Wednesday, 25 May 2016

English Spelling And History

Two things annoy me about how we write in this country.  One of them is our insistence on refusing to count in duodecimal.  We count in tens, like most of the rest of the world, and we have decimal currency and metric units, again like the rest of the world.  This is purely and simply disabling and there's no real reason for doing it.  People don't complain that much about numerical notation even though there is basically no justification for making arithmetic harder for everyone.

The other thing is of course English spelling.  English spelling is far from phonetic and makes literacy much harder for ourselves and people trying to learn English.  Moreover, for some reason the slightly more logical American spelling system is considered infra dig by most Brits, which is quite annoying in itself considering how much people complain about spelling.  However, unlike the use of base ten for numbers, English spelling does have some value and I think I've probably written about that elsewhere on this blog so I won't go on about it here.  The history of English spelling is quite interesting and carries with it the history of the English-speaking people, so it's an educational resource in that, and other, ways.

English writing begins before the English language even existed.  Around the beginning of the Christian era, Germanic tribes in what is now Northern Italy came into contact with the writing of the Rhaetic people, who may have spoken a language related to Etruscan or possibly a Celtic or Italic language, and adapted it for their own language.  Germanic was also written in an Etruscan-like script on the Helmet of Negau, possibly added later, in the form transliterated into our modern Latin alphabet as "HARIGAST TEIWAZ" - possibly "Harigast the Priest".  The word teiwaz lives on in today's English as the first syllable of the word "Tuesday", and means "god".  It's cognate with the Latin deus, the Greek θεός and the Sanskrit devas, all of which again mean "god".

The first widespread script used for Germanic languages was the Elder Futhark:



This was used to scratch inscriptions on the likes of bones, wood and stone, and resembles to some extent earlier rock carvings found in the prehistoric Germanic area.  The earliest Germanic writing found in Britain is in this script.  This is the fifth century deer bone found in Caistor, Norfolk, which has the word raihan written on it, thus:

This means "row" as in the thing you do with oars. At the time it would've been a reduplicative verb, meaning that certain forms referring to events in the past would have done so by repeating the stem, and coincidentally this type of verb survived longer in East Anglia than elsewhere in the seven kingdoms established by the Germanic invaders of the English heptarchy.  There are a couple of interesting things about this spelling.  One is that it uses a different character for "I" than usual, indicating that the proto-Germanic "AI" had a particular kind of pronunciation by this point.  The "H" also has a single bar, unlike the later Old English rune for the same letter, and this single-bar form is also found in Scandinavia.  This artifact dates from within three decades either side of the officially recorded arrival of the ancestors of the English in this land.  Before the arrival of Hengest and Horsa, however, there were already Germanic people living in Britain as part of the Roman army, including Saxons.

For the next century and a half, Old English was written using Anglo-Saxon runes, an alphabet known as the futhorc:

The last rune, stan, is said to be spurious for some reason.  There are not a huge number of inscriptions in this text although runes themselves continued to be used later as symbols for the words they stand for, and in fact I still use runes today when I'm writing something in public I don't want people to be able to read, for instance ideas for confidential matters involving people I know to pray for when I'm in church or medical notes, and the word "rune" originally meant "secret".

At this point in time, spelling was very simple:  you just wrote down what you heard.  Several different dialects of Germanic were spoken in the Heptarchy at the time, meaning that there was different spelling in different parts of the British lowlands, but this spelling represented the different pronunciations and accents rather than real variants in spelling which didn't correspond to a logical plan of some kind.  Reading was always out loud at the time, so it consisted of simply pronouncing the letters written on the page, and this continued well into the Middle Ages.

It appears also that there were still native Latin, and of course Celtic, speakers in lowland Great Britain at this time, the former of whom, if literate, would've been using the same alphabet as we do again today, but not much is known about them.

In 597, Augustine came to Kent and is said to have established the King's School in Canterbury, although to my mind there is a suspiciously long gap between that event and the earliest records of the place.  In doing so, he would've brought the Latin alphabet here and is the ultimate reason this blog entry uses it.  At around the same time, Irish missionaries entered more northwestern parts of Great Britain and introduced the same alphabet there.

Anglo-Saxon writing is dominated by West Saxon, since at that time and for a while after, the Kingdom of Wessex was dominant among the Anglo-Saxons.  The spelling and pronunciation of English was again pretty close.  There are, incidentally, ways of establishing how languages were pronounced before the advent of recorded sound but I can't be bothered to go into them here.  Just take my word for it.  West Saxon spelling is pretty clearly based on Latin but there were a few sounds in it which didn't exist in Latin and weren't even close.  Two of these were written using the relevant runes, namely þ (þorn) for the sound now represented as "TH", and ƿ (ƿynn) for "W".  That said, in some writing W was already written "UU" and "TH" was even written like that in some places.  Another sound, A as in today's southern pronunciation of "cat", was written using the Latin digraph for the diphthong we now pronounce as "I", that is, æ, also known as æsc - ash - after the name of the rune.  A further letter, ð, eð,  appeared later to indicate the softer "th" sound.

West Saxon didn't have a particularly strong influence on later English compared to other dialects, so today it seems idiosyncratic, particularly in its use of "eo" and its longer-vowelled sister.  However, this isn't really a spelling anomaly as far as anyone can tell, except that I suppose it's possible that people with other accents might sometimes have felt the pressure to "talk posh".  Coincidentally, "eo" has re-entered the English language due to a change in the pronunciation of "L", and is now found, for example, in the word "melt".  There is a little deviation from pronunciation also in the "ea" and long "ea" sounds, which started with æ when spoken.

Then we got invaded by the Danes of course, but that doesn't seem to have made much difference to spelling.  Some people think that English might actually be completely Scandinavian, but the Danes and the English in any case spoke languages similar enough to be kind of understood by each other and may have developed a patois to make themselves understood, from which modern English is descended.  After a period during which they controlled much of the Midlands, including Leicester, they left as a political power, though not necessarily the people themselves, and for the next hundred years or so we all sort of spoke English again.  However, one of the changes was that the sound represented by Y, which was previously like the French U today, started to be pronounced as "ee" and short I, identically to the letter I.  This led to the familiar old-fashioned looking confusion between Y and I and spellings like "hys" and "ys" for "his" and "is".  Another difference was that by this time, the English spoken in the Midlands was becoming more important than West Saxon.

Then, of course, the Normans invaded.  This meant that English became the language of the oppressed poor and they were largely illiterate.  The spelling of English then went two ways.  In the South, it started to be written using French spelling, meaning for example that the previous long U, though still pronounced "oo", was now written "ou" as in the French <<tout>>.  This eventually became our "ow" sound.  Meanwhile, in the Midlands and North English carried on being spelt as it was pronounced, more or less, I'm guessing because the Normans had less influence there.  The runes were used less, possibly because they had pagan overtones to the Normans, and were replaced by "TH" and "W" to some extent, though the old thorn survived in shorter words, and even today is recognised in phrases such as "Ye Olde Coffee Shoppe", where the supposed "Y" is in fact thorn.

During the twelfth century, some kind of spelling reform seemed to be attempted, possibly by just one monk called Orm.  He complains about how people are mispronouncing English and attempts to indicate short vowels by doubling the consonants after them and leaving them single after long vowels, using accents to show long vowels at the end of words and using yogh (ȝ) for the "J" sound of G and the newer letter "g" for the hard G.  This didn't catch on but it does serve to indicate a clue as to how Orm's English was pronounced at the time.

Another innovation from this period is the use of "wh" for "hw".  It's thought that this, along with the likes of "th", emerged from the French habit of using "ch" to indicate a sound which at the time sounded like our modern "ch" and therefore also a bit like the hard C.

