Diary, March 1997

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    power(in s : P int, out P P int)
    = { ss : P P int | ss subset s }

Normally, when you want to generate a power set of a set, you use a recursive procedure, which picks an element from the set, and generates the sets with and without that element. But, in TM, being a true specification language, sets are sets, which means you do not have an operation to pick an arbitrary element. (You can split sets based on a criteria, and return the element of a set which contains exactly one element.)

I had almost come to the conclusion that there is no elegant specification of a power set (not using the predicative set), and was explaining this to one of it designers, when I suddenly saw the solution:

     power(in s : P int, out P P int)
     = { s } union unnest (collect power[self](s minus { e }) for e in s)

The reason why I did not see this solution at first, is because I am more of a hacker than a specifier. The method has acceptable performance for sets up to 6 elements, but larger sets become problematic.

Thursday, March 6, 1997

"You are in a concrete room, <with> no exits. In this room there are two things with you, a table and a mirror. How do you get out"

The analysis by Matt

1. an actor's departure ... probably does not apply here
2. a going out; departure ... doesn't make sense
3. a way out

So what is left? To begin, the meaning of "exit" probably either means "obvious exits" or "traditional exits" with the understanding that, "Hey, if you don't figure out some trick, your gonna be stuck here for a long time."

Making the somewhat rash assumption that I am NOT Superman, I look up the word 'table'.

table:

1. orig. a thin slab of metal, stone, etc. ... I guess I could use to this try and bash my way out.
2. a piece of furniture [snip] ... this is the obvious interp.
3. a systematic list of details, [snip] facts, figures ... now this shows some promise (if the table happens to be a list of when a wormhole will open up next to you)
4. any flat horizontal [blah blah blah]

The definitions of 'mirror' and 'you' give little help. 'Out' has more definitions than I care to type here. So what's left beyond this? Puns I guess.

How do you get out? Place the mirror on the wall, thus my image is "out" of the room, and turn the table on it. Or ignoring the other conditions of the question: How do you get out? Three strikes, for example.

The question can be assaulted logically. "You are in a room with no exits." - "No, I am not." - "Pretend for a moment, [snip], how do you get out?" - "I am pretending that I can teleport." I doubt, however, that this is what was intended.

Are we done? Not remotely! We can define ourselves to be out and the rest of the universe contained within the box. We can suggest that though the walls are concrete, they are wafer-thin. We can also appeal to literary characters (as I am obviously Alice, I step through the looking glass).

Many more possibilities spring to mind. Is there some context to this question? Is this, for example, part of a game where additional information would narrow the search for answers?

The answer by Yos

I heard this when I was a kid. Matt, lighten up a little! You took all the fun out of the question with your logical answer.

The answer by Jaybird

Asperger Syndrome

1. Have you never been able to make and sustain friends? (No. I am married right now.)
2. Do you have difficulty recognizing people's faces? (No, but remembering their names.) or Do you have an excellent memory? (No.) Can you do complex math in your head? (Yes.) Can you visualize complex structures and their relationships in your mind? (Yes.)
3. Were you constantly teased and tormented by other kids at school? (Often. And the strange thing was that often I was completely aware of what was happening, but not being able to respond.)
4. Have you seldom or never been able to get a date? If you are in a relationship, it happened almost "by accident"? No long friendship and no romance? (Friendships often, but most of the time nothing further.)
5. Are you very good at computers or engineering, but poor at social relations? (Definitely.)
6. Do you not look at the eyes of the other person when talking to him/her? (I have learned to do this. And sometimes I still find it hard to look people in their eyes.)
7. Do you have few and narrow interests or hobbies, and sometimes become obsessed with them? (Yes.) Do you like to collect things or keep your possessions clearly categorized and listed? (Slightly.) Are routines very important for you? (No.)
8. Are you a loner? An outcast? Do people sometimes call you "eccentric", "strange", "weird", or even "nut" or "crazy"? (In the past yes, not anymore.)
9. Do you have a tendency to fantasize and speculate? (Yes.) Do you spend a lot of time in inner retrospection? (Yes.)
10. Do other people's feelings go 'over your head'? (Sometimes.) And even if you do notice them, do you still feel at a complete loss with how to act when they show some deep feelings? (Yes.) Do you feel incapable of showing compassion? (Sometimes.)

(follow-up)

Programming aptitude test by John Graley

1. (5 points)
   Explain why "too many cooks spoil the broth" in terms of the effect on efficiency of allocating more than one person on a particular (manual or intellectual) task.

2. (5 points)
   Explain how it is possible for a single wrongly set overload circuit breaker to cause a power cut affecting half of America.

3. (5 points)
   Assuming you know nothing of the specialised field of time travel, say as much as you can about how you would make such a machine (this question is not oxymoronic; you need to (a) say anything you can say with certainty and (b) say how you might cope with the things you don't know about).

4. (10 points)
   Choose any form (eg inland revenue, insurance claim, marketing survey etc). Now, analyse the form, and try to "improve" it as much as you can. You decide what is "better". Give details of the improvements you made.

5. (15 points)
   As you probably already know, a quadratic can be solved using the "completing the square" method. For example:

   I want to solve x^2 - 4x + 3 = 0 <---- the quadratic

   STEP 1: Note that x^2 - 4x + 4 = 1
   STEP 2: Note that ( x - 2 )^2 = 1
   STEP 3: Note that x - 2 = -1 or 1
   STEP 4: Note that x = 1 or 3       <---- The solution
   

   Using this single example as a guide, you must derive, and prove (or at least argue for) an equation to solve all quadratics of the form ax^2 + bx + c = 0. Hint: start by normalising a to 1.

6. (10 points)
   Rewrite your quote, above, in as few characters as possible, whilst keeping it meaningful and in English.

7. (10 points)
   Do 6/ again, but this time you can use your own codes, language etc, as long as you provide a key, which is meaningful in English. See if you can get to less characters than your answer to 6/ including the key.

The points indicated are as an effort guide only. I will not be marking any exams, as this seems like a sure way to start a flame war.

Cheers, John

(follow-up)

(follow-up)