Å·±¦ÓéÀÖ

Hi!

I’ve joined the Guardian’s network of science bloggers, so from today my blog will be hosted .

My is on the Golden ratio and female reproductive organs.

Hope to see you there.

This site will continue to contain the appendices for Alex’s Adventures in Numberland/Here’s Looking at Euclid and has details of how to contact me.

Alex

I’m interested in numbers � obviously.

I’m also interested in number psychology, and as a result have set up survey that asks people to submit the first number that comes into their heads.

Please click here to take part:

Don’t think too hard � just click and submit.

Thanks!

(The image is what you get when you type ‘random� into google images. Just in case you wanted to know).

Does listening to music make you better at maths?

School classwork is done in silence, but homework is often done listening to music.

Certainly, when I was younger I always preferred doing maths exercises with the radio or the record player on.

Now when I play around with puzzles, or doodle mathematical thoughts, or do my tax returns I always have iTunes or Spotify providing a soundtrack.

I find it comforting, and I sense that background music somehow stimulates mathematical creativity and the ease of processing numbers � I’m not sure how, but it feels that way.

(Using words is different. I can’t write with music on. At all.)

Which is why I wasn’t surprised by .

When I tweeted about this story last month, a maths teacher at a got in touch to tell me that she plays CDs during her lessons.

Kathryn plays classical chill out music during her maths classes as a way of keeping the pupils focussed.

I’d never heard of this before � and assumed it would not be allowed � but Kathryn’s methods have even been praised by a school inspector as a good way to keep kids calm.

“With teenagers today being always plugged into music, to expect a silent classroom is bonkers,â€� she said. “To fill the silence with musicÌýis better than it being filled with chatter and gossip. I really do find that music keeps them on task and once they get used to it they will ask for it to go on if I have forgotten to turn it on.â€�

She said she doesn’t know if the music has improved results, but she added:

“I do know that it has improved the atmosphere especially in some of my more challenging classes.

Kathryn doesn’t have the music on when she is talking to the class, but she switches the CD player on for exercise work: “not very loud but loud enough for everyone to hear easily.�

Music is off for class assessments, however, as a way of preparing the students for external exams, in which music is forbidden.

Kathryn first played music during a maths lesson 14 years ago as a Friday afternoon treat to a class of 34 stuck in a room for 30.

“I found this kept them far calmer than usual. The pupils would behave all week so that they could listen on a Friday.�

At first she played commercial radio, but after reading about the � the hypothesis that listening to Mozart makes you smarter � she switched to classical.

I wondered if music helped certain areas of maths better than others?

“IÌýhaven’t found anything that doesn’t work well with music in the background, although there are some types of music that don’t work well with the students,â€� she replied. “They don’t mind most classical but opera is a no-no, as they don’t like it so they find it distracting. Also anything with words can be distracting as they will try to sing along.

“As a treat now and again I put more current music on. The younger ones like the Glee CDs, the older ones some Red Hot Chilli Peppers or Foo Fighters. The main CDs I play areÌýrelaxing classical album or chill-out classics. ÌýI think also the more challenging the topic the more music in the background keeps them on task, as they are less inclined to give up and start talking.â€�

In a culture where maths lessons are seen so negatively, maybe introducing music is a way to make children enjoy maths more � and, if the research is correct, it might even make them better mathematicians.

Erik Demaine's hinged dissection font

When creating typographic fonts, designers usually consider factors like elegance, readability and mood.

Erik Demaine was interested in none of the above.

He wanted to create fonts inspired by mathematics.

For example, imagine you have some pink circular gears glued to a table, as illustrated below. Is it possible to find a way to wrap a belt (or elastic band) around them so that the belt is taut and touches all gears? If you know tell Erik, since it’s an open problem.

Erik, together with Belén Palop and his father Martin Demaine, decided to turn this problem into a font in which the outline of each letter is a belt threaded through equal-sized gears. The belt is always taut and touches every gear:

The coolest thing about the font is what happens when you take the belt away. It looks like a painting of random dots (eat your heart out Damien Hirst) � but with fragments of order. When you keep on looking, gradually you can make out the words. It would make a great cipher � or plot puzzle in a Dan Brown-style book�

Erik, who is an MIT professor and a star in the world of recreational maths, is known for his work on computational origami. So it would have been churlish of him not to create an origami font.

In the origami maze font, in which Erik was assisted by his father and Jason Ku, each letter is the origami fold pattern that will produce a 3-d outline of the letter. So, in order to produce this

you have a fold pattern that looks like:

Which looks awesome and gives nothing away visually. Even if you are used to fold patterns � red are mountain folds and blue are valley folds � I dont think you can tell what it says by looking at it. So it would be an even better cipher.

Finally, Erik revisted one of the classic old school puzzles � that of the hinged dissection. In the image below the triangle is split into four pieces joined by hinges, which can be rearranged into a square.

In the hinged dissection font, every letter is made up of 128 small triangles all joined at the hinges and which can be rearranged into a square. Here’s how it works for A:

This font has real character. The constraints of the hinged dissection mean that each letter has the same area and cannot have very thin sections, which creates a chunky, macho and oddly artistic font that gives fashionable fonts a run for their money.

If you want to play around with the fonts, you can do so on , which also has longer papers on each of the fonts (and from which I took some of the images above).

Ìý

Ìý

Ìý

Ìý

Ìý

Ìý

Alan Turing, aged 16, at Sherborne in 1928 ©Sherborne School

My post yesterday about was my most read ever!

There’s obviously an appetite for Turing stuff � and so here is some more.

Rachel Hassall, the archivist at , where Turing was at school, has transcribed his entire school reports, printed below.

It’s interesting to see how he changes from an untidy and careless mathematician to a distinguished scholar.

