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Now that we have an understanding of the resources available at the time, let’s take a step back and think about what it would be like to be an inventor in let’s say the 1600s for a minute. If you wanted to design a machine that would aid in the computation of complex values, what should it do? What does that mean for a computer? Right? If we’re trying to avoid a lot of the human error that we have in calculating specific values, or make our lives easier, what should that computer what should that device actually do?
Based off of that discussion, or based off of that thought, I’m going to suggest four different things that a modern computer should be able to do. It should be able to compute some form of complex value and not just one calculation, but many, many types of calculations. It should be able to accept variable input. So not just a simple calculator that can accept numbers, but accept all sorts of different things like even a program, for example. It should be able to store information and should also be able to output that information as well. Because what’s the point of computing something if you can’t actually see what the result is? So you might see that many of these actually compared to the functions of computers today, right? The processor, a CPU that can compute value, programs for variable input, your RAM or your hard drive for storing information and your monitor or your printer that can output the results. Before we go further, right we need, we’ll need to figure out some way to compute values. And as we discussed earlier, human error is a major problem here. So regardless of how well the machine is capable of computing those values, we need to reduce or eliminate that factor of human error. So we want to design something that doesn’t have any humans involved in the calculation. Because if there is, like the abacus or the slide rule, the result is only as good as the person actually operating the machine.
So one step into that in 1642, Blaise Pascal invented the mechanical calculator to solve that problem. And now it was originally designed to help his father calculate tax revenues and of course if you know a little bit of history during that time period, taxes were pretty big deal and you know, if you collected too much from your townspeople, right, everyone grabbed their pitchforks and torches, and if you were the guy collecting taxes, if you didn’t collect enough, the king would go, you know, off with your head, that sort of thing, right? So this is a pretty big deal. Any sort of error could really literally mean life or death. So this machine was capable of addition and subtraction and could simulate multiplication and division by repetition. So, you know, essentially the beginnings of the calculator that we know and use today. Unlike the abacus, there’s much less room for human error. Here you input the numbers, and out come a result.
To further improve on Blaise Pascal’s design, in 1673 Gottfried Leibniz created a stepped drum, commonly referred to as a Leibniz wheel that greatly increased or enhanced the capabilities of any mechanical calculator that used it. With the innovations of these two guys here, the Pascal and Leibniz, the world now had the capability, at least the mechanical capability, to perform calculations.
That really led to Charles Babbage. And now in 1823, Charles Babbage designed his first Difference Engine, and built the prototype that was showcased in his study in his home for quite some time. Now, this is the, the larger version of that prototype, but the difference engine itself was capable of simple mathematics and could solve even polynomial equations up to six digits. So, this was a huge step forward, but it was only a small part of what Babbage had actually envisioned. The Difference Engine is what we call a fixed program or a single purpose computer, meaning that it could only do the task that it was built for; it couldn’t be reprogrammed to do anything else like our modern computers could. The Difference Engine could calculate the value of any seventh order polynomial, given the correct input by using method of finite differences. While the differentiation itself in its entirety wasn’t built during his lifetime, Babbage’s idea here was really truly revolutionary.