Is Mathematics Alone a safe medium for exploring the frontiers of Science. Or should Observation and Hypothesis lead in front ?

[studiot]

The first ten minutes of this Walter Lewin lecture are a masterpiece of all that has been discussed here.

 

Maths is used in Physics, ie physical laws and principle are stated mathematically.

 

But

 

Physics knowledge is used to determine, alter and tailor the maths to suit the situation.

 

So Physics leads Maths to a useful analysis.

 

But maths strikes back as an ajb type analysis of errors.

 

All is in proper balance.

 

http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-17/

Edited August 31, 2013 by studiot

[swansont]

You have got to be kidding me. I take very seriously all ( every contributors ) comments . I think about them . Then make a decision on whether they are acceptable to me. If they are I many times agree. In fact sometimes perhaps unnecessarily so. if I do not agree with a particular line of thought , I do not agree. Surely that is my right . ( even if I am wrong ) ? I don't just say " yes sir, no sir, three bags full sir " Surely NO ?

Acceptable to you? No sir, you are not the arbiter of facts. Facts are true whether you accept them or not.

[Mike Smith Cosmos]

Acceptable to you? No sir, you are not the arbiter of facts. Facts are true whether you accept them or not.

 

The arbiter of facts, is neither you nor I , nor anyone else . . The arbiter is surely reality. .

 

I have to disappear for 2 weeks to southern climbs and collect my Hypothesis and Research documentation ,

[ ref http://www.scienceforums.net/topic/77276-possibility-for-mass-transport-system-could-take-us-up-a-gear/

 

Then to bring it back and put into the mincer.

 

Be gentle just this once .

 

mike

Edited August 31, 2013 by Mike Smith Cosmos

[ydoaPs]

All verbal logic can be expressed via probabilistic reasoning based on Bayes.

That's demonstrably false. Natural language is inconsistent (arising from it being its own object and metalanguage) whereas probability theory is consistent. One of the many equivalent definitions for a consistent system is a system from which at least one well-formed formula of that system is not deducible. So, there is at least one well-formed formula of a given natural language which cannot be expressed via probability theory.

[kristalris]

That's demonstrably false. Natural language is inconsistent (arising from it being its own object and metalanguage) whereas probability theory is consistent. One of the many equivalent definitions for a consistent system is a system from which at least one well-formed formula of that system is not deducible. So, there is at least one well-formed formula of a given natural language which cannot be expressed via probability theory.

Nope, again you mix it up into a hash. Something is either logical or illogical. That is absolutely black or white. A language has an inherent degree of built in vagueness. I.e. if you try to make the English language fit mathematical rigors no one will be able to follow what you are saying. There is no need for that because then you have mathematics. Why then use a vague say English language? Well it works faster and even having the mistakes it renders results. Better results than mathematics can provide when thus providing quick ways of finding things to rigorously test via hypotheses. Especially needed when you know you don’t exactly enough know what is to be held true.

Probability theory however even can accommodate in exactly modeling the inherent vagueness of any language. Whatever you say in language can be dealt with via Bayes. And shown to be or not be logically consistent with all the rest you said or meant to say. Usually then done via Bayesian nets.

 

So observation and hypothises should lead in front.

Edited November 18, 2013 by kristalris

[ydoaPs]

Nope, again you mix it up into a hash. Something is either logical or illogical. That is absolutely black or white. A language has an inherent degree of built in vagueness. I.e. if you try to make the English language fit mathematical rigors no one will be able to follow what you are saying.

While the vagueness is a huge problem (you can't know if it's true or false if you don't know what it means), that's not what I was talking about. It's a point of fact that consistent and inconsistent languages cannot have exactly equivalent sets of well-formed formulas.

 

English is straight up inconsistent. It being its own metalanguage and object language lets you write things like "This sentence is false" which, if true is false and if false is true. Oops, that's a contradiction. So, 'verbal logic' can prove literally anything and everything regardless of whether or not it accurately describes how reality actually is.

