> it's impossible to do anything not en masse at 8b population
you are missing some simple arithmetic here. yes, x times y can get arbitrarily big if x does (and y is non-negative), but then changes in y would just have even more of an impact. take x to be population and y to be emission per person and you should see your mistake.
and you’re missing the point. no one argued that it’s not worth making changes at the population level.
gp argued that stuff becomes problematic when done en masse. my issue with that is, if you disallow en-masse $thing, who’s going to gatekeep the tiny, exclusive, non-en-masse club allowed to do $thing?
…and in turn “geometric algebra” is the physicist’s name for a subset of the even more general mathematicians Clifford algebra (which of course is a subspace of the tensor algebra over the underlying vector space…)
Clifford Algebra is basically just Geometric Algebra, except with complex numbers shoved into where there ought to be real numbers... because no Mathematician could ever resist doing so.
As a programmer / physicist, the analogy I use is that if I had to represent an 8-dimensional parameter as an array, I would write:
double foo[8];
but a mathematician would be unable to resist writing:
complex foo[4];
They're the same, but the latter is more complex (hah!) for no real (haha!) benefit.
>
They're the same, but the latter is more complex (hah!) for no real (haha!) benefit.
When you consider problems in real geometry, this is plausible. But on the other hand, not all mathematics is real geometry. For some applications in mathematics, the complex-geometric perspective is more natural.
P.S. Of course p-adic (and in particular 2-adic) geometry is even cooler than anything real or complex ... ;-)
It's type confusion caused by duck-typing. Just because can you can add, subtract, multiply, and divide complex numbers doesn't mean they're a natural substitute for real numbers in all scenarios. Sometimes you have '2n' real numbers, not 'n' complex numbers.
If mathematicians designed computer software, their data structures would look like:
I've never seen any convincing argument that Bach is somehow, as frequently claimed, the epitome of baroque music. It seems to be a largely romantic sentiment, that arose moreso to Mendelssohn's circumstances than to anything unique in Bach's music— Mendelssohn simply did not have the access to many other high baroque composers' music to draw from. Aside from how surprisingly late he is, there are many comparable figures to Bach.
I am tired and will content myself with simply mentioning some early baroque composers that, for anyone curious, sadly do not get the spotlight they deserve: Ascanio Mayone (c.1565–1627), Girolamo Frescobaldi (1583-1643), Tarquinio Merula (1595-1665), Johann Jacob Froberger (1616-1667), Giovanni Antonio Pandolfi (1624-1687), Heinrich Ignaz Franz von Biber (c.1644-1704).
> The result of `longer_of` is a projection of the longer argument, so the mutation of `z` by `emphasize` occurs directly on the value of `y`. The value is neither copied, nor moved, and yet it is not being passed by reference to `emphasize`. The body of `emphasize` owns `z` in exactly the same way as it owns `strength`, which is passed by value: `z` is an independent value that can only be touched by `emphasize`.
This evasive phrasing, which continuoes after this excerpt too, has me highly skeptical of their good intentions… Any good reason they are not more explicit?
As someone who has deliberately avoided C++ for the last 20 years (in favour of functional programming) I find the discussions of "reference semantics" and "value semantics" (let alone "mutable value semantics") to be quite opaque. It is as if the C++ community has become an enclave of folks who put up with the extreme complexity of C++ and speak a correspondingly tortuous theoretical language.
What the seem to be saying here is that the "subscripting" operation returns a view into its argument, not entirely unlike the concept of a lens. The only thing that view can be used for is directly accessing the the part of the value that is in focus—the view is not itself a first class value, which means that so-called "reference semantics" don't come into the picture.
I don't think they're being evasive or promoting their idea in bad faith. They are just operating in a characteristically arcane way for C++ language design people.
To me, this seems like a proliferation of distinctions and enthusiastic theorizing. Finding solutions which actually simplify the task of programming and/or clarify matters seems a long way from this attitude.
I returned many times to the Piranesi exhibition in my town showing, among other things, his imaginary prisons. It took me embarassingly many hours to realize the staircase together with the colums in number XIV forms an impossible object / optical illusion. I wonder how much else I missed.
