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Richard Elwes
Works at University of Leeds
Attended University of Oxford
Lived in Leeds
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### Richard Elwes

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Eight perfect shuffles

If you shuffle a deck of cards perfectly 8 times, you get back exactly to where you started... as this video by the magician Adam West shows.

I've written a little blog-post explaining why this happens:
http://richardelwes.co.uk/2014/02/27/faro-shuffles/﻿
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Nope -- I would rather spend the time making it so people can publicly publish worksheets.  But for the next week or so I am finishing up a migration to a new much better way of storing projects (still using ZFS, but with much better cross-data center replication, etc.)...  This backend stuff has to be really robust and scalable to support the frontend properly. ﻿

### Richard Elwes

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Pascal's triangle contains many interesting patterns: the triangular numbers, the Fibonacci sequence, the Sierpinski fractal... But a new one to me is that you can also find the number e lurking inside it, if you know where to look!

This discovery is due to , and the proof here is written up with customary clarity and concision by .﻿
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This is excellent - thank you for sharing!﻿

### Richard Elwes

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Biggest Bacon Number

An actor's Bacon number is the shortest path to Kevin Bacon via a sequence of costars. Some actors may have no path to KB at all, but of those which do, who has the largest Bacon number?

"With my life-long passion for movies, I couldn't resist spending many hours probing the dark recesses of film history until, at about 10 AM on Sunday, I found an incredibly obscure 1928 Soviet pirate film, Plenniki Morya, starring P. Savin with a Bacon number of 7, and whose supporting cast of 8 appeared nowhere else. Evidently I had discovered ALL the solutions: A. Kramer, N. Kutuzov, J. Laptev, V. Podgorny, A. Safroshin, E. Smirnova, I. Strauch, and Dmitri Vasilyev."﻿
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Myself and a couple of friends used to play a similar game with musicians. Two people were linked if they'd ever appeared on the same record (including production credits).

So a challenge would be issued (say: Dean Martin to Sinead O'Connor) and the winner would be the person who found the route with the least links.

Interestingly, we each came up with  a different "centre". In my case it was Brian Eno. If I could get a link from one person to Eno, I was fairly confident I could find my way from Eno to the next person. That would then be my fall back position, though obviously I'd then hunt for a shorter non-Eno-centric route. But it was vital to make sure you had some sort of route, however long... otherwise you had to down your drink in one.

Ah, the good old days.﻿

### Richard Elwes

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A new blog-post: I have recently learned an interesting fact about some dear old friends: permutations and combinations.

If the total number of combinations (i.e. subsets of all possible sizes) from a collection of size n is 2ⁿ, what is the total number of possible permutations (i.e.orderings of all possible lengths)?﻿
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I got a "+1" and my answer is out of scope :-p﻿

### Richard Elwes

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This statue of the priest Ka-aper is a remarkable piece of sculpture. Its rock-crystal eyes, the feeling of movement that comes from being captured mid-stride, and the realistic but unflattering middle-aged paunch all make it unnervingly lifelike. It's even more remarkable when you realise that it's four and a half thousand years old, dating from the old kingdom of Egypt around 2475BC, making it more ancient than many of the pyramids.﻿
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Astonishing! I never heard of this statue. Thank you for sharing, .﻿
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### Richard Elwes

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Maths, Beauty, and Brain Scans

A recent post of about patterns in Pascal's triangle was followed by the following discussion:

Commenter 1: That proof is so simple, an A-Level student could understand it. It's so inspiring that this beautiful result is so lightly hidden!

Commenter 2: Beautiful? It's maths ! What are you on?

Commenter 1: truly, you don't feel delight at this discovery, nor see beauty in that proof?

Commenter 2: Uh..no. Sorry, history and English are more my areas of expertise. However, I realise that everyone has their own loves so,.yeah.

While commenter 2 may have been trolling just a tiny bit, I've no doubt that their sentiments are genuine. We maths-fans are constantly banging on about "beauty" and "elegance" among our formulae, to the utter bemusement of everyone else. Is it just possible that we're a load of smart-arse poseurs?

Happily, we can now point to solid scientific evidence that the answer is no! In a recent paper The experience of mathematical beauty and its neural correlates by the neuroscientists Semir Zeki and John Romaya, the physicist and the Fields medal-winning mathematician Michael Atiyah, fourteen mathematicians were asked to rate sixty equations on a scale of -5 (hideous) to +5 (sublime).

They then had their brains scanned while viewing the equations. The researcher's finding after all this was that "that the experience of mathematical beauty correlates with activity in the same brain area(s)... that are active during the experience of visual, musical and moral beauty... the activity there is parametrically related to the declared intensity of the experience of beauty, whatever its source".

That's good news for mathematical aesthetes!

