I'm asking for your collective help in arriving at a basis for which things become "improbable". (If this is even possible.) My first thought is that we'd need something to help us define what "improbable" is. Something solid, factual, real and known against which to measure possibilities. For starters, we could choose the universe as this beginning point. If you consider all the categories of events above the atomic level that have happened in the entire universe since its beginning, we'd arrive at a very, very large number. This number we can call n.
Then we can start thinking about probabilities. For example, there's probably things that have never happened in the universe, or strings of events that seem common enough, but if put together in sequence, become quite improbable.
If the universe seems to large of a set to consider for our purposes here on Earth, we can just use our planet then. Especially since we seem to be stuck here, at least for a while. Using the Earth, then, common events in the universe become quite uncommon here, and even more so for those aforementioned sequence of events.
With this understanding, can anyone help me quantify the probability of any uncommon event? For our purposes here, we can use some event that's rather uncommon but notable in scale, say the current wildfire in California. Now I know wildfires are not that uncommon, but much less common than a paperboy throwing a paper and hitting his targeted porch or a meteor entering Earth's atmosphere. All replies are welcome.
Establishing a Basis for Improbability
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Sebastian Cole
- Posts: 121
- Joined: Tue Oct 07, 2003 12:30 pm
Have to disagree. Less then 50% chance of occuring when speaking of a working gene insertion is astronomically high! Mutations happen way less then that. Its all realitve.
Improbable in evolution terms is zero. The possiblity of an event occuring is so small that it might as well be nil. Example: The probability of snow to fall on the sun = zero/improbable.
Improbable in other fields maybe different.
Improbable in evolution terms is zero. The possiblity of an event occuring is so small that it might as well be nil. Example: The probability of snow to fall on the sun = zero/improbable.
Improbable in other fields maybe different.
GL, HF, KA, DD!
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Well, see that now you made me go and look the word up in the dictionary. Apparently, it means little more than "hard to believe". I stand corrected but I am not comfortable applying inexact words to scientific endevour such as gene insertion.Shazam0 wrote:Have to disagree. Less then 50% chance of occuring when speaking of a working gene insertion is astronomically high! Mutations happen way less then that. Its all realitve.
Improbable in evolution terms is zero. The possiblity of an event occuring is so small that it might as well be nil. Example: The probability of snow to fall on the sun = zero/improbable.
Improbable in other fields maybe different.
"Teach me the rules and I'll show you how the game is played."
MarkA, since I'm married I have way too much time on my hands, evidenced by this post's subject matter.
Shazam, I like your approach and example. We have to make a clear distinction though, between impossible and improbable. I suppose if an ice molecule from a passing comet where moving toward the sun at such an extraordinary rate of speed, it would have a chance of hitting the sun before melting. We might need some math or some really, really small number, like the inverse of my n above for Earth.
Shazam, I like your approach and example. We have to make a clear distinction though, between impossible and improbable. I suppose if an ice molecule from a passing comet where moving toward the sun at such an extraordinary rate of speed, it would have a chance of hitting the sun before melting. We might need some math or some really, really small number, like the inverse of my n above for Earth.
There is a clear distinction between impossible and improbable as nothing is both. Impossible, IS an exact or scientific word. The task, apparently, is finding a point at which we all agree that the possible has become improbable? That's improbable, if not impossible. 8)Golda wrote: We have to make a clear distinction though, between impossible and improbable.
"Teach me the rules and I'll show you how the game is played."
Now we are dealing with syntax. What you and I think a word means. For me the word improbable denotes that it probably wont happen. For me to wrap my head around that idea i give apply odds to it happening. For the event to probably not happen I'd say it has to pretty much be impossible to happne.
That said, I also have said soething along the lines of: its improbable that Bush could beat Gore, but he DID. so where is the definiation of imporbable?
That said, I also have said soething along the lines of: its improbable that Bush could beat Gore, but he DID. so where is the definiation of imporbable?
GL, HF, KA, DD!
