Does the world need polymaths? | Hacker News Reader

Does the world need polymaths?

bbc.com

142 pointsgt280 comments

While we do need polymaths, the problem with a lot of self described polymaths is that they skip the hard part of different fields and only focus on a 'Gladwellesque' understanding.

I think a better way to be a polymath is to be a real expert on a particular subject, and then augment that with ancilliary knowledge from other fields. If you claim to understand physics but don't know maths, or claim to be an expert on classical literature but don't know how to read greek/latin, then you aren't a polymath but a bullshit artist.

The polymaths I respect are people like Peter Medawar, JD Bernal, etc..

My particular pet peeve lately is people (especially prevalent in the rationalist sphere) that talk about how Bayesian they are, but don't know what a conjugate prior is, or have no understanding of MCMC sampling. There is absolutely nothing wrong with not knowing either of those two things - but if you don't know either, then describing yourself as a Bayesian is just putting on airs.

I have no idea what you are talking, but I love it. There is nothing more satisfying than seeing a peraon be so passionate about something. Thank you for posting this, it made me happy.

Yeah,

The article kind of got off on the wrong foot by talking about trivia masters.

I wouldn't say that the people who make important contributions through being polymaths are those who bring the insights of several fields together.

I think someone like Julian Jaynes, who brought together strands from a variety of disciplines to formulate his theory of Bicameralism is an example of such a wide-ranging thinker [1].

Reasonably respected Marxist economist David Laibman[2] is also a well-know blues singer and well-know mainstream economist Kenneth Rogoff is a chess grandmaster and something of fraud. But the extra expertise of these two experts doesn't seem to matter either in their performance.

[1] https://en.wikipedia.org/wiki/Julian_Jaynes [2] https://en.wikipedia.org/wiki/David_Laibman [3] https://en.wikipedia.org/wiki/Kenneth_Rogoff

>My particular pet peeve lately is people (especially prevalent in the rationalist sphere) that talk about how Bayesian they are, but don't know what a conjugate prior is, or have no understanding of MCMC sampling. There is absolutely nothing wrong with not knowing either of those two things - but if you don't know either, then describing yourself as a Bayesian is just putting on airs.

Mine is related: philosophy types who don't actually know much about the not-philosophy fields they're trying to address. For instance, I once heard someone complain that Bayesianism sucks because of the Problem of New Hypotheses.

I explained what nonparametric models are. They were very surprised and excited to hear that this was a thing.

What.

If you are going to be an expert in one thing, and then augment with ancillary knowledge from other fields, you have to pick a subset of knowledge to learn from the other fields (if you weren't just learning this subset, you would also be an expert in the other fields). It looks to me like you are advocating one specific type of subset, which is something like implementation knowledge or foundations: math for physics, greek/latin for classical literature.

Not to say that's incorrect, but I would be curious to hear why you believe that's the most important subset to go after. Personally, I see foundations as critical for the field that you're going to be an expert in, but if you're picking up ancillary fields, I believe the question is more open (of course you shouldn't be totally ignorant of foundations, but...).

As an example of another subset you could take—which I think is fairly common and perhaps well-justified—meta-knowledge. That seems to be what you're complaining about with folks who are probably of a more philosophical bent who claim to be Bayesians, but don't know MCMC sampling (again, this is knowledge of a particular implementation of Bayesian ideas)—they focus instead on something more like a philosophy of probabilistic thinking, and so what's important to them is the relation of Bayesian probability to frequentist probability. They have no interest in performing calculations in either (doing so could help their goal of course, but it is not their end goal).

So if you have to pick a subset (of knowledge of some field), should it be more about how the field relates to other fields, or should it be more about the foundations of the field? IMO it should probably be taken on a case-by-case basis, but perhaps more often than not it's knowledge about how fields relate to one another that ends up being more useful in your ancillary picks (that totally depends on what you're doing with the knowledge though).

Thanks for the interesting post - however, I respectfully disagree with the example you've picked out.

How can you do intelligent philosophy about probability if you don't have a good detailed understanding of what probability is?

