ones
> 4 twos
> ...



I didn't spot the 8/4 pattern, well spotted! 

Dividing the subesquent terms as you have above is how to get the golden ratio Phi, which is the number found throughout nature. You can see with each division we get closer to the value for Phi, until we hit it pretty much exactly with 89/55.

This is a nice video showing how it works, I used to play this in my GCSE maths lessons when we covered sequences.


_View: https://www.youtube.com/watch?v=greG6_f7Y7Q_


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## Felix Noille (Nov 27, 2020)

This is excellent stuff. I'm totally useless at maths, but this is fascinating.

I grew up with pounds, shillings and pence (and even farthings and ha'pennies), feet and inches, fathoms etc. and I often wondered if decimalisation was some kind of attempt to disconnect us from something. Looks like it may well have been.

Everything to do with measurement seemed to be based on 12 - inches in a foot, pennies in a shilling, a.m. hours and p.m. hours, months in a year. However, then you'd get 20 shillings in a pound (21 in a guinea), 7 days in a week, 3 feet in a yard....? If nothing else it used to keep your mind well exercised.


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## Silent Bob (Nov 27, 2020)

Felix Noille said:


> This is excellent stuff. I'm totally useless at maths, but this is fascinating.
> 
> I grew up with pounds, shillings and pence (and even farthings and ha'pennies), feet and inches, fathoms etc. and I often wondered if decimalisation was some kind of attempt to disconnect us from something. Looks like it may well have been.
> 
> Everything to do with measurement seemed to be based on 12 - inches in a foot, pennies in a shilling, a.m. hours and p.m. hours, months in a year. However, then you'd get 20 shillings in a pound (21 in a guinea), 7 days in a week, 3 feet in a yard....? If nothing else it used to keep your mind well exercised.



I've been saying this for years, decimilisation definately dumbed us down, as well as using calculators and automatic tills etc. Like any skill, if you never use it you lose that skill. Many people think they are useless at maths, just about everyone I've ever taught fell into this category. However, this is just another layer of the deceit as everyone can do it when they need to. They teach maths in a way that most people don't understand, you have to be very left brained to follow it. This is why they want you to use their methods, makes it more confusing than using your own method and keeps you thinking that you can't do maths. 

I read a book recently which was written in the early 1900's 'The ragged trousered philanthoripists', which is in itself an interesting topic for this forum. It's all about painter and decorators renovating old houses. No mention of any new building going up, only renovating quickly and cheaply! I digress, another thread lol. 

The point I wanted to make was one of the characters working out his wages for the week. He worked 40 hours for 7p and hour, and as he walks home from work he casually works it all out in his head as 2 pounds, 3 shillings and 4 pence. As someone who has always been good at calculating in my head, I still found this tricky to work out as easily as he did. I had to work out 7 x 40 = 280p, then 240p in a pound leaving 40p, then 12p in a shilling so 3 shillings = 36p leaving 4p ..... phew, not an easy head calculation and yet back then even 'uneducated' manual workers could do it no problem. How many people can work this out today? Clear evidence of dumbing down! Also evidence that when it's important anyone can work it out. I have talked to many people who thought they were rubbish at maths but they didn't realise they were already very good. Like the milkman who could calculate all sorts in his head from daily practice when collecting money on his rounds, even though he was rubbish at maths at school. Anyone who worked in a shop was good at calculating until the till started working it out for you. The best example was someone I worked with once who was a keen gambler. He was surprised to learn that his maths was not only good, he could calculate odds far quicker than me, especially in texas hold em - all comes down to motivation!

So the movement from imperial to metric has robbed us of being able to work things out for ourselves. There's something natural and comforting about the numbers used in imperial, 12 inch to a foot, 3 feet to a yard, 16oz to a lb, rather than 10, 100, 1000 etc - so bland! I would say imperial is natural whilst metric is artificial. It's interesting that people have always been naturally opposed to the change from imperial to metric, even though it is easier to use. Overall great mind exercise, as you say, to use the old measurements.


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## Felix Noille (Nov 27, 2020)

Silent Bob said:


> Like the milkman who could calculate all sorts in his head from daily practice when collecting money on his rounds, even though he was rubbish at maths at school.



I was a rubbish milkman as well. I lasted one week!


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## wommak (Nov 27, 2020)

This is great guys. Not long ago I was really interested with Mandelbrots. It makes math simple.
Very nice presentation


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## 6079SmithW (Nov 27, 2020)

Great thread.
I wonder how the above info pertains to music being allegedly changed 43 to 44khz?


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## Silent Bob (Nov 27, 2020)

6079SmithW said:


> Great thread.
> I wonder how the above info pertains to music being allegedly changed 43 to 44khz?


 
I've thought about this one, the thing that sticks out for me is the factors of 432 are 'better' than those for 440. By 'better' I'm talking about my preference for 3, 6, 9 etc, the natural feeling numbers.

So you can divide 432 by:  2, 4, 8, 3, 6, 9, 12 - similiar to our imperial measurements

     you can divide 440 by: 2, 4, 8, 5, 10 - the absence of 3, 6 and 9 could be key here, we get 5 and 10 instead making it feel metric....

I love the comparison from this guy, playing at both frequencies. Starts about 4 mins in.


_View: https://www.youtube.com/watch?v=Rt3EAPDn-Ug_


I definately prefer the 432hz version, feels more relaxing to me.


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## Citezenship (Nov 27, 2020)

This is a video that is part of a series that offers some of the best explanations of this phenomena for me, quite long but well worth the time.

