orangutango

For any set of axioms you take, if they are consistent then it is incomplete. You can enhance the axiom set to extend its reach, but an adversary can always find true, unprovable statements.

My main point is I disagree with the view of mathematics as nothing more than some axiomatic program-- in 1903 many were hopeful that a system (like Russell's formal logic in Principia) could simply generate the truths of mathematics. Gödel shattered that dream.

"[A]ll pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of fundamental logical principles ..."

Cue Gödel... [1]

[1] https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompletenes...

I like this visual explanation of the illusion/fallacy: http://www.abarry.org/knee.htm

+1 for Information Theory, Inference, and Learning Algorithms. A fantastic book by the late David C Mackay. Part V has an interesting presentation of neural networks, but really this book is about information theory and Bayesian probability.

http://www.inference.phy.cam.ac.uk/itila/

Whose standard argument?

I always thought: we work 40 hours a week because we work 8 hours a day; and we work 8 hours a day because Robert Owen's mantra "Eight hours' labour, Eight hours' recreation, Eight hours' rest" caught on.

Completely agree, and this hits close to home.

I was a very math oriented student at a high school with a heavy bias towards liberal arts ... So when it came to picking senior year electives, I was delighted to enroll in AP statistics.

The classes turned out to be tutorials on the built-in TI-83 stats functions, with step-by-step instructions on how to answer the various types of questions we would encounter on the test. I forgot everything and gained virtually no statistical intuition.

Thankfully I had a similar experience to you ("Probability and Statistics for Engineers") with a fantastic professor who researched computer networks. His lectures were sprinkled with tangents tying the current topic back to his own field / research, which to me made the biggest impact. Contextualizing a taught subject markedly improves the course experience.

Locally != independently; the training process is recursive, so interactions between layers are present. From the paper: "The parameters of the entire SARM are solved recursively. The current ARM’s parameters are calculated using the output from the previous ARM. Then, the output of the current ARM is fed into the subsequent ARM (or the classifier, if the current one is the last ARM), as its input."