UK Caving
OTHER STUFF => Idle Chat => Topic started by: yrammy on September 29, 2020, 06:16:48 pm

Saw this question on a facebook group page. It asks about geology , i wonder about speleology
Unusual question, but I know the Fibonacci sequence can be seen in nature in small things like pine cones, or flowers, but is it reflected in anything on a bigger scale in nature? When looking at a landscape, is there any sign of it?

I wouldn't read too much into the Fibonacci stuff it's a bit of a myth. People love drawing spirals on things and saying how that is the golden ratio etc. but it's largely a case of people finding something if they purposefully look for it, like how people see Jesus in a tomato etc.
https://www.independent.co.uk/news/science/mathematiciansdisputeclaimsgoldenrationaturalblueprintbeauty10204354.html
https://www.fastcompany.com/3044877/thegoldenratiodesignsbiggestmyth
https://www.maa.org/external_archive/devlin/devlin_05_07.html

Sounds like a question for Drs Rutherford & Fry

I'm afraid Dr. Rutherford is unwell at the moment.

Speleotron, how dare you question the underlying meaning of such an arbitrary number! ;D
But seriously, after a quick scan, those links do not seem to challenge the existence of the sequence in nature (& science), only the higher level meaning of it in art and beauty.

Yes you're right they don't give any evidence against the sequence itself, but the resulting ratio has certainly been overused pretty much everywhere. My own opinion is that the sequence itself is also overused but this is hard to prove. Fibonacci came up with the sequence to model the population growth of animals but I think people fell into the trap (that traps many many scientists) of thinking 'that's neat, let's see where else it appears'. The problem with that is that it's like looking for faces in the clouds: you'll find them everywhere but they aren't actually faces.

I think the problem may be more to do with thinking something is an underlying rule when it is merely an side effect of something else.['

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."
https://en.wikipedia.org/wiki/Pareidolia#:~:text=Pareidolia%20(%2Fp%C3%A6r%C9%AA%CB%88,hearing%20hidden%20messages%20in%20music.
Trouble starts when people start adding 2 and 2 to make 5 and going off at tangents reinforcing what are essentially incorrect perceptions.

Yes, my maths teacher at school said that the number of petals of most flowers is a member of the Fibonacci sequence. I went out and counted petals and found, roughly, that the percentage of flowers which satisfied the 'rule' was about the same as the percentage of numbers which were in the Fibonacci sequence! I think confirmation bias plays a huge role. Somebody sees a Fibonacci spiral on a pinecone and attaches significance to it, but not to the complete lack of Fibonacciness of a coconut or a leek.

I dunno if it's a myth so much as just not very important.
It happens in plants because it happens to be a very efficient way of arranging leaves. It's consequently a "choice" by said plant  but geology can't choose so I wouldn't expect to find it in geography apart from by coincidence

Is it really so efficient though and if so, why? It's something I heard from my maths teachers but they never showed me a source for that claim. It seems to me to be another urban myth, My unscientific field work didn't find many Fibonacci flowers.

Also see lots of people saying it's fibonacci spirals on things, when actually it's just any old spiral.
One I saw the other day was about whales blowing bubbles in a decreasing spiral to compress a school of fish, and it was just a normal spiral..

Look for something and you will find it, even if it's not there!

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.
blackeyed 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

Evolution doesn't work by making things perfect, the best solution for the current conditions, based on what was already there, is what wins through. & if a population is isolated then it can evolve independently to form a new species.
Seeing faces in things is a facet of the way our brain works for identifying each other.

OK, but nobody can tell me why the Fibonacci sequence is in any way optimal for plants or for nature in general, and there doesn't seem to be a statistically significant bias towards Fibonacci numbers in flowers etc. I think it's one of those things that is believed because it sounds good, and gets passed round as wisdom. Maths teachs seem to love it, probably because it sounds semiinspiring to kids.

https://www.youtube.com/watch?v=18jk2oRkyPc

& people like simple explanations (the theory of evolution is simple, but its products aren't)

I remember IF. They don't make 'em like that any more.

Reminds me of this wazzock:
https://www.youtube.com/watch?v=OMq9he5HUU
who thinks he's found the sound of Pi.
Really he's just adding harmony to a random sequence of numbers! Any random sequence of numbers would sound exactly the same, so there's nothing significant about the Pi part.
There are plenty of afibonacciados out there doing the same.
Chris.

And presumably he thinks that the harmonic scale developed in Western culture has some kind of fundamental significance? I think that kind of thing can be fun as long as people realise that it has no underlying meaning or mathematical significance.
By the way I'm not sure that the digits of pi really are random. They don't repeat, that has been proved, but asking whether they are random leads down a rabbit hole. I would say that the digits of pi are not random as there is a formula for finding the nth digit of pi, allbeit in hexadecimal, but nature doesn't favour base 10.
https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula
https://stats.stackexchange.com/questions/44445/arethedigitsofpistatisticallyrandom
https://www.jstor.org/stable/2685604?seq=1#metadata_info_tab_contents
https://www2.lbl.gov/ScienceArticles/Archive/pirandom.html

Is Pi the same if you work in hexadecimal then?

