Hacker News Reader

Comment by chongli | Hacker News Reader

Young man, in mathematics you don't understand things. You just get used to them.

— John von Neumann

Does not sound to me like a man who thought he had the answers. He did the best he could, and his best is among the best all time, but he certainly didn’t know everything.

View on HN

FWIW over the years I've heard variations of the quote from a number of people. Though I'm not versed in advanced mathematics or physics the idea makes a lot of sense to me. I say that because developing expertise in fields requiring mastery of highly abstract concepts (and skill in applying the concepts) works pretty much the same way.

But then again, it's interesting how exposure to target subject matter improves "understanding things". An example is when I needed to learn what the confusing areas of shadow and light on a PET scan image were all about. Viewing such images repeatedly became sort of magic. After a while the images start to actually make sense, structures and processes come into focus and become identifiable. Eventually they're old friends, "yeah I know what's going there..."

Here's my speculation: beyond a certain level of complexity, learning via linear, step-at-a-time algorithms no longer works because the number of items to keep "online" simultaneously exceeds what can be held in working memory. The need to "get used to it" implies ability to "page" sets of symbolic representations into and out of working memory. This is an experiential learning process coalescing as an intuition for the discipline.

I think much more consequential than this educational quote are his takes on nuclear warfare and the extent to which he relied on game theory and idealized rational actors to go as far as to recommend a first strike.

This humility of accomplished mathematicians when it comes to math but ironically complete lack or overuse of it in other domains honestly seems quite common.

His quote was only relevant to preventing other nations from obtaining nuclear weapons. While for now nuclear peace still exists it still remains to be seen in the long term, especially as more and more nations think of developing nuclear weapons, whether the idea of allowing nuclear proliferation was a good one in the end.

Or when the actors are no longer nations modeled on an individual decision-maker but, eg trucker convoys purchasing their way into the club.

I'm pessimistic here. The countries that once pursued/had nuclear weapons, but then signed treaties and gave up on them were screwed one after another: Iraq, Lybia, Iran and now Ukraine. Contrast with North Korea, that pursued them not matter what. Nobody ever screwed them. The failure of the great powers in keep their word with countries that actually took measures to stop or limit nuclear proliferation will seriously backfire.

Yes they were screwed and lots of people did die unnecessarily. However, Saudi Arabia wants nukes, Shinzo Abe (ex Japan PM) said Japan should get nukes, the future of the long term program of Iran is still unsettled. Apartheid South Africa had nukes and only gave them up because they didn't want the native Africans to have them. The problem becomes as more and more countries develop nuclear weapons, the risk of conflict using them grows higher. Already we have a long term conflict between Pakistan and India where both nations are nuclear armed and I very much doubt Pakistan's nuclear security as anywhere as good as say America's or China's. What would happen if 20 or 30 or 40 countries had nukes? They would threaten to use them over every small thing and eventually I guess someone would use them, and who knows what happens then.

Can we claim that if the Soviets develop the bomb first, they wouldn’t have used it on the US as soon as possible? With that in mind, his take is strong, but not irrational.

Ah yes. If only the negotiating team of the West had more humility at Yalta. I'd rather have von Neumann every single time.

He also claimed/“proved” there were no hidden variables possible in QM even though de Brogile had one already and Bohm would soon show his version (which was very similar).

He also claimed human (and possibly) animal consciousness were the only thing able to collapse wave functions.

For your first claim I think you'll find what von Neumann claimed is a lot more limited than you think, and even then what exactly was interpreted is still up for debate, see from last year:

https://arxiv.org/abs/2105.00242

https://link.springer.com/article/10.1007/s10701-021-00474-5

https://arxiv.org/abs/2105.13996

Likewise, for your second claim I think you'll find von Neumann said that the collapse of the wavefunction can be placed anywhere in a measurement chain, from the first measuring device to the observer's conscious perception of the measurement result. The stronger claims about human consciousness specifically causing the collapse of wave functions come from London and Bauer's book "The Theory of Observation in Quantum Mechanics" and Wigner's "Remarks on the Mind-Body Question". Again, this viewpoint is reflected in the literature too:

https://arxiv.org/abs/2105.02314

Reply on news.ycombinator.com