IMO: I think there is a helpful distinction to be made between leadership and management. Leadership provides purpose and inspiration. Management provides, coordination and motivation. I’m not saying one person can’t do both.
I do agree that most management books read like parenting books - but I’d add that whats more important than the method is consistency in whatever approach you believe in. I’m not sure that managers/leaders will ever do that well relying on a book or a special ‘way’ they have read. They really need to have worked this out for themselves.
I think this would be extremely valuable:
“We need to focus far more energy on understanding and explaining the basic mental infrastructure of mathematics—with consequently less energy on the most recent results.”
I’ve long thought that more of us could devout time to serious maths problems if they were written in a language we all understood.
> I’ve long thought that more of us could devout time to serious maths problems if they were written in a language we all understood.
That assumes it’s the language that makes it hard to understand serious math problems. That’s partially true (and the reason why mathematicians keep inventing new language), but IMO the complexity of truly understanding large parts of mathematics is intrinsic, not dependent on terminology.
Yes, you can say “A monad is just a monoid in the category of endofunctors” in terms that more people know of, but it would take many pages, and that would make it hard to understand, too.
Players of magic the gathering will say a creature "has flying" by which they mean "it can only be blocked by other creatures with reach or flying".
Newcomers obviously need to learn this jargon, but once they do, communication is greatly facilitated by not having to spell out the definition.
Just like games, the definitions in mathematics are ethereal and purely formal as well, and it would be a pain to spell them out on every occasion. It stems more from efficient communication needs then from gatekeeping.
You expect the players of the game to learn the rules before they play.
I'd say the ability to take complicated definitions and to not have to through a rigorous definition every time the ideas are referenced are, in a sense a form of abstraction, and a necessary requirement to be able to do advanced Math in the first place.
Many mathematicians do in fact teach the rules of the game in numerous introductory texts. However, you don't expect to have to explain the rules every time you play the game with people who you've established know the game. Any session would take ages if so, and in many cases the game only become more fun the more fluent the players are.
I'm not fully convinced the article makes the claim that jargon, per se, is what needs to change nor that the use of jargon causes gatekeeping. I read more about being about the inherent challenges of presenting more complicated ideas, with or without jargon and the pursuit of better methods, which themselves might actually depend on more jargon in some cases (to abstract away and offload the cognitive costs of constantly spelling out definitions). Giving a good name to something is often a really powerful way to lower the cognitive costs of arguments employing the names concept. Theoretics in large part is the hunt for good names for things and the relationships between them.
You'd be hard pressed to find a single human endeavor that does not employ jargon in some fashion. Half the point of my example was to show that you cannot escape jargon and "gatekeeping" even in something as silly and fun as a card game.
The article does not complain about notation. It describes how the different fields of mathematics are so deep and so abstract that it’s hard to understand them as a professional mathematician in a different field. That’s a hard problem worthy of discussion, but as the article says, it’s not as much a problem of notation or of explanations, rather than it’s just intrinsically difficult and complex because these are abstract and deep fields.
The only thing that sentence says is that it’s impossible to understand math without understanding the language of math and how it is constructed. Not sure how that is controversial or gatekeeping. If you are annoyed at that comment saying “learn” instead of “be taught”, I think that’s a pedantic argument because the argument wasn’t about that at all.
Again, learning notation is part of the process of learning math. No one is gatekeeping anything, at no point you need to do an exam or magically be aware of notation that you never saw. Every book and every class will define new notation at the beginning, in most cases they will do so even when there’s no new notation. I am not sure what your argument is.
That’s a very good gate to keep. Some things are just meant to be gatekept so that the cranks and dilettantes that wastes everyone’s time can stay far outside.
He separates conceptual understanding from notational understanding— pointing out that the interface of using math has a major impact on utility and understanding. For instance, Roman numerals inhibit understanding and utilization of multiplication.
Better notational systems can be designed, he claims.
Yeah, I don't want to be uncharitable, but I've noticed that a lot of stem fields make heavy use of esoteric language and syntax, and I suspect they do so as a means of gatekeeping.
I understand that some degree of formalism is required to enable the sharing of knowledge amongst people across a variety of languages, but sometimes I'll read a white paper and think "wow, this could be written a LOT more simply".
> Yeah, I don't want to be uncharitable, but I've noticed that a lot of stem fields make heavy use of esoteric language and syntax, and I suspect they do so as a means of gatekeeping.
I think you're confusing "I don't understand this" with "the man is keeping me down".
