Selasa, 19 Juni 2018

From Big Science to Deep Science

Physics beyond catching a mouse in the dark: From Big Science to Deep Science
(or Discerning Spirits in Modern Physics)


                                                   Abstract 
The Higgs particle has been detected a few years ago, that is what newspapers tell us. For many physicists, the Standard Model of particle physics has accomplished all the jobs. The game is over. Is it true? Then some physicists began to ask: how to go beyond the Standard Model. But supersymmetric extension of the Standard Model has failed. So if you feel that theoretical physics gets boring, you are not alone. Fortunately, there is a good news too: a new generation of physicists begin to do table-top experiments in their basements, so we can expect new results later. But how the future of physics will look like? This article discusses this question, starting with relation between mathematics and physical reality. This article is written from a perspective of a mathematician and a cosmologist.*


"There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy."
- Hamlet (1.5.167-8), Hamlet to Horatio


Introduction: The art of catching a mouse? 
Probably most of you have read Einstein's biography, perhaps out of mere curiosity or your effort to find out how to unlock the secrets of his brilliant mind. You may have read about how the young Einstein received a gift of math book from a smart medical student, who gave a quite witty remark to him:

"Mathematics is like catching a mouse; you run after the mouse until it gets into a corner of the room. Then you get it." 


Provided that such a remark was true, it is quite understandable that Einstein's mind process was shaped more or less along that line of thought, i.e. how to seek after the eternal mouse, be it in microworld and also in cosmology.
But we can ask: Is it really the correct way to think of the role of mathematics to comprehend Nature?
History tells us that Einstein began his science career by writing up 3 papers in the same year of 1905, including an exposition on quanta of light and also on special relativity theory. Despite opposite comments by senior physicists at the time, including Max Planck, the three papers have been regarded as the cornerstone of modern physics. Nonetheless, recent analysis by Steven Weinberg and others show that Einstein's papers actually contain some errors.(2)
So, this problem leads us to ask a deeper question: "how effective mathematics is to describe physical reality?"


Beyond Platonic world
The question of effectiveness of mathematics in physical sciences has been discussed by many physicists, notably Eugene Wigner (1). And the question was brought to one of us (VC) by a senior professor of physics several years ago (see acknowledgment). As far as he can remember, he (VC) only outlined that perhaps we need to use more advanced geometry, such as fractal geometry (c.f. Benoit Mandelbrot). Yes, there are scientists who hold a view, that we can only expect new physics if we begin to explore new mathematics (Dirac's view).
But the problem may be much deeper than what it looks like at first glance. Perhaps it is true, that mathematics is the art of catching a mouse. But most of real physics problems seem to suggest that they are so delicate, that it may be analogous to "how to catch a black mouse in a dark room, and sometimes you don't even know if the mouse is in the room or not." (see "Mouse hunt" movie)
While most physicists believe that they can catch the mouse with the latest development of mathematical apparatus, there are others who think that probably there is problem with relying too much on such apparatus. Let us give a quote:

"Derek Abbott, Professor of Electrical and Electronics Engineering at The University of Adelaide in Australia, has written a perspective piece to be published in the Proceedings of the IEEE in which he argues that mathematical Platonism is an inaccurate view of reality. Instead, he argues for the opposing viewpoint, the non-Platonist notion that mathematics is a product of the human imagination that we tailor to describe reality.

So if mathematicians, engineers, and physicists can all manage to perform their work despite differences in opinion on this philosophical subject, why does the true nature of mathematics in its relation to the physical world really matter?
The reason, Abbott says, is that because when you recognize that math is just a mental construct—just an approximation of reality that has its frailties and limitations and that will break down at some point because perfect mathematical forms do not exist in the physical universe—then you can see how ineffective math is.
And that is Abbott's main point (and most controversial one): that mathematics is not exceptionally good at describing reality, and definitely not the "miracle" that some scientists have marveled at. Einstein, a mathematical non-Platonist, was one scientist who marveled at the power of mathematics. He asked, "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" (3)

Allow us to emphasize a part from the above quote:

"just an approximation of reality that has its frailties and limitations and that will break down..."(3)

This statement gives us some clues on how we should better think of mathematics. Yes, mathematics is useful for numerous problems, but as with human being himself, it is bound to limitations, contradictions etc. This problem of mathematical consistency has been discussed bluntly in Godel's famous incompleteness theorem.
In other words, provided we accept such a non-Platonic view of mathematics, we should keep being humble. And even if sometimes our theory gives out a series of correct predictions, it does not necessarily mean that we already hit the jackpot of physical reality.
But the problem is more acute because numerous theoretical physicists (except a few), hold a position which can be expressed better in a following joke:

"An engineer considers that his/her equations approximate reality,
A theoretical physicist considers that reality approximates his/her equations,
A mathematician doesn't care what is the difference."

