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

[swansont]

Prof. Lee Smolin of Perimeter Institute has just released his latest book TIME REBORN . Not one Maths formula . True it is the result of many scientists and many years work, but none-the-less surely this demonstrates NEW SCIENCE needs NEW METHODS. No? Maybe subjects like TIME need a conceptual change not more maths.

 

Popular science books are marketed to people outside the professional scientist crowd.

[Mike Smith Cosmos]

Popular science books are marketed to people outside the professional scientist crowd.

 

Yes , but he is presenting the culmination of his life's work to the world on TIME , and he has chosen to do it without a single mathematical equation.

However I have to be honest, that I have just read a part of a previous book by him as his life in theoretical physics ( The life of the Cosmos by Lee Smolin). Here he describes the joy of seeing the nature of reality being illuminated by mathematical models,over and over again, much as DH comments over the last few posts ( as indeed you have ). However having referred in this 'life of the cosmos ' book to the holy grail of every aspiring scientist ,(including himself,)in the theory of physics being to develop the theory that reflects everything he ends that reasoning with :-

 

 

" of course what is both wonderful and terrifying is that there is absolutely no reason why nature at its deepest level must have anything to do with mathematics." ( Modern Science Writing section by Lee Smolin page 365 Oxford University Press ISBN 78 0 19 921681 9 in 2008 )

 

He ends up in this particular missive by discussing

 

" the individual atoms in expanding rubber bands, gases filling in rooms, and biologists reckoning with nature with its tremendous beauty being just a matter of randomness, statistics, and frozen accidents. Perhaps the greatest nightmare of the Platonistsis that, in the end , all our laws will be like this, so that the root of all beautiful regularities we have discovered will turn out to be more statistics, beyond which is only randomness or irrationality. "

 

 

Guess it must look sort of like this :-

 

Edited May 27, 2013 by Mike Smith Cosmos

[D H]

Yes , but he is presenting the culmination of his life's work to the world on TIME , and he has chosen to do it without a single mathematical equation.

 

Of course he is not using math. This is a popularization of science book. Such books tend not to be best sellers; the lay audience is a bit hostile to science. The target audience is someone who perhaps can do math at the ninth grade level and who was quite confused by that low level of mathematical sophistication. One way authors can guarantee their pop sci books won't sell well at all is to sneak some advanced math like [imath]F=ma[/imath] (or heaven forbid, [imath]\vec F = \frac {d^2 \vec x} {dt^2}[/imath]) into their text.

 

It's very hard to find a pop sci book that uses any math whatsoever.

 

 

The language of physics and astronomy is math. It has been since before Newton's time, and the interconnectedness has only grown stronger since then. There is no escaping this fact

Edited May 27, 2013 by D H

[swansont]

Yes , but he is presenting the culmination of his life's work to the world on TIME , and he has chosen to do it without a single mathematical equation.

 

He want to sell books. Equations scare people away.

 

 

"of course what is both wonderful and terrifying is that there is absolutely no reason why nature at its deepest level must have anything to do with mathematics" is true. But you're missing part of the message: that what we have found is that nature is described by math.

[Mike Smith Cosmos]

 

He want to sell books. Equations scare people away.

 

 

"of course what is both wonderful and terrifying is that there is absolutely no reason why nature at its deepest level must have anything to do with mathematics" is true. But you're missing part of the message: that what we have found is that nature is described by math.

 

Surely you mean :-

 

"But you're missing part of the message: that what we have found is that nature can ( among other ways ) be described by, or not including , math."

Edited May 27, 2013 by Mike Smith Cosmos

[D H]

Surely you mean :-

 

"But you're missing part of the message: that what we have found is that nature can ( among other ways ) be described by, or not including , math."

 

I would read what Swansont wrote as he wrote it. Most physicists agree with Max Tegemark on why mathematics is so unreasonably effective in the natural sciences. It's quite simple: The physical world is completely mathematical. The key job of a theoretical physicist is to uncover that mathematics.

Edited May 27, 2013 by D H

[swansont]

Surely you mean :-

 

"But you're missing part of the message: that what we have found is that nature can ( among other ways ) be described by, or not including , math."

