The studies of weak interactions in physics have revealed a prominent, so-called chiral, asymmetry of our world. More widely known is the asymmetry of particles and antiparticles, which is also connected to chiral asymmetry: we know that all neutrinos are left-chiral. The attempts made by many physicists to restore the symmetry between right and left, i.e. to discover "mirror matter", have not been successful. In live beings the asymmetry manifests itself in male and female, the functioning of the right and left hemispheres of the brain, in phyllotaxis, in algebras of genetic alphabets, and other key phenomena. Our world is fundamentally asymmetric, both in physical and biological sectors. To deal with world asymmetry we have developed chiral algebra that describes skew-symmetric relations. This algebra is proven to successfully work in physical theory of spin. Particularly it allows to formulate in a new way the famous Dirac equation. Within this new representation we can better understand this equation and also discover the noise immunity mechanisms built in it. Chiral algebra uses the apparatus of biquaternions in light-like basis with new types of multiplication and conjugation. Another application of chiral algebra is a model of the genetic code built by the author. This model reflects the genetic code internal symmetries, previously studied in other works. As a result, we put forward the following hypothesis: DNA has a quantum-like biological nature, which is based on an analogue of physical spin, which we call "biospin". The concept of biospin also supports the theory of biological field. We assume that both "inanimate" matter and living beings have field nature. We assume that biological field is a nonlinear extension of electromagnetic field. Within field approach a singularity of the field, having operational and projection nature, becomes the most suitable candidate on the carrier of consciousness. As is known, singularities of electromagnetic field are represented by point-like charge particles such as electron. Paradoxically, these point particles have an internal structure described by spin. Having a structure We find that dimensionless objects have an internal structure and that indicates an "exit" to another space. We claim that living beings are represented by field singularities. They exist simultaneously in two spaces, or worlds — inner and outer. Our consciousness, being a field singularity, carries out the connection between these worlds. Inner world is the space of virtual paths, wave functions and potentialities, while outer world is actual physical world operated by fields.