It is just a short bit of the overall series, i used to have this all backed up on an old mechanical drive that unfortunately failed last year, but i will try to hunt it down again.


_View: https://youtu.be/eYDwWbDhCEg_


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## msw141 (Nov 27, 2020)

Felix Noille said:


> Everything to do with measurement seemed to be based on 12 - inches in a foot, pennies in a shilling, a.m. hours and p.m. hours, months in a year.



Is anyone aware of theories linking these measurements to a race other than our own?  I thought I heard that we have a base 10 numerical system because we have 10 fingers, which makes sense.  So then would legends of 6 fingered people (nephilim or otherwise) be a source for these other base 12 systems?


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## Citezenship (Nov 27, 2020)

msw141 said:


> Felix Noille said:
> 
> 
> > Everything to do with measurement seemed to be based on 12 - inches in a foot, pennies in a shilling, a.m. hours and p.m. hours, months in a year.
> ...


Damn good question that i have not considered before!


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## msw141 (Nov 27, 2020)

thanks, but I'm sure I heard it somewhere else.  thinking about it, measurements involving time and zodiac would have to be the oldest knowledge we maintain, and would be more likely to be different than others we developed later as we developed our own knowledge, if they were passed to us from others.


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## Bald Eagle (Nov 27, 2020)

Just to combat a bit of "truthiness":

http://xahlee.info/math/fibonaci_video_fallacy.html


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## Felix Noille (Nov 28, 2020)

I was hoping this thread would get linked to sound. I'm sure it's a key issue with regards to stolen history, just as all the old world constructions used the golden section, there must be an equivalent in sound.

It's all about harmony in all senses of the words - 'harmony' and 'senses.'

Royal Rife was able to cure diseases with sound frequencies, so perhaps if we still lived in an environment that was harmoniously compatible in the architectural and aural sense we wouldn't get the diseases in the first place.

Perhaps this is all linked to how civilisation has degraded to the point where the worst in human nature dominates rather than the best?

(I will be watching the above videos tonight. Many thanks for the links )

PS: Just noticed that the sound card in my PC doesn't support 43.2khz, only 44.1. Will I be able notice the difference?


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## Citezenship (Nov 28, 2020)

Felix Noille said:


> I was hoping this thread would get linked to sound. I'm sure it's a key issue with regards to stolen history, just as all the old world constructions used the golden section, there must be an equivalent in sound.
> 
> It's all about harmony in all senses of the words - 'harmony' and 'senses.'
> 
> ...


I think the sound version is cymatics, sound literally creating shapes, this vid demonstrates how sound has a physical effect on matter.

As for the sample rate of your sound card, that really does not matter as it is just the play back medium, if the sound you listen to, say the instruments are tuned to 432 then it will play back in this, 44.1 is just the sample rate, just like frames on a movies reel but with sound instead of needing 30-60 frames per second sound needs 44.100hz.

The tuning scale of the instruments are where the adjustment is need, I make sounds with a modern day sequencer called logic pro, I used to use one called reason, funny eh, but in these you can set the master tuning to 432 which effects all instruments within.

Anyway here are some fun visuals with the medium of sound!


_View: https://youtu.be/Q3oItpVa9fs_


	Post automatically merged: Nov 28, 2020

Also cymatic has been known about since well the rise of modern sc-eince, s-cience,

Rosslyn Chapel - Wikipedia, 

just one example, there are many many more,

the repeating patterns in most moorish architecture, most religious architecture, it is almost every where in the classical/old world!


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## Blue Ice (Nov 28, 2020)

I saw this 360 days in a year claim, and I was both fascinated and very confused. How could it be, I don’t understand. If there is such a big difference between the true year and conventional year, wouldn’t seasons spill into each other, solistices and equinoxes be displaced? Aren’t these hard numbers?


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## msw141 (Nov 28, 2020)

Blue Ice said:


> I saw this 360 days in a year claim, and I was both fascinated and very confused. How could it be, I don’t understand. If there is such a big difference between the true year and conventional year, wouldn’t seasons spill into each other, solistices and equinoxes be displaced? Aren’t these hard numbers?



My understanding is that for Velikovsky's Worlds in Collision premise this is evidence that something occurred that would explain why there was uniformity of 360 day calendars in ancient times, followed by a shift to 365 day calendars.  Perhaps something knocked us into an altered orbit. 

To your point, being off by 5 days would certainly be noticeable and so rounding it off just to divide cleanly by 12/60 doesn't seem practical or likely given how important it would be for accuracy in tracking these events.


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## Citezenship (Nov 28, 2020)

Even the 365 is not accurate as we need leap years to balance the difference!


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## Jd755 (Nov 28, 2020)

The year is 360 suns or sun ups or sun rises if you prefer.


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## Bald Eagle (Nov 28, 2020)

Felix Noille said:


> Royal Rife was able to cure diseases with sound frequencies, so perhaps if we still lived in an environment that was harmoniously compatible in the architectural and aural sense we wouldn't get the diseases in the first place.



I think there is merit to some of the suspicions about the usefulness of sound in health, but people's ignorance, wishful and magical thinking, and flights of fancy result in any legitimate information getting bogged down in a sea of perpetuated crackpottery.

Consider many of the things that we presently do for health:
brushing teeth
flossing
removing tartar
various minor surgical procedures
massage
chiropractic
Tai Chi practices of tapping and bouncing

All of these involve the intercession of a third party or a tool to enhance the effectiveness of self-care.

Various authors have put forth theories on aging and disease resulting from the accumulation of crud and waste products in the cells, and certainly there are concerns about the accumulation of protein conglomerates in prion diseases, and the ingestion of polymers, fluoride, and other materials not part of normal human physiology and biochemistry.

