# Apple and Microsoft War Now Dictated by Mathematics

The fact that Microsoft's Internet Explorer is steadily declining in market share, monotonically, suggests that there are mathematical market forces at work that cannot be overcome by any action Microsoft takes. The same mathematics applies to Apple's OS market share, and so Microsoft's battle against Firefox is just a warmup.

The most recent data from Net Applications shows that Microsoft's Internet Explorer has dropped to less than 70 percent on the Internet. The decline is a steady, monotonic decline, which begs the question of what market and mathematical forces can lead to that kind of decline.

A monotonic function is one that steadily decreases or increases without reversing. What that seems to suggest is that the market share of IE is outside the control of Microsoft, no matter what improvements they make. Conversely, the monotonic increase in Firefox and Safari suggest the same thing -- market forces are at work.

One way market forces can affect the share of a product is word of mouth and consumer communication on the Internet. It's an effect similar to to how crime increases faster than population growth in a closely bound region. A comparison is worthwhile.

The chart below shows how in a closed population of two people, A can interact with B or B with A. Using the notation of [number of people: number of interactions], the first group is [2:2]. For three people, the result is [3:6]. For four people, the result is [4:12]. Even though the population has only doubled from the first group of two to the final group of four, the number of possible interactions has gone up by a factor of 6. Assuming the probability of any given illegal interaction is a constant, and other factors being equal, the mathematical progression says that the probability of a one-on-one crime goes up faster than the rate of population growth.

Note that this simple analysis doesn't even take into account multiple interactions, such as (A+B) interacting with C. That increases the number of possible interactions even more. In fact, it's a factorial function.

The same thing happens when word of mouth gets around on a particular product, whether it's between IT managers or consumers. As the adoption rate grows, more people talk to more people about their experience and assessment. Instead of a crime happening, as in the example above, a certain percentage of people, call it "p1," will be influenced by their peers during the interaction and make the switch.

My mathematical intuition tells me that this is what is happening with Internet Explorer. It's not happening as fast with on the operating system side because IT managers are fairly fixated on Microsoft and its suite of solutions, but they, and consumers, have an additional degree of freedom to select their browser of choice -- even if they're stuck on Windows.

The fact that there is a monotonic decrease in both Windows and IE market share suggests that there is nothing Microsoft can do, including advertising, to reverse the trend. They can slow it, by reducing the constant p1 via marketing, but it can't be reversed. A similar effect happened to the Netscape Corporation as Microsoft monotonically stole their market share in the late 1990s.

When companies arrive in such a situation, there are two common reactions. One is denial. The other is a radical change in the status quo.

I remember a classic case of denial. When I was at the Oak Ridge National Laboratory in the 1990s, I was a member of an advisory committee for IT managers. We were tracking the purchase of desktop databases by laboratory staff members. The sales data, over a period of about 10 years was roughly as follows:

Our committee recommendation was that Access was coming on strong and would supplant Foxbase. The Laboratory should plan accordingly. Management reaction, upon seeing that chart was basically: "Foxbase has the bigger installed base and would be the standard forever. The data is incomplete."

It was a denial of the mathematics -- in this case, three consecutive Gaussian curves. [Later, MS Access did, in fact, supplant Foxbase well before Foxbase was discontinued.]

The other thing a company could do, and Apple has done this, is to make a radical change. Just as Apple canned OpenDoc, the Newton and Classic, Microsoft could radically rebrand and rethink the browser. That's unlikely, considering their commitment to business -- they've lost a degree of freedom along the way.

When a company can't change and the market forces are driven by the statistics of large populations, there's nothing to be done. Worse, when the statistics contain an implicit factorial function, a market share upheaval happens faster than anticipated. Then the denial morphs into a panic reaction which does more harm than good.

Now is probably the right time for Microsoft to think its way out if this IE market share problem before the same effect happens on the OS side. Apple's market share is also monotonically increasing due to the same market effects: word of mouth, on the Internet or in person.

While the decline in Windows market share is happening at a much smaller rate, similar fundamental forces are at work there as in the browser market. It's just that the mathematical constant, p1, is smaller. Solving the IE vs. Firefox problem will be a warm up for what comes next, an exponentially rising Apple market share that gets out of hand and takes Microsoft by surprise.