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That just means even more limitations, then. (Though the grandparent comment is correct that literally everything is subject to the same Gödel-style limitation on its ability to make negative claims about its own behavior, whether computers, humans, or any other system at all.)
What PC GPU was in mainstream consumer use before the N64?
Remember that the most valuable human in the world is Elon Musk. What it means to be valuable is to be like Elon Musk. Calibrate your goals accordingly.
What is the advantage of asking AI to build an engine cloning these existing engines, vs just using these existing engines.
When you look at Super Mario World, do you see moving animated sprites?
Fine by me. Let's give it a shot.
What if you believe (correctly) that a corrupt government intends to punish you exorbitantly beyond reason for possession of these zines? Is it still immoral to move the zines? Is it so immoral that it therefore justifies 30 years of imprisonment for moving the zines?
Hacker News is for people who believe in the hacker ethos "It is immoral to do anything the government takes issue with and you deserve whatever punishment you get for doing so, unless it was breaking regulations to make money, the highest calling".
A lot of people in these Hacker News comments are accepting the framing that moving the zines is evidence tampering and therefore deserves a 30 year sentence. What crime are zines evidence of?
I watched Sesame Street and Reading Rainbow and stuff like that as a child. Seemed fine and even good.
"You'll leave with a strategy report"
"No report, no lecture"
Somewhat contradictory wording.
This is like how one often wants to distinguish the points of an affine space from the vectors representing displacements in that space (there is no distinguished origin for the physical world, but there is a distinguished concept of zero displacement). One can add a vector to a point to get a point, or a vector to a vector to get a vector, but cannot add a point to a point to get another point. Yet, it is meaningful to treat a linear combination of points in an affine space as yielding another point in the same space when the weights of the linear combination sum to 1.
The exact same thing is happening here, only multiplicatively, where z1^(1/2) * z2^(1/2) is a combination with two weights of 1/2 (thus, summing to 1). It is geometrically meaningful to treat 2d vectors (displacements in a plane) as complex numbers, raise them to exponents summing to 1, and then multiply these together to get another vector in the same plane. But it is not generally geometrically meaningful to just multiply one vector by another vector to get a third vector in the same space (because this would require distinguishing some particular direction and magnitude as "1").
The basic issue with geometric algebra is that geometric vectors generally do not have a distinguished notion of unit magnitude (is unit magnitude 1 meter? 1 mile? 1 inch?), so it is silly to work in a framework that requires pretending they do (since the definition of the geometric product of two vectors is dependent upon this choice). Dimensional analysis (a very handy way of tracking mathematical symmetries and thus sanity checking results) goes out the window when working with mixed grade multivectors.
This is not an issue when working with non-mixed-grade multivectors, for which dimensional analysis works just fine in the ordinary way. As the linked article notes, exterior algebra/the wedge product is great. Thinking about exterior powers of vector spaces is great. It's the further move of forcing everything into a Procrustean bed of Clifford algebra that is misguided for almost any application other than some spinor stuff.
Yes, let's please give police officers the copious (cop-ious?) benefit of the doubt they have earnt.
If it's so worthless, let me have it instead of him.
The stock market is not definitionally "reality" in the sense being used. It's perfectly fine to look at the stock market and consider it "detached from reality", in the sense being said.
I have a PhD in category theory and know what the Leech lattice is and I still don't understand what is going on here. What is the value of using the Leech lattice to store memory?
One bug after another over at GitHub. What is going on over there?
What's stupid about the disclaimer?
Very sad to see Hacker News discussing science funding. This has nothing to do with the hacker ethos of maximizing corporate profit.
Hypocrite didn't even use AI to write this lovely poem.
That's fortunate for you that what you enjoy doing and get meaning from is capable of providing you a living via market income. That's not true of many others. I try to make time for what I enjoy doing and get meaning from. But for me as for many, it does not provide income.
Many of us do not particularly enjoy the work our employer has us do, nor believe in what the company we work for is trying to achieve. It's not like we get to choose its aims, and it's not like we have alternatives where we get to do so either. Our lives are spent working on someone else's goals.
There's always a comment saying "Don't ask for better, because someone else had worse". Fuck that. I want better and I want everyone else to have it too.
Silicon Valley bigwigs supported this administration vocally. I am starting to doubt that their interests and morality align with mine.
But surely the more natural approach than making this undefined behavior would be making the computation of a[i] take place in 64-bit pointer space rather than 32-bit int space? Why does the compiler need the freedom to emit nasal demons?
How is undefined behavior necessary for this transformation?
Apparently, even paying users are being prevented from posting.
The implementation is buggy. Very many users report being banned while being nowhere near the usage limit: https://devcommunity.x.com/t/your-request-looks-like-it-migh...
These links' mentions of quaternions are about a different part of the book (the tea party). Furthermore, even regarding that different part, your first link explicitly debunks the second link and disavows the quaternion connection the latter alleges. Your first link's whole point is to conclude "it is indeed very unlikely that Dodgson had the quaternions in mind when writing the tea-party chapter."