So, the thing I have mused about for some time is the removal of these accumulations from cells, and the removal of similar unnecessary material from the body through the lymph system.  Perhaps manipulation of the body through exterior means allows the traction, gripping, and dislodging, and moving of things that are trapped - allowing the body to more easily remove them.

I think about it as sort of the inverse, or dual, of 3D printing.   We can now manufacture items with captive parts, complex contours, and hollows that are impossible to manufacture by conventional means.   Rather than removing material, we add it - around the voids.  When necessary, we can use removable support materials.
Physical therapies may be able to manipulate areas of the body that the body can't - either through lack of musculature, lack of articulation or opposable structures, or the absence of things like cilia.  Sound might be able to reach areas that physical manipulation can't, or do it more faster and more efficiently.  While we can use a brush to remove particles, a sonicator can reach down into hollows and crevices and remove things from places that even the finest bristles can't reach.  
There's also the emergent field of sonochemistry, whereby chemical reactions can be promoted through the use of ultrasonic vibrations.  So, in the same way that we might use a delayed chemical reaction to get down into and under a particle, so that we can push out from under it, rather then pressing it further down with a brush - perhaps certain sounds can induce chemical reactions, enzymatic activity, protein folding/unfolding, or modulate secondary processes and biochemical cascades which assist the body in doing what it has difficulty accomplishing on its own - through age, disease, toxicity, injury, etc.


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## Silent Bob (Nov 28, 2020)

Velkovski suggested that the orbit of the earth (or orbit of the sun or if you prefer ) took exactly 360 days. Then around 700B.C the calenders changed, and he suggests that this is when there was a disturbance of the orbits of the planets, resulting in all sorts of change. I recall him talking about venus streaming across the sky, linked to the myth of Medusa story of the goddess turned crazy. The god of war, Mars, came very close to us in its orbit relasing electrical disharge between it and us hence it's name. After this the orbit became 365 and a quarter days. Initially these 'extra' days were viewed with 'suspicion' (in Velkovski's words!), as not belonging to the rest of the year. The extra days would be more or less the days between Christmas and new year. Funnily enough I have always felt like these are odd days, as if they didn't belong to the rest of the year.

In addition, there was an 'inbetween' period whilst everything settled down into what we have today. At one point the moons orbit was 35/36 days, at which point we had 10 months in the year. Evidence of this still exists in the names, Sept = 7, Oct = 8, Nov = 9, Dec = 10, July and August the two months added later (Julius Ceaser and Caeser Agustus?) after the moon settled into its current orbit.

The way I look at it our realm has been distorted from what it should be by some past event. I imagine a radio station at 360Hz but I have a faulty receiver which only allows to tune as close as 365.25Hz. I would still hear the station (experience our reality) but with a little distortion/interference. Also it would be possible that another radio station, at say 369Hz, could also be heard at times over the other station. This could explain a lot of paranormal observations! I guess from a creationist point of view 360 days makes a lot more sense, where as from the mainstream science 'it all happened by accident' 365.25 days is just the sort of figure they want to prove their point. It would also make more sense from a flat earth perspective that our realm would be finely tuned to 360 days and 30 days for the sun and moon. From the standard cosmology it would seem an incredible coincidence to have exactly 360 days, they wouldn't like that idea at all. 

You could also link this to the 432Hz vs 440Hz sound comparison, designed to slightly distort what we experience, without it being too obvious and giving the game away.

Some good info on the 360 day year here, with some key bits copied and pasted below link

http://360dayyear.com/
Even though this was as late as 238 B.C., still with great pomp the Egyptians would write, of "_the year of 360 days_ and the 5 days added to their end..." 

The setting aside of the last five days agrees with the practice which Herodotus [~440 B.C.; and see below] ascribes to the Egyptians of considering the five days over the 360 as scarcely belonging to the year, and not placing them in any month. 

Mayan astronomers [made] detailed observations of Venus, leading to a highly accurate calendar." Mayans had varying interrelated calendars but to identify an actual date in history, they used the Long Count calendar of 360-day years. The Maya demonstrated tremendous mathematical skill with their base 20 number system and a representation of their number system in Arabic numerals shows that 1 = 1; 10 = 20; 100 = 400; and 1000 = 8000. However, in a telling departure, transliterating (so to speak) the Mayan Long Count calendar into Arabic numbers results in 1 = 1; 10 = 20; 100 = 360; 1000 = 7200 (rather than 8000); and 10000 = 144,000 (rather than 160,000). This modification of the number system is a stunning fact of ancient history (reminiscent of the Sumerian number system anomaly from far across the ocean). Most worldviews simply cannot account for such extraordinary history. Because many deem an historical, actual 360-day year as a physical impossibility, dramatic worldwide evidence to that effect gets ignored or discounted. 

Archaeology well attests the ancient use of twelve 30-day months in Mesopotamia. 

Then in about 1550 B.C., _The Ebers Papyrus_, written during the reign of Pharaoh Amenophis, presents a 360-day year calendar on the reverse side of the first "page" of the 66-foot long scroll. (The lengthy document preserved many Egyptian medical practices for posterity including their knowledge of the heart as the center of one's blood supply with its vessels extending throughout the body.) And in the 1200s B.C., Pharaoh Ramesses II had engraved an astronomical ceiling depicting a 360-day year. 

*Aztec Calendar Stone:* 12-feet in diameter, the Aztec calendar stone has its Ring B of 18 quincunxes which combines with the 20 uinal day signs for a 360 day year. 