We can observe easily how so many physicists hold such a viewpoint on reality, in their sticking adherence to models, as if the models themselves hold all the answers. This is what happens with the so-called Standard Model of particle physics and also the Standard Model of cosmology. If there are new observational findings against those standard models, then they will be systematically discarded, or else new fancy words will be created, including dark energy, dark matter, and numerous ghosts here and there.

Such a deflecting pattern has become quite a norm in a very large industry called "Big Science," with all their bells and whistles. And there are those illustrious figures who tried to humiliate anyone who dare to ask questions beyond certain (often unspoken) permissible limits.
Long time ago, the late Prof. Robert M. Kiehn from Houston University wrote an email to one of us (VC), that many physicists tend to forget that what they got are only models, i.e. an approximate and tentative description of physical reality.
In retrospect, perhaps the root cause of such a strict adherence to those models can be traced back to blind acceptance of Einstein's photon model and also special relavity theory. A deeper look into those two theories will reveal that they are problematic. For example, special relativity theory rejects the notion of ether, despite some experiments showing ether wind can be observed. (Einstein later on reinstated the ether in his public lecture at the Leiden University, 1920).
Therefore, perhaps now is the right time, to distinguish two ways of doing science: (a) Big Science, emphasizing empiricism and operationalism, and (b) Deep Science, in our attempt to discover the hidden layers of physical reality.


Scaffold to the moon
There is another philosophical question related to Platonic view: "Do we live in a mathematical universe?"
Although this question appears simple, the answer is not. Beyond Platonic and non-Platonic view as we discussed above, we can think of a variety of possible answers, to mention a few:
- Neo-Platonic view; for example the dodecahedron universe model by Prof. Luminet et al from Observatoire de Paris, Meudon.
- number theoretic model of universe (from Pythagoras: “The world is a number”.)
- set theory view
- geometric view
- string theory inspired models
- adhesion universe model
- Voronoi tessellatice model
- cellular model, e.g. Konrad Ranzan : www.cellularuniverse.com
- soliton model, e.g. our recent paper on cellular automaton KdV model
- and so on

So, which one to choose? Our opinion is: you can start with a few assumptions which you find convenient with, work them out seriously. But after your paper has been published, keep on being flexible in mind with other possibilities.
There are a number of analogies which advise us to remain humble in our journey to decipher the hidden layers of physical reality, e.g. the story of an elephant and five blind men, that you may have heard quite often.
And there is also a Zen wisdom saying: "The wise man points his finger to the moon, but the fool only sees the finger not the moon." The message here is: our theory is like a finger. The theory surely helps us to see the moon (Universe), but we should not forget that it is not the Universe. (It is worth noting here, that you are not a good physicist unless you can distinguish the difference between a finger and the Moon)

Or perhaps you do not like Zen koan, then there is another analogy (held by Murray Gell-Mann), e.g. that his theory helps him like a scaffolding, in order to describe certain physical phenomena. Afterward, the scaffolding may be not necessary anymore.
And we can develop our theories more and more advanced in order to explore the hidden reality of Nature. We can consider this approach as: "scaffold to the moon." We hope that the phrase "scaffold to the moon" captures what we mean with distinction between big science and deep science.

(a) When your equations have been confirmed by observations and experiments. Voila! Yes, it is normal that the first thing that comes to your mind is to celebrate it with a champagne or a bottle of vodka. The accumulation of such self-celebrating physical experiment confirmations lead to big science.

(b) But that is only a first in the iteration steps in the scaffold. Perhaps one or two years later, you figure out that there were too many assumptions or logical flaws in your equations, and you find a better and simpler way to figure out the hidden structure of Nature. That is Deep Science. Feynman once remarked something like: "the faster we find out flaws in our theory, is the better, because it will lead us to move one step forward."

