Dear Lorraine Ford,
Let me explain what I mean by saying that the mark is a logical particle. For typographical purposes lets use < > for the mark. Then its formal properties are < > < > = < > and = . Here the = sign means "can be replaced by" and the blank space is a blank space. We could use # to stand for a blank space. Then # would have the formal properties ## = # and # = and = .
Thus IF < > is thought to represent a particle and # the absence of that particle, then < > can interact with itself in two ways: either to produce itself as in -------> < >, or to produce the neutral state # as in < < > > ----------> #. This is all symbolic of course. But it is a symbolism that describes the so-called fusion algebra for a Majorana particle. Having a symbolism for an algebra does not imply the existence of that pattern in the world of physical particles.
But what we do see is that this symbolism can describe the Majorana particle's fusion algebra. We do not know if Majorana particles exist! This was the speculation of Ettore Majorana long ago when he studied real solutions to the Dirac equation. We are struck by a number of things.
1. The formalism of the mark is a way to write the 'arithmetic' behind Boolean logic and it is from
this point of view at a very fundamental place in mathematics. The mark itself stands for and 'is' a
distinction. That is, the mark < > is a mark, a symbo on a page, but it also is a physical instantiation of a distinction that you imagine.
2. A simple fundamental place in mathematics corresponds, as a pattern, with a fundamental place in possible physics.
When we start to talk about how mathematics may be related to physics it is always in the form of a correspondence of patterns. Mathematics studies patterns not things, and so when mathematics and physics come together it is through mathematical patterns being observed in
Nature. When they are observed (as in the Eight Fold Way and its relationship with representations of SU(3)) we are happy, surprised and we have to wonder what is in back of that.
I do not wish to say that mathematics and physical world are identical. I hope to say that they arise from the same source and, just so, that Mind and Nature arise from the same source.
Source is a source of metaphor here, and many come a cropper on attempting to speak this way.
But this way of thinking is natural for me and I prefer it all the way back to the thought that any distinction carries with it an awareness as a side of the dividing of the universe into what sees and what can be seen. It is not a sharp division and therein comes the metaphor of the permeable boundary.