England was basically a Norman colony by this point, but as time went by, ever more territory was lost in France and the focus of English monarchs became England.  This led to the return of English as the vernacular, until in 1362 the Statute of Pleading became law.  This allowed English to be used in court due to the loss of good knowledge of Norman French.  However, the English Crown only dropped the claim to France at the start of the nineteenth century, by which time France was a republic anyway.

English began to be written much more often at this point.  A drift can be seen in London English from a southern dialect to a Midlands one, meaning that the so-called "Queen's English" as heard today is originally not southern at all.  Southern English is more or less extinct nowadays, although there are a few remnants of it in words such as "vixen" and "vat", and the use of Z sounds in the Southwest instead of S at the beginnings of words.

What happened next is a bit of a mystery.  At some point soon after Chaucer, all the long vowels in English began to change pronunciation dramatically in a process which continues today.  The long U, by then written "ou", and the long I, began to change their pronunciation into diphthongs which in a sensibly spelt language would be written "au" and "ai" respectively.  This destabilised the whole system of long vowels, leading to a shift in all of them.  This is known as the Great Vowel Shift and may have been caused by the movement of people southwards after the Black Death killed much of the population of northern England, a process which also led to the increase in wages in the South and the Peasant's Revolt at the Poll Tax in the late fourteenth century.  The practical result of the vowel shift is that the way we write our vowels is dramatically different from virtually all other languages.

Most people were of course still illiterate in the fifteenth century, although being the century the printing press was invented, the production of books suddenly got a lot cheaper.  The Reformation also led to more people reading the Bible in English and William Caxton began to standardise English spelling again.

Later in Tudor times, the English began to explore the New World and establish colonies there.  Early American writing shows very little standardisation in its spelling.  Another effect of colonisation was that many new words entered the English language, for instance the names of fruits and vegetables new to European knowledge.  These were spelt differently and thus more variant spellings entered English although the ground had been laid for this possibility through the fact that the nature of our language had already been opened to foreign influence via Danish and Norman French many centuries before.  Many other languages, for instance Mandarin Chinese, lack the flexibility to allow foreign loanwords to any extent.

Later attempts were made to Latinise spelling, sometimes introducing dubious silent letters such as the B in "debt", which is related to the Latin debit but was never really present in the English spelling of the word, which used to be "dette".  Another non-historical example was the spelling of "could", which introduces an L by analogy with "should" and "would" which was never there at all historically.  Changes in pronunciation also meant that many letters, such as the K in "knight" and "know", ceased to be pronounced but stayed in the spelling, although in those cases they do serve to distinguish between those words and the identically pronounced "night" and "no".

American independence led to a split into two standard dialects of English, one spoken in the Commonwealth and the other in North America.  Canada uses an intermediate version of the spelling system, associated with Melvil Dewey, the inventor of the Dewey Decimal System used to classify library books.  His advocacy of spelling reform can be seen in the spelling of his own name, which he altered from "Melville".  Dewey was in fact much more radical than what survived in American spelling.  For instance, he spelt "philosophy" with two F's, and tried to introduce the macron, a horizontal line over long vowels still used in pronouncing dictionaries.  Although these didn't catch on, other ideas of his were adopted and survive in today's American English.

Speaking of American spelling, users of British English in the twenty-first century frequently find themselves hesitating regarding the way we spell words because the internet exposes us to so much American material.  There are now more words ending in "-ize" than there used to be in British English for this reason.  I would also contend that just as there was a time before English spelling was standardised, we may now be leaving this phase in the history of the language due to the common variant spellings of English found in places like social networks, text speech and internet fora.  Whereas we are very attached to the way English is spelt, I suspect this may soon become a thing of the past, and we will probably return to the idea that we spell as we hear the words in our heads when we write.  There's nothing new about this.  Also, unlike other countries we have never had an official body to standardise the language, which again reflects our history as a collection of cultures.

So there you go.  That's basically my account of the history of English spelling and as you can see it also constitutes a bit of a history lesson.  I can't guarantee everything is correct in this, so you may want to look into it yourself.  I just thought it would be a helpful and hopefully interesting educational resource, which is why it's on this blog.


Tuesday, 10 May 2016

Degrees, Minutes And Seconds

Here's a printable 360 degree protractor:


If you print this on plastic film and cut it out, you will have a protractor.  This to me is a tiny example of how post-scarcity would work because although you could in theory go down the local stationer's and buy a protractor, this one's available for free plus the cost of the ink and plastic.  In an ideal world, oh never mind.

The reason I've put this here, apart from it being a resource for home edders, which in theory is what this blog's supposed to be about, is that it clearly shows the 360 degrees of a circle.  Most people know degrees well enough to be able to understand what's meant by a ninety or forty-five degree angle.  One's surroundings can also be thought of as a 360 degree circle, meaning that the traditional description of objects being at "two o'clock" or "six o'clock" can generally be supplanted by talk of degrees.  It also turns up as a way of describing positions in the sky and on the surface of this planet and other roughly spherical celestial bodies such as Mercury, turning up as latitude and longitude:



In the case of the sky, i.e. the celestial sphere, there's a slightly different system where right ascension and declination replace longitude and latitude respectively, and whereas declination also uses degrees, right ascension uses hours, minutes and seconds.  I tend to think of it as representing the time something rises above the horizon even though that can't be exactly what it is:


This last system, however, is confusing because the words "minutes" and "seconds" refer to different things in different directions.  There are of course 86 400 seconds in a day, so the smallest complete unit of right ascension, a second, is in fact fifteen seconds of arc (arc seconds).  This is the bit I didn't explain.

Minutes and seconds are not just units of time but also of angle.  Perhaps surprisingly, neither of these two systems are completely metricated although metric systems for time and angle do exist.  I'll get back to those.  A minute of arc, or arc minute, is a sixtieth of a degree, that is a relatively tiny shift in direction which would be microscopic if it was marked on the above protractor.  However, in terms of things such as the night sky, the circle of vision and the surface of Earth, arc minutes are fairly large.  An arc minute, coincidentally, is the size of the smallest object visible to the naked eye.  An object an arc minute across would be a tenth of a millimetre across from a distance of twenty-five centimetres.  In fact it's not strictly true that a minute of arc is the smallest part of the visual field discernible because luminous objects are still visible even when they're much smaller and the brighter they are, the smaller they can be.  This means, for example, that the immense distances to the stars still doesn't render them invisible to most people even though they are far smaller than one minute of arc across.

Both big lights in the sky, the Sun and Cynthia, are well over a minute of arc across.  They are in fact both around thirty minutes of arc in diameter from here, meaning that solar eclipses are possible.  This is such an unlikely coincidence that unless there's some reason why habitable planets need such a ratio, solar eclipses are not only a wonder of the world but of the entire Milky Way.  It's unlikely that there are any other planets in this whole Galaxy which have solar eclipses, and in some imaginary Galactic Empire where faster than light travel is possible, this could make Earth a top tourist destination.

Arc minutes also turn up in the form of nautical miles.  If you went a quarter of the way round the equator you would have travelled ninety degrees.   A single degree of longitude on the equator is around fifty miles.  Hence in this context a mile on the equator can be thought of as a measure of angle as well as distance, but it's not a convenient unit because the planet is not exactly 25 000 miles in circumference.  It ought to be exactly 40 000 kilometres in circumference because the kilometre was originally defined as a ten thousandth of the distance between the North Pole and the Equator on a line across the surface passing through Calais.  This is not how it works due to surveying inaccuracies and the fact that the planet is slightly tangerine-shaped rather than absolutely spherical.  However, a nautical mile is defined in a similar way as a minute of longitude, which is 1852 metres, slightly more than the 1609-metre mile.  Knots are then defined as nautical miles per hour, thereby combining two angular sexigesimal (sixty-based) systems in a very neat and appealing way.

