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"Precisely! It can’t be changed to do another job."

By your definition a compiled program is no longer an algorithm either since the binary code cannot be changed. With your logic a computer running only binary code is not a computer because it cannot be changed to do another job.

You are looking for a clear delineation between and analog computer and a binary computer but the Antikythera mechanism remains indicate that it allowed user inputs to adjust for different results so the line is blurry at best. With the Antikythera mechanism the algorithms and logic calculations are built into the gears, the dials, the inscriptions and iconography of the outside, and adjustment dials.

My definition does not imply what you said it does, not even in the slightest. It beats the crap out of me how you could arrive at such an interpretation. Of course a binary computer can be changed to run another program. I can do that with a hex editor if I wanted to badly enough. I have done what you evidently have not, nor will have the opportunity to do: I have programmed digital computers using switches on their front panels. That capability is in the very nature of their design, quite unlike the Antikythera mechanism.

I am not even looking for a differentiation between an analog and a digital computer. The Antikythera mechanism is a mechanical computer that uses wheels and cogs, perhaps cams. Those cannot be changed. The input settings are presets. It is more like a fire control computer used on ships from the late 1800s and through WWII. It is certainly not an analog computer.

I've used analog computers. They consist of a number of operational amplifiers, pots, and even a plug-board. It can be programmed by changing the plug-board and the potentiometer settings. I have also used a hybrid computer, which is an analog computer connected to a digital computer via analog-to-digital and digital-to-analog converters.

Your response is very pedestrian. It all boils down to this: the Antikythera mechanism is not the earliest ancestor of the computer. It is an ancestor of a calculator. I have no idea why you think that thing just HAS to be what the article says its. It is an important device in its own family of instruments.