Zosimus
Active Member
The Maximum Entropy Principle tells us that in the absence of data, the probability distribution that shows the most uncertainty is the best one.
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The difference between Human and animal
- Thread starter Segev Moran
- Start date
Zosimus
Active Member
Formulae are only useful if one uses them correctly. The purpose of the formula is to show the effect on a hypothesis created when new data are obtained that affect the hypothesis. Assumptions are not new data. Assumptions that the conclusion is true cannot affect the a posteriori probability of the conclusion.
It's not very fair to compare the minds of other animals to ours. Where are their written languages, their protected societies,their metaphysical ideology. However, it doesn't come down to how advanced ours and their minds are, it comes down to how they act. Do we have evidence of animals behavior in self talk or slow breathing to cognitively and willfully calm themselves down from anger or excitement? Have they manipulated nature in order to make it more in line with their will, such as creating medications for their sick? Either way it's still pretty irrelevant. The more animals that have super high cognition, despite differing anatomy, capable of changing and questioning nature, the more obvious it is that the mind and nature are somehow separate.
Etritonakin
Well-Known Member
Now I am wondering about the boundaries or limitations of DNA-based evolution.
Is it possible for DNA-based life to evolve by changing its own base into something which was not DNA? Could it do this "naturally" -or would it necessarily be unnatural in the sense that it would require creative acts -such as humans self-evolving by intent -eventually into something extremely different?
If nothing was created thus far -are our acts of self-evolution and creation still evolution?
Could DNA-based life leave earth by adapting to space just as it adapted to land, air, etc.? Would that not require a radical re-design of its base -nature -composition -in order to survive in that environment and take advantage of available energy sources? Or.... Is DNA-based life limited to its local environment?
Also... If life on earth -specifically humans -was not created, would the consideration of immortality by the human imagination be considered an indication of the next major step in evolution? If humans could self-evolve into immortals, would it still be considered evolution?
If we were able to create beings similar to our selves in thought processes -but which had some sort of body which was not bound to the earth for its survival -or if we could self-evolve into such by a step-by-step process, would that still be considered evolution?
Zapping our selves across space to other planets, etc., by will would be awesome.
Is that a direction DNA-based life might take on its own -or does it require creation?
Is it possible for DNA -or similar -to be created out of things which could function similarly -but which were not the specific bases of DNA? Can similar code be written on/with different media?
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Nonsense, you are making up things, again. The formula is valid in general and there is no evidence anywhere that I cannot plug in, as premise, the predicate I want to calculate the probability of. Unless you have books about probability nobody is aware of.
But maybe I made a derivation error; yet, you are failing to show where I am incorrect abut the derivation. Until now you agreed with the first derivation, while you seem stuck with the second, for some reason
So, please show us what is wrong with plugging "superman exists" into B in the same formula you agreed was correct.
C'mon, we are almost there.
Ciao
- viole
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Zosimus
Active Member
No, Viole, I'm tired of your BS. Let's go back to the beginning.Nonsense, you are making up things, again. The formula is valid in general and there is no evidence anywhere that I cannot plug in, as premise, the predicate I want to calculate the probability of. Unless you have books about probability nobody is aware of.
But maybe I made a derivation error; yet, you are failing to show where I am incorrect abut the derivation. Until now you agreed with the first derivation, while you seem stuck with the second, for some reason
So, please show us what is wrong with plugging "superman exists" into B in the same formula you agreed was correct.
C'mon, we are almost there.
Ciao
- viole
You claimed that "you could also say that the probability that superman exists, under the premise that superman exists, becomes 0. Right?"
I responded If one starts with an initial assumption, one is bound to find that the initial assumption is true.
Since then you have launched into a long, tedious attempt to prove using formulae that the chance that Superman exists given that Superman exists is 1. Your goal in this is to prove that your original claim "the probability...becomes 0" is false and thereby you hope to somehow "prove" that I don't know what I'm talking about by refuting yourself.
It's getting old. If you have something to say, say it.
i don't know what you mean. i am not discussing Biblical Scholarship or University degrees here. Yet.
Don't forget the "well, yes" at the beginning of your post #162.
And yes, to be bound to find that the initial assumption is true, entails that the probability of superman existing, under the premise that he exists, is 1. How can it be zero if we restrict our target space to a set that contains the existence of superman? Because that is what conditional probability means: restricting the target space (the space of possible results) to one that fulfills the assumption. And in this space superman surely exists, by definition.
