The Bayesian Machine

[kristalris]

Please make it very clear what you mean by this.

 

It looks like you are just saying something along the lines of if a proof exists then we can be 100% sure a proof exists and thus any proved theorem is true!

 

I think we can agree on this

 

EQ

 

Indeed

 

Q

 

. But so how does this mean that all mathematics can be reduce to Bayes' inference

 

 

EQ

 

I've just done that with the picture in the previous post in answer to Gee. Bayes then infers that all truths are true and all untruths are untrue. The reduction lies in extremely simplifying the Bayes formula so that it can take in all correct mathematical proofs. This then proves that the mathematical correct proof fits the formula of Bayes. And thus that it is scientific given the prior assumptions: i.e. the existence of absolute truths and untruths.

Oh and BTW this immediately puts your idea that not all mathematics can be reduced to logic can be put in B. It is untrue. It can because it fits Bayes and Bayes certainly can be stated in verbal logic and visa versa.

 

 

Q

or how does Bayes' theorem help us get at unknown proofs?

 

EQ

 

Bayes doesn't help you get to unknown proofs when dealing in absolute truths like pure mathematics does. In this part of my reasoning I only show that all mathematics and all logical truths are consistent with the Bayes formula. Please wait for the ramifications.

 

Q

 

Please see my comments above.

 

 

It has been said that all theorems once proved are trivial!

 

EQ

 

Nah,

 

Q

 

The problem is we don't know what you are really trying to tell us. Not all mathematics can be reduced to Bayes' and that I think is not really disputed. It follows from the fact that not all mathematics can be reduced to pure logic.

 

EQ

 

I just have showed you it can. By placing all correct mathematics (or part say the proof of Pythagoras fully written down) in A you have in effect reduced it to "A".

 

Q

 

So once again, make clear your claim. It is either false or trivial, or maybe we are missing what you are saying.

 

EQ

 

I haven't gone into the not being trivial bit yet as I've repeatedly stated. But you lot keep on objecting that you can't put all of mathematics into the Bayes formula. Take Gees peace of paper and write any correct mathematical proof you like and it will reduce it to "A".

 

Q

 

 

Using Bayes', as you have not demonstrated to any of us that you are knowledgeble in mathematics, we conclude that it is unlikely that what you are saying has any worth.

 

EQ

 

Ah well then we can immediately take this remark into the easy Bayes machine: I'm indeed not very knowledgeable in mathematics (might of been though). So you subsequently conclude that it is unlikely that what I'm saying has any worth.

 

Well then now you have made a fallacy as easy Bayes shows. A priori the likely hood pro saying anything of worth is thus small and the likelihood of saying something wrong is great. I.e. the prior odds (the first likelihood ratio and not only "unlikely") is small of me saying anything of worth. Yet you should like Bayes theorem teaches us also look at the likelihood ratio's of all else that has been said and take that in evidence before we can infer or conclude something. You leave it at the a priori sec before what actually? Your reasoning doesn't fit Bayes and is thus not scientifically valid. For all further things I've stated and the formula have been ignored by you. And you don't state the posterior conclusion.

 

You in fact only state a sort of syntax error concerning the LR's. Even though I made use of a formula that you have ignored. You must then state what I in your opinion have done wrong in that, because otherwise it is a Monty Python act.

 

Q

 

 

You have not given us proof of anything.

 

EQ

 

I have correct mathematics fits in A and incorrect mathematics fits in B that is proven, what more do you want. Neigh absolute proof. To which you only state syntax error.

 

 

Q

 

What formula are you refering to?

The last one I gave for crying out loud. #64 q.v. (Suddenly the quote box works again. Magic!)

 

 

No one will dispute Bayes' theorem as it is a well formulated statment within a well founded mathematical frame work. We can prove the statement it true! It is the use and interpretation that we object to in this context.

 

Once again, you will need to make your claim very clear to us. It looks a trivial statment with hindsight and not useful.

Again whether or not trivial will be dealt with later. You got a slight taste of Bayes analysing your reasoning in this post and showing that it can't be made to fit Bayes and is thus not scientifically correct. Not trivial I'd say. But there is more to come. First this hurdle.

