No one knows how nature constructs information or even how does it process. But we humans have created a giant resource of scientific formulations. We feel that the extent of complexity that we have enriched, would not have attained, had we known the true form of information in nature. The science would never have been so complex had we knew how information actually looks like in nature, and how does it integrate. Not just scientific theories, often we talk about data overflow. What is the origin of this Big data? Repeatedly analysts are arguing that we add the world full of knowledge at every six months, but count bits. “bit” does not quantify knowledge. Our perception is that we did not measure information properly, so it grew in an uncontrolled manner like cancer. What is that mistake?
While experimenting with biomaterials we have seen that nature encodes information as changing 3D geometric shape encapsulated inside a sphere. If necessary, it adds new geometric shapes inside its corner points. Driven by Turing philosophy existing scientific formulations read any systems information as a string of a linear set of events. When the topology is used in a scale free manner, by nature, at limited scale linearization works, but not when topology becomes complex. There are ten reasons we have outlined here, why linearization is fatal. Note that the science experienced in terms of topology is new kind of approach to seeing the same science, this is not a rejection of the existing science, but replacing the culture of the methodology of working with the old science culture. Of (i) basic assumptions, (ii) derivations keeping a close eye to derive the expression that would explain the result, (iii) make expressions as complex as possible to add accuracy to the experimental results, (iv) correct basic assumptions if major changes are required.
- Linear observation is non-real, superimpose of two world, one below, one above: When a topology is linearized, we consider that the corners of that topology are not changing, interacting. They are static and absolute. But in reality, every point has a topology inside and it is part of a higher topology. The higher and the lower topologies regulate it, any topology that we observe is a combined effect of the two, the reality is an illusion. When we measure and linearize we lose the cause and read an effect which does not contain any information of nature.
- “bits” to be replaced by elementary topological structures: When we linearize any event happened in nature and then integrate it linearly, we consider that every single event happening in nature is identical fundamentally, it is made of switching between “yes” and “no”. This is highly unlikely that at the elementary level everything is identical. Physics teaches us that there is a fundamental set of symmetries of topology (number of polyhedron that we can create is not infinite) and that is now units of information.
- Two body to many body system transition is fatal, we need topological morphing model to replace it: In creating information architecture in science, we take a stream of bits, but afterward, we use black box methods to reconstruct the models for science. In any physics theory, we consider that an elementary number of particles that exist in this universe is just two, the rest disappears. This is a very non-physical unrealistic situation that demands human bias to a large extent. For simpler events, imagination works, but for complex events, it does not, so human bias takes over, different scientists argue, debates continue for centuries. When we observe that topological structures are the foundation of information not a streamline of bits, we make a grand change because it is simply demanding to create a topological version of all mathematical theories that thousands of scientists developed over centuries. In 2010, in our Nature Physics work we argued to create a new kind of science using topology, but now, we are arguing that it could be 3D topology representing the same theories in science in significantly simpler formulations. For streamlining events, equations containing infinite series often results in non-physical unrealistic significance.
- Directionality if lost it is like losing spin of an electron, even much more than that, losing composition of spins in a spin foam: Topological information when converted to linear stream of pulses, it is directional information, say you are looking into a data, it does not reflect any part of the information completely. Linearization is fractally incomplete. Select any point on a linear information, any part, it is incomplete. We can enter continuously, everything would be incomplete.
- No culture of justifying a basic law by fitting experimental observation, derive all from the pattern of primes: Topological integration follows the pattern of the number system, it does not use any fitting anywhere. So, the science is not born from the elementary basic laws, but metric of primes. This is one of the most fundamental principles of the new science that we want to build. Here instead of mathematical formulations, 12 different metric regulates structural transformation of topologies. Linear streaming of data is dead, gives enormous freedom to a user to twist and play with the reality of the system. Explore wild imagination, we do not have it.
- Topology grows inside and above: it always follows an undefined route: There is no differentiation anywhere. Therefore, linearization cannot be modeled. Imagine a point whose properties are defined by a topology inside which is structurally evolving following multiple clocks. Obviously, the point has no fixed property. We can replicate or morph its behavior as much as possible, but not quite accurately.
- Sequence seen in a burst may not be the real sequence of a topology: Bursts that make a linear string of events, could originate from different corners of a topology, it could be an effect of temporal locking of the system with the measuring device.
- Self-resonance, self-oscillation always requires additional components like different forces but in topology, it does not: When we were kids in our school textbooks it was written, when a double derivative of position is proportional to the position we get a pendulum. Derivatives 90 degree phase regulator, but topology is analogue phase regulator, so, systems within and above could reflect energy to oscillate periodically in a fractal system. In a linear system we need two perpendicular forces and a topological constraint. So, linear systems are not robust to accommodate oscillations.
- The science of equation is always a singular path: Quantum has an infinite path but does not detail the path specifics: Topological architecture when details scientific formulations, it tells topology of paths at every level, this beautiful pathways are missing totally in the linearized science.
- Topology inside a single point holds a topology inside by interference in open space: 3D density of states of fractal topology vibrates and changes its configuration, this is where the phase information is located. Linearization probes the single point burst, so gets a totally different information, which is fundamentally different if one measures topological information topologically. `