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Posts Tagged ‘math’

Maths Symbols, And Why They Matter

Several of my posts on html have contained passing mentions of writing with screen-readers for the visually impaired in mind. This one's a bit more directly aimed at that subject, although using the right symbols for the right job is, I think, a good thing in its own right. Think of it, if you will, as something of a mildly consciousness-raising piece, coupled with a simple "how to" guide.

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Scales Of Confusion

This article by Jerry Coyne got me to thinking. Britain is, supposedly, a decimalised country, though you'd not know it from the road-signs. Certainly kids these days are taught—as they should be—in purely decimal measurements, but the change-over was gradual. This was further exacerbated, in my case, by the fact that we moved around a lot between education-districts when I was a kid; and different districts made the change at different times, leading to me being taught one year in metric, the next in imperial, and the next back to metric. Which, as you can probably imagine, Gentle Reader, led to my preferences for measurement-scales being somewhat confused.

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Charles Darwin AKA Charlie Ismay-Darling

Charles Ismay-Darling, who wasted a good portion of the early part of his life chasing around the world and bringing home dead finches, before finally turning to serious mathematological studies. Suffered from cirripedaphobia—the irrational hatred of barnacles.

One hundred and fifty years ago, pioneer mathenaturalist, Charlie Ismay Darling, advanced the theory that was to change the world of mathematology forever: the theory of evolvomatutics by mutable seduction. Briefly stated, he postulamatated—and has since been proved correct by so many independent methods that only a nutter or a creationist would argue against it—that numbers and shapes evolvomalate over time to become different numbers and shapes.

There are so many pieces of supporting evidamence for this that it would be daft to try to list them all, but here are some of the better known examples. The number 2, it has been discovered, if looked at in a warped mirror with your eyes nearly shut, looks a bit like the number 5—a clear example of evolvomatution. If you think of a number, add the year of your birth and divide by the square root of Russell's Teapot, you end up with an unexpectedly irrational answer. Not only did this add further evidamence in support of Darling's theory, but it also opened up a whole new branch of study; that of irrational, nay stark raving bonkers, number theory. Not since an unknown and possibly stoned 9th Century Indian mathematologist invented the number 58, has the field been so invigorated. Perhaps the greatest triumph in the field of evolvomatutics though, came in the 1920s (so numerologists, who know about arcane stuff like dates, not to mention prunes, raisins and other fruit of questionable taste, tell us), David Hilbert, supreme infinitologist, discovered that the number 8, when turned on its side, produces an infinity of bad mathematological puns. It was a sad loss to the mathematological world when he retired to open what has become the word's most successful chain of hotels. Or possibly just a hotel with infinite entrances; no one's quite sure.

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A Hair’s Breadth

Recession news stories regularly talk about billions and trillions of dollars these days, unfortunately on the wrong side of the balance sheet. Popular TV shows about science describe unimaginably small particles along with equally unimaginably large numbers of stars, galaxies, distances and possible life-bearing planets. Young earth creationists espouse a thousands-of-years history instead of billions, often with no apparent sense of just how much they're shortening the life-span of the universe by. The latter, if we take the current estimate of the age of the universe as 13.75 billion years and the creationist claim of a six thousand year old universe, means that they're claiming the universe is just 0.00004% as old as it actually is. For those who prefer fractions, that's 41,000,000. If we're talking about the age of the Earth, they're closer to correct but still wrong by several orders of magnitude. They're claiming the planet to be just 0.0001% or 110,000 its actual age.

I sometimes wonder if, just maybe, an inability to grasp the sheer length of time that geology and cosmology give evolution to work with—how much time is allowed for tiny, minuscule changes to accumulate—doesn't play a small part in biblical literalists' easy denial of evolution. This post isn't about religion or creationists, though, and they're certainly not the only ones to have a hard time grasping very big and very small numbers.

An example.

