Category Archives: Mathematics

Going up Exponentially …

“The greatest shortcoming of the human race is our inability to understand the exponential function.”

Albert Allen Bartlett

These are depressing times so this month’s contribution (a bit short for time, to be honest), though topically linked to the ongoing pandemic, deserves attention from different angles in its own right.

We’re going to have a quick look at exponential growth.

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AI/Machine Learning for Minefield Clearance

“Glyndwr University researcher seeks real world data to develop AI landmine clearance”

A landmine research project which aims to develop an artificial intelligence approach to mine clearance is being developed at Wrexham Glyndwr University.

The project – which is currently in its developmental stages – is being developed by Computing PhD student Alexander Bruckbauer who is working on building the model under the supervision of Professor of Computing Futures Vic Grout.

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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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