Mathematically Safe:Man Vs Robot.

A mathematician walks one mile south. She then walks one mile east. After that, she walks one mile north. She finds herself back in the exact same place she started. She sees a bear. What colour is that bear?

The observant amongst you will have noted that her three mile walk does not include a westerly stretch and wondered how, without that, she could possibly have ended up in the exact same place. Some of you will have deduced that the only place on the globe that would be possible is the North Pole. So our mathematician (and I'm not sure why this Arctic wanderer needs to be a mathematician) must have been at the North Pole and the only bear you'd be likely to see there is a polar bear. So the bear was white.

This was one of the many fun challenges set to the audience by Junaid Mubeen during last night's Skeptics in the Pub - Online talk, 'Mathematical Intelligence:What we have that machines don't'. Junaid is a mathematician turned educator (and a former Countdown champion) who has worked with the celebrated author Simon Singh and has written a book with the same title as his Skeptics talk.

The book was written because Junaid wanted to counteract some of the hype that surrounds AI and he began by telling us how, in June of this year, Google engineer Blake Lemoine made claims that one of his company's chatbots, LaMDA, had become a sentient being.

Not many took his claims seriously, and Google placed him on administrative leave, but these claims are becoming more and more common. This idea is that AI has become so intelligent that it is sentient but Junaid, and I'd agree with him, would argue that intelligence, especially of the artificial kind, does not equate with consciousness and that consciousness is of more importance when deciding what/who is, or isn't, sentient.

The idea that software can be sentient goes back at least as far as 1966 when the mock Rogerian psychotherapist Eliza was believed to be giving answers that were too complex for a mere computer to come up with. You have a look at the exchange with Eliza below and make your own mind up.

As humans, we have a tendency to anthopomorphise our own creations and in doing so, Junaid contends, this means we place too much trust in them. Ultimately, letting computers and systems make decisions in our life. From something as minor as choosing what car insurance to go for to something as important as deciding when to bomb a factory in Iraq.

Computers are, of course, very good at performing calculations quickly. That's what they're for. But Junaid Mubeen wanted to show us the side of maths that computers are less good at. The side of maths that we humans (for now at least) are better at. He talked occasionally of beautiful maths and ugly maths and he was as passionate about his subject as he was knowledgeable.

It made for a really interesting talk. Junaid believes that mathematics is actually (again, for now - the show included several caveats as our speaker was reluctant to indulge in speculation) resilient to the threat of automation and to make his case he gave us some examples of where computer reasoning can go wrong. Reasoning not being something that can be reduced to algorithms.

Humans look for patterns everywhere. To try to make sense of an often senseless world. Apophenia is a word that relates to finding patterns and connections in the unrelated and when it comes to maths one example is the equation n + n(squared) + 41 = a prime number. See below:-

2 + 4 + 41 = 47

3 + 9 + 41 = 53

4 + 16 + 41 = 61

47, 53, and 61 are all prime numbers and this continues so it appears we have ourselves a pattern. In fact you need to get to the number 40 (40 + 1600 + 41 = 1681) before the pattern is broken. 1681 is divisible by 41 as well as by 1 and itself. We've been led down the path by something that looks very much like a pattern but isn't one.

A series of odd numbers, in sequence, added up always seems to result in a square number. See below:-

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 = 7 = 16

1 + 3 + 5 + 7 + 9 = 25

Four is the square of two, nine is the square of three, sixteen is the square of four - and so on and so on. It looks as if we have identified a pattern here and, in this case, we have. There were far more complex examples of this last night but you probably get the point. It sometimes takes a long time, and a lot of computation, to work out if something is a true pattern or not.

So why do we not, quite simply, hand over these calculations to cold, hard, and rational computers? It's because many computers are not as rational as we like to think they are. They have been programmed by us humans and because of this they incorporate many of our biases.

Machine learning, like us, looks for patterns. A good example is a CV scoring algorithm that was created for Amazon. Based on their previous recruitment agenda, it picked up that there was a strong anti-female bias in Amazon's past recruitment policy and replicated it into its algorithms. If any CV contained female pronouns or any other clear indicators that the applicant was a woman they would be marked down.

To their credit, and I'd rarely be nice about Amazon, the company did delete the algorithm before it went live and one presumes they've come up with something fairer and more even handed now.

Another illustrative puzzle was set for the audience:-

"There are 125 sheep and 5 dogs in a flock. How old is the shepherd?"

It's clear to most us that there is no information whatsoever in that statement from which we can deduce the age of the shepherd. But if you were to ask that question to a group of school children, many of them would at least try to give an answer. Most, apparently, would say the shepherd is 25. 

Possibly because the only sum that results in a reasonably sensible age for a shepherd is to divide the 125 sheep by the 5 dogs. School kids are eager to please - and they're still learning - so that's understandable. But it's interesting to note that when this poser was fed to a very mathematically advanced piece of software it too attempted an answer and came out with a right load of old nonsense!

Suggesting the shepherd was 125 years old because that would be the only age at which there would be the same number of sheep as dogs. Whatever that means. It sounds unhelpful but it's actually helpful in telling us that, in these ways, AI's not there yet. If you write a piece of software in code every single letter, digit, mathematical symbol, and forward slash are vital. They have to be in the right place for things to work.

Anybody who's read a WhatsApp message will know that human communication is rarely so elegant. There are typos, people miss out crucial punctuation, spell words wrong, and make all manner of orthographical howlers. As humans we can normally, except in extreme cases (I remember once waiting for my friend Simon in a pub, he was running late as usual, I got a text informing me he was sorry he was late but would be there by Christmas), work out what the intended message was. But computer software, like Mr Logic from Viz, takes everything as read. Literally.

And that's why, for now, we have the edge over the robots who will probably one day take over. This fascinating talk, in which I've only covered a small part, took in Alan Turing, the Deep Blue chess computer, Euclid, slide rules, DALL-E 2 image generation software, G.H.Hardy, and how the game of Monopoly was once also known as the Landlord's Game and the Q&A took in Fermat's Last Theorem, Terminator 2, Facebook, the Riemann conjecture (or hypothesis), calculus, the singularity, and a robot that is determined to turn the entire planet into a giant paperclip factory.

It was fascinating but then I like maths (maths can be fun, as long as you choose the right sum) and I love it when Skeptics do a mathematical talk so I thank them, and compere Michael Marshall, for that. But I also like it when they do nature and in a fortnight's time, Seirian Sumner will be talking about wasps. I wonder if wasps do maths.