*India Calendar*: Encyclopedia of Indo-Aryan Research, G. Thibaut, states: "All Veda texts speak uniformly and exclusively of a year of 360 days. Passages in which this length of year is directly stated are found in all the Brahmanas." Thibaut further states that the Vedas (1500 - 500 B.C.) never mention intercalary days. 

*Sumerian Calendar*: The resulting system... which without question complemented throughout the 3rd millennium natural, lunistellar divisions, is attested in its basic form of a twelve-month, 360-day year in the archaic documents from the end of the 4th millennium [B.C.]. 

From a maths perspective: 360 is thus divisible by many numbers including those especially helpful (in bold, even today) for calendars and timekeeping: *2*, *3*, *4*, 5, *6*, 8, 9, 10, *12*, *15*, 18, 20, *24*, *30*, 36, 40, *45*, *60*, 72, *90*, *120*, and *180*. A year of 360 days is reasonably divisible even by the 2 equinoxes, 2 solstices, four seasons, 12 months, etc., 24 hours in a day, 24 time zones of 15 nominal degrees each, 60 minutes in an hour, and 60 seconds in a minute. Consider also our comfort using a "dozen" and with 12 inches in a foot, and 36 inches in a yard. Even in major construction, the Babylon sexigesimal (base 60) mathematics beat the Greeks to trigonometry by 1500 years; it was easier to use; and according to the journal _Science_, was even more accurate than today's modern trigonometry. 

*Babylonian Calendar*: The Babylonians inherited from Sumeria the relationship between the calendar and the number system with the 12-month, 360-day year giving rise to base 60. 

*Roman Calendar*: Written within a decade of 115 A.D., Plutarch's Life of Numa states: "during the reign of Romulus [claimed 753-716 B.C.], they had been irrational and irregular in their fixing of the months, reckoning some at less than twenty days, some at thirty-five, and some at more; they had no idea of the inequality of the annual motions of the sun and moon, but held to this principle only, that the year should consist of three hundred and sixty days." 

The setting aside of the last five days agrees with the practice which Herodotus ascribes to the Egyptians of considering the five days over the 360 as scarcely belonging to the year, and not placing them in any month. So completely were these five days considered by the Romans to be something extraneous, that the soldier appears to have received pay only for 360 days.

John wrote of 1,260 days (3.5 * 360) in Revelation 11:3 & 12:6, which equals exactly the three and a half (360-day) years that he mentions in Revelation 12:14. That number also exactly equals the 42 months of Revelation 11:2 and 13:5. These year and month equivalents are exactly equal, and only equal 1,260 days, when calculating with months of 30 days each.


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## Silveryou (Nov 28, 2020)

I thought it was an established thing that the Lunar year was composed of 12 months of 30 days with an intercalary 13th month every now and then (I don't remember when exactly)


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## Felix Noille (Nov 29, 2020)

I had a quick peek at the 441 vs 432 Hz issue yesterday. As usual and quite depressingly, it's clouded and confused with... I think the technical term is 'twaddle.'

You have many conflicting opinions and of course, good old dogma. The Solfeggios thing even manages to include hidden biblical codes (even though the promoters of this system are not Christian), monks and the de facto villain - the Nazis. All of which is unsubstantiated.

There's a very good discussion of the whole issue here: "Solfeggios" - Origin of the Hoax [Warning - it's an ATS link so lock up your daughters]

The *Binaural *phenomena also seems very interesting, but I'm not that familiar with it.


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## Silveryou (Jun 16, 2021)

Silent Bob said:


> When I first stumbled across this I realised that this must be where our measurement systems using base 60 come from. This also strengthens Velokovski's claim that we had 360 days in the year in ancient times, especially when we also have 360 degrees in a circle aswell. I was teaching maths at the time and included this in my lessons. I also discussed it with the head of maths, who was a real maths geek - he had never heard about it. He kept looking at me puzzled and saying 'are you sure?' - completely blew his mind


So it is implied that the subdivision of the "wheel" in 12 parts is a consequence of the conversion from a base 60 system to the decimal base 10... maybe.
With a base 15 we probably have less "hours-zodiacal signs", while with a base 5 they should increase.
So calendars with less (or more) months could be a thing due to the numerical system used... maybe?!?!?!?!?

Obviously assuming that the starting point was always a base 60, otherwise the "wheel" would be different

To explain it better... Fibonacci pattern "magically" creates a subdivision in 12 parts of the "wheel" composed of 60 segments. Fibonacci used our decimal system. What would happen using another system? For example base 12? The Roman calendar was supposed to be of 10 months, so what kind of base system would result starting from a "wheel" (supposedly composed of 60 parts according to Plutarch's testimony of a year of 360 days) divided in 10 parts through Fibonacci's pattern?


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## Silent Bob (Jun 30, 2021)

Silveryou said:


> So it is implied that the subdivision of the "wheel" in 12 parts is a consequence of the conversion from a base 60 system to the decimal base 10... maybe.
> With a base 15 we probably have less "hours-zodiacal signs", while with a base 5 they should increase.
> So calendars with less (or more) months could be a thing due to the numerical system used... maybe?!?!?!?!?
> 
> ...



Sorry it's taken me a while to respond to this, but everytime I think about it I get a headache 

When it comes to different number base systems I can only really think in terms of base 10 most of the time. When we talk about base 60 it's confusing, because we're actually still using the base 10 number system but using larger units such as 60 for certain things. I can understand base 2, binary, but beyond that I've never really tried any other number base system. There are 10 types of people when it comes to binary, those who understand and those who don't..... 

