Here's a red dwarf, courtesy of Swinburne University. Such an object might be stable for as long as a trillion years.

http://astronomy.swin.edu.au/cms/astro/cosmos/R/Red+Dwarf

How many red dwarf stars are there in the observable universe (very roughly) and what is their combined mass (even more roughly)?

(Only estimates required but we want to see you working!  Well roughly.)

J.D. Salinger has died.

The immortal novel he wrote way back (1960?), The Catcher in the Rye, is a magic book, probably the best or second best American novel of the 20-th century.  He wrote some other stuff - short stories - and they are good too.

Something I remember from these stories is an attachment to haiku, I think a famous one by Issa is there somewhere

Don't swat it!
The fly is rubbing
Its hands and legs

Salinger then gave up publishing any work and  famously became an extreme recluse, refusing all publicity and repulsing interviews.

That doesn't seem so surprising or unreasonable; he seems to have been drawn towards a contemplative life, and had an interest in Zen.

We all know the rainbow, which is the result of sunlight (or any other light) bouncing around inside a raindrop.  The different colours return at different angles and so we see the coloured bands, like light shining through a prism.

Sunlight may also bounce round inside tiny prisms of ice.  These of course are six-sided, like snowflakes.  This can produce many different sky effects and where I live -- Cambridge UK -- the one called 'sun dogs' is quite common, in fact much more frequent than rainbows.

Most people have never seen them though, because they don't know where or when to look.

Once you have seen a thing you will probably see it again many times, even if you never previously knew it existed.  Learning makes us more aware.

Visit this site and you can find out more.  The evening sun dogs are the ones I have often seen.

Sadly there are no sun cats.

When a whale dies it usually sinks to the bottom.  This is called whale-fall.

The corpse will then nurture a diverse range of organisms, of a period of many years.  They follow a succession - like trees and shrubs in a forest growing up in a cleared area once it is left alone - and form a unique ecosystem.  A range of organisms are specialised to live only in these whale-falls.

That is quite surprising - to me anyway - but even more so is that fossil deposits have been found that looks like plesiosaur-falls: giant marine reptiles from long before whales existed died and sank and their carcasses supported communities much like those of present day whale-fall ecosystems.

A term from Zen.  The idea is that a beginner's mind is open.  From Zen Mind, Beginners' Mind by Shunryn Suzuki 'In the beginner's mind there are many possibilities, in the expert's there are few'.

I think teachers should always try to keep the beginners mind, so we rediscover our subject over and over again, and don't ever forget what it was like when we were just starting out.

That's the famous pi as in Π.  (I think it should have curly bits but the standard HTML character doesn't show any.)

Fabrice Bellard has just calculated this constant to

2699999999999

decimal places, using only a PC, see

This is a new record, for any computer.

The result occupies a bit over 1 TB (that's 10 Olympic swimming pools).  I think you will not want to download it all. Parts of it are available

here

This is certainly a triumph of human ingenuity and spirit.  But it's hard to say whether all the effort that goes into any sort of record-breaking is worth it or not.  I'd be really glad to know other people's views on this one.

Here's another minature, this time in a different tradition.

Again this is actual size.

There is some evidence we can and in an easy way, by exploiting the effect of 'psychological distance'.

Instead of thinking about a problem solely in terms of here and now, we should project our mind to distant places and times, try to consider the problem from another person's standpoint and so on.  How would the problem appear to an inhabitant of a planet billions of light years away?

Research reported in Scientific American suggest this technique may really help us to be more inventive and creative.

And how did the prisoner divide the rope?

More specifically there is some recent research to suggest that trying to answer the TMA (say) very quickly without any study of the unit - just jot down the best guess you can come up with - and only afterwards reading the relevant bits of the course may improve retention significantly. See http://www.scientificamerican.com/article.cfm?id=getting-it-wrong&sc=MND_20091029

In fact it seems the effect could apply if we do no more than for example try the SAQ before the related section, or even read the unit introduction, section or unit summary etc. before tackling the body of the unit.

I found this idea intriguing and intuitively appealing, but of course that isn't evidence.

Plankalkül

The first high-level programming language was Plankalkül, published in 1948 by the German inventor Konrad Zuse.

This language was very advanced for its time and already displayed many of the same structures we see today. Below is a sample program, followed by a working equivalent in JavaScript.

The program is not at all hard to follow. The only somewhat obscure part is in the declarations e.g. V0[:8.0], where the :8.0 seems to be reserving memory space for an integer represented in 8 bits.

<SCRIPT LANGUAGE=JAVASCRIPT>

/* Plankalkul example from Konrad Zuse
Original code:
P1 max3 (V0[:8.0],V1[:8.0],V2[:8.0]) => R0[:8.0]
max(V0[:8.0],V1[:8.0]) => Z1[:8.0]
max(Z1[:8.0],V2[:8.0]) => R0[:8.0]
END
P2 max (V0[:8.0],V1[:8.0]) => R0[:8.0]
V0[:8.0] => Z1[:8.0]
(Z1[:8.0] < V1[:8.0]) -> V1[:8.0] => Z1[:8.0]
Z1[:8.0] => R0[:8.0]
END
See http://en.wikipedia.org/wiki/Plankalkcül

JavaScript equivalent follows
*/

function max3(v0, v1, v2)
{
	var z1;
	z1 = max(v0, v1);
	z1 = max(z1, v2);
	return z1;
}

function max(v0, v1)
{
	var z1;
	z1 = v0;
	if (z1 < v1)
	{
		z1 = v1;
	}
	return z1;
}

// Try functions out
document.write('The maximum of 2, 3 and 1 is ' + max(2, 3, 1));

</SCRIPT>