There is also the hilariously misguided belief that good coders do not produce bugs so there’s no need for debugging.
i’m terrified of people who think this way. my experience has been that they are much less inclined to check for bugs in their code and tend to produce much buggier code
i wish they would do this in math instead of the boring system where it’s always alphabetical
that’s an extremely rare sighting but it’s so satisfying to read
what are your thoughts on “whence”?
that would be a lot clearer. i’ve just been burned in the past by notation in analysis.
my two most painful memories are:
there’s the usual “null spaces” instead of “kernel” nonsense. ive also seen lots of analysis books use the → symbol to define functions when they really should have been using the ↦ symbol.
at this point, i wouldn’t put anything past them.
unless f(x0 ± δ) is some kind of funky shorthand for the set f(x) : x ∈ ℝ, . in that case, the definition would be “correct”.
it’s much more likely that it’s a typo, but analysts have been known to cook up some pretty bizarre notation from time to time, so it’s not totally out of the question.
i think the ε-δ approach leads to way more cumbersome and long proofs, and it leads to a good amount of separation between the “idea being proved” and the proof itself.
it’s especially rough when you’re chasing around multiple “limit variables” that depend on different things. i still have flashbacks to my second measure theory course where we would spend an entire two hour lecture on one theorem, chasing around ε and η throughout different parts of the proof.
best to nip it in the bud id say
i still feel like this whole ε-δ thing could have been avoided if we had just put more effort into the “infinitesimals” approach, which is a bit more intuitive anyways.
but on the other hand, you need a lot of heavy tools to make infinitesimals work in a rigorous setting, and shortcuts can be nice sometimes
they chose to hide it in plain sight
it also bothers me when people say “my algorithm” to refer to the thing that recommends posts to them. people shouldn’t ever say “my algorithm” unless they personally own a copy of the kick-ass prog-metal band
well, according to the congressional budget office,
In 2023, federal subsidies for health insurance are estimated to be $1.8 trillion
and this report by research america shows that the private sector spent around $150 billion on “research and development” in 2019.
it’s no secret that the private healthcare industry jacks up the prices of things to increase profits. so, some napkin math makes me think it’s not that far-fetched to think that we can save more than $150 billion in healthcare subsidies if we stop privatized healthcare and dramatically lower the costs of medical care. we could then put that $150 billion back into research, without needing to appease the private sector at all.
that’s not the full story though. according to the NIH, the US government spent over 30 billion dollars on the covid vaccines.
and this is not unique to the covid vaccine. here’s a source with two particularly damning quotes:
“Since the 1930s, the National Institutes of Health has invested close to $900 billion in the basic and applied research that formed both the pharmaceutical and biotechnology sectors.”
and
A 2018 study on the National Institute of Health’s (NIH) financial contributions to new drug approvals found that the agency “contributed to published research associated with every one of the 210 new drugs approved by the Food and Drug Administration from 2010–2016.” More than $100 billion in NIH funding went toward research that contributed directly or indirectly to the 210 drugs approved during that six-year period.
the “categorical” way of defining tensor products is essentially “that thing that lets you turn multi-linear maps into linear maps”, and linear maps (of finite dimensional vector spaces) are basically matrices anyways. so i don’t see it as much of a stretch to say tensors are matrices.
(can you tell that i never took a physics class?)
a tensor is a multi-linear map V × … × V × V* × … × V* → F, and a multi-linear map V × … × V × V* × … × V* → F is the same as a linear map V ⊗ … ⊗ V ⊗ V* ⊗ … ⊗ V* → F. and a linear map is ““the same thing as”” a matrix. so in this way, you can associate matrices to tensors. (but the matrices are formed in the tensor space V ⊗ … ⊗ V ⊗ V* ⊗ … ⊗ V*, not in the vector space V.)
“Limiting training data to public domain books and drawings created more than a century ago might yield an interesting experiment, but would not provide AI systems that meet the needs of today’s citizens.”
exactly which “needs” are they trying to meet?
that sounds like a better choice to be honest. i haven’t used signal much and i didn’t know they supported that sort of thing
telegram has “secret chats” that let you set a self destruct timer for all messages sent in those chats. i don’t know of many other alternatives. and even telegram isn’t a drop in replacement, but it could work, depending on what you’re looking for
scary to think of how big the horses themselves must have been
it’s rough when the math gets so complicated that you have to break your finger in order to be able to visualize things