To make a concrete example: the best philosophers of logic (Kripke, Ruth Barcan Marcus, Quine, etc) were also superb logicians with an excellent understand of logic itself. Regardless of how you feel about his atheism, Richard Dawkins is in my mind the best philosopher of biology currently alive, and his first two books (Selfish Gene and Extended Phenotypes) are masterworks. Certain concepts in physics are much clearer when formulated in math - and you can only really explain them clearly once you are firmly grounded in the math. Speaking for myself, I've never met someone who I would describe as having a fantastic understand of QM yet skipped the formal mathematical training to deeply understand the equations.

> How can you do intelligent philosophy about probability if you don't have a good detailed understanding of what probability is?

There is more than one way to answer the question of 'what probability is'; you are advocating for an inductive approach where the general category is arrived at through exposure to particular instances; another approach is to work within a more general framework which expresses different types of probability theories as configurations of more general types. Granted, one must start inductively in order to get the general framework I speak of—but such frameworks are now in place, so it is not necessary for everyone who wants to compare theories of probability to proceed inductively. Then again, if your expertise is philosophy of probability you should do it anyway—but that brings me to the other point I wanted to make, which is: in my original post I was not referring to philosophers of probability, since that would be their expertise; instead I was referring to ancillary knowledge and whether someone acquires foundational or 'philosophical' (i.e. meta) knowledge of these ancillary fields.

As for whether there can be value to knowing about something like QM without knowing the math behind it, consider Feynman's preface to Q.E.D (the edition he wrote for the layman [well, transcription of lectures technically]). In it he describes the six years of training required in order to actually perform the mystical rites of physics, but knowing what the rites are about and what purpose they serve etc. is also valuable, which is why he wrote the book/gave the lectures (sorry, trying to give a rough quick summary, but the analogy he presents in the preface is the best explanation I've seen).

But that's exactly my point. Feynman was only able to give such a clear explanation because he really understood QM inside out.

If you want to describe yourself as someone who can read and appreciate Feynman's books - that's completely fine with me. However, I hope we can agree that reading Feynman's books (the ones for laymen at least) is not enough to call yourself a polymath.

> However, I hope we can agree that reading Feynman's books (the ones for laymen at least) is not enough to call yourself a polymath

Of course not. However, first off, the reason I brought up the specific book of Feynman's wasn't because I believe reading it gives you anything special—I was just referencing an argument that Feynman makes in the preface.

Secondly, I'm addressing what I see as an impossibility in what it appears to me that you're advocating for:

> I've never met someone who I would describe as having a fantastic understand of QM yet skipped the formal mathematical training to deeply understand the equations.

That quote sums up what I'm talking about. Another way of stating it, at the level of generality of the greater question at hand here: "no one who is not an expert in field X understands field X as deeply as someone who is an expert in field X" —since people generally already know that, the more useful question is, "If I'm going to learn some things about field X, even though I'm an expert from field Y and not field X—which things from field X should I focus on?"

I think part of our disagreement here comes from what one pictures the person with knowledge of many fields doing with that knowledge. Are they working professionally as a philosopher and then on the weekends as a physicist? If so, they have to be an expert equally in both. Or, is there something that can be added to their philosophy work by having fairly in depth knowledge of say, physics, linguistics, psychology, history, and literature? If you are going for this second thing, the way you pick up knowledge from the ancillary fields is different from if you're going for the first thing.

> but if you don't know either, then describing yourself as a Bayesian is just putting on airs.

The more charitable, and arguable more correct, interpretation is that there are (at least) two related but distinct meanings of 'Bayesian' being used. One is referencing Bayes' Rule and some of its implications; the other an entire sub-field of statistics. I'm guessing there isn't much overlap between the two groups of people.

It also certainly doesn't seem impossible to be, e.g. "an expert on classical literature but [not] know how to read greek/latin". Surely there's a lot to know about classical literature that isn't strictly pertinent to the actual vocabulary or grammar of ancient Greek or Latin. Or are you claiming that there's only one right way, or only certain right ways, for someone to augment their primary expertise with ancillary knowledge? I haven't previously encountered the idea that being a polymath implied expertise in numerous areas, just knowledge, tho presumably more than most laypeople.