 

If you're relying on 'verbal logic', you're doing it wrong.

[cladking]

Nope, again you mix it up into a hash. Something is either logical or illogical. That is absolutely black or white. A language has an inherent degree of built in vagueness. I.e. if you try to make the English language fit mathematical rigors no one will be able to follow what you are saying. There is no need for that because then you have mathematics. Why then use a vague say English language? Well it works faster and even having the mistakes it renders results. Better results than mathematics can provide when thus providing quick ways of finding things to rigorously test via hypotheses. Especially needed when you know you don’t exactly enough know what is to be held true.

Probability theory however even can accommodate in exactly modeling the inherent vagueness of any language. Whatever you say in language can be dealt with via Bayes. And shown to be or not be logically consistent with all the rest you said or meant to say. Usually then done via Bayesian nets.

 

So observation and hypothises should lead in front.

 

 

 

There may be some apples and oranges being argued here.

 

Our science is based on observation and experiment. There's been a lot of "fudging" in the last century but "science" has been turning out some crackpot ideas for a century as well.

 

I believe there are at least two sciences and one is based on observation and logic. Of course anyone trying to use such a science today will be employing a lot of data and facts learned from experimental science and confounding results. Perhaps, science is actually taylor made for each user already and it's not apparent. We use careful scientific terminology to communicate ideas and results but I doubt any of us are so careful in the use of such terminology to think, form hypothesis, or even analyze experimental results. Each individual will have his own understanding of words.

 

This isn't to cast doubt of the results of scientific experimentation; merely the purity of the process.

[Mike Smith Cosmos]

There may be some apples and oranges being argued here.

 

Our science is based on observation and experiment. There's been a lot of "fudging" in the last century but "science" has been turning out some crackpot ideas for a century as well.

 

I believe there are at least two sciences and one is based on observation and logic. Of course anyone trying to use such a science today will be employing a lot of data and facts learned from experimental science and confounding results. Perhaps, science is actually taylor made for each user already and it's not apparent. We use careful scientific terminology to communicate ideas and results but I doubt any of us are so careful in the use of such terminology to think, form hypothesis, or even analyze experimental results. Each individual will have his own understanding of words.

 

This isn't to cast doubt of the results of scientific experimentation; merely the purity of the process.

 

 

 

I think what appears to be coming from many of the comments , is : that Maths alone is BLIND. It can blugeon on in a blindfold manner with due diligence. But may lead into a pit. Or may by chance to a place of wonder.

 

But Observation and Hypothesis has EYES , after all that's what its doing ' Observing ' .

 

So I do see Observation and Hypothesis being the 'outrunning scout' of the enterprise, and when sufficient argument and debate has refined the NEW observation or tossed it out , it can be handed over to the Mathematicians for producing possible patterns out of the Data , which are not easily spotted or need refining. But I do think the Lead must rest with Observation and Hypothesis , certainly in the initial stages.

 

http://www.scienceforums.net/topic/72725-is-mathematics-alone-a-safe-medium-for-exploring-the-frontiers-of-science-or-should-observation-and-hypothesis-lead-in-front/page-7#entry746743

 

Mike

 

Ps Do not think I don't like Maths or Mathematicians in the right place. Just not too overpowering in those Early days !

Edited November 19, 2013 by Mike Smith Cosmos

[kristalris]

While the vagueness is a huge problem (you can't know if it's true or false if you don't know what it means), that's not what I was talking about. It's a point of fact that consistent and inconsistent languages cannot have exactly equivalent sets of well-formed formulas.

 

English is straight up inconsistent. It being its own metalanguage and object language lets you write things like "This sentence is false" which, if true is false and if false is true. Oops, that's a contradiction. So, 'verbal logic' can prove literally anything and everything regardless of whether or not it accurately describes how reality actually is.

