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

[Humblemunn]

It looks to me that simulation modeling is the same as mathematical modeling. One creates a computerised prototype and tests that before making real physical prototypes. This is all done with numerical or maybe algebraic methods that are hidden in a "black box" within the software being used. Thus, there is no obvious difference between mathematical modeling and simulation modeling.

Professor Ray Paul of Brunel University would disagree with you. One thing I forgot to mention is that once the basic dynamical model is created using the software, on-hand tweaking of the code is needed for a tailored model.

[ajb]

Professor Ray Paul of Brunel University would disagree with you.

Okay, but why?

 

Does simulation modeling not employ lots of mathematics?

[studiot]

Humblemunn, are you sure you are not confusing simulation based on probability/statistics rather than closed form mathematics with non mathematical activity?

 

For example queueing theory, mass behavioural science etc.

Edited August 29, 2013 by studiot

[Bignose]

Professor Ray Paul of Brunel University

Humblemunn. I pulled up a random few of his papers. There is a ton of math in his models. He's just created a nice way of obscuring it behind tools.

 

What I see falls under a broad umbrella known as discrete event simulation. It is used in a lot of industrial settings, job control, etc. And there is a great deal of mathematics behind it. Check out Banks et al Discrete Event Simulation 5th Edition 2009.

 

At it's heart is a large Monte Carlo simulation. This is how a fair amount of obscuring can occur, because usually if you just put in a mean and deviation, it is usually decent enough to assume the probability distribution of an event is Gaussian/normal. That is, meaningful results can still be gathered even if the distribution really isn't normal. And with the speed of computers today, Monte Carlo sims can be done really, really fast.

 

Edited to add:

 

Actually, to a certain extent, it is my opinion that some of these tools have gotten too easy to use. That it is a little too easy to just insert some parameters and then take what the computer spits out as gospel truth. CFD and FEA is also becoming guilty of this.

 

Specifically, the people who use these software need to be trained on the mathematics behind them so that they can recognize when anomalies come up. That is, when the basic assumptions behind the model aren't holding. I.e. an event that really isn't Gaussian/normal, or a fluid that ins't Newtonian.

 

Far too often, people just assume that because the computer said something, it must be right.

Edited August 29, 2013 by Bignose

[Humblemunn]

It's the ability to convey an understanding of a system to a layperson which is it's greatest advantage imv. It means that potential obvious errors within the system can be spotted more easily. It is perfectly suited to exploring the frontiers of science, complementary to mathematical modelling, which is what the OP is asking.

 

The OP is right in suggesting that "Observation and Hypothesis" should be at the forefront of exploring the frontiers of science. That's exactly what I've done which has led to my qualitative prediction for a lateral deviation to the left for the Juno flby. This is COMPLETEY NEW. It isn't a guess about the amount of velocity increase. It's a lateral force prediction, which I've specified will be to the left of the spacecraft flightpath due to the unique hypothesis of left-hand spinning Archimedes screw gravitons.

Edited August 29, 2013 by Humblemunn

[studiot]

 

Actually, to a certain extent, it is my opinion that some of these tools have gotten too easy to use. That it is a little too easy to just insert some parameters and then take what the computer spits out as gospel truth. CFD and FEA is also becoming guilty of this

 

plus1

Edited August 29, 2013 by studiot

[Bignose]

It's the ability to convey an understanding of a system to a layperson which is it's greatest advantage imv.

that may be true, but that does not mean in any way that it isn't still highly mathematical. I don't have any problem claiming better ways of presenting mathematical models, but I'd strongly advise attempting to call the model "not math".

[Humblemunn]

that may be true, but that does not mean in any way that it isn't still highly mathematical. I don't have any problem claiming better ways of presenting mathematical models, but I'd strongly advise attempting to call the model "not math".

You're being pedantic. The software uses math, yes. I don't need to know high level math when using it. I do need to know how to tweak the code. That's the difference between simulation modelling and mathematical modelling.

[Delta1212]

You're being pedantic. The software uses math, yes. I don't need to know high level math when using it. I do need to know how to tweak the code. That's the difference between simulation modelling and mathematical modelling.

So then yes, it's the difference between doing math and using a calculator.

[imatfaal]

!

Moderator Note

 

Humblemunn - stop using other threads to advertise your speculative theory. That behaviour is considered hijacking and future instances may just be hidden - please do not continue.

 

[Bignose]

You're being pedantic. The software uses math, yes. I don't need to know high level math when using it. I do need to know how to tweak the code. That's the difference between simulation modelling and mathematical modelling.

I don't think I am. Probability and statistics fall under "math" don't they?