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Do you ever see comments that are so astoundingly dumb that your jaw bruises as it bounces off your chest? I have a name for them; I call them ‘why are there still monkeys’ comments. That’s how amazingly, stupefyingly silly I mean.

Yesterday I posted this graph, showing sea-ice shrinkage in the Arctic, on a post about climate change.

It wasn’t much of a post, just a whimsical analogy I thought of that seemed worth throwing out there, and I wasn’t really expecting any feedback off it at all. And I was nearly right in my expectation. Nearly. I did, however, get this comment:

“There are nice satellite photos to misspell[sic] the myth that Arctic ice is shrinking. That is, it’s shrinking in some places (hence you can draw a nice graph) and growing in other places.”

My jaw-thud registered on the Richter scale! After a mildly sarcastic reply, however, I left it alone.

But.

It kept niggling at me; an itch in the back of my mind.

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This one’s a guest-post from Fisherman. Fishy’s a keen golfer, fresh-water fisher, quiz enthusiast and, most importantly for us here, a chemistry teacher.

I’ve been after him for a while now to do a piece on kitchen chemistry; something that parents could do with their kids, maybe, or those of us who never grew out of that childhood fascination with the world that makes us gasp with delight when, with some ordinary, everyday bits & bobs, we realise we can discover some quite astounding things.

Anyway, enough from me, already! Here’s Fishy:

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Orders Of Magnitude

When I was a kid, annual government budgets, world spending on this-and-that, and such were discussed in millions and billions. Nowadays we get trillions rolled out regularly. You get the impression, though, that few people have any emotional grasp of just how huge a trillion actually is. Think of it this way:

Take a look at an ordinary (metric) ruler. Specifically, look how small one millimetre is.

  • 1,000 (1 thousand) mm = 1 metre (3' 313" )
  • 1,000,000 (1 million) mm = 1 kilometre (0.6 miles).
  • 1,000,000,000 (1 billion) mm = 1,000 (1 thousand) kilometres (621 miles).
  • 1,000,000,000,000 (1 trillion) mm = 1,000,000 (1 million) kilometres (621,371 miles).

So a trillion is to a billion, what a metre is to a millimetre.

The old British system gives them slightly more intuitive names; a modern/American billion is one thousand million. A modern/American trillion would have been called a billion, but could be expressed as one million million! Kinda puts the figures into perspective, don’t it.

Oh, and to give some sense of scale to this; the circumference of the Earth at the equator is 40,075 kilometres. At a dollar a millimetre, 1 trillion dollars would take you around the world just under 24,953,213 times.

Here’s the thing, though. With international debts now being expressed in cumulative trillions, yet world population being expressed in very low billions, it would seem that, on average, every person on the planet has debts—personally or via their representative governments—to the tune of thousands of dollars. Is it just me, or have we reached the point where, at a personal level, that kind of finance leaves me wondering just who in hell, given the interconnectedness of word-markets and such, we owe all this seemingly conjured-from-thin-air money to?

Here’s some rather depressing figures:

  • Worldwide military spending: $1.6 trillion.
    (Cost of nuclear weapons—which have only been actually used in warfare twice, in 1945—worldwide per year: $100 billion).
    (Cost of one M1 Abrams tank: $621 million. Around 9,000 of this model of tank alone, have been produced and sold.)
  • Worldwide governmental spending on medical research seems amazingly hard to find a figure for. Seems to be in the ballpark of $100-$200 billion, though.
  • Cost of drilling a well to supply water for an average-sized community in sub-Saharan Africa: $3,000.
  • Worldwide spending on space exploration: $35 billion.

I spent half an hour trying to find figures to work out how much revenue would be made if churches paid the same taxes as any other organisation, even taking charitable work into consideration. I gave up. If the figure wasn’t in the high billions or low trillions, though, I’d be very much surprised.

Note how expensive, by an order of thousands of times its nearest rival, the most expensive item on that list is. I’ll leave you, gentle reader, to dwell on that rather unpleasant picture of the human race’s priorities…
—Daz

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