Unsurprisingly, minutes themselves are divided into sixty seconds in this system too.  A second of arc or arc second is a sixtieth of an arc minute, which is such a tiny angle that there are 3 600 in a degree.  Again, this sounds fairly useless but again it has many functions.  I'll just mention two.  Measured six months apart, Earth's orbit is 300 million kilometres across, so objects in space shift very slightly against their background in a process referred to as parallax.  The nearest star apart from the Sun shifts by slightly under one arc second in position due to this.  The distance over which an object would shift by this angle is known as a parsec - parallax of one second.  A parsec is just over three and a quarter light years.  Another use of an arc second is to describe the size of distant objects in the sky, so for instance yesterday Mercury was twelve arc seconds across as it crossed the Sun.  Pluto is between four and seven seconds in diameter as seen from here.

As I mentioned before, there are metric and decimal versions of angles.  One of these is the radian:


A radian is easy to describe but for me very hard to understand the point of.  It's simply the radius of a circle moved onto its circumference, or 360 degrees divided by π.  This is around 57 degrees.  I don't know why this is useful although programming languages tend to use it, so I have to use it.

Another decimal angle system was used on the Peter's Projection map, though not on this one:

By Strebe - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=16115242
I'm not a fan of the Peter's projection but that's another story.  Some versions of the Peter's world map divide the "globe" not into degrees but gradians.  There are four hundred of these in a circle instead of three hundred and sixty and they were probably invented by someone French.  They're used in surveying.

I hope this makes more sense now.

Monday, 9 May 2016

Sic Transit Mercurius Monday

This afternoon, there was a transit of Mercury.  That is, from our perspective the planet Mercury passed in front of the Sun.  This happens at seven, thirty-three and thirteen year intervals, in either May or November, and takes up to three hours.  If I remember correctly, and I might well not, the May transits are better than the November ones because during the May ones Mercury looks bigger because it's closer.  Mercury is on one occasion ten arc seconds across and on the other twelve.  Apparently people don't know what arc seconds are, so here's an explanation.  A circle is divided into three hundred and sixty degrees.  Each degree is divided into sixty minutes of arc and each minute of arc divided into sixty seconds of arc.  If you consider the three hundred and sixty degrees of the horizon and the sky from horizon to horizon to be a hundred and eighty degrees, the smallest non-luminous object which can be seen is one minute of arc across.  Mercury is up to twelve seconds across, so it would need to be magnified five times to be visible even as a dot crossing the Sun,

I've never knowingly seen Mercury.  During the transit of Venus on 8th June 2004, I managed to project the Sun onto a piece of paper and it was quite clear.  Transits of Venus are much rarer than those of Mercury because Venus, being further from the Sun than Mercury, takes longer to orbit it and so passes between us and the Sun less often.  They occur in pairs a few years apart separated by a century or so.  This sounds odd at first until you realise that in order for Venus to pass in front of the disc of the Sun it has to do so in the plane of Earth's orbit.  Normally Venus passes by the Sun on either side, but if it is passing from "below" or "above" through the equator of the Sun it will be clearly outlined.  It also has the "black drop" effect, where Venus looks like a drop of black liquid as it passes the limb of the Sun because of its atmosphere, which is extremely dense.  At ground level, the atmosphere of Venus is about as thick as the water a whole kilometre down in the ocean here on Earth.  I found the transit of Venus to be particularly interesting because Venus is about the same size as Earth and so it gives you an idea of the scale of the Solar System.

Mercury does this much more often, but has no substantial atmosphere and is only a little larger than Cynthia as well as being further away than Venus on the whole, so although its transits are much more frequent they're harder to see.  This is what I got today when I was trying to project the transit of Mercury:

I've posted this as a full size image and you still can't see Mercury on it.  I don't think I was in the right state of mind to image it.  In other words, it didn't work.

What you need to do is get either a refracting telescope or, as in this case, a pair of binoculars and place a plain white surface at the appropriate distance to get a clearly focussed image.  This is a little risky since you're focussing sunlight and it can break prisms and lenses and cause fires.  However, I think people worry too much about this since as a child I used to filter the Sun through overexposed negative photographic film and look directly at it through binoculars and I can still kind of see.  I have multiple blind spots but probably not because of this activity.

What I like about transits, solar eclipses and looking at the sun safely from a home ed perspective is that they're daylight astronomy.  Two big problems with astronomy and home ed are that if you have a bedtime, you generally don't get to do much of it at night and, as a consequence of this, it tends to get rather abstract.  For this reason I didn't do a lot of astronomy with the children when I was doing Big Science and I'm not keen although it and linguistics are probably my personal two favourite subjects.

This is how the planets concerned were lined up this afternoon at about 2 pm:


As you can see, the Sun, Mercury and Earth are in a straight line.  This happens to be true seen from the side as well:


The next question might be why Mercury looks bigger in May, i.e. why is it closer.  This is because of Kepler's First Law of Planetary Motion.  Planets move in elliptical orbits with the Sun at one focus, i,e. the Sun is never at the exact centre of an orbit because that would be too improbable, and orbits are never circular because that also would be too improbable.  The orbit of Mercury is also more elliptical than any other true planet, but less so than that of Pluto.  Here are the orbits of Mercury and Earth side by side:




The Sun is clearly off to one side in the left hand picture and Mercury also clearly has a much less circular orbit.

This is a close up of Mercury:


Seen from even closer, even experts can't distinguish between it and Cynthia although it lacks the seas of the latter.  The craters, however, look very similar.

In fact, although both of them are barren cratered balls of grey rock, Mercury actually has quite a lot in common with Earth and Mars rather than Cynthia.  Mercury and Earth are the densest planets with Venus a close second, whereas Mars and Cynthia are both only about two-thirds as dense as Earth, Venus and Mercury.  It's been suggested that the reason for this is that Mars and Cynthia are formed from the debris of the outer layers of the original body making Earth up and that we are in fact the bits that sunk to the bottom.  Mercury is a bit bigger than Cynthia but quite a bit smaller than Mars, the figures being:

Cynthia:  3476 km diameter.
Mercury:  4879 km
Mars:  6792 km
Earth:  12756 km.

Even though Mercury is quite a bit smaller than Mars, its higher density gives it a surface gravity about the same.  This is interesting because it means that if Mercury were to be at about the same distance from the Sun as Earth is, it would probably have an atmosphere about as dense as that of Mars and also be roughly the same temperature as we are, notwithstanding a weaker greenhouse effect.  However, the air would probably be somewhat thinner than the Martian air because it has a lower escape velocity, as smaller planets have, so gases leak away into space more easily.  This is because an object doesn't have to go as far to orbit the planet, so a gas particle doesn't either and is more likely to be lost.  Even so, if Mercury was at the same distance as Earth is from the Sun, its sky would be blue and have occasional clouds in it and it might even have a little liquid water on its surface.  However, it wouldn't really have seasons because unlike Earth and Mars it doesn't really tilt.  What it might have if its orbit were still the same shape is the same seasons in both northern and southern hemispheres.  It also has a fairly strong magnetic field partly due to having a large iron core, which would protect it from radiation somewhat, and at a greater distance from the Sun it would have a shorter day (its day currently lasts 56 of ours) because of the weaker tidal forces.  All of this, rather surprisingly, adds up to Mercury being a more friendly place for life in this scenario than Mars is.

