The unplanned impact of mathematics (2011)
nature.com
nature.com
You can't predict what avenues of investigation are going to bear fruit, so a good strategy it to encourage people to investigate things that interest them. Most of the time it won't lead anywhere, but once in a while someone will stumble upon penicillin or a microwave oven.
If you see a physicist mucking around with a screwdriver and some beryllium, retreat much further away and preferably with several walls between you and them.
Indeed. And this is a well understood concept. To the point that Tom DeMarco wrote an entire book about the importance of "slack" - over 20 years ago.[1]
From the description:
<DeMarco> reveals a counterintuitive principle that explains why efficiency efforts can slow a company down. That principle is the value of slack, the degree of freedom in a company that allows it to change. Implementing slack could be as simple as adding an assistant to a department and letting high-priced talent spend less time at the photocopier and more time making key decisions, or it could mean designing workloads that allow people room to think, innovate, and reinvent themselves.
[1]: https://www.amazon.com/Slack-Getting-Burnout-Busywork-Effici...
This specific example doesn’t seem like slack as such. The expectation here is that they will spend “more” time making key decisions. Whereas slack means they just have time to do whatever they please, getting bored, sleeping, reading HN, chatting with a neighborhood store owner, or whatever.
How We Got the Lithium-ion Battery
"One notable thing about the evolution of the lithium-ion battery is how hard it is to predict the trajectory of research, and how important it is to allow researchers the flexibility to pursue what they feel is promising. Whittingham stumbled across an intercalation-based battery when researching fast-ion transport through a solid electrolyte, an entirely different phenomenon. And his invention of the first lithium-ion battery cathodes was the result of a serendipitous discovery during work on superconductors. Thackeray discovered the manganese oxide cathode at Oxford ... for a year’s sabbatical so he could pursue the battery ideas he found promising. Early research on a graphite-based anode, performed by Rachid Yazami, was originally aimed at discovering a graphite-based cathode, not an anode, and Akira Yoshino’s battery efforts at Asahi Chemical were pursued in spite of the fact that company thought very little of the battery market, and only bore fruit because the company didn’t actively try and stop him. Likewise, the discovery of ethylene carbonate as an electrolyte that would allow graphite to be used as an anode was an accidental discovery by Moli Energy.
This sort of trajectory, of course, makes it hard to capture the value of research, or to have anything like a reliable, predictable path by which scientific research gets turned into marketable products. Exxon’s efforts to develop a practical rechargeable battery ultimately failed, though its research would spawn a successful battery in the fullness of time."
Source: https://www.construction-physics.com/p/how-we-got-the-lithiu...
I feel that a 100% efficient system is not resilient. Even minor disruptions in subsystems lead to major breakdowns. There’s no room to absorb shocks.
We saw a drastic version of this during COVID-19 induced supply chain collapse. Car manufacturers had built near 100% just in time manufacturing that they couldn’t absorb chip shortages and it took them years to get back up.
It also leaves no room for experimentation. Whatever experiment can only happen outside a system not from within it.
Sic semper mathēmaticīs.
Edit: used "underestimated" when I mean "overstated"
He's very well known and I'd argue his work is generally over rated. His main contribution is a specialization of Von Neumann entropy, which was defined over 20 years earlier. And also some extensions of the work of Nyquist and Hartley in the form of the noisy channel coding theorem.
His work is good and putting it together the way he did was influential. But he's often talked about as the "father of information theory" which has a bit of a hero worship spin to it.
I also suspect -- but this is just my own speculation -- that Von Neumann helped Shannon arrive at the point of view he's famous for. It's known that Von Neumann told Shannon to call his formula "entropy". But Von Neumann was also foundational to computer science and quantum mechanics and was generous to giving credit to others.
Shannon didn't really do much of the same caliber after the information theory paper. So the timeline is he has this encounter with Von Neumann at the Institute for Advanced Study. Then he puts out a paper that synthesizes the work Bell Labs had been doing and which happens to be at the intersection of some of Von Neumann's interests, and then doesn't do much after that. So I've always kind of wondered whether Von Neumann had a short conversation with Shannon where he lays out how he's thinking about information and entropy. And then Shannon took that and ran with it. But again that's just me wondering.
Tdlr if we want to get people excited about math, we should not strive to erase all the complexity and ambiguity, making it fully digestible, because otherwise all that's left are a bunch of lunatics arguing over stacking oranges (prove me wrong).
Something clicked -- I realized mathematics was so beautiful, it was a worthy pursuit in and of itself -- and thus I went on to get a PhD in math, decided not to stay in academia, and be frustrated that most of the web development I was doing wasn't sufficiently mathematical.
Having said that, I also cannot help but think that connections to the real world ought to be pursued -- both because some of the hardest and most interesting mathematical problems come from practical concerns, and because practical concerns draw on math to simplify those concerns and make new discoveries. Indeed, it is a crying shame that there are efforts (at least, on the philosophical level) to try to remove math from physics and engineering, as if the math is what makes those subjects hard!
Also, we don't know what approach will work with each kid. It would be a great benefit if we tried different approaches, some of which may "click", some of which will fall flat.
The Unplanned Impact of Mathematics - https://news.ycombinator.com/item?id=23735236 - July 2020 (57 comments)
Sometimes I wish I had a little more of that self-important energy.
This has been fun — but harder than anticipated! While some topics are clearly and deeply useful, many topics are very difficult to connect to practicalities. And, conversely, some of my favorite math — math that underpins key technologies we use everyday —just isn’t part of the high school curriculum.
It makes me wonder why we teach the high school math that we do— and whether there is a more elegant or effective curriculum we should consider. (For instance, I’m fond of the classical quadrivium)
This is a fascinating relationship, is there a definitive answer / theory on this ? Why are Mathematics so effective to describe the world ? Are Mathematics a feature of the Universe or merely a Human tool ?
I haven't been reading on the subject for quite some time, what are good books on this relationship between Mathematics and Nature?
http://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableEf...
Books, I don't know, I haven't been keeping up.
Nonetheless, I think some proof theorist have a pretty neat way to think about all this. The idea goes as follows: our brain is a computer programmed by millions of years of natural selection and doing math is the activity of trying to decompile some program running in it.
Taking that at face value would give element of answer to the "unreasonable effectiveness of mathematics". For exemple, maybe geometry is trying to make sense of some driver our brain use to interface with our eyes, and this driver better be smart about 3d space for us to have chances of survival.
So the answer would be something like it's not necessarily that the nature of the world is mathematical, but mathematics is the tiny bit of our understanding of what we have best to make sense of the world : our brain. Which we herited from evolution, hence it can be surprinsingly amazing. With this view, saying that the world is mathematical even seem a bit too self centered.
What's backing the idea on the math side of things is that thinking of math proofs as computer programs really makes sense ! There are whole theories on this see Curry-Howard correspondence and/or realizability theory. Provocatively, we can argue computer science generalizes math :-)
For a non technical covering of those ideas by someone who did world class contributions in realizability theory, have a look at Jean-Louis Krivine's last book : "Les décompilateurs". I think it is only available in french though.
and the xkcd.com notation 135: https://xkcd.com/435/