Carlsen's ranking of world champions

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MJMcCready
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Re: Carlsen's ranking of world champions

Post by MJMcCready » Mon May 03, 2021 12:16 am

Ian Thompson wrote:
Sun May 02, 2021 11:10 pm
NickFaulks wrote:
Sun May 02, 2021 8:33 pm
So genius does just mean being very good at something?
The dictionary says:
very great and rare natural ability or skill
To me that means not just being very good at something, but also being noticeably better than the best people at the activity usually are.
I thought much talent at chess was mostly down to pattern recognition, which itself comes from the effort of memorizing the patterns in the first place doesn't it?

Matthew Turner
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Re: Carlsen's ranking of world champions

Post by Matthew Turner » Mon May 03, 2021 9:29 am

NickFaulks wrote:
Sun May 02, 2021 8:33 pm
Paul Cooksey wrote:
Sun May 02, 2021 8:19 pm
Well Professor Elo gave us some help.
So genius does just mean being very good at something?
Here is an idea then,
"A genius is someone whose ability is such that it cannot be sensibly measured on an existing scale"

Here is a little anecdote from one of the first times I met someone who I think the vast majority of people (including myself) would regard as a genius. I was taking an 11 year old to a Maths Competition, but before we went their teacher asked if I could show them some ideas. I found out that combinatorics was an area that was often covered. So, I took an eggbox and 6 golf balls into School and to introduce the topic I asked how many different ways are there to arrange three golf balls in the six holes. The student stared into space for about 5 seconds and replied 20. I asked how they had worked it out and the reply came back "I have no idea".

They could "see the numbers" in the same way as Ramanujan (yes, they really are that good). By the age of 15 or 16 it wouldn't really make sense to say that the student was a better Mathematician than me, because essentially Maths for them is a completely different discipline to what it is for me.

Kevin Thurlow
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Re: Carlsen's ranking of world champions

Post by Kevin Thurlow » Mon May 03, 2021 10:43 am

Robert Kennedy (not a genius) said, "Some men see things as they are, and say why. I dream of things that never were, and say why not."

Perhaps that's a reasonable description of a genius? There have been talented scientists who have worked hard and improved techniques, or thought of new ones. Alexander Fleming found some mouldy slides and thought, "that's interesting, let's have a look", and came up with penicillin, which has been incredibly useful, but didn't really require "genius", "just" very good science. But Newton and Einstein (e.g.) came up with startling new ideas. Maybe Stephen Hawking will join them, if anyone can prove he was right!

The same applies in art and music, there have been mainly talented people, but every so often someone does something different. But for every person saying that Picasso was a genius, you'll find someone saying his work is rubbish as it doesn't look real.

In chess, you could argue that Philidor's work on pawn structure was sufficiently new to be genius, maybe Morphy's attacking ideas? There are many talented players who just know what to do, is that genius? Back in the 60s, there was a really strong Blitz event, where Petrosian wiped everyone out, instead of just drawing with everyone, so obviously he had such immense talent, he didn't need to calculate. So was he a lazy genius?

I doubt you can have a genius darts player, the basic technique is the same - aim at the board - but you can have really technically proficient players.

NickFaulks
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Re: Carlsen's ranking of world champions

Post by NickFaulks » Mon May 03, 2021 11:08 am

Matthew Turner wrote:
Mon May 03, 2021 9:29 am
The student stared into space for about 5 seconds and replied 20. I asked how they had worked it out and the reply came back "I have no idea".
I expect they did have some idea, as I would have had at that age. It is obviously 6.5.4/3.2.1, and if you have to be taught that you are not any kind of a mathematician, let alone a genius.

Unless I'm a genius, which is not an idea I have considered.
If you want a picture of the future, imagine a boot stamping on a human face — forever.

Matthew Turner
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Re: Carlsen's ranking of world champions

Post by Matthew Turner » Mon May 03, 2021 11:18 am

NickFaulks wrote:
Mon May 03, 2021 11:08 am
Unless I'm a genius, which is not an idea I have considered.
It is not an idea I'd considered either.

Matthew Turner
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Re: Carlsen's ranking of world champions

Post by Matthew Turner » Tue May 04, 2021 8:42 am

NickFaulks wrote:
Mon May 03, 2021 11:08 am
Matthew Turner wrote:
Mon May 03, 2021 9:29 am
The student stared into space for about 5 seconds and replied 20. I asked how they had worked it out and the reply came back "I have no idea".
I expect they did have some idea, as I would have had at that age. It is obviously 6.5.4/3.2.1, and if you have to be taught that you are not any kind of a mathematician, let alone a genius.

Unless I'm a genius, which is not an idea I have considered.
I was being careful not to put the name of the student in the public domain, but a quick Google search suggests that is not an issue!
Like this for example

https://bmos.ukmt.org.uk/home/imo-2020-pr.pdf

Joseph Conlon
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Re: Carlsen's ranking of world champions

Post by Joseph Conlon » Tue May 04, 2021 11:23 am

To me the idea of 'genius' connotes someone who is not just a better version of oneself - works a bit harder, with a bit more focus, with a bit more talent - but someone whose thought processes operate in a completely different fashion, often allied to a certain monomania and disdain for social convention.