The Deep Science is quite comparable to Deep Learning, i.e. the merging between Machine Intelligence and Big Data. It becomes crucial in studying physical phenomena, because the data involved is getting very large. One or two decades ago, a PhD student in astronomy may need to analyse a few Gigabytes of data, but soon it reaches Terabyte scale. In the same way, it is not enough to find the logical structure in studying cosmology. We should also learn its pattern. After all, mathematics is not all about logic and proof building, but it is also about pattern recognition.
Two things we should keep in mind:
- physics is more than an acrobatic juxtaposition of latest trend of theoretical jargons
- mathematics is more than a semiotic game of symbols and operators.
In other words, mathematical language is required, but that is not the goal. If you want to find the light at the end of the tunnel, you should ask different questions, and think differently.


The story of a cat tied to the pole
Probably you are an accomplished theoretician. You know all tricks of the trade. You have done all marvellous tasks: group it, geometrize it, knot it, knit it, curve it, gauge it, leave it. But somehow you feel that you missed the real answer. You want to find out the Holy Grail of Nature, the Ancient One. Now, where shall you find the answer?
Allow us to tell you a story:

"Long time ago, a Zen teacher in a distant village was disturbed by voice of a cat in his house, therefore he ordered his students to tie the cat to a pole in the backyard, so he could pray. Decades later, long after that teacher has passed away, all his followers hold a tradition to tie a cat to a pole in the backyard. And they also publish many books discussing spiritual advantage of praying beside a cat."

That is an old story in a book written by Father Anthony de Mello, a wise priest from India. The lesson is simple but it has deep message: "a temporary solution for certain problem can be a cult, worshipped by future generations of ignorant followers."
You may laugh at this story, but let us give you four examples to show that the same problem actually plagues in many areas of our modern life:

a. Max Planck. In a desperate move, he used a partition function in order to solve the blackbody paradox. But his artificial trick was hailed as quanta of energy by Einstein in his 1905 (photoelectric paper), a development that Planck himself remained skeptical. Then photon was accepted as real entity by later generation of physicists. In recent years, other physicists prove that Planck's blackbody law can be rederived by assuming monochromatic wave. Timothy Boyer also derived Planck law by stochastic electrodynamics. Ask this question: does photon really exist or is it just another "cat tied to a pole"?

b. Albert Einstein. Einstein developed his general relativity theory with the help of a friend, Marcell Grossmann. But he was fully aware that his castle assumed many things, including assumption of continuous structures. We can argue that it is actually possible to develop various new models of cosmology starting from discrete space, instead of continuous space assumption. Ask this question: does spacetime curvature exist or is it only in your mind?

c. Murray Gell-Mann. After a few years learning group theory, Gell-Mann developed further Sakata's model in order to explain some experimental results at the time. And he called it quark theory. But Gell-Mann himself never considers quark as real entities, other than a mathematical device. But Zweig and Yuval Ne’eman developed a theory assuming real quarks. Later on, experimenters realized that quark cannot be isolated. There is whole subculture in particle physics devoted to confinement problem. Ask this question: what is the point of confinement problem, if all quarks are just mathematical artefacts?

d. Abraham Maslow. He was father of humanist psychology at the time, who was famous for his hierarchy of needs. Probably you have read that you should fulfill basic human needs first (food, clothes etc.), then begin to meet education and healthy needs and others too, and finally you seek actualization of your life. Millions of people followed Maslow's hierarchy advise. (5) But the story goes that later in his life, Maslow regretted on how his theory was used. Of course, if you think rather deeply, you will find out that if you follow Maslow's receipe, then by the age of 60 you will get no more energy to do actualization, to live meaningfully, let alone to do something good to your community. It is much better to do things the other way around: begin to seek God's purpose in your life, find His Kingdom and His truth, and you will have a purpose in your life. Then gradually God will help you to fulfill all your needs. But unfortunately only a few people can see the way, most people only follow Maslow's hierarchy blindly, and they forget that is just a hypothesis. That is "the road less travelled."


Concluding remarks: Another day in Paradise
Perhaps the true purpose of doing mathematics as well as logic is to purify our mind. To remove all the dusts. But they have limitations too. As Hui Neng once wrote (he was one of the great Patriarchs of Zen teaching) as follows: "Where is the dust? There is no such thing as dust, except in our mind."
In other words, while it is true that it takes years to get mathematical mastery in a field, may be the right answer lies somewhere else. Therefore you need to ask a variety of different questions.
But don't think outside of the box, either.
Box? What box? There is no box except in your mind.
Set your mind free. Unleash and generate new ideas as much as you can. As a title of Rod Judkins's new book: Ideas are your only currency. (6)

Let us close this rambling note with paraphrasing a wisdom saying:

"To err is human, but to generate original ideas is divine."


