10-Heads in a Row (tralala...)
A friend of mine, Pesh by name, recently asked me the following question:
"If a man throws a coin 10 times and it comes up heads each time. What can you say about the next throw?''
Depending on you level of education your response should be 1 of 3.
However the standard answer is often non-intuitive. The people who give it often do not feel comfortable giving it. They often answer so, because they have been taught to say so. And it is this that makes this an interesting question.
If you know a child ask them too, see what their response is and ask them why?
SimplicityIf they have no understanding of probability but a real experience of tossing coins, they probably would exclude the information and rely on their experience and say either heads or tails.
Some EducationIf they have some rudimentory knowledge of probability theory and how it's taught in schools, they'd probably say TAILS. Because in School you're taught to look at the average, long term, ratio of events.
Highly EDUCATED
Still more education.... Gives people like you and me who give the "correct" answer of it being 50:50, an either-or with an equal chance. But even though you've been educated to say that answer... Doesn't it feel wrong! It's not intuitive, is it? And don't you feel uncomfortable saying so?
We say it because of course the coin has got no MEMORY of what it did on the previous other 10 throws.
So why doesn't it feel right?
Is it because we are too much ingrained with the traditional concept of probability as a measure of long-term ratios?
Or is there some deeper significance?
A Deeper Significance?You see there is another school of statistics and probability theory that is called Bayesian. Bayesians say that probability measures not some objective number (a platonic ratio) but a state of belief or unbelief. Where 1 and 0 are states of certainty, and all in between are varying states of uncertainty. They use a theorem (suprisingly called Bayes Theorem) to update their beliefs (probabilities) based on the occurrence or non-occurrence of events. The relative significance of events for the belief or non-belief is given by a ratio... Known as the likelihood ratio.
Whereas the traditional school doesn't have the power to question beliefs unless you formally construct a hypothesis and an alternate hypothesis, Bayesians are given over to questionin their beliefs of things. Traditionally you have to formally construct alternate hypotheses and then both design and carry out an experiment. Granted you can then measure your confidence in your decision. But what a bolava... A 3 step process... Which only allows you to do so after you've formally considered that you might just be holding an ereonous belief.
The POWER of Questions!Once again we've come to a traditional point in my thought..."The power of questions!
"The traditional question is "What can you say about what happens next?"
The Bayesian question is "What can the 10 heads in a row tell you about the nature of things (in this instance being the coin)?"
I believe that the latter question is far more important... powerful than the former!
What's the likelihood of getting 10 Heads in a row with an un-biased coin?
Answer =1/(2^10)... Not very likely is it?
Questioning your beliefs yet?
I didn't cheat as so many traditionalists would have you believe.I never said that I was tossing a traditional coin... Of course with me being who I am... I was tossing a Bayesian's "Head-Head" coin... Just to make a point!
What's the point?
Well if you're into probs and stats... Then I believe that Bayesian Theory is a hell of a lot more powerful than traditional theory.
And if you're not.... Then Questions are a lot more powerful than answers.
But just make sure that they are real questions... Not I told you so ones?
One last Powerful Question!Last but by no means least.... I'd like to ask just one more tiddily lil question, and that is: What's the likelihood of a man announcing to the World, some 1400 years ago, that the Sun has a term fixed?
Yes, you can say that there have been many doomsday predictors throughout the centuries. When they saw the eclipse of the Sun, they said the end of the World was nigh because of the Sins of Man.
This man said something similar but profoundly different, he said that the Sun had a fixed term... that the sun would expire after a fixed period of time.
And then he told us of waters boiling, of mountains vanishing, of the earth convulsing (to it's very core) and of the stars falling...And on the Day of Reckoning, the Sun would be 1 mile above the Earth. And people will be called forth from their graves...
Ask any cosmologist what would happen when the Sun's power gives out....
Would it not implode and then explode into a SuperNova....
Would not the seas burn and boil....
Woul not the sky become red like ointment....
Would not the stars fall....
In the 1920s Einstein witnessed the phenomenon that verified his general theory, and that explains the stars falling! The phenomena was a gravitational lens that bends light, and when the Sun explodes the stars we see in the heavens will fall. But not to the ground, but to the Horizon!
That man was Muhammad (saw) who taught that God was ONE and of the coming Day of Decision...
the Day of Sorting!
Answer =1/(2^10)... Not very likely is it?
Questioning your beliefs yet?
I didn't cheat as so many traditionalists would have you believe.I never said that I was tossing a traditional coin... Of course with me being who I am... I was tossing a Bayesian's "Head-Head" coin... Just to make a point!
What's the point?
Well if you're into probs and stats... Then I believe that Bayesian Theory is a hell of a lot more powerful than traditional theory.
And if you're not.... Then Questions are a lot more powerful than answers.
But just make sure that they are real questions... Not I told you so ones?
One last Powerful Question!Last but by no means least.... I'd like to ask just one more tiddily lil question, and that is: What's the likelihood of a man announcing to the World, some 1400 years ago, that the Sun has a term fixed?
Yes, you can say that there have been many doomsday predictors throughout the centuries. When they saw the eclipse of the Sun, they said the end of the World was nigh because of the Sins of Man.
This man said something similar but profoundly different, he said that the Sun had a fixed term... that the sun would expire after a fixed period of time.
And then he told us of waters boiling, of mountains vanishing, of the earth convulsing (to it's very core) and of the stars falling...And on the Day of Reckoning, the Sun would be 1 mile above the Earth. And people will be called forth from their graves...
Ask any cosmologist what would happen when the Sun's power gives out....
Would it not implode and then explode into a SuperNova....
Would not the seas burn and boil....
Woul not the sky become red like ointment....
Would not the stars fall....
In the 1920s Einstein witnessed the phenomenon that verified his general theory, and that explains the stars falling! The phenomena was a gravitational lens that bends light, and when the Sun explodes the stars we see in the heavens will fall. But not to the ground, but to the Horizon!
That man was Muhammad (saw) who taught that God was ONE and of the coming Day of Decision...
the Day of Sorting!
May Allah t'ala reward him exceptionally, magnanimously and increasingly!
P.S. The above is my interpretation only... And people are subject to limitations and errors..!
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