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Probability and logic


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Here is a new angle for statistics and probability. It is an area that combines probability with logic. Here is the scenario; we have 100 dice with six sides. If you throw these dice, there are certain odds for a particular combination. No big deal. Say we randomly threw these 100 dice into a container that was just large enough to hold all the dice, like a drinking water glass. The number of possible combinations now becomes amplified, beyond expected, because some of the dice can now balance on edges and or apex points because they can be physically supported by other random landing of dice.

 

To lower the odds back to what is expected, traditionally, for 100 dice, we will need to increase the floor area of our container so we increase the odds all the dice will lie flat and not stack and lean on each other. If your container assumptions are not correct, the odds increase beyond expected. If we assume the dice can lie flat in any container, we can get affects that appear to the defy the odds.

 

A good example of this affect is the formation of life on earth. Based on the container of certain assumptions, the odds can get so high it appears like life should not have formed. Yet life did form, so the odds were not quite that high. Is it possible such a theoretical container is too small, such that dice are leaning against each other amplifying the odds? It is still valid probability for that container. But it may not be a minimum probability, which allow all the dice to lie flat.

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Life did not form by chance. It formed by the sequential build up of miniscule successful steps.

 

It's not like one day all of a sudden there was life. It's that one day a cell had a hydrophobic outer layer. That served it well, and after a while more cells had that layer. It got "selected for." Then, mutations would cause new "differenences" from the norm, and some of those proved beneficial. Hence, after a while there were more of those.

 

And on and on and on.... tiny steps... all until there was this thing we now as humans arbitrarily categorize as life.

 

It's not like some purple unicorn flipped a coin and said, "let there be leprehcauns!" Ermm... I mean, life.

 

 

Watch this from start to finish. Try to remember the heart of what it is teaching and demonstrating:

http://video.google.com/videoplay?docid=-690865967686494800&ei=db4VSe-bDZOwrAKxmuXMDQ&q=climbing+mount+improbable&hl=en

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I only used the creation of life because there is no direct data and therefore we need to use a container of assumptions. Depending on which assumptions we use, this will determine how many random events are need to occur at each step of the way. As we add logic the container changes and the odds improve. There is still random but as the container of assumptions evolve the odds get better it can happen. With the knowledge of genetics the predictions got better compared to before we knew about this. Before we differentiated the logic of genetics, this variable would be lumped with other variables, so the dice could more often balance on edge.

 

Let me give a different example. Say we knew anything of the logic of a falling object. We now know it is subject to gravity, pressure, temperature, wind speed and direction, object geometry, lift, etc. A good up draft may lift an object, if is light and/or has large surface area. With pure data collection, and no sense of logic to separate all these variables, anything can happen, since data can be collected to show almost anything, under the right conditions. A leaf can see observed to go up and stop in a tree. If we collected data at a windy spot on the earth, the new earth force is all over the place. Based on that random data the probability of predicting the object is not good (we are blind to the variables beyond observations).

 

To this purely observational data collection, we now add Newtonian gravity so we can predict at least one layer of the analysis with logic. We know all objects will eventually come down to the earth or there is always a pull downward. That data that shows a leaf that floated and stuck into a tree, above the ground, is due to something outside the earth force. Now we limit our random predictions of this earth force, to one plane.

 

We still have all the remaining variables. The up draft is no longer lumped to a feature of gravity. We just changed the container so the odds improve in terms of a final prediction. Next, we add the logic of lift and wind speed to the logic we have of gravity. There are still variables remaining but this container makes the odds even better for predicting. Next, we add the logic of temperature, air density the affects of air flow over surfaces both in terms of local topography and the object. There is still some random variability but the odds, because of this improved container, have improved even more. We know the object will land to the left, within a 20 degree arc somewhere within 10 feet of us. The dice are becoming more predictable. The dice is only needed for part of the analysis and not the entire affect.

 

The very first container could land on 1,2,3,4 all at the same time if all these variables are assumed part of the earth force. The dice is balancing on a apex since we can't really differentiate gravity, air density, wind speed and lift. As we evolve our container, all the dice now can fall flat and the odds for prediction become a lot tighter. It was never as random as we originally thought. All that extra random was due to the choice of container.

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Thanks for this great video but still I think that there are few things that can not be explained using probability theory. coincidences are common but there are few that are very very rare and still they occur at frequent intervals than it should mathematically.

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Thanks for this great video but still I think that there are few things that can not be explained using probability theory. coincidences are common but there are few that are very very rare and still they occur at frequent intervals than it should mathematically.
(emphasis added because that's the particular phrase I want to focus my reply on)

 

How can you say that conclusively? I.e. can you back that up with some math? And, if things happen more frequently than it "should" mathematically, then in all likelihood the model used was probably wrong and needs modified.

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