The unplanned impact of mathematics (2011)(nature.com)
nature.com
The unplanned impact of mathematics (2011)
https://www.nature.com/articles/475166a
13 comments
https://archive.ph/78Qkb
These kinds of unplanned impacts are one reason why I think most jobs need to have a certain amount of "slack" built in so that the workers aren't only spending all their time working, but can spend some time pondering ways that they could be doing it better or even just relaxing and reading a book etc.
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.
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.
These kinds of unplanned impacts are one reason why I think most jobs need to have a certain amount of "slack" built in so that the workers aren't only spending all their time working...
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...
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...
I don't recall what specific keyword they use, but this idea has been thoroughly explored in manufacturing businesses, probably for close to a century now. Having slack in the system allows you to adapt to unforeseen circumstances quickly and over longer periods of time, gives better results than trying to run everything at maximum output. If memory serves well, Andrew Grove dissects this idea and how it carries over to managing people in his book High Output Management from 1983.
Yup, see Theory of Constraints[1]
[1]: https://en.wikipedia.org/wiki/Theory_of_constraints
[1]: https://en.wikipedia.org/wiki/Theory_of_constraints
This book is a good riff on "The Goal" but for software manufacturers https://itrevolution.com/product/the-phoenix-project/
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> 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,
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.
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.
I think this concept is where the linux distro Slackware came from too. Although Slackware has to be pushing 30 by now.
It is also more resilient to have system wide slacks. This is what I wrote in an earlier HN thread
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.
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.
When you look at scientific discovery, random happenstance has an outsized influence. So much so, that one could make a compelling argument of how we could increase the rate of scientific discovery.
When you see some science students mucking around with dangerous chemicals etc. then retreat to a safe distance and see what happens.
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.
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.
let he who has never acted blasé towards safety protocols cast the first plutonium sphere
If we have to couch everything we say online to account for arm chair illogical extremes, then nothing of substance would ever be said.
Sorry, I wasn't really intending my comment to be any kind of criticism of your comment, but more of a kind of humourous (to me anyway) addition.
No worries, I understand.
Explore exploit dilemma, it seems 20/80 is about the right ratio in many fields
This is interesting. Are those examples of inventions/discoveries that probably don't exist in other timelines?
The development of the lithium-ion battery is an example of how scientific discovery does not have a straight-line trajectory.
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...
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 can highly recommend the old James Burke's Connections TV series where he traces ideas/inventions through history, highlighting the random meetings and developments that led to modern technology.
> In the 1970s, Lang developed a modem with 8-dimensional signals, using E8 packing. This helped to open up the Internet, as data could be sent over the phone, instead of relying on specifically designed cables. Not everyone was thrilled. Donald Coxeter, who had helped Lang understand the mathematics, said he was “appalled that his beautiful theories had been sullied in this way”.
Sic semper mathēmaticīs.
Sic semper mathēmaticīs.
Not included in the article: Boolean algebra, invented by an English philosopher in the 1840s, and applied to a new context almost 100 years later in what may be the most influential MS thesis of all time, Claude Shannon's "Symbolic Analysis of Relay and Switching Circuits".
Claude Shannon's contributions to modern technology can't be overstated and yet his name is relatively unknown.
Edit: used "underestimated" when I mean "overstated"
Edit: used "underestimated" when I mean "overstated"
It's interesting that you see things that way because I kind of think it's the opposite.
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.
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.
Wiener also had independent work on information theory around then.
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The article is interesting, but I feel somewhat conflicted re "explaining motivations behind scientific discoveries". The author of the article is trying hard to find simple and elegant examples of applications (eg the optimal orange stacking in a grocery store), but imho makes a disservice, as mathematics ends up looking like a walk in the park taken by complete lunatics that were carried away thinking about stacked oranges. When I was a kid, there were some science fair-esq events / electives for high school kids including sections on mathematics. By stripping off all the mind-twisting weirdness and complexity of the real math to make problems "more approachable" to students, they also stripped them of all the mystery and a sense of discovery that I self-discovered and fell in love with much later during my undergrad.
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).
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).
I decided in 11th grade to be a mathematician because I read Jurassic Park, went down a rabbit hole about chaos theory, and ran smack-dab into a conversation where someone asked Mandelbrot if the mathematicians knew he was using their work in practical ways, and his answer was "No, and they probably don't care."
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.
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.
Do we want to get people excited about math? I think that as long as they're competent in it, it's fine if most people are mostly indifferent towards it and just see it as a useful tool.
Related:
The Unplanned Impact of Mathematics - https://news.ycombinator.com/item?id=23735236 - July 2020 (57 comments)
The Unplanned Impact of Mathematics - https://news.ycombinator.com/item?id=23735236 - July 2020 (57 comments)
These are fun anecdotes, but I can't help but notice the egocentrism of Juan Parrondo calling out his own work as having historical impact and noting two terms named after himself in the same paragraph.
Sometimes I wish I had a little more of that self-important energy.
Sometimes I wish I had a little more of that self-important energy.
I’m working on a project now where we have to take the topics in algebra 1/2 and geometry (high school mathematics) and connect it to real-world activities in science, tech, business, etc.
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 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)
The Unplanned Impact of Mathematics is a great illustration of the mathematical nature of the world.
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?
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?
The one thing that's for sure, is that there is not a definitive answer to that.
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.
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.
I didn't know about Jean-Louis Krivine's book, thanks
Maybe you're aware of the sort of reference essay on the subject, but just in case you hadn't see it, it's very readable and beautiful:
http://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableEf...
Books, I don't know, I haven't been keeping up.
http://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableEf...
Books, I don't know, I haven't been keeping up.
Stakeholders don't pay employees to do things for no purpose !
Are you saying employees are paid to do nothing with a specific purpose in mind?
Anyone who's worked for a big enough company knows that isn't true.
is the eternal (apparent) dichotomy between pure and applied science, canot be said in advance what is egg and what is chicken between the (quite) uncountables branches of knowledge..
Maths stands for Mathematical Anti-Telharsic Harfatum Septomin.
an easy to read book for the mathematically inclined minds by Eric Temple Bell: "Mathematics, The Queen & Servant of Science"
and the xkcd.com notation 135: https://xkcd.com/435/
and the xkcd.com notation 135: https://xkcd.com/435/