I recently tried buying a domain in cloudflare, they refused the payment -- even using my account which I use actively for years -- tried to pay with paypal, no luck. Went to porkbun and bought the same domain in 5 minutes and pointed it to cloudflare name server.
Maybe they should fix the regular flow before automating it with agents?
Exactly! If you didn't strictly limit the operator's complexity, you could just smuggle a Turing machine in via bitwise logic and turn the whole thing into a parlor trick. The beauty here is that eml(x,y) is a pure, continuous analytical function with no hidden branching whatsoever.
To clarify my earlier point: the author isn't trying to build a practical calculator or generate human-readable algebra. Using exp and ln isn't a cheat code because the goal is purely topological. The paper just proves that this massive, diverse family of continuous math can be mapped perfectly onto a uniform binary tree, without secretly burying a state machine inside the operator.
I think the point here is to explore the reduction of these functions to finite binary trees using a single binary operator and a single stopping constant. The operator used could be arbitrarily complex; the objective is to prove that other expressions in a certain family — in this case, the elementary functions — can be expanded as a finite (often incomplete) binary tree of that same operation.
In other words, this result does not aim to improve computability or bound the complexity of calculating the numerical value. Rather, it aims to exhibit this uniform, finite tree structure for the entire family of elementary expressions.
They highlight the exact reliability constraint I was thinking of: that replacing failed TPUs is trivial on Earth but impossible in space. Their solution is redundant provisioning, which moves the problem from "operationally impossible" to "extremely expensive."
You would effectively need custom, super-redundant motherboards designed to bypass dead chips rather than replace them. The paper also tackles the interconnect problem using specialized optics to sustain high bitrates, which is fascinating but seems incredibly difficult to pull off given that the constellation topology changes constantly. It might be possible, but the resulting hardware would look nothing like a regular datacenter.
Also this would require lots of satelites to rival a regular DC which is also very hard to justify. Let's see what the promised 2027 tests will reveal.
Haha, hard pass on the job. I prefer my oxygen at 1 atm.
I'm not a data center technician myself, but I have deep respect for those folks and the complexity they manage. It's quite surprising the market still buys Musk's claims day after day.
Car-grade inference hardware is fundamentally different from data center-grade inference hardware, let alone the specialized, interconnected hardware used for training (like NVLink or complex optical fabrics). These are different beasts in terms of power density, thermal stress, and signaling sensitivity.
Beyond that, we don't actually know the failure rate of the Tesla fleet. I’ve never had a personal computer fail from use in my life, but that’s just anecdotal and holds no weight against the law of large numbers. When you operate at the scale of a massive cluster, "one-in-a-million" failures become a daily statistical certainty.
Claiming that because you don't personally see cars failing on the side of the road means they require zero intervention actually proves my original point: people who haven't managed data center reliability underestimate the sheer volume of "rare" failures that occur at scale.
Maintaining modern accelerators requires frequent hands-on intervention -- replacing hardware, reseating chips, and checking cable integrity.
Because these platforms are experimental and rapidly evolving, they aren't 'space-ready.' Space-grade hardware must be 'rad-hardened' and proven over years of testing.
By the time an accelerator is reliable enough for orbit, it’s several generations obsolete, making it nearly impossible to compete or turn a profit against ground-based clusters.
AI clusters are heavily interconnected, the blast radius for single component failure is much larger than running single nodes -- you would fragment it beyond recovery to be able to use it meaningfully.
I can't get in detail about real numbers but it's not doable with current hardware by a large margin.
I made a comment earlier that was rightly flagged for its tone, and I would like to restate the technical point more constructively.
The post author, Dan Piponi, clearly knows about fractals, but his post raises the question of whether asking Fermi questions in interviews is actually effective. I am skeptical that such questions would have prevented this type of bug.
I suspect the issue stems from small measurement imprecisions accruing over long distances, which is—in my view—tied to the fractal nature of roads traversing natural landscapes.
However, as others have pointed out, it may also be tied to road closures: if closed segments are set to a higher length internally (to discourage routing), these values might be getting summed up blindly over longer distances.
None of these issues would have been prevented by being good at estimating quantities alone.
Apologies again for the unconstructive tone of my previous comment.
My bad. My intention was not to come across as snarky or aggressive.
Dan Piponi, in his post, called for scale questions in interviews, suggesting that whoever worked on the feature at Apple would not have been hired if they had been asked those types of questions.
I found that position non-constructive and wanted to counter it by mentioning that fractals could hint at why the length was so large.
It is hard to predict how others will read my comment beforehand, and I apologize for not meeting the friendliness bar here on Hacker News.
Not really, if you had every grain of sand in the way it would diverge to a much bigger value. The problem is that the roads have >1 dimension at that scale, apple maps is definitely adding up to many details along the way, it's not a straight line and it ends up being 10x the actual distance. No Biggie.
The "fix" is to smooth those details as the straight line distance grows bigger.
All models are "cyber-capable" :P