You seem confused.
It is your original claim, not mine. Posts # 160 and #162, for "no creation" and "superman exists" respectively. I can give you the benefit of the doubt for one mistake, but not for two.
And I assume here that native English speakers do not have reading comprehension problems concerning what they write themselves.
And I don't need to hope. The formula is clear, general and the results are inescapable. There is absolutely no constraint that prohibits me, or anyone else, to put "superman exists" in both the main predicate and its premise. And the results are also correct. If superman exists, then he exists, with certainty. Ergo with probability one. And not: if superman exists, then his probability of existing becomes zero. Which makes no sense. Obviously.
And how am I refuting myself?
To admit that you were wrong, twice, and provably so, would be customary
Ciao
- viole
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Very good.
But somehow you did not hesitate to set the priorities at 1/3 to each of the possible choices in my three choices scenario.
So, why are you hesitating now with a scenario with four choices? Does the maximum entropy principle work only with three choices?
Ok, let me set the probabilities for you, and tell me if I made a mistake and which one:
1) God is a giant invisible turtle namede Bob. 1/4
2) God is the God of the Bible. 1/4
3) God is a giant invisible elephant named Alice 1/4
4) God is neither 1,2 nor 3. 1/4
Correct? If not, why not?
Remember: everything under the assumption that God exists, but we are completely ignorant about His characteristics.
Ciao
- viole
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Zosimus
Active Member
I think you don't get the difference between "Yes" and "Well... yes." What you said was clearly wrong, but I assumed that your befuddled state of mind and lack of English comprehension were at fault. I tried to gently correctly you to the proper interpretation rather than pointing out that your math is complete and utter nonsense.Don't forget the "well, yes" at the beginning of your post #162.
First of all, Superman should be capitalized. I wouldn't normally include that, because it doesn't prevent me from understanding the meaning (so-called) of your diatribe. However, I think I need to include it at this juncture for fear that two messages later you'll claim that I was wrong because I didn't correct your obvious slip-up!
Second, Bayesian statistics doesn't lend itself to probabilities of 1 or 0 for that matter. You see, these numbers you're throwing around are logarithmic odds. So you seem to think that the difference between 0.9999 and 1 is only a matter of 0.0001. However, when you work in log odds, the distance between any two degrees of uncertainty equals the amount of evidence you would need to go from one to the other. That is, the log odds gives us a natural measure of spacing among degrees of confidence.
In other words, you would need an infinite amount of evidence to go from 0.9999 to 1. Thus, you see, your usage of the formula is completely incorrect. It was not designed for and simply cannot be used in the manner in which you want to use it.
Customarily, when one talks about odds in the real world, one talks about 1 chance in 6 of a single die coming up 5 on any given roll. So how would you express the odds that Superman doesn't exist in a world in which Superman is omnipresent? 1 chance in infinity? Such a world does not exist, and odds are there to calculate the odds of something that may happen -- not to discuss your assumptions or to work out the odds of tautologies.
Yes, there is a constraint. The formula is the probability of the hypothesis given the evidence. It is not the probability of the hypothesis given the hypothesis.
Well, that's what I said in my original response, although I personally have some serious misgivings on how assuming X leads you to be infinitely certain of X. Even people who assume that the Bible is inerrant must have private moments of doubt.
Well, if it made no sense, then why did you say it? Other than the obvious point that most of your posts make little sense to start with.
Haha. You are now defending yourself by pointing out how I capitalize superman? Or on the fine difference between "yes" and "well...yes"?
Very well, let me repeat the questions I asked in post #167
What is the probability of "no creation" under the premise of "no creation"?
What is the probability of "Superman exists" under the premise that "Superman exists"?
Is it still zero, or are you revising your BS, as you would put it?
Ciao
- viole
Zosimus
Active Member
The probability of "no creation" under the premise of "no creation" is one chance in... undefined.Haha. You are now defending yourself by pointing out how I capitalize superman? Or on the fine difference between "yes" and "well...yes"?
Very well, let me repeat the questions I asked in post #167
What is the probability of "no creation" under the premise of "no creation"?
What is the probability of "Superman exists" under the premise that "Superman exists"?
Is it still zero, or are you revising your BS, as you would put it?
