Gould wrote a controversial book attacking whole swathes of science done in the past. The existence of a senior lecturer at the University of Hertfordshire who has written a criticism of it doesn't seem that surprising and certainly doesn't seem sufficient evidence that we should disregard what he has to say.
Although von Neumann was certainly a genius who happened to be in the right place at the right time, he's also an example of how groups of people can create a culture seemingly much more important than the effect of one outstanding individual. Lipót Fejér led a school of analysis at Eötvös Loránd University in Budapest. He ran a seminar, was the centre of a large group of young mathematicians who worked together and was enormously influential.
Hungary has a disproportionate number of the world class mathematicians of the 20th century. The numbers are even more extreme when you consider that those mathematicians are all from Budapest, all from Eötvös, and the vast majority of them Fejér's supervisees. It's totally plausible that Fejér created an environment where people who might otherwise have been middling mathematicians, decent engineers, or never have found their niche, were transformed, by collaboration and inspiration, into the likes of von Neumann, Erdős, Pólya.
Even today the Eötvös school of analysis and combinatorics is a significant powerhouse, with most members direct mathematical descendants from Fejér. And there are other branches such as Cambridge combinatorialists where the influence of Fejér's students and grand-students has been key in the formation of world class mathematicians.
I'm sure there are lots of bright people who are coasting at either Stanford or Google. If that's your goal, you might well achieve it. But at the same time, there are people who are going to be vastly more successful than that. The ones who revolutionize whole fields.
Yes, what people competing to get their children into the 0.9% miss is that 1. There are going to be other tests and hurdles in the future which differentiate your child from those with very high natural aptitude. 2. If your child worked 10 times as the top achievers to attain a similar level, at the next stage they will have to work 20 times as hard, then 100 times as hard, until it simply becomes impossible. 3. While they are sacrificing their youth for this, they are missing out on discovering what they are good at and do want to do.
It seems like you are advocating, for a bright but not exceptional child, that they do get pushed to the point where they burn out, just in case they manage to win the lottery of appearing to be in the exceptional group. Even if this dubious plan succeeds, sooner or later it will become clear that they are not as good as their results.
Not sure why you are asking this in this thread, but the implication is that the bullets are fired from ground level, not necessarily horizontally. The maximum distance a projectile can travel when fired from ground level is the basic first result of ballistics.
The author said in a postscript that he was worried about seeming elitist. I didn't think it was elitist at all, and I completely understand why it was a good choice for him to write BASIC code.
However, I also did manual labour in the summer when I was ~20. There was nothing wrong with it. I would certainly recommend a brief stint of it to a young person, especially if you are training towards a sitting down/talking type job.
You are outdoors, you end the day physically tired but with mental and emotional energy for other things. You gain skills and improve your health and fitness. There's usually a good atmosphere among the workers. And you get to point at something concrete and say 'I helped put that up/knock that down/repair that'.
I think he picked a good number. It clearly wasn't $1000 of effort. Jim may not have been interested in hiring someone who, like his previous software guy, was looking to shake him down for as much as possible.
I don't think that Dr Dre gets to evaluate the performance of Apple employees who are women (or Korean, etc) simply because they have a JV making headphones.
I think if you write something which says 'I am biased', the burden of proof is now on you to show hiring managers that it was all a bit, rather than on them to demonstrate that it wasn't.
Absolutely agree. The best and most creative environments I have worked in have been full of people who you could turn to and say "What if we did X?", and they would immediately come up with reasons that X would fail or be impossible. If your idea hadn't been absolutely annihilated after 5 or 10 minutes of this, it was probably pretty decent.
By redefining anyone who has worked very hard and enjoyed success as a 'fierce nerd', you make the term meaningless, and the supposed payoff from being one into a tautology.
I have found a few of his essays very good, indeed expressing things I haven't seen anywhere else. I think he has provided very good advice to young people at times.
The vast majority I would say that he is trying to retcon his huge success and the success of some businesses he has been associated with into a coherent worldview. I believe that in 'Hackers and Painters' he actually goes through some back-of-envelope calculations that show that the money he made when Yahoo bought Viaweb corresponded closely to the real value he had created, in some sense.
It is baffling to me why he isn't able to say "I got lucky - I worked hard and created something very valuable, but I was also in the right place at the right time." Clearly there were special factors at play selling an e-commerce platform to Yahoo in 1998. He's also done intelligent and pro-social things with both his money and his time since then it appears. I don't know what the shame is in saying "I won a lottery - but I have tried to do the right thing with my good fortune."
I think if you asked Jamie Zawinski, who I think was no less technically skilled, nor less purposeful about working on interesting and important things (nor, tbh, any worse at writing thoughtful essays), he would readily admit to having been extremely lucky. I don't know what the difference is between these two personalities. I think I'd rather be jwz in similar circumstances.
That depends on what the alternative is. If it involves clueless people filling up garbage bags with gasoline and storing them in their kitchens perhaps letting the pipeline continue to run would have been safer.
You just end up with a situation where there's intense competition to make cheatbots as good as possible, within the parameters of plausible deniability. People start meta-hacking to find tricks which don't improve the speedrun but keep it impossibly fast while making it look more convincingly human. People spend time obsessively training not to get good at the game, but to make it seem as though they would have been good enough to do a speedrun which was actually automated. Eventually you start to get false positives as the bar for cheating catches the most skilled and dedicated non-cheating players.
Then again some people still enjoy watching professional cycling so maybe it will be fine.
The rest of the world makes a useful distinction between a 'country' (such as France), a 'state' (the public institutions which run France), and a 'government' (the political entity which controls the French state).
However in the US the word 'state' is overloaded, so 'nation state' is used. It's confusing, because 'nation' is sometimes used to mean 'country' (which is how it's intended in 'nation state') and more traditionally used to mean a people with a shared language and history.
It looks like many of these show a construction which you have to follow the details of to check that there aren't gaps or overlaps.
Is there a way of checking these automatically? Eg if you can tile a certain amount of space without gaps then it must be able to continue forever? Or can you write down a vector expression for the location of each shape and show finitely that you have exactly covered all lattice points?
Here's a visualisation that helped me think about the 4-cube:
Cut the 3-cube with a plane which is diagonal to all axes, eg x + y + z = c. Start at a corner and take sequential sections. First you get a small equilateral triangle, then a bigger and bigger one, until the cut goes between 3 vertices of the cube. Next you get truncated equilateral triangles, with bigger and bigger truncations. In the center of the cube the size of the truncations matches the remaining edges and you get an regular hexagon. Then the whole thing in reverse as half the sides get smaller and smaller, until you're back to triangles.
If you're not sure what it looks like at any point, you can easily solve the intersection of x + y + z = c and the equation of one face of the cube (x or y or z = 0 or 1).
Now do it for the 4-cube. Important observations: 1. again you can solve algebraically, either for the 3-cubes which bound the 4-cube or the 2-squares which bound them 2. you can also just try and imagine the intersection with the 3-cubes, since it will be one of the shapes you thought about in the previous exercise (x + y + z + w = c && w = 1 => x + y + z = c - 1) 3. c goes between 0 and 4, with [0, 2] symmetrical to [2, 4]. There are two 'regions' of behavior, c in [0, 1] and c in [1, 2], with the type of shape only changing when the plane intersects with vertices.