At the end of his first term headmaster O� Hanlon writes: “He has his own furrow to plough & may not meet with general sympathy…�

At the end of his second term the maths teacher writes that he “should do well if he can quicken up a little.� Er, yes�

O’Hanlon ends by saying that he will watch Turing’s future career with much interest.

But no one will have predicted quite .

SHERBORNE SCHOOL

FORM IV.b.(i) Average Age 14.5

NAME Turing Age 14.5 MICHAELMAS TERM 1926.

Ìý

SECOND HALF TERM
Place for Half-Term

MASTER


ENGLISH SUBJECTS (Scripture, English, History, Geography)Ìý

No.24
14
Without being lazy, he seems to do his work rather perfunctorily.Ìý I should like to see rather more life in him.
F.J.S.M [Frederick James Stevenson Moore]


LATINÌý

No.
20
Rather poor.
F.J.S.M [Frederick James Stevenson Moore]


Set AÌý

FRENCH

No. 16
14
Improvement there was much room for improvement.Ìý French comes easy to him & he should do very well as I hope he will next term.
A.W. F [Armine W. Fox]


Set 8Ìý

GREEK

No. 17
16
Fair only � work rather capricious.
F.G.B. [Francis Guy Baring]


Set 3Ìý

MATHEMATICS

No. 19 placed
1
Works well.Ìý He is still very untidy.Ìý He must try to improve in this respect.
M.B.E. [Merrick Beaufoy Elderton]


Set 4Ìý

NATURAL SCIENCE

No. 17
3
He is keen & has a natural bent for science, but his work is badly spoilt by extreme untidiness.
A.J.P.A. [Arnold James Parkes Andrews]


Extras â€�Ìý

MUSIC

DRAWING

PRIVATE TUITION

Satisfactory work & progress.
L.D. [Leonard Davies, Art Master]


HOUSE REPORT

Slightly less dirty & untidy in his habits: & rather more conscious of a duty to mend his ways.Ìý He has his own furrow to plough, & may not meet with general sympathy: he seems cheerful, though I’m not always certain he really is so.
G. O’H [Geoffrey O’Hanlon]

Ìý

Ìý

Headmaster.

On back:

Best wishes for Xmas & the New Year. [G. O’Hanlon]

Ìý

Ìý

SHERBORNE SCHOOL

FORM IV.b. (i) Average Age 14.6

NAME Turing Age 14.8 LENT TERM 1927.

Ìý

FIRST ÌýHALF TERM
Place for Half-Term

MASTER


ENGLISH SUBJECTS (Scripture, English, History, Geography)Ìý

No. 20 (17 placed)
6
Very fair: he seems to have some taste for English & is reasonably industrious; but his work is rather lacking in life.
F.J.S.M [Frederick James Stevenson Moore]


LATINÌý

No.
12
Moderate: needs more concentration I think.
F.J.S.M [Frederick James Stevenson Moore]


Set yÌý

GREEK

No. 12 placed
11th
A fair half-term’s work, but he often seems to find the work very hard.
S.H. [Samuel Hey]


Set AÌý

FRENCH

No. 15
8=
His lack of interest is very depressing except when something amuses him.
A.W. F [Armine W. Fox]


Set IIÌý

MATHEMATICS

No. 18 placed
1
Very good.Ìý He has considerable powers of reasoning and should do well if he can quicken up a little and improve his style.
J.H.R. [John Hervey Randolph]


Set IIIÌý

PHYSICS
No order
Has done quite satisfactory work so far.Ìý

N.O.R. [Norman Oswald Rees]


NATURAL SCIENCEÌý

No. 14
-
Chemistry.Ìý Good
L.B.H-W [Lionel Bache Hornsby-Wright]


Extras â€�Ìý

MUSIC

DRAWING

PRIVATE TUITION





HOUSE REPORT

He is frankly not one who fits comfortably for himself into the ordinary life of the place � on the whole I think he is tidier.
G. O’H [Geoffrey O’Hanlon]

He should do very well when he finds his métier: but meantime he would do much better if he would try to do his best as a member of this school � he should have more espirit de corps.

Nowell Smith.

Headmaster.

On back:

I hope he’s going to get a few more games than hitherto: they’ll be good for him. [G. O’Hanlon]

Ìý

Ìý

SHERBORNE SCHOOL

FORM IV.b (i) Average Age 14.7

NAME Turing Age 14.9 LENT TERM 1927.

Ìý

SECOND HALF TERM
Place for Half-Term

MASTER


ENGLISH SUBJECTS (Scripture, English, History, Geography)Ìý

No.20
12
Since his absence from school his work has been very poor & he seems unable to concentrate.
F.J.S.M [Frederick James Stevenson Moore]


LATINÌý

No.
18
Careless & untidy.
F.J.S.M [Frederick James Stevenson Moore]


Set yÌý

GREEK

No. 14 placed
14
He seems to find the subject a very hard one & most of his work has been very poor in quality.Ìý I think he tries.
S.H. [Samuel Hey]


Set AÌý

FRENCH

No. 13
-
He has worked quite well.
A.W. F [Armine W. Fox]


Set IIÌý

MATHEMATICS

No. 18
1
A very good term’s work, but his style is dreadful and his paper always dirty.
J.H.R. [John Hervey Randolph]


Set IIIÌý

NATURAL SCIENCE

No. 14
4Ìý

13 placed

1
Physics Works quite wellÌý

Chemistry.Ìý Good
N.O.R. [Norman Oswald Rees]Ìý

L.B.H-W [Lionel Bache Hornsby-Wright]


Extras â€�Ìý

MUSIC

DRAWING

PRIVATE TUITION





HOUSE REPORT

Not any progress to note in tidiness.Ìý He can be very absent-minded & unmethodical.
G. O’H [Geoffrey O’Hanlon]

Ìý

He has been disappointing since his good start: I wonder why.Ìý Nowell Smith.