Mercury, ironically, probably has no Mercury on its surface since during the day it's hotter than its boiling point.  Strangely, however, Mercury has water ice at one pole, in the crater Chao Meng-Fu, because it's in permanent shadow.

I was going to say a lot more about Mercury but it's past my bedtime, so goodnight!

Saturday, 30 April 2016

Dreamed-Up Alphabets

The last entry on this blog mentioned Vai.  Sarada complained that this was an unwarranted irrelevance, but a while after writing it I realised that the example makes quite an interesting story in connection with autonomous learning and invention.

The Vai people live in Liberia and Sierra Leone.  Almost all languages spoken today in Africa use either Latin or Arabic script.  There are some exceptions, notably Amharic, spoken in Ethiopia and using the Ge'ez script, and Berber languages of North West Africa, which use the Tifinagh scripts.  Coptic, which was originally Ancient Egyptian, uses an alphabet derived from demotic hieroglyphics and Greek, but is now only a liturgical language and is no longer spoken.

Vai, by contrast, uses this syllabary:


Unlike alphabets, syllabaries use one sign per syllable, as the name suggests.  The history of the Vai script is quite remarkable.  It was first written down in the early nineteenth century by Momolu Duwalu Bukele and is said to have been revealed to him in a dream!  This could, of course, merely be a picturesque origin story, but it's entirely feasible that this could have happened.  The Bach flower remedies are another example of a system revealed in a dream and are quite involved and complex.  I feel I should trust the opinion that it did come to him in a dream because the doubts expressed seem to be about not trusting people in an in-group.  It's also difficult to know whether to call the appearance of the Vai script discovery or invention:  did he think it up subconsciously or did he consciously invent it?  If the former, how much is that a revelation and how much is it subconscious invention?  It's similar to the issue of confabulation and false memories, which edges towards Mandela Effect territory.  Whatever else was the case, it's highly likely that Momolu Duwalu Bukele got the idea, consciously or otherwise, from another equally remarkable writing system.

Liberia has an unusual history, and forgive me if you know this because I have no idea what other people do and don't know.  Its history is evident in its flag:


which of course resembles a certain other flag.  In the early nineteenth century, the American Colonization Society established Liberia as an African homeland for free African Americans because they believed their presence in the American South would make slaves there rebel.  This policy was supported by Abraham Lincoln.  Later, other colonies were established in the area which did include freed slaves.  In 1847, the area became an independent republic based on the US constitution.  More recently, Liberia became known for being used as a flag of convenience and had the largest shipping registry in the world.

Due to its connections with North America, members of the Cherokee nation also emigrated there on occasion, and an early Vai inscription was in fact found on a Liberian house belonging to Austin Curtis, who was Cherokee.  This is significant because it so happens that the Cherokee language itself is one of the few Native American languages to have its own script.  Excluding Quechua with its quipu, the knotted strings used for I think accounting purposes, the only languages with their own script there which come to mind are Yucatec Maya, Nahuatl (which is arguably not a form of writing as such) and the Cree syllabary.  There may be others but I don't recall them.

Cherokee is unusual by virtue of the fact that its writing was invented by someone who was previously illiterate, namely Sequoyah.  Here it is in its modern form:



This is Sequoyah.  He was born in the late eighteenth century and invented the syllabary in the early nineteenth.  It was so successful that literacy among the Cherokee soon surpassed that of the European-American settlers around them.  Although he originally intended fot the characters to be ideograms - one symbol per word - he changed his mind and settled on one symbol per syllable, as it is today.  The Vai script has a similar history in that it too used to have ideograms but has mainly dropped them with one or two exceptions.  Latin has a few widely used ideograms today, including "@" and "&", and the numerals we use could also be seen in that way although they're not strictly part of our script as such, being used by peoples all over the world, including Cherokee itself.

Sequoyah developed his script by studying his copy of the Bible, which, being illiterate, he couldn't read.  The script is still used today by the Cherokee.

There are a couple of other examples of illiterate people creating scripts about which I know far less.   One of them is Hmong, a language spoken in parts of China and Indochina.  This is written in a script called Pahawh Hmong:

Once again, this is a syllabary, invented by one Shong Lue Yang, also known as the Mother Of Writing, in the twentieth century.  Living in Vietnam, he was an illiterate farmer and basketmaker living hand to mouth, who probably did see writing at some point.  Starting in 1959, he received a series of visions in which divine twins taught him this writing and commanded him to pass it on to his people, which clearly he proceeded to do.

Finally, although there may be others, there is the Nüshu script, a secret writing by otherwise illiterate women in Hunan province, China:


Nüshu came into existence many centuries ago but nobody knows exactly when except that it was some time between the years 900 and 1600.  Most of the population was illiterate at the time but women learned to write this script, which they used for poetry, and again it's syllabic.  In a sense, like some other forms of communication such as Laadan, it's a specifically female mode of writing.  It was suppressed by the Japanese in their occupation because of the possibility of being used for secret messages, and again later by the Maoists during and after the Cultural Revolution for the same reason.  The last native user of Nüshu died in 2004 although it's not lost, since it's known in academic circles.  I wish I knew more about it, and shortly will.  There's a website here.

The notable feature of all these scripts is that they're all syllabaries in spite of the other writing used where they came to be.  Hmong and Nüshu had ideographic script, namely Chinese characters, used around them and Vai and Cherokee, with alphabets used around them.  To me, this suggests that the "natural" form of human writing is not alphabetic, ideographic or even pictographic but for some reason syllabic - one syllable per symbol.  Also, this has happened at least four times.

Why is this here, on this blog?  Well, to me this is a supreme example of what can be achieved by supposedly uneducated, illiterate people without any formal instruction, at least from other human beings.  Also, given the sources of information, at least two arrived in the human psyche from dreamlike states, at least according to the origin stories.  This shows how there's a sense in which we don't need to be taught to learn how to read and write, although on the whole if we never were we would presumably end up with hundreds or thousands of mutually unreadable forms of writing.  It also illustrates how we can even learn, discover and invent massively useful things in our sleep or at least in non-waking states of consciousness, even if it turns out that the information is from supernatural sources.  That's not a necessary supposition of course, and I prefer to think of this as in those two ways a marvellous instance of how amazing human beings are as a species.

Sunday, 24 April 2016

Introduction To Home Education

This coming Monday, I'll be giving a talk on home ed at my church You And Me friendship group,  As I'm aiming for it to be an informative introduction for the general public, I thought I'd also put roughly what I'm going to say here.

The popular American term for home education is homeschooling.  This rarely describes what happens in families whose children's education does not include school as the approach taken in school is oriented towards large groups of children roughly the same age outside the wider community.  Although there are as many takes as families or even children, few resemble classroom learning.  "School at home" does sometimes happen but is unpopular and considered inappropriate and inefficient, and when it happens it's often a phase.  It's not home schooling.

Nor is it really home education any more than education in schools is school education.  Children and adults learn all the time and it would be very difficult to create an environment where humans don't learn.  People even   solve problems and discover things in their sleep.  Much of organic chemistry is based on something a scientist originally had in a dream and the Vai script in West Africa also came to its inventor in a dream, so educational premises could be seen as the inside of a child's head or the whole Universe.  Less flippantly, home education doesn't mainly take place in the home but in all sorts of places:  on shopping trips, walks, visits to grandma, in the park, in places of worship, at youth clubs and basically anywhere children and their carers might go.  On the whole, so-called "home education" takes place in the community, one reason why the fear that it could be used as a cover for child abuse is misdirected.  Some, though, think stressing home is important because they see the home environment as something which is being unfairly stigmatised and distrusted, which they might see, for example, as part of an attempt to oppose family values.

