
The Entertainer: In Praise of Raymond Smullyan - headalgorithm
https://www.scientificamerican.com/article/the-entertainer/
======
mwexler
I read everything I could get my hands on that Smullyan wrote when I was 12 or
so. I still have many of the copies of articles, old books, and the notes from
my attempts to work his puzzles in a box, and just opening Alice in Puzzle-
Land, like the madeleine from Proust, instantly brings me back to that time.
Highly recommended.

~~~
braythwayt
My daughter is eleven. When she asks me to read her Smullyan before bed...

I melt.

------
sykhi
I met Raymond at a conference in the early 90s. I was an undergraduate in math
then. We talked about philosophy, religion, and mathematics. Just the two of
us. The next day he came up to me and said that he invented a religion for me.

 _God has a number in mind. If the sum total of good deeds minus bad deeds
exceeds this number then everyone goes to heavan. If not then everyone goes to
hell._

Then he said to me, “Imagine, something you do could send everyone to hell.”

~~~
Entangled
God's number is zero and no matter what we do that sum will always be above
zero. As we are programmed in our DNAs to survive, sustain and multiply, the
average outcome will always be positive no matter how many bad apples. If to
the contrary, we were programmed to self destroy, we would've been gone long
time ago.

~~~
sykhi
Raymond just made up a religion for me. It was not meant by him to be serious.
Our perceptions of reality appear to be very different.

------
braythwayt
Raymond Smullyan is one of the biggest reasons that I'm a programmer today,
most of the reasons that I write about programming today, and nearly all of
the reasons for what I choose to write about, when I write about programming.

He was, literally, who I wanted to be when I grew up. It turned out that I
grew up to be Raganwald, not Raymond, and that is very alright with me.

But I am forever grateful for the influence he had on me.

------
tromp
This is the first time I read about his NPRNPR distillation of Gödel's proof
(N=Not,P=Provable,R=Repeat). So clever. And so Smullyan.

I'll always remember his
[https://en.wikipedia.org/wiki/To_Mock_a_Mockingbird](https://en.wikipedia.org/wiki/To_Mock_a_Mockingbird)
as a most delightful introduction to Combinatory Logic.

~~~
mrmyers
Funny enough, a similar trick can be used to give you the Y combinator.

Let comp be the 'compose' combinator

((comp f g) x) = (f (g x))

Let R be the 'repeat' or 'self-application' combinator

(R x) = (x x)

Then (Y f), the combinator obeying the equation

(Y f) = (f (Y f))

can be expressed as

(Y f) = (R (comp f R))

If our f is NP, then we'll have (NP (R (comp NP R))). So, in other words,
NPRNPR is just (Y NP).

Funny enough, taking that definition of the Y combinator, you can get all of
its special forms (normal order, applicative order, and polyvaradic normal &
applicative order), just by changing the definition of the 'comp' function.

Here's a gist that shows how:

[https://gist.github.com/mromyers/b6d7678bf7a04e106b3d7d5b649...](https://gist.github.com/mromyers/b6d7678bf7a04e106b3d7d5b6493a2e7)

------
mrmyers
While his puzzle books obviously deserve a lot of praise, Smullyan's textbooks
and papers definitely shouldn't be overlooked. There's a lot of wonderful gems
to be found there.

Diagonalization and Self-Reference is the single book I would recommend the
most to the HN crowd. There are a few sections on quotation and Quines that
I've found endlessly useful, his 'Elementary Formal Systems' is my favorite
presentation of computability, and there's a lot of really deep stuff in there
about the interaction between incompleteness, uncomputability, and fixed-
points.

Also, Logical Labyrinths is a pretty great textbook on formal logic. The first
half is in the form of one of his puzzle books, introducing notions and
building intuitions, while the second half builds off of them to provide a
more formal perspective, while incidentally giving a kind of eye opening look
at how he comes up with his puzzles and how they map to certain deeper
properties of logic.

------
okl
Smullyan's puzzle books are superbly entertaining and witty.

------
Entangled
"Suppose there is a mapping from the natural numbers onto the decimals."

Infinity is a tricky subject.

There are infinite naturals, fractions and decimals but they are different
kinds of infinities. If we define natural positives as N and both positive and
negatives as the same infinities N * 2 (with a minus sign), we can safely say
that decimals are simply all naturals multiplied by infinity N * N * N * 2 or
N ^ 3 * 2 where for every single integer like 0, 1 or 2 there will be infinite
decimals after the point prefixed by infinite zeroes too like .1 .01 .001
.0001 and even if N * 2 or N ^ 3 are equal to infinity (infinity because we
can't measure it or at least not know its final boundary) both infinities are
different.

And guessable, we're out of hell someday.

~~~
sykhi
Cardinality is the name given as a measure of the size of a set. The
cardinality of the rationals is the same as the integers. The cardinality of
the reals is larger than that of the integers.

There is an arithmetic of cardinal numbers and it is well understood if you
accept the axiom of choice. For instance, using your notation, N*N = N and N^2
= N. You can read more here

[https://en.m.wikipedia.org/wiki/Cardinal_number](https://en.m.wikipedia.org/wiki/Cardinal_number)

~~~
Entangled
> The cardinality of the rationals is the same as the integers.

If you combine N as all possible numerators with N as denominators you get
that cardinality of Q = N * N

Also, I don't accept the diagonal argument as proof. Given all possible
combinations of numbers, any given number will occur in that set no matter
what. If you add special rules of course it falls apart and Cantor's argument
is just a special rule.

If we use fruits as an example, taking a diagonal from their letters won't
form a fruit either.

    
    
        1. [A]PPLE
        2. O[R]ANGE
        3. MA[N]GO
        4. CHE[R]RY
        :
        N. ARNR ?

~~~
sykhi
It might be worth your time to consider the possibility that it is likely that
the whole of the mathematics profession is not wrong in this matter. Are there
any professional mathematicians that agree with you? If pretty much the whole
profession thinks you are wrong about something then it’s quite likely you are
indeed wrong.

It’s worth pointing out that your logic on Q = N times N is a bit faulty too.
Since you are counting things like 4/4 as different than 1/1\. Even so you are
correct that the cardinality of Q is N times N. This is because N times N = N.

