Fibonacci sequence

[Speleotron]

I'm not sure, I was making an educated guess, but with 10 fingers you tend to count in tens, so you might imagine our ancestors counting in convenient blocks of 10, e.g. '4 tens and another 3 fingers' or '10 tens of tens, and another ten, and 4 fingers' which is essentially base 10. This goes into some detail:

https://math.stackexchange.com/questions/8734/why-have-we-chosen-our-number-system-to-be-decimal-base-10

"

    Traces of the anthropomorphic origin of counting systems can be found in many languages. In the Ali language (Central Africa), for example, "five" and "ten" are respectively moro and mbouna: moro is actually the word for "hand" and mbouna is a contraction of moro ("five") and bouna, meaning "two" (thus "ten"="two hands").

    It is therefore very probable that the Indo-European, Semitic and Mongolian words for the first ten numbers derive from expressions related to finger-counting. But this is an unverifiable hypothesis, since the original meanings of the names of the numbers have been lost."

[Canary]

Numberphile did a bit on it:



Not sure where the original claim came from though, might have slowly morphed from sunflowers?

[mikem]

It was more whether Pi also doesn't repeat in hexadecimal...

[ChrisJC]

You can of course have a number system where Pi is used as the base.

I think there are drawbacks to this though.

Chris.

[mikem]

Not if you represent it with a single digit...

[ZombieCake]

People like the Mayans used a base 20.

https://en.wikipedia.org/wiki/Maya_numerals

[Speleotron]

That's interesting, in my head I always count things in 20s. I just remember the number of 20s, and then the number of units less than 20 left over. I've always found 20 to be a practical size.

[Fjell]

I read this as a teenager shortly after it came out and it cured me of ever worrying about this sort of thing ever again:

https://en.wikipedia.org/wiki/Gödel,_Escher,_Bach

Going caving just seemed easier.

[Speleotron]

It's strange how many people say 'worrying' in this context, number theory isn't a source of anxiety it's fun!

[mikem]

6 is the number they reckon you can keep track of without having to count.

& 12 (60 / 360) for times & angles as they divide by more numbers - 1;2;3;4;6 etc

[Speleotron]

The Babylonians were ahead of their time in realising the importance of using numbers that have lots of factors. I wonder if it gave their economy an edge?

I remember reading that, in ancient egypt 4000 years ago, to enter the civil service you had to pass a maths test. People used to sell books to help people pass the test, the blurb on one of them said something along the lines of 'if you are a farmer you will work yourself to death, if you are a fisherman you will drown, only the scribe is happy. This book will teach you the secrets and allow you to pass the test.' I'll have to see if I can find the book online. I find it amazing that this went on 4000 years ago, it reminds me of 'coding bootcamps' these days which promise to take people from minimum wage to a six figure tech salary.

[ZombieCake]

In the music industry the numbers go to eleven.
I do apologise, but couldn't resist it.

[Fjell]

It's strange how many people say 'worrying' in this context, number theory isn't a source of anxiety it's fun!

It certainly cured me of applying to do maths at uni. I realised I was more into building things and doing stuff, even if I could do the maths.

[mikem]

Engineers use fudge factors to overdesign things, rather than accurate maths...

[Mrs Trellis]

As you may be aware I'm a fan of BBC Radio 4 factual programmes     so here is the "In our Time" programme on the Fibonacci sequence:-

https://www.bbc.co.uk/programmes/b008ct2j

[kay]

People like the Mayans used a base 20.

https://en.wikipedia.org/wiki/Maya_numerals

Suspect there may be traces of base 20 in French with "quatre-vingt dix neuf" etc. And of course English, French, Portuguese etc are all about confused between 10 and 20 as to whetehr they're counting in 10s or not. We of course used a mixed base system for money (20,12 and 4 with the occasional 21 for variety). It's always puzzled me why, faced with a class full of children who were used to counting in base 4, 10, 12,14,16,20 and 60, our teachers made such a hash of teaching us about binary. It should not have been a weird and exotic concept.

[kay]

Some it sounds a bit like good old Pareidolia:

"...the tendency for incorrect perception of a stimulus as an object, pattern or meaning known to the observer, such as seeing shapes in clouds, seeing faces in inanimate objects or abstract patterns, or hearing hidden messages in music."

Slightly different from seeing shapes in clouds. If you  are looking at a plant with 5 spirals in one direction and 8 in another, it's either there or it isn't, it's not something in the eye of the observer; what's in doubt as to whether the count is repeatable over different plants.

In the 20thC  the standard taxanomic work on the genus Mammillaria of cacti included the spiral count - 5&8; 8&13; 13&21; or 21&35. That did seem to be a pretty standard thing across Mammillaria.

