"Secondary" Hobbies

[kaos]

Is there any information that can't be represented digitally?

Trancendental numbers? At least not accurately. For example, you can't express pi digitally (i.e. using numerical digits); it just goes on and on.

Technically, any continuous data can only be approximated by a discrete media. For example, while digital audio recording can reproduce sound with much greater precision than any analog reproduction, analog will always have a theoretical advantage in that it can (in principle) duplicate the entire waveform, while digital sound has to use high-speed waveform sampling, and inevitably clips frequencies greater than twice the sampling rate (IIRC).

I would say that a digital recording with a high enough sampling rate would still contain the information held in the analog signal. How high the sampling rate should to be depends on the qualities of the information.

I think that it is possible to store symbolic and/or logical information in digital format describing Pi that would enable a computer to do any reasoning that humans could do with Pi. The value of Pi can be represented digitally to sufficient precision for any practical use of the value of Pi.

You may notice that I am placing limits on the arbitrariness and usefulness of information. I'm not sure if this is technically a correct thing to do; this is dictionary.com's definition:

1. Knowledge derived from study, experience, or instruction.
2. Knowledge of specific events or situations that has been gathered or received by communication; intelligence or news. See Synonyms at knowledge.
3. A collection of facts or data: statistical information.
4. The act of informing or the condition of being informed; communication of knowledge: Safety instructions are provided for the information of our passengers.
5. Computer Science. Processed, stored, or transmitted data.
6. A numerical measure of the uncertainty of an experimental outcome.
7. Law. A formal accusation of a crime made by a public officer rather than by grand jury indictment.

[Solar]

Now if that ain't OT, but well...

I would say that a digital recording with a high enough sampling rate would still contain the information held in the analog signal. How high the sampling rate should to be depends on the qualities of the information.

The sampling could never be identical to the analogous waveform, no matter how high the sampling rate, and thus always remain an approximation. You lose detail; this might be minute, but existent, and you should stay aware of the fact.

In medieval times, mathematicians and philosophers tried a stunt called "Quadratur des Kreises" - to square a circle. Picture them putting a square inside a circle to approximate it's surface. To further approximate, they added smaller squares into the surface not yet covered by the larger square. And yet smaller squares, and yet smaller, ad infinitum. You never get the precise surface of the circle, you only get closer to it. People now thinking of Aristoteles and a turtle: Congratulation. ;D

[kaos]

Now if that ain't OT, but well...

I would say that a digital recording with a high enough sampling rate would still contain the information held in the analog signal. How high the sampling rate should to be depends on the qualities of the information.

The sampling could never be identical to the analogous waveform, no matter how high the sampling rate, and thus always remain an approximation. You lose detail; this might be minute, but existent, and you should stay aware of the fact.

That's not necessarily true.

[Solar]

So you claim you can square the circle? I'd like to see proof on that...

[kaos]

So you claim you can square the circle? I'd like to see proof on that...

No. I am, however, pointing out the possiblilty that time passes in discrete units.

[Solar]

Pfff... Planck time? You're digging deep into quantum mechanics, here.

I simply can't picture a sound sampler capable of generating a sample every Planck time step. (Not to speak of storing, the amount of data would be huge!) Heisenberg would probably throw a fit.

Let's settle this to a "not with today's technology", OK?

[kaos]

I don't know anything about Planck time. We might be able to get around the Heisenberg principle with more scientific breakthroughs.

I agree that not all information can be stored digitally with today's human technology.

If you want to discuss this further, feel free to message me privately.

[Curufir]

So you claim you can square the circle? I'd like to see proof on that...

Nope, but since I can prove (Err...Has been proven...by people considerably smarter than me ;D) there is a minimal unit of length the circle is simply a ploygon with a finite (Although very large) number of sides. So I might not be able to square the circle, but I can certainly "triangle" it .

[Tim]

Yes, but only if length is quantised; that is, the circumference of the circle (and hence the perimeter of the polygon) is a whole number of molecules/atoms/quarks long.

However, if we're looking at it theoretically, we can go to infinite precision. Then again, if we say we can measure the circle's circumference to infinite precision, then we can represent it with an infinte number of bits.

Therefore you can represent anything numerically (i.e. digitally), both in theory and in practice.

[Curufir]

I think everyone who took part in the circle-square set of comments can put down "debate" as a secondary hobby ;D.

[Schol-R-LEA]

I translate Uryomoco erotic poetry into T'daroga for fun. ;D

(And anyone who gets those two references will have a good guess as to the pasttime that's eaten my life the last few years... but then, anyone who got the joke would probably have seen me on the relevant fora anyway. Frequently.)

[Solar]

I think everyone who took part in the circle-square set of comments can put down "debate" as a secondary hobby ;D.

"Pedantism", rather.

[distantvoices]

I 've always thought, programmers are pedantic per definitionem. ]:->

[df]

i have a headache!

[DevL]

i have a headache!

Tsss...this was just getting interesting.