> The cost is measured in an exact complex-register model that assigns unit cost to exact complex field operations. The algorithm accepts every x ∈ Cn, with no bound on its entries or on intermediate complex magnitudes. Its computation on the input uses only addition, subtraction, and multiplication by prepared input-independent scalars. The magnitudes of those scalar coefficients are unrestricted as well.
I'm not very familiar with this kind of low-level theoretical computer science, so please forgive my possibly stupid question: is it common to use a model of computation like this, with registers which can store exact complex numbers? Since no computers like that really exist, would that limit the practical application of this finding?
One of the most memorable tech talks I ever attended was by a junior engineer who had just come back to the office from a major conference. Our workplace had an unusually oral culture -- decisions were made in meetings, and not always written down; there wasn't much in the way of bug tracking or work planning at the time; people generally preferred to talk through problems instead of working them out in email, chat, or forum posting.
He was supposed to present a topic he learned about at the conference. Instead, he gave a cheeky talk which introduced the very concept of written language to the audience, as if we had never heard of it. Starting from the history of writing on tablets and so on, and ending in practical advice like, "when words are written down, you don't have to remember what they were exactly; you can just read the words again." I loved the chutzpah and could barely hold myself from chortling out loudly at some of his slides.
I know that your post is an amusing take on communication, but I find the post you responded to be kind of a horrifying idea. Until recently, writing was like a time machine: somebody, from almost at any time in human history, wanted to tell you something. By writing it down in a common language, you could read what they wanted to say. Writing is flipping amazing.
There has always been bad writing, but historically it has been easy enough to filter the garbage out. Now we get garbage that looks so much like real thoughts that it's hard to tell. This is not a positive development. Separating the wheat from the chaff is extra work, and the overhead is a burden on humanity. I suspect that this is a burden that almost nobody actually wants, but we're getting it anyway.
A person riding a bicycle expends an order of magnitude less energy than does a car ferrying the same person the same distance. So I don't think this really holds.
For comparison: at 50 MPG, traveling one mile by car uses 0.02 gallons of gasoline. This is about 675 Wh of energy or 580 kcal. Travel by bicycle for a ~180lb person is about 60 kcal per mile.
I'm not very familiar with this kind of low-level theoretical computer science, so please forgive my possibly stupid question: is it common to use a model of computation like this, with registers which can store exact complex numbers? Since no computers like that really exist, would that limit the practical application of this finding?
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