Can Science be different? Maths says "NO'

I agree with you:
<<Naturally, we can expect that a new revelation based on holism will lead to a Theory of Everything...>>

Have you ever dealt with the problem "with a hundred-year-old beard" - ontological basification (justification, substantiation) of mathematics, and hence knowledge in general?

Jose Koshy

Rigorously argued essay. But my question is, how can an immaterial, motionless platonic realm of mathematics govern a material world that is made out of basic properties that do not depend on any mathematical law? For mathematics to be able to dictate in the physical world what is allowed and what isn't, it would at least need a logical link between the basic properties of matter and mathematics to ensure that matter logically obeys the mathematical laws; otherwise the hope for a holistic description may be doomed, since the whole framework wouldn't be a logically closed system. Or it would need a causal link between the immaterial and the material to establish such a logically closed system.

As long as you can't answer these questions, your assumption that mathematics' existence is eternal, residing beyond space, time and matter, in my opinion can be as well viewed as another “virtual demon”. The latter then is able to justify not only the existence of a “theory of everything”, but also is used to believe in the unavoidable discovery of that theory in the future. But what if humanity destroys itself before it even could discover that theory? That would contradict your belief that nature, hence human scientists, are simply determined by nature to make that discovery. For nonetheless assuming what you assumed, you therefore also had to assume that humanity will not destroy itself at any point in time. I think such an assumption, based merely on the belief of a platonic realm of mathematics could well be also termed a “virtual demon”.

"Even now, we are able to model science based on discrete
and continuous mathematics. This is possible because discrete entities can create
continuous patterns and a continuous entity can create discrete loops. "
Yes your idea is good and there is proof: for high quantum level the results are the same in classical measures (Bhor principle of correspondance). Bhor principle of correspondance is also a quantum principle: for low quantum levels there is also results emergent from classical physics.
To made a theory of everything the base is discretness modeling. A theory of everything is unique so the base of discritness will be unique. So we should conclude that is lucking a new constant in physics leadind to a new law such us the energy of vacuum. Planck system is not the good system of discritness we search because gravitation and so constant G is emergent.
I love this article . It speakes about a theory of change and the begining should be mathematical modeling.
But I don't agree with the author that if we get "the theory of everything" than perhaps that will not lead to new technology. The new theory will lead to more equality between humans, how, I don't know.

Thanks for your clearly written, accessible essay! I have a question, based on some of what you say (I've excerpted a couple of lines from your essay which I think encapsulates what I am referring to):

"From a philosophical point of view, beauty and logic are essential for any theory in physics. Beauty implies that there should be only one theory; it should be simple and complete with minimum arbitrariness."

I understan

Hi, Jose Koshy . Your essay generates interesting reflections. In the context of science I see math as a tool that participates in the scientific method. So far, Physics has described nature as particles and/or waves, thus applying the appropriate mathematical sets to this context, and here arithmetic has an excellent fit. I wonder if it is possible to still do science with a view other than pure logical analysis. I try to stimulate discussions on this in my essay "More diversity and creativity for a different science", which I invite you to read if interested.

So, when does history end and math begin? Or is religion in the math, too? Then we have the math predicts religion
But: Only nothing real in the way of objects of worship? Surely, if everything is just math, then the existence and nature of God should be in the equations.
Of course, using the logic developed for operations on real (number) systems might not be completely helpful when dealing with the Complex and higher number systems.
As our current understanding with QM seems to indicate.

Anyway, the question becomes: If everything is just algorithm, will the algorithms labeled "Scientists" get off their butts
take responsibility for all of their- checkered past, and take their part in saving the planet. Or do they hope to feed from the silver spoon indefinitely, considering science's failures fail those people as well.
And those successes the wealthy are and are willing to pay for?: The planet cannot afford.
Sure, scientists will be among the last to be pushed overboard. But. The boat is sinking,anyways. (Partly the fault of science and scientists.) And even if the boat doesn't sink, (It will.) it doesn't mean science has a future with them. The mess that is actively being made of public education is drastically reducing both quantity and quality of replacement candidates for future science. Never the increasing up front costs to most aspiring scientists.

Maybe the Masters of the Universe, AKA "your corporate sponsors," many of whom are also the corporate sponsors of 'privatized' 'education,' don't really think science has much of a future.

And certainly no future on their terms.

My complaint is very specific. How many of you have heard of S matrix theory by Geodfrey Chew ? S matrix theory if the complexities of its input output procedures was unfortunately abandoned due to the limitations of how to solve its Input and output parameters and equations. S matrices have re appeared in a ,modified manner in string theory. Now if we had the power mathematically to SOLVE the Geodfrey Chew set up where would particle physics be today ? Fact is, that it was a promising direction which was abandoned. But what if the math had been more able to work with it ? We might see a very different Particle physics.
This is not the only examples. Much of science we have is due to working with the limitations, real and imagined as to solving highly NON LINEAR equations.
;ITs tough. Each generation creates its own work arounds . That procedure of work arounds is why I say bollocks to the supposition as of science being totally rigidly fixed in one direction. Also the choices between digital and analog electronics highly influences detectors and all that for data analysis.

While I agree with you “that a new revelation based upon holism” is needed, I doubt that it will lead to anything close to a Theory of Everything. I find your argument rather simplistic in its assumptions, without the detail of historical accidents (consider James Burke's 'Connections' TV series) or the part of mathematics that is creative, not determined.