Is Pi the same if you work in hexadecimal then?
Being a ratio, the proportions will be constant, regardless of the units used or the base of the numbers... The actual numerical values are relevant?

Any number is the same in any base it just doesn't look the same. The base is just how we display it on a page, nature doesn't care. We probably use base 10 because we have 10 fingers and the Romans didn't use any base as their numerals don't work like that.

If the number of fingers set the base to which we count wouldn't we count to base 11?
I have never been sure about this.

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/whyhavewechosenournumbersystemtobedecimalbase10
"
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 IndoEuropean, Semitic and Mongolian words for the first ten numbers derive from expressions related to fingercounting. But this is an unverifiable hypothesis, since the original meanings of the names of the numbers have been lost."

Numberphile did a bit on it:
https://www.youtube.com/watch?v=sj8Sg8qnjOg
Not sure where the original claim came from though, might have slowly morphed from sunflowers?

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

You can of course have a number system where Pi is used as the base.
I think there are drawbacks to this though.
Chris.

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

People like the Mayans used a base 20.
https://en.wikipedia.org/wiki/Maya_numerals

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.

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.

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

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

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.

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

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.

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

As you may be aware I'm a fan of BBC Radio 4 factual programmes :read: so here is the "In our Time" programme on the Fibonacci sequence:
https://www.bbc.co.uk/programmes/b008ct2j

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 "quatrevingt 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.

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.

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.
blackeyed 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

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.

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.

Interesting but probably irrelevant:
In every chocolate company I've worked with, I've found at least one guy with a finger missing.

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.
blackeyed 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").

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?

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.

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.

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.
That's why they use base 12 in Norfolk.

What have I started!

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 desperately 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.
Today's kids are lucky! We never got anywhere near Fibonacci in the classroom. It was all firmly in the domain of "recreational maths", martin gardner etc.
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?
Interesting conversation with my son "I don't want to go to uni because I don't know what I want to do yet, and I don't want to spend 3 years studying only to realise that I don't want to do that job" "So why don't you do a maths degree?" "Would anybody employ me with a maths degree?" I understand the desire to get kids to think about their future in terms of studying subjects that will lead to a career, but there are some areas where it has gone too far. State school careers advice is leaning too far to the vocational.

What have I started!
In these dark times a bit of light relief is needed.

I like this thread and it shows what a good forum this is that we're on page 3 and it hasn't become an argument!

'Recreational maths'  I love that term. I've done plenty of that ;)
With reference to geology, selfsimilarity is certainly present, especially at erosional boundaries, coastlines etc. And formulas can predict detail levels of those I guess:
https://en.wikipedia.org/wiki/Selfsimilarity (https://en.wikipedia.org/wiki/Selfsimilarity)

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?
Interesting conversation with my son "I don't want to go to uni because I don't know what I want to do yet, and I don't want to spend 3 years studying only to realise that I don't want to do that job" "So why don't you do a maths degree?" "Would anybody employ me with a maths degree?" I understand the desire to get kids to think about their future in terms of studying subjects that will lead to a career, but there are some areas where it has gone too far. State school careers advice is leaning too far to the vocational.
I think that too many jobs now have a requirement for degrees when realistically it just doesn't need it. My job for instance could be done by any old monkey who can use a keyboard and string a sentence together and yet every entry job level in the industry will have a degree as a requirement. I managed to get in without having completed my degree and despite laziness am fairly successful.
Two wasted years at university, and a whoooole load of money. I think that employers need to reduce their requirements for jobs, or be required to take on a certain amount of people without degrees.

Interesting conversation with my son "I don't want to go to uni because I don't know what I want to do yet, ...
Suggest they do a 'proper' degree in a subject they find interesting. Perhaps it would lead to an interesting career.
Chris.

Interesting conversation with my son "I don't want to go to uni because I don't know what I want to do yet, ...
Suggest they do a 'proper' degree in a subject they find interesting. Perhaps it would lead to an interesting career.
Chris.
This this this. do something that is going to hold their interest for 3 years plus (if they want to go to uni at all)

Degrees have become a requirement mainly to reduce the number of applications that employers have to wade through.
On knuckles  you have 3 on each finger & 2 on the thumb, so 14, but it's quite difficult to maintain 14 different positions to make use of them!