 

+++ last post ajb +++

Wookie or no wookie, having one formula to check if something is scientific or not, trivial science or not trivial science, is extremely important and thus not trivial. As I will later on show you, for I guess you now only "Wookie" because you - again incorrectly - ( because via incomplete reasoning i.e. not conforming the Bayes theorem) conclude (I guess) that it thus is trivial. I.e. a Wookie.

Edited December 5, 2013 by kristalris

[ajb]

The fact remains that you are mistaken that all mathematics can be reduced to logic and Bayes' inference.

 

 

If you cannot be convinced of that so be it.

 

You have some stubbornness when talking with people who know more about the subjects than you do. I beggs the question why bother posting on this forum at all? You like to soapbox and not take in anything anyone has said to you.

 

I just can't see any point in further talking with you!

 

If you want to learn some mathematics and science then you will have to loose your attitude.

[kristalris]

Well pose argument and not just state something like "Wookie". That is Monty Python otherwise. If I'm wrong I'm wrong, but I'm not wrong because you just say so.

 

I say you can chuck all truths into A of Bayes i.e. all truths and all untruths into B of the # 64 formula being that of Bayes. That formula is mathematics. That formula is Bayes. All Bayes can be stated as verbal logic Shum dixit.

 

And you can split any thought about triviality because I've yet to address that.

 

Ergo it either is correct or incorrect what I'm stating.

 

I guess I effectively dealt with moving goalposts so that can't be it.

 

Now then tell me what I got wrong then:

 

a Is the formula #64 incorrect?

 

b is the formula #64 not Bayes?

 

c can A of the formula #64 not hold all truths, correct mathematics, logics?

 

d can B of the formula #64 not hold all untruths, incorrect mathematics, un-logics (as long as the absolute opposite of A of course)?

 

e can the formula #64 not be stated as verbal logic and visa versa?

 

f something else is wrong namely................

Edited December 5, 2013 by kristalris

[ajb]

What is all mathematics, what is all correct mathematics, what is all incorrect mathematics, what are all truths, what are all untruths?

[kristalris]

Okay: you want to place me in a probatio diabolica; sorry mate nice try.

 

You can take any part of mathematics that you can think of as correct (= all correct mathematics), like the correct proof of Pythagoras (do you need the link for that?) in A and any incorrect proof thereof that your students can come up with in B. being thus the absolute opposite.

 

This proof (i.e. that all true swans are true and all untrue swans are untrue) can be disproven by you by showing one true swan being untrue or one true swan being untrue or one absolute true or untrue swan not to fit A or B. Otherwise I succeed and you fail the proof.

 

You thus may take the whole or any part providing you take the absolute opposite of any whole or any part you like that you deem absolutely correct A or incorrect B.

 

Your question fundamentally shows you don't understand Bayes BTW. Study Shum some 400 pages BTW.

 

You can put absolutely anything into A that you BELIEVE to be correct AS LONG AS you put the absolute opposite in B. Or visa versa.

Edited December 5, 2013 by kristalris

[ajb]

You can take any part of mathematics that you can think of, like the correct proof of Pythagoras (do you need the link for that?) in A and any incorrect proof thereof that your students can come up with in B. being thus the absolute opposite.

 

So, as I said if I know I have a correct proof then I have a correct proof!

 

This is trivial.

 

You have said nothing of any significance.

 

Again, you are far from proving that all mathematics can be reduced to Bayes' inference which is what you claimed. Or are you now changing that statement?

Edited December 5, 2013 by ajb

[kristalris]

Bloody hell I stated that I will yet prove it to not be trivial!

 

This I then can take that you concede being wrong baring that what I state is trivial, right?

 

Sorry have to go now, Sinterklaas has arrived. A constant of nature on 5 December in the Netherlands.

[ajb]

This I then can take that you concede being wrong baring that what I state is trivial, right?

NO!

