How to use mathematical equations to predict people? History of equations?


by 27Thousand
Tags: equations, history, mathematical, people, predict
27Thousand
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#1
Nov3-09, 04:34 PM
P: 89
I'm interested in if anyone here knows any general principles of how mathematical equations are developed, and turned into something useful? For example, Newton's equations were extremely useful for Physics. The same is true about many equations in other disciplines. Any helpful information here? As far as where I'm coming from, do scientists just personally watch what they want to study and try to visualize equations in their minds, or do they more take segments of equations that already exist and combine them together? What's the most effective method?

I was thinking it would be way cool to develop some equations to predict people? Especially individuals would be nice. This could be used for "technology" and to make the world a better place from that segment! Sounds useful!

As many here probably know, in the experimental-control section of social sciences, they mostly only use null hypothesis testing or bayesian statistics, but I don't see too much falsifying equations designed specifically to predict. They of course make general explanations/observable principles to make predictions, but not equations to do so. Then outside of the experimental-control section, they mostly use statistics just to describe, but of course as I said not much as far as using to predict.

So maybe they can have much more of that in the social sciences? Although maybe not as precise as physics, maybe instead equations that give a general confidence interval after being given several variables. Having a statistics minor I know that they sometimes use "Multivariate Statistics" in the social sciences, although I think it's more for groups than individuals. It's kind of like the Y predicting the X in algebra, but instead you have many many independent Y variable predicting a dependent X variable. Maybe if I track down my R computer programming they use, plus my notes, and then look at peer-review studies and their results sections, maybe I can brainstorm human mathematical equations that we could make falsifiable? Now I'm excited! Although it will most definitely not be apple pie

Need input! Who has information on mathematics and what determines if an equation in Science becomes useful? How do they generally evolve to become that way? Do scientists observe and brainstorm, or look at existing equations and play around until they get what they want, a combination of both, or what goes on?
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fourier jr
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#2
Nov3-09, 05:08 PM
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maybe this would be a good place to start:
http://books.google.com/books?id=RNw...age&q=&f=false

there's a similar chapter with references & the same title in the same author's "mathematical thought from ancient to modern times" which goes into some other stuff like descarte's rationalist philosophy & galileo's creation of the function concept
Pythagorean
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#3
Nov3-09, 07:22 PM
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maybe someday, something like this will be used for predicting people:
http://en.wikipedia.org/wiki/Hodgkin...93Huxley_model

Or maybe it will be used to verify a simpler model that links directly to decision-making.

CRGreathouse
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#4
Nov3-09, 11:40 PM
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How to use mathematical equations to predict people? History of equations?


Just read Foundation?
rootX
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#5
Nov3-09, 11:57 PM
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If you can define all the input variables, it should be possible to come up with an equation using statistical methods. I think you need define variables before coming up with any meaningful equation.

P.S. I am working on two similar problems where I need to use historical data along with current inputs to determine the target state. It's some simple math but interesting enough.
redargon
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#6
Nov4-09, 03:53 AM
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The first thing that came to mind was neural networks, artificial intelligence and fuzzy logic. These principles could be used to model humans, I would think.
tyroman
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#7
Nov5-09, 01:02 PM
P: 138
27Thousand,

There is a classic example of the marriage of the very human field of Economics to the classical laws of Thermodynamics... see;

http://en.wikipedia.org/wiki/Paul_Samuelson

More recently, the chaos-theory / fuzzy-logic people at Santa Fe have expounded on the same subject... see;

http://homepage.newschool.edu/~foleyd/econthermo.pdf

And of course, (as mentioned by CRGreathouse) there are Asimov's great Foundation Series of novels which revolve around social predictions based on the mathematics-based "science" of Psychohistory in a future Galactic Empire.
27Thousand
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#8
Nov5-09, 02:01 PM
P: 89
Okay, just think how cool it would be to predict other people! Roommates? Co-workers? How awesome would it be if you could predict whether attractive members of the opposite sex are flirting with you, and even have an equation for it, etc.

I mentioned how in my Multivariate Statistics class we learned about Statisticians making equations when they've been given multiple variables (although not as precise as Physics, you can still get a general range). Maybe I could use this concept of "Multiple Regression Analysis" as a starting point, and then maybe add much Calculus and other concepts into the pot? Then maybe if certain details of existing statistical methods are tweaked, and combined with other ideas that haven't been combined yet, maybe there can be some innovations? On top of that, in the Social Sciences they usually don't post multiple regression equations in their peer-review journals, even if they have the data to create them in many many situations, so doing so may make an impact and be more unique than not including them in the journal (remember Galileo and Newton claimed much of their success was because of moving toward the mathematical equations ball game). What are everyone's thoughts?

Okay as a starting point as food for thought, remember how your high school algebra teacher had you use X to predict Y, and even make a graph with a line moving through the dots. Then if you've taken Calculus you remember how you can give that line a neat curve, to be more accurate. Although the graph below uses cars rather than people, it gets the job done in getting the concept across. Check out the line moving through it, otherwise known as the Regression Line:



You probably noticed that the line moving through the data gives you a general idea of where something may be if you know the other variable, and equations for a "best fit" can be calculated. Well, if you have multiple variables on the X-axis you can lessen a lot of how much variation the dots are from that regression line you see.

In the field of Statistics they call this Multiple Regression Analysis. Of course there's a threshold where adding more variables into the equation doesn't do much, and at the same time where taking away variables limits how well it predicts what will happen. They call this threshold the "adjusted coefficient of determination".

