Update

mechanical.md

@@ -4,11 +4,11 @@ Mechanical computer (simple ones also being called *mechanical [calculators](cal
 
 { Britannica 11th edition has a truly amazing article on mechanical computers under the term *Calculating Machines*: https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Calculating_Machines. Also this leads to many resources: https://www.johnwolff.id.au/calculators/Resources.htm. ~drummyfish }
 
-If mechanical computer also utilizes [electronic](electronics.md) parts, it is called an electro-mechanical computer; here we'll however be mainly discussing purely mechanical computers.
+If mechanical computer also utilizes [electronic](electronics.md) parts, it is called an **electro-mechanical** computer; here we'll however be mainly discussing purely mechanical computers.
 
 **Disadvantages** of digital mechanical computers against electronic ones are great, they basically lose at everything except simplicity of implementation (in the desert). Mechanical computer is MUCH slower (speed will be measured in Hz), has MUCH less memory (mostly just a couple of [bits](bit.md) or [bytes](byte.md)), will be difficult to program ([machine code](machine_code.md) only), is MUCH bigger, limited by mechanical friction (so it will also be noisy), suffers from mechanical wear etc. Analog mechanical computers are maybe a bit better in comparison, but still lose to electronics big time. But remember, [less is more](less_is_more.md).
 
-Some notable mechanical computers include e.g. the 1882 [Difference Engine](difference_engine.md) by Charles Babbage (aka the first [programmer](programmer.md)), Antikythera mechanism (ancient Greek astronomical computer), the famous [Curta](curta.md) calculators (quality, powerful pocket-sized mid-20th century calculators) { These are really cool, check them out. ~drummyfish }, [Enigma](enigma.md) ciphering device (used in WWII), [abacus](abacus.md), [slide rule](slide_rule.md), Odhner Arithmometer (extremely popular Russian table calculator), [Digi-Comp](digi_comp.md) I (educational programmable 3 bit toy computer) or [Turing Tumble](turing_tumble.md) { Very KISS and elegant, also check out. ~drummyfish } (another educational computer, using marbles).
+Some **notable mechanical computers** include e.g. the 1882 [Difference Engine](difference_engine.md) by Charles Babbage (aka the first [programmer](programmer.md)), Antikythera mechanism (ancient Greek astronomical computer), the famous [Curta](curta.md) calculators (quality, powerful pocket-sized mid-20th century calculators) { These are really cool, check them out. ~drummyfish }, [Enigma](enigma.md) ciphering device (used in WWII), [abacus](abacus.md), [slide rule](slide_rule.md), Odhner Arithmometer (extremely popular Russian table calculator), [Digi-Comp](digi_comp.md) I (educational programmable 3 bit toy computer) or [Turing Tumble](turing_tumble.md) { Very KISS and elegant, also check out. ~drummyfish } (another educational computer, using marbles).
 
 Let's also take a look at how we can classify mechanical computers. Firstly they can be:
 
@@ -35,7 +35,7 @@ As mere [programmers](programming.md) let us focus more on **digital** computers
 
 When building a digital computer from scratch we usually start by designing basic [logic gates](logic_gate.md) such as AND, NOT and OR -- here we implement the gates using mechanical principles rather than transistors or relays. For simple special-purpose calculators combining these logic gates together may be enough (also note we don't HAVE TO use logic gates, some mechanisms can directly perform arithmetic etc.), however for a highly programmable general purpose computer **logic gates alone practically won't suffice** -- in theory when we have finite memory ([in real world](irl.md) always), we can always just use only logic gates to perform any computation, but as the memory grows, the number of logic gates we would need would grow exponentially, so we don't do this. Instead we will need to additionally implement some **sequential processing**, i.e. something like a [CPU](cpu.md) that performs steps according to program instructions.
 
-Now we have to choose our model of computation and general architecture, we have possibly a number of options. Mainly we may be deciding between having a separate storage for data and program (Harvard architecture) or having the program and data in the same memory (intending for the computer to "reshape" this initial program data into the program's output). Here there are paths to explore, the most natural one is probably trying to imitate a **[Turing machine](turing_machine.md)** (many physical finite-tape Turing machines exist, look them up), probably the simplest "intuitive" computer, but we can even speculate about e.g. some kind of rewriting system imitating formal [grammars](grammar.md), [cellular automata](cellular_automaton.md) etc -- someone actually built a simple and elegant [rule 110](rule110.md) marble computer (look up on YT), which is Turing complete, but not very practical. So Turing machine seems to be the closest to our current idea of a computer (try to program something useful in rule 110...), it's likely the most natural way, so that might be the best first choice we try.
+Now we have to choose our model of computation and general architecture, we have possibly a number of options. Mainly we may be deciding between having a separate storage for data and program (Harvard architecture) or having the program and data in the same memory (intending for the computer to "reshape" this initial program data into the program's output). Here there are paths to explore, the most natural one is probably trying to imitate a **[Turing machine](turing_machine.md)** (many physical finite-tape Turing machines exist, look them up), probably the simplest "intuitive" computer, but we can even speculate about e.g. some kind of rewriting system imitating formal [grammars](grammar.md), [cellular automata](cellular_automaton.md) etc -- someone actually built a simple and elegant [rule 110](rule110.md) marble computer (look up on YT), which is Turing complete but not very practical (see [Turing tarpit](turing_tarpit.md)). So Turing machine seems to be the closest to our current idea of a computer (try to program something useful in rule 110...), it's likely the most natural way, so that might be the best first choice we try.
 
