My Most Boring Blog Ever, Probably

Ciao from Italy! The sun is blazing in the sky with a searing, soporific warmth that means it can only be one season. That’s right! It’s…

Exam season.

Which makes even the most interesting things seem dull – especially when you’re studying logic. Allow me to demonstrate.

Take my first sentence – “the sun is out”. As we all know from the ancient proverb, if the sun is out, the guns are also out. We can assume this premise to be true, because Channing Tatum once wore it on a vest.

Logic tells us that if A symbolises the sun being out, and B symbolises the guns being out, then we know that A→B. To make things clearer:

A = the sun is out

B = the guns are out

A→B

Yeah. Not such a cool thing to say anymore, is it? Not when you break it down into its component enunciati.

Mind you, I say it’s dull, but this is in fact how Sherlock Holmes operates. One of my favourite books by Sir Arthur Conan Doyle is the one in which Holmes sees the sun in the sky and instantly deduces that the guns, too, must be out. Sherlock Holmes and the Out Guns, I think it was called. By using these skills, you too can think like Sherlock Holmes. You’re welcome.

So, in the spirit of this most festive of seasons, I’ve set you some questions to see if you understand logic, because I know everyone loves a good exam. Anyway here goes:

1. During the exam season, Alex has two exams. Given that the exam Alex has just completed is female, what is the probability that Alex’s other exam is also female?

The answer is 1/3. This is because there are four combinations of gender for my two exams: MM, MF, FM, and FF. However, because we know that at least one of them is female, we can eliminate MM. However of the remaining combinations, MF, FM, and FF, there is only 1 of the 3 in which a second F is combined with the first F that denotes the exam I have already taken, so therefore-

Yes, yes, ok Alex, I hear you cry. We all did probability in school and it was just as boring then as it is now. Can we just go back a bit and ask how, on God’s green earth, in the Year Of Our Lord 2017, an exam can have a gender?

We may, I say graciously. If you study Italian, you’ll see that philosophical logic and moral philosophy become la logica filosofica and la filosofia morale. Which, yes, you are correct, is entirely illogical, and begs the question of how anyone could possibly be expected to pass a logic exam in Italian.

Anyway, as you can see, my exams were both female – but the probability was still only 1/3. I’m sorry, I don’t make the rules. Bayes makes the rules. At least I think he does. That was the question I couldn’t answer because, sadly for Bayes, he appeared in the penultimate chapter in the book and I didn’t quite leave myself enough time to read about him.

The question in question was “What is Bayes’ Theorem?” Philosophical logic bears a strong resemblance to maths in that, rather irritatingly, it requires an actual answer, and you can’t just use vague mumbo-jumbo that culminates in you saying you don’t know but that technically the examiner also doesn’t know and therefore can’t mark you down. This meant that I couldn’t use my go-to template for answering philosophical questions and say one of either:

• “Can anyone truly claim to know Bayes’ Theorem?” (This one works best if you stroke your beard and look pensively into the middle distance.)
• “It is my belief, examiner, that on some level we are all Bayes Theorem.” (This one works best if you gaze into the examiner’s eyes as you say it, and try to look heartfelt.)
• “But is the Theorem Bayes’s… or was Bayes the Theorem’s all along?” (This one works best if you say it in a deep voice, beginning by looking at the floor, only to look up dramatically and meet the examiner’s eye. You’ll know it’s worked if the examiner responds with something along the lines of “My God… the Theorem’s been playing us like fools…” mirroring your tone of voice and dramatic posturing, and then you both jump out of the window as the building explodes, as do several helicopters…

No wait, that’s Michael Bay’s theorem.

2. Alex goes to the shop and buys 5 apples, 6 bananas, a punnet of cherries, and a quarter of a watermelon.

Trick question! In fact it’s not actually a question – so I don’t know whether that counts as a trick question or not. The point is that, like a typical member of the ethnically diverse, scurvy-free cast of a GCSE maths paper, I really did buy 5 apples, 6 bananas, a punnet of cherries and a quarter of a watermelon. I don’t know if I’ve mentioned Fruit Lady before in a blog, but she sells a wide variety of fruit from a stall close to our house, and it is divine (I’m pretty sure there are already many pictures on Facebook of me gorging myself on watermelon if you look hard enough). That’s one of the reasons for eating so many apples – the other is that my mum recently became a doctor, and I’m hopeful it might scare her away. And I also quite enjoy the fact that I recognise fruit now, which was rarely the case in Peru.

3. What properties of the sun can be inferred from this picture?

Guns ©T. Craig

 

Hint: if you need additional information, refer to the opening section. But beware…

Trick question! Again. And actually a question this time. You will notice in the above picture that the guns are out (incidentally they are not my guns) and, fool that you are, likely assumed that this meant the sun had to be out. If you did this, you are wrong, and I, who learned this a full twenty-four hours ago, scorn and deride you.

Given that A→B, we cannot infer from B that necessarily A, because although guns must be out if the sun is out, the sun doesn’t necessarily have to be out if the guns are out. The guns might be out because you are taking a shower, or because you’re performing a war dance, or because your exams have driven you insane. While in this case the owner of the guns has assured me that the reason for the guns being out was that the sun was out, it was nonetheless an invalid inference and a fallacy.

4. Prior to his exam, Alex has 1 bicycle. When he leaves his exam, he has 0 bicycles. How many bicycles did Alex lose during the course of his exam?

Yeah someone stole my bike during my exam. The answer is 1. I think I forgot to lock it because I was so preoccupied with Aristotle and Frege and Bayes and their probabilities, and some opportunistic fellow decided to steal it. It’s still very annoying though. I mean, what are the chances of that happening?

“Well…”

Okay, quiz over! Add up your scores and post them in the comments, and the person who posts the highest number wins a free bike, provided they can find the man who has it. I have a hunch he lives in Cartagena, and his name rhymes with Bodrigo…

I apologise if you were expecting an interesting blog; it seems that this logic course has ruined me. But this is what my life has been like for the last two weeks. Anyway look out for my next blog, which if I continue on my current trajectory of boringness will probably be written in binary.

Thanks for stopping by ferraread! 01100011 01101001 01100001 01101111 00100001