All fields develop specialized language and syntax because a) they handle specialized topics and words help communicate these specialized concepts in a concise and clear way, b) syntax is problem-specific for the same reason.
See for example tensor notation, or how some cultures have many specialized terms to refer to things like snow while communicating nuances.
> "wow, this could be written a LOT more simply"
That's fine. A big part of research is to digest findings. I mean, we still see things like novel proofs for the Pythagoras theorem. If you can express things clearer, why aren't you?
Statistics is a weird special case where major subfields of applied statistics (including machine learning, but not only) sometimes retain wildly divergent terminology for the exact same concepts, for no good reason at all except the vagaries of historical development.
I'm surprised at how could you get at this conclusion. Formalisms, esoteric language and syntax are hard for everyone. Why would people invest in them if their only usefulness was gatekeeping? Specially when it's the same people who will publish their articles in the open for everyone to read.
A more reasonable interpretation is that those fields use those things you don't like because they're actually useful to them and to their main audience, and that if you want to actually understand those concepts they talk about, that syntax will end up being useful to you too. And that a lack of syntax would not make things easier to understand, just less precise.
>
I understand that some degree of formalism is required to enable the sharing of knowledge amongst people across a variety of languages, but sometimes I'll read a white paper and think "wow, this could be written a LOT more simply".
OK, challenge accepted: find a way to write one of the following papers much more simply:
Fabian Hebestreit, Peter Scholze; A note on higher almost ring theory
What I want to tell you with these examples (these are, of course, papers which are far above my mathematical level) is: often what you read in math papers is insanely complicated; simplifying even one of such papers is often a huge academic achievement.
These papers are actually great examples of what is problematic with mathematics, just as what is problematic with papers in any other specialised field: how do you judge if this could be ever useful to you?
If you want to understand what is going on there, what is the most effective way to build a bridge from what you know, to what is written there?
If you are in a situation where the knowledge of these papers could actually greatly help, how do you become aware of it?
I think if AI could help solve these two issues, that would be really something.
My opinion on this is that in mathematics the material can be presented in a very dry and formal way, often in service of rigor, which is not welcoming at all, and is in fact unnecessarily unwelcoming.
But I don’t believe it to be used as gatekeeping at all. At worst, hazing (“it was difficult for me as newcomer so it should be difficult to newcomers after me”) or intellectual status (“look at this textbook I wrote that takes great intellectual effort to penetrate”). Neither of which should be lauded in modern times.
I’m not much of a mathematician, but I’ve read some new and old textbooks, and I get the impression there is a trend towards presenting the material in a more welcoming way, not necessarily to the detriment of rigor.
The upside of a "dry and formal" presentation is that it removes any ambiguity about what exactly you're discussing, and how a given argument is supposed to flow. Some steps may be skipped, but at least the overall structure will be clear enough. None of that is guaranteed when dealing with an "intuitive" presentation, especially when people tend to differ about what the "right" intuition of something ought to be. That can be even more frustrating, precisely when there's insufficient "dry and formal" rigor to pin everything down.
If it's actually in the service of rigor then it's not unnecessaryily unwelcoming. If it's only nominally in the service of rigor than maybe, but Mathematics absolutely needs extreme rigor.
The saying, "What one fool can do, another can," is a motto from Silvanus P. Thompson's book Calculus Made Easy. It suggests that a task someone without great intelligence can accomplish must be relatively simple, implying that anyone can learn to do it if they put in the effort. The phrase is often used to encourage someone, demystify a complex subject, and downplay the difficulty of a task.
3blue1brown, while they create great content, they do not go as deep into the mathematics, they avoid some of the harder to understand complexities and abstractions. Don't take me wrong, it's not a criticism of their content, it's just a different thing than what you'd study in a mathematics class.
Also, an additional thing is that videos are great are making people think they understand something when they actually don't.
3blue1brown actually shows the usefulness of formalism. The videos are great, but by avoiding formalism, they are at least for me harder to understand than traditional sources. It is true that you need to get over the hump of understanding the formalism first, but that formalism is a very useful tool of thought. Consider algebraic notation with plus and times and so on. That makes things way easier to understand than writing out equations in words (as mathematicians used to do!). It is the same for more advanced formalisms.
In this modern era of easily accessible knowledge, how gate keepy is it though? It's inscrutable at first glance, but ChatGPT is more than happy to explain what the hell ℵ₀, ℵ₁, ♯, ♭, or Σ mean, and you can ask it to read the arxiv pdf and have it explain it to you.
