This is a subject that we’ve discussed repeatedly here, so I thought you might find Tegmark’s narration of this video interesting.
I’m pretty sure that mathematics are not only something humans created, that they are based on relations we observe in the world, but beyond that, I remain largely agnostic on the Mathematical Universe Hypothesis or overall on the precise ontological status of mathematical entities.
The question I’ve asked multiple times lately. Is the universe math, or math the universe? (Click through for full sized version.)
via Saturday Morning Breakfast Cereal.
James Franklin has an interesting piece today at Aeon, asking what exactly mathematics is. He looks at Nominalism and Platonism, but discounts both in favor of Aristotelian Realism, which is something I’d not heard of before but seems equivalent to the idea that mathematics is empirical.
What is mathematics about? We know what biology is about; it’s about living things. Or more exactly, the living aspects of living things – the motion of a cat thrown out of a window is a matter for physics, but its physiology is a topic for biology. Oceanography is about oceans; sociology is about human behaviour in the mass, long-term; and so on. When all the sciences and their subject matters are laid out, is there any aspect of reality left over for mathematics to be about? That is the basic question in the philosophy of mathematics.
via What is mathematics about? – James Franklin – Aeon.
I’m in the final chapters of Max Tegmark’s ‘Our Mathematical Universe’ and will have a lot of thoughts about this soon. Right now, I’ll just note that I do happen to think we learn mathematics initially through perception (some of which is instinctual) but that many derived mathematical structures built on top of those empirical foundations are non-physical.
The question is are those non-physical concepts “real”, meaning Platonism, or are they simply structures built on an incomplete or simplified understanding of our reality, that is built on quantitative relationships and patterns we have observed, but ignoring or in ignorance of constraints that prevent the physical embodiment of those derived structures?
As someone who’s never been good at math, I found this particularly interesting. It’s strange that I’ve always been in the top tier of programmers on any team I worked on, easily gotten As in any programming class I took, and that programmers as a general breed tend to be good at math, but I’ve always invariably sucked at it. Go figure.
I have to admit that the idea of being able to blame it on my genes is appealing.
A new study of math anxiety shows how some people may be at greater risk to fear math not only because of negative experiences, but also because of genetic risks related to both general anxiety and math skills. The results don’t mean that math anxiety can be blamed solely or even mostly on genetic factors, the researchers emphasized. In this study, genetic factors explained about 40 percent of the individual differences in math anxiety.
more at Who’s afraid of math? Study finds some genetic factors — ScienceDaily.
The Higgs Boson was predicted with the same tool as the planet Neptune and the radio wave: with mathematics. Why does our universe seem so mathematical, and what does it mean? In my new book, Our Mathematical Universe, which comes out today, I argue that it means that our universe isn’t just described by math, but that it is math in the sense that we’re all parts of a giant mathematical object, which in turn is part of a multiverse so huge that it makes the other multiverses debated in recent years seem puny in comparison.
via Why a Larger Multiverse Shouldn’t Make You Feel Small | Max Tegmark.
Max Tegmark’s post at HuffPost promoting his new book, which discusses his theory that the universe is mathematics, not described by mathematics, but is mathematics. Of course, the observational difference between being fully described by mathematics and actually being mathematics might be semantic at some level.
I think Tegmark’s idea is interesting, but as one of the commenters on his post said, this isn’t science, it’s philosophy. What observation could ever falsify it? If we observe something that we can’t come up with a mathematical description of, someone can always assert that it’s just a temporary gap in our knowledge.
That said, reading his reasoning will probably be instructive about just how abstract our knowledge of particle physics is. My blog’s name is a reflection of the fact that we and the universe may ultimately be nothing but patterns, structure, all the way down. A possibility that would completely fit with Tegmark’s thesis.