Headmaster.

On back:

Rather disappointing reading but your last letter perhaps suggests an answer.Ìý His ways sometimes tempt persecution: though I don’t think he is unhappy.Ìý Undeniably he is not a ‘normalâ€� boy: not the worse for that, but probably less happy. [G. O’Hanlon]

Ìý

Ìý

SHERBORNE SCHOOL

FORM IV.B (I) Average Age 14.8

NAME Turing Age 14.11 SUMMER TERM 1927.

Ìý

FIRST HALF TERM
Place for Half-Term

MASTER


ENGLISH SUBJECTS (Scripture, English, History, Geography)Ìý

No. 22
4
He has done fairly well on the whole, written work must be neater, though.
F.J.S.M [Frederick James Stevenson Moore]


LATINÌý

No.
17
His Latin work is for the most part careless & slovenly: he can do much better when he tries.
F.J.S.M [Frederick James Stevenson Moore]


SetÌý

GREEK

No.





Set AÌý

FRENCH

No. 18
14
Idle, he could do very well.
A.W. F [Armine W. Fox]


Set IIÌý

MATHEMATICS

No. 22
10
Not very good.Ìý He spends a good deal of time apparently in investigations in advanced mathematics to the neglect of his elementary work.Ìý A sound ground work is essential in any subject.Ìý His work is dirty.
J.H.R. [John Hervey Randolph]


Set IIÌý

NATURAL SCIENCE

No.
-
Chemistry.Ìý Promising.Ìý

Physics (Light) Good work.
C.P. [Clephan Palmer]Ìý

L.B.H-W [Lionel Bache Hornsby-Wright]


Extras â€�Ìý

MUSIC

DRAWING

PRIVATE TUITION

Science.Ìý His knowledge, though scrappy, is considerable.Ìý He will make rapid progress.
L.B.H-W [Lionel Bache Hornsby-Wright]


HOUSE REPORT

No doubt he is a strange mixture: trying to build a roof before he has laid the foundations.Ìý Having secured one privileged exemption, he is mistaken in acting as if idleness and indifference will procure further release from uncongenial subjects.
G. O’H [Geoffrey O’Hanlon]

Ìý

I hope he will not fall between two stools.Ìý If he is to stay at a Public School he must aim at becoming educated.Ìý If he is to be soley a scientific specialist, he is wasting time at a Public School.Ìý Nowell Smith.

Headmaster.

On back:

I am inclined to think his head is a little turned by his science.Ìý And now he has retired with mumps. [G. O’Hanlon]

Ìý

Ìý

SHERBORNE SCHOOL

FORM IV.b.(i) Average Age 14.10

NAME Turing Age 15.1 SUMMER TERM 1927.

Ìý

SECOND HALF TERM
Place for Half-Term

MASTER


ENGLISH SUBJECTS (Scripture, English, History, Geography)Ìý

No. 22 (13 placed)

Absent.



LATINÌý

No.





SetÌý

GREEK

No.





Set AÌý

FRENCH

No.





Set IIÌý

MATHEMATICS

No. 21
-
Despite absence he has done a really remarkable examination (1st paper).Ìý A mathematician I think.
J.H.R. [John Hervey Randolph]


NATURAL SCIENCEÌý

No.
-
Absent for the most part.
L.B.H-W [Lionel Bache Hornsby-Wright]


Extras â€�Ìý

MUSIC

DRAWING

PRIVATE TUITION

Science.Ìý It is a great pity he has been absent so much.Ìý He is very promising and gets on very quickly.
L.B.H-W [Lionel Bache Hornsby-Wright]


HOUSE REPORT

Rather more tidy:Ìý & the one paper I looked over of his was certainly better than I expected in neatness.Ìý He certainly has ideas & imagination.
G. O’H [Geoffrey O’Hanlon]

Ìý

He owes his place & prize entirely to Maths & Science, but he shewed improvement on the literary side.Ìý If he goes on as he is doing now he should do very well.Ìý Nowell Smith.

Headmaster.

On back:

He did very good exams, & confounded many folk.Ìý Slightly more tidy, but not noticeably willingly so.Ìý I hope you’ll enjoy trigonometry, & on holiday! [G. O’Hanlon]

Ìý

Ìý

‘Copied out. ÌýRegret original spoiled.Ìý A.H.T-R.â€�

SHERBORNE SCHOOL

FORM IV a (2) Average Age 16.5

NAME Turing Age 15.6 MICHAELMAS TERM 1927.

Ìý

SECOND HALF TERM
Place for Half-Term

MASTER


ENGLISH SUBJECTS (Scripture, English, History, Geography)Ìý

No. 23
23
I append one sheet of a recent History Paper, as it probably says more eloquently than I can where his weakness lies.Ìý I am bound to add that his work so far in exams, is of a higher standard, but that rather emphasises the needlessly low standard of the term.Ìý I fear he trusts too much to exams to pull him through â€� I like him personally.
A.H.T-R. [Alexander Trelawny-Ross]


LATINÌý

No. 21
21




SetÌý

GREEK

No.





Set AÌý

FRENCH

No. 14
6Ìý

placed
Still very untidy, but he has worked well.
E.P.C.C [E.P.C. Cotter]


Set IÌý

MATHEMATICS

No. 16
1
I think he has been somewhat tidier, though there is still plenty of room for improvement.Ìý A keen & able mathematician.
E.H. [Ernest Hodgson]


Set IÌý

NATURAL SCIENCE

No.