Ciao
- viole
The probability of "Superman exists" under the premise that "Superman exists" is one chance in... undefined.
Now if you want to call the first chance 0 and the second chance 0, then that's your choice. Personally, I don't see it that way.
I think that if "no creation" is assumed, that the chance of "no creation" is assumed to be very high - close to 1. Previously, however, you said 0... which is an interpretation of probability that I don't endorse. Now if you said the chance of CREATION under the premise of NO CREATION I would have agreed that the chance was very low.
Then, when you asked me the probability of "Superman exists" under the premise that "Superman exists," I stand by my answer that if you assume that Superman exists, you assume that Superman exists. I don't see how that's a problematic statement.
And I still think that every single post you've made since you started this "gotcha game" should be modded and that you should be called on the carpet for your behavior.
Unintelligible. "If X exists, then X exists" is a true statement. Period. This predicate is true for every X. That does not entail that X exists, obviously.
1) if Superman exists, then Superman exists and
2) Superman exists
Are very different claims. The first is always true, by modus ponens, the second is very possibly false.The first does not require evidence, the second does. The first is an analytical proposition, the second is not.
I hope you are not confusing the two.
Why only close to 1?
When did I ever say that?
Nope. P(A|A) is a perfectly legit. That this is not allowed, is only in your mind. You can plug in any set you want in the premise, unless you can show me on what book it says you cannot do that. And P(A|A) is the probability of A, under the assumption of A. Not the probability of the assumption of A under the assumption of A or whatever it is that you believe to be the case. Where did you read that stuff? I am not aware of any probability book claiming that nonsense.
And P(A|A) = P(A AND A)/P(A) = P(A)/P(A) = 1 , since obviously A AND A = A.
The formula breaks only when we know, a priori, that P(A) = 0, because you cannot divide 0 by 0. Therefore, since we can agree that "no creation" has not probability 0 (you set it yourself to 0.5) we deduce that P("no creation" | "no creation") = 1.
But no matter what, it is either 1 or undefined. For sure, it cannot be zero. As you claimed.
QDE
Aww. Poor Zosism wants to be the only one with license to ridicule and to use words like "idiotic" and "BS". Not to speak of juvenile non-words like "pwned" and accusing not native speakers of not understanding them.
Now he is in that little suffocating corner and he needs external help. Lol.
Ciao
- viole
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I am still waiting for a response to my reply to this. Just in case you forgot it
But take your time. I am not in a hurry.
I set you on "follow", so I should get your response soon enough.
Ciao
- viole
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Zosimus
Active Member
No, they're not different claims. In fact, only one of them is a claim. "Claim" 1 is a tautology – like natural selection.
Claim 2 is an actual claim. It needs to be supported by reasons for believing it.
The only confused one here is you.
Probabilities of 1 are reserved for logical truths. Superman is not a logical truth.
No, it's completely wrong. What you seem to be saying is that by assuming A you can prove A. If this were true, the Christians would have proved the existence of God thousands of years ago.
Another demonstration that you don't know what you're talking about. When you say P(A and A) you are referring to the probability that two things occur. Thus, saying that A and A = A is wrong and pointless. The correct thing to say would be that P(A and A) = P(A), by which we mean that the probability that both Superman and Superman exist is the same as the probability that Superman alone exists. That's obvious. However, when you say Superman and Superman = Superman, you're just talking nonsense.
No, the formula breaks anytime 1 or 0 is used because if P(A) = 1 then P(~A) = 0 and that will require division by 0 just as surely as P(A) = 0 will require division by 0.
QDE? Quantum Detector Efficiency?
I don't use words "like" idiotic – I use words SUCH AS idiotic. Apparently, you don't know the difference.
And a tautology is necessarily logically true, isn't it?
You are still confusing the probability of a claim without dependant with the probability of the same claim with a dependant. Which is puzzling for a self-anointed expert of Bayesian statistics.
I am saying exactly that. It is called modus ponens. And if X is true, then X is true, and this is tautologically true. One of the basic tautologies. Useless, like most tautologies, but true. Or are you telling us that is false? And if it is not false, what is it?
If I assume that Bob loves fish, then the probability of Bob ordering fish at a restaurant is vastly different from the probability of Bob ordering fish if I do not make the assumption. Ergo, I did not prove that Bob is likely to order fish without the assumption. It can be that Bob hates fish. In the same way, if I assume that Bob orders only fish, then the probability of him ordering fish is 1. But that does not prove that the probability of Bob ordering fish (without strings attached) is 1. You really seem confused.
