Apollo 11 only has a 32k memory on their computer?

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The 2009 machine only needs 64 MB because it has an over-bloated operating system and fancy graphics.

Right. People who make the argument about computing power largely can't describe accurately what the computer is doing in each of those cases.

A general-purpose home computer has a certain memory and CPU capacity because it can, and because it must in order to anticipate all the potential uses to which its purchaser might apply it. Commensurately the operating system and application software are written to those benchmark values because they can be, and must provide for a variety of applications. The Apollo computer has no need for a sound card or a graphics driver. In fact, the Apollo computer didn't even require a representation for text. No one is going to edit photos on the Apollo computer. No one is going to connect to Facebook.

My clothes washer has a microcontroller in it. The CPU probably costs under $10 and operates at a very slow speed. Clothes-washing is not a very demanding application: you read timers and water-level sensors. You open and close valves. You run pumps and drive motors. However, to simulate the experience of washing clothes, including modeling the washer for three-dimensional graphics and rendering it with photorealistic lighting would indeed require a considerable amount of computing power. If you also wanted to model the fluid dynamics of what goes on in the wash basin you'd require a computer that would cost more than your house. If you wanted one that could do that in real time, the computer would cost more than an office building (and be larger than the washer itself). Simulation of a task on a computer is not the same problem as using a computer to solve the task in real life.

And the washer I had before this one used a fairly standard cam-based mechanical sequencer. That was common technology from the 1800s, used extensively until the 1970s. That raises the point: how much computing power is required to wash clothing? The answer, obviously, is none. We use computers to run washing machines because a small CPU can do the task effectively, cheaply, and reliably -- not because there's something inherent to the task of clothes-washing that requires a computer.

Similarly how much onboard computing power is required to fly to the Moon? Again, the answer is none. The Apollo spacecraft used a computer because a computer was available, not because flying requires one. A Boeing airliner uses many computers to automate the task of commercial flight, making it safer, cheaper, and more reliable. That doesn't mean the Wright brothers were frauds because their airplane didn't have a computer. We use computers because we can, not because we have to. Hence the Apollo guidance computer was assigned tasks its designers knew it could accomplish.

The notion that the Apollo computer was not up to the task is actually one of the sillier arguments because there exists enough detail in the surviving documents and examples to duplicate the computer. It is within the ability of the hobbyist to build one. It is within the ability of almost any computer science student today to program it. The source code for Colossus and Luminary (the software loads for the CM and LM respectively) survives and can be run on emulators and new hardware. In short, it is quite possible for practically anyone to verify that the AGC and LGC worked as advertised.