Which is what I was thinking when I said that anything with less than a 50/50 chance is improbable. Whereas, anything with greater than a 50/50 chance PROBABLY will happen by simple virtue of the fact that it is more likely than not. I extended that logic to conclude that, if something was not probable, it was improbable. Of course, that still leaves me with anything having exactly a 50/50 chance as being improbable as it is not probable. <Bangs head on keyboard and calls it a day>.Shazam0 wrote:Now we are dealing with syntax. What you and I think a word means. For me the word improbable denotes that it probably wont happen.
"Teach me the rules and I'll show you how the game is played."
This is all assuming that there is only one chance for occurrence.Sansake^ wrote:Which is what I was thinking when I said that anything with less than a 50/50 chance is improbable. Whereas, anything with greater than a 50/50 chance PROBABLY will happen by simple virtue of the fact that it is more likely than not. I extended that logic to conclude that, if something was not probable, it was improbable. Of course, that still leaves me with anything having exactly a 50/50 chance as being improbable as it is not probable. <Bangs head on keyboard and calls it a day>.Shazam0 wrote:Now we are dealing with syntax. What you and I think a word means. For me the word improbable denotes that it probably wont happen.
Given that event x is given a number of chances approaching infinity and it still will most likely not happen, then event x is improbable.
Synedri
After discussing this idea with other ppl in my lab I think that the term 'improbable' can be applied to different areas of our life. In gene mutation for something to be improbable it has to be fanomonally unlikely to occur. In other areas of life like horse racing (i know nothing about this just surmizing) the odds need to be 10:1 of not happing to be improbable. The term can adapt different numerical values as the context of what is being refered is changed. So to say that improbable values have to be outside 3 SD, well thats not right in politics, or in baseball, but is accurate for certain cases.
Improbable can be defined as a term used to describe something that is unlikely to occur. 'Unlikely' is a loose term that can be taken many different ways, depending on what is being discussed.
Improbable can be defined as a term used to describe something that is unlikely to occur. 'Unlikely' is a loose term that can be taken many different ways, depending on what is being discussed.
GL, HF, KA, DD!
Yes Shaz, we have to use a closed set in order to really arrive at a number we can use. At the beginning of this thread I first proposed only the universe and its super-atomic events as this closed set. Then I thought better and nominated just Earth. Perhaps this too was too big a set. Perhaps we should limit the set further to recorded Human History. A "for example" that might arise out of our study of our set might be something like determining the probability of The Great Plague happening in terms of % of affected population up until that point in time. Was it improbable that so many died or was it bound to happen (probable)?
OK, this thread made me contact an old professor at my university. He explained two guys (Ralph Abraham, and Edward Lorenz) puzzled over this very issue.
They came up with the 'Chaos Theory'. I haven't read or heard anything about this other then what my professor told me:
Probability of a random event occuring in a random place at a random time, is equal to the product of the probability of each of these events occuring times the number of random places.
However, this assumes that each random event occurs just as likely in all random places, which is not true (ex: more likely to snow in mountains then in tropics). Also does not take into effect refractery periods for random events (ex: A mountain can't erupt and blow its top off everyday, but a wave can crash on a beach every few seconds).
They came up with the 'Chaos Theory'. I haven't read or heard anything about this other then what my professor told me:
Probability of a random event occuring in a random place at a random time, is equal to the product of the probability of each of these events occuring times the number of random places.
However, this assumes that each random event occurs just as likely in all random places, which is not true (ex: more likely to snow in mountains then in tropics). Also does not take into effect refractery periods for random events (ex: A mountain can't erupt and blow its top off everyday, but a wave can crash on a beach every few seconds).
GL, HF, KA, DD!
Ahh good reply! Now we can start defining what is probable and what is improbable. I'd like to focus on a more individual basis and thoughts about what improbable actually is to an individual. I did some further research about what experts consider improbable and after having all the known variants defined as to their particular probabilities of occurance, we then use simple math to arrive at a set of results that if plotted, were to result in a curve which had a rate of decline (in regard to probability) that starts to approach infinity rather quickly at some point in the string of occurances. As applies to individuals, where on the "steep slope of increasing improbability" you sit is up to you and decides for you what is impossible and what is merely improbable.
