Flick Harrison wrote:
> I can understand the temptation to reduce "digital" to "numbers."
> 
> But I think it borders on tautology to define digital as "computable  
> numbers... computable only by a computer."  Defining a computer as "a  
> hardware machine running software by which these numbers can be  
> processed etc" seems to confirm this.

The definition of "digital" I'd give, at least for the purposes of 
this discussion, is "comprised of a linear sequence of tokens or 
symbols drawn from a finite set."

This would include things like the text of Moby Dick encoded in 
US-ASCII, or the encoding of a video clip as a sequence of bytes 
in some particular video format, as well as things that might not 
be quite so obviously digital, like the human genome.

This definition does indeed have powerful connections to 
computability (and, I would argue, to human cognition) but it's 
not just about numbers.

I think you conflate "digital" with "binary", which may be common 
enough in everyday usage, but is technically incorrect, and this 
leads you to exclude all sorts of things that in fact are digital, 
simply because they don't happen to be binary.

> As a filmmaker, I like to draw the line between analogue vs digital at  
> the binary code. And binary code is only "numbers" if you choose to  
> call it that.  A 1/0 switch is also an on/off switch.  You could also  
> call it an a/b switch. (Maybe I'm missing some basic computer tech -  
> are there non-binary computers?)

An abacus would be an early example.  What we call a Turing machine, 
as Alan Turing defined it, is another.  The Turing machine is in no 
way required to use a binary code, but it is required to use symbols 
drawn from a finite set.

> The reason the digital system works is the yes/no nature of its basic  
> information method.  It's not about units or numbers; it's about on/off.

A ternary computer based on three distinguishable states (-5V, 
0V, 5V, say; or perhaps, red light/blue light/no light) would 
be no less digital, so it's not about on/off (two states), it's 
about states that can be distinguished from one another.

The reason the digital system works, the essential characteristic 
that allows deterministic computation, is that there are a finite, 
enumerable set of distinguishable states.  In contrast, an analog 
system would be one in which, for example, the exact voltage, or 
the exact wavelength of the light, was relevant. 

> Likewise with written text.  Yes, you can rearrange the letters in the  
> bible to write "War and Peace."  You can also rearrange the bricks in  
> the White House to create the Sistine Chapel.  Is the White House,  
> therefore, digital?

The White House and the Sistine Chapel are defined by context, 
location, and provenance, not merely by the arrangement of bricks.

The Bible, though, doesn't exist in the same way the White House 
exists.  Individual bibles exist, but if "the Bible" means anything 
it all, it must mean something closer to a sequence of symbols than 
to a physical object.  There's some sense in which the Bible is 
/essentially/ digital, while the White House is not.

What Florian Cramer pointed out is that this can be true for texts 
to a greater or lesser degree, and the degree of "digital-ness" of 
a text ‒ the amount of information lost when the text is reduced to 
nothing more than the linear sequence of symbols ‒ varies between 
texts, for reasons that can be interesting in their own right.

> Binary code written on paper is not digital, even though it can be  
> reproduced 1:1, because it's simply a picture of binary code, not  
> actual binary activity.

Can you define precisely what "actual binary activity" is?

A binary code written on paper is no more and no less fundamentally 
digital than encoded on a hard disk drive platter as adjacent areas 
which are magnetized differently.

> This is not a pipe, eh?  A lightswitch, on  
> the other hand (to borrow McLuhan), is a digital system - the binary  
> switch gives light if it's "yes," or darkness if it's "no."  The on/ 
> off is as much a "state" as a "number."

As is the state of ink on paper forming a numeral 1 or 0 or letter 
from the Latin alphabet.

Any physical manifestation or transmission of digital information 
always has this characteristic: we or our tools can distinguish it 
as being in one particular state from some finite set.

The only thing digital about the ink on paper or about the light 
switch is the interpretation given to it.

We partition the immeasurably vast number of states such a system 
can be in, and only then can we talk about the light being either 
on or off, the ink as representing this character or that.

-- 
http://inimino.org/~inimino/blog/






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