I've often thought about if we used another number base system all the time, how this would change things, but again this is when I get a head ache lol. Imagine having 60 digits to describe our numbers, so that 10 is equal to 60 in base 10, 20 would be 120 etc. So time is in base 60 but still using base 10 digits, and then seconds, minutes and hours for the first three place values. So 100 in base 60 would be like 1 hour, 0 mins, 0 secs which would be 3600 in base 10, or 3600 seconds. However, our four place value then switches to base 24, i.e. days, so we're really mixing and matching number bases, but still always using base 10 notation if that makes sense?


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## Silveryou (Jun 30, 2021)

Silent Bob said:


> Sorry it's taken me a while to respond to this, but everytime I think about it I get a headache


 same here, glad I'm not alone!



Silent Bob said:


> I've often thought about if we used another number base system all the time, how this would change things, but again this is when I get a head ache lol. Imagine having 60 digits to describe our numbers, so that 10 is equal to 60 in base 10, 20 would be 120 etc. So time is in base 60 but still using base 10 digits, and then seconds, minutes and hours for the first three place values. So 100 in base 60 would be like 1 hour, 0 mins, 0 secs which would be 3600 in base 10, or 3600 seconds. However, our four place value then switches to base 24, i.e. days, so we're really mixing and matching number bases, but still always using base 10 notation if that makes sense?


Yes. It's very tricky. I've started my own try with a 15 base system but I had to stop (not a great mathematician + headache). This is my partial result. I've used letters to represent the nonexistent numbers:
1-2-3-4-5-6-7-8-9-A-B-C-D-E-0

1, 1, 2, 3, 5, 8, D(13), 16(21), 24(34), 3A(55), 5E(89), 99(144), 108(233), 1A2(377), 2AA(610) ...

So the first repetitions of the last digit are 8 (8 and 108), then 2 (2 and 1A2), then A (3A and A2A). It would be interesting to know when the pattern above repeats itself to see how many subdivisions it possess and if it's possible to divide the "new wheel" in new hours/zodiac signs.

I would like to know if there is a program to calculate these new numbers (using fake digits as the ones above). The thing to accomplish (at least for me) is to see the last digits and the eventual repeating pattern. Do you know some program to do it? Thank you in advance.



Silent Bob said:


> When we talk about base 60 it's confusing, because we're actually still using the base 10 number system but using larger units such as 60 for certain things.


Yes it is. In fact it seems that base 60 is just the final result of Fibonacci sequence using base 10. Am I right?


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## Silent Bob (Jun 30, 2021)

I don't know of a program to do that, but it may be easier to try it with a lower number base first, less than 10 to avoid new digits. Also, yes, the 60 base is produced by fibonacci in base 10.


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## Silveryou (Jun 30, 2021)

Silent Bob said:


> Also, yes, the 60 base is produced by fibonacci in base 10.


This is huge regardless. It has so many implications... mind blowing!



Silveryou said:


> The complete sequence around the clock:
> 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1.597, 2.584, 4.181, 6.765, 10.946, 17.711, 28.657, 46.368, 75.025, 121.393, 196.418, 317.811, 514.229, 832.040, 1.346.269, 2.178.309, 3.524.578, 5.702.887, 9.227.465, 14.930.352, 24.151.817, 39.082.169, 63.233.986, 102.316.155, 165.550.141, 267.866.296, 433.416.437, 701.282.733, 1.134.699.170


It was incomplete and wrong in some digits. This is the correct one:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1.597, 2.584, 4.181, 6.765, 10.946, 17.711, 28.657, 46.368, 75.025, 121.393, 196.418, 317.811, 514.229, 832.040, 1.346.269, 2.178.309, 3.524.578, 5.702.887, 9.227.465, 14.930.352, 24.151.817, 39.082.169, 63.239.986, 102.322.155, 165.562.141, 267.884.296, 433.446.437, 701.330.733, 1.134.777.170, 1.836.107.903, 2.970.885.073, 4.806.992.976, 7.777.878.049, 12.584.871.025, 20.362.749.074, 32.947.620.099, 53.310.369.173, 86.257.989.272, 139.568.358.445, 225.826.347.717, 365.394.706.162, 591.221.053.879, 956.615.760.041, 1.547.836.813.920


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## Silveryou (Jul 1, 2021)

I have calculated the sequence in base 15 and I have called it the Silveryou Sequence:

TAB 15 (this is a tab to convert numbers to base 15):
1       (15   225     3.375     50.625   759.375     11.390.625   170.859.375    2.562.890.625    38.443.359.375      576.650.390.625  )
2       (30   450     6.750    101.250  1.518.750   22.781.250   341.718.750    5.125.781.250   76.886.718.750      1.153.300.781.250)
3       (45   675     10.125  151.875  2.278.125   34.171.875   512.578.125    7.688.671.875   115.330.078.125    1.729.951.171.875)
4       (60   900     13.500  202.500  3.037.500   45.562.500   683.437.500    10.251.562.500  153.773.437.500    2.306.601.562.500)
5       (75   1.125  16.875  253.125  3.796.875   56.953.125   854.296.875    12.814.453.125  192.216.796.875   2.883.251.953.125)
6       (90   1.350  20.250  303.750  4.556.250   68.343.750   1.025.156.250  15.377.343.750  230.660.156.250  3.459.902.343.750)
7       (105  1.575  23.625  354.375  5.315.625   79.734.375   1.196.015.625  17.940.234.375  269.103.515.625  4.036.552.734.375)
8       (120  1.800  27.000  405.000  6.075.000   91.125.000   1.366.875.000  20.503.125.000  307.546.875.000  4.613.203.125.000)
9       (135  2.025  30.375  455.625  6.834.375   102.515.625  1.537.734.375  23.066.015.625  345.990.234.375  5.189.853.515.625)
A/10 (150  2.250  33.750  506.250  7.593.750   113.906.250  1.708.593.750  25.628.906.250  384.433.593.750  5.766.503.906.250)
B/11 (165  2.475  37.125  556.875  8.353.125   125.296.875  1.879.453.125  28.191.796.875  422.876.953.125  6.343.154.296.875)
C/12 (180  2.700  40.500  607.500  9.112.500   136.687.500  2.050.312.500  30.754.687.500  461.320.312.500  6.919.804.687.500)
D/13 (195  2.925  43.875  658.125  9.871.875   148.078.125  2.221.171.875  33.317.578.125  499.763.671.875  7.496.455.078.125)
E/14 (210  3.150  47.250  708.750  10.631.250  159.468.750  2.392.031.250  35.880.468.750  538.207.031.250  8.073.105.468.750)
0

