Virgin Physicists

Its funny the first thing I thought of was, at what temperature.

Too true, and my problem is about to be your problem and the cycle continues comrade.

OK, the solution is "how accurate will make the physicist and accountants both only kinda mad"

i did not know what all those bins of tiny electronic hobby parts were for, but I desperately wanted to learn.

From what I understand, prior to the personal computer boom of the 1980's, HAM radio was kind of a big deal with nerds. The parts were there for all manner of electronics tinkering, but a big mainstay was building and modifying radios. Yeah, you had people tinkering with computers in the 1970's too, but it was more niche (until it wasn't).

Yeah we’re living in the ruins of the old America already and have been for like 25 years.

It’s dirty they just use the same business names they did in the 20th century. While making smoke and mirrors versions of the old products.

After calculus though, they just expect you to cope with fucked up coefficients. In Diff Eq, sometimes you do just get something like 3/111 cos (6/111 x). It gets harder to come up with examples that work out with nice integers.

Physics can also have some really beautiful math, look at Lissajous figures. Once you understand the connections between e, the imaginary plane, and sine/cosine, you get some profound understandings about how electric and magnetic fields work.

Mathematically yes. Practically, right now? No.

So you need a resistor of this value for your widget.

For that many places of precision you're looking at a potentiometer with a 10 nano-ohm precision.

I am not aware of any commercially available resistor that can do that but you could create one using microelectronic structures used for ICs and derive a 10 nano-ohm resistor by design and then chain enough of these elements into a resistor network or potentiometer to create the super precise resistance value you want.

Cool, congratulations.

Now how are you going to use this 10 nano-ohm resistor? What voltage will you be applying across it? What current do you expect it to handle? And therefore what are your power requirements? What are your tolerances, how much can the true value deviate from the designed ideal?

Because power generates heat through losses, and that will affect the resistance value so how tightly do you need to manage the power dissipation?

How will you connect to this resistor to other circuit components? Because a super precise resistor on it's own is nothing but an over-engineered heating element.

If you tried connecting other surface mount devices (SMDs) from the E24 or even E96 series to this super precise resistor then the several orders of magnitude wider tolerances of these other components alone will swallow any of the precision from your super accurate resistor.

So now your entire circuit has to be made to the same precision else all of your design work has been wasted.

Speaking of which, now your heat management solution now needs to be super precise as well and before you know it you've built the world's most accurate widget that probably took billions of dollars/euros/schmeckles and collaboration from the worlds leading engineers and scientists that probably cost more time and money than the Large Hadron Collider.

The tolerance would be greater than the difference anyway.

For starters resistance changes with temperature.

Also even in a multi-turn potentiometer, getting a precision of 1 in 10^{9 would require an equal level of precision in the angle you rotate that potentiometer to (for example, a 0.1 degree error in a 10 turn potentiometer - which I believe is more turns than anything that actually can be bought - translates into a 1 in 36,000 error in resistance, so about 3000 larger than 10}9) even if you had a perfect material whose resistance doesn't change with temperature.

(PS: Just out of curiosity I went and dove down further and to translate a 1/3000 deg movement in a rotating potentiometer into a 1mm movement at the end of a bar attached to it, you would need a 176m long bar - i.e. the radius for 1/(360*3000) of a circumference to be equal to 1mm, is aproximatelly 176 m. This of course has serious mechanical problems even if you remove the bar at the end of the process as the removal process itself would shift the potentiometer by much more than 1/3000 degrees)

The joke here isn't even specifically about resistances and electronics, it's that the real world has all sorts of limitations that when you're doing things wholly in the mathematical world you don't have to account for, and that's a hard realisation for Physicists (having gone to study Physics at uni and then half way in my degree changing to Electronics Engineering I can tell you that's one of the shocks I had to deal with in the transition).

(In a way, it's really a joke about Theoretical Physicists)

See also the "assuming this chicken is a spherical ovoid" kind of joke.

Don't sneeze right next to it with that kind of precision.

Sure, except the resistance will constantly change with time, temperature and other environmental variables.

I had a potentiometer on a circuit board that adjusted a timer, but I found that the timer varied in timing. I ended up replacing with a few resistors and it corrected the variations.

Until finding out about finite measurement resolution

I can assure you they are not.