Because the true goal is AGI, not just nice little tools to solve subsets of problems. The first company which can achieve human level intelligence will just be able to self-improve at such a rate as to create a gigantic moat
There's no particular reason to assume a human level AI would be able to improve itself any better than the thousands of human level humans that designed it.
Sure, but: that single human with the intelligence of a top tier engineer of scientist will have immediate access to all human knowledge. Plus, what do you think happens the moment its optimizes itself to run in 2, 4, 8, 16, etc. parallel instances?
Well, A) "top tier engineer/scientist" is a significant step above generic human, B) the human engineers/scientists also have immediate access to the same database, C) The humans have been optimizing it for even longer, so what makes us think the AI can optimize itself even a couple percent?
For example, if the number of AIs you can run per petaflop started to scale with the cube root of researcher-years, then even if your researcher AIs are quite fast and you can double your density in a couple years, hitting 5x will take a decade and hitting 10x will approach half a century.
> The first company which can achieve human level intelligence will just be able to...
They say prostitution is the oldest industry of all. We know how to achieve human-level intelligence quite well. The outstanding challenge is figuring out how to produce an energy efficient human-level intelligence.
If Apple doesn't offer a Linux product, they cannot be used seriously in headless computing task. They are adamant in controlling the whole stack, so unless they remake some server version of macOS (and wait years for the community to accustom themselves with it), they will keep being a consumer/professional oriented company
I believe this is correct: x/x = 1 everywhere except 0, where it has a removable singularity. So you can extend x/x holomorphically to full C.
This is completely different from the phenomenon described in the article: arccosh discontinuity can’t be dealt the same way. In fact complex analysis prefers to deal with it my making functions path-dependent (multi-valued).
PLEASE explain "So you can extend x/x holomorphically to full C" to someone with only a BSc in math/cs; something about this thread is giving me an existential crisis right now.
- function extension is defining a function where it is not defined
- <Adj> function extension is an extension that keeps (or gives) Adj property
- extended function is usually treated as originals if extension is good enough. Real analysis starts with defining real numbers and extending familiar functions onto them
- in this particular case we do not need C - even continuous extension on R works and agrees with x/x = 1 at 0
- holomorphic (analytic) extension makes function infinitely differentiable at every point of C
- because of the nature of discontinuity you can’t extend the simple arccosh in any reasonable way on C without introducing multivalued or path-dependent functions
- this continuity makes x/x=1 a reasonable simplification for CAS imo but not for complex functions as in the OP
- many things with point singularities in R have more structure in C, but x/x is not one of them. Even 1/x is of a different nature.
“You do not divide by zero” that forces you to carry x != 0 is more of a high-school construct than a real thing. Physicists ignore even more important stuff, and in the end their formulas work “just fine”.
Thank you, but, now I have 10 further “explain it to me” questions. (I never did analysis so this stuff is entirely over my head. I had one semester of algebraic structures. It was the hardest class I ever had in my life.)
Well LaTeX formulas are not part of standard Markdown, which is a few different Header levels, simple lists, bold, italics, blockquote and... that's about it?
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