SEQUENCE:
1, 1, 2, 3, 5, 8, D(13), 16(21), 24(34), 3A(55), 5E(89), 99(144), 108(233), 1A2(377), 2AA(610), 45C(987), 717(1.597), B74(2.584), 1.38B(4.181), 2.010(6.765), 3.39B(10.946), 5.3AB(17.711), 8.757(28.657), D.B13(46.368), 17.36A(75.025), 25.E7D(121.393), 3D.2E8(196.418), 64.276(317.811), A2.56E(514.229), 116.7E5(832.040), 1B8.D64(1.346.269), 2D0.65E(2.178.309), 499.4BD(3.524.578), 779.B27(5.702.887), C24.0E5(9.227.465), 1.49D.C1C(14.930.352), 2.1C1.162(24.151.817), 3.66E.D7E(39.082.169), 5.842.B91(63.239.986), 8.EB2.A20(102.322.155), E.805.6B1(165.562.141), 18.7B8.1D1(267.884.296), 28.0BD.892(433.446.437), 41.886.A73(701.330.733), 69.955.415(1.134.777.170), AB.2DB.E88(1.836.107.903), 125.C42.39D(2.970.885.073), 1D2.02E.336(4.806.992.976), 307.C71.6D4(7.777.878.049), 4D9.CA0.A1A(12.584.871.025), 7E2.A22.1EE(20.362.749.074), CCC.7C2.C19(32.947.620.099), 1.5C0.2E4.E18(53.310.369.173), 2.39C.AB7.B32(86.257.989.272), 3.96C.DAC.A4A(139.568.358.445), 5.D1A.975.67C(225.826.347.717), 9.788.833.1C7(365.394.706.162), 10.5A4.2A8.854(591.221.053.879), 19.D3C.ADB.A2B(956.615.760.041), 2A.3E1.D95.380(1.547.836.813.920)...

...45.22E.981.DAB(2.504.452.573.961)

LAST DIGITS:
*1, 1, 2, 3, 5, 8, D, 6, 4, A, E, 9, 8, 2, A, C, 7, 4, B, 0*, B, B, 7, 3, A, D, 8, 6, E, 5, 4, E, D, 7, 5, C, 2, E, 1, *0,
1, 1, 2, 3, 5, 8, D, 6, 4, A, E, 9, 8, 2, A, C, 7, 4, B, 0*, B...

I have stopped at number 61 but it is clear that the second half of the second line repeats itself. Apparently in base 15 the wheel has 40 numbers on it, with 2 "points 0" every 20 numbers (instead of 4 every 15 numbers for the base 10 wheel).
An important difference is that there are no intermediate subdivisions. In base 10 there are two "fives" that divide every section of 15 numbers between the zeros in 3 parts. In base 15 there is no such thing.


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## Silent Bob (Jul 1, 2021)

I didn't expect that, it surpises me that we get another repeating pattern! That fact it is fewer numbers is also conterintuitive, I would have expected more if anything. I wonder what a lower base would look like, maybe a repeating pattern with more than 60 numbers? 

So, had we used base 15 we could have had a 40 minute hour, split into 2 parts. I notice the 5th number is either 0, 5 or A if we spilt our hour into 8 five minute sections. It would be interesting to see the 40 numbers arranges around a clock, I might have a go at drawing it out.


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## Silveryou (Jul 1, 2021)

Silent Bob said:


> I didn't expect that, it surpises me that we get another repeating pattern! That fact it is fewer numbers is also conterintuitive, I would have expected more if anything. I wonder what a lower base would look like, maybe a repeating pattern with more than 60 numbers?
> 
> So, had we used base 15 we could have had a 40 minute hour, split into 2 parts. I notice the 5th number is either 0, 5 or A if we spilt our hour into 8 five minute sections. It would be interesting to see the 40 numbers arranges around a clock, I might have a go at drawing it out.