 

There is no description of nature that does as well as math. All others are attempts to do so without equations, perhaps, but they are still mathematical. The less rigorous they get, the worse the description is.

[Mike Smith Cosmos]

I would read what Swansont wrote as he wrote it. Most physicists agree with Max Tegemark on why mathematics is so unreasonably effective in the natural sciences. It's quite simple: The physical world is completely mathematical. The key job of a theoretical physicist is to uncover that mathematics.

 

There is no description of nature that does as well as math. All others are attempts to do so without equations, perhaps, but they are still mathematical. The less rigorous they get, the worse the description is.

 

I think you are staking too big a claim on the territory .

 

Namely the following :-

 

I think a more reasonable territorial claim would be the following :-

 

There is no description of nature that does as well as math. All others are attempts to do so without equations, perhaps, but they are still mathematical. The less rigorous they get, the worse the description is.

 

But that is how half at least of nature is: Based on hugh numbers , random etc Hence variety, beauty,living things hurricanes, floods etc etc

 

True the other half that is based on equations :- lifts, I pods , Railway systems most of our industrial way of life. The net .Banking systems

 

But look where it is leading us at the moment . To Rack and Ruin .

Edited May 27, 2013 by Mike Smith Cosmos

[cladking]

Both, actually.

 

Math is the bedrock of many of the sciences, and in physics, ALL CAPS is the way to say this. If you aren't using math you aren't doing physics. You're at best explaining physics to your grandma by means of (inevitably poor) analogies.

 

As far as not getting to the bedrock, science doesn't do that. It at best tries to create an ever improving model of what can be observed. Science provides models of behaviors, and it is inherently limited by what can be observed. If you want bedrock, you want religion. That religious bedrock might not be right (and oftentimes it is at odds with observable reality), but it is comforting.

 

That's part of the appeal of pseudoscience. Just like religion, pseodoscience purportedly offers simple explanations that claim to be deeper than those offered by the sciences. That it is counterfactual is irrelevant. Don't be lulled by pseudoscientific mumbo jumbo such as that put forth by Robin Pike.

 

Dance and music can be expressed well mathmatically as well. Math is critical and essential for almost all modern technology but a bird doesn't need to calculate the radii when employing a twig to lever an insect out of a hiding place. My grandmother doesn't need to understand the operation of internal combustion engines while explaing to a cop she couldn't have been going 60 miles an hour because she was at home only five minutes before.

 

As things become more everyday and mundane they can become understood on any number of levels. Yes, at this time it's been true for decades that the fronteirs of physics are owned by math but who's to say that this can't change and some other method sometimes become more effective. As higher and higher tech becomes understood by more people in their various ways who's to say no breakthrough can be made by a dancer or swimmer?

 

Math will always be, and has always been, the language of science but this is as much for its ability for precision and expression as its ability to make new discoveries. So long as nature can be expressed by math it will be.

 

It's difficult to imagine Star Trek's Q, God, or nature sitting down and doing the math before their next miracle.

[swansont]

But that is how half at least of nature is: Based on hugh numbers , random etc Hence variety, beauty,living things hurricanes, floods etc etc

 

True the other half that is based on equations :- lifts, I pods , Railway systems most of our industrial way of life. The net .Banking systems

Modeling hurricanes and floods does not involve math? You can do a better job without it? Seriously?

[Kramer]

I think you both ( Mike and swansont ) are wrong, because both of you disregard the main fact:" nature is material,
and mater is particularised in some Democritis indivisible particles".
Mike believe in power of word, which is ridiculous, because word without material support is emptier than emptiness.
The nature of word is sociological, as this it can't have power to act without stick and koulach, with out hell and paradise,
etc.. and they all are materialistic means.
The debate about prescription of nature with word is sociological too, especially in the field of philosophy.
It is impposible to be non biased, hence not true.This we see in modern physic that try to throw out of scene of science
notions of particle, of mass , of a space without limits, of an eternal time without flow,of a reality that has nothing to do with
what we think or debate.
Swanson hiporbolise the power of math in description of nature. But the math is a by product of brain, and has its limits
in being absolute. The brain, scientist say, is kinda of a computer. But exactly as in computer what you input, derive the
out put. Let say for example: why disciple of quantum physic use only one constant of Plank --"h" and disregard all the
others constant? Simple because : if it will use the Plank frequency this will throw in trash can Heisenberg principle this
cornerstone of extreme quantum mechanic. There will not be carta bianca in math like h / 0 = infinity, with a manipulation of
metaphysics interpretations that derive of.
Sorry by interfering in your debate, with my lay-mans scarce knowledge in essentials of thread by two elitist.
I hope have not irritated too much the readers and muddied the waters.