The challenge with the classics example is that if you aren't capable of translating yourself then you are dependent on other peoples translations and therefore their interpretations, so you are adding a layer of indirection, sometimes more than one.

My Latin is woefully poor, but armed with a grammar and dictionary I can make a stab. Just doing that shows me just how much interpretation happens.

I doubt anyone would disagree "the world's foremost authorities" on classical lit need to know greek/latin.

But carefully reading and comparing several translations while following centuries of commentary can surely make one an expert on, say, themes in Greek epic poetry. I mean, if it doesn't then I'd just want to introduce into our conversation a distinction or two in the area of "knowledge use" and just stipulate which branch I'm intending by "expert"...

(This doesn't really matter for the previous point, but I actually think this just follows from agreeing with you and then taking even more seriously "how much interpretation happens".)

I think in terms of, to keep it simple, a 1-10 scale.

1 is nothing, you may or may not have heard of the field. 7,8,9,10 are increasing degrees of expertise

Given that sort of scale, I'd argue that a true polymath rates a 7 in three or more fairly distinct fields that don't have significant overlap with each other.

I think the problem, or watering-down of the term, are the abundance of folks that are around a 3 or 4 in a bunch of areas, maybe enough to get an entry level job that requires knowledge of the field, or roughly equivalent to minor or concentration in an undergrad program. In short, Jack of All Trades != Polymath.

Bayesian involves integration over priors, and conjugate prior/MCMC are tools for integration, which are implementation steps IMO, rather than essential part of understanding the Bayesian approach.

The two species are complementary; hedgehogs have the knowledge and expertise necessary to develop fine-granularity models of their domains, whereas foxes find commonalities and connections between many coarse-grained models. Foxes rely on hedgehogs to form their knowledge base; hedgehogs can use foxes' insights for new directions of research and development. Innovation (as opposed to optimization) is the result of cooperation occurring across vertical and horizontal model boundaries.

very nice comparisons!

All this discussion is with the implicit assumption that only humans can handle knowledge. But we have machines to help us.

So today it's easily possibly to talk with people from diverse fields, to search for knowledge of specific characteristics in different fields, or to reuse knowledge using code or patterns from a far field.

So it feels that with the right tools and technology and training, people could connect ideas from multiple fields, without deep investment, and being a polymath could be "democratized", similar to how many other complex tasks have been democratized.

And this field seems somewhat under-invested, relative to the potential.

Until computers get a lot smarter in understanding research papers, you'll always have the problem of unknown unknowns. How do you discover things in other fields if you don't even know the terminology? For example a medical researcher reinvented (or at least claims to have reinvented) some calculus: https://academia.stackexchange.com/questions/9602/rediscover...

If you never heard of calculus, googling for solutions can be difficult.

This is a paper from 1994, before the Internet etc we're popular.

But let's try:

1. Google to find what the relevant fields are - you get math. Search a forum about math -> discover math.stackexchange.com -> ask for help or even just terminology regarding "area under my graph/curve"? Once you get that , you could follow on it(say ask for a library of the most accurate integration method we know of today).

2. Google that, find relevant results and dig for terminology, and follow on it.

And sure , this isn't a bulletproof method, and you won't get 100% coverage. But it help find connections .

Its still people answering the stack overflow questions, and its still people writing the posts Google finds.

Not to mention knowing what to search for and how to find it is itself a very broad skill that requires ploymath type knowledge to really get the most out of it.

Same reason librarians seem to know a bit of everything.

Sure, there are still people writing stackoverflow answers, but they don't need to be polymaths to share their knowledge.

I think that Paul Otlet may be your man for that sort of thing. He was obsessed with how to organize and catalog not only things, but knowledge and information.

Interesting guy, and ahead of his time. It's too bad that his work (along with the rest of the world) was mostly dropped on the floor in the chaos of WWI and II. There's a book about him called, "Cataloging the World: Paul Otlet and the Birth of the Information Age."

https://en.wikipedia.org/wiki/Paul_Otlet

> being a polymath could be "democratized"

I'd see the optimum as the opposite type of "democratization": replacing most narrow experts with smarter and smarter AI/ML systems (that will sooner or later surpass human-level specialist knowledge in most areas), and have like 90% of human beings educated to be integrators/"polymaths"/expert-generalists instead! That would make 1000x more sense!