Also keep in mind, in Psychology, they already have experimental-control studies where if you have two groups identical except for an independent variable manipulated by the researcher, then that means the independent variable had a cause-effect impact on the dependent variable, depending on how well you controlled for everything else. Although you can't observe mental processes, you can observe observable behavior. Although you can't prove mental processes, you can generally make them falsifiable through observable behavior. For example, you can randomly assign participants to two groups just like in the Medical Field, manipulating one independent variable, and afterward giving each group a questionnaire about attitudes, or see how they behave differently - to see if the independent variable affected it. (For instance taking a picture and then using a computer to change one independent variable while all the other variables the same and then having experimental and control groups rating the attractiveness of pictures on a scale of 1-10). Sometimes they use physiological methods, for example there are instruments which measure pupils and when people see pictures of things they like their pupils dilate, on the other side of the coin when they see pictures of things they don't like their pupils contract. So what about combining the experimental-control methods with the multiple regression equations, plus maybe add our own spin to it?

What are your impressions of using this as a starting point, or do you think I'm looking in the wrong places?
27Thousand
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#9
Dec6-09, 11:41 PM
P: 89
Quote Quote by fourier jr View Post
maybe this would be a good place to start:
http://books.google.com/books?id=RNw...age&q=&f=false

there's a similar chapter with references & the same title in the same author's "mathematical thought from ancient to modern times" which goes into some other stuff like descarte's rationalist philosophy & galileo's creation of the function concept
fourier jr, I've found that link on Galileo/Newton and how mathematical equations gave them an edge over competition very interesting.

As far as being able to make equations for behavior, check this out from the U.S. National Institutes of Health. I think it's interesting!



http://www.ncbi.nlm.nih.gov/pmc/arti...-85-02-02-f02/

The link and graph have two equations to measure how the strength of behavior reinforcement is affected with time delay. Although this equation was for pigeons, they've come up with similar for humans, just weaker but still good. Maybe similar equations can be made for other basic areas of behavior? Then for the complex areas of behavior we could try the:
Predictive Modeling http://en.wikipedia.org/wiki/Predictive_modeling
Predictive Analytics http://en.wikipedia.org/wiki/Predictive_analytics
discussed posts above? Then we could use Isaac Newton's style to combine parts of already existing concepts in unique and useful ways to innovate!

It could be used to make the world a better place! Think technology and engineering
Pyrrhus
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#10
Dec7-09, 12:16 AM
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Look for Kenneth Train's books for Consumer Behavior, and look for Thursgood papers in Psychometrics. There are a lot of attempts at formulating behavioral models. However, for dating? I don't know.
27Thousand
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#11
Dec7-09, 12:23 AM
P: 89
Quote Quote by Cyclovenom View Post
Look for Kenneth Train's books for Consumer Behavior, and look for Thursgood papers in Psychometrics. There are a lot of attempts at formulating behavioral models. However, for dating? I don't know.
Thanks a lot for those sources!

Since this is the General Discussions forum, I try to keep my dating equation thoughts to the Relationships forum, and just talk about human equations in general here. Although that topic is extremely extremely interesting, I have to keep dating to the other forum (at least a PF Mentor suggested).
humanino
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#12
Dec7-09, 12:26 AM
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Quote Quote by 27Thousand View Post
How awesome would it be if you could predict whether attractive members of the opposite sex are flirting with you, and even have an equation for it
If you can not tell whether somebody is flirting with you, I am not surprised that the perspective of having an equation for it appears "awesome" to you. It occurred to me that people I could have a healthy relationship with are also those for whom I would not need such an equation to tell whether they are flirting with me.
27Thousand
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#13
Dec8-09, 01:15 AM
P: 89
Now I found this interesting: Online Tutorials on Mathematical Psychology http://www.mathpsyc.uni-bonn.de/tutorials.htm I didn't even know that existed, but there's a field in psychology that works on creating mathematical models to explain/predict! Wow!

So as far as being creative goes, Newton took others' mathematical ideas and then combined them in unique/useful ways. I need to use R computer language for Statistics to teach myself the different techniques on that Mathematical Website link, then I'll use playful imagination to see what I can come up with!
fatra2
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#14
Dec8-09, 01:46 AM
P: 478
Quote Quote by 27Thousand View Post
Now I found this interesting: Online Tutorials on Mathematical Psychology http://www.mathpsyc.uni-bonn.de/tutorials.htm I didn't even know that existed, but there's a field in psychology that works on creating mathematical models to explain/predict! Wow!
And they are used in many other fields, when human behaviour needs to be quantified.

I had to look at a few examples in the past, and found that these models explain and predict the behaviour of a group of many humans, but cannot give any precise prediction in the behaviour of one of them (which is kind of normal).

Cheers
27Thousand
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#15
Dec8-09, 02:00 AM
P: 89
Quote Quote by fatra2 View Post
And they are used in many other fields, when human behaviour needs to be quantified.

I had to look at a few examples in the past, and found that these models explain and predict the behaviour of a group of many humans, but cannot give any precise prediction in the behaviour of one of them (which is kind of normal).

Cheers
Sorry if I'm confusing, what I meant was I knew Psychometrics and then also many Statistical Methods exist (minor in Statistics). I just didn't know there was an actual field named Mathematical Psychology.

In answer to individuals, I wonder if you can combine randomized experimental-control followed with the ABA experimental design or the reverse to get a method that gets the best of both worlds, both studying cause-effect plus individual patterns?


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