Jul 10, 2011

OECD Better Life Index

This is to complement the news telling of Aussie cities becoming the world's priciest (Sydney jumped to 6th from 32nd in 2 years!).

To live well, getting rich is only half an answer

Sydney Morning Herald, July 6, 2011
Ross Gittins (SMH Economics Editor)

What matters is not how much income you have, what matters is how you spend that income. Ross Gittins explains.

How important is money to enjoying a high quality of life? It's an eternal question - mainly because there's no simple answer. But we can use the new ''better life index'' compiled by the Organisation for Economic Co-operation and Development to shed more light on the topic.

The short answer is that once a country reaches a reasonable level of affluence, it's not how much money it has so much as how well it uses what it's got. For the individual, the key is understanding money's limitations.

In an effort to get away from using gross domestic product as a de facto measure of wellbeing, the organisation has developed a better life index for each of its 34 member countries (which include, along with its 23 original rich countries, six former communist countries plus Mexico, Chile, Turkey, Israel and South Korea).

<em>Illustration: John Shakespeare</em>

Illustration: John Shakespeare.

Each country's index is compiled from 21 indicators covering 11 dimensions of wellbeing: income, jobs, housing, health, work/life balance, education, social connections, civic engagement, environmental quality, personal security and life satisfaction.

I guess the key question is the extent to which money - income - determines how well you do on the other 10 dimensions. The Economist has taken each country's score on the better life index and plotted it against that country's GDP per person, finding a reasonably strong correlation between the two.

But the correlation's a lot stronger for the new, poorer members of the organisation than it is for the old, richer members. And this is consistent with the research evidence on subjective wellbeing: rich countries are happier than poor countries, and poor countries get happier as their incomes rise, but once a country joins the other rich nations, having a bit more income than the next country doesn't necessarily mean your people will be happier than theirs.

Consider this: according to The Economist's figuring, Norway's income per person is getting on for double New Zealand's, yet the Kiwis' score on the better life index is a bit higher than Norway's. Clearly, though having enough money helps, there's a lot more to it.

The explanation goes partly to the question of how a country (or an individual) uses the money it has, though it may also involve factors that have little to do with money. But it also suggests income suffers heavily from what economists call ''diminishing marginal utility''. The first, say, $15,000 of annual income buys you a lot more wellbeing than the last $15,000 does.

But let's focus on the better life index. Partly because the organisation chose not to draw attention to the fact (and most journalists are weak at doing their own sums), surprisingly little attention has been paid to the news that Australia had the highest rating among the 34 countries, beating Canada by the narrowest of margins.

Sweden runs a close third. And, indeed, all the Nordic countries do well, yet again defying the Anglo-Saxon notion that countries do best when their governments do (and tax) least. Sweden, Denmark, Norway and Finland remain an excellent advertisement for what the libertarians contemptuously refer to as the nanny state.

The index's big hint that maybe money isn't everything comes when we compare our performance with that of the US. On the index's measure of income - household disposable income per person - the Americans come top, with incomes almost 40 per cent higher than ours.

And yet we score more highly than them on seven of the 10 other dimensions, coming equal with them on one. We equal them on quality of housing, measured mainly by number of rooms per person.

We have 72 per cent of our working-age population in employment to their 67 per cent. Americans work 5 per cent more hours a year than we do. This puts them a bit above the average and us a bit below.

In the US 73 per cent of mothers are employed after their children begin school, compared with 70 per cent in Australia. The organisation says this ''suggests that women are able to successfully balance family and career'', though some would dispute that interpretation.

One dimension in which the Americans beat us is educational attainment. They have 89 per cent of adults with the equivalent of a high school diploma, whereas we have only 70 per cent, putting us below the average.

Whether you want a highly educated workforce so as to earn more income or you value education for its ability to broaden people's horizons, this is a dimension in which we aren't doing nearly as well as we should.

On work/life balance we don't score well - worse than the Americans - because we have such a high proportion of people working more than 50 hours a week.

