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Topic: mathematical formalization? (Read 5969 times) |
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loddoss
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mr. wu,
your psychology pages are very interesting and well written. i wish i had lecture notes like these when i was in school.
anyways, i noticed in the description for this forum, you wrote "mathematical formalization". this seems peculiar and not related to psychology. what did you mean?
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reZ
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Re: mathematical formalization?
« Reply #1 on: Sep 6th, 2002, 8:07pm » |
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i talked with will about this once. he has some ambitious ideas about drastically formalizing psychology so it's more scientific. personally i think psychology is inherently not rigorous so i don't know how this would work.
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xplorer
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Re: mathematical formalization?
« Reply #2 on: Nov 3rd, 2002, 12:31am » |
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If you are referring to something like Asimov's Seldon project
and the mathematical treatment of social prediction,
I am extremely interested in what is going on in this realm.
Please post if there is any good basic work pursuing this.
When I first tried to get into that, I ran into so much
scholarly driftwood I had to give up.
Even mentioning the cocept of mathematic analysis of
social and/or psychological behaviour got me into trouble.
cheers, from Java
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william wu
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Re: mathematical formalization?
« Reply #3 on: Nov 3rd, 2002, 5:22am » |
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xplorer: Actually I've never heard of what you're talking about, sorry.  Feel free to enlighten me though.
I recenlty found this site on the Journal of Mathematical Psychology:
http://www.academicpress.com/www/journal/mp.htm
I haven't read it yet though ... I'll have to spend more time with it. I'm guessing that it doesn't satisfy what I would like psychology to be, but we'll see.
Basically, Mr. Michael Kran and myself were taking Social Psychology over the summer, and we had a few conversations about how unscientific psychology is. So I suggested that we adopt the overwhelming task of rehauling all of psychology to make it a science. Aside from a couple four-hour cafe chats and some e-mails, this endeavor hasn't really gone anywhere 
One of the frustrating trends in psychology that many modern-day professors grieve over is the decreasing scope of newly published theories. From the 1900s to 1950s, people like BF Skinner and Carl Rogers and Freud produced theories that were elegant in design: simple, but capable of explaining wide ranges of phenomena. These characteristics make a good theory. An example in mathematics is geometry, which all flowers from merely 5 postulates. Today however, new psychology theories explain very specific phenomena. You can think of a theory as a tiling on a spherical surface of phenomena. Currently we have some very large tiles from 50 years ago, and a smattering of tiny tiles of various shapes peppered across the surface. We'd really like just a handful of uniformly-sized tiles with shapes that interlock so that they tesselate the whole surface, leaving no region uncovered.
Noting this trend, we realized we needed to merge some of the smaller theories. But the question was how. Tiny theories can be partly wrong and partly right, but if they're partly right, exactly in what context are they right, and can a larger theory encompass these theories or would that be disastrous? To do all this the right way, you need math. We'd like to solve equations for the intersections and unions of theories. But how do you apply mathematics to psychology?
Failing the application of mathematics for now, we brainstormed all the ideas we had learned in psych, and thought about how we tie them all together using only eight or nine really big concepts.
One example of a big concept is pattern-matching, or induction. Pattern-matching is a skill used from day one to make decisions quickly. If we didn't do any pattern-matching we'd be overloaded with sensory information and never get anything done. We're natural scientists even as babies, and we compare things to other things we've seen before, so we can try to predict what will happen and have some notion of control over random things in life. Clearly, pattern-matching can be used to explain stereotyping, schemas and cognitive miserliness. But we can extend this to intelligence and neural networks. You could make a good argument that most of intelligence is just pattern matching, as IQ tests seem to suggest. Also related to pattern-matching is a desire for control. A curious phenomenon among kids is that they have a pathological desire to make rules! Just observe elementary school boys on a playground, you'd be surprised. They can spend hours arguing over rules of their own invention, about rankings and roles in their group, or who the leader is, or who should be ostracized this week. I can still remember this sort of disturbing behavior. Or when they're playing: he's IT, he's freezetagged and he's not, she has cooties, double-stamped it, NO takebacks! It seems like a love for rules is ingrained in us. We can also talk about how pattern-matching relates to our desire for meaning. We like it when everything follows a pattern, some guiding plan. Perhaps that is what propels people toward religions and cosmology.
So that's a taste of what I meant by the statement "mathematical formalization" ... making psych a science. I've got a bunch of stuff about this, so if you're interested in talking about this more feel free to voice your thoughts. Maybe someday I'll put my transcripts with Mr. Kran online.