And of course, humans can be augmented with higher bandwith interfaces when these becomes available, then have their minds uploaded and become "software", when that becomes possible etc. The general idea is that human-pattern minds (whether human or future human-like ones) are one of the best type of minds for integrating/generalizing/being-polymaths etc.!

Imho our whole educational systems are 100% wrong for focusing on training narrow-experts and not of a mix of mostly integrators and "T-shaped people" instead! It's like we're training fishes to climb trees! Human brains are inherently bad at focusing and specializing by nature of how evolution built their freakin hardware even.

For those not familiar with the fox/hedgehog analogy the parent is using, it's something Isaiah Berlin originally wrote about: https://en.wikipedia.org/wiki/The_Hedgehog_and_the_Fox

Forgive the analogy, I know its leaky, but I believe it to be approximate.

I liken the mindset that leads to advances to something similar to the Rete algorithm, with human knowledge representing the alpha nodes and with human intellect representing the beta nodes, and human memory and computation power encompassing the whole graph. Once you match knowledge with a potential use of that knowledge, you create innovation. This can happen forwards or backwards, driven by new knowledge matching with existing applications (the research lab model) or with new applications matching with existing knowledge (the startup model).

The thing is, the rete graph requires enough working memory to store the graph. It really only works if knowledge and application can be co-located. And that means that polymaths have a huge advantage: their graphs are much bigger, so any new information has a much higher probability of matching up with something existing in their heads. This also explains why the greatest scientists and inventors tended to make their most significant discoveries later in life: their brain's graph had grown and become more useful and more connected.

The thing is, by using IPC with distributed memory and computation abstractions, you can expand that graph to be represented across multiple humans. That works too. But we must remember that our abilities to innovate across a multi-human graph absolutely rely on our speed and quality of communication, and it must navigate past filters that represent our own philosophical world view. And while that really puts a damper on our collective innovation abilities, it doesn't impede it and we shouldn't be discouraged by it.

TL;DR: The world doesn't need polymaths, per se. We can innovate by collective minds communicating with each other. But it's not as good, and so it's still really beneficial to have polymaths around.

Came here to say this.

As a post-doc in developmental cog neuro I feel I have to be a 'poly math.' Cognitive theory, Developmental processes theory, Brain theory, developmental brain processes, structural and fMRI methods and software, multiple regression (including mixed models, structural equation modeling) intermediate programming, linux administration, technical writing, experimental design, administration of research activities, teaching (??), and recently throw in autism research. On top of that, I'm reasonably informed on current events, read HN daily, keep tabs on the outlines of advances in medicine and other sciences.

I think I'll go back to sleep.

I am curious why the parent is earning down votes. Is it the comment about teaching?

Not trying to be critical, but I suspect that the gist comes out as "I am SO smart". If you chose a third person account you might have avoided them. Not sure, but that's my guess.

I was indicating that my field pulls me in so many directions that I am overwhelmed.. But I see now that I didn't articulate that well.

I didn't downvote it but it's possibly the "r/iamverysmart" feeling of it. It exists between the aforementioned and adding value to the conversation (ie, that certain current fields require both depth and breadth).

All I meant that in my field we are asked to have competence in a wide range of disciplines. In contrast to the 'r/iamverysmart' and consistent with the article, I feel intimidated by those that do specialize in those things I use. I am aware of a lot, but I feel like I am pretender in all of them. I constantly come into contact with the limits of my intelligence and I am not impressed.

This is what being active in life sciences research is like unfortunately. There is no luxury of concentrating one 1 or 2 things.

Not entirely sure, but maybe it's your last line...

I think I am going to sleep is indicating that I can feel overwhelmed.

The biggest pressure against polymaths is the structure of the modern university. From department organization, mentoring, battles for funding, it is very difficult to find an encouraging environment if you don't stay within a narrow niche.

As an aside, I feel like most interesting innovation in academic computer science happened before the field was full of computer scientists. In the early days, the field was a meeting point of trained mathematicians, physicists, economists, engineers, and linguists, and innovation flourished. To some extent, I credit people exploring and communicating about similar concepts from multiple perspectives. Now, everybody in academic CS has taken the same path in life, and it makes things quite boring.