[Speleotron]

I'm not saying that the Fibonacci spirals don't exist in plants, just that they don't seem to be nearly as common as people say they are because of selective reporting. It's even more the case with petal numbers, there doesn't seem to be any statistically significant bias towards Fibonacci numbers despite what my maths teachers said. People just report that flowers that do have a Fibonacci number, not the many that don't:

"Wilson cites numbers of petals on flowers.

lily                    3
violet                5
delphinium        8
mayweed          13
aster                21
pyrethrum        34
helenium           55
michelmas daisy  89

These examples associate with Fibonacci numbers. But Wilson neglects to mention these others:


many trees                      0  This is a Fibonacci number. [3]
mustard, dames' rocket    4  Not a Fibonacci number.
tulip, hyacinth                  6  Not a Fibonacci number.
starflower, eggplant          7  Not a Fibonacci number.
gardenia                          8, 9 or 10 petals. 9 and 10 are not Fibonacci numbers.
Greek anemonie (various) 14 or 15 Not Fibonacci numbers.
black-eyed susan (some)  14  Not a Fibonacci number.
mountain laurel               10  Not a Fibonacci number.
gazania                          16  Not a Fibonacci number."



https://www.lockhaven.edu/~dsimanek/pseudo/fibonacc.htm

[kay]

Yes, my maths teacher at school said that the number of petals of most flowers is a member of the Fibonacci sequence.

That's clearly bollocks, if he knew the first thing about flowers. Most flowers have 4 or 5 petals if they're in one of the major groups; and 3 if they're in the other. Usually Fibonacci in flowers is presented for those flowers which are in a tight flowerhead, eg sunflower, Romanesco cauliflower, where the theory is that it comes about because of the packing into spirals.

[Speleotron]

If you count on your fingers you get to a full set of fingers which is 10. You then start with a new set of fingers and remember 'I've already counted 1 ten'. That is base 10.

[Roger W]

Interesting but probably irrelevant:

In every chocolate company I've worked with, I've found at least one guy with a finger missing.

[kay]

The petals thing is another Fibonacci myth, based on a very selective reporting, see this quote:

Wilson cites numbers of petals on flowers.

lily                    3 
violet                5
delphinium        8
mayweed          13
aster                21
pyrethrum        34
helenium           55
michelmas daisy  89

These examples associate with Fibonacci numbers. But Wilson neglects to mention these others:


many trees                      0  This is a Fibonacci number. [3]
mustard, dames' rocket    4  Not a Fibonacci number.
tulip, hyacinth                  6  Not a Fibonacci number.
starflower, eggplant          7  Not a Fibonacci number.
gardenia                          8, 9 or 10 petals. 9 and 10 are not Fibonacci numbers.
Greek anemonie (various) 14 or 15 Not Fibonacci numbers.
black-eyed susan (some)  14  Not a Fibonacci number.
mountain laurel               10  Not a Fibonacci number.
gazania                          16  Not a Fibonacci number.



https://www.lockhaven.edu/~dsimanek/pseudo/fibonacc.htm

For a start, Wilson is getting confused about petals and flowers - from mayweed onwards he's counting flowers not petals (they're all in the daisy family, where each "petal" is in fact a flower complete with sexual parts), and there's no reason which you should expect flowers to be part of the same sequence as petals.

The higher numbers in the second list are not necessarily the basal number of petals, they're varieties chosen for stamens having changed into extra petals, so again no reason to expect them to be part of a sequence. And Gazania is another daisy family plant, so the count there is of flowers not petals.

So it's pretty easy to debunk any theory that number of petals has anything to do with the Fibonacci sequence. It's more convincing when related to spirals. But even so, how meaningful is it to take a single number, or even two numbers, and say "this is a part of THIS sequence"?

But I suspect it all originates with a desire to find a divine order to things (or even any order). Musical notes were tied up with trying to unravel "the music of the spheres", and our western scale comes from dividing frequencies in simple ratios, then finding out you don't get quite the same answer depending on which order you do the divisions in, and making compromises ("The well tempered Clavier").

[Speleotron]

But even so, how meaningful is it to take a single number, or even two numbers, and say "this is a part of THIS sequence"?

But I suspect it all originates with a desire to find a divine order to things (or even any order).

I agree. I think Fibonacci has so many myths because it's too pretty not to be true! The Fibonacci sequence and the Golden Ratio are like catnip for maths teachers who are desperatly trying to make things interesting for a classroom full of bored kids. I don't know why my maths teachers didn't just say that maths underpins the whole global economy as well as science, instead of making dodgy links to spirals and flowers.

P.S. Why did my maths teachers never mention the fact that you can make lots of money out of maths? I get that they are more interested in the beauty of nature and it's mathematical patterns, but to a bunch of teenagers thinking about career options, why not mention this?

[Fjell]

Using chain

Interesting but probably irrelevant:

In every chocolate company I've worked with, I've found at least one guy with a finger missing.

Using chain to make up pipe is the thing for getting rid of superfluous fingers.

The original question was on geology, and the answer is no, you don’t get pretty patterns like that. But one of the most fascinating things is that the number of opinions on a piece of rock is always proportional (and indeed equal) to the number of geologists present. And it always seems to be a prime as well. I once spent a happy day watching 11 argue if a turbidite outcrop was inverted or not. The length of the argument is generally proportional to the square of the sum of papers they have had published between them. This is why you should never allow geologists to cluster, they must be kept isolated and subdued.

[JoshW]

If you count on your fingers you get to a full set of fingers which is 10. You then start with a new set of fingers and remember 'I've already counted 1 ten'. That is base 10.

if i'm pacing out I count to 56 (100m), after each 100m I have 1 finger on my right hand, once I've got all five fingers up on my right hand, I put 1 finger up of my left hand, so can pace out 3km if required (luckily not needed to yet!).

The vietnamese (and I'm sure other places in Asia) had a way of counting where each 'knuckle' on their hand counts so can count to 12 on each hand.