The Bayesian Machine

[kristalris]

The philosophy of science is based on the scientific method. This is really a basic guide as we may need a little room in practice and the standards of evidence differ in different branches of science.

 

The question here must be "is Bayes' inference equivalent to the scientific method?"

 

I know that people like to interpret the scientific method in light of Bayes' inference, but I don't think we have a direct equivalence here. One point must be the fact that the scientific method is not a strict mathematical statement, Bayes' theorem is.

 

This is not to take away the fact that Bayes' is useful in science, but it is not the first or final word on science.

 

Based on our previous discussion, I don't think you are in much of a poistion to judge the typical education of undergraduate physicists.

Well, yes and no. Bayes is to be seen as the first word of science, the second word is Occam. If what follows in science doesn't fit this - sufficiently - then one can indeed say that what is presented is not science or best scientific practise. I do agree with you in part, because that too is Bayes; namely that there is latitude to be given. This because being too strict concerning something where you know that you don't exactly know what the exact science is, requires this. Yet again it is then Bayes & Occam that only provide this latitude in the form of use of verbal logic, because normal language is nice and woolly.

 

Because having any scientific method in any field that is strict all across the board, for instance demanding the exclusive use of mathematics concerning issues where you know you don't know the exact science is a contradiction. A contradiction Bayes doesn't allow for because then you are inherently claiming more than anyone can deliver and thus no-one may demand. Neither does Bayes via Occam allow anyone in science to use too difficult methods such as mathematics at least forbids demanding the use thereof in issues that can be and thus should be dealt with via the simplest method or tool available. I.e. normal language. Thus even in physics concerning issues where you know that you don't know all the relevant questions that Bayes forces you to address, should these questions if need be by guessing have been answered, prior to claiming correct / best scientific method.

 

Not complying to this is per definition thus pseudo scientific.

 

The ultimate irony is thus that it is the demanded mathematics in physics is provided by Bayes because that is mathematics the physicists demand, yet it forces them into verbal logic and answering questions their dogma prohibits on specific questions. Finally adhering to Bayes & Occam would speed up the furtherance of science enormously.

Edited November 28, 2013 by kristalris

[swansont]

Well, yes and no. Bayes is to be seen as the first word of science, the second word is Occam. If what follows in science doesn't fit this - sufficiently - then one can indeed say that what is presented is not science or best scientific practise.

 

Bollocks.

 

Occam is a guideline, not an unbreakable rule. Even the statement of it — that the simplest explanation is usually the right one — tells you that it does not universally hold.

 

Also it is a much stronger statement to claim that Bayes is always useful than to say that it can always be applied. A system where the probability is low and yet occurs anyway isn't a particularly useful application.

[kristalris]

 

Bollocks.

 

Occam is a guideline, not an unbreakable rule. Even the statement of it — that the simplest explanation is usually the right one — tells you that it does not universally hold.

 

Also it is a much stronger statement to claim that Bayes is always useful than to say that it can always be applied. A system where the probability is low and yet occurs anyway isn't a particularly useful application.

 

I don't quite know why I can't get rid of the bold lettering but anyway. I just apologized for not doing as the Romans do on this Forum Romanum, and now I get treated by the senator of the site on a Freudian Bollocks. Well then senator you are in for a spanking:

 

Empirical[edit]

Occam's razor has gained strong empirical support as far as helping to converge on better theories (see "Applications" section below for some examples).

In the related concept of overfitting, excessively complex models are affected by statistical noise (a problem also known as the bias-variance trade-off), whereas simpler models may capture the underlying structure better and may thus have better predictive performance. It is, however, often difficult to deduce which part of the data is noise (cf. model selection, test set, minimum description

length, Bayesian inference, etc.).

 

 

Now I know you love empirical. Care to edit the Wikipedia on Occam? Think you should or withdraw your bollocks.

Occam is thus a very very widely held empirically based guideline, for probability, yet also a basic rule of science namely lex parsimoniae. Lex means law BTW in the Forum Romanum of Science mate. I know that there are quite a few physicists that think like lawyers and try to (unnecessarily) complicate the issue. Is that what you mean with bollocks BTW, no mate, not unbreakable? What do you mean then not unbreakable? Example please, for you are then in for a further spanking.

Further more you clearly need to reread what I've explained on Bayes and the proper use thereof for you still don't get it even after simple explanation. If you can use empirical statistics because Occam sais so then Bayes sais you should, as I've pointed out several times.

Bayes & Occam are probably wondering if the bollocks hurt now?

Edited November 29, 2013 by hypervalent_iodine
got rid of the bold font type

[Popcorn Sutton]

Can someone give an example of the mathematical process of Bayesian inference? I'm a strong supporter of it but I haven't taken an actual mathematics class that makes use of the equation. Can someone clarify the process step by step? I'll provide an example in computational linguistics lingo if someone can do me this favor.

[ajb]

Occam is a guideline, not an unbreakable rule. Even the statement of it — that the simplest explanation is usually the right one — tells you that it does not universally hold.

Also, how do we define simplest?

Well, yes and no. Bayes is to be seen as the first word of science, the second word is Occam.