Here is another sequence in base 20 this time. I have not completed because it was waaay too long but it seems clear where the repetition happens:

TAB 20 (this is a tab to convert numbers to base 20):
1    (20  400   8.000   160.000   3.200.000  64.000.000    1.280.000.000  25.600.000.000  512.000.000.000  )
2    (40  800   16.000  320.000   6.400.000  128.000.000   2.560.000.000  51.200.000.000  1.024.000.000.000)
3    (60  1.200 24.000  480.000   9.600.000  192.000.000   3.840.000.000  76.800.000.000  1.536.000.000.000)
4    (80  1.600 32.000  640.000   12.800.000 256.000.000   5.120.000.000  102.400.000.000 2.048.000.000.000)
5    (100 2.000 40.000  800.000   16.000.000 320.000.000   6.400.000.000  128.000.000.000 2.560.000.000.000)
6    (120 2.400 48.000  960.000   19.200.000 384.000.000   7.680.000.000  153.600.000.000 3.072.000.000.000)
7    (140 2.800 56.000  1.120.000 22.400.000 448.000.000   8.960.000.000  179.200.000.000 3.584.000.000.000)
8    (160 3.200 64.000  1.280.000 25.600.000 512.000.000   10.240.000.000 204.800.000.000 4.096.000.000.000)
9    (180 3.600 72.000  1.440.000 28.800.000 576.000.000   11.520.000.000 230.400.000.000 4.608.000.000.000)
A/10 (200 4.000 80.000  1.600.000 32.000.000 640.000.000   12.800.000.000 256.000.000.000 5.120.000.000.000)
B/11 (220 4.400 88.000  1.760.000 35.200.000 704.000.000   14.080.000.000 281.600.000.000 5.632.000.000.000)
C/12 (240 4.800 96.000  1.920.000 38.400.000 768.000.000   15.360.000.000 307.200.000.000 6.144.000.000.000)
D/13 (260 5.200 104.000 2.080.000 41.600.000 832.000.000   16.640.000.000 332.800.000.000 6.656.000.000.000)
E/14 (280 5.600 112.000 2.240.000 44.800.000 896.000.000   17.920.000.000 358.400.000.000 7.168.000.000.000)
F/15 (300 6.000 120.000 2.400.000 48.000.000 960.000.000   19.200.000.000 384.000.000.000 7.680.000.000.000)
G/16 (320 6.400 128.000 2.560.000 51.200.000 1.024.000.000 20.480.000.000 409.600.000.000 8.192.000.000.000)
H/17 (340 6.800 136.000 2.720.000 54.400.000 1.088.000.000 21.760.000.000 435.200.000.000 8.704.000.000.000)
I/18 (360 7.200 144.000 2.880.000 57.600.000 1.152.000.000 23.040.000.000 460.800.000.000 9.216.000.000.000)
J/19 (380 7.600 152.000 3.040.000 60.800.000 1.216.000.000 24.320.000.000 486.400.000.000 9.728.000.000.000)
0

SEQUENCE:
1, 1, 2, 3, 5, 8, D(13), 11(21), 1E(34), 2F(55), 49(89), 74(144), BD(233), IH(377), 1AA(610), 29H(987), 3JH(1.597), 694(2.584), A91(4.181), GI5(6.765), 1.776(10.946), 2.45B(17.711), 3.BCH(28.657), 5.FI8(46.368), 9.7B5(75.025), F.39D(121.393), 14.B0I(196.418), 1J.EAB(317.811), 34.5B9(514.229), 54.020(832.040), 88.5D9(1.346.269), DC.5F9(2.178.309), 120.B8I(3.524.578), 1FC.H47(5.702.887), 2HD.8D5(9.227.465), 4I6.5HC(14.930.352), 7AI.JAH(24.151.817), C45.589(39.082.169), JF4.JJ6(63.239.986), 1.BJA.57F(102.322.155), 2.BEF.571(165.562.141), 4.3E5.AEG(267.884.296), 6.F90.G1H(433.446.437), A.J36.6GD(701.330.733), H.EC7.2IA(1.134.777.170), 18.DFD.9F3(1.836.107.903), 26.880.CDD(2.970.885.073), 3F.23E.28G(4.806.992.976), 61.ABE.F29(7.777.878.049), 9G.CF8.HB5(12.584.871.025), FI.373.CDE(20.362.749.074), 15E.G2C.A4J(32.947.620.099), 21C.J9G.2ID(53.310.369.173), 377.FC8.D3C(86.257.989.272), 590.F24.G25(139.568.358.445), 8G8.AED.95H(225.826.347.717), E59.5GI.582(365.394.706.162), 1.31H.GBB.EDJ(591.221.053.879), 1.H77.28A.021(956.615.760.041), 3.094.J01.EG0(1.547.836.813.920)...

...4.HGC.18B.EI1(2.504.452.573.961), 7.I5H.08D.9E1(4.052.289.387.881)

LAST DIGITS:
1, 1, 2, 3, 5, 8, D, 1, E, F, 9, 4, D, H, *A*, H, H, 4, 1, 5, 6, B, H, 8, 5, D, I, B, 9, *0*, 9, 9, I, 7, 5, C, H, 9, 6, F, 1, G, H, D, *A*, 3, D, G, 9, 5, E, J, D, C, 5, H,
2, J, 1, *0*...
1, 1, 2, 3, 5, 8, D, 1, E, F, 9, 4, D, H, *A*, H, H, 4, 1, 5, 6, B, H, 8, 5, D, I, B, 9, *0*, 9, 9, I, 7, 5, C, H, 9, 6, F, 1, G, H, D, *A*, 3, D, G, 9, 5, E, J, D, C, 5, H,
2, J, 1, *0*

I have underlined the part I've not actually calculated.

So it seems we have again 60 numbers, with two zeroes falling in position 30 and 60. We have two As in position 15 and 45. It would be cool to see it on the wheel too. I am going to do base 5 (and others too) later.

Is it possible that base 5 will give us a wheel with 40 numbers?