Another important idea to get past is that we are a group apart from the rest of society.  Almost all parents home educate and almost all children are home edded almost all the time.  Five hours of lessons over 200 school days a year and twelve years of school education, makes twelve thousand hours.  Childhood lasts 157 788 hours, so over 92% of a schoolchild's life is spent outside lessons.  Some of that is in school of course but most isn't.  Moreover, almost all children are educated at home full time for the first few years of their lives, and it's been argued that almost everything a child learns is in those few years.  Supposedly we learn 80% of what we know as adults takes place by our second birthdays, about which I'm sceptical but it still expresses an important truth about how people learn.  When you consider that during that time we became fluent in English, much of what else we might achieve later is not that much more of an achievement. It isn't us and them.  Almost all parents home educate, even after the children go to school.  If we're in a shop with a child who tries to take something without paying for it, it's more our responsibility to discipline that child than the police or the shop, and that's a form of moral and legal education.  In a sense, home education is just parenting.  We just carried on doing what everyone else did before their children went to school, adjusting as we went along according to age.  Parents don't just keep pre-school children at home.  They take them shopping, on holiday, to the park and to parent and toddler groups, and the same is true of us.  Also, when parents do take their children on holiday or to parent and toddler groups, they're generally trusted to look after them and there are plenty of other adults around to ensure that they do so, another safeguard against child abuse.

Universal compulsory education has only been around since the late eighteenth century anywhere in the world, and for the English only since mid-Victorian times.  Before, there were dame schools and ragged schools.  Although these have been much maligned, it's important to remember that history is taught by the winners.  Before that, children learned on the job, and although this involved appalling exploitation and wasted potential, it still brought us through from our earliest stone age beginnings to a fully-fledged industrial society.

Responsibility is one motivation for home education.  Few people think twice about feeding, clothing or providing shelter for their own children because we just are responsible for them in this way.  A parent wouldn't expect others to take responsibility for their child in these respects.  Similarly, we  didn't consider it the responsibility of other adults to take care of our children's learning.  That doesn't mean that they shouldn't be taught if the need arose.  Even so, the law states that parents, not schools, are responsible for their children's education, and also according to the law, the school system is an opt-in system, not an opt-out one, a point which is obscured by the fact that most people do in fact opt in, sometimes because they're unaware of the fact.

One very important and valuable function of schools is that they take care of children while parents are doing paid work incompatible with having their own children around, so it's clear that schools will sometimes be needed.  Moreover, we all benefit from people who have been through the school system in all sorts of ways and our society depends on such people.  That doesn't mean, however, that everyone or even most people should go to school.  If they didn't, society would have to be very different from how it now is and parenting would probably have to be more evenly divided and probably also shared with other relatives and neighbours.  Workplaces would also have to be more flexible in their acceptance of children, more people would have to work from home and more people would probably be self-employed.  There would have to be all sorts of changes, but I see most of these changes as good.  Nonetheless, society being the way it now is doesn't stop home ed from happening.

This raises the question of whether home education is time-consuming.  To answer that question I want to assume for a moment that we actually had done school at home.  Going back to the thousand hours a year spent in lessons, we can think about the traditional two-parent family with one home educated child, which however isn't the only kind of family that does this.  A thousand hours spent a year in lessons, which are 365 days a year rather than two hundred, makes two and three quarter hours of lessons a day.  Since there are two parents, dividing this workload between them gets us to one hour and twenty-odd minutes a day per parent.  Add to that the fact that the child gets much more attention than they could ever get in class from teachers and teaching assistants and that not all teaching is input and the situation looks even easier.  This scenario is rather unrealistic though, because as I've said, most parents don't do school at home and they don't do things in isolation, so there will be all sorts of other adult helpers out there among family friends, people running activity days for children and even private tutors if that's considered necessary.  This means the workload really wouldn't be very heavy even with school at home.

As I said. few people do school at home.  Our structure was largely in my head and partly in Sarada's, but not really presented to the children as structure.  What I mainly did was to plan a whole load of possible educational programmes in my head first and wait until the children expressed an interest.  When they did, I could launch them on their way with a few ideas, activities, discussions and the like and because the interest had come from them, they would learn very efficiently due to being highly motivated.  It's also possible to make connections across subject areas more easily, meaning that rarely would such an interaction merely involve, say, geography, science, language or history, but more often all of them at once, again motivated by their interest.  Thus although we didn't follow the National Curriculum, I did have it in my head as a sort of bingo card where I was able to fill in the blanks.  What I found was that topics in the National Curriculum were covered so fast that a year's worth of work would take a maximum of about six weeks, meaning that if I had just followed the National Curriculum I would be twiddling my thumbs most of the time.  This is because there's no need to proceed at the rate of a whole class of children and do so regardless of interest or motivation, which are other factors in rendering schooling quite inefficient.

It's neither necessary to be an expert or a teacher to do this, and it's not required by the law either, although it so happens that Sarada is a qualified schoolteacher.  We are instinctively capable of helping others learn, particularly our own children, and they are instinctively capable of learning, because those two things are part of the human condition in the same way as migration might be for a bird or gathering nectar and spinning cobwebs are for bees and spiders.  We just are capable of doing these things.  Teacher training is necessary and important for the kind of education which takes place in schools, but learning otherwise than at school doesn't have such constraints and happens much more fluidly.  Studies show that home educated children are on average about two years ahead of their contemporaries at school.  They also show that adults who have not been to school are more likely to be successful entrepreneurs, are more motivated and productive in their paid work, are better adjusted psychologically and more active citizens socially and politically.  They also earn more.  If you want to look at it this way, home education is in some ways like private education compared to state education.  It also shares with much private education a full-time learning environment and small staff-student ratios.  Unlike that, it's accessible to even the poorest while giving them the same benefits.

A home edding parent needn't be an expert.  Children learning by osmosis continue to do so.  In particular, with online resources, museums, public libraries and other institutions, plenty of resources are available.  Where parents do teach, it often becomes clear that it's superfluous.  As with many educational situations they are learning just ahead of their pupils and then passing it on to them, and this can sometimes be helpful but it often becomes clear that you should just cut out the intermediary and let the children get on with it.  Where experts are of benefit, they are often available through social contacts because in general adults do use their education in work, so if you don't know someone else very often will.  I offered various sessions during my time, such as natural dyeing, nature walks, cookery, classical languages, German, biology, chemistry, physics and maths.  Other people offered other things such as literacy, music, French, Spanish and pottery, some at IGCSE level.

This brings me to the question of interacting with conventional education.  It has been possible to get into university via testimonial or directly by interview, and to get paid work in similar ways.  Home educated children tend to access higher education earlier or later than children who have been through the school system.  In terms of formal qualifications, there are a number of options.  One is to do IGCSEs, which are the international equivalent of GCSEs and have no coursework element, making them easier to do because of no need for official supervision of the work.  I made a point of splitting the science into three subjects, or more precisely biology and the two others, in order to account for people unable to reconcile evolution with their belief systems.  After a short period, I found that even separating the subjects at GCSE rather than doing simply science only occupied us for a couple of months.  There is also the problem of mistakes in the curriculum having to be taught and the lack of emphasis on scientific method.  Science at GCSE level tends to be about a series of "facts" rather than science itself.

It's often asked how home edders can do science or maths, but these are in fact extremely easy.  Maths in particular is one of the easiest of all subjects to study as it requires no special equipment at all but simply clear thinking.  Something I would have liked to pursue more but lacked the chance to was the possibility of approaching maths as intuitive rather than relying on conscious thinking and methods to arrive at results.  I'm still sure this can be done for various aspects.  Science can require more equipment but it's still possible to get quite a long way by choosing carefully.  For instance, it's possible to make copper sulphate from electrical wiring and a type of sink unblocker, and from this, the principle of exothermic reactions and water of crystallisation can be demonstrated.  If there is any special equipment, it can be borrowed or bought second hand from other home edding groups which have got further than you.  Learning in groups is generally about socialising for the children but they do pick things up quite readily even so.