I'm very happy with the idea of talent, or innate aptitude. I can see it in my own family - there is a talent for high-level maths/physics that some have and some don't, across multiple generations with strong variations in the level of home support.

Chess I think is also clear - anything where certain 6 year olds can be at a level where they are better than most adults diagnoses an innate aptitude for something. What the fundamental nature of that aptitude is - spatial pattern recognition? Analytical thought? - is another question.

On this topic of innate aptitude, if anyone hasn't done so, it is instructive to look at Carlsen's games from his first tournament. Between the first round and the last he seems to go from a total beginner to a competent player with solid strategic sense.

https://www.chessgames.com/player/magnus_carlsen.html

MartinCarpenter
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Re: Carlsen's ranking of world champions

Post by MartinCarpenter » Tue May 04, 2021 11:53 am

Matthew Turner wrote:
Tue May 04, 2021 8:42 am
I was being careful not to put the name of the student in the public domain, but a quick Google search suggests that is not an issue!
Like this for example

https://bmos.ukmt.org.uk/home/imo-2020-pr.pdf
Impressive :) Not sure she'll match Ramanujan but that's a frighteningly high standard of course.

I've worked with/for some very clever people, maybe only one I'd call a genius.

Roger Lancaster
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Re: Carlsen's ranking of world champions

Post by Roger Lancaster » Tue May 04, 2021 2:11 pm

Matthew Turner wrote:
Mon May 03, 2021 9:29 am
NickFaulks wrote:
Sun May 02, 2021 8:33 pm
Paul Cooksey wrote:
Sun May 02, 2021 8:19 pm
Well Professor Elo gave us some help.
So genius does just mean being very good at something?
Here is an idea then,
"A genius is someone whose ability is such that it cannot be sensibly measured on an existing scale"

Here is a little anecdote from one of the first times I met someone who I think the vast majority of people (including myself) would regard as a genius. I was taking an 11 year old to a Maths Competition, but before we went their teacher asked if I could show them some ideas. I found out that combinatorics was an area that was often covered. So, I took an eggbox and 6 golf balls into School and to introduce the topic I asked how many different ways are there to arrange three golf balls in the six holes. The student stared into space for about 5 seconds and replied 20. I asked how they had worked it out and the reply came back "I have no idea".

They could "see the numbers" in the same way as Ramanujan (yes, they really are that good). By the age of 15 or 16 it wouldn't really make sense to say that the student was a better Mathematician than me, because essentially Maths for them is a completely different discipline to what it is for me.
I've just learnt a new word, 'combinatorics', but it's highly possible the student already knew about factorials and simply calculated 6!/3!x3! and either couldn't articulate an explanation or else didn't think it worth explaining to a [perceived] simpleton who had just asked him or her a very easy question. It may be that the person in question is indeed a genius but I don't believe this is a clear example of "seeing the numbers".

Jon Underwood
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Re: Carlsen's ranking of world champions

Post by Jon Underwood » Tue May 04, 2021 4:52 pm

A long time ago I was a theoretical physicist and met people like Hawking, Witten, Penrose, Atiyah etc on a number of occasions plus loads of lesser lights. The people I regarded as genii had had ideas that invited the response "I never would have thought of that in a million years".

Alistair Campbell
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Re: Carlsen's ranking of world champions

Post by Alistair Campbell » Wed May 05, 2021 4:32 pm

NickFaulks wrote:
Mon May 03, 2021 11:08 am
Matthew Turner wrote:
Mon May 03, 2021 9:29 am
The student stared into space for about 5 seconds and replied 20. I asked how they had worked it out and the reply came back "I have no idea".
I expect they did have some idea, as I would have had at that age. It is obviously 6.5.4/3.2.1, and if you have to be taught that you are not any kind of a mathematician, let alone a genius.

Unless I'm a genius, which is not an idea I have considered.
WHy is it obviously 6.5.4/3.2.1? (I assume the golf balls are meant to be theoretically identical.)

Alistair Campbell
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Re: Carlsen's ranking of world champions

Post by Alistair Campbell » Wed May 05, 2021 4:43 pm

Several other points.

(Perhaps this should be part of a separate thread, but that might mean it was punted to one of the more obscure parts of the Forum).

To amplify my previous point about measurement.

If there were some way of measuring “genius” or “ability” one could use a linear scale. 100 might be “average”, 125 “bright”, 150 “very bright” and so on. 200 may be “genius”. (This is reminiscent of the old BCF gradings).
The difficulty with such a scale is we must classify 199.49 as merely “very, very bright” whereas 199.51 is genius, which doesn’t seem to correspond with the view that genius should be exceptional. Perhaps there is a parallel here with the electro-magnetic spectrum – do colours run into each other or are they distinct?

I think Matthew may be arguing that genius cannot be measured on a linear or two dimensional scale.