But again, I don't see that it is true that Bayes is equivalent to the scientific method; people like to interpret the scientific method in this light but I don't think anyone has properly shown that they are completely equivalent.

 

And then Occam is a general useful guideline, as is the scientific method really.

 

The problem with Occam is first how to define "simplest" and then how do we deal with theories that are mathematically different but show exactly the same phenomenology to the same degree of accuracy? Which one is best?

[kristalris]

Well one shouldn’t mix up bollocks with buttocks like I seem to have done, in my Double Dutch way, because it can be a very painful mistake, complicating matters. Because both Bayes and Occam are thus infringed I have to say I’m sorry.

 

The simplest explanation is per definition the shortest one. That is simply easy. The problem lies in the Yin and Yang of Bayes and Occam.

 

The Bayesian machine is a cutting Razor that runs on high octane Occam gas.

 

Occam in its simplest form is the algorithm keep it as short as possible. => the law to strive towards this & (what swansont clearly only thought: the probability that the hypothesis with the least assumptions is probably best.

 

Putting this in the Bayes machine that covers everything OR any limited issue if you so choose. But then a full blown Bayes will require you to address or assume where the boundaries are of the limitation. Assuming thus that what is outside those chosen boundaries is irrelevant to the issue you ask Bayes to solve, will make it fit Bayes again.

 

Ergo both GR & QM in their respective fields are the simplest ways of explaining at the most accurate way currently possible all that the assumed scope of GR & QM can be assumed to cover. Because GR is in conflict with QM in their respective fields you may not assume that both are valid all over the infinite universe as an estimate using fewest assumptions. (said in short hand).

 

If you accept that Bayes covers it all and accept Occam in this context then you’ve not only got your equivalence but even surpassed it. Bayes also covers the bit you assumed irrelevant, and makes you state that.

 

For the scientific method to be chosen Bayes and Occam dictate you strive to the simplest way (= Occam) dealing with the integral problem (=Bayes). Ergo the shortest quickest way doing that. Otherwise it can’t be made to fit these two fundamental mathematical algorithms of science.

 

To answer your question which mathematical system is best: If both are equal then neither is best.

 

Furthermore a serious misunderstanding of Bayes in science is the “best practice” dogma. Correct Bayes & Occam does nothing of the sort. Take DSM V as best practice. Doing that infringes on Bayes and Occam. If you know that you don’t know what it is to a sufficient degree (which is the case on diagnosing mental illnesses) then one should expect several “best practices” adjunct to each other. Only when you have sufficient data that you can prove that you outrun the best experienced guessers in the business, all across the appropriate board may you claim best practice in that sense.

 

In short Bayes & Occam tell you when to use your common sense and when not to in the sense that that then is also common sense to use complicate mathematics.

 

Ergo Bayes & Occam are the alpha and omega of science. It covers it from its smallest simplest short cut method to the all-encompassing full blown mathematical analysis of everything or anything. It even deals with the problem when not to use Bayes (because full blown Bayes is extremely complicated.)

 

Again current neurology even finds probable that even a mathematician doing non-statistical mathematics first guesses intuitively unwittingly via the Bayes in the brain algorithm what to do and then doing it.

 

Too many current scientific methods are too complicated, proof: they can be cut down too their essence by razor deleting the humbug.

“If it ain’t Bayes & Occam it ain’t science” is thus the better adagium. Proving even I’m still learning Bayes. Always also include Occam. Otherwise its Yin without Yang.

 

Also, how do we define simplest?

But again, I don't see that it is true that Bayes is equivalent to the scientific method; people like to interpret the scientific method in this light but I don't think anyone has properly shown that they are completely equivalent.

And then Occam is a general useful guideline, as is the scientific method really.

The problem with Occam is first how to define "simplest" and then how do we deal with theories that are mathematically different but show exactly the same phenomenology to the same degree of accuracy? Which one is best?

Edit: I seem to have had yet again a problem with the quote box for I thought I posted it underneath. I'm in part a digibeet yet fiercely proud of that. Though it does tend to give the John Cleese moments of man against the system. Last one I shouted at the bloody machine only to discover that it shouted back because I unwittingly was also recording what I was shouting. Great fun.

 

Now just to put another important point to the Bayes razor machine it is of course the goal: the ultimate truth. => You must be honest.

 

Ultimate truth via Bayes and Occam implies that it isn't magic because the Bayes machine runs on logic. Yet it even can deal with the extremely improbability of it all being magic as well.

 

Ergo if we as a thought experiment see it as the scientific radar observing there is a dark side under the radar due to the curvature of the earth. Any plane (idea) that is based on magic like Krauss et all is more than a trillion to the trillionth miles away, any God more than a trillion and any integral idea that is simple and consistent with it all and testable concurs with Occam and Bayes with whatever tool has been used and is thus to be assumed the closest to the goal and thus scientifically most valid.

 

Any scientific dogma that is based on ignoring part of the issue is not compatible with Bayes but only with Occam. So then you're out. Disqualified on the game of science but the mathematics of Bayes and the algorithm of Occam (asap)on the stated goal: the ultimate truth.

