In truth, the interpretation of Stonehenge as an astronomical calculator is, at best, controversial. Interpreting it as an observatory is much less controversial, although there is much difference of opinion on the probable purpose of observations made from the site.
One thing is certain, you can tell the time of day and the season of the year by where shadows fall and by where the sun, moon, and prominent constellations are observed, relative to the stones. (Some have called Stonehenge a giant astrolabe, although the moving parts would be people using it, in such a comparison.)
Which brings me to the first leg of my working definition of a computer:
A (generally physical) device which is
capable of receiving some sort of input
capable of producing some sort of output
and capable of deriving the output from the input
and, of course, there were procedures, functions, and protocols in its use
Interpreting Stonehenge as a computer by this definition is perhaps stretching definitions a bit. However, it clearly can be used as a physical aid to the computation of the positions of celestial objects.
And this is precisely the function that even modern supercomputers perform, to aid us in our computations.
It may be a little hard to see the trees for the forest, but input is the observation of the stars through the stones. Processing is in the observer, properly positioned, as is output. Storage is the stones themselves, but also the memory of the observer.
If you go looking around for early examples of calculating devices, one commonly mentioned device is the abacus. I think many people would complain if we call it a computer, or even a calculator, again, because it is not in the same form as the devices we commonly apply the terms to. But it cannot be denied that we can use it to aid our calculations (and, therefore, our computations).
Analyzing it as a computer, we see that the input device, the storage device, and the output device are combined, and the processing function is obtained by user interaction with the abacus.
In other words, the beads or disks are where the numbers are stored. Input is directly from finger to storage, and has some rules that the user must follow. Calculation at the same time as the input, according to the rules:
Move the beads.
If there aren't enough beads to move,
record a carry/borrow in the next column and
move the beads the other direction.
Output is directly from storage (beads) to eyeball.
The difficulty in perceiving the abacus as a computer is that none of the functions are automatic, and all the modern computers we see around us are very automatic. At least, they perform a whole lot of operations without human intervention, where the abacus requires human intervention at every step.
An abacus may be built with ten beads per column for decimal arithmetic, or eight for octal, sixteen for hexadecimal, or, really, any number of beads per column for any arbitrary numeric base.
A variation common in Japan is a split column with, say, four below (to count ones) and one above (to count fives), to reduce the number of beads and make unintended bead motion less likely, but also to aid in certain "tricks" (mathematical games that speed certain calculations) which the student would learn from the master.
A common variation in China was two or three fives beads and five ones beads, which aided in certain tricks with lazy carries.
(It may be stating the obvious, but the number and arrangement of the beads allowed a certain degree of customization in the construction of an abacus, ergo, programability.)
The abacus is definitely an aid to computation. Again, unless we include some implicit hidden requirements in the definition,
abacus + user = computer system
Even more so, if the user has a paper and pen to record his or her results.
(For what it's worth, the English word "calculator" shares roots in the Latin for "abacus".)
Astrolabes are devices which can be used to calculate the location of celestial objects, among other things. Some can be very complex; the Antikythera mechanism (dated about 100 BCE) can be viewed as an extreme form of an astrolabe, although its construction is much closer to that of many early mechanical computers.
Looking for elements of a computer in the astrolabe, we again see the input, output, and memory devices combined.
An astrolabe consists of several disks (or spheres, in some versions), one or more pointers, graduations or scales engraved around the perimeters and elsewhere, and tables of various sorts. Many included sights. The construction allowed one to move the pieces around to predict or check the positions of the sun, stars, and other things in the sky. Many versions allowed several different upper disks to be traded in and out with the same base, allowing the same astrolabe to be used at different latitudes.
Again, programability is in the physical construction of the astrolabe. Exchangeable parts allows a certain amount of what we now call re-programability.
I'm afraid someone will call foul when I call clocks computers, but let's be real here.
Maybe they should be classed separately, but they also share the input, processing, output model. You set the clock as one input, then you wind it, install the battery, plug it in, or fill the water or sand tank, as another. Then it free runs to continuously calculate the current time. Output, of course, is the face (usually). Alarm clocks have additional inputs, and recording clocks have additional outputs. There is memory (as in read-only) in the cogs and circuits which keep the output time accurate and readable in the 12:60:60 base time numbering system we traditionally use.
The slide rule is really simple. Take two rulers in the same scale, centimeter/millimeter makes it nicely base ten, and set them side-by-side. Line up the zero point on one with with the first number of a pair to be added on the other, as measured on the scale, say 3 centimeters 1 millimeter for thirty-one. Now look for the second number on the offset ruler, and look across to the first ruler to read off the sum.
If one of the scales is a regular scale, and the other is graduated logarithmicaly, the slide rule can be used for multiplication, and even for multiplication by trigonometric functions (sine/cosine) of a number, etc.
You have input, output, and methods (procedures), and the scale is the memory. Programmed by the construction of the scale. The operator doesn't even have to worry about carries.
It's a computer.
Slide rules have been around since about the middle of the last millenium. So have other mechanical calculators capable of handling carries automatically. Typically, carries are handled by the number of teeth on a cog or gear. For example, a digit would be represented by a compound gear with 0 - 9 printed in between two sets of teeth, with ten times the number of teeth on the input side compared to the number of teeth on the outside. The input side would be the digit to be added to that column, and the output side would be the carry generated, and the integers printed around the middle would be the display/memory.
Wait, each cog has an input and an output? And memory?
Why, yes. Computers are generally made of smaller, simpler computers.
Thermostats are relatively recent. The basic elements of the ordinary thermostat is a bi-metal strip. (Semiconductor heat sensors have been developed, but are not yet in very common use in thermostats.) The two layers of metal, when subject to a change in temperature, will produce small amounts of electric current and flex. Either the current or the amount of bending is used to activate some sort of switch, and things are turned off and/or on according to set temperatures.
All very very simple. Surely this is too simple to be a computer? Let's take a look at it.
The most common point of view would have the bi-metal strip be one input. Another input is some sort of adjustment of the position of the switch, in one case, or the adjustment of the current sensitivity in the other, to set the temperature. Power is another input. The switch is the output device. The processor is the combination.
Programming is again in the physical construction or design of the elements, and sets the amount of vaiation in temperature that is ignored switching either on or off and switching back again.
The temperature setting is an input, but it also constitutes memory of the most recent temperature setting.
"Wait!" you say, "This can't be right! You're seeing computers everywhere!!!"
"What isn't a computer?"
How about people? Let's take a break from machines and take about people.
In particular, about job titles.