I have a silly question, sorry Ian. But is the reason square waves appear different than a sin wave because of the predictable period of time between high low high low, or because like you said there’s less info than in a sin wave (so 1s and 0s)

this is actually an excellent question with which you have inadvertently revealed your deep & intimate understanding of engineering as construction of the fundamental laws of mathematics and physics

i told you a bold faced lie when i said there’s less info in a sin wave than a square wave. a square wave is actually only a transformation of the sine wave just as any wave is a construction (summation) of numerous or infinite sine waves. jospeh fourier figured this out over 200 years ago when he discovered the fourier theorm

a sine wave contains an infinite amount of information as no matter how small you divide it, each segment is quantifiably different than the last. in the case of the sine wave, this difference follows the simplest mathematical function possible which is why it is the sole building block of every waveform ever

it follows that, as every waveform ever is a construct of sine wave, that every waveform ever has an infinite amount of information contained within itself. “infinity” is much more than “two”, which is the target amount of information we want in a square wave (as it needs to describe two states, 1 and 0)

it does describe only these two states, but only during the periods of the waveform where the waveform is not switching to a 1 to a 0 or a 0 to a 1. for it to be always only 2 states, you’d have to have the voltage described by the waveform go from ‘high’ to ‘low’ in an infinitely short amount of time. during this singular, indivisible quantum of time your voltage would be both ‘high’ and ‘low’ simultaneously, which is impossible since waveforms are described by functions and functions always resolve to exactly one, and only one value. this is something that was proven to be absolutely true no matter what the case is (a law in mathematics). since the waveforms we’re talking about are continuous, which is to say they always have a value no matter what and can’t just “break” suddenly forming a discontinuity. all of this was discovered, tested, and logically proven by people who existed long before christ

so what the fuck then, right? let’s look at another wave: when you grow up and put your big boy pants on, this is what a square wave looks like. it’s all fucked up. the voltage doesn’t suddenly jump from high to low in an instant, in fact, i can see the slope of the leading and trailing edges. what the fuck is it doing once it reaches the intended voltage level? what the fuck is that squiggly shit? jesus christ

you see, the flip side of engineering, the opposite side of all the nice, poetic mathematical truths we’ve just discussed, is the dirty, shifty-eyed bandit side of engineering that exploits these beautiful, fundamental truths in conjunction with cheap tricks & lies as to come up with a realistic design of something that could possibly be constructed in the real world with economically-sound levels of success & function. this is my favorite side of engineering

you see, instead of the voltage dropping from high to low instantaneously, we just build a dope ass transistor that switches so quickly as to trick the other parts of our circuit into thinking it happened in an infinitely small amount of time. it switches it so fast that it overshoots the intended voltage and has to be frantically reeled back in (which also happens too quickly, resulting in a frantic push in the original direction yadda yadda yadda that’s that squiggly shit you see at the corners of the square wave)

this lascivious chicanery comes at a price, however. if we keep making circuits operate at faster and faster frequencies, those previously-immediate lookin voltage transitions quit lookin so immediate. as you cut the line closer and closer you get increasingly more unstable circuits and eventually cross a threshold where your computer effectively becomes a space heater

if you have a solution to this problem, you can exchange it with intel, qualcomm, freescale, AMD, micron, and other such Illuminati-sized companies for rockafeller money and probably a few nobel prizes

anyway

this might have been the best question anybody has asked me throughout my apparent career of making people furiously flick that scrollwheel on their dashboard. usually i have to tediously dumb-down an explanation of a simple hardware or software concept but for this i had to walk around the block a few times and smoke a few cigarettes to bring this question from start to finish

people like you make me nervous about career competition in my field

i told you a bold faced lie when i said there’s less info in a sin wave than a square wave. a square wave is actually only a transformation of the sine wave just as any wave is a construction (summation) of numerous or infinite sine waves. jospeh fourier figured this out over 200 years ago when he discovered the fourier theorm

a sine wave contains an infinite amount of information as no matter how small you divide it, each segment is quantifiably different than the last. in the case of the sine wave, this difference follows the simplest mathematical function possible which is why it is the sole building block of every waveform ever

it follows that, as every waveform ever is a construct of sine wave, that every waveform ever has an infinite amount of information contained within itself. “infinity” is much more than “two”, which is the target amount of information we want in a square wave (as it needs to describe two states, 1 and 0)

it does describe only these two states, but only during the periods of the waveform where the waveform is not switching to a 1 to a 0 or a 0 to a 1. for it to be always only 2 states, you’d have to have the voltage described by the waveform go from ‘high’ to ‘low’ in an infinitely short amount of time. during this singular, indivisible quantum of time your voltage would be both ‘high’ and ‘low’ simultaneously, which is impossible since waveforms are described by functions and functions always resolve to exactly one, and only one value. this is something that was proven to be absolutely true no matter what the case is (a law in mathematics). since the waveforms we’re talking about are continuous, which is to say they always have a value no matter what and can’t just “break” suddenly forming a discontinuity. all of this was discovered, tested, and logically proven by people who existed long before christ

so what the fuck then, right? let’s look at another wave: when you grow up and put your big boy pants on, this is what a square wave looks like. it’s all fucked up. the voltage doesn’t suddenly jump from high to low in an instant, in fact, i can see the slope of the leading and trailing edges. what the fuck is it doing once it reaches the intended voltage level? what the fuck is that squiggly shit? jesus christ

you see, the flip side of engineering, the opposite side of all the nice, poetic mathematical truths we’ve just discussed, is the dirty, shifty-eyed bandit side of engineering that exploits these beautiful, fundamental truths in conjunction with cheap tricks & lies as to come up with a realistic design of something that could possibly be constructed in the real world with economically-sound levels of success & function. this is my favorite side of engineering

you see, instead of the voltage dropping from high to low instantaneously, we just build a dope ass transistor that switches so quickly as to trick the other parts of our circuit into thinking it happened in an infinitely small amount of time. it switches it so fast that it overshoots the intended voltage and has to be frantically reeled back in (which also happens too quickly, resulting in a frantic push in the original direction yadda yadda yadda that’s that squiggly shit you see at the corners of the square wave)

this lascivious chicanery comes at a price, however. if we keep making circuits operate at faster and faster frequencies, those previously-immediate lookin voltage transitions quit lookin so immediate. as you cut the line closer and closer you get increasingly more unstable circuits and eventually cross a threshold where your computer effectively becomes a space heater

if you have a solution to this problem, you can exchange it with intel, qualcomm, freescale, AMD, micron, and other such Illuminati-sized companies for rockafeller money and probably a few nobel prizes

anyway

this might have been the best question anybody has asked me throughout my apparent career of making people furiously flick that scrollwheel on their dashboard. usually i have to tediously dumb-down an explanation of a simple hardware or software concept but for this i had to walk around the block a few times and smoke a few cigarettes to bring this question from start to finish

people like you make me nervous about career competition in my field