 

And when you "tweak the code"... you do realize that in the end you're changing how things are calculated. i.e. math, right?

 

I don't see how one can call 'simulation modelling' (discrete event modeling) "not math".

[studiot]

Interesting question.

 

Say you take a surveyor's measuring wheel and trundle it along the road, recording the distance.

 

Are you doing 'maths' ? ie utilising the inherent properties of a circle to obtain your result ?

 

I would say yes.

Edited August 29, 2013 by studiot

[ajb]

Far too often, people just assume that because the computer said something, it must be right.

And undergrads often believe their calculators rather than me!

You're being pedantic. The software uses math, yes. I don't need to know high level math when using it. I do need to know how to tweak the code. That's the difference between simulation modelling and mathematical modelling.

Okay so it is mathematics.

I would say yes.

At some level I think it is hard to say what is mathematics and what is not. The human brain seems hardwired to see patterns and take advantage of them. This really is the ''meaning'' of mathematics.

[studiot]

 

And undergrads often believe their calculators rather than me!

 

Unfortunately far to many medical staff believe their calculators, rather than my wife who tries to teach them to understand.

 

The result is a sometimes fatal drug error.

 

Thank you for your comment on my simple example. Yes there is a grey area (as always) and it can be difficult to know at what point to decide "this is not maths".

 

Here is a simpler example, again from the domain of surveyors.

 

In days of yore surveyors used to measure distance by laying out a physical chain. Surveyors were advised to count the number of layings of the chain by picking up a small stone and placing it in a pocket each time or by transferring a stone each time from a collection.

 

An what about tally sticks used by primitives, who cannot actually count up to their tally?

Edited August 29, 2013 by studiot

[Mike Smith Cosmos]

 

There's certain problems which are better suited to simulation modelling and some better suited to mathematical modelling.

 

Maths is saying how things SHOULD behave by a very precise set of written Formula,

Simulation may incorporate all sorts of probable behaviors which may not be precise . Say like shrinkage due to theft or unforseen errors. Slop, Or the nature of parts of the system to be based totally on probability.

 

Pure Mathematicians try to Grab everything into the realm of maths, rather than accepting things like OBSERVATION and HYPOTHESIS as a respectable discipline ( although that might not be the best word , as it is inherently undisciplined) . At the stage of OBSERVATION and HYPOTHESIS no pre-prescribed maths is necessarily thought. It is true many things in nature are regular, geometric and indeed fall into the realm of math. However the mathematicians MUST LET GO of trying to include probability or even unpredictable events. These can be included in simulation, because simulation is simulating everything ( or attempting to ) Maths only dares go with accurate predictions. Observers and Hypothesisers dare to go " where angels fear to tread"

 

mike

[Delta1212]

 

Maths is saying how things SHOULD behave by a very precise set of written Formula,

Simulation may incorporate all sorts of probable behaviors which may not be precise . Say like shrinkage due to theft or unforseen errors. Slop, Or the nature of parts of the system to be based totally on probability.

 

Pure Mathematicians try to Grab everything into the realm of maths, rather than accepting things like OBSERVATION and HYPOTHESIS as a respectable discipline ( although that might not be the best word , as it is inherently undisciplined) . At the stage of OBSERVATION and HYPOTHESIS no pre-prescribed maths is necessarily thought. It is true many things in nature are regular, geometric and indeed fall into the realm of math. However the mathematicians MUST LET GO of trying to include probability or even unpredictable events. These can be included in simulation, because simulation is simulating everything ( or attempting to ) Maths only dares go with accurate predictions. Observers and Hypothesisers dare to go " where angels fear to tread"

 

mike

You seem to be under the impression that probability isn't math.

[Mike Smith Cosmos]

You seem to be under the impression that probability isn't math.

 

Maths really needs to back off a little on occasions . If as has been described 'Science makes predictions', science needs maths to make predictions, 'No predictions , no science'. 'science is maths ' This is a serious mistake I believe !

 

Probability in maths is poor-ish at making predictions, by dint of the very nature of things in nature that rely on things that are more statistical and probability based.

 

Physics, the nature of the world is part statistical, part probability based, part predictable, fundamentally reliable precise able to be formalised into a mathematical formula Maths is poor at making predictions used in the probability type of environment. Why can it not be happy staying over in its corner , doing its calculating, playing with its formulas making beautiful, accurate predictions on things that can be accurately predicted , and stop giving people a hard time when they are trying to explore the frontiers of science with observation and hypothesis ?

