Patterns are not enough – Numerology

Numerology, the art of putting numbers together to get out other numbers and being convinced you’ve discovered something brand new…

Or something like that.

If you are unsure about what I’m talking about here please take a quick look at the wikipedia article on numerology. This seems to cover it quite well. But I shall explain how I most often come across it. And a possible root cause, or at least a push for those who are likely to fall this way .

My most influential interaction with numerologists is on science internet forums.  Here they come in a range of varieties, from those that believe if you count every occurrence of “the” in the [insert any book title you like here] you can derive the mass of an electron, to those who think starting with two physical constants (numbers) and applying a lot of operators to them you can find another physical constant proves all of physics wrong or that they are the greatest scientist ever.

The first is clearly just crap.  There are no grounds for picking the word “the”, nor any grounds for the units that they finally end up using.  There are any number of numbers you can come up with from applying such processes to pretty much any text, and there are so many observable numbers (mass of particles is a tiny subset) that some of the meaningless numbers are bound to be the same as another number with some meaning… It doesn’t imply the process to find the first number has any merit what so ever.

The second is a more interesting situation… kinda… Let us take an example that someone presented recently,

π*π=g,

So, we have a constant squared is equal to the acceleration due to gravity at the earth surface.  This isn’t actually true.  To a low level of accuracy they can both be rounded to 10, but that’s about as good as it gets.  g is assumed to be 9.81m/s/s, this is in most cases good enough, it does fluctuate depending on where you are though (here, have another wikipedia link).  And π squared is 9.86…

But, and it’s a big but, the gravitational acceleration value given there has units, Units Are Important. I cannot stress that enough, it is just as valid to state that g=32ft/s/s, that certainly isn’t anything close to π squared and our choice of units is arbitrary.  As long as they are consistent and we define them accurately the underlying physics does not change.  The predictions scale with the units, unsurprisingly.  Again we have a case of there being many many numbers to start with and an equally great number of finishing points, if you play around with the numbers long enough you end up having some that are kinda similar.  And if you play for long enough ones that to quite a few decimal places are identical.

So, why are people so attacked to numerology?

I have an idea here, and I’m afraid to say that the following is complete conjecture based on anecdotal evidence, sorry.

Humans are good at pattern recognition.  This has been well documented, a quick google scholar search will give you any amount of reading. So it is understandable that people see numbers, they recognise them and they build a pattern and fall for believing it means something.  We are pattern recognisers, it’s what we do.  That’s why planethunters.org wants real people to look through the data to look for patterns, we’re great at it.  Incidental if you are unfamiliar with the above link, or have yet to try it, give it a go, you might find an exoplanet!  I’m not saying this is bad, patterns can be very useful, but because you see a pattern doesn’t mean that there is a link.  As I’ve discussed there are many numbers, you can do a lot of operations to them, patterns are bound to appear, and humans will spot even the most tenuous link.

This natural ability is compounded by a small area of education.  This might be a very British thing, but that is my only reference point, so please bear with me.

For GCSE maths we were required to conduct some coursework.  That is a piece of written work for the qualification you receive when you are 16, or at least attempt to receive.  This coursework is basically pattern recognition.  We did several practise pieces and then the final one.  They were all pretty similar in concept.

There was some repeating growing sequence and you had to find the matching process.  This was around 10 years ago for me now, so my recollection of the precise piece of work may be somewhat faulty.  I believe we had to draw tessellating shapes with a given number of sides, starting at say 3, given the number of shapes we had to make a prediction about the number of sides the system would have.  This required coming up with some equation.

We then had to repeat this for a greater number of sided shapes.  I realised that it would be possible to include the number of sides each shape had and create some universal equation for tessellating shapes.  Which I assume, looking back, was the aim for the better students.

This process and piece of work has several merits I can see.  It is the closest I recall coming to anything like modern predictive science where a numerical prediction is made and compared to some experiment.  Admittedly the experiment is drawing shapes, but it is a clearly falsifiable system.   This is great, but the word falsifiable was never said to me, nor was any indication that this is anything like science, but only maths.  Science was mostly mixing stuff up, and learning facts, which isn’t in my opinion science.  This is a great shame, and a lesson on predictive, falsifiable theories was missed.

But why does this relate to numerology?  Well here we have some equation that has been picked out of the air.  There was no basis for the equation I used other than it seemed to work.  I was doing pattern recognition.  I realise now that for me to state anything other than the abstract it seems to work I’d need some understanding, some underlying reason why that equation results in the right number of sides.  That is what takes us from just making stuff up and to doing science.

If you have the understanding of the underlying reasons why x equation works, then it might be possible to derive another equation that predicts situation y.  Without that understanding you have just seen a pattern.

If my science education had ended at that point, which for many people it does.  I would still have been able to do some maths, I’d have been able to do the π squared statement above.  And I might have even seen the pattern, and because I had never been taught that a pattern is not enough I might have thought there was some deep understanding that I have discovered, not realising that the understanding is that patterns appear all the time.  My time spent at school would have then damaged my understanding of the universe and because I’d then be much older I would probably have been a little resilient to people just dismissing me, my discovery and even if the situation had been explained to me, still might not have understood just why patterns are not enough.

Please, humour me and let me continue (I am aware that this post is rather long now, 1282 words!).

Science does include pattern recognition. It has to. But (and it’s a big but) the equations used by physicists are not pulled out of the air.  Einstein (sorry about using this example, it makes me cringe, but it’s someone everyone can recognise) for example didn’t sit down and stare at a wall for a while until he wrote down E=mc squared.  He derived it from some very simple assumptions.  That what we do, we make some assumptions about how the world seems to work and then see where that leads us. If the numbers that predicts work then the assumptions we made are true.   Normally the assumptions are only true for a given subset of the universe, it is normal to assume that adding two velocities together works by v1+v2 = v3, but that assumption only works if the velocities are much smaller than the speed of light.  If you tried to derive anything based on that it would work for slow velocities but as soon as they started to approach c it would fail.  Make assumptions, make predictions (numerical, falsifiable) and make experiments.  That’s pretty much it.

Thank you for reading.  I hope you’ve enjoyed my little rant.