## What’s the chance that you ever take the lead?

Posted in Cute Problems on January 25, 2014 by telescoper

Here’s one of an occasional series of cute problems, which I offer as a challenge for whiling away a wild and rainy Saturday afternoon..

You enter a competition which consists of a never-ending series of contests. The probability that you win any single contest is p, and the outcomes of the contests are independent of one another.

Let X be the probability that you ever take the lead in the competition. What is X in terms of p, for any value of p?

UPDATE: Since a correct answer has now been posted, here is my solution:

Consider the first contest: the probability that you win it is p and if you do you take the lead straight off.

If you lose the first one, with probability (1-p), you are down by 1. Now you must (a) make up the deficit and (b) go on to take the lead. Clearly the probability of (a) is just X (the same as getting ahead from a level start). The probability of (b) is also X.
Hence X=p+(1-p)X^2.

There are two solutions of this quadratic equation: X=1 and X=p/(1-p). But the answer must be a probability so cannot exceed unity. Hence if p>1/2 then X=1, in accord with intuition: in the long run you’d expect to lead sometime if p>1/2. If p<1/2 then the other solution is correct. The two solutions match at p=1/2.

Simples.

## The January Man

Posted in Uncategorized with tags , on January 25, 2014 by telescoper

The January man he walks the road
In woollen coat and boots of leather
The February man still shakes the snow
From off his hair and blows his hands
The man of March he sees the Spring and
Wonders what the year will bring
And hopes for better weather

Through April rains the man comes down
To watch the birds come in to share the summer
The man of May stands very still
Watching the children dance away the day
In June the man inside the man is young
And wants to lend a hand
And grins at each new colour

And in July the man in cotton shirt
He sits and thinks on being idle
The August man in thousands take the road
To watch the sea and find the sun
September man is standing near
And Autumn is his bridle

The man of new October takes the reins
And early frost is on his shoulder
The poor November man sees fire and rain
And snow and mist and wintery gale
December man looks through the snow
To let eleven brothers know
They’re all a little older

And the January man comes round again
In woollen coat and boots of leather
To take another turn and walk along
the icy road he knows so well
For the January man is here for
Starting each and every year

by Dave Goulder (1939-)

Posted in Education, The Universe and Stuff with tags , , , on January 24, 2014 by telescoper

An exciting new paper by a leading theoretical physicist prominent educationalist has just appeared on the arXiv. In it the author addresses the important question of whether information is destroyed in black holes students actually learn anything during lectures.

Until recently it was generally believed that any information falling into a black hole entering the mind of a student was lost forever even though black holes do evaporate students do take examinations after a finite time. This belief is motivated by the properties of Hawking radiation produced by black holes observations of examination scripts written by students, which some claim to be entirely random, i.e. devoid of any information content whatsoever.

This picture has however been challenged by a number of educationalists theorists with a variety of counter-arguments. For example, some have argued for a statistical interpretation in terms of the multiverse a very large class; although information may be destroyed in individual black holes students, in a infinite multiverse large enough class, there may be a finite number of examples in which some information is retained.

The latest article (referred to above) offers a different resolution of the Black Hole Information Student Education Paradox which rests on the idea that information radiated by black holes examination scripts written by students are not in fact entirely random, just produced so chaotically that, although information is present, for any practical purposes such information is so garbled that it is impossible to decipher.

This intriguing suggestion has led to a number of interesting, if somewhat speculative, extensions. Some have even argued that there may after all be some information present in the speeches of Education Minister Michael Gove, though this idea obviously remains highly controversial.

Stephen Hawking is 72.

## Eleven Plus Forty Years On

Posted in Biographical, Education with tags , , , on January 23, 2014 by telescoper

Today is the fortieth anniversary of an important historical event. Well, no. It’s not actually. It is however the fortieth anniversary of an important event in my life or, as they say on Facebook, a life event on my timeline.

On January 23rd 1974 (in the middle of the “Three Day Week“), I arrived at the Royal Grammar School in Newcastle upon Tyne to take the Eleven Plus entrance examination. The RGS was basically a private school, but it operated under what was called the Direct Grant system, which meant that applicants who did well in the entrance examination could have their fees paid by the local authority. That was the only possibility for me to go to there, in fact, as there was no way my parents could have afforded the fees. It wasn’t my idea to go for the examination either. I would have been happy to go to the local comprehensive with my friends from Pendower Junior School and in any case thought I faced humiliation in the examination, as I’d had no preparation for it (unlike many of the more well-to-do applicants). Nevertheless, my parents insisted and I turned up on a cold Thursday morning to take the test.

I remember little about the examination, except that it comprised several papers including one on English comprehension and another on Arithmetic. I’d never sat an examination before and I do remember that I found the whole thing excruciatingly hard. I think I found the Arithmetic paper so difficult that I almost decided to get up and leave; I may even have cried. I left with a sense of relief that it was all over, and a certainty that I would not be going to the RGS.