Of course, your Christians and me about Bob would use circular reasoning, without evidence of the dependant, but that does not make our claim logically wrong, just useless. It is useless, because the probability of God existing, under the assumption that He does not exist is 0. And the latter is also true.
I wonder what is so difficult to get.
The predicate A = "superman exists" is idempotent under the operation AND. The same with OR. Like all predicates. P AND P = P for all P. The same with sets if we use the corresponding operations (intersection and union).. So, I do not understand what you are talking about. You seem also to lack knowledge about the basics of (formal) logic and set theory, which is formally isomorphic to the first. i thought set theory is taught at what? First grade?
A predicate is a statement that can be true or false. Just in case you ignore that, too.
Ridicolous.
The formula P(A|B) = P(A AND B)/P(B) is valid in general, as long as P(B) is greater than zero. For obvious reasons. B can be a greater set than A, a smaller, or be equal to A. Or do you have a book or a reference that says otherwise? Until you post your evidence that this is not the case, I will make the (non circular) assumption that you are making things up. Again.
Quod Demonstrandum Erat. It is latin. Later period, I believe. I prefer it to QED. My German bias of putting verbs at the end, probably.
BS (such as). Post #169.
Ciao
- viole
P.S. What happened to my probability of God being a giant invisible turtle? It seems to be floating.
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Zosimus
Active Member
This statement avoids every point that I made. That's apparently your strategy. You pick and choose what to respond to so as to make yourself look as good as possible.
I'm not a self-anointed (or even self-appointed) expert on Bayesian statistics. In fact, I reject Bayesian epistemology. I am on this site looking for someone who supports it so that I can have an interesting discussion. Bayesian epistemology is supposed to overcome all the logical fallacies of the scientific method. I am skeptical that such a thing is possible.
Modus ponens is not a subject for Bayesian statistics. Bayesian statistics exists so that one can consistently and mathematically update one's subjective degree of belief in something. Modus ponens is out of scope.
No. The probability of Bob ordering fish is an unknown variable. Regardless whether you assume that he likes or doesn't like fish, his probability of ordering fish will remain unchanged. What will change is your subjective degree of belief.
This is a bad example because what you did has nothing to do with the logical consequences of whether Bob will order fish. A far better comparison would be to say, "If I assume that Bob orders fish, then it will become 100% probable that Bob will order fish." It's still a wrong statement, but it's far closer to what you said initially.
No, you're the confused one. Even if you assume that Bob orders only fish, the probability of him ordering fish does not go to 1. Your subjective degree of belief may be higher (certainly not 1, assuming that you are rational). However, Bob's actual probability of ordering fish does not change. It remains unknown.
My Christians? I don't have any Christians. Slavery is not legal where I live. Why would my hypothetical Christians and you use circular reasoning? Don't you know that this is a formal logical fallacy?
Again, you're completely misusing the formula. There's no probability that God exists. God is not something that exists 60 percent of the time (to make up a number) whereas Bob may order fish 60 percent of the time that he's at that restaurant. Such an occurrence could be open to a frequentist description of Bob's habits. If Bob orders fish 60 percent of the time, then his statistical likelihood of ordering fish is 0.6. Bayesian statistics exist to allow for the measurement of a subjective degree of belief in something that occurs only once. One cannot, for example, put Jesus in Jerusalem 100 times and see how many times out of 100 he gets crucified for proclaiming himself. It is something that either happened or did not happen. It's not for us to measure the probability that Jesus gets crucified. It's for us to determine whether we believe that this actually happened based on the evidence that can be collected. Of course, some people may assign ridiculously high or low a priori probabilities of the same based on alogical arguments, such as "My mommy said the Bible is 100% true so, let's start with 0.999999 as an initial probability." That's why Bayesian epistemology is basically worthless without principles that mandate a certain starting probability. It doesn't matter whether you call the tool the principle of indifference, the principle of insufficient reason, the principle of maximum ignorance, or the principle of maximum entropy.
I was wondering the same thing!
Set theory is a tool, and yes I'm familiar with it. Of course, I'm also familiar with Russell's Paradox, which shows that set theory is irreparably flawed. If you find it useful, then good for you. However, don't think that an appeal to set theory is going to save you.
