Mathematics has confused everyone since the dawn of civilization.
Math is supposed to be the pure science, but numbers appear to be far less pure than mathematicians let on.
There are examples of this everywhere. Consider the latest process nodes. One foundry’s 10nm is another foundry’s 7nm. And 7nm isn’t necessarily 7nm. It might be 7.5nm or 6.5nm. It’s not so much that the measurements aren’t accurate. It’s how they’re applied that causes the problem.
But numbers have been abused and misused for many years. Nearly two millennium before the semiconductor was invented, numbers were being thrown around in the name of science with the introduction of the first modern calendar. The Julian calendar, named after Julius Caesar, took effect on Jan. 1 in the year 45 B.C. in celebration of Rome’s conquest of Egypt. Unfortunately, the pontiffs who oversaw it mistakenly added a leap year every three years rather than four.
And that was just the beginning of the confusion. The Julian calendar was off by 11 minutes a year, or roughly one day every 128 years. The Gregorian calendar, which replaced it in 1582, is off by one day every 3,030 years. But it took more than three centuries for all countries to adopt the new calendar. That created an even bigger problem because when the Gregorian version was first introduced, Pope Gregory XIII issued a decree to eliminate 10 days.
So nearly 435 years ago, in the name of pure science, it is well documented that people were just as confused by numbers as they are today. And it doesn’t stop there. Politicians use numbers regularly to support their claims, but the numbers are often wrong, subject to interpretation, or in need of further explanation—and sometimes all three. And there are enough lawsuits by corporate shareholders to show that earnings results were slanted to either put an unrealistically positive or negative spin on numbers.
Fortunately for all of us, there is binary code, which boils things down to a much simpler implementation. There are either ones and zeroes. And, in theory, there is no possible way to mix those up. But the floating-point unit introduced in 1994 in one giant chipmaker’s processors produced erroneous results sometimes. That was well documented. The company even replaced the chips, no questions asked. What wasn’t clear was how often the errors would occur. The chipmaker claimed it would happen once every 27,000 years. The company’s chief competitor claimed it would occur once every 24 days.
Computer viruses and malware purposely mix up the ones and zeroes. And there are strange phenomena being reported with GPS systems, which should present a finite set of coordinates, that show visitors to Moscow’s Red Square that they are not actually in Red Square.
So is math really as pure as its proponents suggest? The answer isn’t clear. Even with ones and zeroes, quantum computing threatens to blur the lines. There really is only one answer to a mathematical problem, but people have a knack for redefining problems using numbers and coming up with different answers. Numbers, it turns out, are much simpler to manipulate than electrons or photons. And while they are a mathematician’s primary tool, a lot of people with less pure motives seem to be using those tools, as well.
As we head into 2017, or whatever year it really is, developing chips at whatever node people are calling it, remember that numbers are sometimes no different than the people who use them. And no matter how much it appears one number is the same as the next, that isn’t always the case.
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