 Turing machine has a separate memory for program and data. To build it we need two main parts: memory tape (an array of [bits](bit.md)) and control unit (table of states and their transitions). We can potentially design these parts separately and let them communicate via some simple interface, which simplifies things. The specific details of the construction will now depend on what components we use (gears, marbles, dominoes, levers, ...)...
 
@@ -197,6 +197,6 @@ Whether the use of fluids/gases (water, air, steam, maybe even sand, ...) is sti
 
 ### Other
 
-Don't forget there exist many other possible components and concepts a mechanical computer can internally use -- many things we leave out above for the questionability of their practical usability can be used to in fact carry out computation, for example dominoes or slinkies. Furthermore many actually useful things exist, e.g. teethed **cylinders/disks** may be used to record plots of data over time or to store and deliver read/only data (e.g. the program instructions) easily, see music boxes and gramophones; **[punch card](punch_card.md)** have widely been used for storing read-only data too. Sometimes deformed cylinders were used as an analog **2D [look up table](lut.md)** for some mathematical [function](function.md) -- imagine e.g. a device that has input *x* (rotating cylinder along its axis) and *y* (shifting it left/right); the cylinder can then at each surface point record function *f(x,y)* by its width which will in turn displace some stick that will mark the function value on a scale. To transfer movement **strings, chains and belts** may also be used. [Random number generation](rng.md) may be implemented e.g. with [Galton board](galton_board.md). If timing is needed, pendulums can be used just like in clock. Some mechanical computers even use pretty complex parts such as mechanical arms, but these are firstly hard to make and secondly prone to breaking, so try to avoid complexity as much as possible. Some old mechanical calculators worked by requiring the user to plug a stick into some hole (e.g. number he wanted to add) and then manually trace some path -- this can work on the same principle as e.g. the marble computer, but without needing the marbles complexity and size are drastically reduced.
+Don't forget there exist many other possible components and concepts a mechanical computer can internally use -- many things we leave out above for the questionability of their practical usability can be used to in fact carry out computation, for example dominoes or slinkies. Furthermore many actually useful things exist, e.g. teethed **cylinders/disks** may be used to record plots of data over time or to store and deliver read/only data (e.g. the program instructions) easily, see music boxes and gramophones; **[punch card](punch_card.md)** have widely been used for storing read-only data too. Sometimes deformed cylinders were used as an analog **2D [look up table](lut.md)** for some mathematical [function](function.md) -- imagine e.g. a device that has input *x* (rotating cylinder along its axis) and *y* (shifting it left/right); the cylinder can then at each surface point record function *f(x,y)* by its width which will in turn displace some stick that will mark the function value on a scale. To transfer movement **strings, chains and belts** may also be used. [Random number generation](rng.md) may be implemented e.g. with [Galton board](galton_board.md). If timing is needed, pendulums can be used just like in clock. Some mechanical computers even use pretty complex parts such as mechanical arms, but these are firstly hard to make and secondly prone to breaking, so try to avoid complexity as much as possible. Some old mechanical calculators worked by requiring the user to plug a stick into some hole (e.g. number he wanted to add) and then manually trace some path -- this can work on the same principle as e.g. the marble computer, but without needing the marbles complexity and size are drastically reduced. Another ideas is a "combing" computer which is driven by its user repeatedly sliding some object through the mechanism (as if combing it) which performs the steps (sequential computation) and changes the state (which is either stored inside the computer or in the combing object).
 
 BONUS THOUGHT: We have gotten so much used to using our current electronic digital computers for everything that sometimes we forget that at simulating actual physical reality they may still fail (or just be very overcomplicated) compared to a mechanical simulation which USES the physical reality itself; for example to make a simulation of a tsunami wave it may be more accurate to build an actual small model of a city and flood it with water than to make a computer simulation. That's why aerodynamic tunnels are still a thing. Ancient NASA flight simulators of space ships did use some electronics, but they did not use computer graphics to render the view from the ship, instead they used a screen projecting view from a tiny camera controlled by the simulator, moving inside a tiny environment, which basically achieved photorealistic graphics. Ideas like these may come in handy when designing mechanical computers as simulating reality is often what we want to do with the computer; for example if we want to model a [sine](sin.md) function, we don't have to go through the pain of implementing binary logic and performing iterative calculation of sine approximation, we may simply use a pendulum whose swinging draws the function simply and precisely.