Where, exactly, is the intersection between Math and Patterns?

Initially patterns are a visual experience and not an analytical one.

Delving deeper, there are always math connotations, such as with fractiles.

The two skills are different.

An eye for patterns would have been very usefull in matrices up untill recently, but now freely available software makes that obsolete.

Speaking outside my realm of expertise here, and with all due respect to Gail, I see a great deal of overlap. Patterns mean some sort of regularity of relationship (unless you’re talking about patterns such as seeing crabs and archers when you look at the stars), and what is that but mathematics? You can generate a pattern from a formula and create a formula to describe a pattern.

Aren’t the patterns in numerical relationships a path to discovery of mathematical principles? And can’t those relationships typically be expressed graphically, whether by models, graphs, or abstract depictions?

As to how you might use the skill you have and its relationship to mathematics, I have no idea, but I’m sure there must be a way.

@Nullo I think you’d enjoy Doodling in Math Class.

@Jeruba: Gail fellow, well met. Have you noticed that spell-check is getting more and more annoying?

@phaedryx I actually did that sort of thing, but not in math class. I waited for the state-required (and therefore easy as all heck) government class. :D

One definition of mathematics is the study of patterns. So in that view there’s complete overlap.

There is intellectual overlap, of course. But that is not the same as having a brain that can process both the aesthetics and the math.

The mathematician’s pattern’s, like those of the painter’s or the poet’s, must be beautiful, the ideas, like the colours or the words, must fit together in a harmonious way. There is no permanent place in the world for ugly mathematics.

George Hardy, mathematician

Included in these quotes

@phaedryx that was the first thing that came to my mind when I saw this question as well.

@Nullo What an excellent question. Maths deal well with place and pace, the first great leaps forward that maths made. The first math, developed by the ancient Greeks, was Geometry. It dealt with place. Then came Algebra and Calculus, which together were sufficient to deal with “pace”. No sequential math is sufficient to deal with an ever-changing pattern, however. Modeling the behavior of a hurricane, for instance, would not be possible without computer simulations that evolve to be ever more predictive.

For pattern, we need a whole new math that, unlike the previous two, is completely beyond the grasp of the current human brain. It can only be handled in massively parallel computing. There, you can take a truly junky collection of programs, feed them all the known data-points that might impact the pattern in question, and see which produce the most accurate predictions. Those, you then allow to “survive” along with mutated progeny. You repeat the process over and over. Bear in mind that in each iteration, you are crunching billions or trillions of complex equations. And generation after generation, the survival of the fittest few evolves an ever more accurate model. Brilliant as it may be, the human mind has nowhere near the raw processing power to do this. We can’t even fully comprehend what our simulations are doing. We just know roughly how well they work.

It’s an old book now, but if you’re interested in this, I recommend James Bailey’s after thought: the computer challenges to human intellignece.

Nullo, one topic in math you may enjoy is that of sequences and series. Pattern-seeking abilities are absolutely invaluable here.

Say you have a sequence like 1, 3, 5, 7, 9… Anyone can understand intuitively what this is and where it is going, but not just anyone could give me an answer when I ask what the 1047th term in the sequence is. They might believe they have to actually list out 1047 terms in order to answer me. This is not necessary when you are a good pattern seeker. You can define this sequence with an expression involving n that, when substituting a value for n, will yield the nth term of the sequence. The expression for this particular example is 2n-1 (and the 1047th term is 2*1047–1 = 2093). All odd numbers are one less than an even number, and all even numbers are twice an integer. A good pattern seeker can see this far more easily than someone without that skill.

Of course that is a simple example. If you are interested and look into it further, things just get more fun from there.