Thoughts on finding patterns
June 19th 2007 04:12
If it's asserted that a piece of music is characterized by its "gentleness", or a movie by its "passion", there's going to be subjectivity there, and differences in opinions.
So given an object, it sometimes seems debatable what the features are (though perhaps, in reality, the ambiguity lies in language).
The problems are bigger with multiple objects -- collections of things, sets of data.
Even assuming that the features of the individuals are clear, say you want to talk about what they all have in common, or what patterns they form.
You might want to define "science" (or "philosophy"), or speak of a particular author's style, or condemn the behaviour of politicians.
People are frequently put in the generalizing situation.
What's the next member in the series "1, 2, 3..."?
A couple of observations here.
Firstly: Even when the group is clear, and the features of its members are clear, there's an infinite number of ways to continue or complete a pattern. You can generalize over any of the features that the given members individually or jointly possess. For instance, "1, 2, 3..." could be a series of rational integers, and the rule could be "plus 1", sure -- but maybe it's a series of primes, or maybe there's some more complex rule like "list three numbers then skip a number, then list three numbers then skip a number..."
Secondly: But "plus 1" is the obvious rule.
Just as it's obvious that a number is to be the answer, and not a breed of sheep, or a star system.
Okay, what makes these things obvious?
Well, a whole host of cultural and genetic and environmental factors: how you were trained, how commonly this rule is used and encountered, what conventions there are, what you think the questioner expects, what particular purpose the question serves, what's reasonable, what the most probable explanation is, what the simplest explanation is, what the practical constraints are (you can't get too complex) -- as well as what's on your mind, where you're standing in the sun, what drugs you've been smoking...
Or, for a better example of cultural specificity, consider asking a non-English speaker what the next letter is in the series "M, T, W, T, F, S..."?
Or, for a better example of genetic specificity, consider (as, I'm told, Nelson Goodman once remarked) that a portrait photograph better resembles a piece of paper than a person.
So probs with identifying the features, and multiple possibilities in drawing out the pattern, though culture, nature, practicality will lead to some sort of obviousness -- will favour an answer.
And if there's insufficient obviousness, it seems to me that the following will become possible replies:
1. That there's multiple correct answers. -- So, in a science context, there's no limit on the hypotheses you can form to fit a set of facts. In a literary context, there's no limit on the possible ways to draw up genre boundaries. In a legal context, you've got a lot of characterization leeway in deciding whether something falls within the Commonwealth's power "with respect to x" -- with respect to corporations, foreign affairs, whatever.
And in an optical illusion context, is there any real way to decide whether it's a rabbit, or a duck?
2. That there isn't an answer. Our charity is strained. We question the questioner. Perhaps a mistake has been made.
There's plenty of times when humans give up -- for instance, where it's been possible to draw a pattern, but the numbers seem so random that people think it's more likely that there isn't one -- or we can't get the joke, and, rather than favour an implausible explanation, conclude that there wasn't anything funny in the first place...
So given an object, it sometimes seems debatable what the features are (though perhaps, in reality, the ambiguity lies in language).
***
Even assuming that the features of the individuals are clear, say you want to talk about what they all have in common, or what patterns they form.
You might want to define "science" (or "philosophy"), or speak of a particular author's style, or condemn the behaviour of politicians.
People are frequently put in the generalizing situation.
***
What's the next member in the series "1, 2, 3..."?
A couple of observations here.
Firstly: Even when the group is clear, and the features of its members are clear, there's an infinite number of ways to continue or complete a pattern. You can generalize over any of the features that the given members individually or jointly possess. For instance, "1, 2, 3..." could be a series of rational integers, and the rule could be "plus 1", sure -- but maybe it's a series of primes, or maybe there's some more complex rule like "list three numbers then skip a number, then list three numbers then skip a number..."
Secondly: But "plus 1" is the obvious rule.
Just as it's obvious that a number is to be the answer, and not a breed of sheep, or a star system.
Okay, what makes these things obvious?
Well, a whole host of cultural and genetic and environmental factors: how you were trained, how commonly this rule is used and encountered, what conventions there are, what you think the questioner expects, what particular purpose the question serves, what's reasonable, what the most probable explanation is, what the simplest explanation is, what the practical constraints are (you can't get too complex) -- as well as what's on your mind, where you're standing in the sun, what drugs you've been smoking...
Or, for a better example of cultural specificity, consider asking a non-English speaker what the next letter is in the series "M, T, W, T, F, S..."?