Physics.Ìý He shews considerable promise, but he must learn to express himself adequately.
H.S.G.[Henry Shorland Gervis]


Extras â€�Ìý

MUSIC

DRAWING

PRIVATE TUITION

Science.Ìý His intelligence is always good and he acquires a considerable amount of knowledge, but his methods in practical work are at present deplorable.Ìý He must learn the importance of scrupulous cleanliness and neatness, & of being able to set his work down on paper to advantage.
L.B.H-W [Lionel Bache Hornsby-Wright]


HOUSE REPORT

I have seen cleaner productions than this specimen, even from him.Ìý No doubt he is very aggravating: &he should know by now that I don’t care to find him boiling heaven knows what witchesâ€� brew by the aid of two guttering candles on a naked wooden window sill.Ìý However he has borne his afflictions very cheerfully: & undoubtedly has taken more trouble, e.g. with physical training.Ìý I am far from hopeless.
G. O’H [Geoffrey O’Hanlon]

Ìý

He is the kind of boy who is bound to be rather a problem in any school or community, being in some respects definitely anti-social.Ìý But I think in our community he has a good chance of developing his special gifts & at the same time learning some of the art of living.Ìý Nowell Smith.

Headmaster.

On back:

Not so anti-social as he was.Ìý He certainly has a saving sense of humour. [G. O’Hanlon]

Attached:

A copy of Turing’s history homework on Marius and Sulla.

Ìý

Ìý

SHERBORNE SCHOOL

FORM V.b.(II) Average Age 16.9

NAME Turing Age 15.8 LENT TERM 1928.

Ìý

SECOND HALF TERM
Place for Half-Term

MASTER


ENGLISH SUBJECTS (Scripture, English, History, Geography)Ìý

No. 22
20
His mind seems rather chaotic at present & he finds great difficulty in expressing himself.Ìý He should read more.
M.D.T. [Meredith Dillon Thomas]


LATINÌý

No. 21
20
He seems to try, but his work is dreadfully muddled.
M.D.T. [Meredith Dillon Thomas]


SetÌý

GREEK

No.





Set AÌý

FRENCH

No. 15
5
Quite satisfactory work.
W.J.B. [W.J. Bensly]


Set IÌý

MATHEMATICS

No. 16
3
Easily the best mathematician in the set.Ìý His position is caused byÌý untidiness and carelessness due largely to impatience to let on something great as soon as he has seen his way through a problem.
E.H. [Ernest Hodgson]


Set IÌý

NATURAL SCIENCE

No.

Physics.Ìý He has done some quite good work by himself in my room. Ìý

Good work.
L.B.H-W [Lionel Bache Hornsby-Wright]Ìý

H.S.G. [Henry Shorland Gervis]


Extras â€�Ìý

MUSIC

DRAWING

PRIVATE TUITION

Chemistry.Ìý His methods in practical work are, I hope, improving â€� otherwise good intelligent work.
L.B.H-W [Lionel Bache Hornsby-Wright]


HOUSE REPORT

He may be given a chance of taking the school certificate next term.Ìý If so he must be prepared to give up some maths & Science, & set to work at Latin, French & English.Ìý It would be worth his while.
G.O’H. [Geoffrey O’Hanlon]

I am recommending his trying for the School Certificate.Ìý He must obviously learn his lesson that the literary part of his work is not unimportant & needs his best efforts.Ìý C.L.F. Boughey. Headmaster.

On back:

I strongly recommend some work in writing.Ìý This as a preparation for Mr Bensly, who will feel no compunction in making life a burden & giving work to be done again.Ìý He has as good brains as any boy that’s been here, & they are good enough for him to get through even in ‘uselessâ€� subjects like Latin & French & English. His manner of presenting work is still disgusting & takes away much of the pleasure it should give.Ìý He doesn’t understand what bad manners bad writing & messy figures are . [G. O’Hanlon]

Ìý

Ìý

SHERBORNE SCHOOL

FORM V.b. (i) Average Age 15.6

NAME Turing Age 16.0 SUMMER TERM 1928.

Ìý

FIRSTÌý HALF TERM
Place for Half-Term

MASTER


ENGLISH SUBJECTS (Scripture, English, History, Geography)Ìý

No. 24
24
It is hard to believe that a boy who is so promising at Mathematics should be so feeble at English and Latin.Ìý Yet he has every inducement to do his best, and I take it that he is doing it.Ìý I detect slight improvement.
W.J.B. [W.J. Bensly]


LATINÌý

No. 24
24




SetÌý

GREEK

No.





Set AÌý

FRENCH

No. 18
4
Good work & progress.
A.W. F [Armine W. Fox]


Set IÌý

MATHEMATICS

No. -
_
He is now revising the work for the additional Mathematics Papers of the School certificate.
D.B.E. [Donald Birkby Eperson]


NATURAL SCIENCEÌý

No.

Revision work.Ìý

Set I Physics.Ìý Good work.
L.B.H-W [Lionel Bache Hornsby-Wright]Ìý

H.S.G. [Henry Shorland Gervis]


Extras â€�Ìý

MUSIC

DRAWING

PRIVATE TUITION





HOUSE REPORT

I only hope he will dish his form-master’s expectations.Ìý

(He did so with 7 credits in school certificates including English, French, Latin. [?Sara Turing].)
G.O’H. [Geoffrey O’Hanlon]

Ìý

C.L.F. Boughey.

Headmaster.

On back:

If he fails in Latin, his punishment will be that no facilities will be given for doing little, so in term time, & he will have to take the exam in holidays . [G. O’Hanlon]

Ìý

Ìý

SHERBORNE SCHOOL

FORM V.b.(i) Average Age 15.9

NAME Turing Age 16.1 SUMMER TERM 1928.

Ìý

SECOND HALF TERM
Place for Half-Term

MASTER


ENGLISH SUBJECTS (Scripture, English, History, Geography)Ìý

No. 27
21
His English work is becoming less feeble.Ìý He undoubtedly has brains, but is only slowly learning to apply them to subjects for which he has little interest.
W.J.B [W.J. Bensly]


LATINÌý

No. 27
25




SetÌý

GREEK

No.