 

This is NOT a democratic principle. It is the dictatorship of Bayes and Occam on the stated goal.

 

Yet Bayes and Occam also show you why It is that democratic science believes that rigid systems like DSM V become more and more the winning best practise even though it is evidently wrong. The way in which the Bayes in the brain is distributed by MN / God as probably DNA in the population in order to have this population the best chance of surviving. The Big Five as simple model shines through in all cultures. In the highest level of quick thinkers you have but a few of the best Bayes guessers who keep it simple as best leaders in R&D breaking the rules; a lot of production leaders abiding by the authoritive rules for production guessing that that is best and thinking it isn't a guess, and a few emotionally intelligent sales men and woman. In an open culture many production minded persons dare to be creative. In an authoritive culture only the open minded emotionally dare to oppose. Only rationally putting the brake on.

 

Only when everybody is honest about oneself and the strong and weak points by working together does the pareto optimum become possible. Say the collective algorithm / goal of having a long as possible happy life, with the least possible infringement to others. Seeing us as DNA driven robots with a Yin deterministic and Yang dice of chance "free will". Given this and the DNA division I can build you the entire legal system. And describe proven to work well societies. Such as successful R&D driven companies such as Apple Inc. And also why it is that in this internet age the emotionally intelligent leader will more and more become the boss. (The actor / salesman / great communicator.) No problem when advice is given from R&D what is to be taken in or out f production. On the long run or short run in a crises a bloody disaster, when that is not dealt with, by getting the team to conform the Bayes / Occam machine. (BTW whether it is ultimately nature or nurture is immaterial given the Big Five.)

 

The Bayes in the brain machine (by MN/ God) creates the illusion of being broad minded due to the great volume of current science. Knowing a lot doesn't imply being open minded and thus a good Bayesian guesser. R&D needs to pass a new paradigm to sales in order to get it into production in time. The problem is that our current society changes faster than our social Bayes in the brain DNA limitations allow for to quickly accommodate.

 

BTW the proof that we humans are good Bayesian machine guessers is that we haven't gone extinct yet. Yet we might still go extinct, if we don't get this in order.

 

When R&D types are out of the loop the Bayes machine in our brains will go into an ever more ISO 2000 quality system like DSM V. Simple statistics.

Edited November 29, 2013 by kristalris

[ajb]

The simplest explanation is per definition the shortest one. That is simply easy.

It cannot be that simple.

 

Shortest is not so well defined in this context. For example, one may be able to understand some aspect of nature in some very complicated mathematical framework, but if you know this framework then the explanation of some phenomena could be a very short calculation (with lots of maths already assumed).

 

In contrast, you could have a more simplistic set-up but the calculations could be horrendous.

 

Occam razor cannot tell you which theory is best; it may even by a matter of taste at some level!

 

Occam in its simplest form is the algorithm keep it as short as possible.

As above, this is not necessarily well defined.

 

Ergo both GR & QM in their respective fields are the simplest ways of explaining at the most accurate way currently possible all that the assumed scope of GR & QM can be assumed to cover.

Unless we only need to understand things to an accuracy sufficient for classical mechanics and Newtonian gravity to be applied!

 

Also, do we really know that they are the "simplest" ways of explaining these phenomena? They are for sure the best descriptions we currently have, but that does not mean that it is not possible to find other explanations. Occam's razor does not tell us anything about QM or GR being the only or best way to describe nature. They are however, the simplest in the sense that we have minimized the inputs as far as we know how to and still agree well with nature.

 

Because GR is in conflict with QM in their respective fields you may not assume that both are valid all over the infinite universe as an estimate using fewest assumptions. (said in short hand).

Okay, everyone agrees that the standard model of particle physics and general relativity cannot (or should not at least) be the final words on the fundamental nature of our Universe.

 

 

If you accept that Bayes covers it all...

This I don't understand.

 

 

 

In short Bayes & Occam tell you when to use your common sense and when not to in the sense that that then is also common sense to use complicate mathematics.

Common sense is not enough in science or mathematics.

 

Ergo Bayes & Occam are the alpha and omega of science.

You have not convinced me of this, only that they can be useful tools.

Edited November 29, 2013 by ajb

[Popcorn Sutton]

Lucky for you guys, I know how to define the boundaries

Take this example (in its simplicity).

 

Evidence = ['my name is popcorn sutton']

Hypothesis = 'your name is popcorn'

Add hypothesis to evidence and you get -

 

['your name is popcorn', 'my name is popcorn sutton']

 

There are two ways to define the boundaries, one is this-

 

If the probability of 'n' given 'popcor' > .5 then add 'n' (= 'popcorn')

 

Or

 

If hypothesis = 'your name is popcornmy name is popcorn sutton' then if 'your name is popcorn' + 'my name is popcorn sutton' is in evidence, then the hypothesis equals 'your name is popcornmy name is popcorn sutton'

 

I prefer the prior because it disregards spelling errors.

[kristalris]

It cannot be that simple.

 

Shortest is not so well defined in this context. For example, one may be able to understand some aspect of nature in some very complicated mathematical framework, but if you know this framework then the explanation of some phenomena could be a very short calculation (with lots of maths already assumed).

