Analog vs Digital: How Digital Representations Reflect the Analog Universe

[GregoryC]

What makes us believe we can represent an analog universe with digital representations? We can only know the radius of a circle or it's circumference with precision because Pi is an approximation.

 

[russ_watters]

What makes us believe we can represent an analog universe with digital representations?

We don't have to "believe", we do it.

We can only know the radius of a circle or it's circumference with precision because Pi is an approximation.

Yes. So what's wrong with that?

 

[sophiecentaur]

Whenever we write down a value that's been measured, we have 'gone digital'. In Science, all measurements have a limited accuracy and have a certain number of significant figures.
Pi is a transcendental number and, as you say, cannot be represented in a limited number of digits. There are other transcendental numbers (e) and also many familiar irrational numbers (√2) for instance.
We don't claim to represent the Universe perfectly - all our Scientific Laws are based on limited measurement accuracy. Everything is calculated 'near enough' to justify the many theories in which the Maths assumes a continuum of values.
No need to lose any sleep over this - unless you want to stray into the realms of Philosophy (third year work and beyond!)

 

[CWatters]

What makes us believe we can represent an analog universe with digital representations?

Is the universe analog? I thought the jury was still out on that.

We can only know the radius of a circle or it's circumference with precision because Pi is an approximation.

Can you explain why we can a only calculate the circumference with precision because pi is an approximation? Normally approximations reduce precision.

 

[bsheikho]

Neuron activity seems pretty digital to me.

 

[Drakkith]

Neuron activity seems pretty digital to me.

I believe neurons have both analog and digital "properties", but that's a topic for the biology forum, not this thread.

 

[jbriggs444]

What makes us believe we can represent an analog universe with digital representations? We can only know the radius of a circle or it's circumference with precision because Pi is an approximation.

Pi is exact. Any real figure is only approximately a circle.

 

[Delta Kilo]

What makes us believe we can represent an analog universe with digital representations?

https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem
https://en.wikipedia.org/wiki/Shannon–Hartley_theorem

 

[sophiecentaur]

There seems to be a bit of a confusion between "Analogue / Digital" (Types of electronic and other signal processing) and "Continuous / Discrete" (variables). Maths can handle integers, (the only discrete variables) rational, irrational and transcendental variables and all types turn up in Science.
Between Scientists and Science there is always the 'measurement barrier'. Every measurement has a certain resolution and accuracy and, as soon as we write it down or process it in a digital processor, it becomes a discrete quantity.
Before digital processors had sufficient capacity, we used to employ Analogue Computers which would take the analogue values from sensors and potential dividers and, with clever use of Op Amps, would produce an Analogue output signal. The whole information chain used continuous variables (Volts and current values). However, of course there was noise /hum / drift etc and the output value was not an 'exact' outcome. So you could not actually rely on a set of monotonic input variables giving you a monotonic answer.

 

[DarkBabylon]

I believe neurons have both analog and digital "properties", but that's a topic for the biology forum, not this thread.

Actually they do, the chemical aspect is analog, and the patterns can be argued for digital. But yeah like you said, not in this thread's current location.

 

[Aaron Crowl]

I'm an engineer not a scientist but I'll tell you what a professor told me once. "Every tool we have is an approximation". That doesn't mean that they are bad tools that cannot do remarkable things. Look at how we are communicating for instance. When the approximations fail that's where the interesting research starts.