Mathematics and logic have their own history, evolution and challenges. It took over 2000 years to realize there was something beyond Euclidean geometry (which impacted science). Mathematics has only generated three levels of numeric systems to represent numbers. There are counting number systems, like Roman numerals, which represent Integers; ratios/fractions, which represent Rational numbers, and our current positional numeric systems (e.g., decimals, octals, binary), which represent Real numbers. We know about Complex numbers, yet we do not have a numeric system capable of representing them (as single values). In fact we currently believe this is either not needed or not possible. Finding one could have a large impact on both mathematics and science (and how many more Number and numeric systems might there be?). Yet representational systems involve creative acts and are not pre-defined symbols that must look a certain way. Measurements, values, what we refer to as ‘Numbers’, really are symbols for numbers and not the numbers themselves. While simple arithmetic might be the same regardless of the symbols used, the creative aspect of devising appropriate symbols for mathematical concepts has been crucial to the development of mathematics.

I would challenge your concept of ‘complete theory’, especially for mathematics. While one or a couple of mathematical theories can provide a complete description of one theory, each ‘outside’ theory will need to be completed by some other outside theory. Strictly looking at Godel’s incompleteness theorem, this requirement of completing a theory with outside theories implies it goes on ad infinitum - which would suggest there is no single complete theory possible. If science is simply built on mathematics, then the same would also hold for scientific theories.

A true ‘Theory of Everything’ - the ultimate theory - should be able to explain and predict any activity down to any level of accuracy desired. This would mean it could even explain and predict singular activities - that happen only once. However, there is the problem of scientific experimental results being “consistent” using statistical results. When all laws and theories require multiple experimental results to agree (to some level of accuracy), there is no room for singular events. Even if we rule out singular events, the statistical nature of results means the exact details of any one of the results in an experiment are discounted. Experimental results always have an error term beyond which individual results are not considered important. This implies that our current experimental method cannot produce theories accurate to any level of detail for specific events. This is not a question of experimental accuracy, but of the methodology used in the scientific experimental method. It works fine, while we are a long way from such a Theory of Everything, and statistical averaging provides ‘consistency’, however if we start to approach such a theory our methodology will fail us. This would suggest we are still a long way from such a theory.

We are actually close to a theory of everything. There's only so much math it could be, and pretty much all the important math has been discovered. It's mostly a matter of assembling into a coherent whole. A "Phenomenology of Mathematics." And it helps not to assume there are no constraints just because you don't know what they are. Space beyond "The Universe" where all those other universes can exist? When you don't even know what makes space and the shape of space in this "Universe?" When there is no "Out" you can point to? When you don't know the WHY? of space time?

This sounds a bit like the quote erroneously attributed to Lord Kelvin in 1900 “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.”

Not sure where you get the idea that "pretty much all the important math _has_been discovered" - the Mathematicians I know about do not have that perspective.

I am not sure where the connection between group theory and the ultimate theory of physics comes from. Mathematics involves concepts beyond groups (mathematical fields, rings, etc.), so this connection would seem to be too simplistic (especially if science builds off of mathematics).
More importantly, the Monster Group is limited to Real numbers, when we already know of complex numbers. Part of mathematical progress is extending existing concepts over additional domains (polynomials with integer co-efficients and positive exponents; polynomials with rational or real co-efficients; polynomials with rational, negative, and real powers - groups and fields over the integers, over reals, etc.) Since we are still working on expanding to the complex numbers, I think there is space for quite a bit more new mathematics, upon which newer science can be built.

Charles St Pierre
RE “But here's a speculation for you: Is the Monster Group the most complicated thing, or at least sets the limit on, the most complicated thing, which can exist?”:

There is no connection between group theory and physics. The only real-world numbers that could be said to exist are the numbers obtained from measurement of (e.g.) relative position or mass. The Monster Group is not the most complicated thing that can exist, simply because it doesn’t really exist at all, except in the human imagination, like fairies at the bottom of the garden.

Myrtle Coral concludes: “Thus we can conclude that our science, its evolution, its philosophy, its institutionalization, etc. are deterministic, and cannot be different from what we have seen. As far as we know, the universe is built of the same 'stuff' as we are, and so the science and the path of evolution of science will be the same for any aliens.”
I would argue that consciousness trumps determinism, and as a consequence the path of evolution of science can be different, and will be different when we meet other galactic aliens.
I previously commented that Lovelock and Margulis developed a hypothesis they called Gaia, in which living organisms interact with their inorganic surroundings on Earth to form self-regulating, complex system that helps to maintain and perpetuate the conditions for life on the planet.
I wonder if Gaia could be part of the Universal consciousness? Could it extend to whole galaxies as well? And I suggest that with faster than light communication a universal “being” may be possible.

Lorraine Ford

Lorraine Ford There is no connection between group theory and physics.

So I think your assertion needs supporting evidence. Or proof. Which ever is more convenient for you. Until then it is more of a- speculation, unsupported by fact.

Charles St Pierre
I'm saying (in my essay) that numbers have no inherent category, i.e. numbers have no inherent relationship to anything else in the physical world, therefore they don't and can't exist. I'm saying that the only numbers that can actually, physically, be said to exist are the numbers that are associated with a genuinely existing, measurable, physical category like relative position or mass. Other than that, and having studied mathematics, I'm quite happy to say that numbers and groups, and indeed most of mathematics, are merely a figment of the human imagination. The human imagination is interested in relationships between things, hence mathematics. The world is built out of genuinely existing relationships between things, hence physics.

Physics is about a world that actually exists. It is not up to me to prove anything, it is up to you to explain what is the difference between what actually exists in the world/ universe, and what only exists in the human imagination.