Chapter 3. The IF… THEN machine¶

You need the first two chapters.

The boxes are different¶

The OR and NOT-AND machines had identical boxes: it didn't matter whether yours was the left or the right one. Today's machine is not like that. Its boxes are different: the left one is called "if", the right one "then". And which of them is yours changes everything.

The machine's rules¶

The table, as always, is known in advance. Don't try to match it to how people say "if… then" in everyday talk — these are simply the machine's rules, agreed on before the game:

"if" (left)   "then" (right)   light
yes           yes              YES
yes           no               NO
no            yes              YES
no            no               YES

Look carefully: there is exactly one NO — when "if" holds "yes" and "then" holds "no". Every other row says YES.

The two bottom rows may look strange: "if" holds "no", yet the light still says YES. That is how this machine is built, and that is its strength — you'll see in a moment.

Your box is "then"¶

Say the trickster has "if", and "then" is yours.

You put in "no". The trickster puts in "yes" to "if". The table: if yes, then no — NO. The trickster got what he wanted.

You put in "yes". The trickster thinks. "Yes" in "if" — if yes, then yes — YES. "No" in "if" — if no, then yes — YES. Whatever he does — YES.

Your box is "then" — put in "yes".

Your box is "if"¶

Now the other way round: "if" is yours, and the trickster has "then".

You put in "yes". The trickster puts in "no" to "then". Yes and no — NO.

You put in "no". The trickster thinks. "Yes" in "then" — if no, then yes — YES. "No" in "then" — if no, then no — YES. Whatever he does — YES.

Your box is "if" — put in "no".

That is what those two "strange" bottom rows are for: they are exactly what saves you when your box is "if".

Two moves — one idea¶

For NO the trickster needs two notes at once: "yes" in "if" and "no" in "then". One of these two boxes is yours. Put in it not what he needs — and his plan is gone:

your box is "if"     →  put in "no"
your box is "then"   →  put in "yes"

As in the previous chapters: look at the table to see what the machine needs for NO, and wreck that plan with your note.

And if both boxes are the trickster's?¶

He puts "yes" in "if" and "no" in "then" — NO. Against two of his boxes you can do nothing.

Try it with a friend¶

On slips of paper, as before, but now agree whose box is "if" and whose is "then". Play both ways round and see: in "if", "no" saves you; in "then", "yes" does.

Puzzles¶

Your box is "then". What should you put in?
Your box is "if". What should you put in?
You put "yes" in "if" (the trickster has "then"). What does the trickster put in, and what does the machine show?

Think it through first, then check.

Answers. 1 — "yes". 2 — "no". 3 — he puts in "no" to "then", and the machine shows NO.

So we have three machines on which the trickster can be stopped: OR, NOT-AND and IF… THEN. In the next chapter: new words — "true", "false" and Z.