Understanding technology

This is a small excerpt from Not Your Usual Clever Ideas, which is about crazy ideas that occasionally pay off. I published it some years ago, and I will upload a revised version in the first week of September.

Don’t worry about what anybody else is going to do…The best way to predict the future is to invent it. Really smart people with reasonable funding can do just about anything that doesn’t violate too many of Newton’s Laws!

—Alan Kay.

Legend has it that Niels Bohr said “Prediction is difficult—especially about the future”. Bohr himself always claimed that somebody else said it, but whoever said it first, the statement remains true. Logical consequences only look logical when we view them from the other side, when we can see which scraps of context really counted. Even Arthur C. Clarke (who predicted communications satellites in 1945) never saw the full potential when he wrote his first outline of it.

Some many years ago, I proposed the idea of the 50-year effect, when I was writing a history of rockets. While I pursue many temporary obsessions in my writing, I have allowed room for only one permanent obsession, and this is it, because the 50-year effect explains why we can never predict the social effects of any technology when it is invented.

The effect probably has the same duration as a human working life because it takes a while for the old fogeys who do not know, understand or appreciate the new technology to die off, making room for younger people who are familiar with the technology to reach the top of the ladder. In fact, the real effects generally begin to appear about 30 years after an invention, but they remain less than totally clear until 50 years after the invention was first set loose in public.

Consider this 1884 essay, describing how a New Zealand lighthouse keeper’s life might be changed for the better, by the application of the telephone, a device that was invented in 1876, and thus well-known and talked-about by then, but little-experienced at that time:

We have been in the habit of thinking that no life was so lonely as that of the keeper of a lighthouse, and are apt to compassionate the men who are cut off from all intercourse with their kind for weeks by stormy weather or by the difficulties of their position. But the telephone (says a New Zealand paper) has cured all that as by a miracle. Let the storm rage how it may, the lighthouse keeper at Tiritiri can speak in a whisper to Auckland or Waiwera. He is not permitted to forget the days of the week as they slip by, or when the Day of Rest comes round, for the clerks in the Auckland office, when discharging Sunday morning duties, can connect him through, and in his lonely watch-tower, with the moaning sea all round, he can hear the Salvation Army band in Shortland-street and Queen-street playing ‘The Sweet By-and-by,’ or some other of Moody and Sankey’s airs. From the same place he can, too, hear every morning someone in the office at Waiwera read the newspapers. All this through several miles of cable at the bottom of the sea, and, by the detour as it goes, some sixty miles of land line.

It conjures up a pretty picture, but one that would fall foul of the dreadful acoustics of the early telephones, not to mention that the clerks’ telephone in Auckland would be bolted to a wall, far from the band. In other words, the journalist must have made it all up as he went along.

The telephone was slowly winning acceptance in some offices around 1900, but it had apparently led Sir William Preece, the chief engineer in the British Post Office to say, some years earlier, when asked if the new device would be of any value:

“No, sir. The Americans have need of the telephone—but we do not. We have plenty of messenger boys”.

By 1914, people in New York could talk to people in San Francisco by telephone, and it became common in at least the wealthier homes in the western world around 1930, 54 years after it was invented.

(There is an amusing side-story here, known to all those who have worked in surveying and statistical sampling: in 1936, the Literary Digest surveyed its own subscribers and automobile owners, followed up by a phone poll, and concluded that Landon would beat Roosevelt in the Presidential elections. FDR won by a landslide, and the error happened because all three sample groups were well-off or rich, and so less likely to vote for Roosevelt.)

After 20 years, people have mostly heard about a new idea, after 30 years, the technology is growing popular but still developing. After 50 years, we can call the technology mature. It does not matter if you look at printing, the telescope, the telegraph, the railway, photography, cinema, radio, heavier-than-air flight, television, or the internet. Within a tolerance of a few years, the 30-year/50-year effect holds in every case.

It is no coincidence that the books produced in the first 50 years after Gutenberg started using the printing press are called incunabula, a term that refers to the clothing of infants. It was only after one full human working life that the idea of printing had been taken on board by both scholars and the people in the printing trade. It had become a mature technology.

When he produced the second edition of his second book, the Mainz Psalter in 1459, Gutenberg had proven the technology of printing. Even so, he could never have anticipated two books published 400 years on, in 1859, Charles Darwin’s The Origin of Species or Charles Dickens’ A Tale of Two Cities—or those books’ effects.

Equally, he could not have anticipated that a woman, George Eliot (Mary Ann Evans) might publish Adam Bede, nor could he have anticipated Isabella Beeton’s Household Management, or John Stuart Mill’s On Liberty, all of which came out in 1859. He most certainly would have been utterly confused by Alice’s Adventures in Wonderland, conceived in 1862 and published in 1865.