The decline in the pace of discovery, if it is real, could also be because the early researchers took the low hanging fruit.

I thought a polymath was someone who had mastery of more than one very difficult / elusive / elite skillset.

Someone like, say, Brian May (Queen guitarist and astrophysicist).

The guys profiled know a lot of trivia, which is certainly impressive -- but does this really make them polymaths?

Reminds me of Dan Spitz, lead guitarist of Anthrax and master watchmaker, and John Urschel, Ravens offensive lineman and mathematician.

We are living in a 'cooperative/corporate' age, where the prime drivers of innovation are collections of humans rather than individuals. The problems we face are more complex than ever before and exceed the individual capabilities of even the brightest among us.

Visionary thinkers still have their place. A Cooperative needs leaders to chart its course. In a complex world, people who can derive inspiration from multiple domains of knowledge will always be valuable.

Groups of people have issues scaling. At the scale of the say the DoD you end up with a lot of inefficient redundancy which pushes organisations to specialize.

Google for example does not actually do that many different things, it just has crazy amounts of leverage.

I think people are (slowly) re-learning the importance of redundancy. Having multiple, competing implementations makes you far less vulnerable to shocks.

Using relational databases as a model for the structures in question, some form of redundancy (secondary and primary keys) is needed to avoid more redundancy (dublication). I actually don't know what I'm talking about, if it made sense to someone, please correct me where I'm wrong.

This is not really productive redundancy as for example the Navy and Air Force can't easily swap HR systems. This is mostly everyone being their own little snowflake.

Individuals have even more trouble scaling.

I am reminded of a bit, possibly apocryphal, that when the first three-fin rocket (instead of four, as had been the case with the V-2 and successors) was proposed it was questioned whether or not it would be stable, up until someone pointed out that arrows with three fletching feathers had been flying straight for quite some time.

I'm reminded of Nietzsche's Zarathrusta where there's an encounter with an expert on the brains of leeches. For me the question of whether we need polymaths is one about what sort of society we desire and it's a very easy question to answer. I wonder whether the much discussed decline in productivity, which can of course be debated, isn't largely the result of becoming a society of leech brain experts.

I'm grateful to share the world with anyone who is trying to think and is brave enough to communicate their ideas in the face of career stagnation.

That said, I expect most geniuses are polymaths by conventional standards, whether we need them to be or not. Their intellectual development is neither a well-rounded curriculum nor a steady progression but marked by series of deep obsessions.

We probably need polymaths more than people writing clickbait headlines for the BBC.

We should all be encouraged to be polymaths since school. But I believe the great challenge is not really to push such idea to students, but to actually make them find interest on what they're expected to learn, be it to become polymaths or leech brain experts.

I'm saying that given the education background from my country, Brazil. I was surprised, back when I was teaching programming to kids, at how seem to care so less about the actual learning process, while still having a lot of learning potential.

“The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite insane.” (Nikola Tesla)

I feel that when I read old textbooks, even the children's ones.

People have gotten less coherent, I don't know why, but I suspect it is so.

I know a lot of companies in the engineering/science world that hire PhDs who are experts in very specific fields and others who have broad knowledge in a lot of fields. They try to balance these 2 types of people: broad versus specific and have them work together for synergy.

The article doesn't go very deep in to the answer.

Maybe they aro good managers, maybe communicatiors, but either way it's a bit of a specialization in itself that benefits greatly from broad knowledge. I don't see how exactly they could bring together different sciences directly.

While I'm not sure I'd say I'm qualified to be an expert on all of these subjects, and thus not a 'polymath', I've at least understood enough to teach software development, game design, and writing to others, and have worked professionally in each of those fields, and I've consumed a good amount of articles, podcasts, and books on each as well.

I've actually found myself drawing from each of these fields as well as other subjects I have a cursory knowledge in (linguistics, philosophy, psychology, etc) to come up with new ideas for the other subjects, so I personally think having a decent amount of knowledge in multiple fields and cross-pollinating between them is very useful.

Scott Adams even suggests becoming very good at two or more things in his blog about career advice.