A predicate is the part of a sentence that is not the subject.
Are you criticizing or are you combating Boggarts?
First of al, I have no idea why you are so enamored of this formula. I can only assume that you did some Googling and came up with it, and you're trying to beat me over the head with it. However, if you look back at , you will see that the formula I included was:
and this is NOT THE FORMULA YOU ARE USING. So again, I am firmly convinced that your formula and examples are all about you trying (and failing) to prove yourself smarter than others rather than actually addressing the issue at hand.
As you can see, the graphic I posted clearly shows the probability of the hypothesis given the evidence. It's not the probability of the hypothesis given the hypothesis. So you can clamp your hands over your ears, and yell "nya, nya, nya, I can't hear you" all you want, but you'll never convince me that (mis-)using another formula is going to refute the proper use of the one I used.[/URL]
Personally, I don't think there is much of a difference. We are all meatbags of one type or another. Some, like humans, have a higher level of consciousness, but nothing more.
I want to add something. I have a big house and one elderly cat. He can choose to be anywhere in the house, but he always chooses to be next to me, even making sure he's touching me.
What do you suppose that is?
There's much more to animals than meets the eye.
Segev Moran
Well-Known Member
This statement avoids every point that I made. That's apparently your strategy. You pick and choose what to respond to so as to make yourself look as good as possible.
I'm not a self-anointed (or even self-appointed) expert on Bayesian statistics. In fact, I reject Bayesian epistemology. I am on this site looking for someone who supports it so that I can have an interesting discussion. Bayesian epistemology is supposed to overcome all the logical fallacies of the scientific method. I am skeptical that such a thing is possible.
Modus ponens is not a subject for Bayesian statistics. Bayesian statistics exists so that one can consistently and mathematically update one's subjective degree of belief in something. Modus ponens is out of scope.
No. The probability of Bob ordering fish is an unknown variable. Regardless whether you assume that he likes or doesn't like fish, his probability of ordering fish will remain unchanged. What will change is your subjective degree of belief.
This is a bad example because what you did has nothing to do with the logical consequences of whether Bob will order fish. A far better comparison would be to say, "If I assume that Bob orders fish, then it will become 100% probable that Bob will order fish." It's still a wrong statement, but it's far closer to what you said initially.
No, you're the confused one. Even if you assume that Bob orders only fish, the probability of him ordering fish does not go to 1. Your subjective degree of belief may be higher (certainly not 1, assuming that you are rational). However, Bob's actual probability of ordering fish does not change. It remains unknown.
My Christians? I don't have any Christians. Slavery is not legal where I live. Why would my hypothetical Christians and you use circular reasoning? Don't you know that this is a formal logical fallacy?
Again, you're completely misusing the formula. There's no probability that God exists. God is not something that exists 60 percent of the time (to make up a number) whereas Bob may order fish 60 percent of the time that he's at that restaurant. Such an occurrence could be open to a frequentist description of Bob's habits. If Bob orders fish 60 percent of the time, then his statistical likelihood of ordering fish is 0.6. Bayesian statistics exist to allow for the measurement of a subjective degree of belief in something that occurs only once. One cannot, for example, put Jesus in Jerusalem 100 times and see how many times out of 100 he gets crucified for proclaiming himself. It is something that either happened or did not happen. It's not for us to measure the probability that Jesus gets crucified. It's for us to determine whether we believe that this actually happened based on the evidence that can be collected. Of course, some people may assign ridiculously high or low a priori probabilities of the same based on alogical arguments, such as "My mommy said the Bible is 100% true so, let's start with 0.999999 as an initial probability." That's why Bayesian epistemology is basically worthless without principles that mandate a certain starting probability. It doesn't matter whether you call the tool the principle of indifference, the principle of insufficient reason, the principle of maximum ignorance, or the principle of maximum entropy.
I was wondering the same thing!
Set theory is a tool, and yes I'm familiar with it. Of course, I'm also familiar with Russell's Paradox, which shows that set theory is irreparably flawed. If you find it useful, then good for you. However, don't think that an appeal to set theory is going to save you.
A predicate is the part of a sentence that is not the subject.
Are you criticizing or are you combating Boggarts?
