One of my favourite (not) Sydney charlatans is the woman who teaches people that they can get all of the nutrition they need from a diet of nothing but raw vegetables, because our closest relatives are gorillas (no, they’re not) and look at how big and strong they are! (And look at just how radically different their digestive systems are from those of anatomically modern humans.) Those who exploit gullible and vulnerable people for financial gain deserve to be held up publicly to ridicule. She wasn’t – her ‘work’ was promoted by government funded news media, paid for by taxpayers.

On the other site you linked to, I particularly enjoyed the bit about how “Even the dimensions of our teeth are based on phi.” No, they’re not.

]]>(b) Whether pi is algebraic or not has absolutely no effect whatsoever on the amount of time it takes to run complex computations. We use approximations of pi that are easy to compute with all the time. What makes computations slow is the intrinsic computational complexity of those.

For one example, to train a deep neural network requires performing massive numbers of training steps, each of which involves a complex back-propagation of information through the multi-layered structure of the network. It is, by the nature of the problem, a complex multi-step computation. Even if you could replace all irrational and transcendental numbers by simple rationals, it wouldn’t change that. How do I know that? Because in computations, *we already do that*.

For another example, weather prediction is a highly complex computation. The reason that it’s complex is that the calculations are based on a system of equations for which we have not discovered a closed form (and a closed form may not exist). That means that the only way we can perform the computation is by dividing space into tiny cells, and performing separate computations on each of those cells, and propagating information between them. By sequencing many of those cell-wise computations, we can produce highly accurate weather models. The problem in the computation isn’t that there are some weird numbers like pi – it’s that we need to perform lots and lots of computations.

]]>While your ultimate contention may be correct, your logic would appear suspect as well. The mere fact that one observes a predictable and repeatable series resulting from a repetitive operation is neither evidence for or against its substantive value. Under your logic, the Fibinocci series is likewise rubbish, despite its near universal admiration for its presence in the real wold. The fact that the operations yield similar repeating series in other bases is likewise not dispositive in proving or disproving whether the observed series has intrinsic merit. Where your argument gains currency is in its application to our observable and testable physical universe. It appears to have no valid existence or manifestation under the scrutiny of scientific method. No physical phenomena can be predicted and tested under the system, not has anyone demonstrated it can produce better results than conventional applied maths. That said, when we examine the question of the reality of complex numbers, we find them routinely used in advanced physics to describe quantum systems. Yet, the existence of the complex conjugate space is beyond the reach of provability. As pertains VBM you are right to intimate it seems to be much more based in metaphysical interpretation than anchored in physical reality. Thusly, it is of little utility and is tantamount to one making up their own vocabulary with implied meanings for things already known by other names. A rose by any other name…

Where science loses credibility is when it’s arrogant advocates chastise and belittle rather than employ sound reasoning and engage in logical discourse. Averring to the point that complex mathematics are used in conventional physics such a tensor math does little other than to serve as a crude rhetorical device. In totality, your missive is unnecessarily critical, dismissive and serves to alienate rather than educate.

]]>You have a very good response to this anti-Cantor argument. But, instead of pairing the naturals with the reals, if our friend tried to pair the naturals with the irrationals. Then your objection would no longer work, and Cantor would still have a problem since the naturals should not be possible to pair with the irrationals.

This thread has haunted me for the past few months, and if I were a young mathematician, I would certainly try to formalize this argument. From where I sit, it looks promosing.

Adam

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