Decades-Old Graph Problem Yields to Amateur Mathematician
quantamagazine.org
quantamagazine.org
He's also Thiel backed.
Just to precise if you were confused like me, Cambridge gave him an actual PhD in Biology based on the book - meaning the book satisfied all the prerequisites of a PhD at Cambridge and he had to do a viva - not just an honorary degree.
That's quite an impressive fellow.
a) write a thesis
b) find examiners (internal and external) who agree to examine you; if you're a grad student this is your advisor's job. The examination is by thesis review followed by pass/pass-with-corrections/fail oral exam. It can take as long as it needs to (typically three to four hours), and is in private; it's not like public defenses elsewhere, which are for show, this is a real live-fire exam and I know people who have failed
c) pass
d) ... that's it; there is no part d)
In particular, there are no quals or other requirements; the degree is an old-school medieval masterwork deal. You submit your thesis and get examined on it. Typically you write your thesis through an apprenticeship to your advisor, but that's not actually required, it's just conventional; in Aubrey's case, the thesis was the book and the research proceeded by unusual means over a long period of time. Nevertheless, he got examined in the same way everyone else does, he passed like everyone else did, so he has his PhD.
(source: my own memory, I know Aubrey and have worked with him on a couple of non-science things fifteen years ago, and I got my PhD from Cambridge through the traditional route of being a grad student – thesis at https://aspace.repository.cam.ac.uk/handle/1810/218854?show=...)
The alternative 'special regulations' apply only to graduates of the Cambridge University, or graduates of another university who have been admitted "to some office in the University or to a Headship or a Fellowship of a College" [3].
> d) ... that's it; there is no part d)
Well, the most likely outcome of the viva is a pass with minor corrections, so there typically is a part d - "make the corrections requested by the examiners and re-submit".
[1]: https://www.admin.cam.ac.uk/univ/so/2017/chapter02-section9....
[2]: https://www.admin.cam.ac.uk/univ/so/2017/chapter07-section13...
[3]: https://www.admin.cam.ac.uk/univ/so/2017/chapter07-section13...
I think the spirit of what I wrote is broadly accurate. d) was definitely a rhetorical indulgence!
https://www.undergraduate.study.cam.ac.uk/applying/entrance-...
I wasn't familiar with this term; apparently it refers to the "oral defense" of a PhD thesis.
However amateur often means - in British English - simply "low skilled" as professional can mean "formally carried out with high competence".
Doesn’t surprise me at all to hear this.
Is having Thiel's association a positive thing still? Serious question.
Even if you know the story well, the book is worth a read or listen.
I don’t care, I’m an atheist with no kids who’d be bored out of my mind before I hit 300 years old, much less 1,000.
My father in law was at the bikini islands for the test runs (died of cancer), my great uncle was on the ground in Japan shorty after they dropped Hiroshima (died of cancer), and great uncle’s kids has Japanese rifles he recovered from sites that glowed in the dark as late as the mid 70s.
(Probably anyway, I don't personally know anyone that is Thiel backed)
* Half a million people die each year and 400 million fall ill [with malaria]
* 70% of them are children under 5
* #1 killer of pregnant women
* Malaria is preventable
Malaria nets cost $2. Antimalarial drugs are dirt cheap in the developing world. If you want to impact human suffering and increase human health, this is a good place to start. Not with trying to extend the long and already pleasant lives of rich people in the West.
it’s an utterly worthless comment. I don’t want waste my time explaining why you’re wrong but I did blog a related response a year ago:
https://h4labs.wordpress.com/2017/03/28/stories-that-should-...
The short answer is that there are lots of people and lots of resources. It’s not going to hurt if some of those resources work on problems that you don’t think have a high priority.
I bet you can find plenty of people who aren’t working to solve any problems. Why don’t you berate them instead of someone who picked a problem that you think is less important.
Probably not for most problems, but even ignoring the QALY calculations, pathogenic diseases (like malaria) are kind of unique amongst the landscape of global issues right now, in that you can actually permanently solve them with some level of attention, at which point they no longer require any donations but continue to provide benefits forevermore.
Polio is just... gone. We don't need to fight it any more. But that's only true because we (or rather, our governments) spent a whole lot of money over a very short period. If they had spread that money out over a longer period (equivalent to what would happen if fewer people were donating), polio would still be here, and not just because we "killed it slower"—it would still be thriving, because it was only being fought with half-measures. If someone only has enough money to pay for half a course of antibiotics, they may as well not take any.
Pathogens are the best justification we have for "focus firing" public resources toward a single goal. It really is a case of "we should be spending money on nothing else until we've solved this." (At least, if we're bothering to spend any money on the problem at all. 100% or 0%, but don't bother in between.)
