Reasoning under uncertainty #2b - mathematical foundation

[suffering44]

just imagine the world expands, and only the physical things will expand? will it not expand in its diamention of binary things like truth and false plus and minus?

[suffering44]

if we have more than 3 spatial diamentions we might also have other diamntions the trick is to discover and invent them

[VeritasEtLibertas82]

This is awesome.

Thanks.

[shintopunk]

You pointed out in your video that your state of knowledge determines your value of probability (and I suppose what's bugging me is probability and truth are only both evaluations of knowledge anyway). So without the knowledge of the total number of gods, their mutual exclusivity, or any objctive evidence for the respective likelihood of their emotions I suppose 'probabilistic reasoning under uncertainty' is pretty fruitless?

[trondreitan]

No. You can classify the possible God models using boolean expressions (Good/Evil, all-poverful/not all-poweful, Christian/not Christian) as far as it is necessary to consider if that God would love a person that stabs his mother or not. Using existing knowledge and/or symmetries, you could then assign priors.

[trondreitan]

That being said, using your data to update the priors for the different God models would be of little use, as the data and the models would for the most part be independent. -> posterior=prior

[shintopunk]

However, I'm sure that myself and my twin brother could establish that we worship an identical God and come up with entirely different probabilities as to his love for me given what I had done. Clearly my twins knowledge of what I had done would change his posterior estimation of God's love for me even if it didn't mine.

[trondreitan]

If the probabilities are unequal then either the models are different or the priors (the belief) are different. If I were you, I would then communicate with your brother and find where your models+beliefs differ.

[shintopunk]

Plus, surely, if I believed God would love me if I killed my mother and he believed god wouldn't love me if I killed my mother, the probabilities would be redundant because we would both have reached certainty, albeit on different sides of the coin, I suppose leaving the jury in a certain state of uncertainty.

[shintopunk]

Don't worry, I know what you're saying, I give in. Thanks for the chat.

[suffering44]

well I thought we cannot talk of truth and god living in side our language of reasoning.

I thought that trying to explain what truth is using the rules of truth underlining our mind is not valid. But it has nothing to do with your video I only said that because they started to talk about it. And truth according to me has to be replaced by "rigorous beauty"

[shintopunk]

So what is the probability that "God loves me" (M) given that "I have just stabbed my own mother" (D)?

[trondreitan]

If you consider several mutually exclusive models for God, Mi, with Pr(love|Mi,D), you would get Pr(love|D) = sum Pr(love|Mi,D)Pr(Mi|D) = sum Pr(love|Mi,D) Pr(Mi), since the data would not tell anything about the probability for each God model.

[trondreitan]

Of course, you should also consider models where the equstion is basically meaningless, i.e. models where there is no God.

[trondreitan]

For each God model, Mi, Pr(love|Mi,D)=Pr(God Mi loves me even if I stab mother).

[trondreitan]

The proposition "God loves me" would not ordinarily be considered a model, since you would normally not have the probability of the data given such a proposition. But as you can see, you can decompose that proposition into a collection of (quasi)meaningful models.

[suffering44]

why do we only have defined complement and the set and not anything other than it? so e have only A and notA. I have long things to say about that but I know you are busy.

[trondreitan]

I'm not sure if I understand you correctly. it is so that for any element, e, it has to be either in a set A or it's complement. That's per definition of the complement. And if you have a set A, then the only other set you can construct using only A is the complement. That doesn't mean that you can't operate with other sets as well, though. Set's that may contain some elements both in A and in the complement of A. But this discussing has more to do with clip 2a than this clip, I think.

[suffering44]

well yeah thats the current definition in set theory. I didnt like that because it didnt sound very beautiful to me but it is simple and far more usefl and efficient. And more over I thought that even though we can select one apple out of two apples, and divide in to two sets, selected apple and unselected apples we cannot nessasaryly have it as a universal law to use in mathematics. but it was my thought that we must always have something that doesnt follow a certain law in real world.

[jas2754]

I had a thought/ Question ..has anyone applied these ideas to the Global Warming Problem?.... what reasoning decisions should be made given the uncertainty in the observations and extrapolations as it relates to Gl. Wmg.?

[trondreitan]

I do not know if Bayesian probability analysis specifically has been used for studying global warming. I feel confident that at least some statistical analysis on existing data has been done.

[trondreitan]

However, the standard frequentist way of doing statistics is by formulating zero-hypothesis and then testing it. This approach may not be the best here, since it may be unclear what the zero-hypothesis should be. The risks and costs involved are pretty high, so a Bayesian analysis should be called for. But I do not think a definate such analysis has been performed.

[jas2754]

Thank You .....Given the importance and costs of these decisions you would think that careful analyses is being done incorporating the uncertainty of the

data...... it could be an interesting project for someone.

[trondreitan]

Definately. A thorough Bayesian analysis would be a lot of work, as it should incorporate the physics, chemistry and geophysics involved. But it can and ought to be done. While nothing that thorough exists, a quick tip from a collegue gave me the page:

3 x w realclimate org

Search for "Bayesian".