'Recreational maths'  I love that term. I've done plenty of that ;)
With reference to geology, selfsimilarity is certainly present, especially at erosional boundaries, coastlines etc. And formulas can predict detail levels of those I guess:
https://en.wikipedia.org/wiki/Selfsimilarity (https://en.wikipedia.org/wiki/Selfsimilarity)
Please don’t post any more interesting links. That’s going to be another evening gone and I’ve got a lot on already. It’s like UKC meets U3A :)
And I thought an interest in selfsimilarity was the reason folk put their phone on a stick, albeit in front of something more interesting still.

Degrees have become a requirement mainly to reduce the number of applications that employers have to wade through.
On knuckles  you have 3 on each finger & 2 on the thumb, so 14, but it's quite difficult to maintain 14 different positions to make use of them!
they used their thumb to do the counting, so 3 on each finger and a 'pointer' thumb.

Interesting conversation with my son "I don't want to go to uni because I don't know what I want to do yet, ...
Suggest they do a 'proper' degree in a subject they find interesting. Perhaps it would lead to an interesting career.
Chris.
If you read the rest of the post, that's what I suggested. Or don't you consider a maths degree to be a proper degree? ;D

6 is the number they reckon you can keep track of without having to count.
I once had a job in a magazine warehouse, sorting pallets of each publication into packing boxes to go to the newsagents. We always worked in 3's on the basis that you can always visualise 3 without needing to count them.
They had found that if you tried grabbing more than 3 at a time, you would either take longer due to (subconsciously) counting, or mistakes would be made. 3 was optimum for speed and accuracy.

Interesting conversation with my son "I don't want to go to uni because I don't know what I want to do yet, ...
Suggest they do a 'proper' degree in a subject they find interesting. Perhaps it would lead to an interesting career.
Chris.
This this this. do something that is going to hold their interest for 3 years plus (if they want to go to uni at all)
From what I've heard, uni isn't the fun it used to be, first excessive fees, so students feel the need to study instead of going caving, now with Coronavirus, it just sounds bloody awful.
If I was that age again now, I'd be asking myself serious questions before going to uni...
Asside from the lack of fun, I'm not sure how well it stacks up careerswise either any more. For example, we have apprentice engineers, who have gone on to do a degree on day release from work. 5 years after leaving school, they have an engineering degree, 5 years experience, no debt and a deposit for a house.
5 years after school, those that went to uni have an engineering degree, less than 1 year's experience and a motherload of debt.

It's about 23% of lifetime earnings for someone earning decent money. The way to get decent money is to go to a top uni. Also gives you options on marrying well, which is double money.
Although if you have the maths, I would recommend economics over engineering these days at a top 10 uni. Right up there with medicine for average earnings.

Do a Fine Art degree, and then it's almost guaranteed you'll never get a proper job ever again. And you certainly won't 'marry well' either, but may have much more fun instead. Worked for me  though I'll die in a ditch for sure ;)

Although if you have the maths, I would recommend economics over engineering these days at a top 10 uni. Right up there with medicine for average earnings.
Maths and/or computer science would be a better bet for working in finance. Hedge funds can't get enough of maths/compsci PhDs.

I have an engineering degree from a top 10 uni (albeit a 2.2), my brother has a history degree from a top 10 uni (he got a 1st).
I work in engineering, my brother works in financial management and earns at least 3 times what I do.
I'd speculate that a good degree from a good uni simply demonstrates to an employer that you are capable of learning and capable of working hard, regardless of the subject you choose to study.
Obviously some jobs do require specific subjects and if you aren't sure what you want to do, maths or computer science are probably a pretty safe bet :thumbsup:

https://www.economist.com/graphicdetail/2018/06/15/whichtraitspredictgraduatesearnings
And while you are at it on the subject of maths:
https://www.economist.com/graphicdetail/2020/10/03/itsbettertobeapoorpupilinarichcountrythanthereverse

I suppose it's related to what you like to do. Money isn't necessarily the be all and end all (although I guess it's very nice to have some). Three years at university isn't a bad thing, although these days it comes at a price. At eighteen did everyone really know what they wanted to do? Even if we think we did.
Arts isn't a bad thing, for example we wouldn't have a great film industry (panicdemic aside) if everyone wanted to screw over the stock market for as much cash as possible. Different people have different aims, and those aims change over time.
I'm certainly doing something very different to what I went to Uni for, and I'm probably still not sure what I really want to do.

I'm not saying that everyone should do maths so they can be a quant and they must prioritise making money, just that I think it's odd that maths teachers and careers advisors, in my experience, never mentioned that this was an option. In fact the most lucrative branch of mathematics careers wasn't given a mention at all. It's not all about the money but from the point of view of careers advice it's kind of important to talk about it.

I have long concluded that a career you can happily pursue somewhere like North Yorkshire resolves many issues.

That's true for us maybe but kids need to know about all the options they can choose from.