 

Not all mathematics can be reduced to logic and so cannot all be reduced to Bayes'. Bayesian probability can be viwed as an extension of propositional logic, but I have no idea about other logical calculi. You would need to show that Bayesian probability is an extension of first order logic and then argue that Zermelo–Fraenkel set theory with the axiom of choice can be described by Bayesian probability.

 

Once you have done that you could argue that the bulk of mathematics can be reduced to Bayesian probability, but not all of it.

 

You could then try to look at other forms of set theory and continue to build the theory.

 

Unless you make strides in this direction your claims are unfounded...

 

other than if I have a correct proof, I have a correct proof! Even then mathematics is not just about the existence or construction of proof, though that is a large part of it.

[swansont]

Well pose argument and not just state something like "Wookie". That is Monty Python otherwise.

 

South Park, actually.

 

If I'm wrong I'm wrong, but I'm not wrong because you just say so.

It is up to you to show that you are correct. You won't change anyone's mind until you can actually demonstrate your claims.

 

I guess I effectively dealt with moving goalposts so that can't be it.

No, not really. Other people giving up rather than wade through your ramblings is not agreement.

 

You made a claim, and were never able to back that up. You claimed victory based on a different claim. That's moving the goalposts.

[Cap'n Refsmmat]

other than if I have a correct proof, I have a correct proof! Even then mathematics is not just about the existence or construction of proof, though that is a large part of it.

 

http://www.youtube.com/watch?v=aX6XMIldkRU

[kristalris]

NO!

 

Not all mathematics can be reduced to logic and so cannot all be reduced to Bayes'. Bayesian probability can be viwed as an extension of propositional logic, but I have no idea about other logical calculi. You would need to show that Bayesian probability is an extension of first order logic and then argue that Zermelo–Fraenkel set theory with the axiom of choice can be described by Bayesian probability.

 

Once you have done that you could argue that the bulk of mathematics can be reduced to Bayesian probability, but not all of it.

 

You could then try to look at other forms of set theory and continue to build the theory.

 

Unless you make strides in this direction your claims are unfounded...

 

other than if I have a correct proof, I have a correct proof! Even then mathematics is not just about the existence or construction of proof, though that is a large part of it.

 

Now you are indeed posing argument. I've looked up the points you have made and I think I've found the problem, why you / mathematics via Gobel think that it can't be reduced to probability.

 

If you have the nominator go to infinite the denominator goes to zero and leaves an error. Yet you don't have this problem with Bayes. They both go to 1: i.e. 1/1 leaving 1. I.e. Bayes' formula stays functional.

 

Nowhere in the proofs I found do I see Bayes come into the picture. You mathematicians clearly forgot Bayes.

 

It is you who states the proof that all swans are white: I only have to show one black one and have done so. I don't have to show full mathematical proof that it is black (for Bayes is Black and White). It is for Gobel to show that he excludes Bayes in his proof for he is the claimant of the proof. I only question it.

 

Because you can't burden me with a probation diabolica of asking me to prove that all mathematics fits Bayes. You only have to provide one (you tried and failed with Pythagoras) that doesn't fit Bayes to disprove. And for Gobel and you to hold your claim you must show that Bayes was included in the proof.

South Park, actually.

 

 

It is up to you to show that you are correct. You won't change anyone's mind until you can actually demonstrate your claims.

 

 

No, not really. Other people giving up rather than wade through your ramblings is not agreement.

 

You made a claim, and were never able to back that up. You claimed victory based on a different claim. That's moving the goalposts.

 

Woekee is Star Wars actually and used the way ajb did more Monty Python than South Park the later owing tribute to the former for absurdist humour.

 

The burden of proof is as I showed ajb for science to back up the claim that mathematics and probability can't be combined in light of just stating the question that Bayes might fit, seeing that the proof of Gobel et al left this out.

 

In effect I / anyone only has to say to Gobel/ ajb: Oy mate, does your proof include Bayes? Yes? How then? You didn't show it yet do claim it.

 

I showed in #74 that no goalpost is moved. It shows this in reference to the formula in #63. Just stating Woekee doesn't suffice, stating a formula that doesn't fit does.