First of al, I have no idea why you are so enamored of this formula. I can only assume that you did some Googling and came up with it, and you're trying to beat me over the head with it. However, if you look back at , you will see that the formula I included was:
and this is NOT THE FORMULA YOU ARE USING. So again, I am firmly convinced that your formula and examples are all about you trying (and failing) to prove yourself smarter than others rather than actually addressing the issue at hand.
As you can see, the graphic I posted clearly shows the probability of the hypothesis given the evidence. It's not the probability of the hypothesis given the hypothesis. So you can clamp your hands over your ears, and yell "nya, nya, nya, I can't hear you" all you want, but you'll never convince me that (mis-)using another formula is going to refute the proper use of the one I used.[/URL]
Not really. i used the same formula you identified as "the real formula" in post #169. By the way, your formula is derived from my formula. So, I guess it is not only right (if yours wants to be right) but it is more fundamental. And I did not google it. It must be on the first pages of any book about probabilities. May I ask what book do you use as a reference of your claims? Google does not count.
But if you really are into google, here is how your formula (Bayes Theorem) derives from mine:
https://brilliant.org/wiki/bayes-theorem/
Therefore, undermining my formula, undermines yours. Your call, really.
But I am sure you knew that....
And my case stands. You are unable to show any reference that shows that my use of the formula is wrong. Obviously, since it is not wrong. There are no restrictions on the sets I want to choose as long as the probability of any element in them has not probability zero. I just have to swallow your futile attempts to redefine the laws of probability in order for you to get out of that corner you put yourself in, and you expect that I swallow them.
By the way, did you know you can have probability 1 of event X to happen, and yet it does not happen? Conversely, X can have probability zero to happen, but it still could happen. This is also probability theory 101 which basically destroys your previous claim that probability 1 is reserved for logical truths.
So, I have a growing feeling that I am beating a dead horse. All I can do is give you some serious introductory books references and ask you to come back when you have worked out all the exercises in them. At leeast the ones in the very first chapters.
So, what about answering my other questions about your application of the maximum entropy principle? The initial probability of God being the God of the Bible, or being a giant turtle named Bob, is vanishing the longer I think about that
Ciao
- viole
Zosimus
Active Member
No, hon, you have the cart before the horse.Not really. i used the same formula you identified as "the real formula" in post #169. By the way, your formula is derived from my formula. So, I guess it is not only right (if yours wants to be right) but it is more fundamental. And I did not google it. It must be on the first pages of any book about probabilities. May I ask what book do you use as a reference of your claims? Google does not count.
But if you really are into google, here is how your formula (Bayes Theorem) derives from mine:
https://brilliant.org/wiki/bayes-theorem/
Therefore, undermining my formula, undermines yours. Your call, really.
But I am sure you knew that....
And my case stands. You are unable to show any reference that shows that my use of the formula is wrong. Obviously, since it is not wrong. There are no restrictions on the sets I want to choose as long as the probability of any element in them has not probability zero. I just have to swallow your futile attempts to redefine the laws of probability in order for you to get out of that corner you put yourself in, and you expect that I swallow them.
By the way, did you know you can have probability 1 of event X to happen, and yet it does not happen? Conversely, X can have probability zero to happen, but it still could happen. This is also probability theory 101 which basically destroys your previous claim that probability 1 is reserved for logical truths.
So, I have a growing feeling that I am beating a dead horse. All I can do is give you some serious introductory books references and ask you to come back when you have worked out all the exercises in them. At leeast the ones in the very first chapters.
So, what about answering my other questions about your application of the maximum entropy principle? The initial probability of God being the God of the Bible, or being a giant turtle named Bob, is vanishing the longer I think about that
Ciao
- viole
The basic theory is for calculating the probability that both A and B happen.
What's the P(A&B)? Simple. It's P(B) x P(A|B)
Let A = the ground is wet
Let B = it has rained.
So what's the probability that the ground is wet AND it has rained.
Well that's the probability that it has rained times the probability that the ground is wet given that it has rained. If you stop and think about that for a moment, it's obvious.
So no, the formula that you have mentioned is not the original formula.
Of course, we can use the same logic to say that:
P(A&B) = P(A) x P(B|A)
It's basically the same formula.
Thus we can say that P(B) x P(A|B) = P(A) x P(B|A)
Divide both sides by P(B) and you get Bayes' Theorem. So both the formula that you are using and the one that I am using is a rearrangement of the base formula. It's simply that the form I have placed it in is useful whereas the form you have placed it in is so that you can grind your axe.