Gutenberg was content to have created a system that could produce 180 bibles in the time that a diligent penman needed to complete a single copy by hand. He could never have dreamed that in Mainz in 2008, outside a museum devoted to his work, newspapers from many nations would be sold to foreign tourists on the day of their publication, after being flown in. Museums, newspapers, tourists and flying would have made no sense to him at all.

There's more, but you'll have to buy the book :-)

Three mathematical puzzles

 This is another selection from my book Playwiths, available from Amazon or through Polymoth Books. The apparent supplier is really just me, trading as Polymoth Books, but I set the firm up so I can supply booksellers and libraries more cheaply (note that some conditions apply).

This bit is free.

The crossed house puzzle

Your task looks simple: draw the diagram below by putting your pencil down on the paper, and drawing a single continuous line. You are not allowed to draw over any of the lines.

There is a solution, and in time, you will see a pattern!

You can solve this with a lot of difficult trial and error, or you can be mathematically clever, and work out a basic principle that applies to problems like this one and the next two as well. That’s a hint!

The question you have to ask yourself is this: “how many times do I enter or leave from one of the key points?” There is something very special about the points with odd numbers of starting and finishing points. The rest is up to you, but the problem does have a solution.

The prisoner and the cells

A prisoner in a rather strange prison (with even stranger guards!) was told that if he could find a way to walk through all of the doors of all of the cells, once and once only, he would be allowed to go free. The diagram below shows how the cell doors were arranged.

The prisoner’s puzzle.

* Image by en:User:Booyabazooka - http://en.wikipedia.org/wiki/Image:15-puzzle.svg, Public Domain, https://commons.wikimedia.org/w/index.php?curid=1059593

Analyse the problem and see whether it is possible, and if it is, work out the solution. If it is not possible, prove it. Well, if you had any sense, you would have done the crossed house problem first. And that’s a hint. If you draw this figure on a torus in such a way that the hole of the torus is inside the middle cell at the bottom, it might be a bit easier—and that’s another hint.

The Königsberg bridge problem

In the city that was once called Königsberg, there were two islands in the river, linked to each other and to the shore by bridges as you can see in the diagram. The river is blue and the bridges are white. The problem for the citizens of Königsberg was this: was there any way of walking around the city and crossing each of the bridges once and once only?

 

A map of ancient Königsberg, with two islands in the river, and seven bridges.

Well, if you had any sense, you would have done the prisoner and the cells problem first. And that’s the last hint, for now. Now a research question: were/are there islands and bridges like this in Königsberg?

Notes

The three problems all have a common theme: entries and re-entries to certain points. If a cell in the second problem has an odd number of doors, you must either start inside it, or you must end in it, but not both. In the Königsberg bridges problem, each island has an odd number of entry and exit points, as does each bank. There is no solution to the second and third problems.

To find out about Königsberg reality, look for maps of Königsberg online.

The Two Cultures and strange circles

This is another selection from my book Playwiths, available from Amazon or through Polymoth Books. The apparent supplier is really just me, trading as Polymoth Books, but I set the firm up so I can supply booksellers and libraries more cheaply (note that some conditions apply).

This bit is free, and it probably is not for the faint-hearted

1. The Two Cultures

In very early 1959, I argued with a pompous headmaster who had a Master of Arts degree, because I wanted to continue my studies in Latin, and also study physics. He rejected my request with a crushing dismissal: “Boys who do physics do not do Latin.” That was how I became the victim of something neither of us would have heard of back then, the notion that learned society was made up of “two cultures”, the Arts culture and the Science culture.

The divided cultures had been around for a century or more, but the name “two cultures” was only proposed in 1958 by C. P. Snow, a physicist who wrote fine novels, making him a member of both cultures. Snow said that, as the Arts people saw it, the “Arts Culture” contained all the witty, urbane and articulate people.

The “Science Culture” was, according to the Arts people, made up of scruffy men (and just a few equally scruffy women back then) who were incredibly clever about extremely difficult things, but who were absolutely useless when it came to dealing with people. Scientists were stolid and uncreative manipulators of objects, lacking in personal skills.

The scientists were often absent-minded, we were told, where the Arts culture people were clear-thinking. Leave us to do the ruling, puffed the Arts people. The scientists and engineers let this go, but in their turn, they puffed that the Real Work should be left to them.

According to this divisive pair of stereotypes, creativity is only found in the Arts people, and practicality lies only with the Science people. Fuelled by these notions, the two camps are encouraged to regard each other with a less than friendly contempt. My regard for people who accept that view is far less polite. To survive and do well, it helps to have a foot in each camp. To work in STEM, you badly need the art of debate, the ability to write clearly, sketch neatly, take photos and more. You need STEAM, and the M is important.

2. Strange circles

Some non-standard round shapes. 