Set AÌý

FRENCH

No.

Good: he should certainly succeed.
A.W. F [Armine W. Fox]


Set IÌý

MATHEMATICS

No.
-
He has been reading for the additional Mathematical Certificate papers more or less on his own, & should do well.
D.B.E. [Donald Birkby Eperson]


Set IÌý

NATURAL SCIENCE

No.

Physics. Good work.Ìý

Chemistry. I have seen very little of him this term.Ìý I hope he is doing very well in Cert.
H.S.G. [Henry Shorland Gervis]Ìý

L.B.H-W [Lionel Bache Hornsby-Wright]

Extras â€�Ìý

MUSIC

DRAWING

PRIVATE TUITION

Latin.Ìý Slow & unenterprising & very untidy.Ìý He ought to pass the Cert. but he may fail through carelessness.
R.S.T. [Reginald Stanley Thompson]


HOUSE REPORT

What work I glanced at in the Certificate appeared astonishingly legible & tidy.Ìý In person he is less untidy: in his study he is such that were I with him he would be daily belaboured.Ìý On the whole he is more hopeful.
G.O’H. [Geoffrey O’Hanlon]

Ìý

There is much advice in this report to which he had better attend, if he is to achieve any real success.Ìý C.L.F. Boughey.

Headmaster.

On back:

We must wait for results in September.Ìý But whatever the results, he will have to learn to do well drudgery-work work even in his own subjects. [G. O’Hanlon]

Ìý

Ìý

SHERBORNE SCHOOL

UPPER SCHOOL.ÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌý ÌýÌýÌýÌýÌýÌý REPORT FOR TERM.

FORM V.a (Group III) Average Age

NAME Turing Age 16 MICHAELMAS TERM 1928.

Ìý

MASTER


DIVINITY




PRINCIPAL SUBJECTS
Mathematics. This term has been spent, & the next two terms will have to be spent, in filling in the many gaps in his knowledge & organising it.Ìý He thinks very rapidly & is apt to be “brilliantâ€�, but unsound in some of his work.Ìý He is seldom defeated by a problem, but his methods are often crude, cumbersome & untidy.Ìý But thoroughness & polish will no doubt come in time.Ìý

Physics. Theoretical work is good but his practical work is poor � he is not a neat experimenter.

Chemistry.Ìý Good work on the whole.Ìý I hope he is trying to be less slovenly.
D.B.E. [Donald Birkby Eperson]Ìý

E.D. [Edwin Davis]

L.B.H-W [Lionel Bache Hornsby-Wright]


SUBSIDIARY SUBJECTS
French.Ìý [?Order 8th out 20]. Quite satisfactory.Ìý

English.Ìý Too sloppy.Ìý Must improve his reading.
C.W.W. [Charles William Wordsworth]Ìý

R.S.T. [Reginald Stanley Thompson]


MUSICÌý

DRAWING

EXTRA TUITION




HOUSE REPORT
Satisfactory.Ìý I am very glad that he is sociable & makes friends: & he seems unselfish in temper.Ìý He is certainly ambitious.
G.O’H. [Geoffrey O’Hanlon]

Ìý

This report is full of promise. ÌýÌýC.L.F. Boughey.

Headmaster.

On back:

Best wishes for Xmas. [G. O’Hanlon]

Ìý

Ìý

SHERBORNE SCHOOL

UPPER SCHOOL.ÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌý ÌýÌýÌýÌýÌýÌý REPORT FOR TERM.

FORM VIth. Group III Average Age

NAME Turing Age SUMMER TERM 1929.

Ìý

MASTER


DIVINITY




PRINCIPAL SUBJECTS
Chemistry.Ìý He is at last trying to improve his style in written work, with good results.Ìý

Mathematics.Ìý His work on Higher Certificate papers shows distinct promise, but he must realise that ability to put a neat & tidy solution on paper â€� intelligible & legible â€� is necessary for a first-rate mathematician.

Physics.Ìý He has done some good work but generally sets it down badly.Ìý He must remember that Cambridge will want sound knowledge rather than vague ideas.
A.J.P.A. [Arnold James Parkes Andrews]Ìý

D.B.E. [Donald Birkby Eperson]

H.S.G. [Henry Shorland Gervis]

SUBSIDIARY SUBJECTS
French.Ìý Fair. Ìý

His proses have been very weak.Ìý Most of the mistakes are elementary and the result of hasty work.

English. Reading weak.Ìý Essays show ideas but are more grandiose than [?pointed].
C.W.W.[Charles William Wordsworth]Ìý

H.H.B. [Herbert Henry Brown]

R.S.T. [Reginald Stanley Thompson]

A.K. [Alexander King]


MUSICÌý

DRAWING

EXTRA TUITION




HOUSE REPORT
I am quite satisfied with him: & am very glad he is ready to come out of his shell.Ìý His Higher Cert: papers were pretty good.
G.O’H. [Geoffrey O’Hanlon]

Ìý

Good.Ìý CL.F. Boughey.

Headmaster.

Ìý

Ìý

SHERBORNE SCHOOL

UPPER SCHOOL.ÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌý ÌýÌýÌýÌýÌýÌý REPORT FOR TERM.

FORM Group III.Ìý Sixth. Average Age 18.3

NAME Turing Age 18.1 SUMMER TERM 1930.

Ìý

MASTER


DIVINITY




PRINCIPAL SUBJECTS
Mathematics.Ìý He has faced the uninspiring task of revision & consolidation of his previous knowledge with determination, and I think he has succeeded in improving his style of written work, which is more convincing & less sketchy than last year.Ìý If he does not get flustered & relapse into slip-shod work, he should do very well in the H.C. this year.Ìý

Physics.Ìý He is doing much better work than this time last year partly because he knows more but chiefly because he is getting a more mature style.