 

In contrast, you could have a more simplistic set-up but the calculations could be horrendous.

 

Occam razor cannot tell you which theory is best; it may even by a matter of taste at some level!

 

 

As above, this is not necessarily well defined.

 

 

Unless we only need to understand things to an accuracy sufficient for classical mechanics and Newtonian gravity to be applied!

 

Also, do we really know that they are the "simplest" ways of explaining these phenomena? They are for sure the best descriptions we currently have, but that does not mean that it is not possible to find other explanations. Occam's razor does not tell us anything about QM or GR being the only or best way to describe nature. They are however, the simplest in the sense that we have minimized the inputs as far as we know how to and still agree well with nature.

 

 

Okay, everyone agrees that the standard model of particle physics and general relativity cannot (or should not at least) be the final words on the fundamental nature of our Universe.

 

 

 

This I don't understand.

 

 

 

 

Common sense is not enough in science or mathematics.

 

 

You have not convinced me of this, only that they can be useful tools.

Now it can be that simple. The error in your thinking lies in the idea of a "best practise" at least in the idea that that is always something that can be mathematically shown to be that.

 

When you know that you have too little data you can't claim that. (Bayes dixit) So then you are left with several possible scientifically valid "best practises" from which you indeed may choose indeed conforming to your taste. Bayes and Occam let you do that intuitively as long as you honestly state that that is what you've done and as long as you haven't skipped already present observations that are already present in science especially when these contradict. That is why it is called - intuitive statistics - remember? You may / are forced to guess in order to get an integral picture. Bayes and Occam will simply say: one of these three methods is probably best and there is at this moment no way to distinguish between them: you may choose one or all if you like.

 

You whish to place R&D of science in a box. Yet Bayes doesn't know why you want to do that? The whole of Science isn't in a box, only the knowledge part of it, the research part is per definition out of the box.

 

Bayes and Occam show (mathematically if need be) that you have your expectations and thus put your norms to high all across the board.

 

The reason is probably that you don't accept the fact that there are far above average good guessers in the game of human nature. Who only need these simple starting points to get the show of science going. Compare it to a fractal. Simple beginning spinning into a complex system.

 

I can't give you a full Bayesian mathematical proof myself, but it is evident that it is possible to do so.

 

Now you show me one example of a scientific problem even in pure mathematics that Bayes and Occam can't solve. Then I'll put that forward to a real statistician and see if he agrees. Ok? Mind you that Bayes and Occam might solve that problem by stating: use empirical statistics. This because although a full blown! Bayes will render - exactly - the same result Occam will rule out Bayes for being to bloody complicated in comparison. So Bayes and Occam can claim to cover the results achieved by empirical statistics in being simple by ruling out themselves. Empirical statistics can't do it the other way round. It can only say: don't use me for this problem.

Edited November 29, 2013 by kristalris

[ajb]

Now you show me one example of a scientific problem even in pure mathematics that Bayes and Occam can't solve.

The ground state energy of the hydrogen atom.

 

Bayes and Occam cannot solve that. What you can do is go away and measure the ground state energy of the hydrogen atom and see it is agrees with the models you use. From there you could use Bayes and Occam to lower your confidence that a given model describes nature well. Though that is probably an overkill for this example unless maybe you have lots of models or families of models.

 

Lots of other mathematical and physical questions I could ask have little or nothing to do with Bayes.

 

Then I'll put that forward to a real statistician and see if he agrees. Ok? Mind you that Bayes and Occam might solve that problem by stating: use empirical statistics.

You are certainly free to ask you local friendly statistician to give you the ground state energy of the hydrogen atom. I doubt he will reach for Bayes' theorem!

[kristalris]

The ground state energy of the hydrogen atom.

 

Bayes and Occam cannot solve that. What you can do is go away and measure the ground state energy of the hydrogen atom and see it is agrees with the models you use. From there you could use Bayes and Occam to lower your confidence that a given model describes nature well. Though that is probably an overkill for this example unless maybe you have lots of models or families of models.

 

Lots of other mathematical and physical questions I could ask have little or nothing to do with Bayes.

 

 

You are certainly free to ask you local friendly statistician to give you the ground state energy of the hydrogen atom. I doubt he will reach for Bayes' theorem!

Is there any mathematical model that already can do this provide the ground state energy of the hydrogen atom?

 

If not then still Bayes and Occam can take a shot via guessing. And if there is, then certainly Bayes and Occam will point towards that same method. Indeed the friendly statistician will not reach for Bayes, but that is not the question then is it? The question is, can Bayes get then the same result. If so, it fits and proves you wrong.

 

If no other form of mathematics can solve the problem then why should Bayes not be allowed on this probandum to fail as well? Bayes BTW doesn't fail we do with the garbage guess having too little data.

