I can understand removing some of the smallest countries, but Bosnia has a larger population than Albania or any of the three Baltic countries. I guess this would have been much more legible if it wasn't presented as a map.
I've been recently moving back and forth between Italy and France and there is one thing that bothers me with eurotariff: if I'm in Italy, a French friend is visiting me, and I send them a text with my non-roaming Italian phone I pay about 30 cents and this sum is not regulated anywhere. If I fish out my French SIM card then that amount is capped to 7 cents. Funnily enough once I finish my monthly allotment of SMS's, I can still message my Italian friends, from my Italian phone at 10 cents per message, which is more expensive than what I'd pay roaming and is not regulated.
So what I'm saying is that already today, without roaming charges being abolished, using a foreign phone is generally cheaper than anything without a plan in Italy, and I know that Italy is one of the cheapest countries in Europe for non-monthly deals.
Same thing in the UK - using my O2 pay as you go in Spain is cheaper than a pay as you go in Spain for voice/sms, also using my UK phone in Spain for voice/sms is cheaper than using it in the UK.
Mobile pricing is mental - completely detached from technological restriction or infrastructure cost.
Also, some provider in EU ( as in France ) are making roaming free in most Europe already. However, unlike what the article suggested, you need to live in France to get them ( and remember the terrorists - you don't want to add yourself to some government shit-list just to save a few euro on holidays )
Not necessarily the most efficient though: the Box-Muller transform that is probably used in the call to randn is related to the transform you'd need to start from uniformly distributed reals.
So your solution ends up pretty much using the same math (while probably calling cos a few more times) and throwing away at least one random number and possibly half of them (depending on the implementation of randn).
Yeah, the Gaussian trick is like programming in a high-level language: using existing abstractions lets you write clean and concise code, at the price of some efficiency versus the optimal engineered-from-scratch solution.
It seems a bit pretentious to flag something because you haven't heard of him. There is a bunch of stuff on HN daily that I don't know about, and often the article doesn't provide much context. However, I usually hit wikipedia and try to learn more rather than hitting flag.
Most of the time that's how I feel about it, too. I'd never flag an article about some framework or technology I had never heard of. But in this case I'm not seeing the connection to technology or startups or general interest; it just seems off topic. I'm sure it's a great article, I'm just not sure it belongs on HN, so I flagged it.
I was discussing usage, not theoretical existence for some subset of cases. Direct debit is rare in Australia/New Zealand (most people prefer to perform transactions themselves on a one-off basis), I've never seen it in Asia in 15 years, and according to my US bank the American implementation is often fundamentally broken and based on some kind of print-and-mail-a-check system, though widely used.
Unless you are relying on some non-general meaning of Direct Debit, then as an Australian - No, it's very common, and can used by everyone, everywhere for almost everything that reoccurs, and is reliable.
Our banking system has some rough edges for the average customer, but in terms of day to day usage; Internet banking, ubiquity of EFT, bank interchange, etc, it's quite good.
If only the banks would open up with some APIs. :)
> Fair enough. Out of interest, used to = how many years ago? I'd wager it's waning.
Quite a while: 10 years-ish?
I doubt it's changed towards credit card; most companies have a 3% surcharge for using a CC.
I might believe that more people are using BPay.
But direct debit is the easiest: no interaction required from customer, and merchants prefer it as you need to do less in the way of credit checks.
> Direct debit is rare in Australia/New Zealand (most people prefer to perform transactions themselves on a one-off basis)
Some companies offer a discount for direct debit (over credit card or other payment types). From the data I have direct debit is over 50% of transactions and payments (large Australian company). 50% is far from rare and that is excluding credit card payments...
In Singapore, direct debit is known as GIRO, and practically any large organisation supports or prefers it as a payment option. Companies of all sizes take cheques, fewer take cash or NETS in person. Credit cards and one-off e-banking bill payments are often supported by the larger companies but not always. In fact, my insurance company outright refuses to take credit cards, and tries their very best to push customers onto GIRO. 
GIRO authorisation ("Direct Debit Authorisation") until recently was fully paper, often on carbonised forms with manual signature, but some of the banks have started offering electronic authorisation recently.
People here tend to fall into three camps: the cash/NETS (local debit card) folks who queue up at the post office or AXS machines to pay, those who do one-off bill payment on e-banking, and those who use GIRO/credit card. It depends on how comfortable people are with technology and e-banking in particular, as well as how skeptical they are of the billing organisation automatically charging the right amount.
Another "used here too" comment, it's common enough in the UK that many bank accounts don't consider you to be actively using your current account (and therefore eligible for add-ons or reduced fees) unless you have two direct debits set up.
Direct debit is very common in Japan and South Korea, although credit cards are also used for recurring payments. My phone bill is paid via direct debit. My parents' utility bill is paid via direct debit. A client of mine collects membership fees via direct debit.
It's ridiculously easy to set up. It's also easy for fraudsters to abuse. But then again, a fraudster would need to register his business with the appropriate authorities in order to start making debits, and many payment processors require additional details such as the account holder's date of birth. So nobody seems to be particularly worried. People here hand out their bank account #'s like they hand out business cards. A lot of small businesses even have their bank account #'s posted online. Heck, even I have my bank account # posted online, to collect donations for an open-source project.
So, direct debit is everywhere, fraud is everywhere as well, but for some reason, Americans seem to be the only ones who freak out when someone else figures out their bank account #.
One thing a few countries do (at least Denmark, not sure where else) to cut out most instances of direct-debit fraud is requiring that the first debit from a new merchant is approved by the account owner. This might not technically be a direct debit, though, but is the electronic adaptation of the old "giro" system to function mostly through the direct-debit machinery. When a merchant wants to set up a new client's payments, they send a "giro" request, which is basically a bill with some codes. The client could pay this in the old-fashioned way by taking it to a post office and paying it there in cash; the post office then transfers the payment to the merchant. But what most people do nowadays is log into their online banking, enter the giro #, and say they want to pay it with direct debit. That authorizes all subsequent bills in the same series (i.e. for the same product or recurring subscription) to get direct-debited automatically. But merchants can't normally just pull directly without this initial authorization.
Interesting. I've never lived in Japan/South Korea, but in mainland China (1.4 billion people) as far as I can tell it doesn't exist. Never seen in Thailand, Laos, Vietnam either. I'd be surprised if it exists in India. Probably does in SG/HK, but who'd live there? :)
(PS. Typical HN this thread .. make a valid comment, get called out on a tangent and voted down to obscurity. At least we're all learning something ;)