 

You et all only have to come up with one, just one thing that doesn't fit that formula to disprove my claim, yet I have to prove infinity in your opinion. That is the world upside down.

 

And indeed as ajb so aptly put it some say that all proofs are trivial. Well so then this one. But given Bayes the opposite is then also true for all proofs: they are all fundamentally important.

 

This one the more so because it is this simple algorithm in all our brains that is probably at the heart of all our thought processing. And again there is much more to Bayes that you lot seem to miss.

Edited December 6, 2013 by kristalris

[swansont]

Woekee is Star Wars actually and used the way ajb did more Monty Python than South Park the later owing tribute to the former for absurdist humour.

 

 

The reference is South Park

http://en.wikipedia.org/wiki/Chewbacca_defense

 

This just follows the pattern of never admitting the possibility that you are wrong, and all the more reason to just ignore this.

[kristalris]

The reference is South Park

http://en.wikipedia.org/wiki/Chewbacca_defense

 

This just follows the pattern of never admitting the possibility that you are wrong, and all the more reason to just ignore this.

 

Oh the pattern of - never - admitting the possibility of being wrong? well mate I've done even better than that admitted to being wrong to you on at least two counts in my very first thread on this site. The first time was if I recollect about GPS and the second time that GR had photons exerting gravity. So that is untrue.

 

Secondly I didn't say that South Park didn't have a Woekiee because I'd of course found the link you are giving. Yet you haven't found the further link within that link when you click to Woekiee. You get Star Wars. The form of humour is absurditic in South Park. Anyway I'll grant you that this is probably what ajb meant with his Woekiee.

 

I'm having problems getting the link to a red herring fallacy that you imply / state I make. How the hell can I do that when showing that the Bayes formula can hold for instance Pythagoras's proof where you lot say it can't be a red herring? The only last stand you have is stating that it is trivial. I've yet to further counter that, but first things first: you lot admitting that this indeed is your last stand.

 

The goalpost & red herring position is you lot not admitting that you are wrong. You have to state first that Pythagoras' proof doesn't in anyway fit Bayes and also that I haven't shown that it does in the way I did it. Which amounts to a slight formality of copy pasting it. From the start I've stated that Bayes can take it all in excluding nothing. The goal post was infinite to begin and still is infinite. No movement of the goalpost then. Well I still say that and have shown that what you thought didn't fit i.e. Pythagoras does fit. That proves you wrong. Because that is the proverbial black swan in your only white swan position.

 

The thing you et al are doing is trying to needlessly complicate the issue. In effect what South Park is about as well.

 

Or don't you lot know what a probatio diabolica is, and that it is un scientific as norm in this thread?

Edited December 6, 2013 by kristalris

[swansont]

 

Oh the pattern of - never - admitting the possibility of being wrong? well mate I've done even better than that admitted to being wrong to you on at least two counts in my very first thread on this site. The first time was if I recollect about GPS and the second time that GR had photons exerting gravity. So that is untrue.

 

Secondly I didn't say that South Park didn't have a Woekiee because I'd of course found the link you are giving. Yet you haven't found the further link within that link when you click to Woekiee. You get Star Wars. The form of humour is absurditic in South Park. Anyway I'll grant you that this is probably what ajb meant with his Woekiee.

 

I'm having problems getting the link to a red herring fallacy that you imply / state I make. How the hell can I do that when showing that the Bayes formula can hold for instance Pythagoras's proof where you lot say it can't be a red herring? The only last stand you have is stating that it is trivial. I've yet to further counter that, but first things first: you lot admitting that this indeed is your last stand.

 

The goalpost & red herring position is you lot not admitting that you are wrong. You have to state first that Pythagoras' proof doesn't in anyway fit Bayes and also that I haven't shown that it does in the way I did it. Which amounts to a slight formality of copy pasting it. From the start I've stated that Bayes can take it all in excluding nothing. The goal post was infinite to begin and still is infinite. No movement of the goalpost then. Well I still say that and have shown that what you thought didn't fit i.e. Pythagoras does fit. That proves you wrong. Because that is the proverbial black swan in your only white swan position.