This still sounds like school, but a popular approach is autonomous education as inspired by John Holt and John Taylor Ghatto.  This involves little or no input from parents and trust that the children will learn as they go along.  This formed a substantial part of our educational philosophy although we were probably more structured than most.  Other influences include Montessori, which we didn't pursue, the Rudolf Steiner approach, based on Goethean thought, and the Trivium, popular among Christian groups.  The Trivium as approached today is based on classical education as found among patricians in Roman times but differs from it in that it doesn't use the Quadrivium and uses grammar, logic and rhetoric arranged chronologically for three stages of education, the first involving the learning of facts, the middle their mental processing and the final the nature of expression and persuasion.  For all I know there are also people who use classical education as such, but I haven't come across them.  This may be more popular in North America.

Motives for home education vary.  In the UK, religion is seldom the reason families choose it although it's quite common among Muslims.  Whatever the faith, the choice often arises from objecting to the values seen to be instilled among children who go to school, and this does sometimes include sex education.  Having said that, those who object to the idea that children are being kept away from school by their parents because they prefer them to be homophobic and transphobic might want to consider how they would feel if things were the other way round, as was the case when Section 28 was in force.  From the late-1980s onwards, when teachers were banned from promoting homosexuality, which was clearly homophobic, and it would be entirely understandable for a child to be removed from school for that reason.

This raises the issue of bullying, which is another reason for home education.  If parents feel that a school will not address it, they sometimes withdraw their child from school.  This relates to the LGBT issue if it's motivated by some form of non-conformity such as gender.  On the subject of bullying, this has been known to happen between all groups at school - of children by teachers, of teachers by children and between staff and parents, and preventing it was one motive we had for making our children aware of their choice to attend school or not and to change that at any time.  Non-neurotypicality or special needs are other reasons parents choose not to send their children to school or withdraw them.  The general idea with all of these involves the thought that parents understand and know the needs of their children better than strangers even if those strangers are educational or healthcare professionals, which opens up another set of concerns regarding choices over healthcare and medicalisation which are too complex to go into here.

Another set of people are those pursuing the continuum concept.  This begins with contact parenting, co-sleeping and breastfeeding which is perceived as long-term by some others.  Many such parents find it feels very unnatural to have the children go to school after they've done that.

People often ask "Is there a problem with socialisation?", to which the flippant answer is "yes, there's too much of it!".  Home edded children are not socially isolated at all.  They are out in the community, they see their extended family, they may go to youth groups such as the guides and the scouts, they have after school clubs, places of worship, gym, dance classes or simply their neighbours.  Within the home ed community there are regular social get-togethers, sleepovers, educational activities pursued together and they make friends at least as readily as other children do. Less prevalent are bullying, cliquishness and anti-intellectualism, which helps both socialisation and other kinds of education, although these can also occur.

It might sometimes seem that this can only be done by people able to rely on a large reliable income or staying out of paid employment, but this is not usually so.  However, it is the case that I have personally lost opportunities due to the situation, although this may be more down to my own attitude than anything else.  

Personally, the situation was as follows.  As a child, I went to a primary school with very large class sizes. Mine had forty-six pupils.  This meant that much of what went on in the classroom was management and discipline rather than learning.  I seem to be unable to perceive what conformity is and even less able to conform,  Consequently, the teacher used to discipline me in various ways, such as locking me in a cupboard all day or making me stand out in the snow in my underwear.  There was also a problem in that none of the content of the curriculum was unfamiliar to me and they didn't teach anything I hadn't already found out years previously.  I was later moved to another school which was much smaller and less problematic and of course later went to secondary school.  The chief benefit of secondary school was that I made friends and was able to have some independence from home life.  Consequently, my view of school education became that it tended to aim very low academically and was a distraction from proper learning.

Sarada's experience seems to have been more on the side of teaching.  She was subject to a lot of workplace bullying when she taught and eventually left school teaching altogether.  Therefore, when we got together, we were both very much against the idea of our children having to go to school if they chose not to.  They eventually decided to go to college at about the age of fourteen, so they did.

I freely admit that another motive of mine for home edding was the fact that I was the children's father rather than their mother, which meant there was an enduring sense of longing and bereavement that I had neither carried nor breastfed my own children.  This is clearly unusual and influenced my decision but at the same time, although the motive of compensating for not being their mother existed, I see it more as something which helped me discover the right choice for them.

Our daughter is now in her second year at university reading for a bachelor's degree in English Literature with Creative Writing.  Due to the fact that she only started formal education a few years ago, she has not undergone the commonly seen steady decline in enthusiasm found in some other students and she has chosen consciously to do a degree rather than it simply being the next stage and what everyone else does.  She's involved in student politics, has a job and lives with her partner of three years.  Our son was able to start college a year early and achieved a lot, but his progress has been waylaid somewhat by succumbing to a critical illness which involved long-term hospitalisation.  It's impossible to know how things would've turned out had they gone to school but we don't regret our decision at all.

Tuesday, 12 April 2016

Indigo Children



I'm going to try to plough a middle furrow here.  There are people who are very into the idea of indigo children and there are others who regard them as mumbo-jumbo.  I don't really fall into either camp, as usual.

Science fiction, although generally about the present rather than the future, is often quite good at prediction, often with technology and its social consequences.  I often feel that it's slightly spoilt by a tendency to change only one variable, like a scientific experiment.  Just plucking a random example out of the air, Asimov's robot stories tend to be very much set in the mid-twentieth century when they were written with the difference that there are robots with similar intellectual capabilities to human adults.  Change in the real world occurs along many lines at once, so for example we have the influence of social media following on from the advent of the Web at the same time as medical innovations changing the way we look at ourselves, genetic modification, fracking, climate change and a resurgence in religious fundamentalism combined with increasing tolerance of sexual minorities, just to pluck a few things out of the air.  Then again, sometimes there are apparently single changes so momentous that history gets divided into before and after.  9/11 would clearly be an example of this, as would Tim Berners-Lee's invention of the World Wide Web.

One example of such a change depicted in science fiction, but somewhat tangential to the mainstream view of science and technology, is that of special children appearing with super powers, and I've just discussed this elsewhere.  It's found in various other places as well, not always in such a positive light.  



Jerome Bixby's It's a Good Life, published in the same year as Clarke's Childhood's End is particularly haunting in this respect.  There's a similar character in Stapledon's Odd John, but the majority of superhumans in that book are basically good, though morally ambiguous from a baseline human perspective.  This moral ambiguity reflects alternative ways of seeing children.



A somewhat similar idea applied to real life is that of Indigo Children.  The name comes from Nancy Ann Tappe about forty years ago, who said that she saw indigo auras around some children whom she expected to be special in the new age to come.  Indigo children are said to be highly intelligent, not compliant with schooling, empathic, strong-willed, having strong innate spirituality, intuition and purposefulness.  They are also seen as strange by others and are described as having a strong sense of entitlement.  I have come across children described as Indigo myself, as it was a popular in the 1990s and 2000s in home ed circles, which considering their perceived resistance to schooling is unsurprising.