[hoola]

I have just started to try to understand the bayes theorem, whatever the precise meaning....and thank you for an interesting thread, but the first cartoon image at the top of the thread is of two people wondering if the sun has exploded in the middle of the night......well, if it merely exploded that would seem to be unrecognizable for 8 minutes...but if it disappeared..."poof"... we would immediately know, as the speed of gravity in newton's equations require an instantaneous rate, thus, immediately the earth would fly off it's normal orbit .....as the gravity of an exploded sun wouldn't change much, but a disappeared sun's would, although the day side of the planet would continue to see the sun for a short while as we flew off towards deep space.....it seems an effect of this rapid release of gravitational force would be a radical change in the ocean's tides with tsunamis as a primary effect. I don't see yet as to where the rolling dice come into play....please explain ....edd

[kristalris]

I've been thinking how to explain Bayes further:

 

It ranges from n absolutely 0 via n1 to n plus or minus infinite at infinitely every point infinitely accurate or infinitely inaccurate in any chosen bandwidth of accuracy. Ergo it can describe anything or nothing.

 

Combined with Occam in a Yin and Yang with Bayes Occam maximum simple Bayes Integrally infinite striving to answer the question on ultimate truth being that God, magic or a fundamentally simple set of formulas and constants or whatever.

 

It can describe an infinite amount of relationships or any limited amount.

 

It ranges from common sense to the most complex mathematics conceivable. It catches all observations and makes it possible to fill in all that is perceived as missing via imaginative guesswork.

 

It is both descriptive and prescriptive minimum norm on what science is and what it can possibly be.

Edited November 29, 2013 by kristalris

[ajb]

Is there any mathematical model that already can do this provide the ground state energy of the hydrogen atom?

Yes, for example we have the Schrödinger equation with a 1/r potential. This does a good job as it is, but one can add corrections or look at the relativistic version known via the Dirac equation. This is well known and as you talk about TOEs I though you would have known this.

 

If not then still Bayes and Occam can take a shot via guessing. And if there is, then certainly Bayes and Occam will point towards that same method.

How?

 

Indeed the friendly statistician will not reach for Bayes, but that is not the question then is it? The question is, can Bayes get then the same result. If so, it fits and proves you wrong.

How can Bayes give us a model of the hydrogen atom?

 

At best I can see how it could be used to formulate the scientific principal and then be used to help us decide if we have confidence in a model.

 

If no other form of mathematics can solve the problem then why should Bayes not be allowed on this probandum to fail as well?

How would you even apply it?

 

Bayes BTW doesn't fail we do with the garbage guess having too little data.

Right, there are questions it just does not help us with.

 

It is both descriptive and prescriptive minimum norm on what science is and what it can possibly be.

It gives us a way of formalising the scientific method, that much is true.

 

From what I can gather there has been lots of developments in applying Bayes' theorem to model selection in particle physics and astrophysics. However, note this is in model selection, that is testing models against our observations and then each other, by itself Bayes' does not really help us construct these models in the first place.

 

References include

Roberto Trotta, Bayes in the sky: Bayesian inference and model selection in cosmology, Contemp.Phys.49:71-104,2008. arXiv:0803.4089 [astro-ph]

 

Louis Lyons, BAYES AND FREQUENTISM: A PARTICLE PHYSICIST'S PERSPECTIVE, to appear in Contemp.Phys. arXiv:1301.1273 [physics.data-an]

Edited November 29, 2013 by ajb

[kristalris]

Yes, for example we have the Schrödinger equation with a 1/r potential. This does a good job as it is, but one can add corrections or look at the relativistic version known via the Dirac equation. This is well known and as you talk about TOEs I though you would have known this.

EQ

 

I can't split the box so in red then: Yes I talk TOE and I solve Schrodinger via common sense verbal logic. That fits Bayes. I thought you knew that.

Suddenly the box split. This proves it's magic. Back to black then. (must of done something right that I can't replicate yet this digibeet will get there (possibly)

 

Anyway there is no mathematical formula that can't be described via Bayes. So this mathematics you take can be done via Bayes as well, only I'm near certain that it will be more cumbersome. So Occam rules out Bayes. Yet Bayes can describe it just as accurate or even more accurate. The opposite isn't true.

 

 

How?

(Now don't think I can do this again split the quote box at will, anyway:)

 

I'm puzzled where your problem is at? Bayes can describe anything mathematics can describe. So what is the problem? Mathematics is a tool. Don't expect the tool to build the building. You will have to do that yourself. Bayes sec will not solve Schrodinger (though I claim I have via Bayes using common sense = Bayes & Occam)

How can Bayes give us a model of the hydrogen atom?

(I think based on mounting testing of guesses that the trick is to click the left mouse and then enter. I.e. Bayes is getting me there.)

 

In exactly the same way as I'm finding out how to split the quote box. Just mucking around and guessing and testing.

At best I can see how it could be used to formulate the scientific principal and then be used to help us decide if we have confidence in a model.

You keep missing the point that Bayes points to non Bayes (that can be described by Bayes.) So any useful mathematics that you agree can be used can be replicated by Bayes. That doesn't mean you should use Bayes.

How would you even apply it?

Use the correct mathematics you need (= concurs with Bayes)

 

Right, there are questions it just does not help us with.

No there aren't. Any and all questions can be dealt with using common sense. That is Bayes. It can help you go from lower level to higher level.