 

If you're relying on 'verbal logic', you're doing it wrong.

You simply can’t get your head around this now can you?

 

Again: probabilistic reasoning covers EVERYTHING that logic can do by providing the mathematics for that. So it even covers deterministic mathematics a la Rutherford. This is an UNDISPUTED & UNDISPUTIBLE because – unanimously!! held FACT OF SCIENCE for crying out loud. Yet you logically defy this clear cut scientific fact.

 

It is this mathematical formula in combination with the probabilistic !!!!! rule of Occam that shows you that when you know that the problem you are trying to solve isn’t an – exact - scientific one for lack of data you had PROBABLY (= Bayes + OCCAM!) best use verbal logic.

 

 

Furthermore it is this formula that DICTATES (via MATHMATICS!!!) that observation and hypothesis go in the lead. Check the bloody formula and see, you simply don’t understand your Bayes.

 

=> Proof that this OP is correct.

 

The vagueness of any language like English isn’t thus bad, but good in dealing with AS YET inherently vague issues due to lack of observations. Like drawing a picture via observations of the face of MN who doesn’t sit still. You go from a rough sketch (in proper science) making a lot of mistakes and correcting them as you get more observations in via testing hypothesis showing you where to catch more glimpses of this running bitch. IT SHOWS YOU WHERE TO START LOOKING FOR DATA via hypothesis. Only when you get sufficient data do you crossover to other forms of mathematics, usually in physics immediately to empirical statistics. Creating the illusion you can dispense with Bayes. You can’t:

 

Bayes rules all of science. The ultimate arbiter of science.

[studiot]

 

Something is either logical or illogical.

 

Rubbish.

 

Statement:

 

The grass is green.

 

That statement is neither logical nor illogical.

It may be true if I am standing in a field at noon in May,

It may be false if I am standing in the same field at midnight, under a sodium street light.

[ydoaPs]

You simply can’t get your head around this now can you?

 

Again: probabilistic reasoning covers EVERYTHING that logic can do by providing the mathematics for that. So it even covers deterministic mathematics a la Rutherford. This is an UNDISPUTED & UNDISPUTIBLE because – unanimously!! held FACT OF SCIENCE for crying out loud. Yet you logically defy this clear cut scientific fact.

Take your meds and a deep breath. Feel better? Ok, now listen. You said, "All verbal logic can be expressed via probabilistic reasoning based on Bayes. This is blatantly false. It is false for the reason I said and independently because of the inputs that the Bayesian machine takes.

 

English is inconsistent, so it can literally prove anything that is a well-formed formula of English to be true regardless of whether or not said formula in fact accurately represents the world. Bayes's theorem, however, is a deductive consequence of probability theory which is in fact consistent. This means there are some well-formed formulas that it can't prove-mainly, the false ones.

 

This means you cannot simply translate one into the other. Natural language isn't good enough.

 

Then there's the other thing. Have you ever gone golfing? A golfer often fails to sink her put. She knows deep down, however, that she could have sunk her put. That's a subjunctive. Bayesian reasoning is of no use when it comes to the modal and the subjunctive, because it only applies to the actual world. You can't get evidence from worlds which never happened.

 

Bayes can only tell you what probably is; it can't tell you what probably could be, but isn't.

 

Bayes rules all of science. The ultimate arbiter of science.

That is irrelevant.

[kristalris]

Rubbish.

 

Statement:

 

The grass is green.

 

That statement is neither logical nor illogical.

It may be true if I am standing in a field at noon in May,

It may be false if I am standing in the same field at midnight, under a sodium street light.

EQ

 

On a probandum of course i.e. a true or false issue. You reason in a way that gives lawyers justly so a bad name: i.e. useing the algorithm: can I misunderstand this? If so, do so.

