The common rationalist-reductionist argument against synchronicity boils down to: the total explananda for this phenomenon can be reduced merely to the law of large numbers, to the mechanical distribution of statistics over a long enough time line with enough evaluative constraints and parameters. You think of a person and pick up the phone to call them, and when you turn the phone on and dial the numbers, nothing happens: because that person, in that exact instant, called you: they’re already on the line. The argument is that enough people make phone calls every day that, statistically, this is bound to happen every so often. But, using this purely statistics-driven, mechanical model of reality… it is as certain a conclusion that, because it is statistically far more likely (infinitely more likely) that a single brain emerged from the quantum foam through random interactions between particles (a brain whose connectome or synaptic configuration just happens to contain all the memory and experience I have mistakenly believed is my life up to the moment I am typing this, none of which ever happened, corresponding to nothing ‘real’ behind the experience outside of my Boltzmann brain, isolated in the vacuum) than it is that an entire universe populated by billions, trillions of brains emerged from the same. But this Boltzmann brain hypothesis is ridiculous,-- and yet those who decry the idea of synchronicity (of what has been called, more ecstatically, the unus mundus, or what Bohm calls the implicate order: an order to events that emerges retrocausally, out of a determinant force beyond the mechanical interactions of one-to-one particle collisions) must, if they are to maintain the logical consistency of their world-view, (which I assume is important to them, given the rationalist, reductionist programme they advance) accept it as the most solid conclusion of their line of argument, for this conclusion is what a purely statistical model of reality necessitates.
The real problem with the Boltzmann brain hypothesis is that consciousness is simply not reducible, that is, consciousness is non-computable. Even if an exact replica of my brain, every single cell in the same place, in the same state of firing, were to be automatically produced at the same instant my own brain were to be blinked out of existence, my consciousness would not move from one to the other structure- there would be no continuity between the two. Likewise, my connectome cannot be uploaded to a computer with any hope of reproducing my own consciousness in a digital form, though a new consciousness could perhaps be engineered in this way. The same idea extends to synchronicity. Synchronicity would be some non-computable (implicate) order in the structure of causes and events. In this sense, consciousness ITSELF is a synchronicity emerging in the series of causes and events, in the causal chain, as constituted by the activity of my neurons.