D.B.E. [Donald Birkby Eperson]Ìý

Ìý

Ìý

Ìý

Ìý

H.S.G. [Henry Shorland Gervis]

Ìý


SUBSIDIARY SUBJECTS
Chemistry.Ìý Much sounder.Ìý He is now getting a much more all-round knowledge of the subject.Ìý

English.Ìý His reading is too deliberate.Ìý On paper he is usually sensible.

A.J.P.A. [Arnold James Parkes Andrews]Ìý

Ìý

R.S.T. [Reginald Stanley Thompson]

A.K. [Alexander King]


MUSICÌý

DRAWING

EXTRA TUITION




HOUSE REPORT
A good term.Ìý With some obvious minor failings, he has character.
G.O’H. [Geoffrey O’Hanlon]

Ìý

He seems to be going on very well indeed.Ìý C.L.F. Boughey.

Headmaster.

Ìý

Ìý

SHERBORNE SCHOOL

UPPER SCHOOL.ÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌý ÌýÌýÌýÌýÌýÌý REPORT FOR TERM.

FORM Group III. Sixth Average Age

NAME Turing AgeÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌý MICHAELMAS TERM 1930.

Ìý

MASTER


DIVINITY




PRINCIPAL SUBJECTS
Physics. He has done some excellent work, mostly strict training for his scholarship examination.Ìý I can only hope Cambridge will think as well of him as I do.Ìý

Mathematics. A really able mathematician.Ìý His trouble is his untidiness & poor style, but he has tried hard to improve in this.Ìý He sometimes fails over a simple problem by trying to do it by complicated methods, instead of by an elementary one.

Chemistry. If the questions suit him, he is certain of getting a scholarship: but I do not feel that his knowledge is sufficiently all-round to make him independent of luck in the examination.

H.S.G. [Henry Shorland Gervis]Ìý

M.B.E. [Merrick Beaufoy Elderton]

A.J.P.A. [Arnold James Parkes Andrews]

SUBSIDIARY SUBJECTS
German. He has made a good start, he should try to cultivate faster work.Ìý

English. Is perhaps more interested than he seems.Ìý I think he has gained something.

G.J.B.W. [Geoffrey John Bromehead Watkins]Ìý

A.H.T-R. [Alexander H. Trelawny-Ross]

MUSICÌý

DRAWING

EXTRA TUITION




HOUSE REPORT
A very good term.Ìý He wins respect both by brains & character.
G.O’H. [Geoffrey O’Hanlon]

Ìý

A good term.Ìý He is a distinguished & useful member of the community.Ìý I am very glad about his Scholarship.Ìý C.L.F. Boughey.

Headmaster.

Ìý

Ìý

SHERBORNE SCHOOL

UPPER SCHOOL.ÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌý ÌýÌýÌýÌýÌýÌý REPORT FOR TERM.

FORM Group III.Ìý Sixth. Average Age 17.5

NAME Turing Age 18.8 LENT TERM 1931.

Ìý

MASTER


DIVINITY




PRINCIPAL SUBJECTS
Mathematics.Ìý He has done some post-scholarship reading without encountering any serious difficulties.Ìý He should be able to take the Higher Certificate next July in his stride.Ìý

Physics.Ìý He continues to take a genuine interest in physics.

D.B.E. [Donald Birkby Eperson]Ìý

H.S.G. [Henry Shorland Gervis]

SUBSIDIARY SUBJECTS
English. Steady and intelligent work.Ìý

German. He does not seem to have any aptitude for languages.

A.H.T-R. [Alexander H. Trelawny-Ross]Ìý

G.J.B.W. [Geoffrey John Bromehead Watkins]

MUSICÌý

DRAWING

EXTRA TUITION




HOUSE REPORT
A good term.Ìý He takes a fatherly interest in his dormitory, & no doubt imparts his learning & curiosity to them. He played footer really well.Ìý

G.O’H. [Geoffrey O’Hanlon]

Ìý

C.L.F. Boughey.

Headmaster.

Ìý

Ìý

SHERBORNE SCHOOL

UPPER SCHOOL.ÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌýÌý ÌýÌýÌýÌýÌýÌý REPORT FOR TERM.

FORM Group III.Ìý Sixth. Average Age 17.8

NAME Turing Age 19 SUMMER TERM 1931.

Ìý

MASTER


DIVINITY




PRINCIPAL SUBJECTS
Mathematics. He has gone on with his reading as well as revising the elementary work for the Higher Certificate, & I expect him to get a Distinction with ease.Ìý He has my best wishes for an equally successful career at Cambridge.Ìý

Chemistry. He has done some useful revision.

Physics. He has done well: I wish him success at Cambridge.

D.B.E. [Donald Birkby Eperson]Ìý

A.J.P.A. [Arnold James Parkes Andrews]

H.S.G. [Henry Shorland Gervis

SUBSIDIARY SUBJECTS
German. He has worked hard.Ìý

English. Sound work with imagination and interest.

G.J.B.W. [Geoffrey John Bromehead Watkins]Ìý

A.H.T-R. [Alexander H. Trelawny-Ross]

MUSICÌý

DRAWING

EXTRA TUITION




HOUSE REPORT
He has had an interesting career, with varied experience: & brought it to a very successful close.Ìý I am grateful to him for his essentially loyal help: & I hope he will reap further reward at King’s, both in work & friendships.
G.O’H. [Geoffrey O’Hanlon]

Ìý

A gifted & distinguished boy, whose future career we shall watch with much interest.Ìý I have found him pleasant & friendly & I believe that he has justified his appointment as a School Prefect.Ìý C.L.F. Boughey.

