Category Archives: Mathematics

Spurious Accuracy

“At one point, the drone was estimated to be approximately 98 feet from the passenger jet.”

“Estimated?”  “Approximately?”  98 feet actually looks astonishingly accurate doesn’t it?  Is someone having a laugh?  No, not exactly; it’s just the sort of thing that happens when people do silly things with numbers.

We’ll come back to that one.  For now, to get an idea of what’s going on, let’s take another example, adapted from Darrell Huff‘s magnificent How to Lie with Statistics

Suppose you’re a would-be statistical researcher and you’ve decided to write something on how long people sleep.  You’re going to talk to 100 people (which isn’t a huge number for a study but things have been published on less data) about it.  And here’s where it starts to go wrong …

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Conscious

Now available as eBook and paperback

What makes something sentient?  What does it take for an entity to be aware of its own existence and to want to interact with the world of its own accord?  Is it a gift from God or hard science?  Is it something fundamentally human or animal in nature or is it a simple technological principle based on brain size?  There are many models, of course.  But, if consciousness is simply a natural product of neural complexity then eventually, in theory, we might build something – a computer or a machine – that was actually big enough to wake up!

Oh, wait …!

The widespread ramblings, which have appeared on this blog over the years, now make a partial contribution to a novel.  (See http://www.lulu.com/spotlight/vicgrout)

hiresfront

Vic Grout’s Conscious is set a year or three into the future.  The ‘Internet of Everything’ is making the world a more connected place than ever before.  People’s lives are becoming increasingly automated.  But something odd is happening … ‘Things’ are beginning to misbehave and no-one can work out why.  What starts as an amusing inconvenience quickly becomes very serious indeed!

A ragged bunch of academics, scientists and philosophers are on the case – and may know the answer.  But now they have to convince people that their crazy explanation is true.  And that’s only the start.  Against a backdrop of a world suddenly beginning to fall apart, they’re in a race against time to get someone to do anything about it.  And not everyone is on their side!

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New Novel: ‘Conscious’ by Vic Grout

What makes something sentient?  What does it take for an entity to be aware of its own existence and to want to interact with the world of its own accord?  Is it a gift from God or hard science?  Is it something fundamentally human or animal in nature or is it a simple technological principle based on brain size?  There are many models, of course.  But, if consciousness is simply a natural product of neural complexity then eventually, in theory, we might build something – a computer or a machine – that was actually big enough to wake up!

Oh, wait …!

The widespread ramblings, which have appeared on this blog over the years, now make a partial contribution to a novel: http://tinyurl.com/VicGroutConscious

hiresfront

Vic Grout’s Conscious is set a year or three into the future.  The ‘Internet of Everything’ is making the world a more connected place than ever before.  People’s lives are becoming increasingly automated.  But something odd is happening … ‘Things’ are beginning to misbehave and no-one can work out why.  What starts as an amusing inconvenience quickly becomes very serious indeed!

A ragged bunch of academics, scientists and philosophers are on the case – and may know the answer.  But now they have to convince people that their crazy explanation is true.  And that’s only the start.  Against a backdrop of a world suddenly beginning to fall apart, they’re in a race against time to get someone to do anything about it.  And not everyone is on their side!

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Mathematicians and Computer Scientists

It’s the holiday time of year: so a slightly lazy post for August.  Adapted from a letter published in this month’s edition of Mathematics Today

For anyone who’s worked in the ‘Twilight Zone’ between mathematics and computer science for any time, June’s Mathematics Today article, Urban Maths: A Roundabout Journey [on rounding issues in computer calculations], would have struck a distinct chord.  They will have often come across situations in which mathematicians and computer scientists don’t quite see eye to eye.  The following, fairly well-known, combinatorial exercise is another good example.

How many ordered ways are there of summing contributions of 1 and 2 to a given integer, n?  So, for example, 1+1+2+1+1 and 2+2+2 are two of the 13 different ways of making 6.  Call this number f(n) so that, in this example, f(6) = 13.

The standard combinatorial approach is to consider the first term.  The only two options, 1 (leaving n-1 to make) and 2 (leaving n-2) lead readily to the recurrence relation f(n) = f(n-1) + f(n-2).  Easy enough, yes, but the interesting question now is what to do with it?

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