Gratification

On Friday, during the partial eclipse I was tempted to look at the Sun.
I had heard the warnings.
I looked at it, and my eyes smarted.
I was still tempted to look at it.
What’s this deferring gratification thing? Weighing a glimpse of the sun as a crescent against the chance of permanent damage to eyes, I am still tempted!!

I then spent much of the day with the Three Guardians puzzle. Before I came up with the right questions, I spent hours with wrong questions and what various answers to them would mean. I am very pleased with having the right answer, and having thought of a fourth guardian which answered randomly, like a coin-toss, could answer that more complex problem with between five and eleven questions. Probably I should have done my washing, and in the beautiful sunshine a walk round the lakes might have been more relaxing, but working on that puzzle was the immediately gratifying thing.

A hug felt sexier than an ordinary friendly hug, and was followed up with an email addressed “Dearest Abigail”. She would be in touch, she said. Over a week later, I am on tenterhooks and wondering if she is messing with me, which feels cruel: that “dearest” touched my heart. I create theories of why she might deliberately hurt me, which feel possible but unlikely; but likelier the longer time goes on. Why would she would want to mess with me? Becoz I is trans, or because I had irritated her in some way I cannot imagine, or randomly without reason. The thought that she might not be in touch because of shyness or vulnerability in her came to me only later.

In The Last Battle, the dwarves go into the barn which is actually the gate of Heaven. The children see Heaven with its beautiful scenery getting more beautiful as you go further up and further in, but the dwarves see only a derelict barn with stinking old straw. So the children pick flowers for the dwarves, and the dwarves react angrily: Why are you shoving straw in our faces?

I came across “thetruthisstrangerthanfiction” on Violet’s blog. He is creationist. I find the complex, interlocking explanations of all the evidence of the age of the Earth fascinating and beautiful, and he finds them repellent: the desire to keep a meddling God with His meddling “morality” and call for “repentance” etc., is the real motivating factor at play behind the scientists’ rejection of young earth creationism, rather than the search for Truth which I perceive. Then again, his flowers- a literal interpretation of Genesis- are mouldy straw to me.

I want to persuade him. He is not persuadable, because he is immovably convinced that he has something better (as, mutatis mutandis, am I). I put long comments on his blog, rather than walking by the lakes or doing my washing. I wrote on facebook, to acclaim, I do not need you to be other than you are to validate who I am but one benighted stranger on another continent and a woman who may be hostile seem to indicate otherwise.

What I want may not be what is best for me.

Alte Pinakothek, Munich

Logic problem

In The Pyramids of Mars, Sarah-Jane Smith is trapped. There are two switches, one of which will release her, one of which will kill her. There are two guardians,  one of which tells the truth, the other always lying. The Doctor can ask one guardian one question. He asks,

“If I asked the other guardian which was the life switch, which would it indicate?”

The liar will lie about the truth-teller, and so indicate the death switch. The truth-teller will tell the truth about the liar, so indicate the death switch. The Doctor presses the other switch and Sarah is released.

John Finnemore did a sketch in which the guardians are fed up because everyone now knows what to ask- so they introduce a third guardian who strictly alternates, lying in one answer then telling the truth in the next. You will not know whether the alternator will lie or tell the truth, because you do not know which it did last time, to the last intrepid explorer. It will only change from lying to telling the truth if asked a question. There are still a life switch and a death switch. The only permitted questions are those which can be answered by a guardian pointing at a switch.

If you ask the first guardian, which is the Life switch, then ask the first the same question again, and the answers are different, you know that the first is the alternator, and you can ask the second guardian the Doctor’s question about the third. If the first’s answers are the same, and you ask the second guardian the same question twice, if the second’s answers are the same the third is the alternator: ask the first the Doctor’s question about the second; but if the second’s answers differ then it is the alternator, and you ask the first the Doctor’s question about the third. So you can always identify the life switch in five questions, and sometimes with three.

However, I can always identify the life switch with three questions.

What questions do you ask so that, whatever the answers, you can always find the life switch with three questions?

Call the guardians 1, 2 and 3 and the switches X and Y. Kudos to anyone who answers this. If anyone asks, I will answer it in a week, in the comments. (Added: The answer is now below, in the comments.)

I have no idea if anyone else has worked on this puzzle. It seems likely someone has. I thought I had answered it, then found a flaw in my argument, and scheduled this post for 1 April; but now, I am clear that I have answered the puzzle.