That’s a totally dubious opinion misstated as fact.

Without American materiel (lend/lease ships, tanks, bomber aircraft) and manpower (D-Day landings, continental fighting, naval convoys) the war effort would have been almost inevitably lost. This does not mean that the UK mightn’t have eked out a long-term stalemate and perhaps even an uneasy truce, but the defeat of Nazi Germany would have been out of the question. What ultimately defeated Germany was not the war on two fronts, but an expensive, resource-intensive war on two fronts that exceeded the country’s ability to regenerate. Without the virtually bottomless reserves of resources provided by the USA, the USSR would have been eventually brought to heel, and the West would have followed suit.

The USA was pivotal.

**LOCATION INDEXED**

I hadn’t actually, but thanks for the insight.

I suppose that in the light of this I should return and revise “usable” to read “usable at the prevalent conditions within the given environment”. In that form the statement still stands and accommodates for your observation, too.

Clearly the original poster intended to signify a to-be-defined set of “usable” chemicals. It is clear to everybody versed in even rudimentary chemistry that a concentration of noble gasses would not give rise to life for the simple reason that though concentrated they do not react. Thus the expected reactivity of the chemicals under consideration becomes a key concern. The building blocks of life as we know it (carbon, oxygen, nitrogen, & cetera) is a pretty reactive bunch of stuff.

I expect professor English has already formalised this (fairly trivial) observation in his work. If that is not the case, it could no doubt be effortlessly included. I do not believe it to be a profound point. I especially resist the tendency Slashdot users often display of building straw-men absurd logical reductions.

In the Journal of Chemical Physics, England describes YOU!

I think he’s referring to the Chrome/Chromium browser, not the Chrome browser-on-linux self-contained-computing-environment thing.

Not only are you assuming that a web-browser is already loaded, you are also assuming that that exact web-browser is loaded.

This is how bloat begins: with an apparently clever insight that ignores actual common sense.

They’ll strip us naked and then charge us for indecent exposure.

Thank-you I’ll look into it.

Practical users of math have already switched by virtue of the fact that programming applications or spreadsheets requires entering formulas in a textual format.

And how can you imply that enjoying the benefits of a computer do not qualify as a massive advancement? Infact it’s such a massive improvement that practical users of mathematics have already switched.

Likely what drags US education down is the underlying notion that things must be ‘fun’ for children to do them. Most of the highest-achieving education systems are significantly less technology- and fun-orientated than the US system. And you can hardly argue that the young adults who emerge from these systems are psychologically scarred by the lack of ‘entertainment’.

Oh, and regarding note-taking: I’d argue that there’s a strong distinction between the need to record notes and the ability to use those notations in an ‘active’ or ‘computable’ form. Until very recently there was no ‘self-computing’ notation at all simply because everything had to be processed by a human. The idea that a notation should be machine-readable is obviously a fairly recent one (whether by ‘recent’ you imply either Turing or Leibnitz is fairly irrelevant in the grand scale of things). Arguing that notation must be machine-readable and ‘standard’ is somewhat inconsistent.

Standard mathematical notation is wildly inconsistent already (witness the confusion that arises when students first encounter subscripts and ‘powers’ in tensor notation); I don’t see any reason why this inconsistent ad-hoc hodgepodge should be protected to the extent of impeding further advancement.

I disagree.

Usually (though not necessarily) it makes students dependent on mysterious ‘black boxes’ and engenders them to become dependent on one implementation and it’s quirks. Technology should only be introduced gradually to provide ‘shortcuts’ for that which is already understood but tedious to perform.

And never, ever, should we promote reliance on technology. If we provide students with tablets and on-screen keyboards and spellcheckers, are we going to exempt them from having illegible handwriting and awful orthography when we examine them? Or are we going to examine them on tablets, allowing millennia of calligraphy and writing skills to be lost?

People, we’re technologists. It’s fine for us to love gadgets. It’s harmful for us to try to use technology to solve every single problem - particularly problems that either don’t exist or have arisen precisely because of technology.

Most of the most proficient education systems are significantly lower-technology than the current US system. I think that is no coincidence.

I hadn’t realised (and don’t quite accept) that I am unusually ‘flexible’ in using text-mode mathematical entry. Indeed I think you’ll find that if you consider the sum total of programmers and spreadsheet users most non-academic users of mathematics are already using non-traditional notations for mathematics (though, I do readily admit, spreadsheet formulas and program statements are not terribly convenient for deriving symbolic statements).

Notations do change, have changed, and will change again - consider for example the switch from Roman to Arabic numerals. That brought a huge boost in convenience, sufficient to promote the adoption of the unfamiliar new notation.

Anyway, it is education that we are talking about here. Quite distinct from the fact that I do not believe adding more technology to the mix is the solution to a (non-existent) problem, I think you’ll agree that since education teaches ex nihilo, we can easily teach new learners whatever new notation we please, and it will be accepted by them as the norm. Provided they are sufficiently acquainted with the old notation to translate from it (and into it) if and when the need arises, there is no disconnect in their experience.