Or, for a better example of genetic specificity, consider (as, I'm told, Nelson Goodman once remarked) that a portrait photograph better resembles a piece of paper than a person.
***
So probs with identifying the features, and multiple possibilities in drawing out the pattern, though culture, nature, practicality will lead to some sort of obviousness -- will favour an answer.
And if there's insufficient obviousness, it seems to me that the following will become possible replies:
1. That there's multiple correct answers. -- So, in a science context, there's no limit on the hypotheses you can form to fit a set of facts. In a literary context, there's no limit on the possible ways to draw up genre boundaries. In a legal context, you've got a lot of characterization leeway in deciding whether something falls within the Commonwealth's power "with respect to x" -- with respect to corporations, foreign affairs, whatever.
2. That there isn't an answer. Our charity is strained. We question the questioner. Perhaps a mistake has been made.
There's plenty of times when humans give up -- for instance, where it's been possible to draw a pattern, but the numbers seem so random that people think it's more likely that there isn't one -- or we can't get the joke, and, rather than favour an implausible explanation, conclude that there wasn't anything funny in the first place...
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Comment by Uula Limanski
Thinking The World
considering that an infite quantity of facts influence every fact that happens, any pattern that we found will be a "simplification" of what happened. I mean, as you said, we try to find similarities between things so that we can classify them. And in the same way, we can use this reasoning to predict things.
Unless a fact has a finite quantity of "causes", it's causality is relied on an infinite model. In this case, we are in the limit of causality. Then, is causality still valuable?
For instance, in the case of 1,2, 3... we have not only a pattern, but created a model for to predict the next step ( 1..). Considering Newton, we have once decided that F=ma, but Einstein showed this wasn´t (completely) correct...hehe
So, from the world we find patterns, and them create laws, just to see later that the patterns we created were too "simplificating" fir what really happens..
Nice post! Cheerrs (as Scotsmen say..)
Uula
Comment by JohnDoe
Film & TV on DVD
It deals with life and existence as a mathematical equation. A guy actually sees the patterns and coding in nature, the cityscape and life itself. It has some very interesting theories on this question.
Comment by Nonymous
Philosophy Blog
Dear JD,
I haven't seen "Pi" (yet another one to add to the list). Your description reminds me a little of the sequences in "A Beautiful Mind" that show numbers jumping out at Russell Crowe.
Maybe seeing the patterns among things is something that everyone experiences, in a less obvious form -- the connection between the blurb on the back of this library book to a conversation you had a month ago to a song you half-remember from your childhood (just as everyone experiences "Memento" in a less obvious form -- suddenly finding yourself in a situation, moment to moment, as if the past had never existed).
Speculating out loud here: perhaps the way that humans can generalize patterns is something that separates them from computers. So when a chess player "smells danger", the intuition could be due not to their unconsciousness doing calculating work ahead of the consciousness, but simply to spotting a pattern that they've learned from experience.
Dear Ulla,
I think you're correct, depending on how one wants to talk about causality. It's arguable, for instance, that for any event to occur, the entire universe had to be precisely as it is. If one believes this, then when we say that something "caused" something else, our specification of the relevant states are, in practice, always going to be incomplete.
I'd add a qualification to this...
Okay, so I've already said that, from a certain point of view, our state-specifications for the purpose of causality are always going to be limited. We say "F=MA", and we idealize the situation -- we don't take into account all the variables. But even when the situation is idealized like this, could it be the case, as you're suggesting, that the suggested causal patterns will always be incorrect or inadequate?
Well, experience has certainly shown us that this is true. So, for instance, I went to a talk recently by some Nobel physicist who pulled a number out of his arse to describe how likely it was that quantum would be the dominant theory in a 100 years time (I think he said 75% chance it wouldn't be; will have to check my notes).
But there's no logical necessity that this is true -- that our causal laws will prove to be inadequate. It's possible that quantum laws, or relativity laws, or whatever, might stand for all eternity.
There do seem to be some regularities of experience, some patterns, that are exceptionless... I think, for instance, of "logical laws" or mathematics (although the exceptionlessness even of these has been questioned).
Incidentally, in philosophy of science, there's a recent view called "new experimentalism", and I suspect you'd have sympathy with it. The claim is something like: "Progress in science can be measured in terms of the accumulation of experimental results -- and not in terms of better theories. The theories change, the results stay the same."