Mathematical progress

This post is about product development, innovation, and problem solving NOT of the equation and math variety. It’s about an interesting (to me) parallel I made between the progress of an unfolding new product and formulations of mathematics.

Once you get past the basic mathematics of addition, substraction, multiplication, and division, you end up moving further into (often very practical) abstractions known as algebra and calculus. It hardly matters what their value and technique is about at this point. What’s important is the following:

• Algebra is about problem solving.  That is, it is about finding the right answers to a dilema which in an equation is an unknown variable.  You know, in 2x(2)+4xy-y(2), solve for x…
• Calculus solves as well, but in its case the solution is to find the rate of change, which is where all that integral and derivative stuff comes in handy.

Admittedly, that’s a pretty vague and insubstantial summation of two bodies of extremely complex abstract thought. Whatever. Remember, I’m making a bit of a parallel for another purpose.  That purpose is this.

As an assessment of a business, business opportunity, product, service, market, etc. develops from the first thought (i.e., “Here’s an idea:  I wonder if socks with no seam at the toe would be a cool product?”) through to a more complicated strategy or plan (or assessment of ongoing activity (i.e., “How well are the no-seam socks doing against pantyhose?”), the type of math being done changes.

It seems to me that in the earliest stages what we’re doing is algebra. The objective is to solve for an unknown. Given a bunch of assumptions or informational points, we’re searching for (probabalistic) answers. The equation’s results help define whether we have an opportunity or whether a choice is (more) right or wrong than another. The financial and other models’ concern is to provide a darker or lighter shade of grey to indicate a solution. From that solution we make decisions and choices.

On the other hand, after the business or project or what have you is established, the nature of our enquiring is no longer, or should no longer be algebraic. It should move to the calculus of the situation. We have effectively solved the equation, albeit that there may be a host of valid solutions for x and y. There’s no point in trying to find the exact solution because it doesn’t exist. Now, the challenge is to understand the velocity of the chosen solution set. That is, keeping up with the parallel, we picked an x,y set that is valid and now we need to make certain that its rate of (positive) change is maximized. So, algebra doesn’t do us any good; integrals and derivitives are required.

I recognize that almost nobody is operating with this (or perhaps any other) explicit such purpose or method. But, if you buy into this change, then you, too, have to beg the question:

So, why the hell do so many intelligent people continue to do algebra long after its value has become obviously purposeless, instead of doing calculus, which will provide more value in the circumstance?

I’ll ponder the answer in another post later. Stay tuned.