Headmaster.

Ìý

Ìý

Alan Turing 1912-54

Ìý

Alan Turing was in the papers this week after scientists at Kings College vindicated his 60-year-old .

So it was very timely that an old friend who teaches at Sherborne, the school Turing attended between 1928 and 1930, got in touch this morning with a new information about the computer pioneer and codebreaker’s school years.

Sherborne archivist Rachel Hassall has uncovered the list of books Turing took out from the school library while he was a pupil. I’ve listed them below.

As you can see, and as you might expect � heavy on the sciences.

The AJ Evans, a memoir about the author’s escape from imprisonment in the First World War, is the only non-scientific book.

What struck me most however is that the physics books he took out all look very serious, but the maths ones are lighthearted: the Lewis Carroll and the Rouse Ball, which for decades was the classic text in recreational maths problems.

In fact, Hassall says that the book chosen by Turing for his school prize was a copy of the Rouse Ball.

Even teenage geniuses like to have fun.

NOTE: John Graham-Cumming has kindly provided links to free downloads to most of the books , since most are out of copyright.

AUTHOR
TITLE
EDITION
COPY


?
Illusions




?
Journal of the Chemical Society, vols. 95, 96, 97




?
Lead




?
Modern Electric Theory




?
Money




Aston, Frederick William
Isotopes
1922



Ball, W.W. Rouse
Mathematical Recreations and Essays
1905 ed.
Yes


Carroll, Lewis
Alice in Wonderland




Carroll, Lewis
The Game of Logic
1886



Carroll, Lewis
Through the Looking Glass




Clifford, William Kingdon
The Common Sense of the Exact Sciences
1885



Eddington, Sir Arthur Stanley
Space, Time and Gravitation
1920



Eddington, Sir Arthur Stanley
The Nature of the Physical WorldÌý

1928
Yes Ìý

(Physics Library)


Einstein, Albert
Sidelights on Relativity
1922



Evans, A.J.
The Escaping Club
1929



Fichte, Immanuel Hermann.Ìý Translated and edited by J.D. Morell.
Contributions toÌý Mental Philosophy
1860



Haas, Arthur. Translated by R. W. Lawson.
The New Physics
1924



Henderson, Hubert D.
Supply and Demand
1922



Jeans, Sir James Hopwood
The Stars in their Courses
1931



Jeans, Sir James Hopwood
The Universe Around Us
1929
Yes


Lodge, Sir Oliver
Atoms and Rays
1924
Yes Ìý

(Physics Library)


Lodge, Sir Oliver et al
Phases of Modern Science.Ìý Published in connection with the Science Exhibit arranged by a committee of the Royal Society at the British Empire Exhibition 1925.
1925



Maxwell, James Clerk
Matter and Motion
1876
Yes


Preston, Thomas
The Theory of Heat
1894



Roberts, Isaac
A Selection of Photographs of Stars, Star-Clusters & Nebulae, together with information concerning the instruments & the methods employed in the pursuit of celestial photography.
1893



Rood, Ogden Nicholas
Modern Chromatics: with applications to art and industry
1879



Sanford, Vera.Ìý Ed. John Wesley Young
A Short History of Mathematics
1930



Webb, Thomas William
Celestial Objects for Common Telescopes
1859



Whetham, William Cecil Dampier
The Recent Development of Physical Science
1904



Whitehead, Alfred North (OS)
Science and the Modern World
1925



Wood, Alexander
Sound Waves and their Uses
1930
Yes Ìý

(Physics Library)

Ìý

Ìý

Brazil may be the land of sunshine, sex and football � but it is also land of the rising nerd.

I’ve been in São Paulo this week giving a talk at what is billed as the largest nerd camp in the world.

It’s called and is a week-long jamboree for gamers, hackers, bloggers and black T-shirt wearers of all shapes and sizes.

It has taken over the largest conference space in Brazil � a massive hangar in central São Paulo. Most of the attendees, called “campuseiros�, are staying in one of the 5,500 tents in the indoor camping area, pictured above.

We’re in the middle of a tropical Summer here, so you can imagine how fuggy and muggy it is in there. Nice.

Another 2,000 or so people are staying in local hotels.

So, what are the campuseiros here for? Next to the camping area is a huge open space that includes stages for talks, stalls, chill-out zones and most importantly thousands of cables each with a 200MB internet connection. This space is open 24 hours a day for the length of the seven day event.

It seemed to me that most campuseiros were taking advantage of the connection in order to play games, download files and hang out on Facebook.

Not that interesting, at first. But when you look around you realize that this is a really fascinating event.

For a start, look at the list of sponsors � almost every large company in Brazil. Not only are they hoping to advertise to the smartest geeks in the country, but they are also here in order to recruit. This is where the best young programmers and tech entrepreneurs are hanging out.

As a measure of the event’s financial clout, it has flown in several speakers from all over the world, not just me�

There are lots of competitions, debates and demonstrations. Fun!

Campus Party was originally a Spanish idea, and there are similar events in Mexico and Colombia.

But nowhere has taken to it quite like Brazil, whose event is apparently the largest.

Brazilian nerds may be nerds, but they are also Brazilians: naturally sociable and easygoing. I spoke to one of the organizers and he said that the campuseiros in Brazil mixed much more with each other than the Campus Parties in other countries.

In other words, Campus Party is where connections are being made, where friendships are being formed. It’s a gigantic incubator of ideas.

This year for the first time a Campus Party will be held in a non-Spanish or Portuguese-speaking country. One is planned for San Francisco and another for Berlin.

We tend to assume that all the big nerd or geek movements come from the United States, Northern Europe or Japan.

Yet here is something that feels new and exciting that’s coming from the south.