It's difficult to mention the idea of a sense of entitlement without seeing it as a criticism, but in this case it seems to be seen as positive.  I don't know what I think about that to be honest, but then again, I don't know what to think about the whole thing,  However, there are other people who do know what they think about the whole thing, and it's not the same as what the indigo children's parents think at all.  Some psychologists take the view that the construction of the concept of these children is a response to the diagnosis of particular developmental issues in them such as ADHD, ADD and autism.  The idea is that parents of indigo children prefer to see them in this way rather than as labelled as in some way defective.  That idea suggests a certain degree of self-assurance on the part of both the parents and the healthcare professionals involved, and also an idea that the current social status quo is in some way the right way to be, or in some way unchangeable.  It is possible that this is the case, of course, but in view of the fact that this society gives the impression of always having been massively dysfunctional, I don't see it this way.  My view of diagnoses such as ADHD and autism is that where they are accurate in terms of criteria, they reflect a poor fit between the cultural milieu and the way the person receiving the diagnosis is, which may or may not be helpful for them. It may be helpful as a source of explanation to them for their difficulties which suggests a way forward, and there's no real need to explain why it might not be helpful.

There is a more significant problem with the idea of indigo children, namely that it sets certain children aside as more special than others.  Many people whose children's education doesn't include time at school would say that schooling simply fails most children both as a means of letting them be children and as a way of enabling them to achieve anything like their full potential.  Hence the criterion above of children who are not compliant with schooling could apply to almost any child in many people's views.  That said, there is a growing issue of various degrees of non-neurotypicality among children recently, in areas such as being on the autistic spectrum, dyslexia, ADD and ADHD.  I would also suggest that gender non-conformity and pathological demand also belong here.  The question of why this issue is growing could reflect increasing recognition of the issues, medicalisation or increasing prevalence.

Just to depart into a somewhat fantastic realm for a while, just suppose that something like the scenario described in science fiction of really "special" children did emerge.  Suppose, for instance, that children clearly began to demonstrate abilities such as telepathy, telekinesis and precognition as a matter of course.  How would the system deal with them?  Would it be able to accommodate or nurture such abilities?  Would it even recognise them?  Or, would children with telepathy and precognition be considered psychotic and medicated in such a way that they ceased to have such abilities?  Or, would it be a case of such children being sidelined and just not being accommodated in anything which would enable them to develop their talents?

Getting back to the real world, these stories and the idea of indigo children, even if they reflect nothing else, communicate the truth that children, in the form of the next generation, will eventually take over the world, and when they do so, they will need to have the adaptability and resourcefulness to find solutions to the problems previous generations have presented them with.  In order for that to happen, they need to be able to develop whatever talents they have and engage with such talents with the world.  If schooling can't find a place for children to do this, it needs to be replaced, because now a utopia has become a pressing need, not something we can even survive as a species without.

Wednesday, 30 March 2016

How Can Something Finite Not Have An Edge?


It will eventually become clear why there's a picture of a tardis here.

Somebody just wrote that if something is finite it must have an edge and be sitting inside something else.  The purpose of this entry is to show why this need not be so.

I wrote elsewhere about how probability might measure the physical distance between universes or timelines.  It seems to me that if we are living in a world which is constantly branching, the older branches would be in the way of the newer ones off our timeline, so it follows that the newer branches must be closer.  Otherwise they would cross the older ones and for an instant they would be identical, and that wouldn't happen.  It also seems that the less likely events are, the further away they would be.

There is a problem with this though.  Probability is usually between one and zero.  Apparently calculations in quantum physics sometimes come out with the result that something is infinitely probable, and nobody knows quite what to do with this, but since I don't understand what that's about, I'm going to leave it alone for now.



An event which is certain has 100% probability or a probability of one.  A completely impossible event has zero probability or 0%.  Clearly the probability of certain events depends on what's happened before, so if your house is already on fire and the fire brigade has run out of water, the chances of you dying in the fire are higher than if your house wasn't on fire or the fire brigade hadn't run out of water.  Also, not all events with zero probability are impossible.  If an infinite number of dice were rolled, an event which is impossible because they would be frozen facing in particular directions because of their mutual gravitational attraction unless they were infinitely far away from each other, they would have a particular arrangement of numbers on their faces, so looking from one direction, one might have six facing one, another one, another five and so on, and the probability of that arrangement would be zero but it would have happened, assuming them to be truly random.

If probability varies between zero and one, it looks like the multiverse might be very small and crowded and have a limit to it.  This need not be so though.  It could be, for example, that fifty to a hundred percent probability is one unit, then 25% is two, 12.5% is three and so on, meaning that events of zero probability along with impossible events are infinitely far away.

It's been suggested that space could in fact be like this.  In order to imagine that, consider this Escher picture:

(A print of this can be ordered here).  This is a circular picture whose devils and angels shrink the further away they are from the centre, and although this can't be done in reality, in an ideal such world there would be no limit to the shrinkage and to any one of the angels (devils being angels too), the plane would be infinite.  Moving across it would involve shrinking in proportion to how far from the centre one was, and consequently it could have a limit but still be infinite to its denizens.  This can easily be extended to three dimensions.  One could be in the centre of a sphere twenty metres across, but find that once one has swum or flown five metres from that centre, one was half the size one was at the centre and so on, so even though the surface was clearly visible and you might think you could reach it, it would be impossible.

This is known as hyperbolic geometry and it comes down to parallel lines.  We think of parallel lines as staying the same distance apart, but in hyperbolic geometry the distance between them increases.  This is similar to what happens on a pseudosphere, where apparently parallel lines fan out towards the equator from the poles, within limits:

At first, hyperbolic geometry might seem useless, but oddly it's found a home amongst a few Young Earth Creationists (YECs).  If you believe the Universe is only six thousand years old, there is immediately a problem with the sky.  It can be demonstrated that the Universe is more than six thousand years ago as follows:



The moons of Jupiter orbit it at a known rate and can easily be observed through a small telescope.  Jupiter's distance from the Sun can be known because of how long it takes to go round it, since Kepler's Third Law of Planetary Motion states that the square of the time taken to orbit the Sun is proportionate to the cube of the mean distance from the Sun, which in turn follows from the fact that we live in a three-dimensional Universe and the force of gravity diminishes as the square of the distance from a mass.

When Earth is on the opposite side of the Sun to Jupiter, it's 300 million miles further away from it than when it's on the same side because of the width of our orbit.  The movements of the four big Galilean moons are delayed by around a quarter of an hour, a thousand seconds, because of the time taken for light to get here from there.  This means light travels at about 300 000 kilometres a second.  Alternatively, if the speed of light is known but not the diameter of our orbit, it can be worked out from that, the speed of light itself being calculated by shining a light at a rapidly spinning mirror and working out how much the beam reflected back shifts if the rate of rotation is known.  Incidentally I've tried this between Elizabeth House in Leicester and Old John in Bradgate park, and the difficulty is getting a clear enough day for it to work.



Having established that, the next stage is to look at how the stars shift against the background over a period of six months, the background being much more distant objects such as galaxies.  In the above diagram, it can be seen that the star will be in front of the object in the background in December from our perspective, and closer to the next object down in June from our perspective.  Trigonometry makes it easy to work out the angles involved and the base of the triangle is already known to be about 300 million kilometres, so distances to nearby stars can be measured.  This is known as the first rung on the distance ladder.



The next one can be worked out by observing Cepheid variables.  Not all stars shine steadily.  Some of them fluctuate in brightness, and the way in which they fluctuate indicates what kind of variable star they are.  The brightness of a Cepheid variable fluctuates in a curve indicated by the graph above, and is determined by the speed of sound within the star, as it involves a shock wave moving back and forth in the star.  This information is not needed to understand that the brightness of the star is directly linked to how long it takes to flash, but it turns out to be because it pulsates at the speed of sound and similar sizes and temperatures of stars have similar magnitudes of brightness.  The closest Cepheids are near enough to show parallax, and sufficiently bright ones can be seen from far away.  Because their real brightness, or "absolute magnitude", can be known, their distance can be known.  This is slightly complicated by the fact that there is more than one type, but the principle remains the same.  This also enables distances to nearby galaxies to be measured.

