I don’t really want to participate in this discussion, however:
As I stand on the flats of Salt Lake, the Earth is definitely flat. Also, I’m sure there are brown cows that produce milk that’s turned to chocolate milk. And since I didn’t directly observe humans landing on the moon, I can’t be certain of it to say.
Am I being facetious, perhaps. But I want to illustrate that people can be broadly split in to two camps. Those that believe individual agency is necessary for all. And those that believe individual agency can only be preserved for all by restricting it to the chosen.
If you’re happy with affairs however whatever camp you’re in differs from whatever camp your society is in, you will turn a blind eye. However, if you’re unhappy then you’ll feel all your problems must stem from your society’s fundamental misconception.
The world has lost, on my opinion, a mass of level-headed people. We don’t need to agree, but we need to talk. Forums like this depend on people taking their time to be nuanced and clear, however there is little reward in this as the quality of the HN audience slowly decays as the attention span of the general populace from which this audience is derived itself decays.
You give me a rational candidate for √2 and by the argument of the submitted article I “construct” another rational candidate with strictly smaller numerator and denominator.
You give me a rational candidate p/q for log 2 and by the argument of the article I “construct” that p = q = 0.
In both instances I create a contradiction thus showing that you could not have provided me such a rational to begin with.
Now let me show you non-constructively that there are irrationals a and b with a^b rational.
To prove this I consider c = √2^√2. I don’t know whether this is rational or irrational so I invoke the law of the excluded middle.
Suppose c is rational. Then take a = b = √2 and we have a^b = c where a and b are irrational and c is rational.
Otherwise suppose c is irrational. Then take a = c and b = √2 and we have a^b = (√2^√2)^√2 = √2^2 = 2 and again we have our result.
What is the difference here? I have no idea whether c is rational or irrational. Either way I can make it work but I can’t tell you which possibility is the genuine one.
You can actually make better choices of a and b and show this result constructively.
This leads to a deeper question. Are there statements with no constructive proof and how do you prove that. This is beyond my expertise, but there are indeed high-powered logical tools that allow you prove such results for certain statements.
The stuff that human beings have done by simply looking at the stars and dreaming really hard is pretty awe-inspiringly incredible.
To be a little more concrete, what it means to prove a negation ¬P (not P) is to assume P and construct an impossibility from it, like 0=1 (assuming those symbols exist in the theory you are working with) or more generally A∧¬A (A and not A) for some A (0=1 being a absurdity, hopefully, because your ambient theory already proves 0≠1).
Now to prove P by contradiction, is to assume, the contrary, ¬P and construct an impossibility. But what you have really done here is prove ¬¬P. Now if you are a normal mathematician, you are classical, and hence you believe every statement A is either true or false, i.e. A∨¬A (A or not A, from any statement A, i.e. the law of the excluded middle). It just so happens that if you accept the law of the excluded middle then from ¬¬P you can deduce P.
An interesting question is why is the meaning of a proof of negation the construction of an absurdity? I guess this is philosophical, but if you accept the point of logic is to only conclude true things, then concluding an absurdity must be impossible, and hence if you assume something that leads to an absurdity, it follows that there must be no proof of the assumption because otherwise you'd have a proof of absurdity, and hence the meaning of a negation is showing that there is no proof of the pre-negated statement. In logic, ⊥ is used as the symbol for absurdity. Hence ¬P is really shorthand for P⇒⊥ (P implies absurdity), which is why earlier I identified A∧¬A with absurdity since when you have A and A implies absurdity, you immediately deduce absurdity.
I don't think this is an IPv6 address literals problem per se, but instead a URL encoding/specification problem. There really is too much historical baggage here to unpack. That's why URL routing is delicate, not to mention canonicalization, fragments, queries, caching, security…
If someone gives you a link-local address, you have to know which interface they want you to use, either implicitly or otherwise.
The problem with this ambition is that it turns mathematics into software development. There’s absolutely nothing wrong with this per se, however what happens is that, as in software, certain ideas get ossified. That’s why, for example, every OS has a POSIX layer even though technically the process/namespace/security model could be radically reimagined possibly to create more easily engineered, correct software.
Mathematics is going through a huge, quiet, upheaval. The litmus test will be when, if ever, someone wins a Fields using a proof-assistant in an essential way.
I agree. It’s the same specious argument that equates a human experiencing a work, be it art or code, with AI training on that work.
I wanted here to write a more detailed rebuttal, but I ended up deleting it all. I don’t think people like antirez can be swayed. They’re committed to the grift, or at the very least are in comfortable enough economic circumstances not to care.
I believe they were attempting to link to https://eprint.iacr.org/2006/454 a paper titled How to Win the Clone Wars: Efficient Periodic n-Times Anonymous Authentication.
Thanks for the link to the post. I also watched her talk posted elsewhere in these comments. We’re lucky to have people like her doing the hard work for free software.