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## Simon Ruszczak (Jul 1, 2021)

Fibonacci has a negative side.​-987,610,-377,233,-144, 89, -55, 34,-21, 13, -8, 5,-3, 2,-1, 1, 0, 1, 1, 2, 3, 5, 8


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## Silveryou (Jul 1, 2021)

Simon Ruszczak said:


> Fibonacci has a negative side.​-987,610,-377,233,-144, 89, -55, 34,-21, 13, -8, 5,-3, 2,-1, 1, 0, 1, 1, 2, 3, 5, 8


Who doesn't have one!


Silveryou said:


> Is it possible that base 5 will give us a wheel with 40 numbers?


Apparently no. This is base 5, stopped before reaching number 60:

TAB 5 (this is a tab to convert numbers to base 5):
1 (5  25  125 625   3.125  15.625 78.125  390.625   1.953.125 9.765.625  48.828.125  244.140.625 1.220.703.125 6.103.515.625  30.517.578.125  152.587.890.625 762.939.453.125  )
2 (10 50  250 1.250 6.250  31.250 156.250 781.250   3.906.250 19.531.250 97.656.250  488.281.250 2.441.406.250 12.207.031.250         61.035.156.250  305.175.781.250 1.525.878.906.250)
3 (15 75  375 1.875 9.375  46.875 234.375 1.171.875 5.859.375 29.296.875 146.484.375 732.421.875 3.662.109.375 18.310.546.875     91.552.734.375  457.763.671.875 2.288.818.359.375)
4 (20 100 500 2.500 12.500 62.500 312.500 1.562.500 7.812.500 39.062.500 195.312.500 976.562.500 4.882.812.500 24.414.062.500   122.070.312.500 610.351.562.500 3.051.757.812.500)
0

SEQUENCE:
1, 1, 2, 3, 10(5), 13(8), 23(13), 41(21), 114(34), 210(55), 324(89), 1.034(144), 1.413(233), 3.002(377), 4.420(610), 12.422(987), 22.342(1.597), 40.314(2.584), 113.211(4.181), 204.030(6.765), 322.241(10.946), 1.031.321(17.711), 1.404.112(28.657), 2.440.433(46.368), 4.400.010(75.025), 12.341.033(121.393), 22.241.133(196.418), 40.132.221(317.811), 112.423.404(514.229), 203.111.130(832.040)...

LAST DIGITS:
*1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0*,
*1, 1, 2, 3, 0, 3, 3, 1, 4, 0...*

A wheel of 20 numbers divided in 4 by 4 zeroes


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## Silveryou (Sep 2, 2021)

Another pattern in the wheel...




The sum of all the ending numbers gives 280 as a result. The sum of the first quarter is 56, the second 72, the third 84 and the fourth 68. Then again 56...

The difference between 56 and 72 and between 84 and 68 is *16*.
The difference between 72 and 84 and between 68 and 56 (second turn of the wheel) is *12*.

So we have a pattern 16-12-16-12-16...



Silent Bob said:


> The Maya demonstrated tremendous mathematical skill with their base 20 number system and a representation of their number system in Arabic numerals shows that 1 = 1; 10 = 20; 100 = 400; and 1000 = 8000. However, in a telling departure, transliterating (so to speak) the Mayan Long Count calendar into Arabic numbers results in 1 = 1; 10 = 20; 100 = 360; 1000 = 7200 (rather than 8000); and 10000 = 144,000 (rather than 160,000). This modification of the number system is a stunning fact of ancient history (reminiscent of the Sumerian number system anomaly from far across the ocean). Most worldviews simply cannot account for such extraordinary history.


So the 'string' _1 = 1; 10 = 20; 100 = 360; 1000 = 7200 (rather than 8000); and 10000 = 144,000 (rather than 160,000) _is problematic because I think there is an error inside it.

_1 = 1; 10 = 20 _is clearly base 20, no doubt about it;
_1000 = 7200 (rather than 8000); and 10000 = 144,000 (rather than 160,000) _is also base 20, because 7.200/20=360 and 144.000/20=7.200;
_100 = 360 _this is the problem! suddenly the string uses a different base to obtain 360 instead of 400. It is approximately base 18,9736659 because 18,9736659 X 18,9736659 = 359,9999976848228 (!!!!!!!!!!!!!!!!!!)
So they start in base 20, they switch to base 18,whatever and then, having obtained 360, they return to base 20... *it doesn't make sense!*

In fact it doesn't make sense also because as I previously 'calculated', base 20 naturally gives the possibility to obtain those 360 'degrees' after 6 turns of the wheel, exactly like in base 10.


> 1, 1, 2, 3, 5, 8, D, 1, E, F, 9, 4, D, H, *A*, H, H, 4, 1, 5, 6, B, H, 8, 5, D, I, B, 9, *0*, 9, 9, I, 7, 5, C, H, 9, 6, F, 1, G, H, D, *A*, 3, D, G, 9, 5, E, J, D, C, 5, H,
> 2, J, 1, *0*...
> 1, 1, 2, 3, 5, 8, D, 1, E, F, 9, 4, D, H, *A*, H, H, 4, 1, 5, 6, B, H, 8, 5, D, I, B, 9, *0*, 9, 9, I, 7, 5, C, H, 9, 6, F, 1, G, H, D, *A*, 3, D, G, 9, 5, E, J, D, C, 5, H,
> 2, J, 1, *0*



Isn't it possible that the mistake was done by those who 'transliterated' the Mayan Long Count calendar? It seems a more logic conclusion to me...


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## Simon Ruszczak (Sep 5, 2021)

The sum of any two opposite numbers on the wheel gives a value which has last digit of zero,  i.e. 0 or 10. 

Or in other words, the sum of two numbers thirty places apart (or 30 plus multiples of 60) in the Fibonacci Sequence will give a value which has a last digit of zero.


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