Dreams

Welcome All.

Welcome to the Alti Math FB group. I have created the group to discuss alternative maths. Alternative maths are the new mathematics created to complement the current mainstream modern math which is based on the set theory. The current math is in turn succeed the classical math based on the concept of one dimensional number and flat 3-dimensional Euclidean space. The classical physics is based on the classical math. The modern relativistic and quantum physics is based on curved 4-dimensional Riemannian space and the linear algebra of operators on the infinite dimensional complex Hilbert space.

Realizing Einstein's Dream

Now, we are in the post-modern era where there are 5 equally true theories of fundamental superstrings vibrating in the compactification of the flat 10-dimensional Minskowskian space.

Well, that situation is in harmony to the spirit of postmodern view of plurality of relative truths. However, the the Einstein's modern dream is to find the one and only one fundamental true theory is still lingering in the minds of 21-st century particle physicists. For example Edward Witten , in the spirit of Dirac who unified the 2 equally true quantum mechanics (the Heisenberg matrix mechanics and the Schrodinger wave mechanics) in the first quarter of the 20-th century, tried to unify the 5 superstring theories with one supergravity theory into one 11-dimensional supermembrane theory which he called the M-theory . The M-theory unify the four fundamental forces of nature at a deeper level: at the distance smaller than Planck length and at the high energy beyond the Planck energy.

In fact, the M-theory is greater than the dream of Einstein which is only trying to unify gravitation and electromagetism. Last century,. physics has finally unify the electromagnetic force with the weak and strong nuclear field in a theory of elementary particles called the standard model. M theory is trying to unify the theory of gravitation with the theory of electro-magneto-nuclear forces. The trouble is M-theory as the generalization of superstring theory predict many unknown super-partner particles of the currently known particles. So probably there is a new mathematics for the M-theory to eliminate the unobserved particles. This new math will save M-theory from becoming a kind para-physics rather than physics.

Sometimes, the M-theory is called matrix theory. This reminds us the Heisenberg matrix formulation of quantum mechanics theory which is complemented by the Schrodinger wave function formulation of the same theory. Currently, the matrix theory of Witten is complemented by the loop theory of Ashtekar . Lee Smolin is trying to unify both theories in a theory of spin network using the Jordan algebra. Meanwhile, John Baez is expecting the unification of M-theory and loop quantum theory with the new general high dimensional algebra called n-category theory. But Baez has a grander vision where he sees that physics and topology is like logic and computation. He hopes that category theory is the deeper unification between those four different disciplines.

Dreaming Bigger Dreams

Now, for a long time, in the the internet I watch those different attempts to unify sciences. If the unification is realized, I think there will be a new scientific revolution, but the revolution has many different directions. In fact there are many alternatives development of the new physics based on different new extended mathematics. For example Rugerro Maria Santilli has discovered the current mathematics is only a part of a greater mathematics. The new mathematics is structured hierarchically into four systemic levels: the current mathematics, the iso-mathematics, the geno-mathematics, the hyper-mathematics each with its own isodual. The four levels is differentiated through the different lifting of the ordinary multiplication of two numbers and matrices. Santilli hopes that the new greater mathematics will unify physics, chemistry and biology. In fact Santilli started the science revolution by reforming the quantum mechanics by turning it to what he called hadronic mechanics and that distressed mainstream physicists.

That is the story of future revolutions of science. The Santillian and Baezian dreams are not contradicting each other. They are complementing each other. Consequently, I think the category theory has to be generalized so it can adapted to the expansion of mathematics as seen by Santilli. So, the Santillian dream will be a deeper foundation of unification of different sciences. Ultimately, we will have a much greater dream than Einstein's dream who wished to unify different fundamental forces in physics. Far from just unifying physics, the new dream will unify different sciences with the new generalized mathematics.