[Mike Smith Cosmos]

I think you both ( Mike and swansont ) are wrong, because both of you disregard the main fact:" nature is material,

 

 

 

I hope have not irritated too much the readers and muddied the waters.

 

 

 

 

 

 

Not at all. This is a forum. A place where minds meet and debate . As this is the "speculation" section ,it is more open than the specific subject debates.

 

 

Modeling hurricanes and floods does not involve math? You can do a better job without it? Seriously?

 

No , and I am not suggesting that as a way forward, predicting hurricanes on an abacus . You are potentially making me out to be a 'Luddite', which I am not. But I am very zealous that other ways of understanding the bigger picture, which may not be seen if we have our eyes down on the keyboard, when the answer lies out there in observation and concept development, perhaps at a systems level rather than a detail level.

 

If the hurricanes come sometime,somewhere , maybe we will have to reorganize ourselves not to be where the hurricanes come ,and when they come.

If the floods come regularly to some lands, maybe we should arrange to re distribute land area. The herds of animals have sussed this one out thousands of years ago. It is really time to question what and how we do things. I am sure there is refined technology that can work in with a redistributed globe.

[cladking]

 

Modeling hurricanes and floods does not involve math? You can do a better job without it? Seriously?

 

Actually I can watch the satellite pictures and get a better feel for coming weather than the weather service. Of course they can be right for months on end and I'm wrong much more frequently. I do a little better job with the long range forecast than they do, I believe, but they rarely post one further than seven days out so it's hard to be sure. I tend to consistently be about 70% accurate and they often achieve about 98% accuracy for months on end and then go through short periods they get it all wrong. I can't predict the path of hurricanes at all and must be missing something fundamental. I'm sure they are pushed by highs but they seem able to push back as well.

 

I knew New Orleans was flooded several hours before the Army Corps of Engineers figured it out. Of course this was one of the few times they were grossly incompetent. They didn't have a clue until they dispatched a truck to investigate reports of flooding and found the highway under water in the morning. From the flood's viewpoint is was truly the big easy.

[Mike Smith Cosmos]

Modeling hurricanes and floods does not involve math? You can do a better job without it? Seriously? Swansont

 

I am not totally sure of my facts here, but I think a lot of the weather forecasting is less to do with maths and formulas and more to do with probability based on mass numbers , statistics and models as you say. Perhaps an analogue computer/machine as opposed to digital computers [ highly maths driven , whereas analogue computers are more measurement of values driven]. would be more suitable for this sort of prediction .

 

Rather than a down side to my argument , this is supportive. unless, as I say you are going to use the word MATHS to swell up and take over the whole territory of physics . Perhaps for the sake of argument we should leave Maths in the deterministic, accurate predictive camp. And put probability and emergence and models and non determanism ideas, into the Physics camp .

 

This might prevent potential physics students from running screaming into the ARTS !

Edited May 28, 2013 by Mike Smith Cosmos

[swansont]

I am not totally sure of my facts here, but I think a lot of the weather forecasting is less to do with maths and formulas and more to do with probability based on mass numbers , statistics and models as you say.

 

Probability and statistics are math.

 

 

 

Perhaps an analogue computer/machine as opposed to digital computers [ highly maths driven , whereas analogue computers are more measurement of values driven]. would be more suitable for this sort of prediction .

 

Rather than a down side to my argument , this is supportive. unless, as I say you are going to use the word MATHS to swell up and take over the whole territory of physics . Perhaps for the sake of argument we should leave Maths in the deterministic, accurate predictive camp. And put probability and emergence and models and non determanism ideas, into the Physics camp .