 

mike

Edited August 29, 2013 by Mike Smith Cosmos

[ajb]

However the mathematicians MUST LET GO of trying to include probability or even unpredictable events. These can be included in simulation, because simulation is simulating everything ( or attempting to )

We have lots of mathematics to deal with stochastic behavior.

 

And how would you include stochastic systems in simulations without mathematics?

 

 

Maths only dares go with accurate predictions.

This depends a lot on what you mean. For instance one may make approximations and be able to give estimates of the errors. Or the answer could be probabilistic.

Probability in maths is poor-ish at making predictions, by dint of the very nature of things in nature that rely on things that are more statistical and probability based.

This is under representing what we do have. There is a wealth of knowledge on probability, random variables and stochastic systems. All these have application in testable physics in the form of quantum mechanics or statistical physics.

 

...stop giving people a hard time when they are trying to explore the frontiers of science with observation and hypothesis ?

This is just going round in circles! Observation and (the use of) mathematics are not so distinct in physics. One uses mathematics to analyses experimental data and then this can be compared to theoretical predictions based on mathematical models. Both these drive hypothesis.

Edited August 30, 2013 by ajb

[Mike Smith Cosmos]

We have lots of mathematics to deal with stochastic behavior.

 

And how would you include stochastic systems in simulations without mathematics?

 

 

 

This depends a lot on what you mean. For instance one may make approximations and be able to give estimates of the errors. Or the answer could be probabilistic.

 

Are you saying that Probability or statistics is a "conjecture" that maths wishes to adopt into its family.

 

What slightly un-nerves me is that mathematics as a discipline is attempting to "Take Over " Physics as a discipline in its own right " and even Take over "Science " , by saying Mathematics can explain everything.

 

Much as I respect you as a Mathematician, I think it would be a sad day if 'Mathematics Alone' became the 21st century version of Physics and Science of Yesteryear.

 

Gone would be the Thinkers like Rodans thinker, Gone would be the Philosophers like Aristotle, Plato , Socretese and all that followed......

 

We would be left with ............................................. Please no ..........Do not take over everything ......... Sad will be the day you do

 

Nobody will understand you apart from other mathematicians it will be like H.G. WELLS the time machine with the Meek and the Warlocks .........Aghhh !

Edited August 30, 2013 by Mike Smith Cosmos

[arc]

 

So what was your answer to my question

 

If it is possible to specify an exact amount of water to achieve a desired workability, what is the formula?

 

When I use my 1950's steel barrel mixer around the home I use the rhythmic sound of the mixture, adding a little water changes the tone that the sand and gravel make like a pair of mismatched maraca's. You can mix with your eyes closed.

Singing is optional.

[ajb]

Are you saying that Probability or statistics is a "conjecture" that maths wishes to adopt into its family.

No, rather we have some self-consistent branches of mathematical knowledge give us some understanding of random events. Probability theory and statistics are part of this.

 

 

What slightly un-nerves me is that mathematics as a discipline is attempting to "Take Over " Physics as a discipline in its own right " and even Take over "Science " , by saying Mathematics can explain everything.

What is this based on?

 

It seems clear that, especially for the physical sciences, that mathematics has been a very powerful tool that has made it possible to understand and use many natural phenomena.

 

This may appear to be less so in say biology, but them one uses statistical methods to analyze the data gained from experiments. This then can be used to support or reject some hypothesis or indeed suggest some new hypothesis. But note, the mathematical work may just be "in the background" in analyzing the experiment. In particular one would like to show that some trend is statistically significant. This means that it cannot just be a random artifact of the experiment.

 

One general aim of mathematical biology would be to develop mathematical models of biological phenomena and provide the necessary tools to analyze them. Is this "taking over" or is it "adding a new string to our bow"?

 

 

Much as I respect you as a Mathematician, I think it would be a sad day if 'Mathematics Alone' became the 21st century version of Physics and Science of Yesteryear.

I don't see that it will.

 

What may be true is that the next generation of theoretical physicists may need much more modern mathematics than his ancestors. Especially at the forefront of fundamental physics.

 

Also, as computers are becoming more and more powerful I would expect more and more computer modeling to drive science in all areas. However, that will still need to be checked against actual observations.

 

In short mathematics should be seen as the right language for science to express itself and check itself.

[Mike Smith Cosmos]

I don't see that it will.

 

What may be true is .................

 

Gone would be the Thinkers like Rodans thinker, Gone would be the Philosophers like Aristotle, Plato , Socretese and all that followed......