Once upon a time, astronomers were certain that all the moving bodies in space travelled in circles, “because circles are perfect”. In many ways, modern science began when Johannes Kepler saw that the orbits of planets were ellipses.

Or maybe science emerged when Isaac Newton proved that the orbits had to be that shape, because of the way gravity worked. Whichever way it happened, those odd squashed circles called ellipses were involved. 

 

A 19th century engraving of a Gatling gun: notice the shape of the wheels. 

To me, ellipses are important, because in perspective, circles look like ellipses, but I am no artist, and I need help to get my ellipses right. When I am drawing on paper, I use plastic templates to draw my ellipses, but with a simple graphics program like Paint.Net, I can draw ellipses of any shape and size.

If you want to work on shading and stippling geometric shapes, use a colour printer to print out pale sky-blue ellipse outlines. Make just enough fine black points on the paper to show the outline, then photocopy it: pale blue (often called “dropout blue”) usually fails to show in a photocopy, and away you go.

We will meet Piet Hein again in chapters 15 and 20 of my book (and I may get to them here, one day), but now we need to look briefly at his superellipses, which were adopted as a suitable shape for rounding-off a space in the centre of Stockholm, rather more nicely than the rounded rectangle above. If you look online for <Sergelstorg>, you can see the result in maps and aerial photos of Stockholm.

By an odd chance, Hein came up with his solution in 1959, the year in which I encountered the two cultures, and C. P. Snow published a book about his them. Surely, if anybody ever showed how the Two Cultures notion breaks down, it must be Hein. And now, we need to venture into mathematics of a Heavy Kind. 

There is a whole family of curves with this formula:

As a group, they are called Lamé curves, after Gabriel Lamé, who discovered them. If n is between 0 and 1, the figure is a four-pointed star. If n= 1, it is a parallelogram, and for n between 1 and 2, it is a rounded-off rhombus. If n=2, we get an ellipse or a circle (depending on the values of and b), and above that, we get squircles, or superellipses.

Sergelstorg has n=2.5, and a/b=1.2. Over to you, but look around on the internet for 3D supereggs and ellipsoids…

Möbius strips and more

I have taken a short break from cleaning up The Cornish Boy Quartet, which is Australian YA historical fiction, because I wanted to share something on this topic, after it came up on a librarian list which does not allow attachments. It is a selection from my Playwiths, available from Amazon or through Polymoth Books. The apparent supplier is really just me, trading as Polymoth Books, but I set the firm up so I can supply booksellers and libraries more cheaply (note that some conditions apply).

That said, this next part is free, and teachers looking for ideas can get those from the e-book, available at the Amazon link, for $5.

Cut a 5 cm strip lengthwise from paper (an old newspaper will do). Holding the strip out straight, give one end a half twist (180º) and glue or tape the two ends together. Your piece of paper is now a Möbius strip. When you twisted your strip, the inside and the outside became one continuous surface. There is also only one edge.

Take a pen and carefully draw a line along the centre of a new uncut strip. Where do you end up? Is the line drawn on the inside or outside of the paper? Now cut the strip along the line you drew. How many pieces do you get? It may help if you use the picture below to make an ant-covered Möbius strip: here is a link to a PDF that you can download and print.

Möbius ants!

You can use the PDF (this is recommended), or blow the above image up on a photocopier, so the chain of ants is 23 cm long then join two copies, as shown below, and do back-to-back photocopies. You need to experiment to get the ants on opposite sides of the page, going in opposite directions.

I had a bit of trouble following my own instructions, so here’s a step-by-step set of photos: remember that you need to print both sides

(1) PDF on-screen; (2) printed out; (3) cut up; (4) trimmed; (5) joined; and (6) a finished Möbius strip.

Cutting the Möbius strip in two different places.

Next, take the photocopied or printed sheets and cut two strips, 23 cm x 7 cm, and join them, so all the ants are in columns, and make a Möbius strip which you can cut, either straight down the centre (see left, above), or off to one side, as shown in the right-hand picture.

Try this again. But this time, give the paper a full twist. Then try one and a half twists, and see what happens. Last of all, see what you can discover about Klein bottles.

Notes

The pictures below show what you get when you cut the strip. The first picture shows that a cut down the middle gives a single loop, but there is a surprising result when you test for Möbiusness (my own word). The test is simple: draw a pen line along one side until you get back to the start: If the paper is still a Möbius strip, the line will be on both sides, but in the picture below, that doesn’t happen:

Now in the last picture, there are two interlinked loops. I cut off the big ants, and something odd happened: the little ants are isolated on a Möbius strip, but the big ants are on a non-Möbius strip.

Playwiths is full of STEAM ideas, and arose from a website of the same name. No publisher would take it on, even though the site drew more than 4 million visits over 20 years. That is why it is self-published.

Sometimes, you wonder about these people!