 

The thing you et al are doing is trying to needlessly complicate the issue. In effect what South Park is about as well.

 

Or don't you lot know what a probatio diabolica is, and that it is un scientific as norm in this thread?

 

I never accused you of a red herring.

 

The goalpost moving is because you are completely mischaracterizing the objections people have made. You claim that you can derive all of mathematics from Bayes, but then focus on if "Pythagoras' proof doesn't in anyway fit Bayes". The two claims are not equivalent. You can't validly substitute one for the other. The fact remains that you did not derive the Pythagorean theorem from Bayes. Your subsequent claims of success are because you changed what "success" was to being able to apply Bayes in some way that involved Pythagoras, something that was never in question.

[ajb]

Now you are indeed posing argument.

I have mentioned this in earlier posts.

 

Nowhere in the proofs I found do I see Bayes come into the picture. You mathematicians clearly forgot Bayes.

Why would you expect see Bayes' in a general mathematical proof?

 

Because you can't burden me with a probation diabolica of asking me to prove that all mathematics fits Bayes.

But that is your claim and thus it is up to you to provide evidence of this.

 

You only have to provide one (you tried and failed with Pythagoras) that doesn't fit Bayes to disprove.

Right, if I can show that there is no way you can prove a given statement using just Bayes' inference then I would have clearly disproved your claim. I have no idea how to clearly show that this is impossible. Maybe someone with a good grounding in foundational issues could point to a simpler example.

 

But again it is your claim and you have provided us with no supporting evidence at all. More than this, your claims go against what I would consider "common knowledge". Details need to be chased up with someone with a good grounding in foundational mathematics.

 

And then I cannot see where you proved Pythagoras' theorem using just Bayes'.

 

 

 

The burden of proof is as I showed ajb for science to back up the claim that mathematics and probability can't be combined in light of just stating the question that Bayes might fit, seeing that the proof of Gobel et al left this out.

But we are not making such unfounded claims!

 

Without a proof of your claim we cannot trust any consequences of this claim. It is that simple.

 

I showed in #74 that no goalpost is moved. It shows this in reference to the formula in #63.

Okay, you stick to the claim that all mathematics can be reduced to Bayes' inference. But prove it!

 

You et all only have to come up with one, just one thing that doesn't fit that formula to disprove my claim, yet I have to prove infinity in your opinion. That is the world upside down.

Just show us one clear example that is not obviously linked to probability theory or basic logic.

 

 

And indeed as ajb so aptly put it some say that all proofs are trivial. Well so then this one. But given Bayes the opposite is then also true for all proofs: they are all fundamentally important.

All theorems are trivial once the proof has been found. (Not my words!)

 

 

And again there is much more to Bayes that you lot seem to miss.

I am sure this is true, but irrelevant to your claims!

Your subsequent claims of success are because you changed what "success" was to being able to apply Bayes in some way that involved Pythagoras, something that was never in question. [/size][/font][/color]

Absolutely right.

 

I am happy that in principal given a pile of attempts at a proof by well-versed mathematicians of any statement known to be true (within the bounds of what that means), that it is likely that at least one of the well-versed mathematicians has produced a "true" proof.

 

Now what about statements we just don't know are true or even those we cannot prove in light of Godel?

[kristalris]

Swansont,

 

Sorry but the quote box system keeps on acting more and more weird.

 

Okay then with Woekiee only ajb implied / stated a red hearing because that is what the Wikipedia link refers to in the context of South Park.

 

Now then deriving Pythagoras's proof out of Bayes and visa versa is the case when you can merge both formulas and get from one to the other. Without using incorrect mathematics. Well, if you use the formula of Bayes in the form given by me in #63 and put the mathematical proof of Pythagoras in A and an incorrect proof thereof in B you have derived Pythagoras out of Bayes and Bayes out of Pythagoras. Deriving means that you mathematically can get there without using any shortcuts or logical inconsistencies. Well then that is the case. It is not historical one way street but a systematic two way street.

