Part of this job is keeping up to speed with the latest developments, tricks and methods of analysis. It means dedicating time to read articles, papers and specialised tomes. It is an interesting feature of numbers, that many people feel confident to start using them, but like a tourist in a foreign country, can often find themselves taking the long way around.

I’ll give you two examples of how someone trained in  mathematics will save you thousands of dollars, and hundreds of hours of specialised effort.

I am working through a veritable Bible of theory on a particular sampling method. It has lots of equations and theories and goes into detail setting up the system for a particular example. Having completed that (a whole chapter) it proceeds to explain the need for a secondary measuring system, and rederives the equations in this new frame.

After pages of work and justification, the new equations are revealed. We can now apply the sampling regime in two different scenarios. This seems a great idea, and very helpful to all involved, so why would I criticise it?

Because any competent mathematician can see that the answer could be derived in one line of work, through a coordinate transform. One thing that all “numerati” are aware of, is that the rulers and tape measures you use to measure things are independent of what you measure. You therefore pick your measuring devices to suit the problem at hand. This means, you can change devices (coordinates) at any time, and generate the same outcome. With this knowledge, the two limiting cases expounded, become all possible cases.

Do you want to measure radially and azimuthally? What about two linear coordinates, that aren’t at 90 degrees to each other? Would it be easier if one ruler was elastic, and could stretch? Done. And all in the safety of a calculator.

The second case involves taking the long way around, because of a lack of knowledge of synonyms. Again, we are talking about an expert in one field, who has taken up numbers as an interest. What happens is a specific path is chosen, typically because someone else in the field used it. Then analyses are drawn out and complex because the underlying tool is unwieldy. 

With a bit of knowledge, one can look at the system, identify a surrogate or proxy that is just as accurate, but better behaved, and generate the same insight, in a flash of the time. This requires knowledge not of the specialty field or objects, but of the methods used to record and interpret them i.e. numbers.

The moral here is that doctors understand disease, but don’t let them design the method to look for sick people. A ship’s captain knows how to pilot the ship, but it’s a navigator who plots the path.

Oh, and if anyone ever says there is only one method to do something, it’s more likely that they only know one method.