 

And, you disprove your own position BTW. Bayes inherently will say - as you do - that your statement is both to be taken as logically true and false at the same time, dependent on all the rest of the relevant evidence concerning the statement. So you may say based on your statement sec a priori it is true: the grass is green is probably taken the most often used context true, as a prior odds in the formula. Given then the most often used norm. Bayes will allow (and require) you to ellaborate on what you mean in order to state something more exact. As you do. Bayes is the mathmatics of common sense and proving the OP as correct.. Quite common sense realy.

 

 

 

 

Take your meds and a deep breath. Feel better? Ok, now listen. You said, "All verbal logic can be expressed via probabilistic reasoning based on Bayes. This is blatantly false. It is false for the reason I said and independently because of the inputs that the Bayesian machine takes.

 

English is inconsistent, so it can literally prove anything that is a well-formed formula of English to be true regardless of whether or not said formula in fact accurately represents the world. Bayes's theorem, however, is a deductive consequence of probability theory which is in fact consistent. This means there are some well-formed formulas that it can't prove-mainly, the false ones.

 

This means you cannot simply translate one into the other. Natural language isn't good enough.

 

Then there's the other thing. Have you ever gone golfing? A golfer often fails to sink her put. She knows deep down, however, that she could have sunk her put. That's a subjunctive. Bayesian reasoning is of no use when it comes to the modal and the subjunctive, because it only applies to the actual world. You can't get evidence from worlds which never happened.

 

Bayes can only tell you what probably is; it can't tell you what probably could be, but isn't.

EQ

 

I have two Books full of Bayes the thickest one by Schum: "the evidential foundations of probabilistic reasoning" filled with translating verbal statements and the such of witnesses of crimes being put into mathmatics. Bayes is all about what probably could be but isn't. It is the fundamental part of it. The formula clearly shows the OP as correct. I.e. take your observations and put them in a hypothesis pro and a hypothosis con and see how this logically all adds up showing you what is more probable and what not given all the evidence pro and con and showing you thus on a given norm what is thus given the inherent assumptions what is true and what then is to be seen logically as false.

 

Q

 

That is irrelevant.

 

EQ

 

??????

Edited November 21, 2013 by ydoaPs
quote tag fix

[ydoaPs]

I have two Books full of Bayes the thickest one by Schum: "the evidential foundations of probabilistic reasoning" filled with translating verbal statements and the such of witnesses of crimes being put into mathmatics. Bayes is all about what probably could be but isn't. It is the fundamental part of it. The formula clearly shows the OP as correct. I.e. take your observations and put them in a hypothesis pro and a hypothosis con and see how this logically all adds up showing you what is more probable and what not and showing you thus on a given norm what is thus given the inherent assumptions what is true and what then is to be seen logically as false.

Good for you; it's still irrelevant. Bayes has no bearing on the contingently false nor can it tell you what is necessary. It can only tell you what likely is. You cannot get around the fact with your poorly executed hand-waving of your new favorite toy that it simply is not the case in any way that "If I can imagine it, then it is possible" is true.

[studiot]

Wow !*!

 

What have said to deserve such opprobrium?

 

You made an absolute statement - no exceptions - you said yourself it was absolute.

 

I will quote it again since you chose to exclude the context from my comments.

 

 

Something is either logical or illogical. That is absolutely black or white.

 

 

Now tell me what the logic output of a 74C126 buffer can be?

 

I will give you a hint; this a Tri State buffer electronics chip.

[swansont]

You know what they say: when the only tool you have is Bayesian analysis every problem looks like a nail.

[kristalris]

Good for you; it's still irrelevant. Bayes has no bearing on the contingently false nor can it tell you what is necessary. It can only tell you what likely is. You cannot get around the fact with your poorly executed hand-waving of your new favorite toy that it simply is not the case in any way that "If I can imagine it, then it is possible" is true.

What do you mean? The formula forces you to put any problem into the correct form in order to answer all questions you like. You forget that the formula allows you to put in a norm in oder to assertain whether you/ any group is to hold something as being tue or false.

