Time and space are basic properties of the Universe.
Consciousness is clearly another.
Time and space are indivisible. We speak of segments: minutes, miles -
but we know that they are not real divisions of time and space - they do not actually have any effect on these basic properties at all. They are convenient units of measurement existing only in the human mind.
Divisions of consciousness are the same. One speaks of 'you and me', 'them and us', but these are words which do not refer to actual things. Consciousness is coextensive with time and space; and, like them, is an indivisible, curved, curlicued, continuum.
'Individuals' seem to have their 'own' thoughts, and act independently; however, action and thought are not what is meant by consciousness. One is conscious of thoughts and actions.
There is nothing wrong with using terms of measurement: 'this millisecond', 'that cubic lightyear', 'me' - as long as one remembers that these terms do not actually divide anything, or cause anything.