The final rung in the distance ladder is the rate at which other galaxies are moving away from us.  For a reason I'll go into in a bit, most other galaxies in the Universe are moving away from Earth, and the further they are away, the faster they are moving away.  This can be measured because the light is stretched to longer wavelengths in a predictable manner, so the further away something is, the redder it is.  This enables the distance of all large visible objects to be measured, until eventually they are moving away faster than light, which is why the night sky is black - the light can never get to us from an object travelling faster than light.

It turns out that the light left distant galaxies billions of years ago and is only now reaching this planet.  Consequently the Universe must be billions of years old.  I made this observation to a fundamentalist Christian postgrad biologist housemate once, and she said she couldn't explain it but there was an answer.  It's no good to say it was created in transit because that would mean God was deceiving us, so Young Earth Creationists need an answer as to why this happens.

They find an answer in hyperbolic geometry.  In my humble opinion, they've spelt the word "hyperbolic" slightly wrong, but they aren't bad people because nobody is, and it could also be said that a detail like the age of the Universe isn't very important in everyday life for most people.  Anyway, their solution to the problem is to suppose that space is warped into a shape rather like the pseudosphere illustrated above, but in four dimensions.  This would mean that we are near the centre of the Universe and that time travels more slowly here because of relativity, which in turn means that you can get away with Earth only being six thousand years old and the rest of the Universe being much older, because time passes more quickly here than further out in the Universe.  This is rather surprising and ingenious, but since it places us near the centre of the Universe, it probably isn't true and it isn't really any better than the idea that the Sun goes round us rather than the other way round.  Nonetheless it does illustrate an application of hyperbolic geometry.  

In such a Universe, a spacecraft travelling away from Earth towards the apparent edge of the Universe would never reach it because as it travelled it would shrink, and as it shrank it would move ever more slowly, meaning that it would never get there.  This is one way in which something finite can get away with not having an edge.

Hyperbolic geometry is what you get if you assume parallel lines move apart.  It applies for real in some situations regardless of what YECs think about the Cosmos.  For instance, inside the event horizon of a black hole it would apply because of the warping of space there, meaning that one would be confronted with relentless movement towards the end with a tantalising prospect of the rest of the Universe being visible but unreachable even if it was possible to travel faster than light because of the shrinkage issue.  If, on the other hand, you assume parallel lines converge, you get Riemann geometry, which surprisingly is probably the way real space is.

Imagine the Earth wrapped in bandages.  If you were to have an infinite supply of bandages stowed somewhere outside the Universe which you could constantly call upon to wrap this planet fairly evenly, as you wrapped it, it would become an ever-larger sphere with an ever-flatter surface due to its size.  However, once your layer of bandages was more than a few billion light years thick, you would in fact find it was no longer convex or even flat, but concave. You would end up inside the bandages surrounded by them in all directions, with the ground in all directions away from you as if it was hollow and you were inside it, until eventually you would be trapped inside a cosmic layer of bandages many billions of light years thick.

In fact this would never happen for various reasons.  One of these is that the Universe is constantly expanding in all directions.  Getting back to the idea of galaxies moving away from us in all directions, this sounds at first like cosmic egocentrism, but the real reason this happens is that space is getting bigger, and this is where things get misleading.

Here's a picture of the Hubble Deep Field on which I've doodled a few arrows:


Just to say, the Hubble Deep Field is a photograph taken by the Hubble Space Telescope of an area of the constellation of the Plough less than a hundredth the apparent size of the Sun in which three thousand galaxies can be seen.  It's not unusual except that there are unusually few stars in the way, so that suggests that over the whole sky the same project, if there weren't any stars nearby, would show more than 70 billion galaxies.

The arrows show the directions the galaxies are likely to be moving in, that is, away from each other and away from the Milky Way too.  The distances, on the whole, are getting bigger.  They are sometimes getting smaller because even galaxies orbit something and if the orbit is edge on they will be moving towards us if they're close enough, but on the whole everything is moving away from everything else because space constantly gets bigger.

This is usually when a very misleading image is introduced of a balloon inflating and people are asked to imagine being an ant on that balloon with spots moving away in all directions from her.  The reason this is misleading is that it makes it seem like the Universe is expanding into something.  Whereas this might be the case, it doesn't follow from the description just made that it is, and this is one reason Riemann geometry is important.

What is really going on is that large distances constantly increase.  If that's so, it would be fair to ask why the stars in galaxies themselves don't get more scattered, why planets and suns don't get farther apart and ultimately why atoms don't just get ripped apart by this expansion, which is also known as the Cosmological Constant or Dark Energy.  The answer is that it isn't expanding enough to overcome the attractive forces which pull everything together, although it is expanding enough to make sure that everything won't be pulled together into a black hole.  The Universe will go on expanding forever.  As it expands, from any point in the Universe it's only possible to see as far as the speed of light will allow, because great distances expand faster than the speed of light.  Since nothing can travel faster than light, that means that two bits of matter separated by that distance can't interact in any way.  This distance may be getting constantly smaller.  Some cosmologists believe that it will eventually get smaller than a galaxy, then a solar system, then a planet and ultimately a person, meaning that objects of smaller and smaller size will get ripped apart, including in the end any people who might be left alive at that point.  This is called the Big Rip, but it might not happen.

The question of what the Universe is expanding into may be an improper question because it isn't certain that space is a "thing" at all so much as a relationship between objects which describes how far away they are and what direction they're in from each other.  This graph shows income distribution in the UK from 1979 to 2009:

It would only help to think of this graph as a street of stripy skyscrapers if you were distressed by being in one of the purple ones and preferred not to think about it, or if you were in one of the beige ones and didn't want to think about the people in the purple bits.  They aren't real objects.  Likewise, temperature is a scale but not a "thing" as such, and so on.  It could be that space is merely a combination of angles, i.e. directions, and distances, each expressible as a scale, rather than a container for objects, as it were.  If this is so, the idea of Riemann geometry is roughly this:  There is a maximum distance between two points and once this distance is reached, directions reverse.  You can think of this as a four-dimensional sphere, but ultimately that's misleading because then you might start asking yourself what it's expanding into, and the answer is "nothing".  The expansion merely represents the idea that distances tend to increase, including the maximum possible distance between two points.

One odd consequence of this is that it means that on the whole any sufficiently large object is bigger on the inside than the outside.  Go back to the idea of wrapping Earth in bandages and instead imagine it being contained in ever-larger hollow spheres.  In that situation, each sphere has a smaller surface than its volume would lead you to expect.  If this planet is at the centre of a sphere half the size of the Universe, it would take one and a half times longer for light to get to the surface of that sphere than it "should".  This means that the volume of the sphere concerned is getting on for four times its expected size.  Also, over large enough distances parallel lines converge, meaning that a square is kind of this shape:

and a cube is like this:

There would be some variation and some squares and cubes would be more symmetrical, but all of them would be wonky.  Many of them couldn't be reflected onto themselves.  Also, this applies to all squares and cubes, and in fact all shapes which look regular on a small scale such as spheres, circles, squares and cubes.

The reason space doesn't have an edge, therefore, is that it isn't a "thing", or it may not be.  Temperature and velocity both have limits, but those limits recede in such a way that infinite energy would be needed to reach them.  The same is true of space.  This is confusing but it does at least mean that tardises are kind of real, except for the time travel bit.