A classic example of the importance of spending money wisely is health. The Americans spend far more of their income on healthcare than we do, but we get better results. For instance, our life expectancy at birth is more than 81 years, compared with their 78 years.

In terms of social connections, 92 per cent of Americans believe they know someone they could rely on in time of need, whereas 95 per cent of Australians say they do.

Turning to what I regard as the bottom line, satisfaction with life, they have 70 per cent of people expressing satisfaction, whereas we have 75 per cent.

Poverty has nothing to recommend it. Having money is nice. But there's a difference between a high material standard of living and a high quality of life.

We need to remember that, and we need our politicians to remember it.

Ross Gittins is Sydney Morning Herald economics editor.

Source: http://www.smh.com.au/opinion/politics/to-live-well-getting-rich-is-only-half-an-answer-20110705-1h0om.html#ixzz1RIMKj3To

Jul 5, 2011

Collatz Conjecture

Siapa yg mau coba?
 
74 Tahun Tak Terjawab
Teka Teki "3n+1" Mungkin Terpecahkan
Yunanto Wiji Utomo | A. Wisnubrata | Rabu, 8 Juni 2011 | 11:40 WIB
 

Ilustrasi teka-teki matematika

KOMPAS.com — Teka teki matematika yang belum ditemukan jawabannya selama 74 tahun sebentar lagi mungkin akan terpecahkan. Adalah matematikawan dari Universitas Hamburg, Gerhard Opfer, yang mengklaim telah menemukan solusinya.

Teka teki matematika itu yang bernama Collatz Conjecture atau "3n+1" itu diajukan oleh Lothar Collatz pada tahun 1937. Teka teki itu melibatkan operasi bilangan bulat yang dilambangkan "n". Singkatnya, ada dua syarat yang berlaku dalam Collatz Conjecture. Jika bilangan bulat (n) adalah bilangan genap, maka dibagi dua (n/2) dan jika ganjil maka dikalikan 3 kemudian ditambah 1 (3n+1).

Nah, dalam Collatz Conjecture diungkapkan, jika operasi terus dilakukan berulang kali, berapa pun angka yang dipilih untuk memulainya akan selalu didapatkan angka 1 sebagai hasilnya. Verifikasi telah dilakukan hingga angka 5,76 x 10 (18). Namun, tanpa pembuktian matematis yang tepat, selalu ada kemungkinan bahwa angka yang sangat besar akan melenceng dari "hukum" ini. Pembuktian matematis inilah yang telah dimiliki oleh Opfer. Ia menuliskannya dalam paper yang kini telah masuk ke jurnal Mathematics of Computation untuk ditinjau ulang sebab bisa saja pembuktiannya tak tepat.

Nah, apakah puzzle matematika ini nantinya akan benar-benar terselesaikan? Kita tunggu saja. Sementara menunggu, mungkin Anda bisa mencoba mengoperasikan angka berdasarkan Collatz Conjecture.

Coba ambil angka 6. Karena 6 genap, maka dibagi 2, hasilnya 3. Nah, 3 adalah bilangan ganjil, maka dikali 3 dan ditambah 1, hasilnya 10. Lalu, 10 dibagi 2 karena bilangan genap, hasilnya 5. Kemudian, 5 dikali 3 dan ditambah 1, hasilnya 16. Angka 16 dibagi 2, hasilnya 8. Kemudian 8 dibagi 2 hasilnya 4 dan 4 dibagi 2 lagi hasilnya 2. Angka 2 adalah bilangan genap, maka dibagi 2 lagi dan hasilnya 1. Nah, jika diurutkan, maka deretannya adalah 6, 3, 10, 5, 16, 8, 4, 2, 1. Untuk angka 6, berarti terbukti kebenarannya. Anda bisa mencobanya dengan mengambil angka lain. Mau lebih menantang, ambil angka yang besar.

Sumber: Kompas, 8 Jun 11