We would be left with ............................................. Please no ..........Do not take over everything ......... Sad will be the day you do

Nobody will understand you apart from other mathematicians it will be like H.G. WELLS the time machine with the Meek and the Warlocks .........Aghhh !

mike

Edited August 30, 2013 by Mike Smith Cosmos

[ajb]

Gone would be the Philosophers like Aristotle, Plato , Socretese

But they are gone. Today's thinkers have new tools, and part of that is modern mathematics.

Nobody will understand you apart from other mathematicians

Which is why popular science is important. The general public need to have some science and mathematics awareness in order to make good life decisions and not get conned by wild claims.

[Mike Smith Cosmos]

But they are gone. Today's thinkers have new tools, and part of that is modern mathematics.

 

Which is why popular science is important. The general public need to have some science and mathematics awareness in order to make good life decisions and not get conned by wild claims.

 

Fair comment . Its more the size of the tool.

 

So not Maths the size of JCB digger and all the rest like thinking ,being hand tools. rather ALL being hand tools of different sorts , Maths being one, Thinking another etc etc.OR pull in the occasional digger ( like in Time Team Archeology to rip off the surface turf , then hand dig with a trowels of various sorts ). The start up Digger could be from whatever discipline is relevant. Could be a Big Conceptual C change idea, Could be a Major new Mathematical Tool like Calculus . Or a major observation like The Moon is the exact same size as the Sun in the Sky. Or a major speculative thought like..... uhm .......I wonder if the universe is like edom cheese with holes in as well as solid cheese. that is why the universe is

 

 

Part deterministic,[exact, precise ,calculable ,mathematical ] and part random, [probable , loose, non-deterministic, non predictable NON mathematical ] by M.K.S

 

then go from there, now the earth has been scrapped off. Back to the hand tools

 

BUT MATHS must surely NOT BECOME the language of science , or else ONLY MATHEMATICIANS will understand the language. and only mathematicians will be able to think new scientific thoughts and concepts and develop science into the future. That is the very essence of my original Question. You Mathematians with your mathematical brains think in a very Particular way MATHEMATICALLY . You will limit the future growth of Science to a specialised Maths-Science not to a Universal -Science . I am not meaning you personally AJB as I know you like the applied maths end of the spectrum. But, even you , I have tried to read some of your Published Papers and the lay person could not get beyond the title of most of them.

 

 

 

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

 

No you ( Maths) must not be allowed to LEAD in FRONT , you could lead us into a swamp before the ordinary Population realized it.

 

It could even be argued that Science has already lead industry and the modern industrial world into the swamp and only now possibly too late , are the human population waking up to the swamp like condition they are finding the world in.

 

I fear for my daughters what world are we scientists ( including myself , having been a part of 20th century industry ) leaving them to grow up in.

 

NO, the language of science needs to be a language we ALL can understand. Be some of the precision gears, the technical background boys, by all means. Calculate, Fix, Predict, explain as you are able. But please do not become our Mind,our Language, our conceptual Thinking capability, our Leaders. The ground under your feet is able to be crossed with your mathematical feet. But with our feet we sink into the swamp! I accidentally upset Swansont previously but that was not my intent. But the danger is allowing you mathematicians to become the Priests of Science , speaking only in Latin , which the lay person could not understand. I take my hat off to these popular science writers ,[some very qualified scientists many, who translate into ordinary language so that the ordinary person can understand, to some extent.[As you previously commented] But if you as mathematicians are allowed to take over... well ... it will be a sad day . MATHTOCRACY NO !

 

 

 

Mike [MKS]

Edited August 30, 2013 by Mike Smith Cosmos

[ajb]

So not Maths the size of JCB digger and all the rest like, thinking being hand tools. rather ALL being hand tools of different sorts , Maths being one, thinking another etc etc.

You cannot view thinking as a tool in that way. Mathematics can help you think and formulate your ideas about just about anything in a concise way. Mathematicians also think about mathematics quite a lot!

 

 

 

OR pull in the occasional digger ( like in Time Team Archeology to rip off the surface turf , then hand dig with a trowels of various sorts ). The start up Digger could be from whatever discipline is relevant. Could be a Big Conceptual C change idea, Could be a Major new Mathematical Tool like Calculus . Or a major observation like The Moon is the exact same size as the Sun in the Sky. Or a major speculative thought like..... uhm .......I wonder if the universe is like edom cheese with holes in as well as solid cheese. that is why the universe is

Of course, it is possible to use the wrong tools, in this case the wrong mathematics or the wrong interpretation of the results of mathematics.

 

But remember, experimental scientists are totally dependent on mathematics. Otherwise they would just have long lists of data that means nothing. They have to do some mathematics on this set to really see the pattens and single out the important features. A rather mathematically illiterate biologist told me this!