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Posts Tagged ‘probability’

This is somewhat of a follow up to my playful post on Absolute Truth. (read the comment there too for a nice follow up).  Here I explore the validity of “laws of nature” as a concept.  It appears more and more (at least to me) that our stated laws of nature are as Betrand Russell says, “They are statistical averages such as would emerge from the laws of chance.”

Betrand Russell provides a nice set of statements of the dubiousness of “natural laws”:

We now find that a great many things we thought were natural laws are really human conventions. You know that even in the remotest depths of stellar space there are still three feet to a yard. That is, no doubt, a very remarkable fact, but you would hardly call it a law of nature. And a great many things that have been regarded as laws of nature are of that kind. On the other hand, where you can get down to any knowledge of what atoms actually do, you will find they are much less subject to law than people thought, and that the laws at which you arrive are statistical averages of just the sort that would emerge from chance. There is, as we all know, a law that if you throw dice you will get double sixes only about once in thirty-six times, and we do not regard that as evidence that the fall of the dice is regulated by design; on the contrary, if the double sixes came every time we should think that there was design. The laws of nature are of that sort as regards a great many of them. They are statistical averages such as would emerge from the laws of chance; and that makes this whole business of natural law much less impressive than it formerly was.

Why I am Not A Christian

Here’s a decent philosophical backgrounder on laws of nature.  A passage that resonates with the economic mess we’re in now and the growing body of “exceptions to the rule” explantions spilling forth from economists.

it is striking how little attention is given to the possible effects of context. Mightn’t it be that, when the economist utters a certain strict generalization sentence in an “economic setting” (say, in an economics textbook or at an economics conference), context-sensitive considerations affecting its truth conditions will have it turn out that the utterance is true? This might be the case despite the fact that the same sentence uttered in a different context (say, in a discussion among fundamental physicists or better yet in a philosophical discussion of laws) would result in a clearly false utterance. These changing truth conditions might be the result of something as plain as a contextual shift in the domain of quantification or perhaps something less obvious.

Consider these stated “economic laws”.  how many exceptions to these laws do we find in todays world?

Some of this discussion of “laws” gets into the Fine-Tuned Universe discussion.  This is the idea that our universe is “finely tuned” for nature as we see it and any variation in physical constants would change the laws of physics to make the universe unfit for nature.  This is a counter-factual discussion for now as we have no way of tuning the universe differently to see what would develop and we don’t have sufficiently powerful technology to simulate or create our own universes.

NIST provides a killer resource for all these constants.  Also worth reading are the guidelines on understanding and reporting on uncertainty.

Conclusion:

I’ll borrow from the comments on the post on Absolute Truth mentioned at the beginning of this post.

The issue of validating or discovering new laws comes down to asking the question:

“Have any absolute truths been demonstrated and validated?” The answer to that question is also “no.” Two important things are different about asking the latter question. 1) it avoids a conundrum of syntactical verbiage allowing for an answer that can be understood without pleading to a meta language that is itself a problem. 2) it keeps open the idea that if an absolute truth were to be demonstrated and validated it would be interesting and a significant exception to what has been found to that date.

Personally, I’m highly skeptical of all generalizations and require a huge amount of evidence, both logical and empirical to accept abstractions from context.

Some who know me will claim I turn to math and logic a lot and it’s somewhat funky for me to decry generalization.  Yes, I have some training in and bias towards mathematical explanation, but I recognize math as useful modeling and analytic tool that helps us thinking through complicated situations.  When we’re really fortunate the math cuts through the noise and exposes relationships in a simple and understandable way.  Even when that happens, it still doesn’t provide us universal/absolute laws.

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The image below is a newly released panoramic (biggest ever view) of the Milky Way.  (find more here)

We’re on a planet, in a city, so small and hidden in this picture.  Don’t bother squinting, you can’t see us :).  

Question: Does this indicate the improbability or inevitability of our existence to you? Why? 

Question 2: Does it suggest a purpose to you? Why?

 

(Click to enlarge)

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The Ask Marilyn column in Parade magazine featured this question and answer in 1990 and 1991.  It received over 10,000 responses and over 1000 from PhDs.  Can you solve it and do you think Marilyn is right? (yes, this is an old topic but I just encountered it for the first time 🙂  )

Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?

Craig F. Whitaker
Columbia, Maryland

Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?

Read the ensuing archived discussion and rebuttals here:

http://www.marilynvossavant.com/articles/gameshow.html

What a simple problem, right?  So simple, you don’t need any math training to solve it correctly.  Chances are, though, your brain won’t get it right and even after you read the explanation it won’t stick and/or you won’t quite feel right about it.

That’s probability for you.  There’s a bevy of books and research materials out now on uncertainty, probability and chance.  From The Black Swan to The Drunkard’s Walk to Chance to Fooled by Randomness.  It seems to be a hot topic whenever the markets appear to be haywire, when finances get tough, when wars carry on, when we start the red vs blue discussion.  

Decision theory, quantum physics, analysis of behavior, managing your daily life, parenting… all involve studying probability of events.  Frankly, we’re bad it.  We’re bad at researching it and we’re bad at really understanding it.  We’re really bad at talking about it.

Not only does the above type of problem vex us, we fall prey to the “if I recognize any detail about a fact, I’m more likely to agree with that fact than something I know nothing about” situation.  Same Names, same birthdays, cities you’ve lived in, color of your skin, same employer, political party…. we tend to those things we know even when it might not help us.

Some evolutionary psychologists will offer the explanation that we evolved into taking chances on partial information that are familiar with because it aided in survival more often than not. hmmm.

To me, that’s a stretch.  I think we just suck at probability.  There’s no evolutionary advantage or disadvantage.  It simply might just be that way because of the way everything else about us is put together.

OR, the big OR.

It’s really about behavior.  We are conditioned by the environment.  We gravitate to people, things, situations we have behavior for – we’ve been punished or reinforced for.  When we haven’t yet experienced the other options, we can’t attribute any value to them.  If we don’t value something, we can’t chase it or pick it.  As soon as we pick or don’t pick it and we experience what happens, we then can assign value to it for the next encounter.

So, why do we suck at probability calculations?  We don’t behave based on calculations.  We literally do not connect the dots via probability.  We associate stimulus (sounds, words, smells, information) with other stimulus.  When the connection is made, it’s not a probability statement.  Why that is biologically, I don’t know.  I know that you don’t get partial action potentials and partial connections and partial patterns in the nervous system.  We get patterns and if the stimuli/situation matches a pattern (neural, muscular, etc.) we associate it.

In the game show problem above, it’s uber important to the math and to the behavior to understand the actual sequence.  You pick an option first then the host picks a losing option.  You’re learning at each step and assigning value – people over value the option they pick first (don’t switch!), the other option is unknown.  

You can research this on that old clips of Let’s Make a Deal or just watch Deal or No Deal – people over value their own case they chose and they associate all sorts of crazy data in choosing cases – the strategies mostly stink.

So… our ability or inability to accurately determine probabilities may not be some cause or end to itself but is simply an intervening variable or side effect of how we learn.  Now, why we learn the way we do is a big discussion and is worthy of writing about behavior every day!

I sure wish I evolved a better way of gambling… I’d be rich!

 

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