> most of the reasons are probably not even technical, but legal/strategic - patents and stuff
I think fighting for specified interoperable interfaces is important and we must be vigilant again forces that undermine this, either knowingly or through ignorance.
I don’t know which of my detractors to respond to, so I’ll respond here.
It should be clear that I’m only interested in compute and not a GPU expert.
GPUs, from my understanding, have lost the majority of fixed-function units as they’ve become more programmable. Furthermore, GPUs clearly have a hidden scheduler and this is not fully exposed by vendors. In other words we have no control over what is being run on a GPU at any given instant, we simply queue work for it.
Given all these contrivances, why should not the interface exposed to the user be absolutely simple. It should then be up to vendors to produce hardware (and co-designed compilers) to run our software as fast as possible.
Graphics developers need to develop a narrow-waist abstraction for wide, latency-hiding, SIMD compute. On top of this Vulkan, or OpenGL, or ML inference, or whatever can be done. The memory space should also be fully unified.
This is what needs to be worked on. If you don’t agree, that’s fine, but don’t pretend that you’re not protecting entrenched interests from the likes of Microsoft, Nvidia, Epic Games, Valve and others.
Telling people to just use Unreal engine, or Unity, or even Godot, it just like telling people to just use Python, or Typescript, or Go to get their sequential compute done.
Uuugh, graphics. So many smart people expending great energy to look busy while doing nothing particularly profound.
Graphics people, here is what you need to do.
1) Figure out a machine abstraction.
2) Figure out an abstraction for how these machines communicate with each other and the cpu on a shared memory bus.
3) Write a binary spec for code for this abstract machine.
4) Compilers target this abstract machine.
5) Programs submit code to driver for AoT compilation, and cache results.
6) Driver has some linker and dynamic module loading/unloading capability.
7) Signal the driver to start that code.
AMD64, ARM, and RISC-V are all basically differing binary specs for a C-machine+MMU+MMIO compute abstraction.
Figure out your machine abstraction and let us normies write code that’s accelerated without having to throw the baby out with the bathwater ever few years.
Oh yes, give us timing information so we can adapt workload as necessary to achieve soft real-time scheduling on hardware with differing performance.
Security is the big thing for me. Anything non-trivial requires me to trust you are not snooping on any compute I’m performing on your platform. Solving this for your users in a proper way is difficult. Recently 3mbed has developed open source firmware for a Gigabyte server supporting AMD-SEV. If your service can leverage this technology to provide confidential compute in an affordable way then, assuming your network connectivity is good, you’ll have a really compelling offering.
Doing this is not easy and will require excellent technical expertise, but it is doable, and will be a big one up over 2nd tier cloud operators.
Good luck. I look forward to being a future customer of yours.
You and your coauthor need to write up a detailed account of your “Metatron model”. This paper, if it were to count as research, should be how other phenomena can be simulated by choices of parameters for your model.
Otherwise, you’ve just described yet another synthetic model that exhibits criticality (without proof no less). Which is not particularly interesting, unless your model subsumes other phenomena.
The naïveté of workers in tech is astounding. Workers at Google have been complicit in the unravelling of the social fabric of the US since before Eric Schmidt. I only point to the destitution of the fourth estate by search advertising as the most egregious example.
Yes, the technical problems are interesting, the pay is good, but what society are you building?
The fifth estate is now, also, all but extinguished. Machine-driven psyops, in the form of algorithmic engagement, and AI-generated sentiment, mean that social fabric is no longer woven by people, but synthesized by corporations in service of their paperclip-maxxing agendas.
The recent case of Rob Pike, and today’s post by Brenden Gregg, only serve to remind me that the only thing one can depend on is the human mind to delude itself.
What else can explain the flagging of this submission? Google is the tech company of the internet age. That these goings on within it are worthy of being brushed aside by some members of this forum is indicative of a deep malaise in this community, an inability to see reality as it is.
I should end by saying, in my view, the only appropriate employee activism is handing in your resignation. Tech can’t unionize, as the workers don’t see themselves as equals, as disposable cogs in the service of corporations.
As I stand on the flats of Salt Lake, the Earth is definitely flat. Also, I’m sure there are brown cows that produce milk that’s turned to chocolate milk. And since I didn’t directly observe humans landing on the moon, I can’t be certain of it to say.
Am I being facetious, perhaps. But I want to illustrate that people can be broadly split in to two camps. Those that believe individual agency is necessary for all. And those that believe individual agency can only be preserved for all by restricting it to the chosen.
If you’re happy with affairs however whatever camp you’re in differs from whatever camp your society is in, you will turn a blind eye. However, if you’re unhappy then you’ll feel all your problems must stem from your society’s fundamental misconception.
The world has lost, on my opinion, a mass of level-headed people. We don’t need to agree, but we need to talk. Forums like this depend on people taking their time to be nuanced and clear, however there is little reward in this as the quality of the HN audience slowly decays as the attention span of the general populace from which this audience is derived itself decays.