 

You have no scientific logical basis to exclude these lower levels that Bayes allows for. And yes, that helps. It gets it going. It is first gear, second to third gear. Yet not fourth and higher gear (even though it can describe that if you like even though it's too much work) Current science only accepts overdrive and only slower and slower gets off the mark. That is illogical and impractical. Yet explainable: DNA and the distribution thereof / psychology. The lower gears need - probably the DNA / possibly only nurture - imagination. The higher gears need - the DNA / nurture - for hard conscientious work.

 

It gives us a way of formalising the scientific method, that much is true.

Yes, by razoring it down as well. It is not only descriptive but also prescriptive.

Edited November 29, 2013 by kristalris

[ajb]

Anyway there is no mathematical formula that can't be described via Bayes. So this mathematics you take can be done via Bayes as well, only I'm near certain that it will be more cumbersome.

 

Yet Bayes can describe it just as accurate or even more accurate.

 

Bayes can describe anything mathematics can describe.

 

So any useful mathematics that you agree can be used can be replicated by Bayes. That doesn't mean you should use Bayes.

Use the correct mathematics you need (= concurs with Bayes)

 

No there aren't. Any and all questions can be dealt with using common sense.

 

What is your claim here? All mathematics can be reduced to Bayes' theorem?

[kristalris]

What is your claim here? All mathematics can be reduced to Bayes' theorem?

Yes

 

Bayes can describe all logic.

 

mathematics is the a tool of logic.

 

=> Bayes can describe all mathematics

 

Bayes is mathematics => mathematics is the ultimate tool of all logic

 

Bayes is the mathematics of intuitive common sense set in language

 

=> mathematics doesn't exclude language as first gear of science concerning any probandum

Edited November 29, 2013 by kristalris

[ajb]

Bayes can describe all logic.

I don't know enough about formal or mathematical logic to refute that, but it sounds unlikley to me.

 

mathematics is the a tool of logic.

Okay, so mathematics is used in formal logic.

 

=> Bayes can describe all mathematics

But not all of mathematics can be reduced to logic.

 

Bayes is mathematics => mathematics is the ultimate tool of all logic

This I could agree with, but I am not well versed in logic.

[kristalris]

 

I don't know enough about formal or mathematical logic to refute that, but it sounds unlikley to me.

 

EQ

 

And like magic the trick doesn't work anymore. (John Cleese rant intermission.......sorry) Looks like MN is playing tricks or performing magic. Or I'm indeed to stupid.

 

Well this "it sounds unlikely to me" is perfectly Bayes. Now you being the mathematician I'd check that if I were you. Yet before hitting the books just ask your friendly Bayesian versed statistician what he/ she thinks.

 

Q

Okay, so mathematics is used in formal logic.

 

 

But not all of mathematics can be reduced to logic.

 

EQ

 

 

Yes it can. The only thing you do is mathematically exactly state how inexact you may be and if that exceeds the level that can be reached by normal language use the later.

 

Q

 

This I could agree with, but I am not well versed in logic.

(No, this was easy leaving the quote box.)

 

Logic is always logical as is (correct) mathematics. You are a mathematician. Logic (by language) only has a large bandwidth of inaccuracy and accuracy. The latter bandwidth is needed to quickly solve problems. Even - if not especially so - the most complex ones.

 

It makes it possible to draw a quick sketch, showing where to start extremely accurate testing if required.

[ajb]

Well this "it sounds unlikely to me" is perfectly Bayes.

I know it is!

 

No where have I said Bayes' is not useful, though here I have used it informally.

 

Yes it can.

No, we know this is not the case.

 

There was a school of thought that said that mathematics was an extension of logic and thus all mathmetics could be reduced to logic.

 

However Gödel's incompleteness theorems tell us that mathematics cannot be reduced to a set of statements (axioms) in which one can prove all possible statements. Thus, mathematics cannot be reduced to just logic.

 

Logic is always logical as is (correct) mathematics. You are a mathematician.

So I apply logic all the time in my work, but this is rather informal logic well within the accepted practice of my branch of mathematics.

[swansont]

I don't quite know why I can't get rid of the bold lettering but anyway. I just apologized for not doing as the Romans do on this Forum Romanum, and now I get treated by the senator of the site on a Freudian Bollocks. Well then senator you are in for a spanking:

I am not going to include the disaster of a quote with all the links.

 

If you are going to refer to the Wikipedia article, perhaps you should include the part that says

 

"In the scientific method, Occam's razor is not considered an irrefutable principle of logic or a scientific result."

 

http://en.wikipedia.org/wiki/Occam%27s_razor

 

Thus there is no need to edit the article. It already agrees with what I said.

 

Ergo both GR & QM in their respective fields are the simplest ways of explaining at the most accurate way currently possible all that the assumed scope of GR & QM can be assumed to cover. Because GR is in conflict with QM in their respective fields you may not assume that both are valid all over the infinite universe as an estimate using fewest assumptions. (said in short hand).

 

Newtonian gravity is simpler than GR, and classical mechanics is simpler than quantum.

[kristalris]

I know it is!

 

No where have I said Bayes' is not useful, though here I have used it informally.

 

 

No, we know this is not the case.

