When Confronted with An Explanation that is Based on Mathematics

[adios]

First off I'm not a mathematics expert especially when compared to many on this site. However, I know that many, many real world situations and phenomona can be modeled mathematically. I'm fairly certain that most people eschew explanations that are based on mathematical models. I'm not sure why this is. I was explaining some basic portfolio theory concepts mentioning mathematical concepts the other day and the reaction I got was a typical one. It went something like, " I don't know about the math you're mentioning but common sense tells me this ..." in a slightly condescending way. I wasn't offended at all but I wonder why people seem to believe that their common sense is a superior way to analyze complex problems. Of course my viewpoint is subjective so maybe others don't agree but that's my take. I suppose the short answer is that mathematics is an abstract, difficult subjet but what I was referring to wasn't sophisticated mathematics at all and in fact I would expect anyone who had a grasp of high school math to understand. I guess what I'm saying is that I've found that even explanations that are based on relatively unsophisticated mathematical concepts are eschewed. I'm not complaining I'm just curious if anyone else shares my viewpoint and has some insight.

[Paul2432]

I'll start by saying that I agree completely with you. Any explanation that cannot withstand mathematical scrutiny is of dubious value. That said, I think there a couple of things going on here. First, many people are untrained in the scientific method. They simply rely too heavily on anecdotal evidence and gut feeling. They "know what they saw" and to challenge them is considered a personal affront.

One example of this is the "hot hand" in basketball. Statistical analysis has shown that this is a myth. That is a particular player has exactly the same chance of making his next shot whether he has missed his last five shots or made his last five shots. Every discussion I have seen of this topic has resulted in vigorous rebuttal from basketball players. The rebuttal is always based on personal experience and never on the actual statistical analysis.

I do believe intuition has some value. If a mathematical model is not consistent with intuition then the assumptions of the model should be looked at. All mathematical models are based on observations and assumptions.

Paul

[OrianasDaad]

I think that many people who are bad at math, or just don't like it or trust it, tend to rely on "common sense". In order to sway people with a mathematical argument you have to dumb it down quite a bit, and that isn't worth doing most of the time.

The best response to your questioner is probably something like: "Why does that work?" or "Could you elaborate on that?". Feel them out to see where exactly they are missing the point, to make it easier to explain to them.

You probably give people too much credit in having a grasp of high-school mathematics.

[fnord_too]

Many words ended up on the cutting room floor for this response.

Suffice it to say, I hate the fact that most people do not put any thought into their decisions. People like the one you mentioned probably feels threatened by math, for whatever reason, and finds it easier to attack with emotional arguments than to think about the situation in a regimented way.

(In some cases, there are overriding considerations that make the math/logic that is being discussed moot. Usually though in these cases, the person with the big picture will let you know why your analyses are pointless, e.g. "It doesn't matter how much money we could save outsourcing new Navy construction to another country because that compromises national security.")

[BarronVangorToth]

You can't stick all the time with the math either, because pure math will get you nonsensical results like .9999999 = 1.0, in that old puzzle of:

1/9 = .111111111111111111111111111111111
x9
9/9 = .999999999999999999999999999999999

9/9 = 1.0

1.0 = .999999999999999999999999999999999

But, back to the point, the problem is that people are mathematically illiterate in many respects and explaining things in such a fashion will only get glassy-eyed looks of ignorance.

Such is life.


Barron Vangor Toth
www.BarronVangorToth.com

[splashpot]

[ QUOTE ]
One example of this is the "hot hand" in basketball. Statistical analysis has shown that this is a myth. That is a particular player has exactly the same chance of making his next shot whether he has missed his last five shots or made his last five shots. Every discussion I have seen of this topic has resulted in vigorous rebuttal from basketball players. The rebuttal is always based on personal experience and never on the actual statistical analysis.

[/ QUOTE ]

Not really on the subject of mathamatical debating, but I disagree with your belief that the "hot hand", as you call it, is entirely mythical. There is such a thing as a player getting into his rhytem. It probably has to do with muscle memory or something similar. I agree that it's not because he is just "on fire tonight" or some other made up explaination, but science and human anatomy can prove that muscle memory is very real, and could very well affect the performance of a basketball player.

[Triumph36]

Intuition has its place, and mathematical analyses have their place. Neither is the absolutely correct way to make a decision. Paul's example of the 'hot hand' myth I feel is incorrect; how is mathematical analysis going to take into account all of the factors that go into making a shot? Of course it isn't going to do that, it only looks at the results. Such things have little basis when we're looking at one event. The theory of probability and statistical analysis are based on ceteris paribus (all else being equal). Since we know that isn't the case in the "hot hand" example, our intuitions of human psychology may do a hell of a lot better than statistical analysis.

Human intuition is obviously far more flawed than statistical analysis and people make far more errors when they use intuition incorrectly. But it still has its place.

[CORed]

0.1111111... infinitely repated is equal to 1/9.
0.9999999... infinitely repeated is equal to one.
0.1111111 (not infinitely repeated) is not equal to 1/9. It is a little less than 1/9.

[CORed]

I think a lot of people don't really understand math, beyond very simple arithmetic (and some not even that), always struggled with math, and therefore don't really trust math. For example, it amazes me that many people can't understand why roulette is a -EV game. This is not a good thing for society in general, but it is a good thing if you want to play winning poker, because many people would rather trust their gut feeling that that gutshot is going to hit this time than realise that they are not going to make enough money when it does hit to pay for the times it doesn't hit.

[ThaSaltCracka]

[ QUOTE ]
I guess what I'm saying is that I've found that even explanations that are based on relatively unsophisticated mathematical concepts are eschewed.

[/ QUOTE ] If people are not familiar with things that rely heavily on % or statistics, they probably don't realize that Math is right more often then their hunch. And if they still don't want to accept that, then they are stubborn idiots.