Nevertheless, a short time later, in February I think, I was summoned for an interview which experience terrified me despite the fact that the staff involved were really very kind and friendly. I was very surprised to have got that far.

Surprise turned to astonishment in March when the letter arrived (left) confirming that not only had I passed but I had been awarded the scholarship that I needed to allow me to go there. And before you ask why I kept the letter, I’ll admit that I also still have all my school reports from the RGS. Vanity is part of the reason, I suppose, but the other is to remind me of how lucky I’ve been with the opportunities that have come my way. I remain completely convinced that I got my place and scholarship as a result of some form of administrative error, but I vowed to make the best of the opportunity.

The UK education system has all changed (several times) since then, of course, and I often wonder how many youngsters far cleverer than me from working class backgrounds would nowadays have any chance of following a path like that which presented itself to me.

## Hot News! Supernova in M82

Posted in The Universe and Stuff with tags , , , , , on January 22, 2014 by telescoper

Very exciting news today – a supernova has gone off in Messier 82. In fact, according to this sequence of images from Japan it actually started to brighten about a week ago:

Being arranged in Japanese fashion, you have to read these from top to bottom but starting at the right, so the supernova can be seen to be steadily brightening, i.e. decreasing in magnitude from 17.0 to 11.9. That means it’s now visible with binoculars and will have been seen already by many amateur astronomers. The exciting question this time is whether we’ll get any neutrinos from it!

UPDATE: I’m told that, close as it is, M82 is probably too far to detect neutrinos. Boo.

This is the nearest supernova since 1987a which was observed in, er, 1987. This is the nearest Type Ia supernova for a very long time (possibly 1937), so it’s of considerable interest for the use of such objects in cosmology. There have been other close ones since the nearest one I can remember, 1987a, which was observed in, er, 1987 but all have been Type II.

UPDATE: Thanks for the people who pointed out my error which I’ve left in to show that I don’t know much about supernovae so you shouldn’t phone me up to ask.

## Tutorial 27: how to publish an open-access paper in a paywalled journal

Posted in Open Access on January 22, 2014 by telescoper

Some tips on how to get your paper published open-access despite a publisher’s paywall. Personally, I think you should go direct to Step 5…

I got in a conversation recently with a friend who is about to have his first paper published. It’s been through review and is now accepted at a well-respected old-school journal owned by a legacy publisher. It’s not an open-access journal, and he asked my advice on how he could make the paper open access.

We had a fruitful discussion, and we agreed that I’d write up the conclusions for this blog.

First, you can pay the publisher to open-access your paper. That’s a legitimate option at “hybrid OA” journals, which by this point is pretty much all paywalled journals. But even when the journal invites it, that’s not always possible. In this case, my friend has no institutional funds available, and really isn’t in a position to bung the publisher \$3000 out of his own pocket.

The second option is to write to the journal saying that you select the…

View original post 623 more words

Posted in Literature with tags , , on January 22, 2014 by telescoper

I work all day, and get half drunk at night.
Waking at four to soundless dark, I stare.
In time the curtain edges will grow light.
Till then I see what’s really always there:
Unresting death, a whole day nearer now,
Making all thought impossible but how
And where and when I shall myself die.
Flashes afresh to hold and horrify.

The mind blanks at the glare. Not in remorse
– The good not used, the love not given, time
Torn off unused – nor wretchedly because
An only life can take so long to climb
Clear of its wrong beginnings, and may never:
But at the total emptiness forever,
The sure extinction that we travel to
And shall be lost in always. Not to be here,
Not to be anywhere,
And soon; nothing more terrible, nothing more true.

This is a special way of being afraid
No trick dispels. Religion used to try,
Created to pretend we never die,
And specious stuff that says no rational being
Can fear a thing it cannot feel, not seeing
that this is what we fear – no sight, no sound,
No touch or taste or smell, nothing to think with,
Nothing to love or link with,
The anaesthetic from which none come round.

And so it stays just on the edge of vision,
A small unfocused blur, a standing chill
That slows each impulse down to indecision
Most things may never happen: this one will,
And realisation of it rages out
In furnace fear when we are caught without
People or drink. Courage is no good:
It means not scaring others. Being brave
Lets no-one off the grave.
Death is no different whined at than withstood.

Slowly light strengthens, and the room takes shape.
It stands plain as a wardrobe, what we know,
Have always known, know that we can’t escape
Yet can’t accept. One side will have to go.
Meanwhile telephones crouch, getting ready to ring
In locked-up offices, and all the uncaring
Intricate rented world begins to rouse.
The sky is white as clay, with no sun.
Work has to be done.
Postmen like doctors go from house to house.

by Philip Larkin (1922-1985).