 

If you can imagine it then it is per logical definition possibly true. The only exception is the assumed existence of an absolute truth that you a priori know of when imagining it. Thus indeed proving the OP.

Wow !*!

 

What have said to deserve such opprobrium?

 

You made an absolute statement - no exceptions - you said yourself it was absolute.

 

I will quote it again since you chose to exclude the context from my comments.

 

EQ

 

Try the context of the thread. In that context it was placed, yet still it proved you wrong.

 

 

Q

 

 

 

Now tell me what the logic output of a 74C126 buffer can be?

 

I will give you a hint; this a Tri State buffer electronics chip.

 

EQ

 

Become a lawyer.

You know what they say: when the only tool you have is Bayesian analysis every problem looks like a nail.

Don't forget to hammer it down then. I'm not saying (and have stated the opposite) that every problem should be solved via Bayes, I'm only saying that every problem can be analylised and solved via Bayes contrary to any other fom of mathmatics.

 

Oh and BTW don't forget the tool of verbal logic i.e. common sense. You lot do. Mathmatics of Bayes proves you wrong.

 

Proving the OP.

 

You lot keep on dodging the OP issue.

Edited November 19, 2013 by kristalris

[ajb]

You lot keep on dodging the OP issue.

I thought we more or less sorted the opening question with the answer "both are needed".

[Mike Smith Cosmos]

I thought we more or less sorted the opening question with the answer "both are needed".

 

 

Yes both are definitely needed, most certainly , for their respective roles. However the " thinkers" and dreamers, and hypothesisers , need to be given a bit of flexibility ( bit of Space , Latitude, etc), while they are musing and dreaming, Otherwise they will wake up too early before the " baby in the bathwater completes its Dream " and thus never fully realises His/Her Hypothesis.

 

ORIGINAL STATEMENT

 

 

 

(IS Mathematics ..alone ....safe ...at the frontiers of science....or .should .....Observation and Hypothesis.................." lead in front " )

 

. Even though they have their eyes closed half the time. [necessary for thinking and dream periods] and the bathwater is looking a bit murky on occasions ! [ need to explore 'murky' ideas for 'suck it and see purposes' , now and again ] ]

 

mike

Edited November 20, 2013 by Mike Smith Cosmos

[Mike Smith Cosmos]

..Quote -----------------------------------------

.ajb, on 25 Mar 2015 - 07:06 AM, said:

Indeed, interpretations and analogies are useful. However they should come after the mathematics and for sure not separate from it.

.unquote. ---------------------------------------

 

.

 

. WA HEY , WOW ! . I AM NOT SO SURE ABOUT THAT ,!

 

I met up with a well known colleague of this forum ,in person yesterday . We discussed this very subject .

 

That mathematics is in fact a HUMAN construct.

 

The terminology composed by man, the transforms identified by man , etc, YES drawing its structure from what man perceives the much underlying structure or reality that exists BENEATH maths . One layer down.

 

What this is , or what one could call it , I do not know . Whether Plato had some ideas on this , I am not too sure. In this underlying structure are all the ridged reality from which mathematics is able to derive its formulae, it's transforms , it's mathematical mechanism for doing its calculations , relationships , it's ability to work with separateness and thus Number . Yes in some ways it might look like maths IN PART . But the bit we know and think of as maths is only an image of the reality beneath . It may not be complete, it may be wrong in some areas , it may have many more types to discover, yet that incorporate flexibility, probability , statistics , and something not yet even named.

 

To use the term mathematics to describe everything down there in that reality , say like Mike Tegmark has attempted to do , is likely to persuade mankind that mathematics and for that matter science covers everything.