 

This might prevent potential physics students from running screaming into the ARTS !

 

You seem to be laboring under the mistaken notion that if it's not deterministic then it's not math.

[D H]

I am not totally sure of my facts here, but I think a lot of the weather forecasting is less to do with maths and formulas and more to do with probability based on mass numbers , statistics and models as you say.

As you've already been told, probability and statistics are a part of mathematics. Some rather advanced mathematics, measure theory, is needed to properly understand probability. Secondly, there's a whole lot more to mathematics than just numbers and formulae. Many professional mathematicians never deal with numbers and formulae except in the abstract.

 

Finally, modern weather forecasting is extremely math-based. A hugely complex computational fluid dynamics model lies at the heart of a modern weather forecasting system. The model has to be propagated over time and space according to the laws of physics. Along the way it is updated with measurements of various degrees of fidelity and resolution. It's math as far as the eye can see.

 

Perhaps an analogue computer/machine as opposed to digital computers [ highly maths driven , whereas analogue computers are more measurement of values driven]. would be more suitable for this sort of prediction.

Analog computers also are (or rather, were; see below) highly math based. The first step in building an analog computer is to develop the differential equations (math!) that describe the system to be modeled. The next step is to build an electric circuit that follows the same set of differential equations (more math!) as the system to be modeled. The mathematics of the electric circuit are dictated by the differential equations that describe each of the components in the circuit and the differential equations that describe the wiring between components.

 

The key problem with analog computers is that solving a new problem involved creating a brand new analog computer. "Programming" analog computers is a painstaking, time-consuming process. With digital computers, different problems to be solved merely require different programs. The computer itself doesn't change. That's a huge advantage over analog computing and it is the key reason that analog computers pretty much bit the dust half a century ago with the advent of digital computers.

 

Rather than a down side to my argument , this is supportive. unless, as I say you are going to use the word MATHS to swell up and take over the whole territory of physics . Perhaps for the sake of argument we should leave Maths in the deterministic, accurate predictive camp. And put probability and emergence and models and non determanism ideas, into the Physics camp .

 

This might prevent potential physics students from running screaming into the ARTS !

There is no such thing as physics without math. It is just pre-scientific story telling.

 

The real problem here is that western cultures have taken on this attitude that being at all adept at mathematics is a subject for nerds and geeks only, and if you are good at mathematics, you must be a nerd or a geek. Could you imagine a congress critter (or your country's equivalent) admitting that they can only read at the sixth grade level? Why is it acceptable for them to only be able to do math at the sixth grade level? It's not only acceptable, it's chic.

Edited May 28, 2013 by D H

[Mike Smith Cosmos]

 

As you've already been told, probability and statistics are a part of mathematics.

 

 

There is no such thing as physics without math. It is just pre-scientific story telling.

 

 

 

I really need to get a hold of this push to move maths from the previously 'Percieved public perception' that maths was ridgid , equation based, calculable, deterministic, reliable, predictive,precise etc etc., into the areas of non predictive, non deterministic, no equations, probabllistic, statistical , dealing with huge numbers, like the sort nature uses to get thing done, which I have been attempting to describe in terms of emergence, genetic algorithm, mold type solutions, with ' Dogs and Ducks ' which you say is not science , because where is the formula, where is the exact prediction?.

 

Surely you cannot have it both ways !, Or as I say, that you are inferring Maths is taking over Physics like an infection taking over the whole body. You will kill the body ! I have been saying there is an area in Physics for Language, discussion of conceptual ideas, hypothesis, speculation, exploration of ideas , which are not ready for the maths and possibly never will be, but are none the less part of physics ,( experiment Yes) and see how the universe is, yet to be discovered and understood, hopefully.

 

Prof Cox Whom I quoted in another post , recently gave a lecture to Manchester University quoting and showing a clip from Richrard Feynman where he was spelling out "the scientific method" where IT MUST START WITH OBSERVATION AND A good GUESS ,. Then you move on to experiment and proof or falsification of the GUESS. Then if the experiment works look for any maths that can be applied.

