Bertrand Russell was a great encourager of free-will, and individuality. My conclusion of Phil’s day off was that as our society has developed, we’ve come to better terms with more customizable lifestyles. Opposed to living life to aim for a supposedly “acceptable” career and lifestyle, people are now living more for themselves and to their own aspirations.
The mirror represents the idea of how the only important image is your self-image. The mirror only shows how you see yourself, and not the reflection others see off of you. There’s a sense of liberation with living life for yourself, and Russell found that the ability to feel so came with the unity of the world and the acceptance of each person in society.