On a side note, it's perhaps unsurprising that Euler's identity was voted as the most beautiful formula: http://en.wikipedia.org/wiki/Euler%27s_identity

And the ugliest? Ramanujan's astonishing series expression for 1/pi: http://math.stackexchange.com/questions/14115/motivation-for-ramanujans-mysterious-pi-formula I'd have a little bet, though, that people would rate it as more beautiful if they understood it. (I don't.)﻿
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Ah, I remember hearing about that, but always from secondary sources. Still, 43 digits is still a slight bit shy of ten million.﻿

### Richard Elwes

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The Ideal Mathematician

To his fellow experts, he communicates these results in a casual shorthand. "If you apply a tangential mollifier to the left quasi-martingale, you can get an estimate better than quadratic, so the convergence in the Bergstein theorem turns out to be of the same order as the degree of approximation in the Steinberg theorem".

This breezy style is not to be found in his published writings.... His writing follows an unbreakable convention: to conceal any sign that the author or the intended reader is a human being.

From the sketch "The Ideal Mathematician" by Phillip J. David & Reuben Hersh. That's not "ideal" as in "perfect", but as in "archetypal".﻿
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I've never actually read this before, perhaps because unlike Dennis the Peasant I was insufficiently repressed by the Powers That Be. I can't help filing "The Ideal Mathematician" alongside "The Tenured Professor Who Does No Research And Does No Teaching And Flavours His Cocktails With The Tears of Adjunct Serfs".

<rant>
I think I used to go along with rhetoric such as in this piece when I first started out; now I'm more jaded, after refereeing dross and marking the work of students who really, really have no solid understanding of the difference between "A implies B" and "B implies A", and why "A and B imply B" is unhelpful.

Moreover, the "mathematics as social construct" line of David and Hersh, which I've glanced at elsewhere, is all well and good until one runs into people who use that slogan as an excuse to say "you're only saying that X is crap because of your systemic socially constructed hegemonically enforced practices". (Qv. time given to the likes of Fuller giving time to the likes of Intelligent Design.)
</rant>﻿

### Richard Elwes

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Congratulations to on his 1000th MathOverflow answer! (In fact he's up to 1002 now.)

His top-scoring answer so far is to the question "What are some reasonable-sounding statements that are independent of ZFC?"

(Explanatory note before revealing Joel's answer: ZFC="Zermelo-Fraenkel Set Theory", which is the strongest logical theory of numbers and sets most mathematicians will ever need to call upon. However, as Gödel's theorem guarantees, even ZFC cannot answer all questions about numbers and sets. Some statements remain independent of ZFC, but, perhaps comfortingly, most such examples are highly esoteric and, for most people, not worth worrying about. The question could be paraphrased as asking for the least esoteric example.)

And Joel's answer.... "If a set X is smaller in cardinality than another set Y, then X has fewer subsets than Y."

Truly remarkable - I didn't know that!﻿
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Thanks very much for the congratulations, Richard, you are very kind to mention it.﻿

### Richard Elwes

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"Suppose aliens invade the earth and threaten to obliterate it in a year's time unless human beings can find the Ramsey number for red five and blue five. We could marshal the world's best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey number for red six and blue six, however, we would have no choice but to launch a preemptive attack."

- Paul Erdős

The Ramsey number for red five and blue five is the smallest number of dots with the following property: if you join all pairs of dots with either a red line or a blue line, using whatever method you like to decide which dots should be joined with which colour, whatever system you use it will be possible to find 5 dots which are either all joined to each other with red egdes or all joined with blue edges. It is known to be between 43 & 49 though its exact value is still unknown, while the Ramsey number for red six and blue six has been pinned down to between 102 and 165.﻿
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Well, I was going off what I remembered from when I looked this up as a PhD student for a postgrad talk. So no progress on that lower bound in ten years, it would seem...﻿

### Richard Elwes

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Stone Age Sculpture

The Venus of Willendorf is a paleolothic sculpture of a woman, dating from at least 25,000 years ago, discovered in Willendorf in modern Austria. Of course it is anachronistic to call it "Venus", but the suggestion is that it represents some sort of fertility symbol or deity - as evidenced by its enormous breasts. Other "Venus" figurines and carvings have been found, including the Venus of Hohle Fels which is carved from mammoth ivory and is even older (maybe as old as 40,000 years) and has even more gigantic boobs:
http://news.bbc.co.uk/1/hi/8047319.stm﻿
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The cheerful anachronism reminds me of one I came across recently. My son came back from school with a reading book called Dinosaur Trouble, by Dick King-Smith, which contains a discussion between a pterodactyl and his mother of the etymology of the word "pterodactyl". They don't actually mention the Greeks, but even so I thought that was stretching things a bit.﻿
People
Have him in circles
4,054 people
Work
Occupation
Employment
• University of Leeds
Mathematician, present
Places
Previously
Leeds - Oxford - London - Freiburg
Contributor to
Story
Tagline
A UK based maths lecturer & writer.
Introduction
Lives in Yorkshire, writes about Maths.
Bragging rights
Author of Maths 1001 & How to Build a Brain (AKA Mathematics Without The Boring Bits) & some other stuff, mostly on the subject of maths
Education
• University of Oxford
Mathematics, 1997 - 2001
• University of Leeds
Mathematical logic, 2001 - 2005
Basic Information
Gender
Male