Further more, on the path to improbability there arise other outcomes that become more probable when opening up our closed set of occurances a little bit and considering them.
For example: A dead cat is discovered outside your door. You know there are stray dogs that roam around. You also know that there are several older cats unclaimed by neighbors. Also, there's been reports of teen ruffians taking liberties with strays lately. Also there was a lightning storm last night that resulted in several lightning strikes in your area. Upon further examination of the cat, you discover more occurances to the cat that further define the equation and add to or take away from the probability of any one occurance to our dead cat.
Please add your thoughts.
Further more, on the path to improbability there arise other outcomes that become more probable when opening up our closed set of occurances a little bit and considering them.
For example: A dead cat is discovered outside your door. You know there are stray dogs that roam around. You also know that there are several older cats unclaimed by neighbors. Also, there's been reports of teen ruffians taking liberties with strays lately. Also there was a lightning storm last night that resulted in several lightning strikes in your area. Upon further examination of the cat, you discover more occurances to the cat that further define the equation and add to or take away from the probability of any one occurance to our dead cat.
Please add your thoughts.
Golda, you mean we are looking at a finite amount of occurences of event x. And we are only looking at a few x events. And we are not looking at the probability of the occurance, rather the improbability...
I care much more about the probability of events then the imporbability. I believe that improbability is a loose term, the meaning of which may change from person to person (like the syntax problem we had earlier).
I cant wrap my head around the quantifing paramaters that make an event improbable. Online Dictionary states:
I care much more about the probability of events then the imporbability. I believe that improbability is a loose term, the meaning of which may change from person to person (like the syntax problem we had earlier).
I cant wrap my head around the quantifing paramaters that make an event improbable. Online Dictionary states:
Not probable; unlikely to be true; not to be expected under the circumstances or in the usual course of events; as, an improbable story or event.
Last edited by Shazam0 on Mon Nov 17, 2003 9:09 pm, edited 1 time in total.
GL, HF, KA, DD!
Ok we're getting somewhere now. Actually the difference between improbable and probable from a purely statistical/mathematical viewpoint is simply applying an inverse to one in order to get the other. So defining the probability of an event is just as good. With our dead cat example above, we can (not should) start out by presuming that the dog killed the cat. We can add factual evidence that we happen to find that futher supports or contradicts our presumption or theory. (At this point I do feel like we are leaving statistics and entering scientific reseach theory though. Accepting that, in any event, I want to keep our conclusions purely scientific and as mathematical as possible.) So for the possibilities that were named above, we can start anywhere and randomly assign probablities to those events of our poor kitty. Let's say the first event has a 40% probability, the second 30, the third 20, the forth 5 and we'll leave a miscellaneous bucket of another 5%. For our first additional fact, we'll throw in some moisture found on the cat's neck and no where else. Also, there does not appear to be any burn marks on the cat. Now how does that shift our probability %'s above? It might affect the probability of the lightning strike the most and maybe affect the teen ruffians' chances as well. Upon further examination we see dog hair near the scene. How do you think that might affect our %'s ?
Surely as all things are potentially possible, given infinite space and infinite time, nothing is impossible and therefore all things are probable.
The degree of probability labeled as improbable is an abritrary value below 50% defined by the viewers perspective.
However as 50% of infinity is itself infinity this is obviously absurd.
Oh dear I have a headache now
The degree of probability labeled as improbable is an abritrary value below 50% defined by the viewers perspective.
However as 50% of infinity is itself infinity this is obviously absurd.
Oh dear I have a headache now
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It is amazing what you can accomplish if you do not care who gets the credit.
Harry S Truman (1884 - 1972)
Well Golda, you sure can keep a conversation going!
If you just look at the dead cat closely you can probably deduce how it got there, and how it died. The further you examine it, and the more involved you do your research and detective work the closer you get to the answer of how and why it is where it is.
