Norman Wildberger on the Scientific Method, Mathematics and Infinite Sets

I'm listening to this, ... 

I don't understand the problem: I am personally quite happy with the idea of "finite but unbounded" which is something I intuitively grasped at about the age of five when I was taught how you could always add one to a number and get the next one, and you didn't need to invent any new names for bigger numbers as long as you were happy writing them as a formula (finite but unbounded in length) d_1 + 10 d_2 + 100 d_3 + 1000 d4 + ... In just five steps you already have 10,000 digit numbers, so in 10,000 steps, well, you get the idea, right?

He's done several videos on this, some in conversation with other mathematicians and computer scientists, for example, here's one he did in September 2014 with James Franklin (see Infinity's end: Time to ditch the never-ending story?)

Norman is a bit of an extremist. For example, of this finite (and rather small number, relatively speaking) which he wrote on his whiteboard (11:53), he states flatly: "this number has no prime factorization!" 

He claims the Universe is not big enough to contain the "things" that ought to be prime factors for it, so the prime factorization doesn't exist. The reason being that he claims there is no ordinal notation efficient enough to be capable of materially representing most of those potential factors (10:34), given what we know about the material Universe. More details in this video of Norman's.

Jim Franklin presumably doesn't go that far (21:02) But in other news, see Neil Turok Also Going into The Sci-fi Movie Busines. This problem has a connection with the ideas Jade talks about here: Jade on the Pigeon-hole Principle and Jade on Time and Information. Is it really just a coincidence that Wildberger picks the question "How far can a person walk?" at 35:39? See Peripatetic school, ... These things all ultimately end up being based on what you know about the world of substance, and that can always change. See Aristotle on reincarnation. Jim's book is An Aristotelian Realist Philosophy of Mathematics.

On the sociological criterion for deciding what is a bona fide scientific or mathematical question, one needs to include the economic "realities". The reason is just that one might prefer one's idea of science or mathematics to be aligned with those of whatever funding bodies one hopes would fund ones future research career. I don't think it is a coincidence that the definition of Science that he opened the video with was one taken from the NAS and NRC (National Academies of Sciences, Engineering, and Medicine. 1992. Responsible Science: Ensuring the Integrity of the Research Process: Volume I. Washington, DC: The National Academies Press. https://doi.org/10.17226/1864.):

See https://www.nationalacademies.org/about 

"The National Academies of Sciences, Engineering, and Medicine provide independent, objective advice to inform policy with evidence, spark progress and innovation, and confront challenging issues for the benefit of society. ..."

See also https://tethys.pnnl.gov/organization/national-research-council-national-academies-nrc

"The National Research Council (NRC) is the operating arm of the United States National Academies of Sciences, Engineering, and Medicine and is overseen by a governing board that consists councilors from each of the three Academies. The National Academies of Sciences, Engineering, and Medicine are private, nonprofit institutions that provide expert advice on some of the most pressing challenges facing the nation and world. Their work helps shape sound policies, inform public opinion, and advance the pursuit of science, engineering, and medicine. ..."

... and http://www.nasonline.org/about-nas/history/archives/milestones-in-NAS-history/organization-of-the-nrc.html

"Like the National Academy of Sciences (NAS), the National Research Council was organized in time of war. Whereas the Academy was founded in 1863 in the midst of the American Civil War, the Research Council was founded in 1916 against the backdrop of the First World War, which had consumed Europe since August 1914 and threatened to involve the United States as well. ..."

And coincidentally, here's a story that appeared in Nature on December 9, 2022: The end of infinity: Testing the Universe:

Filip Wiltgren reveals the inspiration behind The end of infinity.

I’ve always been fascinated by the belief people put on the economy — an entirely imaginary field. Contrary to popular belief, stocks, derivatives, even money itself, have no intrinsic value. All the value we assign to them, the ability to convert one dollar into a can of Coca-Cola, for example, is entirely imaginary and could shift at any moment. In reality, the only difference between the 2022 dollar and the 1923 hyperinflating German Papiermark is one of belief.

This view does not go down well with people less interested in the philosophy of value than me. I’ve incensed a number of stock-investing friends to the point where we had to stop talking to each other simply by claiming that all their stocks have no absolute value, and that at any moment, the perceived value of the stocks could turn to zero (or infinity, but that’s something people don’t complain about).

So when I got the idea for a story about how to discover if we’re living in an entirely virtual reality, going with virtual value on virtual coins seemed like the right way to go.

And if it happens to disparage a technology that’s causing some real environmental harm to our possibly non-virtual world, then that’s fine by me.

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