Once we run out of "easily"-eradicable pathogens, though, the calculus of comparative advantage resumes, and it makes sense again to donate to a variety of things.
There are major efforts to treat malaria, for example. Bill Gates is putting in billions.
https://www.reuters.com/article/us-health-malaria-summit/glo...
There’s this great effort too:
https://malariaelimination8.org
I’ve even donated money for nets myself.
Part of the problem isn’t money but changing attitudes. A lot of nets, for example, end up being used for fishing.
https://learningenglish.voanews.com/a/mosquito-nets-widely-u...
On the other hand, aging is unique in that solving it (or even just pushing it back a bit) gives multiplicative effects to productivity against any problem that requires decades of expertise, because it lets researchers have more productive decades and/or spend more years learning to be productive and yet still spend just as many years being productive. Malaria, at this point, isn’t quite the type of problem this would help—but there certainly are many problems where more grabbing out more productive researcher man-years from the aether would be extremely helpful.
It’s rather interesting to think in these terms: trying to figure out which advance will have “unblocked the tech tree” the most 50 years down the line. I rarely see this kind of analysis being done, though, which I find disappointing; surely there are people far better equipped than I to do it.
Consider all the problems you need to solve to “cure death”.
The US GDP is $17 trillion. If people starting spending billions on a more youthful old age, we’d get more research. More venture capital would go to aging research.
It's also, in a sense, an unfair argument. You could say the same thing about any other startup. "Oh your goal is to create some new app/service/software? Why not instead focus your efforts on preventing malaria?" The fact that this startup is focused on longevity should not make it more deserving of your above criticism.
Would you? If given the option between extending your life to the age of 200 through yearly payments of $10,000 -- or instead donating that money to save countless lives a year, which would you do? Maybe you would donate it, I don't know you, and I won't presume the answer. But is it a callous indifference to pick yourself instead? Maybe it is, and if so, I'm callously indifferent.
We could play with those numbers though, to see how you would value an additional year of your life vs. saving a year for one of the world's poor. Would you value them the same? It's only natural to value your life, and your family's life, higher than others. What's the number where it's not callous indifference? It's worth thinking about, although I don't think the answer to these questions is pure nihilism or anything, we should definitely work to improve the world, and certainly donate more than we do now.
But the point I'm arguing against is that this doesn't mean we also need to put on hold work to improve longevity of our lives.
(It's also worth noting that this entire argument is far more nuanced and second order than the simpler one I offered above, which is that holding this business to a different standard than, say, Facebook, doesn't make sense. Any time you choose to start a business or work, you can always instead choose to go work for a firm with a mission to help the world's poor.)
As for your previous claim that it's in my direct interest to support the world's poor, that's true, but it's also not weighing it against the appropriate benchmark. The appropriate benchmark being what else could I do with that money that would benefit me.
Just don't fool yourself. The reason we value our own happiness over the lives of others is because we are weak. That's something we have to live with, but it doesn't make it good.
>You could say the same thing about any other startup.
And I do!
If you say the same about other startups, then at least you're being consistent, and it's the inconsistency that irks me.
I don't know if I'm weak or if I should be comfortable with my selfishness. I donate, but not as much as I could. I'm not sure I'll ever know the answer. I find that wrestling with the question, at least, prevents me from going down the path of buying luxury goods and signalling, so I guess it's somewhat useful.
While I totally understand your point, I think that the associated value judgment (you are weak if you value your own happiness over that of others) is misguided. Is strength to be solely associated with selfless altruism? What is the end-game of this ethic?
* Half a million die each year of influenza
* Most are very young or very old
* Flu is preventable ($1 face mask)
* Flu is easy to treat in the developing world
The way we think of flu in the west is roughly similar to how Africans think of malaria: a pain in the butt but not the end of the world. Imagine what we would do if rich Africans arrived and started handing out face masks during flu season. We'd probably do what Africans do with malaria nets: say thanks and throw them in a drawer.
That's incredibly misleading, ignorant, and even disrespectful. First of all, malaria is a scourge that's not even comparable with common flu (even thought the latter, through sheer virulence, rivals the former in number of anual deaths). Secondly, you are absolutely talking out of your butt when you say "Africans throw our nets in the drawer"; much to the contrary, these sort initiatives are constantly shown to be one of the most effective ways to reduce malaria infections, indeed one of the most effective ways to prevent suffering in general.
https://www.givewell.org/international/technical/programs/in...
For those who don't know, Givewell is a charity devoted to evaluating charities and writing recommendations for the most efficient and effective use of your donation money.
Anyway, my point is just that if you're looking to make optimal use of money to save or improve human lives, there are many things that should be higher priorities than stopping people dying "of old age" in the West.
https://theguardian.com/environment/2018/jan/31/global-use-o...
