I interviewed at Palantir last month, and the process is still very similar to what you've described. However, regarding the last point, after the product demo they did directly address the potential for misuse of the product.
They described a culture that encourages asking hard questions, and doing the right thing in ethically complex situations, even if that meant turning down a business opportunity. It came across as frank and sincere, and I didn't get any sense they were grooming for a cult, more that they were looking for people who were smart and passionate.
I'd say it's an excellent way to get a feel for what it takes to build a home. There are a TON of details, especially if you don't want it to rot.
If you intend to heat it in the winter, be sure to consider the effects of condensation. I made the mistake of building my first shed without proper ventilation, and it was like indoor rain when I turned on a space heater. For my second, more permanent shed I've followed building codes for real homes to avoid making any more big mistakes like that.
Thanks for the link. The author is an editor of the Princeton Companion to Applied Mathematics, which also contains very high quality writing and a book I recommend to anyone interested in mathematics and engineering.
I agree that this is a flawed article: the ads are irritating, the grammar is flawed, and calling boolean algebra an algorithm is inaccurate.
But looking past the flaws, I wouldn't describe it as vapid. I see it as more of a very high level survey of some truly important algorithms targeted at general population and students. This kind of writing can be an incredibly important source of inspiration for young people.
I agree with splitting up CF stacks this way. It reduces the the blast radius, that saved me on a number of occasions when stack updates went sideways.
The problem introduced by that approach is how to manage a large number of CF stacks. First I used a homegrown Python library to manage them, then switched to having Terraform manage CF.
At first Terraform on CF was just intended to be an expedient measure to facilitate migrating everything to Terraform, and eventually we did migrate to pure Terraform. But then we started hitting all the rough edges in Terraform. In hindsight, the hybrid approach had actually been more stable and manageable than using either tool in isolation.
That's not how I'd interpret this sentence: "We have skin and other barriers that protect the cells." It sounds to me like the author claims that humans have skin, which is true, and that skin forms a barrier that protects internal cells, which is extremely plausible.
I always liked how Feynman dealt with complex numbers in 'QED: The Strange Theory of Light and Matter'.
He focuses on the intuitive concept of a particle having a spinny arrow attached, the arrow rotates as the particle flies through space. He only casually mentions that this is in fact a complex number, whereas the bulk of the text focuses on developing intuition around arrows.
I read that book in high school, and it certainly influenced the direction I took in university. It helped to understand that the physical universe often appears to behave in extremely non-intuitive ways, but using mathematics we can develop a model that transforms the phenomenon into something that actually does make intuitive sense.
I think some of the harder concepts in math are difficult because they act like stepping stones into aspects of our world that just don't make sense based on day-to-day experiences. But modern technology depends on this! Pedagogy is improving, but it still lags advances in technology.
To follow one of the more common patterns for identifying a class of functions, it could have been named after one of the early pioneers in the field. But yeah, it would be hard to do worse than random variable, which is illogical and misleading.
Many people have recognized the need for improvement in mathematics education, and I think it really is evolving in positive directions. I worked at DreamBox Learning for a few years, they produce an adaptive math learning program for elementary schools (and gradually reaching higher levels) which as been very popular with children.
The kind of math that was traditionally taught in schools is still relevant and important, but I think we can leverage modern visual and interactive media to help children develop a broader class of mathematical reasoning skills, which includes much, much more than a bunch of rules, symbols, and rote procedures.
I can't think of any examples of mathematical objects being renamed, do you have any?
There may be some amount of drift over time, but you can go to the research library of any university math department and find books from pre-WWII that are still totally readable because although style has shifted somewhat, the basic nomenclature hasn't.
But you propose to simply relabel as function, which doesn't work in general because random variable corresponds to a specific type of function. You could compromise by calling it a probability function, but then you start to collide with other uses of that word.
I agree random variable is awkward, though. I always avoided stats courses because it's full of so much jargon that collides with nomenclature used by mathematicians.
The result of the determinant might be negative, which doesn't make sense for a volume, so you need to take the absolute value to interpret it that way.
The definition of a vector space says nothing about whether it does or does not have a multiplication operation defined on it. A vector space having a multiplication operator has additional structure, but is still a vector space.
Example: The space of NxN matrices. There are 2 distinct forms of multiplication on this space: between a vector and a scalar (scalar multiplication), and between vectors (matrix multiplication).
What would happen if we started renaming mathematical objects to reflect changes in the English language? English will continue to evolve, and the vast body of mathematical literature would have to be constantly rewritten.
Wouldn't that cause much, much greater confusion due to mathematical nomenclature being a moving target rather than remaining stable?
Intuitively elements of R2 are not numbers, they're vectors, or points in a 2 dimensional vector space. You can also treat complex numbers as vectors in the 2 dimensional complex plane.
Fully understanding the math in this book requires a solid background in linear algebra, calculus, differential equations. But I find it an incredibly interesting book even without understanding all the math: the engaging writing style and numerous illustrations capture the intuitions behind differential geometry and relativity, but without sacrificing the rigorous mathematical formulations underlying it.
Absolutely. And in mathematics, advanced structures and theorems are built up layers by layer upon more elementary material. A professor who has mastered presentation of undergraduate material on a topic also likely teaches a graduate course on it, and mentors students on it, and does research on it.
They can talk about their chosen topic at many levels to many different audiences, from general audience (who may provide funding to them), high school students (outreach and recruiting), university students, and peers. This flexibility is an important part of being a very successful mathematician, and you have to burn it into your brain to reach that level of fluency.
No, I was never under that impression. I once had a discussion about the creation of the book with one of Federer's students who had also helped proofread it. The book was essentially an outgrowth of his personal and course notes, since of course he couldn't keep all this in his head.
What he likely did have in his head was an index into the contents, that's the crux of my observation. If I am very good at organizing my workshop, I can quickly grab the tools and materials needed for a particular task without breaking my flow of thought. Same basic principle applies to mathematicians and other intellectual workers, just as it does with physical trades.
I think many highly productive mathematicians are very good at organizing formulas and facts in such a way that they can be retrieved easily from memory based on context. Maybe something analogous to a hash function from computer science.
Some mathematicians seem to index facts based on geometric images, others seem to be more inclined to symbolic or algebraic statements. Whatever the representation, when confronted with a new mathematical situation they then scan quickly for matches to various aspects of the problem at hand.
Maybe to some degree my observation here is obvious. But I thought a lot about it while I was in grad school studying a book called Geometric Measure Theory by Herbert Federer. That book is enormous, and full of highly intricate technical proofs that require pulling together a large number of detailed technical facts.
The book is also very highly structured, and that led me to conclude that the text likely mirrored how Federer organized this information in his head. It reads like code for a complex but cleanly architected software system, and that's a big part of what led me from math to software development.
Is it being characterized as a major discovery somewhere in this article? I see it described as an elusive problem, and it's claimed that the solution is a major paper worthy of publication in Annals of Statistics, but mostly it just comes across as an interesting story about how this proof came to be.
They described a culture that encourages asking hard questions, and doing the right thing in ethically complex situations, even if that meant turning down a business opportunity. It came across as frank and sincere, and I didn't get any sense they were grooming for a cult, more that they were looking for people who were smart and passionate.