Postscript:
Allow us to add a few more words in the end of this article. You may learn somewhere that to become a good scientist, you should have great ambition to dominate the entire world. You should be fast like a jaguar, strong like a gorilla, and cruel like a shark. If you follow such an advise, no wonder you gradually become a beast. And that is what they urge you to become in numerous universities. If you are a professor, you are forced to publish 25 papers and may be more each year. They call it "publish or perish" policy. Actually that is a Draconian social "darwinism" policy.
And the plan is to make your life miserable like in a jungle. No wonder, many leading professors have no time anymore to give lecture, because they are too busy to catch up their schedule. If you follow this story in USA, you will find out why the scientific productivity in USA tends to gradually decrease, as a recent article in the Economist magazine reports. (www.economist.com)

One of us (FS) has his own story to tell:
"Myself, when I came to America I was advised to apply my math, so I changed from abstract algebra and number theory to neutrosophic set/logic/probbaility, to multispace (since our world is composed of many spaces), hybrid geometry (called Smarandache geometry) where the axioms are valid in some points and invalid in other points.."


But the truth is, you can do science in entirely different way:

Find the inner peace, feel the rhythm of your heart, know how much God love you, and begin to love your family and your neighbors. The truth is not out there, but it is inside you.
Instead of living like an animal in a jungle, and doing cruel things to your colleagues, try to listen to a soft voice of the Old Friend: "You can walk with Me in Paradise, right now."
Yes, contrary to what most people tell you to become a mean and cruel animal, or to dominate the whole world, you can ask: "What is the benefit of dominating the world, if I lose my life? Where can I find purpose and happiness?"
At the end, if you begin to seek peace and happiness for you and your neighbors, hopefully you will find that you live not in the jungle. Instead, you will find that this is just another day in Paradise.

That is what we mean with Deep Science.
Deep Learning. Deep Meaning. Deep Purpose. Deep Life. Deep Spirituality.
Don't live a superficial life.

Hopefully you get our message.
God really love you.


Version 1.0: 18 june 2018, pk. 7:41
Version 1.1: 18 june 2018, pk. 16:37
Version 1.2: 18 june 2018, pk. 21:19
Version 1.3: 21 june 2018, pk. 12:03
VC & FS 

(Don’t follow us, because sometimes we got lost too in this Labyrinth. Follow God only.)


Ackowledgement 
One of us (VC) dedicates this paper to Prof. Liek Wilardjo, an emeritus professor of physics, for his deep insights not only about philosophy, physics, but also the wisdom behind wayang kulit (leather puppet show). And special thanks to Prof. Bambang Hidayat, a senior professor in astronomy, for sending two articles from Nature magazine. All opinions presented in this article are our responsibility.


Endnote:

*In this occassion of FIFA World Cup 2018 held in Russia, one of us (VC & FS) would like to send greeting to a number of colleagues in the Institute of Gravitation and Cosmology, RUDN, Moscow: to Alexander, Mikhail, Kyrill, Vladimir, Vitaly, Anastasia, Tonya, Yuri, Sergey, Milena, Igor, Vsevolod. Also to Dmitri, Larissa, and other friends who live there. Enjoy the party, feel the rhythm, and have a nice summer. God bless you.


References:

(1) Eugene Wigner. On the unreasonable effectiveness of mathematics in natural sciences. Comm. Pure and Applied Math., 1960. Url: https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.3160130102
(2) Goldhaber and Ohanian's comment on Steven Weinberg's article on Einstein's mistakes. Physics Today, 2005. Url: https://ftp.rush.edu/users/molebio/Bob_Eisenberg/Reprints/2006/PhysicsTodayLetter2006.pdf
(3) Lisa Zyga. Phys.org, url: https://phys.org/news/2013-09-mathematics-effective-world.html
(4) V. Christianto & F. Smarandache. On Maxwell-Dirac isomorphism. Prespacetime J., june 2018. Url: http://prespacetime.com/index.php/pst/article/download/1425/1389
(5) 
https://en.m.wikipedia.org/wiki/Abraham_Maslow
(6)Rod Judkins. Ideas are your only currency. https://www.hodder.co.uk/books/detail.page?isbn=9781473640061
(7). John D. Barrow. Godel and Physics. https://arxiv.org/pdf/physics/0612253.pdf






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