Ìý

Ìý

A travelling salesman tour of the Mona Lisa

Ìý

The beauty of mathematics is essentially abstract, describing the aesthetic joy of a particularly clever proof or an unexpected result.

Yet some mathematics leads to a more traditional kind of beauty, the kind you might see in a piece of art.

Few research areas combine mathematical and visual beauty quite like the travelling salesman problem � a very simple problem that touches on incredibly deep maths, and generates gorgeous illustrations some of which have indeed hung in galleries.

The travelling salesman problem, or TSP, is the problem faced by a travelling salesman who must visit several cities and design the shortest route between them. The salesman must return to where he started after visiting each city only once.

As William J Cook explains in his fantastic new book,, the TSP is interesting to the mathematical community because it is so goddam hard!

To try to find the shortest route between 33 cities you need choose between

131,565,418,466,846,765,083,609,006,080,000,000 possible routes.

(And this is not because there are lots of different roads � we are considering only direct lines between the cities).

If we were comparing them one by one, and using, say, IBM’s Roadrunner supercomputer, one of the most powerful computers in the world, it would still take 28 trillion years to solve. Since the Earth has maybe only, this is evidently not ideal.

Cook tells the story of the race to solve the travelling salesman problem, as mathematicians thought up ingenious strategies � and also were helped out by increasing computer power.

In 1954, the fastest route between 48 US cities was known (It is shown on the cover of Cook’s book). In 1977, the TSP was solved for 120 cities. By 1992, the optimal route between 3038 cities had been calculated and the current record is a tour of 85,900 cities, calculated in 2006 using software called Concorde.

The ultimate travelling salesman problem � between all 1,904,711 cities, towns and villages in the world is still an open problem.

While the theoreticians were concerning themselves with the maths, other mathematicians saw that the TSP algorithms could provide remarkable artworks.The basic idea is to draw a number of dots and then just link them using the shortest possible line. In other words, each city is a dot, and the quickest tour of the cities provides you with an arresting image.

Here are some great examples:

Traveling Salesman, Julian Lethbridge, 1995

Because the salesman always returns to the starting point, you always get a closed curve, which means there is an inside and an outside. Here the inside of the curve is dark red and the outside lighter red.

A similar pattern can be seen in the artwork below. The artist Philip Galanter explains in some detail the maths behind the image

Ìý

mural by Philip Galanter

The gurus of TSP art however are the computer scientists and . (Click on their names to see their sites) Robert’s Mona Lisa below is created by placing 100,000 dots on a blank screen depending on the colour of the original painting, and then asking a computer to join them up in the shortest possible line. The solution is not optimal, however, meaning that there might be a solution with a shorter line, and if you find it Robert and William Cook are offering a Good luck!

POSTSCRIPT: William Cook has just launched a TSP app for iPhone and iPad, as a companion to the book. You can see how it finds the shortest route between a selection of random dots.

A Salford maths professor says this is the best possible arrangement of numbers around a dartboard.

No sport requires a knowledge of numbers quite like darts.

The rules are these. Each player starts with 501 points and every number hit must be subtracted from the total. The game is won by the first player to reach zero, with the added requirement that the last dart thrown must hit a double or the bull.

(A dart in the outer ring is a double, in that it doubles the value scored, and in the inner ring is a treble, which triples the score. The bull is worth 50.)

The fact that you can only finish on a doubleÌý favours players who are good at sums. When I interviewed darts legend Bobby George a couple of years ago he said: “If I hadn’t learnt to count I wouldn’t have won what I have won.

“For example, just say you have 126 left. People who can’t count go for treble 20. But if you miss and you get 20 you cannot finish from 106 with two darts.

“I would go for treble 19. If you you miss and get 19 you have 107 left, and you can finish with two darts � treble 19 and bull.�

George said that when he was starting out he would take his dartboard to bed with him to work out which numbers gave more chances to finish if he missed the treble of the number he as aiming for. He said that at first his opponents described his number selections as “unorthodox� but they soon saw the wisdom of his approach, even if some of them (mentioning no names) weren’t clever enough to work it out themselves.

“You can win more games if you can count.�

I was thinking about this last night as I was watching the World Darts Championship from Lakeside. I can’t really explain it, but I find watching darts incredibly nostalgic and addictive.

And i was reminded of an excellent talk I saw at the Mathsjam last year by about an issue that has interested mathematicians for years: What is the best possible positioning of numbers round a dartboard?

The current dartboard positions were devised by Brian Gamlin in 1896, pictured right. The 20 is at the top and the others are arranged in such a way as to put low numbers next to high numbers so that you are penalized if you go for � and miss � the highest numbers.

Dave decided he would have three constraints for his perfect board:

1) low numbers near high numbers to penalize over-ambitious players as above.

2) let the numbers alternate between odd and even.

3) let the board have rotational quasi-symmetry � in other words, let the different parts of the board look as similar as possible, so the same kinds of number are more or less evenly spread out.

When he crunched the numbers (and the theory here is not for beginners) he came out with the board at the top of this post, which is the optimal solution for the constraints. Ta-dah!

It’s interesting to note that 8 of the 20 numbers are in the same place as in Gamlin’s board.

A full analysis of Dave’s optimal dartboard will be appearing in a forthcoming issue of Mathematics Today.

Ìý

Ìý

Ìý

© Jeff Thompson

Following on from about pi’s random walk, just uploaded this:

It’s the square root of two randomly walking for a MILLION digits!

Looks like wispy smoke to me.

But then I always failed my Rorschach tests�

Actually, on Twitter people have suggested that it looks like:

A map of Japan.

A man on a hill standing over a defeated foe.

Now I see a kid in a hoody looking at his long shadow.

This site has a gallery of :

How about a new gallery of random walks that look like things?

Ìý