> “There are two ways to make the world a better place. You can decrease the suck, and you can increase the awesome… And I do not want to live in a world where we only focus on suck and never think about awesome.” - Hank Green
That said, connecting this utilitarian reasoning to the guidelines of what research to pursue, never mind the moral aspect would lead to an impoverished field of science.
On the everyday perspective, if one is suffering from ill health, but not from poverty and malaria, the idea that concern for your suffering should be set aside until the numeric quantification of the suffering of other populations is brought in line with your own, lacks compassion.
Value systems that lack compassion defeat their own purpose.
Compare this to number theory, where every interesting extant problem appears to require ten years study.
(I realise people may infer a value judgement from shallow/deep, but none is intended.)
I don't often come here to comment but as someone in progress on an original research masters in number theory I can say this is utter bullshit. I assume your 'interesting' qualification (somehow) excludes obvious candidates like Landau's problems [0]. Some examples. I was taught about the ABC conjecture as an undergrad. You can easily teach the Brun sieve [1] method of working out that the sum of the reciprocal of the twin primes converges. Novel solutions to Diophantine problems are sometimes accessible to undergrads. Richard K. Guy wrote a whole book on unsolved problems in NT, some of which have been solved using undergraduate number theory and someone's upper bound you can just use (as easy as apt-get installing this_dope_bound). You can start reading papers without a PhD, never mind ten years of study. I think it's possible to get an utterly unrepresentative sample of either field by only sticking to "elementary" results. There are some extraordinarily subtle results in graph theory! Conversely, you can find NT problems amenable to elementary techniques [2].
[0] https://en.wikipedia.org/wiki/Landau%27s_problems
https://books.google.com/ngrams/graph?content=graph+theory%2...
Afterthought: I wonder what caused the decline in the 80's (also true for other branches of math)
> [de Grey] found his way to the chromatic number of the plane problem through a board game. Decades ago, de Grey was a competitive Othello player, and he fell in with some mathematicians who were also enthusiasts of the game. They introduced him to graph theory, and he comes back to it now and then. “Occasionally, when I need a rest from my real job, I’ll think about math,” he said. Over Christmas last year, he had a chance to do that.
"Many thanks to Brendan McKay and Gordon Royle for letting me know overnight that they had successfully 4-coloured my 1567er; as a result I found a bug in the part of my code that implements the relaxation described in section 5.4 and now it agrees. "
Source: https://gilkalai.wordpress.com/2018/04/10/aubrey-de-grey-the...
Elementary graph theory and combinatorics are somewhat outliers in this regard, as there is not so much "theory" per se that one has to build on or work with. Tim Gowers's "Two Cultures" essay is an interesting read on this topic: https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf
[1] http://www.cs.virginia.edu/~robins/YouAndYourResearch.html
https://en.wikipedia.org/wiki/August_Kekul%C3%A9#Kekul%C3%A9...
Musicians commonly report waking up with song ideas fully formed. We shouldn't be too surprised, really; the complex sentences out of our mouths (more often than not) arrive without any conscious thinking. Jung said that our egos are like planets orbiting a Sun they're unaware of.
And then within a few minutes I quickly forget the music. And there’s no way to remember it because it’s not anything that I can just find and listen to.
Animations showing how the larger graphs are built from smaller graphs would be amazing and illustrative for mortal non-mathematical-geniuses.
Why is the Moser Spindle drawn to make it look non-planar, when it obviously is planar? The drawing obscures the point of the Moser Spindle, which is how to construct a 4-color graph from 2 simple 3-color graphs.
It's also confusingly colored to make it not clear why it requires 4 colors
https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/04/Chroma...
Better: https://en.wikipedia.org/wiki/Moser_spindle#Application_to_t...
If those three nodes (blue, yellow, yellow) were in fact connected by short edges, then another problem would be that the two yellow nodes were connected, which they couldn't be by the constraints of the original problem.
I don't know much about de Gray, but this piques my interest in what else he has done.
With respect to his work on resisting human aging, he hasn't produced anything of value.
https://hn.algolia.com/?query=%20Aubrey%20de%20Grey&sort=byP...
Curing death doesn’t get much buzz these days. Maybe we’ll give it another look?
I do not understand what 'everything lies on the plane' means. I take it as meaning 'everything is laid out in two dimensions' but that doesn't make sense. Can HN help?
Nelson asked: What is the smallest number of colors that you’d need to color any such graph, even one formed by linking an infinite number of vertices?
The Wikipedia page describes the infinite-vertices version of this graph as
an infinite graph with all points of the plane as vertices and with an edge between two vertices if and only if the distance between the two points is 1.
This of course is impossible to draw but Wikipedia shows seven-vertex and ten-vertex subgraphs of it:
https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_proble...