The butterfly dream is one of the most well-known text passages of Chinese Philosophy. It was written (dreamed) by Chuang Tzu, who lived around the 4th century BCE and who was, together with Lao Tzu, one of the great Taoist philosophers. The dream goes as follows:
One night, Chuang Tzu dreamed of being a butterfly — a happy butterfly, showing off and doing things as he pleased, unaware of being Chuang Tzu. Suddenly he awoke, drowsily, Chuang Tzu again. And he could not tell whether it was Chuang Tzu who had dreamt the butterfly or the butterfly dreaming Chuang Tzu. But there must be some difference between them! This is called ‘the transformation of things.’
As probably many before me, I have wondered about its meaning. In my humble opinion, the dream exemplifies the distinction between existence and non-existence. We would typically think of the person having the dream as an existing entity, and the world he is living in as reality, while the dream world would be fiction and thus non-existing. However, Chuang Tzu’s butterfly dream tells us that we do not know which is which; meaning we cannot distinguish between the existing and non-existing worlds. Actually, in some sense, both worlds are existing (or non-existing). In our effort to identify one of both worlds as ultimate reality, which the dream tells us is not possible, we are constantly switching between both worlds, living in either one and taking it for real.
This difference between existence and non-existence is a classical Yin-Yang opposite. And yet, because existence is regarded as so fundamental, many would rather abandon the concept of Yin and Yang than to give up their sense of reality. Too strong is our desire to identify the real world and to classify Chuang Tzu as being part of reality. Only few dare to accept the fact that our dreams are as real as our bodies, although this is exactly what Chunag Tzu’s dream tells us in my opinion. Scientists, and mathematicians in particular, are no exception to this. Mathematicians would shudder with horror at the mere thought of performing calculations on objects (sets) that do not exist. In mathematics, everything needs to exist. On the most fundamental level of mathematics, where formal proofs are a rare guest, mathematicians have introduced a plethora of axioms to guarantee the existence of sets, numbers, etc. This clearly shows their ignorance about non-existing things, which are not worth to be considered simply because they do not exist. However, I think that Chuang Tzu’s butterfly dream tells us to incorporate non-existing objects into our formal considerations; and that mathematics needs to embrace the intrinsic uncertainty between existence and non-existence.