 

There was a school of thought that said that mathematics was an extension of logic and thus all mathmetics could be reduced to logic.

 

However s incompleteness theorems tell us that mathematics cannot be reduced to a set of statements (axioms) in which one can prove all possible statements. Thus, mathematics cannot be reduced to just logic.

So I apply logic all the time in my work, but this is rather informal logic well within the accepted practice of my branch of mathematics.

Gödel doesn't as far as I can see allow for guessing. So given that he's right it doesn't completely capture all logic. Bayes does for allowing you to guess. The only limitation Bayes prescribes is that you formally at least follow all the steps for it to be science. I.e. there is logic outside science. Yet Bayes also allows for informal logic via Occam.

 

Science is the systematic i.e. logical enterprise to reach the ultimate truth as close as possible in the simplest way possible (=> honesty is prerequisite and speed an issue)

So you get problem => probandum => hypothesis => prior odds => discovery => LR x LR etc. => posterior odds => norm => proof/ no proof

 

Via this method you can even tackle the "this sentence is false". Bayes: as a short cut: what sentence? This actual one? Honest? No => non scientific problem. If you want to go further Bayes can do that as well dear Gobel. Because you can say honest? Yes. Then what probandum? Fill in here please.................

 

I am not going to include the disaster of a quote with all the links.

 

If you are going to refer to the Wikipedia article, perhaps you should include the part that says

 

"In the scientific method, Occam's razor is not considered an irrefutable principle of logic or a scientific result."

 

 

 

 

Well, you clearly still don’t understand the further implications of Occam: as stated earlier they are twofold as the link portrays: one the law that you should strive to catch the ultimate truth in its simplest form and the other as a rule of thumb that you should choose the simplest i.e. idea with the fewest assumptions as best. The latter is indeed not a law but a rule of thumb. You still only think it is about the latter.

 

The first is a law: describing our solar system taking the earth in the center is incorrect when viewing the problem within a Newtonian context i.e. problem and thus probandum (see my reaction in the prior post to AJB.) It is not scientific to render as a scientific fact that within that context the earth is in the center. If you go to larger problems outside the Newton context you may for instance take any point as the center even the earth. All conforms to the dictate of Occam AND Bayes. You thus don’t.

 

Ergo you break the law of science if you do that differently.

 

The second issue you don’t grasp is the Yin and Yang issue of Occam and Bayes. You only talk Yin OR Yang. That’s wrong in science.

 

Let me try and explain it in a different more elaborate way then:

 

Zero gear: Bayes AND Occam in our intuitive brain: googling through its content and observing input. Unnoticed letting idea’s pop into our brain, probably via the Bayes and Occam algorithm. Even when n0 or n overload;

 

First gear: verbal logic of language we become aware of the output of our brain and start of in ever complicated logic that we communicate with others. When conforming Bayes & Occam => in a scientifically valid way; The idea at least is n1; or much larger;

 

Second gear: more or less formal Bayesian probabilistic reasoning n1 to infinity; Again with Occam reigning in Bayes otherwise galloping off to infinity. Keeping it practical on the stated probandum.

 

Third gear: Bayesian statistics: n sufficient to infinity. Again Occam pushing back.

 

Fourth gear: Empirical statistics n is large to infinity. Again Occam pushing back.

 

Fifth gear: deterministic Rutherford reasoning either accept the fault rate or demand n extreme. Again Occam pushing back. Bayes can describe this as well.

 

Now zero gear lets you intuitively skip immediately to fifth gear if need be. Yet when put to the test zero gear will sometimes for instance let doubt pop into your brain: oops, shouldn’t I better be using statistics on this?

 

So Bayes & Occam state use Newton when dealing with an apple falling out of the tree. And use GR when talking redshift of a photon. And apply QM when talking spin. BTW if need be QM and GR can be described via the mathematics of Bayes. But Occam prohibits this via THE BLOODY LAW to strive for maximum simplicity and economics. I.e. if you can get there simple then you are prohibited IN SCIENCE to go complicated and state that as science.

 

However during research you may do as you please as long as it is honest striving to the goal, because even Bayes and Occam are under their own scrutiny. I.e. you are allowed to make mistakes and still call the route as following scientific procedure. That still concurs with Bayes and Occam.

 

What you further more are not allowed to do is require everything in physics to be dealt with in fourth or fifth gear. Especially not when you haven’t given Bayes all the answers that the MATHMATICAL formula requires of you on the probandum following the problem.

 

You must answer the question whether or not the universe is infinite or not before venturing to state anything pro or con on any issue concerning TOE. Because then you are inherently talking marrying GR to QM. And then you are in the realm of an inherent infinite shortage of data. You are thus in zero to first gear in science and no higher. Breaching this is pseudo-scientific per definition. The same goes for demanding these gears to be used before it has any meaning to you. This is not a democratic affair. Even if you were to stand alone and everybody in science state that it is to be demanded, you must oppose. Stating nothing by science on the whole is also in conflict with Bayes in science.

