Gödel proved that within any formal system sufficiently powerful to include ordinary arithmetic, there will always be undecidable statements that cannot be proved true, yet cannot be proved false.
Turing proved that within any formal (or mechanical) system, not only are there functions that can be given a finite description yet cannot be computed by any finite machine in a finite amount of time, but there is no definite method to distinguish computable from noncomputable functions in advance. That’s the bad news.
The good news is that, as Leibniz suggested, we appear to live in the best of all possible worlds, where the computable functions make life predictable enough to be survivable, while the noncomputable functions make life (and mathematical truth) unpredictable enough to remain interesting, no matter how far computers continue to advance.
For handsome, smart, educated, awesome, people such as myself, it is a lifetime of treasures, hidden within RSI-inducing key bindings, no matter where on the keyboard one puts C and M.
For leprous, primitivist, stinky, bottom-feeding, monkey-scratchers, it may be a befuddling plethora of options and flexibility that forces the user to form their own opinions regarding the pursuit of goals.
The best description of Emacs I ever read – via comment on HN
0 vs. nothing is one of those abstract distinctions that’s almost impossible to talk about directly; you more have to do it with examples. Imagine there’s a certain math class, and in this class there’s a fiendishly difficult 100-point midterm, and imagine that neither you nor I get even one point out of 100 on this exam. Except there’s a difference: you are not in the class and didn’t even take the exam, where as I am, and did. The fact that you received 0 points on the exam is thus irrelevant — your 0 means N/A, nothing — where are my 0 is an actual zero. Or if you don’t like that one, imagine that you and I are respectively female and male, both healthy and 20—40 years of age, and we’re both at the doctor’s, and neither of us has had a menstrual period in the past ten weeks, in which case my total number of periods is nothing, whereas yours here is 0 — and significant.
From Everything and More: A Compact History of Infinity (Great Discoveries)
At very least, I conclude that we have no general reason to think that non-human animals feel pain less acutely than we do, and we should in any case give them the benefit of the doubt. Practices such as branding cattle, castration without anaesthetic, and bullfighting should be treated as morally equivalent to doing the same thing to human beings.
The wheel’s hub holds thirty spokes
Utility depends on the hole through the hub.
The potter’s clay forms a vessel
It is the space within that serves.
A house is built with solid walls
The nothingness of window and door alone renders it usable.
That which exists may be transformed
What is non existent has boundless uses.
– by Lao-Tse