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| « Last Edit: Nov 3rd, 2002, 5:24am by william wu » |
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Icarus
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Re: mathematical formalization?
« Reply #4 on: Nov 18th, 2002, 5:01pm » |
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Asimov's "Seldon" project refers to a series of novels that he wrote, his "Foundation" novels. He wrote the first three back in the 50s or 60s, then returned to it to write several more in the 80s and 90s before his death. They were based on an idea he had that possibly given an extremely large number of people, the seeming randomness of their individual behavior would average out to produce an aggregate behavior that could be predicted by a mathematical model. Much the same way that Thermodynamics describes the behavior of large numbers of molecules, without having the describe the behavior of the individual molecules themselves. Asimov's protagonist Harry Seldon develops such a theory in the distant future, when the galaxy holds several trillions of people. While it makes a good story, Asimov himself did not place much stock in it actually being possible.
It seems to me that the real difficulty in introducing hard science into psychology is that it is impossible to do controlled experiments. (It is theoretically possible, but only at the expense of joining history's most despicable villians!) Mathematical formalism comes from being able to measure, but accurate measurements are not possible without controlled situations.
Psychology is presently in a state similar to that of physics ("natural philosophy") in ancient Greece. Big names have come up with a lot of attractive ideas that seem to explain a lot, and smaller names are filling in little bits and pieces. But the evidence that even the core ideas are correct is very shaky. I suspect as more information becomes available, even the ideas of Skinner, Rogers, and Freud will need major overhauling, or outright scrapping, just as did the Aristotlean universe.
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Kd
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Re: mathematical formalization?
« Reply #5 on: Jan 22nd, 2003, 12:14pm » |
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Hello there,
This is a very interesting discussion. I like mulling over all these kind of things. "These" meaning - those that are abstract in nature. 
The one very basic question that arises is, why do we need to indulge in exploring things like psychology, philosophy etc. which "apparently" do not seem to affect our day to day lives. :-|
If we look at the basic necessities of a human being.They are food, shelter and clothing. Some might say sex and internet. If one has these, he/she can LIVE. And to get this apparently, one does not need to mull over things like functioning of the psyche.
I believe the reason we involve such activities is because we want the basic necessities fulfilled in a better way, ofcourse once they are satisfied in their basic form. And then we set out on a journey to better ourselves, unconciously thinking that bettering ourselves is the means to the end. The end being the attainment of our desires or put it simply, fulfillment of our necessities.
After a point of time, we confuse the means with the ends. The end goes out of focus. The means acquire the focus.
And then question remains. Are we here to live. Or find the way to live. But the good thing is, no matter what, we would have lived
-Kd
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BNC
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Re: mathematical formalization?
« Reply #6 on: Jan 23rd, 2003, 12:22am » |
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on Nov 18th, 2002, 5:01pm, Icarus wrote:
<snip>
While it makes a good story, Asimov himself did not place much stock in it actually being possible.
<snip>
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Are you sure about that, Icarus?
I’m holding in hand now the collection “gold” (“the final science fiction collection” of Asimov), in which there’s a reprint of the assay “psychohistory” from 1988. Let me summaries the assay:
Asimov starts by stating the “psychohistory” is one of the three words he is credited for in the Oxford English dictionary (the other tow being “robotics” and “positronic”), and the only one he thought wasn’t well-spread when he first used.
He then described what psychohistory is, how he thought of it, and the roots of the name. I will skip this part, as it is outside the scope of this post.
Then comes the relevant part. Asimov writes that he thought the term (in his intended meaning) would “fade out”, as it became used by psychiatrists for the study of the psychiatric background of individuals (such as Woodrow Wilson, Sigmund Freud or Adolf Hitler). He then thought psychohistory doesn’t have much actuality.
But then he writes: “Imagine, then, how exciting it is for me to see that scientists are increasingly interested in my psychohistory…” He goes on to quote a piece from the April 23, 187 issue of Machine Design, saying “A computer model originally intended to simulate liquid turbulence has been used to model group behavior… <much snipped>”. He quotes also from the September 11, 1987 issue of Science an article by Roger N. Shepard, titled “Toward a universal law of generalization for psychological science”, in which he claimed he couldn’t understand the math (or the text…), but that deals with similar concepts. The abstract reads:
”A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with distance, and (ii) dies so in accordance with one of two metrics, depending on the relation between the dimensions along with the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, through evolutionary internalization, tend to govern the behaviors of all sentient organisms.”
The final paragraph of the assay is (in full):
“As I said, I don’t really understand this but I have the feeling Hari Seldon would understand it without trouble. I am also concerned, suddenly, that psychohistory may be developed within the next century. I placed its development 20,000 years in the future. Is this going to be another case of my science-fictional imagination falling ludicrously short?”