 

link http://www.scienceforums.net/topic/74345-why-are-physics-speculations-so-popular/page-2

 

two thirds don this page Lecture by Brian Cox 7.02 minutes into lecture clip on Feynman

Lecture by Brian Cox

Brian Cox

If Feynman has any credibility, after all he did do Quantum Electro Dynamics and won a Nobel Prize.

Surely what he was saying IS the very description of THIS THREAD

I rest my case . Or at least until I get a barrage reply.... ziiiing........................duck............oops! that's a bad choice of word !

Edited May 30, 2013 by Mike Smith Cosmos

[swansont]

Mike Smith Cosmos, on 30 May 2013 - 06:38, said:

I really need to get a hold of this push to move maths from the previously 'Percieved public perception' that maths was ridgid , equation based, calculable, deterministic, reliable, predictive,precise etc etc., into the areas of non predictive, non deterministic, no equations, probabllistic, statistical , dealing with huge numbers, like the sort nature uses to get thing done, which I have been attempting to describe in terms of emergence, genetic algorithm, mold type solutions, with ' Dogs and Ducks ' which you say is not science , because where is the formula, where is the exact prediction?.

Probabilities still give predictions. If I run an experiment and the theory says I should get one result 30% of the time and another result 70% of the time, I run many trials and see if the results match. I can't run it just once or twice is all, I need to have a statistically valid sample. It's still math.

Mike Smith Cosmos, on 30 May 2013 - 06:38, said:

Surely you cannot have it both ways !, Or as I say, that you are inferring Maths is taking over Physics like an infection taking over the whole body. You will kill the body ! I have been saying there is an area in Physics for Language, discussion of conceptual ideas, hypothesis, speculation, exploration of ideas , which are not ready for the maths and possibly never will be, but are none the less part of physics ,( experiment Yes) and see how the universe is, yet to be discovered and understood, hopefully.

Can you give an example of doing actual physics that does not involve math?

Mike Smith Cosmos, on 30 May 2013 - 06:38, said:

Prof Cox Whom I quoted in another post , recently gave a lecture to Manchester University quoting and showing a clip from Richrard Feynman where he was spelling out "the scientific method" where IT MUST START WITH OBSERVATION AND A good GUESS ,. Then you move on to experiment and proof or falsification of the GUESS. Then if the experiment works look for any maths that can be applied.

 

link http://www.scienceforums.net/topic/74345-why-are-physics-speculations-so-popular/page-2

 

two thirds don this page Lecture by Brian Cox 7.02 minutes into lecture clip on Feynman

 

Lecture by Brian Cox

Brian Cox

 

 

 

If Feynman has any credibility, after all he did do Quantum Electro Dynamics and won a Nobel Prize.

Surely what he was saying IS the very description of THIS THREAD

Sure. And he's disagreeing with you.

 

When Feynman says guess what the new law is, he's talking about guessing at a mathematical model — that's what a scientific law is. He then says compute. That's all math.

[Mike Smith Cosmos]

 

 

When Feynman says guess what the new law is, he's talking about guessing at a mathematical model — that's what a scientific law is. He then says compute. That's all math.

 

The reality comes AS IS . Then Guess at what Reality is comes First as a verbal Concept (model ) First Surely

 

Then you try to create a mathematical model that best suites either reality or your conceptual model of reality and compute . Second. Surely .

 

You are attempting to remove Concept, Hypothesis totally out of the picture , which is precisely what I fear !

 

What happened to the past masters on top of the Accropolis in Greece, Debating and Philosophising . Thesis and Antithesis

Edited May 30, 2013 by Mike Smith Cosmos

[swansont]

The reality comes AS IS . Then Guess at what Reality is comes First as a verbal Concept (model ) First Surely

 

Then you try to create a mathematical model that best suites either reality or your conceptual model of reality and compute . Second. Surely .

 

Conceptual does not mean free of math, and for the bazillionth time, the math requirement does not exclude other avenues of inspiration or development. But math will always be involved at some point.

 

 

You are attempting to remove Concept, Hypothesis totally out of the picture , which is precisely what I fear !