>Capitalism rewards things that are both rare and valuable. You make yourself rare by combining two or more “pretty goods” until no one else has your mix.

http://dilbertblog.typepad.com/the_dilbert_blog/2007/07/care...

Yes, because a lot of innovation comes from transferring knowledge between unrelated fields. There is a lot of benefit to cross disciplinary knowledge.

FWIW and/or for anyone interested, here's a related Wikipedia on the subject, talking about the different types of knowledge spillovers (MAR, Porter, Jacobs).

https://en.wikipedia.org/wiki/Knowledge_spillover

Sweet, I didn't realize there was a formal term for this concept, but it makes sense that economists would have tried to formalize this :-)

Can a polymath not be a scientist by training? It seems like so many topics today require substantial grounding in quantitative skills that are almost impossible to gain outside grad-school-level studies in science and engineering. Can a polymath whose expertise spans the sciences truly come from elsewhere -- math, economics, philosophy, etc?

In a similar vein, I have yet to read a popular science book written by a non-scientist that comes close to the incandescent prose of the best scientist authors -- all of whom seem to be professional scientists (Dyson, Sagan, Morrison, Wilson, Medawar, etc).

Of course their skill came not only from academics, but from that rare mix of curiosity and rigorous inquiry essential to separate what we know from what we don't, and of course, the passion to push beyond into the unknown.

So can such skills essential to a polymath also arise from outside science?

Even in this day and age, you can become a "quasi-polymath" if you like learning and are efficient at it. By that I mean, reach 80% understanding of a lot of fields with 20% the effort of becoming an expert. You can do that by choosing good learning resources and focusing on conceptual understanding and fundamentals.

This is something I wish to do over time, learn about a bunch of fields to, say, about undergraduate level. Right now I'm reading Molecular biology of the Cell (best textbook I've ever come across by the way) and it's rewarding to be able to understand much more of biology research news for example. And when you want to learn about some specific sub-topic on Wikipedia, you have the fundamentals to do that without saying "I know some of these words".

Is this really an article about polymaths that doesn't mention a single Islamic polymath?

The whole concept of polymath is not that you're a genius or even knowledgable about a bunch of stuff. In the Islamic tradition the concept insists that you can't understand math without knowing poetry. Can't understand medicine without understanding geometry etc. All elements of human interpretation and expression are linked and help you explore the other.

Here's a list of polymaths that the article didn't mention: https://en.wikipedia.org/wiki/Islamic_Golden_Age

> The whole concept of polymath is not that you're a genius or even knowledgable about a bunch of stuff.

Actually, I think that's exactly what it means. The Wikipedia entry on Polymath[1] says basically the same thing as the article as does my dictionary.

[1]: https://en.wikipedia.org/wiki/Polymath

> A polymath (Greek: πολυμαθής, polymathēs, "having learned much")[1] is a person whose expertise spans a significant number of different subject areas; such a person is known to draw on complex bodies of knowledge to solve specific problems.

The first paragraph from that article.

That's almost exactly what my dictionary says. I think you and I are in agreement. Pretty much by definition, a polymath is knowledgeable about a bunch of stuff.

> Pretty much by definition, a polymath is knowledgeable about a bunch of stuff.

Certainly. I was (misunderstandingly I guess) getting at the genius part, as that's not really required. Also, I guess SandersAK was giving the islamic perspective on polymathness, not his.

Genius isn't required, but I'd wager polymaths are geniuses at a higher rate than the general population.

I think your point concerns the 'value' and not so much the 'definition'. As for 'concept', I think that's just the wrong word here.

Great contribution to the conversation if it were worded with the specificity those interested in the topic will probably be looking for.

Ultimately, this article is mostly clickbait; nothing novel or conceptual.

Yes. The industry calls them system engineers.

Like this woman? http://slippedisc.com/2017/08/i-gave-up-a-career-in-the-defe...

She sounds like this:

https://slippedisc.com/2017/08/last-night-the-aida-missed-he...

A friend of mine is a Ph.D. philosopher, playwright, director, actor, singer-songwriter, and retired [due to training injury] undefeated (3-0) professional boxer. Do they qualify?

