Friday, February 8, 2008
Bits are a Platonic Ideal
Taking some time out from inventing the FPGA, I read dchud's post about linking data, and it made me think, in turn about a Perlmonks post that I read last week (specifically the part in the beginning about expressions versus values). That, in turn, made me think about a paper by Claude Shannon, which in turn made me think this linking thing is much like my brain.
I digress.
Which is both true, and is how linking is like my brain.
What I started out to say when I wrote the title for this post, is that an expression has a Platonic ideal: it is the representation of that expression in a string of bits, which may, in turn, be compared to a different string of bits.
In practice, there are a lot of other bits besides the value that get taken into consideration. The machine that is holding the bits needs to know what to do with them. We call those bits meta data, and an obvious candidate for inclusion in this sentence is character encoding. The bits in this post would be different bits (for the "same" expression) if it were encoded in MARC instead of ASCII. These bits are, nonetheless, a value. A Platonic ideal. They can be compared quite directly to other strings of bits, and if all that meta data lines up, the comparison might be meaningful.
Which is where Claude Shannon entered my thinking.
His whole shtick was that when you transmit a bit over a channel, it's an answer to a specific question that both sides know in advance. An encoding is also a way of doing that, except instead of asking "Is it by land? Is it by sea?" you're asking "Is it an a? Is it a c?" This is done in the exact same way for every bit sequence. This string of questions is the so-called meta-data.
Knowledge, and representations of knowledge, is much harder, in part because the list of questions is so much longer. The meta data is shared experience. Possibly, the list of questions is exactly one lifetime's worth for the originator of the knowledge (and ostensibly the representation of the knowledge). Can we hope to encode this context in the same way we encode twenty-six or so letters?
No.
However, that's not the end of the story. Imagine German text has been encoded into a format that is unknown to the recipient. It might be an Enigma initially, but even a few simple hints can be enough to back into the encoding. And I mean a very, very few hints.
Transmitting knowledge is more like that than it is like a character encoding. Take it down into a representation (like this one you're reading), and transmit it over a channel (like this tube I'm sending it over). A few hints may be all the human brain requires in order to derive more interesting and possibly useful information from the bits sent over the tube.
Heck, the recipient brain may even derive some information from the representation that the transmitting brain did not intend to include.
I digress.
Which is both true, and is how linking is like my brain.
What I started out to say when I wrote the title for this post, is that an expression has a Platonic ideal: it is the representation of that expression in a string of bits, which may, in turn, be compared to a different string of bits.
In practice, there are a lot of other bits besides the value that get taken into consideration. The machine that is holding the bits needs to know what to do with them. We call those bits meta data, and an obvious candidate for inclusion in this sentence is character encoding. The bits in this post would be different bits (for the "same" expression) if it were encoded in MARC instead of ASCII. These bits are, nonetheless, a value. A Platonic ideal. They can be compared quite directly to other strings of bits, and if all that meta data lines up, the comparison might be meaningful.
Which is where Claude Shannon entered my thinking.
His whole shtick was that when you transmit a bit over a channel, it's an answer to a specific question that both sides know in advance. An encoding is also a way of doing that, except instead of asking "Is it by land? Is it by sea?" you're asking "Is it an a? Is it a c?" This is done in the exact same way for every bit sequence. This string of questions is the so-called meta-data.
Knowledge, and representations of knowledge, is much harder, in part because the list of questions is so much longer. The meta data is shared experience. Possibly, the list of questions is exactly one lifetime's worth for the originator of the knowledge (and ostensibly the representation of the knowledge). Can we hope to encode this context in the same way we encode twenty-six or so letters?
No.
However, that's not the end of the story. Imagine German text has been encoded into a format that is unknown to the recipient. It might be an Enigma initially, but even a few simple hints can be enough to back into the encoding. And I mean a very, very few hints.
Transmitting knowledge is more like that than it is like a character encoding. Take it down into a representation (like this one you're reading), and transmit it over a channel (like this tube I'm sending it over). A few hints may be all the human brain requires in order to derive more interesting and possibly useful information from the bits sent over the tube.
Heck, the recipient brain may even derive some information from the representation that the transmitting brain did not intend to include.
// posted by David @ 6:00 PM 
Subscribe to Posts [Atom]