tildedave
tildedave on Hacker News
steve yegge is not tptacek (thanks for cryptopals, tptacek!)
This book is the reason I was able to pass my computer architecture exams in grad school. Just lugged the 800 page monstrosity around an entire semester and read it every chance I could. A really wonderful book ... I should get a recent copy and re-read it again.
The continuum hypothesis is more like Euclid's parallel postulate than a Gödel sentence - assuming ZFC consistent there are models with CH true and CH false (the cardinality of the continuum doesn't have to be the first uncountable cardinal).
Everything gets qualified with "assuming ZFC consistent" or "assuming Peano consistent" because any inconsistent theory proves any statement. More of a proof technicality than anything too profound.
There is a construction of a model of Peano arithmetic, so it is consistent, as long as you accept the system used in the proof: https://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof
Not sure if this sheds light on the parent commentator's question ... the terminology can be quite tricky.
As someone who took a number of mathetical logic classes between undergrad/graduate I always found this Gödel-sentence argument on the face-laughable, since the logical inconsistency was so easy to repair. My favorite critique of this was Hans Moravec's dialogue between Penrose and a robot AI, having resurrected his brain long past humanity's extinction:
http://www.calculemus.org/MathUniversalis/NS/10/10moravec.ht...
Not a historian, but _Why the West Rules - For Now_ by Ian Morris was a good read. Covers the sweep of world history with the audacious goal of quantifying human development at all moments in history. It mainly focuses on the west (starting in the Mesopotamian region) and the east (starting in the area surrounding the Yellow river) and addresses questions like "why didn't China discover America" (basically - too far away). You might also find it interesting!
I'm really excited for the movie and the casting looks incredible so far. I wonder how the 2 movie split is going to work narratively. The book itself has kind of a perfect 3 act setup but I'm not sure breaking the story at the end of the book's part 1 (or halfway through part 2) is going to feel very satisfying.
I'd guess comments like this come from people thinking the primary complexity of Redux is the data store, rather than the "all changes to your state are represented as plain objects". The Redux FAQ goes into this:
https://redux.js.org/faq/general#when-should-i-use-reduxCan't blame them missing the forest for the trees when you spend all your time writing the reducers and connectors vs the actions themselves.
I've been pursuing mathematics as a hobby for the last 2 years or so. I got a mathematics major in undergrad so my motivating factor was mainly to explore some areas that I hadn't done coursework on, primarily algebra and number theory. (I focused more on logic in undergraduate/grad.)
I really enjoy how the subject is divorced from a lot of the modern attention demands and encourages more of a 'zen' thinking style.
As others have highlighted, it can be difficult. I work full-time as a software engineer and at the end of the day there's usually not much left in the tank in terms of "creative work". The morning is usually more productive for me - generally I'll spend 10-15 minutes on the commute in reading over the proof of some lemma or working through some computational exercise.
Things that have helped me:
- Focusing on a particular problem area rather than just "mathematics". The classical problems of Gauss and Euler tend to be more my speed than the modern mathematical problems of Hilbert or beyond. What started my journey was looking into the insolubility of the general quintic polynomial equation, something you learn in high school as a random factoid but has a lot of depth.
- Studying from small textbooks that I can fit in a backpack, so I can "make progress" during my commute. Dummit + Foote might be a great algebra reference but it's just too bulky to transport.
- Limiting the scope of how I think about the activity - my goal isn't to master these concepts on the level of a mathematics graduate student, it's more on the order of Sudoku. If I don't get something, that's okay. People spend their whole lifetimes learning this material and I'm just trying to fit this into whatever creative time I have left after the full-time job is done.
Appreciate what you're saying, but the linked paper is talking about results in F_p[T], the polynomial ring.
Even if the number field is finite, there are an infinite number of polynomials for it. For example the finite field F2 has two elements {0, 1} but an infinite number of polynomials 0, 1, x, x + 1, x^2, x^2 + x + 1, x^2 + 1, «x^2 + x, and on and on. Some of these have nontrivial factors (x^2 + x = x(x+1)) and some don't (x^2 + x + 1 has no factors beyond itself and 1).
(The other answer to your question is more complete but also a bit more advanced, figured this was worth surfacing.)
Ah, just making the point that the questions don't occur in a vacuum. By the time something's bad enough to consult random strangers on Reddit the problem has sometimes escalated beyond the point. Often the "dump him" answers come with people also sharing their own life experience. (I've seen my share of the silly questions/answers too of course.)
A more charitable interpretation is that people have gotten into situations bad enough where they've ended up seeking advice from strangers on the internet. (Not every relationship squabble ends up in a reddit post.)
I've been attending a local UU Church for the last few months (raised no religion, this is my first spiritual community). While there's mention of the spiritual life I think about half the congregation would identify as atheists. There's no creed or mention of 'religion' and the individual search for meaning is repeatedly stressed. It's been a good addition to my life and very nurturing for the soul.
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Agree. The assumption underlying this is that you should use a bulk of your outside-of-work time to advance your career and grow your technical skills. True for some, not true for others.
My personal favorite is _The Tombs of Atuan_ - it introduces a new character, creates an entire world around her, then pulls all the assumptions beneath the world apart.
This is one of my go-to sites for optimizing Postgres queries. While all the information is available in the text output there's something nice about the site highlighting the rows scanned for the bad parts of the queries in a dark red ;)
My only nits - it's kind of annoying to have to click a checkbox to make sure my analysis is not public and to keep the window open so I can delete it after I'm done.
Great eassy. I read a few of her novels last year (Left Hand of Darkness, the Dispossessed, and some of her Earthsea novels). What struck me is even with the amount of effort that goes into building her worlds, she turns her lens back on her characters near the end, with them either figuring out something about themselves or how they relate to other people.
The "fate of the world" gets evoked a lot in popular fantasy/scifi nowadays but I really appreciate the way she chose to make her protagonists the final focus of her narratives. Don't want to spoil anything ;) so I'd encourage anyone that's interested to seek her work out.
If you turn off the "show the best tweets first" option in your content preferences you get a chronological timeline back. (They made this change a month or two ago)
One of my favorite video series on YouTube is Francis Su's _Real Analysis_.
https://www.youtube.com/watch?v=sqEyWLGvvdw He walks through the basics of constructing the real numbers, defines metric spaces and proves some topological properties, defines continuous functions, and goes into differentiable functions.
The video quality isn't great but his teaching style is phenomenal - he's really great about engaging the class and getting them to walk through the reasoning for each of the theorems.
I thought this was very well and succinctly put, thank you. Having made many similar mistake to those in the original article, it's obvious to me when looking back at those situations that the real issue was team fit. Individual acts get washed over but fundamentally you need to be compatible with the people you work with.
http://askakorean.blogspot.hk/2013/07/culturalism-gladwell-a... has a little bit of a different take on this - mainly aimed at Malcom Gladwell's _Outliers_ discussion of these incidents.
The article goes a bit broader and it's been a few years since I read it in depth, but you might be interested the counter-perspective.
I took Jeff's senior level Algorithms class at UIUC back in 2002. His lecture notes are really high quality and presented in a very engaging style. Definitely worth checking out!
He also gave some very difficult homework problems. UIUC lore has one student noping out in a pretty amusing way: http://jeffe.cs.illinois.edu/teaching/pikachu.html
I think there's a lot true in what you've written. However the root cause fix applied in a development environment is not always the fastest way to stop a user facing problem. Things get weird on live servers. I'm not suggesting altering code willy-nilly but a solid knowledge of production (logging, service status, etc) can lead to more effective debugging scenarios and faster time to resolution when things do go bad.