 

Further more it is then evident that this same trick (Bayes is in fact a cleaver mathematical trick in the first place) can be used in an infinite amount of cases. For you like the attempt with Pythagoras by one of you to disprove. Because otherwise I'd have to also come up with all future mathematics. That would be idiotic. If you lot are right it should be easy to come up with some truth, logic or mathematics that doesn't fit formula #63.

 

So no, I didn't in no way change what I claimed or changed what others poised that Bayes couldn't do. I didn't come up with Pythagoras one of you lot did.

 

Oh and BTW the trick won't work for empirical statistics like it does with Bayes.

 

So that in effect leaves you only one objection as far as I can see namely your first objection and that is that this is trivial. Well then state that this is indeed the case and then I'll prove to you that it isn't trivial at all.

Edited December 6, 2013 by kristalris

[swansont]

Swansont,

 

Sorry but the quote box system keeps on acting more and more weird.

 

Okay then with Woekiee only ajb implied / stated a red hearing because that is what the Wikipedia link refers to in the context of South Park.

The more direct interpretation is "I am going to confuse you in an attempt to get you to agree with me." Which is related to the adage "if you can't dazzle them with brilliance, baffle them with bullsh**" But the tactic only works on people who lack familiarity with the topic.

 

 

Now then deriving Pythagoras's proof out of Bayes and visa versa is the case when you can merge both formulas and get from one to the other. Without using incorrect mathematics. Well, if you use the formula of Bayes in the form given by me in #63 and put the mathematical proof of Pythagoras in A and an incorrect proof thereof in B you have derived Pythagoras out of Bayes and Bayes out of Pythagoras. Deriving means that you mathematically can get there without using any shortcuts or logical inconsistencies. Well then that is the case. It is not historical one way street but a systematic two way street.

"If you start with Pythagoras, you can confirm it is correct" is not what is meant by "proof" or "derivation" in mathematics. Perhaps that is the crux of the problem. There is terminology that has a specific meaning, but you are using different definitions of those words. If that's the case, you literally don't understand what you are actually saying.

 

 

In math, the proof would go along the lines of : start with some axioms and/or other statements we know to be true based on them. They end with showing that c² = a² + b² Many such proofs exist. I doubt any invoke Bayes.

 

 

[kristalris]

Swansont & ajb,

 

After some googling I've found several links for axioms involved for the Bayes theorem and proofs thereof. I can't get links posted for an odd reason.

 

The same of course applies for Pythagoras.

 

So simply start with all involved axioms of both involved start with either Pythagoras or Bayes axioms and prove that and subsequently start with the other axioms and you prove that they are consistent providing you do it the way I showed you concerning Bayes. I.e. assuming absolute 100% probability. Bayes in fact swallows - and contrary to any other mathematical formula - will remain consistent with any other truth, mathematics, or logic.

 

Oh and BTW You don't have to fill in anything in B of the #63 Bayes formula like I stated earlier (you may of course). Bayes answers that for you providing the exact opposite.

 

Now that proves that Bayes and Pythagoras can be derived from the same set of axioms.

 

Lets say that is n1.

 

Now just take any other mathematics/ logic/ truth you think won't fit as n2.

 

How far must I go n33? Or n654? Because Bayes can swallow anything you like that you believe to be correct derived from any set of axioms. It will say that that thus is absolutely correct and the opposite in B absolutely incorrect. (As with all mathematics whether the outcome of Bayes is correct or not depends on the garbage or non-garbage you put into the formula)

 

You can't do the same with say empirical statistics and Pythagoras. The reason is that any statistical formula other than Bayes will have to divide by zero. In that sense Goble is thus correct. He simply forgot to look at the fact that Bayes can also handle absolutes.

 

For Bayes he's incorrect.

[ajb]

After some googling I've found several links for axioms involved for the Bayes theorem and proofs thereof. I can't get links posted for an odd reason.

No problem, we all believe that Bayes' theorem is correct and it can be derived as a consequence of conditional probability. I once had to prove Bayes' theorem as part of a job interview, so I have seen a proof.