I can hardly call that “not placing much stock”. It seems to me that in later years, he came to believe (or at least hope) it would become true.
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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Icarus
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Re: mathematical formalization?
« Reply #7 on: Jan 23rd, 2003, 7:56pm » |
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Hmmm... What I was recalling obviously came from a bit earlier, when he still "thought psychohistory doesn’t have much actuality".
From my understanding of that abstract, it does not really sound like psychohistory as he described it (though there may be more in the actual article that is). But the first reference definitely sounds like psychohistory, and both appear to be solid use of mathematics in psychology (whether these theories are accurate is another matter, requiring extensive testing).
Thanks for the update!
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I wonder: Which is larger
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xplorer
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Re: mathematical formalization?
« Reply #8 on: Apr 5th, 2004, 7:28am » |
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on Nov 3rd, 2002, 5:22am, william wu wrote:
I recenlty found this site on the Journal of Mathematical Psychology:
http://www.academicpress.com/www/journal/mp.htm
{missed that one - it appears to have gone now}
>...X...<
Basically, Mr. Michael Kran and myself were taking Social Psychology over the summer, and we had a few conversations about how unscientific psychology is. So I suggested that we adopt the overwhelming task of rehauling all of psychology to make it a science. Aside from a couple four-hour cafe chats and some e-mails, this endeavor hasn't really gone anywhere
>...X...<
Noting this trend, we realized we needed to merge some of the smaller theories. But the question was how. Tiny theories can be partly wrong and partly right, but if they're partly right, exactly in what context are they right, and can a larger theory encompass these theories or would that be disastrous? To do all this the right way, you need math. We'd like to solve equations for the intersections and unions of theories. But how do you apply mathematics to psychology?
>...X...<
One example of a big concept is pattern-matching, or induction. Pattern-matching is a skill used from day one to make decisions quickly. If we didn't do any pattern-matching we'd be overloaded with sensory information and never get anything done. We're natural scientists even as babies, and we compare things to other things we've seen before, so we can try to predict what will happen and have some notion of control over random things in life. Clearly, pattern-matching can be used to explain stereotyping, schemas and cognitive miserliness. But we can extend this to intelligence and neural networks. You could make a good argument that most of intelligence is just pattern matching, as IQ tests seem to suggest.
Also related to pattern-matching is a desire for control.
A curious phenomenon among kids is that they have a pathological desire to make rules!
>...X...<
So that's a taste of what I meant by the statement "mathematical formalization" ... making psych a science. I've got a bunch of stuff about this, so if you're interested in talking about this more feel free to voice your thoughts. Maybe someday I'll put my transcripts with Mr. Kran online. |
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I'm back - I got distracted for a while:
Although not a psychologist, I have been interested in this subject for quite some time (30+yrs).
Recently I revisited my interest after stumbling onto Theodore Modis' book Predictions (1992) and scoured the web for stray links.
Semantics:
I believe Asimov made one tiny mistake, in that he labelled the concept psychohistory, when the proper mathematical treatment of mass psychology might better be described as SocioPhysics.
Sociophysics would treat social/political/(+??) trends as physical, measureable quantities, analogous to energy, mass, charge, etc. as treated by classical Physics.
This is simplistic, I realize, but the best foundation is basic.
Perusing google for links, I see that someone else has already realized this, and there are already some interesting studies resulting from this kind of thinking.
Example of Benefits:
At this point in time it might be (n-dimensionally) profitable to know what happens next, regarding upcoming (American) elections and ensuing politics.
The key to doing this would be to map social dynamics at work in the run-up to the election.
This is 'way out of the league' for an armchair 'SocioPhysicist' like myself, but just examining news media and those reactions that are publicly available shuld provide some enlightenment, in the context of forces and behaviours which might be known from the field of Psychology.
I did visit the 'official' site for PsychoHistory, but they appear mired down in verbal interpretations rather than mathematical treatment of population masses. That said, ignoring some of the stray comments there, a certain amount of quite valid insight can be gleaned from commentary at that site.
I already have some ideas on this, and continue to develop a knowledge base in the hopes I can someday begin to quantify what I see in the news media.
One final toss-off thought: linguistic detection of meme spreading as an analytic tool for quantifying population orientations prior to an event. Any ideas on how best to go about this? I am developing software for detecting verbalized memes, but rather than re-invent the wheel....
If all this is too far out on the fringe, please refer me to a forum where it would be more in context.
Thanx
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