 

Not at all. Observation, hypothesis, concept are not mutually exclusive with math. It's all part of the mix, rather than being either/or. (A bazillion and one)

 

 

[Mike Smith Cosmos]

 

Conceptual does not mean free of math, and for the bazillionth time, the math requirement does not exclude other avenues of inspiration or development. But math will always be involved at some point.

 

 

 

Not at all. Observation, hypothesis, concept are not mutually exclusive with math. It's all part of the mix, rather than being either/or. (A bazillion and one)

 

 

 

 

Ah yes, But I want to see it the other way round. I want to see the idea being discussed first, The Concept developed and all the 'argy bargy'

 

Having come to some form of mutual resolution of the 'Crazyness '

 

Then the mathematichians go off and do there best to get a fix.

 

I do not dispute occasionally the maths alone will point at a phenomenon like Pauli and Dirac with neutrino and antimatter, But I have a mind that is the exception rather than the rule.

 

And I would expect occasionally NO maths may be found , at least for the moment. But nonetheless a way forward is still possible with Concept followed by hypothesis followed by Experimental proof YET with NO maths yet found to support the Hypothesis and Experimental proof. In other words Physics need not be held up by the maths, They can come along later sometimes, not always. If I get you to agree on this point I deserve a drink.

Edited May 30, 2013 by Mike Smith Cosmos

[swansont]

Ah yes, But I want to see it the other way round. I want to see the idea being discussed first, The Concept developed and all the 'argy bargy'

 

It does, sometimes. You're asking for something that already takes place, but phrasing it as if it was something new. Like someone with button-fly jeans demanding that someone invent the zipper.

 

And I would expect occasionally NO maths may be found , at least for the moment. But nonetheless a way forward is still possible with Concept followed by hypothesis followed by Experimental proof YET with NO maths yet found to support the Hypothesis and Experimental proof. In other words Physics need not be held up by the maths, They can come along later sometimes, not always. If I get you to agree on this point I deserve a drink.

 

I invite you again to come up with an example of this happening.

[Mike Smith Cosmos]

It does, sometimes. You're asking for something that already takes place, but phrasing it as if it was something new. Like someone with button-fly jeans demanding that someone invent the zipper.

 

 

I invite you again to come up with an example of this happening.

 

 

Ok I will give it a bit of thought, When I have had my drink.

[Mike Smith Cosmos]

Rather Like This is better :-

 

 

 

Than this which appears to be the case :-

 

 

 

 

Maths priority has over-run ,pushing aside the concept thinkers ! Taking their place at the frontiers of Physics .

Taking over the territory of exploration and blue sky research.

 

Instead of their role in support, validation, precision when necessary and prediction when possible.

 

Then :-

a quote by Bernard Lovell of Godrel Bank telescope in Uk

 

" the decline of Blue Sky research will bankrupt our future"

 

 

The Future of ideas ....is in ....jeapody ( cant spell either )

Edited May 31, 2013 by Mike Smith Cosmos

[D H]

Rather Like This is better :-

 

concept thinkers.jpg

 

Than this which appears to be the case :-

 

 

concept thinkers 2.jpg

 

You are creating a false dichotomy here. Your diagrams, along with much that you have said in this thread, implies that "math boffs" are incapable of being creative thinkers. That in turn is motivated by your view that mathematics is a rigid world of numbers, canned formulae, and not much else. Neither one is the case.

 

The fact is that physics and mathematics have long been intertwined. Sometimes physics has pushed the boundaries of mathematics. Other times new mathematics have allowed physicists to push the boundaries of physics.

 

Your rigid view of mathematics as comprising numbers, canned formulae, and not much else is simply not the case. In fact, professional mathematicians can go for months, years, and entire career without using algebraic formulae. The only times professional mathematicians do touch numbers and formulae are when they have to do something mundane such as balancing their bank account statement or paying a restaurant bill.

 

There is plenty of room in the sciences for people who think calculus is hard mathematics. (It isn't. Calculus is what budding mathematicians and physicists learn when they first enter college, if not earlier.) Vast portions of the life sciences and social sciences are largely void of mathematics. Not in physics, however. There is no escaping the deep entanglement between physics and mathematics. If you aren't doing math you aren't doing physics.

Edited June 3, 2013 by D H