 

And indeed Newton is more simple than QM or GR so that is indeed what one should use it to describe a COE on a way to TOE still now in first gear, yet testable Newton way if at all possible in any gear. Winning flat out on the fundamental DNA of science that Bayes and Occam entail as minimum requirement. Simply by doing what Bayes and Occam demand that you do. Answer all the relevant questions if need be by guessing and present it in a most probable way consistent with the essence of all observations in a testable way in the applicable gear that Bayes and Occam demand and no higher.

 

Bayes and Occam do, you & physics don’t.

Edited November 30, 2013 by kristalris

[ajb]

Gödel doesn't as far as I can see allow for guessing. So given that he's right it doesn't completely capture all logic.

Your claim was that all mathematics can be reduced to Bayes' theorem, or have I missundersood that?

 

It does not matter if some forms of logic can capture guesses or not, the point is not all mathematics can be reduced to a single axiomatic system in which all statments can be proved. Thus mathematics is not "just" logic.

 

Similarly, not all of science can be reduced to Bayes', but rather Bayes' based methods are a very useful tool.

 

 

BTW if need be QM and GR can be described via the mathematics of Bayes.

This is some claim. Can you please make this a tight statement and prove it, or at least point us to a reference?

Edited November 30, 2013 by ajb

[kristalris]

Your claim was that all mathematics can be reduced to Bayes' theorem, or have I missundersood that?

 

It does not matter if some forms of logic can capture guesses or not, the point is not all mathematics can be reduced to a single axiomatic system in which all statments can be proved. Thus mathematics is not "just" logic.

 

Similarly, not all of science can be reduced to Bayes', but rather Bayes' based methods are a very useful tool.

 

 

 

This is some claim. Can you please make this a tight statement and prove it, or at least point us to a reference?

 

 

 

 

Bayes can infer ALL relationships via a proof system. No-one as far as I know has ever disputed this. Do you? So all mathematics can be translated into a Bayesian proof. Like translating Dutch into English. Because Bayes does all relationships - what can't be said of all other mathematical languages - it doesn't work the other way round. For instance Bayes can solve more proofs (because it can do it all) than empirical statistics that can't handle n1.

 

So there can't be any reason why Bayes can't handle GR and QM. No one will of done that because it would be in breach of Occam. Using Bayes would only make it more complicated without getting better results. So it would be silly attempting it. (Edit: or maybe not so silly come to think of it)

 

Edit BTW this doesn't mean that if you put GR and QM to Bayes that you have married the two. Bayes will then say that they are in conflict. (Edit: and might show you where to start looking for a marriage of the two.)

 

Logic is more than mathematics. All scientific logic can be put into mathematics.

 

How can you say that taking in guesses doesn't matter? It rules out Gobel for his position doesn't cater for that. Bayes does and can thus handle all proofs. I guess Gobel forgot to take Bayes into account. His proof is I guess deterministic.

 

The question should be the other way round: can you name one form of mathematical proof that can't be handled by Bayes? You are the mathematician.

 

Whether or not Bayes can solve all logic I guess not for there is logic that is outside science. For instance religious logic given a priori contradictions to be taken as a fact. Bayes can't handle that other than rejecting it, what it is on religious grounds not allowed to do.

 

Because science is about the furtherance of knowledge it doesn't per definition handle logical truisms. A Bayesian inference is the minimum. And Bayes also provides the maximum encompassing all of mathematics and scientific logic. In fact thus Bayes & Occam are the minimum requirements of science. The norm of science as condition sine qua non.

Edited November 30, 2013 by kristalris

[ajb]

Bayes can infer ALL relationships via a proof system.

Tell me what a proof system is and then give me a reference or two that states what you have said.

 

No-one as far as I know has ever disputed this. Do you? So all mathematics can be translated into a Bayesian proof.

I have never heard anyone state that. Please provide us with some references.

 

So there can't be any reason why Bayes can't handle GR and QM. No one will of done that because it would be in breach of Occam. Using Bayes would only make it more complicated without getting better results. So it would be silly attempting it. (Edit: or maybe not so silly come to think of it)

This is just a wild claim at this stage. What do you mean by handle GR and QM?

 

All scientific logic can be put into mathematics.

Okay, so again we have a mathematical was of describing the scientific principal in light of Bayes.

 

How can you say that taking in guesses doesn't matter? It rules out Gobel for his position doesn't cater for that. Bayes does and can thus handle all proofs. I guess Gobel forgot to take Bayes into account. His proof is I guess deterministic.

So we do have some mathematics that cannot be described by Bayes or not? Your claim was that all mathematics can be reduced to Bayes' inference, right?

 

 

The question should be the other way round: can you name one form of mathematical proof that can't be handled by Bayes? You are the mathematician.

Are you talking about methods of proof theory here, or do you want me to state a theorem and allow you to try to prove it using Bayes'?

 

Most modern proofs today are in the sense of proof theory, informal. They do not employ the machinery of foundational mathematics.

 

This is outside my area of expertise.

 

And Bayes also provides the maximum encompassing all of mathematics and scientific logic.

You are making this claim again without backing it up in any way.

 

It is like you are in court making statements about a defendant without anything to suggest what you say is true. No witnesses, no CCTV, no phone records, no forensic evidence... What is the judge going to say to the jury?