I say the same thing about the universe. There is some gate keeping going on there. My 3 inch chimp brain at the age of 3 itself was quite capable of imagining a universe. No quantum field equations required. Then by 6 I was doing it in minecraft. And by 10 I was doing it with a piano. But then they started wasting my time telling me to read Kant.
This highlights one of the big problems with liberal democracies - how do you provide efficient (and even innovative) public services? There is no free market for many public services like water (and where there is I’m all for privatisation). But the people (I am in the UK) do not tend to elect a government on its ability to manage these types of services. I do wonder if there some other structure that blends a not for profit ethos with employee ownership and just enough competition…
> I do wonder if there some other structure that blends a not for profit ethos with employee ownership and just enough competition
Legislate that certain public services are to only be managed and administered by the civil service managed and autonomous statutory boards. That's probably the easiest thing to do in a parliamentary system like the UK. Sort of like a "Water Management Board".
Not every function in a democracy needs to be democratic in nature.
Heck, this is how the UK managed colonial territories like Singapore and HK with the civil service run HDBs, and how a lot of the UK was run before Thatcher's privatization.
This is the classic answer to these problems, but I think these "non-profits" and "civil managements" are inherently problematic.
Let's say that John Doe is a very accomplished visionary individual, and has quite a few revolutionary good ideas around improving the water system. Obviously Mr. Doe needed lots of lab equipment to gain experience and insight into these systems, and realistically needs a lot more if he wants to live to his full potential and benefit the public. He is determined to work towards the greater good, but also needs a lot more power [than the average citizen] to test his ideas.
Therefore in order to [be able to] accept this role, he has to be well-compensated (as a one in the world person). Therefore the payment package must look a lot more like the CEO compensation or a high-end management position, which is contrary to the idea of civil management.
Said differently, money can be a good proxy of the power to bring about changes, and if we truly want to try radical ideas (as we should in challenging problems), we need powerful individuals that can risk [their own fortune of course], not committees of less powerful people best suited for maintaining the status quo. In other words, the average citizen is much too risk averse to accept (or approve the payment package of) John in this position, and this can lead to stagnation.
I believe a better way to manage these systems that simultaneously protects the public from adverse incentives and allows high risk high reward behaviour is a middle ground. For example a risk averse non-profit for day to day operations + prize systems + modest (not too big) government-run research facilities.
Fundamentally speaking, there is always a risk / reward tradeoff, and I believe the current society is too conservative and is missing out a lot of opportunities (compared to let's say the cold war or WW2 era). We need to somehow rebalance this scale to live near a better operating point.
> but I think these "non-profits" and "civil managements" are inherently problematic.
I'm not talking about "non-profits" or NGOs. I'm talking about legislating autonomous organizations within ministries with full autonomy and remit to execute on their jobs and only report directly to the Minister or the Permanent Secretary.
This is what Singapore does, which itself is based on the British colonial model.
At some point, too much democracy is delerious, and Tom, Dick, and Harry need to know their place. Not everything needs to be politicized and democratized.
> Therefore the payment package must look a lot more like the CEO compensation or a high-end management position, which is contrary to the idea of civil management
What country are you from? Even the UK has begun developing statutory boards like the FCA and SFO that pay market rate salaries for critical roles.
And until the Thatcher era, civil service pay was comparable or slightly better paid compared to other white collar roles.
That sounds like more quangos? I'm not an expert on them but the way people complain about them, they have a penchant for wasting fantasic amounts of money, and have no accountability even by the standards of the civil service.
Politicians are simultaneously engaged in a desperate struggle to close down the defunct ones while opening up more, because they are a great way to avoid responsibility, which of course is one of the major operational goals of the civil service.
Not like Quangos - Statutory Boards at least in Singapore are a part of a ministry, but they are given full autonomy [0] to recruit, administer, and manage within their remit as legislated.
Quangos are a half assed attempted at doing something similar while trying to include some "inclusion", but with none of the checks and balances.
The reality is, not every Tom, Dick, and Harry should have a say on water management or R&D prioritization.
Was not aware of these - thank you for sharing. But I’d be concerned that such organisations will not stand the test of time, from say a sustained period of governmental (on in this case institutional) incompetence. I’d like to see some mechanism (competition perhaps) that would allow the system to self correct - when the group responsible fail for a sustained period of time. Not saying I have any answers.
A triumvirate of Unions, government, and private enterprise are supposed to be balanced and keep each other in check the same way the three branches of government in the United States are supposed to keep each other in check.
And just as the executive branch has bloated into a monolith at the expensive of Congress, private enterprise has bloated at the expense of Unions (just as true in the U.K. as far as I can tell).
