If you want to go down the rabbit hole however (and since you asked), hereâ€™s my advice: read SICP. If youâ€™ve been programming in Algol-inspired languages for the last 15 years, your head will probably explode. It is worth it. Do the examples. Follow along with the videos: they contain all kinds of little nuggets of wisdom that may take time to sink in.
SICP, I thought, what the hell is that? It transpires that this book is, as they say in colloquial circles, like frikkin’ huge man. Huge in fame (it’s taught in a lot of places that I could only dream of attending when I was as an undergraduate) and, as it turns out, also huge in terms of sheer quantity of information inside it. So I ordered it on Amazon, waited a few weeks for it to arrive and then queued it up on my bookshelf.
About a month ago I started gently plodding my way through it, scratching my head, doing the exercises and all. It really is very good, but I have no idea how I would have done this as an introductory programming course at Uni. Let’s just say the exercises can be a little challenging, to me at least.
The amazing thing is I’ve only really just finished Chapter 1 and I feel like I’ve put my head through a wringer. So I’d really like it if you can come and visit me at the funny farm after I’ve done Chapter 5. Visiting hours are 9-5 and please don’t shout at the other patients it freaks them out. Anyway, today’s mind melt is Exercise 2.5 and it asks us to …
Exercise 2.5. Show that we can represent pairs of nonnegative integers using only numbers and arithmetic operations if we represent the pair a and b as the integer that is the product (2^a * 3^b). Give the corresponding definitions of the procedures cons, car, and cdr.
Up until now all the really hard problems had ‘Hints:’ in parentheses. That’s usually how I know when I’m going to be screwed. I wrote some numbers down, first on paper then in Egg-Smell but I just couldn’t see how I was going to extract two numbers from the encoding. Then, bizarrely, whilst reading about Church numerals (eek) I discovered that there’s a fundamental theorem of arithmetic that I never knew about. How does that happen? How did something that fundamental escape me all these years? Reading it was like being told by a German co-worker that the only time an apostrophe is appropriate in “it’s” is for a contraction of “it is”. ScheiÃŸe.
Not only is there a fundamental theorem but it suggests the answer to Exercise 2.5. Perhaps one day I’ll be able to program & punctuate. One day.