| PlagueOfLocust said: First off, you're clearly confused, as evident in the first two lines. If, and only if, you first decided - arbitrarily - that my opinion was absurb and then provided your absurd scenario to mock this, the absurdity makes sense where it is. And yet you don't deal with this scenario as an absurd thereafter; you've been trying to defend it as a rational point. One does not defend absurdity unless they think it somehow makes a rational point. You can't have it both ways. Pick, and then note how your scenario is either unintentionally irrational or purposely absurd and indefensible, and either way useless. Then you get into phony math. Again, your scenario is faulty, albeit much less likely unintentionally so this time. First of all, someone does *not* have to win the lottery. Second of all, we're not talking about how likely it is that someone, anyone, will win. Those odds are decent. We're talking about how likely it is that a *specific person* will win. That's the proper scenario to make the comparison. I can't believe I actually had to walk through the math on this one to show that, if you think this was a random placement of highlights, it's unlikely that this one would come up over any other... particularly when even the best alternatives for messages with a scrap of meaning (thank you, Borkachev) pale in terms of coherency to the one we have showing up here. It puzzles me that you go ahead and call your scenario of unintentional coincidence "rational", and "more likely" even, without backing this up in any other way... in the very sentence that accuses me of not providing evidence. Admit that you just simply *feel* like it wasn't done intentionally, and that that feeling alone is the basis of your argument. Like it or not, the math supports what I'm saying. It could still be a freak happening, as I've said. That is a possibility I've allowed for from the start. All I'm saying is that it's unlikely that this could have been random... that's the mathematical fact, that it's *unlikely*. Period. But you aren't allowing for it to be anything but chance, so either way I have nothing on the line here. |
If by defending it you mean I was saying it needs no defense then you are correct. In any case you are going in circles on the issue, and quite honestly just need to admit that there was nothing wrong with my statement or at least drop it.
Actually my numbers were quite accurate, as you will find if do some reading in the field of discrete probability. As we are given 16 choices and at each choice we are presented with two options (ie highlight or don't highlight) we have 2^16 possibilities.
As you may or may not be pondering this probability problem actually doesn't fall under the heading of a combinatorial or permutational probability alone. A combinitorial problem involves an r-combination which means selecting r elements from a set (sets are unordered by definition). This is not our overall problem because we have 16 sets with cardinality of 2. To be more specific each set contains a "highlight" and a "don't highlight".
And it is not a permutational problem because order doesn't actually matter to us in the sense of a traditional permutational problem. Permutations assume the choices can be made in any order but in our case the choices are made in a specific order.
As a result what we actually have is 16 combinitorial events. For those keeping score at home you solve combinitorial problems using the formula C(n,r)=(n!) /((n-r)!*r!), where n is the cardinality of our set and r is the size of the combination (ie how many elements to use from the set for our combination). The result is of course that we have C(2,1)=(2!)/((1!)*2!)= 2 possible outcomes and with only one selection being made we have 1/2 or 0.5 probability of a given letter being highlighted.
Now that we have an established probability for each event and I have clearly defined how many choices we have lets take a look at the product rule which states "Suppose a procedure can broken down into a sequence of two tasks. If there are n ways to do the first task and m ways to do the second task then there are n*m ways to do the procedure." Utilizing the result of our single combinitorial event above we see that there are 16 tasks in this procedure each with 2 ways of completing them. So utilizing the Product Rule we see that 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 is the solution or the easier way to read it being 2^16 which simplifies to of course 65,536 possible ways to highlight those letters into saying different things.
Now your assertion that we should focus on the outcome of a single event's chances of happening is silly, but does highlight precisely where your line of reasoning goes wrong.
When looking at an improbable event with a single occurence it is absurd to jump to the conlusion that it is a statistical anomoly and assume its intentional on that basis alone. If we were faced with two occurences of the event, well then things are different and we can assess the possibility of an anomoly, but before that when every possibility is just as likely as the one that has occured it is an exercise in ignorance to assume its intentional without some other form of supporting reasoning.
This idea that we are supposed to look at the *specific person* is all well and good and you can take up that perspective if you so choose. But its the same odds from that scenario as it is from the overall view. Your position is the same as the average nutjob who is convinced that the lottery is rigged because he never wins.
PS - If you would like to play semantics thats fine, I won't play along with you. You knew precisely what I meant by the lottery statement and ignored it because it wasn't conveniant to your argument. I happen to be quite well versed in the field of probability and I am confident far beyond a "feeling" that you lack any amount of mathematical proof that the occurence is intentional. But should you feel that you are indeed more knowledgable in this field I am always willing to learn more so feel free to explain the gritty details of where you are coming from as I have.
Edit: I also will add that since there are 2 A's in "GALAXY" that the odds of the event occuring actually double since out of the 65,536 ways of highlighting/not highlighting there are actually 2 ways to get the exact phrase of "URMRGAY". So this outcome is actually more likely then most of the possible results.
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| To Each Man, Responsibility |
