Sharing is more than easy and natural, it's good. Sharing is so important to civilzations that early ones developed writing systems to facilitate it, and later ones have been improving it ever since. Reading and writing used to be only for the nobility, for the practical reason that educating everyone was more expense than was thought worthwhile, though this was also correctly seen as an excuse not to educate the masses. Words were terribly subversive, best if the people can't read them. The pen is not mightier than the sword if no one can read. Democracies changed that, deciding that 100% literacy was a desirable and nearly obtainable goal.
Now here we are today, and what are our supposedly democratic governments doing? Siding with those who think they have a right to lock away knowledge, those who think the worthy desire to compensate artists justifies all kinds of monstrosities and public expense, and that fair compensation can only be done through Holy Copyright.
Sharing should be encouraged. By everyone.
Math is all about being precise, logical.. Communicating exactly one concept at a time. Natural languages do neither.
Except math is almost never actually done that way in practice. Euclid was wonderful, but almost all modern math does not work that strictly (and Euclid really should have been more careful with the parallel postulate -- there's "more than one thing at a time" involved there). Yes, proofs are careful and detailed, but so is, say, technical writing in English. Except for a few cases (check out metamath.org, or Homotopy Type Theory) almost no-one actually pedantically lays out all the formal steps introducing "only one concept at a time".
Some lawmakers were not so keen on the fast-tracking of this legislation. Checks and balances are there for a reason, it's a shame that they can be sidetracked when politically expedient.
Not every programmer deals with these [mathematical] questions regularly (which is why I donâ(TM)t think math is necessary to be a programmer), but if you want to be a great programmer you had better bet youâ(TM)ll need it.
I don't think you need math even to be a great programmer. I do think a lot of great programmers are people who think in mathematical terms and thus benefit from mathematics. But I also believe you can be a great programmer and not be the sort of person who thinks in those terms. I expect the latter is harder, but then I'm a mathematician so I'm more than read to accept that I have some bias in this topic.
Math IS sequencing. So is using recipes. That is how math works.
Math is a language. Just because you can frame things in that language doesn't mean that that language is necessary. Recipes are often in English. English is sequencing (words are a serial stream after all). That doesn't mean English is necessary for programming (there seem to many competent non-english speaking programmers as far as I can tell).
Disclaimer: I am a professional research mathematician; I do understand math just fine.
College education wastes countless hours teaching academic stuff that a great majority of programmers will not use on the job, while neglecting critical skills that could be immediately useful in a large
Of course there was a time when college education was supposed to be education and not just vocational training.
I think part of the problem is that "programming" is itself so diverse.
The other part of the problem is that math is so diverse. There's calculus and engineering math with all kinds of techniques for solving this or that PDE; there's set theoretic foundations; there's graph theory and design theory and combinatorics and a slew of other discrete math topics; there's topology and metric spaces and various abstractions for continuity; there's linear algebra and all the finer points of matrices and matrix decompositions and tensors and on into Hilbert spaces and other infinite dimensional things; there's category theory and stacks and topos theory and other esoterica of abstraction. On and on, and all very different and I can't even pretend to have anything but cursory knowledge of most of them
Calculus is perhaps not the best measure however. Depending on where you go in the programming field calculus is likely less useful than some decent depth of knowledge in graph theory, abstract algebra, category theory, or combinatorics and optimization. I imagine a number of people would chime in with statistics, but to do statistics right you need calculus (which is an example of one of the directions where calculus can be useful for programming).
Of course the reality is that you don't need any of those subjects. Those subjects can, however, be very useful to you as a programmer. So yes you can certainly be a programmer, and even a very successful and productive one without any knowledge of calculus, or graph theory say. On the other hand, there may well be times when graph theory, or calculus, or statistics could prove very useful. what it comes down to is whether you are inclined to think that way -- and if so it can be a benefit; if not it won't be the way you think about the problem anyway.
Er, pegged to the right, I mean. That fridge may have been the least efificient model available in 1995.
I hypermile too. But here again, you'll do better with a better car, rather than sweating to make a bad car do a little better. If we took energy savings seriously, we'd smooth the undersides of our cars for starters. No more of this having the car's guts exposed to the world.
I can't quite match you, but I have our house just under 300kwh in the months with the most pleasant temperatures. There are 3 of us, and it sounds like only 1 of you. You live in a place with a friendlier climate, while I am stuck in north Texas. Last year, we used about 5200kwh. Was hovering around 10000kwh in the 1990s. Improvements in lighting, displays, and A/Cs have made more difference than being an activist about turning things off all the time. However, the biggest saver is being willing to live with greater temperature differences, setting the thermostat to 83 in the summer and 70 in the winter.
I'm looking forward to about a 10% improvement now that we have finally ditched our old fridge. It was made in 1995, and the efficiency of refrigerators was greatly improved starting in 1996. It wasn't even efficient for a 1995 model, being pegged all the way to the left on the energy usage label.
The hardest part of climbing the ladder of success is getting through the crowd at the bottom.