 

IT DOES NOT . At the moment maths and science only glimpses a small portion of reality. There is ( I believe) and I agree I could be entirely wrong , a whole sea of reality that looks nothing like our current scientific and mathematical view of reality. And to limit our horizon to ' only that which can be calculated , and only that which fits in with our current methodology for conducting science , is likely to blind us to future discoveries, and dismiss observations that can give us a clue to the REAL REALITY that lays beneath. ( or sideways and above , for that matter, )

 

Mike

 

Ps. . I do , none the less concede that mathematicians and scientist are digging , ever deeper into the ' substructure into the earth so to speak ' , but there may well be a 'whole sea of reality up the other way ( into the sky and beyond ) "

 

.

Edited by Mike Smith Cosmos, Today, 09:12 AM.

Edited March 25, 2015 by Mike Smith Cosmos

[StringJunky]

Which system transfers information from one mind to another with the highest fidelity, with regard to the intent of the author.: English, Art or Maths? The one with the least potential ambiguity in interpretation is the best one for the purposes of describing and sharing scientific ideas.

[studiot]

 

StringJunky

Which system transfers information from one mind to another with the highest fidelity, with regard to the intent of the author.: English, Art or Maths? The one with the least potential ambiguity in interpretation is the best one for the purposes of describing and sharing scientific ideas.

 

 

 

Since there are differences between Physics and Maths, why have you missed out Physics?

[StringJunky]

 

 

Since there are differences between Physics and Maths, why have you missed out Physics?

Maths art (images) and English are techniques of communication. You don't 'talk' in physics; it's not a language. This is the point I'm focussed on.

[Strange]

That mathematics is in fact a HUMAN construct.

 

Maybe. That is a topic of much debate. However, the analogies devised (after the fact) to explain the mathematics to non-specialists are definitely a human construct. They are also approximations and often grossly inaccurate.

 

For example, we have had people question the big bang theory because they don't understand the "surface of a balloon" analogy. (Or perhaps they don't understand it is an analogy.) But that is just a crude attempt to visualise the pseudo-Riemannian manifolds used to describe the intrinsic curvature of space-time , for those who don't have a solid grasp of differential geometry

 

https://xkcd.com/895/

[studiot]

 

StringJunky

Maths art (images) and English are techniques of communication. You don't 'talk' in physics; it's not a language. This is the point I'm focussed on.

 

 

Maybe you are focused on something, but the title of this thread is about two things.

 

Mathematics v Observation and Hypothersis.

 

Observation represents Physics which represents the real or concrete.

 

Mathematics represents the abstract.

 

I didn't see any reference to Art or English in that title, or the original post.

 

I would suggest that rather than combine hypothesis with observation I would say hypothesis represents the link between the abstract and the real.

Edited March 25, 2015 by studiot

[Mike Smith Cosmos]

Maybe. That is a topic of much debate. However, the analogies devised (after the fact) to explain the mathematics to non-specialists are definitely a human construct. They are also approximations and often grossly inaccurate.

 

For example, we have had people question the big bang theory because they don't understand the "surface of a balloon" analogy. (Or perhaps they don't understand it is an analogy.) But that is just a crude attempt to visualise the pseudo-Riemannian manifolds used to describe ...".....".5/[/url]

.

I think to focus on ,one , or many analogies as an example of how vague compared to maths , analogies can be . Is a fair comment .

 

This however does not exclude scientists or other disciplined persons , or just anyone making an observation, maybe by dint of circumstance, or by chance , or by Serendipity as a convenient coincidence . Then seeing a model that appears to work in nature one way, and wonder if it could work in another set of circumstances .

 

Such an hypothesis should NOT be ' tossed out ' . But rather listened to, considered, tested for possible patterns and not suffer the fate of chucking the ' baby out with the bath water ' just because it does not have ' calculus ' or ' la place transforms ' in the hypothesis. I am sure Einstein never had this rebuttal when he noticed pollen grains on the surface of water , being buffeted , as his insight to Brownian motion of atoms, giving him the right to hypothesise about Atoms behaviour .

 

Mike

Edited March 25, 2015 by Mike Smith Cosmos