 

The same of course applies for Pythagoras.

Okay, so we also believe that Pythagoras' theorem is true and that proofs can be constructed.

 

(Did you claim earlier that it was untrue? I think you did.)

 

Now that proves that Bayes and Pythagoras can be derived from the same set of axioms.

No, you have really just claimed that here.

 

It is true?

 

The Euclidean axioms are equivalent to the Kolmogorov axioms (which via Cox's theorem links it back to logic)?

 

In that sense Goble is thus correct.

The work of Godel and others is to do with what is an axiom, are they "evidently true", do we have to accept something as an axiom, can all true statements within an axiomatic system be proved within that axiomatic system, can all mathematics be reduced to logic... and so on.

 

Foundational stuff.

[kristalris]

No problem, we all believe that Bayes' theorem is correct and it can be derived as a consequence of conditional probability. I once had to prove Bayes' theorem as part of a job interview, so I have seen a proof.

 

 

Okay, so we also believe that Pythagoras' theorem is true and that proofs can be constructed.

 

(Did you claim earlier that it was untrue? I think you did.)

 

 

 

I only claimed it was untrue when you take it outside its absolute theoretical setting in the real world. Bayes (then (as normally done with Bayes) only assuming that the absolute truth can be approximated yet take it there and then show that it probably won't work in extremely large or extremely small scales. Pythagoras then also becomes more or less an approximation.

No, you have really just claimed that here.

 

It is true?

 

The Euclidean axioms are equivalent to the Kolmogorov axioms (which via Cox's theorem links it back to logic)?

The latter I don't quite know, yet you start of with all axioms for both Bayes and Pythagoras. You do both proofs and with #63 formula of Bayes you introduce the assumption that A is 100% true and B is 100% untrue, and you put the then proven formula in A because it's true (you just proved it). You are allowed in proofs to combine proofs given the same axioms. You've thus derived a fully functional formula whereby Bayes effectively holds the formula of Pythagoras to be absolutely true. Which it is.

The work of Godel and others is to do with what is an axiom, are they "evidently true", do we have to accept something as an axiom, can all true statements within an axiomatic system be proved within that axiomatic system, can all mathematics be reduced to logic... and so on.

 

Foundational stuff.

You can simply use Bayes for all that.

 

Now let me then show why this is not trivial:

 

There is no reason whatsoever to assume that this trick with the proof of Pythagoras won't work with any other proof you choose. Because if it is proven it always must per definition fit A in the formula #63.

 

This now is indeed fundamental:

 

#63 formula is the alpha formula of all science and a full blown Bayes formula also the omega formula of all science, it can do everything yet mostly even not as economical as other methodes, yet then having many forms.

 

The thing is you can add on to the #63 formula.

 

Take the lex parsimonious: (Actually part of) that goes in B. Because A wants to find the infinite truth and wants to gallop of to infinity, it is B that reigns it in. As much truth as need be on the stated goal(s) yet B: as short / economical as possible. It is Yin and Yang built in from the start. Yin and Yang that we see in all of nature, but also as the logic / mathematical true vs untrue.

 

So the formula itself shows the way how to grow: you need a goal or goals, you need a probandum and norm you prior odds your LR's and you will get your answer in the posterior to any question.

 

You can have short cuts or make it as subtle and elaborate as you like.

 

It can even handle errors in A. Say you / science absolutely believes the world is flat and that this is thus the best way to navigate the Atlantic. Bayes will say well if that is true then you indeed should navigate that way, but beware if it is not true you should not.

 

Look on the formula of #63 as the stem of a tree with roots. All of science can go through that stem. be it the small stem of ³63 or a large many different stems that Bayes can produce. Bayes can show you all possible and probable routes that can follow.

 

The formula #63 is probably in all our brains doing all analytic jobs before we even become aware of it. This because it is inherently compatible with everything held to be true or un-true.

 

I'd say that is not trivial, yet in the same Bayesian way it is trivial at the same time, as Bayes shows you.

