Fishy distributions

I have been looking at a distribution for determining the number of fish in the sea. This is because I am actually interested in calculating the number of bugs in a block of codes, and thought (probably erroneously) that this would be a good start. The size of the fish population was modelled by a Japanese scientist called Niwa in a way that matches the observed shoal sizes quite well.

However, I am not so sure the model has any physical similarities to the number of bugs in a block of code, because although

he modeled this situation with a stochastic differential equation


performed merging-splitting simulations to estimate variance.

I am not so sure this is relevant for bugs. Nevertheless, it is a start.

The fish distribution is called the Niwa distribution (

I made a picture of the Niwa distribution with Grapher and compared it to the Poisson (blue), Gaussian (green) and Exponential Function (red).

The Niwa distribution

has exponential-like tails that are much ‘fatter’ than Gaussian ones. Thus, observations of large schools are likely to be much more frequent than Gaussian statistics suggest. This indicates that the use of familiar Gaussian models may easily overestimate the total population.



10 Startup Rah Rah Scams

I get a lot of spam. This is not a boast about the size of my Junk-mail box. In the era of trumped up news, pumped-up stereotypes, musky tropes, frankenstein-monster-like memes and recycled group-think, I thought I would tout a diagnostic 10-of-the-best innovation bullshittery.

Most pre-approved personal loans, must-see housing estates, certifications and Agile training land up in Trash. (To think that some poor shmo spent hours crafting the mail shot that has a 1-in-a-gazillion chance of being read is just sad. And then, to think they spent money on a sad-ass mailing list with email addresses like Ah well.

However, what still gets through is the highly personalised startup / innovation / entrepreneur sludge. Admittedly I am sensitive to this world. But I am standing up and saying enough to the sharks and duds and politicians that feed off the dreams of our  dreamers.

#1 First up, politicians always say yes.  This is a warning to the people who may think that going through politicians is a way forward. I have not yet seen government using their spending power in anything other than short term spending. Really they should be doing more, but quite frankly they are so wrapped up in twars to understand really understand your tech, or anyone else’s for that matter. (As for tenders, just don’t do it.)

#2 Making stone soup used to be a funny aphorism to me, until I realised that many events get organised by people who get paid to sit around.  The organisations they represent do not have anything real to offer. They are not incentivised by doing a deal. I got invited to a big national conference, with speakers and agendas and a Plan. We was shocked, when the roadmap turned out to be “we have got you all in a room, now talk”. Big deal.

#3 Beware of the usual suspects. Look at the organisations sponsoring the pitching sessions / conference / etc. There are some organisations who are really not worthy (they may have a big brand, but in terms of delivery they take more than they give).

#4 Trust your friends. They are better than strangers bearing gifts.

#5 Marketing experts are best at marketing themselves. (In any field, an expert is a rare bird.)

#6 Hustlers will hustle you. Give me someone who actually makes something any day.

#7 Beware of invitations to submit to an award. Especially awards you have apparently already won (no kidding). These are often just information gathering. I never unsubscribe from a mailing list, especially if I never joined. If an unsubscribe URL (e.g. http://www.<name>.com/unsubscribe?<david>) is to the organisation in question (http://www.< that requires no more information than already in-play I may unsubscribe.

#8 Beware of permutations of the basic 419 scams. They go like this: we want to publish a position piece on your company that will be seen by Bill Gates, Elon Musk and Angelina Jolie. All you have to do is buy an advert in our illustrious mag.

#9 Never ever ever give up your day job to be an entrepreneur. Especially when the guy telling you to do it gets a pension and uses logic like “a real entrepreneur perseveres despite …” Rubbish – a few exceptions might have succeeded despite … But a real entrepreneur picks their fights, runs away scared and never ever takes chances.

#10 Real innovators don”t read about real innovators. They are busy making stuff that matters.

Unfortunately the list goes on. I will conclude with an opening statement at a recent conference: “Despite investment what is it [that entrepreneurs] really need …” Here are three things: economic growth, an addressable market and, oh, investment.

Bates Distribution

I have been playing with MacOS’s grapher application. It is free and works really well, to understand the Bates distribution (compared to Normal / Gaussian).

As an intermediate step I plotted the following which I find quite cute:

Here is the normal distribution plotted against the Bates distribution.

Here are the two equations and the plot params (we used n= 4

The plot goes wild for x>1 or x<1 – it almost looks chaotic.

Here it is again for n=7