Pretending that a finite amount of detective work is possible, and will only eliminate part of the possibilities and not all of them. Then we are looking at the probability of each of the remaining events that could end up with a cat on your porch.
As the number of events that could have occured are reduced the probability of each of the remaining event increases. To find the amount each probability changes, divide the individual event's probability by the the sum of all probabilities left. (right?) and then subtract this from the original probability and you will get the change in probability from using detective methods to eliminate one of the events from have occuring.
However it is impossible to say that we can quantify how many of the possibilities can be eliminated for all cases. It is also impossible to know the probability of all events possible. In our world things are changing so rapidly, and the smallest event can have multiple reactions that can have a final result very much larger then the first.
Sheesh i whought we were done...Ok we're getting somewhere now.
If you just look at the dead cat closely you can probably deduce how it got there, and how it died. The further you examine it, and the more involved you do your research and detective work the closer you get to the answer of how and why it is where it is.
Pretending that a finite amount of detective work is possible, and will only eliminate part of the possibilities and not all of them. Then we are looking at the probability of each of the remaining events that could end up with a cat on your porch.
As the number of events that could have occured are reduced the probability of each of the remaining event increases. To find the amount each probability changes, divide the individual event's probability by the the sum of all probabilities left. (right?) and then subtract this from the original probability and you will get the change in probability from using detective methods to eliminate one of the events from have occuring.
However it is impossible to say that we can quantify how many of the possibilities can be eliminated for all cases. It is also impossible to know the probability of all events possible. In our world things are changing so rapidly, and the smallest event can have multiple reactions that can have a final result very much larger then the first.
GL, HF, KA, DD!
Ok after doing some research on this topic for quite a while I finally found what I was looking for. Here's some improbabilities for categories of events. These figures come from a doctorate research paper I found online from a group of students at Illinois Institute of Technology. It was to be a foundational principal upon which they were going to build their doctoral thesis.
Here are some exerpts, some random catagories for which they had taken sample data, some pretty solid calculas and standard statistical forumlas to arrive at a range or in some cases an actual number for which events in the category start to become improbable. (1 being the highest level or probability, 0.5 being a 50% chance, and so on.)
Sporting Events
Any average MLB team would win the world series: 0.030017
The White Sox would win: 0.0349 (Sox park is right across the street from IIT)
The Cubs would win: 0.0338
The Yankees would win: 0.1741
Financial Events
Dow Jones will hit 7000 this year: 0.8892
Will hit 11000: 0.91301
Social Events
A new US president will be elected: 0.4366
Another significant terror attack will occur in the US: 0.02794
Scientific Events/Theories
A significant comet will hit earth within the next 1000 years: 0.91502
A major earthquake will strike the US central or eastern regions within the next 20 years: 0.8944
Intelligent life exists somewhere else in the Universe: 0.9662083
The highest form of intelligent life in the Universe has harnessed the ability to create/form massive material structures, such as planets: 0.90115
The research goes on to explain in the summary in laymens terms how they arrived at what they called a "significance threshold" number: a number of possibilities that contributes to the final probability in a significant way and defines a plateau that other possibilities must reach in terms of significance, being able to move the final probability value in a significant way, either increasing it or decreasing, so that in relation to the possibilities on the plateau, they stood a reasonable chance (reasonable being defined by the nature and number of possibilities versus the universe of possibilities) of defeating all the other possibilities on that plateau, given the amount of time. This plateau changed in relation to the universe of possibilities surrounding the event, but was often expressed as a small number, usually between 0.001 to 0.000412 in the examples I looked at. The simpler examples, like the sporting events, had the largest numbers for plateaus.
Here are some exerpts, some random catagories for which they had taken sample data, some pretty solid calculas and standard statistical forumlas to arrive at a range or in some cases an actual number for which events in the category start to become improbable. (1 being the highest level or probability, 0.5 being a 50% chance, and so on.)
