The essay does not mention the transcendentals at all and mentions causality briefly. Hughes does not evidently believe in the uncertainty of quantum futures and the fact that our matter is quantum entangled with all of the matter in the universe. Quantum phase noise plays a particular role in our differentiation of a classical determinate reality from the many possible futures of the actual quantum reality in which we actually live.
In the end, though, Hughes essay does conclude that even though civilization is not very massive compared to the universe, the neural resonances and Grand Narratives of civilization are most of what matters to us here on earth. So even though the size of the universe boggles the mind... so what? Likewise, the microscopic size of matter also boggles the mind... so what?
"And whether or not they are objectively valuable, the ends that matter to us, the things that we care about most – our relationships, our projects and goals, our shared experiences, social justice, the pursuit of knowledge, the creation and appreciation of art, music and literature, and the future and fate of ours and other species – do not depend to any considerable extent on our having control over a vast but largely irrelevant Universe...Most of what matters to us is right here on Earth."
Also, the matter equivalent energy needed to maintain 1 g acceleration for 15 years is beyond science today but there might be ways to use galaxy spiral gravity waves to boost future journeys at this scale, so called gravitization waves. Gravity waves, after all, are something that science is just learning about and so maybe we can catch a gravity wave and surf our way to the galaxy center. It would take the matter equivalent of ~600 MW nuclear reactor to accelerate a 100 MT ship at 1 g for a year. After all, spacecrafts already use the gravity assist of earth and other bodies to accelerate and so future spacecraft may surf gravity waves for space travel.
We do matter in the cosmos since it is us who determines what matters to us and not anybody outside of our own local universe. The definition of a universe is the matter and action that we affect and that in turn affects us during our lives. The universe that we imagine does not exist until we experience that universe and so we are in fact the most important part of our own universe since neither it nor its uncertain future would exist without us observing it.