A logician who tried to generalized mathematics is Charles Muses who develop the concept of complex number as two dimensional number into a ten dimensional numbers which is called the hypernumbers.. He hoped that the hypernumber theory will unify physics with psychology. Another mathematician who is interested in unifying physics and psychology, Ben Goertzel , is using an 8 dimensional extension of complex number, used by quantum physics, octonion as mathematics of psychology. Octonion is one first two levels of musean hypernumber. Octonion algebra is also just a member of series of hypercomplex number which is known in the mainstream math as Cayley-Dickson algebras.

In the Cayley-Dickson sequence of the of ever doubling dimension of numbers, quaternion the 4-dimensional number, is between the 2-dimensional complex number and the 8-dimensional octonions. Above the octonions there is a system of sedenions, the 16-dimensional numbers. Above them there are 32, 64 and generally 2^n dimensional numbers which like the sedenions behave very strange where different non zero numbers can multiply themselves into zero. The algebraic Cayley-Dickson has a curious property. Every doubling of the numeric space dimension weakens the compositional properties of the number system. Complex number system is not well ordered. Quaternions system is loosing the associativity of multiplication. Octonions are non-commutative like quaternions but they loose the associativity of the quaternion. Sedenions are non-commutative and non-associative like octonions but they are loosing the property of unique multiplication because they have zero divisors.

Ultimate Dream

Well there is a philosopher sociologist, Kent Palmer, who identified the sedenions and higher dimensional CD system as the mathematics that can be used to the science of the enviromental meta-systems surrounding the reflexive social systems which in turn can be formulated with octonions and the less complex autopoietic living system with quaternions and dissipative chemical system with complex numbers. So the whole Cayley-Dickson numbers describes the multi-level complexity of the holistic nature not just the physical one. The interesting part is that Kent Palmer see system and metasystem is a pair of eight levels of schemas from the facet to the pluriverse which described the whole reality, so set-based mathematical n-category theory must be complemented by the mass-based mathematical n-blob theory. Both n-dimensional theories can be synthesized into n-aggregate theory which he hope can be used to describe the whole reality.

Ben Goertzel and Kent Palmer are the friends of Tony Smith. Tony Smith is a lawyer who is doing physics in his spare times. He has an alternative unified particle physics theory complementing the M theory and loop quantum gravity. He called his theory as VoDou physics. The D4-D5-E6-E7-E8 Voudou physics is a physics model of particles in 8 dimensional octonionic space-time rather than physics of super-membranes in 11 dimensional space of M-theory. He discovered the parallelism between his unified physics theory and the Vodou religion in the Africa. And he believes that many different system in different part of the world is the degeneration of the scheme of Ifa religious oracle. That's why he was not so surprised when he discovered many aspects of his theory is numerically parallel to the commandments of Jewish prophet Moses , the philosophy of unity of Muslim mystic Ibnu Arabi , the 16 schemes of Christian Ramon Llull , the Taoist I Ching oracle of the Chinese, the Hindu Vedic math of the Indians. The source of similarities is the Clifford algebras at the foundation of his unified theory. So he believes of the ultimate unification of the reformed postmodern science and the ancient religious wisdoms.

My Dream

Well, the infinite hierarchy of n-categories and their generalization, Palmerian n-blobs and n-aggregates, the finite hierarchies of Santillian 8 new maths, Charles Muses 10 meta-dimensional hypernumbers, the infinite hierarchies of dimensional doubling of Cayley-Dickson algebras and Clifford algebras are the examples of alternative mathematics. Many of them are outside of the mainstream mathematics. All of them is potentially able to bring revolutions within of the mainstream science. They will revolutionize science by bringing the so-called paranormal phenomena into the plethora of normal natural phenomena of the conventional science. They will make science becoming more comprehensive. Hopefully some of them will become the mainstream mathematics. That is my high hope after reading them in the great cyber-book Internet which is comprehensively indexed by google search engine. That's why I create the Facebook group alti math. Join me celebrating the metamorphosis of the restricted conventional modern science into the more comprehensive future post-modern science which is now called pseudoscience. Be creative to find new alternative maths. Report your discoveries here: the FB group Alti Math.

Thank you.
best regards
Arma.