Contrary to Betteridge's law, yes we need polymaths. Asimov wrote a story along these lines. Already there are cases of esoteric knowledge in one field being applicable to another. I recall, though cannot find the reference, of a pure maths technique being applied to quantum physics which only happened by the fortunate meeting of two researchers.

Heck, it already happens entirely inside of a field: probably once a year and at least once a decade, there's a major paper in math or physics that is basically "applying standard technique in subfield A to subfield B".

Indeed, one of my professors in grad school defined a research contribution as adding an edge in a metaphorical bipartite graph to link formerly disparate subfields.

For the curious, the Asimov story is called Sucker Bait, from 1954.

That's the one!

Feynman did most of his physics using straight calculus. He hid his work to make it look like it was easy for him...

The pure maths technique you are thinking about is the Monster group [1]. Sadly, I don't recall the names of the two researchers involved in the chance meeting.

[1] https://www.quantamagazine.org/mathematicians-chase-moonshin...

Looking back at 2018, how is it possible that just before our flourishing age of polymaths, it was not uncommon to see nonsense written like "Two hundred years ago, it was still possible for one person to be a leader in several different fields of inquiry. Today that is no longer the case."? I suggest it was a lack of situational awareness, about several issues.

About having time to excel. Artificial light capturing the night was a century past. Electrification and its labor saving was almost that. Few still farmed, and the cultural memory of the effort required had decayed. Commuting was common, and it was rare to be able to work during it. Consumer robotics and AI were still novelties. Major industries, both legal and illegal, were focused on encouraging people to squander their time. So there was no sense that people had more time available in the present than in the past, or might have more in the future.

About education. Education was still a wretched disaster, largely unchanged for centuries. Science content was particularly abysmal. There was some professional recognition of this (for example, chemistry education research characterizing high-school chemistry content as incoherent), but it was not widely appreciated. Popular focus was on the relative gap between "well" performing and poorly performing students. With no thought that future primary school students might soon be outperforming their present undergraduates. An educator might speak of nanometers as being "unimaginably small", rather than something played with in pre-K. The Internet was just old enough to be taken for granted, so on the eve of AR/VR mass deployment, people were mumbling the same nonsense as in decades past "I can't imagine these computers/internet/AR will have any noticeable effect on people's lives". Past progress, such as mass education regardless of class, was taken for granted. Such progress as was happening, such as attending to misconception ecologies, was not widely appreciated. They knew in the abstract that civilization advances by a teacher being able to pass on knowledge more easily then they themselves learned it. But having no sense of existing change, or of the backed up logjam of potential change, they were blindsided by the rate of change once the jam broke.

About science. Access to scientific knowledge was still highly circumscribed. Many journals were still not open access. Some research talks were on youtube, but it was still rare. Much insight into fields was still localized to conversations at conferences, and spread by word of mouth. Again, the world of paper journals and paper card catalogs was sufficiently past that there was no sense of the velocity of progress. "Non-scientists" contributing to science was seen as a novelty - the parents of a child with a rare disease becoming experts on it; or children with bees by chance asking an interesting question. Larger examples, such as community characterization of galaxies, were seen as isolated cases. Because hybrid AI-human systems, and computer supported cooperative work, were still in their infancy, and unappreciated. There was little sense that science had profoundly changed in the preceding half century, or would similarly change in the next.

So I suggest their blindness was rooted in a failure to understand their present, and a neglect of looking beyond it. A neglect of looking at their past, and thus of appreciating the velocity of change marked by their present. A failure to understand their present, and its defining constraints. And a neglect of reflecting on how those constraints were about to change. They lived in a bubble of time, peering myopically at the world, and thought themselves unmoving.

Dot connectors are always welcome.

I am not an expert in anything, but I am working on it. When I try to focus on studying one discipline consistently for a period of time, I get distracted (and excited!) when I notice patterns that could inform other disciplines. While it is distracting, the patterns are able to help me digest new concepts faster. I have noticed this connection-making inspires heaps of my creativity.

Explaining computer science to otherwise non-technical philosophy grads is not only easy; it is what I would call a 'downhill process'. This probably depends on them being decent philosophy students, of course.

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