I thought the claim was that you don't need calculus for coding theory, not that there exist branches of advanced mathematics where calculus isn't necessary. So it's germane to produce a book on coding theory and show that the mathematics of the continuum begins literally on page 2.
I appreciated DFW's book for even attempting to do a popular treatment of what we would now call the history of real analysis. But there were some serious technical problems with it: http://www.ams.org/notices/200406/rev-harris.pdf
It's on the high end, but it's only a factor of three off of the roughly $7 million the EPA uses in cost-benefit analysis. Perhaps a bad call, but not wildly innumerate.
Not to mention that $100 per vehicle is probably wildly high. The quality on these things isn't great (and doesn't need to be). If I can buy a fully featured IP camera at a retail price of $50 complete with pan and tilt, I doubt car makers are going to pay more than $10 or so wholesale for a lesser camera with no networking and no motors. The screen is going to cost something too, but most cars already have those now.
The raw parts cost may be less. But it'll have to be covered by new-car warranty so it can't be complete garbage. It will also have to be worked into the design of the car and the manufacturing process, which are one-time costs but they are costs. Automakers will also have to amortize in the expected cost of defending lawsuits and paying awards to car owners who will claim the camera failed causing them to have an accident, etc.
hell, you can get a chinese android phone for $100 -- and that includes the camera and color display, plus all of the rest (battery, storage, wifi, wireless, gps, bluetooth, etc). Anyone who claims adding this to a car costs $100 is ridiculous.
What does that have to do with manufacturing a car, or sliding in a prefabbed camera into an area of the car already covered with cabling (brake lights, backup lights, rear door open indicator switch)?
That would be weird if so, because the rule doesn't require adding it to existing vehicles, and nobody else is talking about upgrading existing vehicles. The important question regarding this rule is how much it costs to add a backup camera to a vehicle design for production of new units.
I'm always surprised when reading the notes of scientists and mathematicians working in previous centuries to see just how steeped they were in synthetic geometry. This was taken to an extreme in the case of the Principia, but one can't read Gibbs or Maxwell either without realizing that they felt Euclid in their bones in a way that few people do today, with possible exceptions for mathematicians trained under the Soviet system.
I don't know-- usually the answer to such questions about academic priorities is "because it was cheaper", but they just seemed to emphasize geometry much more at the K-12 level. It's a generalization, of course, but a pretty robust one. One of my professors came from Kazakhstan, and once casually remarked that a certain problem on a homework set was "impossible unless you were Russian", since the proof was easy if you knew a certain proposition from Euclid, but extremely tedious without it.
EDIT: this interview with Izaac Wirzsup comparing the Soviet and US systems confirms my prejudice:
Another extremely harmful feature
of [the US] school mathematics programs
is that only about half of our students
take geometry, and for only one
year, generally in a concentrated high
school course. Students cannot be
expected to master the material taught
in this way. Moreover, they are not
being taught solid geometry, and they
rarely have a workable perception of
three-dimensional space, which is so
essential for studying science,
technical drawing, or engineering.
Soviet children study geometry
extensively for ten years, including
two years of solid geometry.
Jut from my own common sense it seems like geometry is important for understanding the relationship between abstract things and concrete things. It's easily understandable that shapes are described by geometry and it seems obviously useful. The square footage of a house. The volume of a bath.
If you try to describe what Calculus is or does, it's abstractions of abstractions. Rates of change or 'angle of a curve for a certain values. I think it's hard for students to see this as something useful or even see how it's a description of the world that opens up ways of understanding it.
I don't see calculus as an abstraction of abstractions. The fundamental idea is completely geometric: "break the domain of a problem into a bunch of pieces that can be easily described and related (e.g. by physics) then put the pieces back together." Time is a first-class dimension. Abstractions only enter the picture when you want to separate the problem of picking a mesh from the problem of representing mesh elements.
Differential operators perform the task of "breaking into pieces" in a mesh-invariant way. Differential forms are mesh-invariant pieces. Integration is the mesh-invariant description of putting the pieces back together.
It's convenient that differential forms can be interpreted physically (by normalizing, associating with geometric elements, etc) but I'd hesitate to associate them with any single physical interpretation (e.g. rates of change) because doing so de-emphasizes the generality of the approach; you can have a rate with respect to distance, area, or volume just as easily as a rate with respect to time.
Leibniz notation makes the hop from the geometric approach to the "operator that maps a function to a function" approach seamless, and since the latter description isn't nearly so intuitive, I've always suspected that the geometric approach could profitably be taught first.
> One of my professors came from Kazakhstan, and once casually remarked that a certain problem on a homework set was "impossible unless you were Russian", since the proof was easy if you knew a certain proposition from Euclid, but extremely tedious without it.
Do you remember what was the problem, by any chance?
I don't remember-- it must have been either differential geometry or topology, but I think the theorem in question was the inscribed angle theorem: http://www.proofwiki.org/wiki/Inscribed_Angle_Theorem. Not a difficult theorem, but you had to know it well to be able to see the application immediately.
There is an excellent chapter called 'on teaching of geometry in Russia' [1] discussing how Geometry stayed important even after west moved away from euclid.
What does "the impulse towards genetic determinism" mean here? Comparisons of identical twins raised apart show that physical appearance is highly heritable, so it would seem that "the impulse towards genetic determinism" is in this case correct.
> it's considered a settled issue that everyone is equally likely to get HIV.
I have no idea what this is supposed to mean. Under every interpretation I can think of, it is incorrect. In the first place, people vary in their CD4 and CCR5 (&c.) receptors, so they also vary in their susceptibility to HIV infection given exposure. My understanding is that some alleles confer such resistance to infection that carriers are considered naturally immune. As ever in immunology, that's not the entire story, but it certainly enough to falsify the view that "everyone is equally likely to get HIV" _even given exposure_.
More importantly, people have different rates of exposure. Those rates depend on what sort of potential transmission events one faces, and the prevalence of infection among partners for potential transmission events. Both of those differ between groups of people.
Hence, not everyone is equally likely to get HIV. That implies nothing, of course, about what we ought to _do_ about that.
I think the OP is saying for the general public it's considered a settled matter that everyone is equally likely to get HIV. Not that it's true, but that for PC reasons thats the acceptable "truth". To imply or state otherwise, regardless of its actual truth, would be some kind of ism.
It is a dreadful poesy to think that the last stargazer from this planet might have been a robotic rocket, looking up once at the fixed stars for all of humanity before ending it.
http://www.inference.phy.cam.ac.uk/itila/