You have the two primary governmental/economic systems of balance failing in the same way, at the same time, both failing due to the actions of corporations.
This kind of failure may be common with liberal democracies but is not inevitable. We have simply been bad stewards and let corporations vacuum up everything with little resistance.
I think it would be better to describe this as an ‘organelle’ transplant as it would be easier for people to understand and discuss. Yes there is a donor (egg) and yes the new child will pass on the mitochondria to her children. But calling it a 3 person baby is unhelpful and misleading as IMO mitochondria DNA is of a different category to chromosomal DNA.
It's inheritable so it's more than a liver transplant.
I agree that DNA in mitochondria is much smaller than DNA in the nucleus. But in each person there are many mitochondria and they nay have slightly different DNA. And the DNA in mitochondria has a different variation than the DNA in the nucleus. So it's difficult to weight both.
Can we say 2.1 parents? A long time ago I read that most binary classifications are not completely binaries, it's just that 2 options cover almost all the cases. (Are virus alive?) I guess integer classifications also have hidden corner cases.
I also remember from a biology book that in a lab they mixed two blastula(?) of small lizards(?) or something like that. They had different skin color and the baby had patches of both colors. Does that count as 2 or 4 parents?
Certainly Mother Nature is not obliged to have simple easy to understand binaries where it would be convenient for us and so if we think we see such a binary we should keep in mind that maybe we hallucinated it into existence because it was convenient and that's all.
I agree wholeheartedly. This strikes me as the way science works. Theories are useful because of their predictive value. If we think of biological sciences as different than physical or mathematical, it seems we have set ourselves up for failure. Yet that seems like exactly the kind of perspective missing and trying to be pointed out by the earlier comment's attempted splitting of the difference to "2.1 parents" to me.
> I think it would be better to describe this as an ‘organelle’ transplant as it would be easier for people to understand and discuss.
Unlike previous attempts, the donor mitochondria are not transferred into the mother egg. Instead the donor cell is denucleated, and the nucleus from a mother's egg is transferred into the denucleated donor cell. Consequently, there is a wide variety of donor specific material, which may influence the early stages of development and only "wash out" after a number of cell divisions.
> But calling it a 3 person baby is unhelpful and misleading as IMO mitochondria DNA is of a different category to chromosomal DNA.
How so? Arguably, mitochondrial genes are much more essential than most nuclear genes.
1. Mutations in any mitochondrial gene often have dire consequences, whereas variants in nuclear genes are much more frequent.
2. Mitochondrial DNA is the most expressed in pretty much any cell by a huge margin. Mitochondria express 13 (IIRC) protein coding genes and two dozen other RNAs. Those 30 odd genes often make up 1-5 % of a cell's whole transcriptome. Only genes coding for ribosomal RNA are more strongly expressed.
While it is a different category that chromosomal DNA, it is still an essential part of mammalian life. None of use would exist in our current forms without mitochondria
As I understand it, a human egg has about an equal quantity of nuclear and mitochondrial DNA. The mitochondrial DNA is highly replicated, though (about 100,000 mitochondria, each with ~16600 base pairs of DNA).
> For most organisms the "stop codons" are "UAA", "UAG", and "UGA". In vertebrate mitochondria "AGA" and "AGG" are also stop codons, but not "UGA", which codes for tryptophan instead. "AUA" codes for isoleucine in most organisms but for methionine in vertebrate mitochondrial mRNA.
I found the following paper helpful in understanding the evolutionary pressures on a species (https://www.science.org/doi/10.1126/sciadv.abg5391). It's possible for two different genetic ancestries to arrive at the same phenotype independently where there environment is virtually identical. The example here, cichlid fish in lakes like Tanganyika and Victoria, evolved similar traits independently from different genetic lineages.
One could imagine (climate change not withstanding) that different geographic human populations would always tend to evolve to the same phenotype over time.
Thank you for posting this. Someone had told me this and attributed it to Clausewitz - so I've never been able to track it down. I've used it to make the case that laziness is not always a bad thing - i.e. lazy people find it easier to delegate.
I can agree with this. Growing up in the UK, with an Irish mother, I was taken to funerals as a child that I really did not want to attend. Like the author I now always go the funeral, and have found it strange this attitude is not more pervasive.
I do agree that most management books read like parenting books - but I’d add that whats more important than the method is consistency in whatever approach you believe in. I’m not sure that managers/leaders will ever do that well relying on a book or a special ‘way’ they have read. They really need to have worked this out for themselves.
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