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My book states that the fact that :"Viruses can be crystallized" is a proof of their "Non living character" Does that mean living things cannot be crystallized? If yes, why is that so?
Crystallization involves removing extraneous molecules, so that remaining molecules - here, virions, or virus particles - can form a crystalline or ordered structure. https://en.m.wikipedia.org/wiki/Crystallization
As far as cells go, cellular proteins can be crystallized (some more easily than others), as well as nucleic acids, but having those crystals alone is not sufficient for life. You need an input of water, energy, etc.
Making crystals from the constituent parts of cells would effectively kill that lifeform. On the other hand, you can take virus crystals, add a bit of disorder, and they will "wake up" and regain their infectious properties.
Viruses sit on a fine line of what constitutes life. To some extent, the discussion is philosophical in that definitions are chosen and the subject either meets those criteria or not, and some criteria are a bit more arbitrary than others.
Some have argued that viruses in infectious virion form are life, at the stage when infecting a cell and redirecting its machinery to make more virus particles. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2837877/
Over the decades, biology has shifted from a study of cells in Petri dishes, or monks growing peas, to a more abstracted investigation into information science and related fields and subjects: mathematics, entropy, statistics, physics. That perspective started with scientists like Schrödinger, Turing, and Von Neumann, and it continues in the modern day with work by Dawkins, England, and others.
Viruses have and continue to shape the evolution of life around them. In a way, they are frozen information, and the definition of life may be changed over time, as we gain a more broader picture of how things work.