Sporting Events
Any average MLB team would win the world series: 0.030017
The White Sox would win: 0.0349 (Sox park is right across the street from IIT)
The Cubs would win: 0.0338
The Yankees would win: 0.1741
Financial Events
Dow Jones will hit 7000 this year: 0.8892
Will hit 11000: 0.91301
Social Events
A new US president will be elected: 0.4366
Another significant terror attack will occur in the US: 0.02794
Scientific Events/Theories
A significant comet will hit earth within the next 1000 years: 0.91502
A major earthquake will strike the US central or eastern regions within the next 20 years: 0.8944
Intelligent life exists somewhere else in the Universe: 0.9662083
The highest form of intelligent life in the Universe has harnessed the ability to create/form massive material structures, such as planets: 0.90115
The research goes on to explain in the summary in laymens terms how they arrived at what they called a "significance threshold" number: a number of possibilities that contributes to the final probability in a significant way and defines a plateau that other possibilities must reach in terms of significance, being able to move the final probability value in a significant way, either increasing it or decreasing, so that in relation to the possibilities on the plateau, they stood a reasonable chance (reasonable being defined by the nature and number of possibilities versus the universe of possibilities) of defeating all the other possibilities on that plateau, given the amount of time. This plateau changed in relation to the universe of possibilities surrounding the event, but was often expressed as a small number, usually between 0.001 to 0.000412 in the examples I looked at. The simpler examples, like the sporting events, had the largest numbers for plateaus.
Snippets from "Living Waters" website:
Did you know that the eye has 40,000,000 nerve endings, the focusing muscles move an estimated 100,000 times a day, and the retina contains 137,000,000 light sensitive cells?
Charles Darwin said,
"To suppose that the eye could have been formed by natural selection, seems I freely confess, absurd in the highest degree."
George Gallup, the famous statistician, said,
"I could prove God statistically; take the human body alone; the chance that all the functions of the individual would just happen, is a statistical monstrosity."
Albert Einstein said,
"Everyone who is seriously interested in the pursuit of science becomes convinced that a spirit is manifest in the laws of the universe—a spirit vastly superior to man, and one in the face of which our modest powers must feel humble."
Did you know that the eye has 40,000,000 nerve endings, the focusing muscles move an estimated 100,000 times a day, and the retina contains 137,000,000 light sensitive cells?
Charles Darwin said,
"To suppose that the eye could have been formed by natural selection, seems I freely confess, absurd in the highest degree."
George Gallup, the famous statistician, said,
"I could prove God statistically; take the human body alone; the chance that all the functions of the individual would just happen, is a statistical monstrosity."
Albert Einstein said,
"Everyone who is seriously interested in the pursuit of science becomes convinced that a spirit is manifest in the laws of the universe—a spirit vastly superior to man, and one in the face of which our modest powers must feel humble."
There is no question of does evolution occur, we know it does. We have imperical data proving speceis have evolved. What is disqiueting is that there is no precursors to so many specieses and so many features present today in the eukaryote domain (includes everything except bacteria and archea). The vertebrate eye is one of these, that has no precursor. nothing before it was functional that would keep it present until the day it was finally done randomly mutating to become a functional organ. insect wings are another. pre-cambrian and cambrian explosions of plant and animal life another.
GL, HF, KA, DD!
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Raaz Satik
- Taggart Director
- Posts: 2026
- Joined: Wed Aug 25, 2004 2:40 pm
On a tanget, http://www.tradesports.com has financial markets on nearly all of these outcomes. US President, Bin Laden, Sports, Financials etc etc. The resulting markets give you expected probabilities of the events occuring. Now obviously market implied probililites which are driven by human emotion will be different than statistical implied probabilities which are driven by models, but it gives you a picture none the less.Golda wrote:Sporting Events
Any average MLB team would win the world series: 0.030017
The White Sox would win: 0.0349 (Sox park is right across the street from IIT)
The Cubs would win: 0.0338
The Yankees would win: 0.1741
Financial Events
Dow Jones will hit 7000 this year: 0.8892
Will hit 11000: 0.91301
Social Events
A new US president will be elected: 0.4366
Another significant terror attack will occur in the US: 0.02794
