Category Archives: Mathematics

New edition of ‘Conscious’

Yes, indeed, there’s a new edition of the novel!

Updated slightly to reflect changing world events (although, sadly, all the initial predictions are pretty much coming true now).  And with a swish new cover!  Just search for ‘Vic Grout Conscious’ on Amazon in your region (and choose the one with the cool blue cover) or use the direct links below.


Incompleteness, Inconsistency and Those Pesky Words!

With the exception of an image demonstrating an argument so utterly and awfully illogical, it deserves public shaming, this post largely works with abstract cases as examples in the hope of not upsetting quite as many people as it otherwise might.

We start with the background stuff …

Kurt Gödel, in 1931, dropped a bit of a bombshell on a mathematical and logical world (that was quietly believing the opposite) by showing that there are things that can’t be proven or disproven.  In other words, in all ‘vaguely normal’ systems, there are propositions that can be either true or false and it doesn’t really matter.  ‘Mathematics is incomplete‘.  In 1936, Alan Turing proved that there are problems that can’t be computed/solved and the rest of the computer science research community spent the next few decades realising that these were kind of the same thing.

Pretty disastrous, huh?

Well, no, not really.  The mathematical and computer logic world dusted itself off and got on with it.  And anyway, other branches of science – and beyond – had similar problems.  In physics, for example, there’s a limit to how closely you can measure something before you change what you’re trying to measure.  Turns out, in one form or another, ‘incompleteness’ is pretty normal in life.

So, no, incompleteness, isn’t that much of an issue.  (it just means we don’t know everything – in fact, can’t know everything: there’s some bits of science, philosophy, etc., we can’t do from our little three-and-a-half-dimensions backwater of the universe; or we’re not God, if you like.)

However, rather than ‘incompleteness’, something called ‘inconsistency’ would be a problem.  Why?  And what does that look like?

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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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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


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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