Like infinity singularity is an intractable subject. Thinking too much on infinity or singularity will surely lead you to insanity and that’s why I don’t write explicitly about singularity but ignoring this subject does not help me either.
Singularity in the context of physics
The traditional definition of singularity in physics is
- Zero volume, infinite density.
- Laws of physics are no longer valid.
Charles Misner proposed a different definition for singularity in 1963. He defined singularity as the point where time ends (history ends).
In 1965, using Misner’s definition of singularity, Roger Penrose showed mathematically that a singularity occurs inside a black hole. Previously, based on Einstein’s equations of gravity, many other physicists argued that the universe started from a singularity.
Arguing that there was a singularity 13.7 billion years ago does not create an emotional impact. The argument is rather abstract. But, if you say that singularity is happening right now somewhere in the universe then you have my attention. In 1965, Roger Penrose received a lot of attention.
Later, Stephen Hawking showed mathematically that black holes evaporate. The mass/energy contained inside the sphere of the “event horizon” is radiated away slowly because of the quantum mechanical effects.
So, there is a singularity inside the black hole but the black hole is evaporating. This picture is very confusing and contradictory! The concept of singularity bothered Einstein too. He never accepted the possibility of a space-time singularity even though such a possibility was clearly implied by his equations of gravity.
“He believed just like Aristotle 2000 years before him, that there should be no physical infinities in the universe. Any that appeared in mathematical descriptions of the universe must be artefacts of an inappropriate idealization in the description of the universe, or a breakdown in the assumptions on which the mathematical theory producing that model was based.” 
Einstein’s sentiment motivates the entire enterprise of the String/M theory of physics. This theory is still in its infancy. The fundamental impetus for the String/M theory is the sentiment that elementary particles cannot be point particles as the Standard Model (SM) of particle physics suggests. String/M theorists hate infinities as Einstein did. SM hides the infinities arising from the treatment of elementary particles as point particles by using clever mathematics.
We may criticize SM for its ugliness and for its many deficiencies but we cannot deny the fact that it has been a successful theory. The singularity implied by the presence of a point particle (physical existence with no physical extension) remains a mystery.
The elementary particles of SM are singularities. The String/M theory is trying to prove that this is not the case without any success.
We manipulate singularities (point particles) every day. We observe their interaction with other singularities (different kinds of point particles). It is becoming a routine now. It is a routine not only in the state-of-the-art accelerators but also in our electronic devices! Even in the 19’th century we were using these singularities (electrons) without questioning their mysterious nature as singularities.
We started by saying that singularity is rare. After some reflection we now realize that singularities are everywhere.
Singularity in the context of Spiritual Philosophy
The realization that singularity is not so rare leads us to the acceptance that the soul is a type of singularity. The infinity of the Absolute Being is hidden in the dimensionless singularity of the soul.
Singularities are dimensionless. Singularities do not have attributes. But, singularities have event horizons where dimensions and attributes manifest.
The event horizon of the soul is the mind. The soul is a singularity whereas the mind is not. The existence of the soul can be deduced from the radiance of the mind.
My suggestion to professional physicists is that singularity is unavoidable. A concept similar to “event horizon” is needed in particle physics. The reconciliation of the SM and String/M theories may be possible by such a construct.