Learnt this week… 24 January


My friend and former colleague Adam Higgitt every Friday posts a list of “five things I have learned this week”. It’s popular and good fun – especially as Adam is not afraid of an argument if you challenge some of his claims.

For a while I tried to do the same thing myself, but failed miserably.

I am not going to try again, but I am proposing to try something different, if inspired by Adam.

So here is the first list of things “learnt this week” scientific or mathematical facts and amusements. I will aim for five, but this week just did not make it.

1. A random walk can be used to build a binomial distribution – but not a very good one!

Imagine a left-right ruled line centred on zero and a marker than can, in every time step move either left or right be one step where the probability of moving left p_l and of moving right, p_r are both the same: i.e., p_l = p_r = 0.5 . At the “beginning of time” the marker stands at 0.

Then if we count the times the marker is at any given position they will be distributed bionomially (well, as we approach an infinite time). The BASIC code below (which I wrote using BINSIC) should give you an idea (this code runs the risk of an overflow though, of course and the most interesting thing about it is how unlike a binomial distribution the results can be).


10 DIM A(1001)
12 FOR I = 1 TO 1001
14 LET A(I) = 0
16 NEXT I
20 LET POS = 500
30 FOR I = 1 TO 50000
40 LET X = RND * 2
50 IF X > 1 THEN LET POS = POS + 1 ELSE LET POS = POS - 1
60 LET A(POS) = A(POS) + 1
70 NEXT I
80 PRINT "*****BINOMIAL DISTRIBUTION*****"
90 FOR I = 1 TO 1001
95 LET X = I - 500
110 PRINT X," ",A(I)
120 NEXT I

Here’s a chart of the values generated by similar code (actually run for about 70,000 times):
Not much like a binomial distribution2. Things that are isomorphic have a one-to-one relationship

Up to this point I just had an informal “things that look different but are related through a reversible transformation” idea in my head. But that’s not fully correct.

A simple example might be the logarithms. Every real number has a unique logarithm.

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A little plug for BINSIC


Thirty-three years ago my brother and I got a new cassette player for Christmas.

That allowed us to write and save games for our ZX80 computer (like many ZX80 owners we found that an older cassette player just didn’t work) and in 1981 I wrote a Z80 machine code version of Conway’s Game of Life – still my proudest programming achievement.

Last year I sought to complete the circle by writing an interpreter/DSL that mimiced ZX80 BASIC and called it BINSIC as “BINSIC Is Not Sinclair Instruction Code” and then wrote a BASIC version of the Game of Life (see the screenshot below).

Game of Life in BINSICSo, if you are from that generation computer users, or even if you are not, why not give it a try – more details here: BINSIC

Getting booted from Wikipedia


A short article on “Binsic Is Not Sinclair Instruction Code” (BINSIC), my BASIC-like interpreter/DSL for Groovy faces getting deleted from Wikipedia on the grounds of lack-of-notability.

It would not be right or proper for me to intervene to stop this, but if you have been a BINSIC user then a proper third-party reference to it (followed by a clearance of the deletion message in the prescribed manner) would be very much appreciated.

The BINSIC article does not generate much traffic here (perhaps a visit a day), so I admit it is not a particularly important project in the world of computer science, but I hope it has been fun for at least a few people and it is worth keeping as a link to a quick and easy way to get BASIC on your computer.

More than a game: the Game of Life


English: Diagram from the Game of Life
English: Diagram from the Game of Life (Photo credit: Wikipedia)

Conway’s Game of Life has long fascinated me. Thirty years ago I wrote some Z80 machine code to run it on a Sinclair ZX80 and when I wrote BINSIC, my reimplentation of Sinclair ZX81 BASIC, Life was the obvious choice for a demonstration piece of BASIC (and I had to rewrite it from scratch when I discovered that the version in Basic Computer Games was banjaxed).

But Life is much more than a game – it continues to be the foundation of ongoing research into computability and geometry – as the linked article in the New Scientist reports.

For me, it’s just fun though. When I wrote my first version of it back in 1981 I merely used the rubric in Basic Computer Games – there was no description of gliders or any of the other fascinating patterns that the game throws up – so in a sense I “discovered” them independently, with all the excitement that implies: it is certainly possible to spend hours typing in patterns to see what results they produce and to keep coming back for more.

  • “Life.bas” should run on any system that will support the Java SDK – for instance it will run on a Raspberry Pi – follow the instructions on the BINSIC page. A more up to date version may be available in the Github repository at any given time (for instance, at the time of writing, the version in Git supports graphics plotting, the version in the JAR file on the server only supports text plotting). On the other hand, at any given time the version in Git may not work at all: thems the breaks. If you need assistance then just comment here or email me adrianmcmenamin at gmail.