Then you have the prevalence of genius. We talk of “flashes” of inspiration, or genius. The penny drops. Sometimes. Perhaps we have a sudden realisation that if we do things in a different order (sac the rook, then play the bishop check), we get the result we are hoping for. Presumably you can’t be a genius all the time, but is the occasional incident enough, or do you have to be geniising more frequently?

How about “genius” in other realms?

Was Bradman a genius, or did he just practice a lot? George Best? Seve Ballesteros? Lester Piggott? (is the “10,000 hour” theory rubbish?). Is synesthesia a form of genius, or is it just perception in a different plane?

Presumably, if you are proficient in your chosen field there are things you can do that may look hard to the layperson but are easy for you, and things that you make look easy, but are actually quite hard. I know nothing about acting, so memorising lots of lines looks hard, but apparently is a basic, unremarkable skill (as discussed elsewhere).

With this concept in mind, perhaps only experts in their field can assess genius?

Finally for now, is genius different from innovation? Was Phil “The Power” Taylor’s concept of reverse stacking genius? How about if MVG started throwing (and winning) underarm?

Matthew Turner
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Re: Carlsen's ranking of world champions

Post by Matthew Turner » Wed May 05, 2021 5:23 pm

Alistair Campbell wrote:
Wed May 05, 2021 4:32 pm
NickFaulks wrote:
Mon May 03, 2021 11:08 am
Matthew Turner wrote:
Mon May 03, 2021 9:29 am
The student stared into space for about 5 seconds and replied 20. I asked how they had worked it out and the reply came back "I have no idea".
I expect they did have some idea, as I would have had at that age. It is obviously 6.5.4/3.2.1, and if you have to be taught that you are not any kind of a mathematician, let alone a genius.

Unless I'm a genius, which is not an idea I have considered.
WHy is it obviously 6.5.4/3.2.1? (I assume the golf balls are meant to be theoretically identical.)
So, if you haven't come across the ideas before you should be able to work it out logically. There are 6 places to put the first golf ball then there are five slots left for the second and four for the third. So that gives you 120 possibilities. However, with identical golf balls then you soon realise that each possibility is not unique. There are quite a few ways to get to the idea that each configuration occurs 6 times.

This is why combinatoric problems are popular in Maths Competitions because anyone can have a go at working them out. Hopefully, the more Maths you know the quicker you can get to the answer.

Alistair Campbell
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Re: Carlsen's ranking of world champions

Post by Alistair Campbell » Thu May 06, 2021 1:58 pm

Matthew Turner wrote:
Wed May 05, 2021 5:23 pm

So, if you haven't come across the ideas before you should be able to work it out logically. There are 6 places to put the first golf ball then there are five slots left for the second and four for the third. So that gives you 120 possibilities. However, with identical golf balls then you soon realise that each possibility is not unique. There are quite a few ways to get to the idea that each configuration occurs 6 times.

This is why combinatoric problems are popular in Maths Competitions because anyone can have a go at working them out. Hopefully, the more Maths you know the quicker you can get to the answer.
Thanks for the response.

I did a course on combinatorics years ago – I remember that you get different answers if you sample with or without replacement, and whether the ordering is important.

I recall that there was some symbol (pronounced “n choose k” I think) which gave a formula n!/ (n-k}!*k! or thereabouts.

My question was – why was this formula “obvious”? Why not an alternative formulation? E.g. the answer is also 4+3+2+1+3+2+1+2+1+1. Judicious use of brackets may reveal a pattern – perhaps a moment’s thought suggests a sum of triangular numbers?

I tried to enumerate the possibilities in my head, and got 19, which I assumed could not be correct…

BTW – most golfers would assume golf balls were very much not identical – even if they have the same make and number if you are Bryson DeChambeau (another genius, or merely an oddball??)

Matthew Turner
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Re: Carlsen's ranking of world champions

Post by Matthew Turner » Thu May 06, 2021 3:51 pm

Alistair Campbell wrote:
Thu May 06, 2021 1:58 pm
Matthew Turner wrote:
Wed May 05, 2021 5:23 pm

So, if you haven't come across the ideas before you should be able to work it out logically. There are 6 places to put the first golf ball then there are five slots left for the second and four for the third. So that gives you 120 possibilities. However, with identical golf balls then you soon realise that each possibility is not unique. There are quite a few ways to get to the idea that each configuration occurs 6 times.

This is why combinatoric problems are popular in Maths Competitions because anyone can have a go at working them out. Hopefully, the more Maths you know the quicker you can get to the answer.
My question was – why was this formula “obvious”? Why not an alternative formulation? E.g. the answer is also 4+3+2+1+3+2+1+2+1+1. Judicious use of brackets may reveal a pattern – perhaps a moment’s thought suggests a sum of triangular numbers?
I think you might this formula by relating the problem to Pascal's triangle which is where my 'lesson' went next! However, I am not sure how you would get to this intuitively. An awareness of Pascal's triangle is quite useful in getting a feel for when your answer is probably wrong as in the case of your 19.

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