 

It even shows you when not to use the mathematics of Bayes but via the Lex parsimonious we should use verbal logic instead.

 

So

 

Bayes can handle everything and place it like I showed with Pythagoras place it in the right even infinite if you need to context and compare if it fits.

 

If it ain't Bayes, it ain't science.

 

Again there is much, and much more to Bayes. Dangers as well BTW. (The latter is also Bayes BTW)

Edited December 7, 2013 by kristalris

[ajb]

The latter I don't quite know...

So despite not knowing much foundational mathematics you have made some huge claims about foundational mathematics, now including that Bayes' can help you decide what axioms are required in mathematics?

 

You are in over your head on this one.

 

As to your much better claim that "If it ain't Bayes, it ain't science", that is okay as a motto. We are happy that you can use Bayes' inference to formularise the scientific method. But your claims go well beyond that.

[kristalris]

ajb

 

The quote box is a problem and the cookie monster is on the prowl again in some guise or other.

 

Anyway, over my head or not, the chosen axioms of Bayes & say Pythagoras (or any other axioms of proofs) are either consistent or not. If they are consistent then there can be no problem. A truth is always dependent on the chosen norm. Bayes can handle al norms even the absolute one. If the axioms are inconsistent then at worst - given the correctness of Bayes - you've chosen something true that isn't. That happens in science given a paradigm, it is inherent otherwise we would be all-knowing Gods. I'm not, are you? Or do you know such Gods?

 

So the only thing for it is to check whether or not the axioms of Bayes are compatible with whatever axioms of products of proofs to be put in A of #63 formula.

 

Now what formula is capable of checking whether something is absolutely or relatively consistent with anything else? Indeed Bayes. It is valid from short cut common sense, empirical statistics to deterministic reasoning. It can deal with any chosen small domain to infinity. And if an inconsistency for any current or future axiom is found that is inconsistent then that poses a problem to be solved. So what then can your problem be? Being over your head as I am for not being a God?

[Popcorn Sutton]

The problem with Bayes is that if you automate the equation and use it to detect plausible inference, there is only one way you can detect the best answer, and the only way to do that is to question the algorithm every time it receives a new input. This would only work if the question was remembered only once or less because obviously if you question a person the same thing over and over, they will say a different phrase eventually.

 

In my experience, a lot of actual humans have experiemented with this one. But why? Why? Why? Why? Why? Why?

 

It's the only question word that I know of that can continually be answered. Indefinitely.

 

But if you automate both the algorithm and the questioning of the algorithm, you can only hope that a human receives the answer because the actual chance of hearing the right answer at any given point is 1 over 7000000000000. 1/700000000000 approximately. The chance of any given person to reply at any given second is at a guess 100,000 in one second (whatever it may be). One person can only read one message every 10 minutes at most, and make inferences of their own at approximately 15-45 minutes before they conclude on the subject. I can do the math but it's going to take a minute.

It's still going to take a while to evolve.

1/7000000000 people. 7000000000/ 52.1 / 7 / 24 / 60 / 10 - 45 / 7000000000.

 

7 billion people divided by 52.1 weeks in a year. That divided by 7 days in a week divided by 24 hours in a day divided by 10 to 45 minutes spent on inference divided by 7 billion people means that our chance of finding the quickest path of evolution is .00008% chance of one person finding the most likely answer in a single year on the best average.

Edited December 8, 2013 by Popcorn Sutton

[ajb]

So what then can your problem be?

I think many times people have told you about the problems, but you don't seem to care. You have stated that you don't know much about mathematics, which is fine, but please stop just soapboxing and try to learn something. Otherwise I have to question why you bother posting on this site at all?

[kristalris]

I think many times people have told you about the problems, but you don't seem to care. You have stated that you don't know much about mathematics, which is fine, but please stop just soapboxing and try to learn something. Otherwise I have to question why you bother posting on this site at all?

Sorry, but I've some drawings I made in order to give a proper reaction. Yet a drawing of A4 size is evidently too large. And I have two. Still working on the problem.

Edited January 3, 2014 by kristalris