In the third part of his series on Islam in south-east Asia, Roger Hardy asks if the world's biggest Muslim country can shake off extremism and make the transition to democracy.
You can still see the crater outside the Australian embassy in Jakarta where a truck, packed with explosives, blew up last September - killing 11 people.
The bomb attack was blamed on the Jemaah Islamiah group
Experts were quick to see the hand of Jemaah Islamiah - the group held responsible for the Bali bombings of 2002, and widely seen as the regional arm of al-Qaeda.
The attack came at a sensitive moment, when this huge nation of 220 million people was about to elect a new president - a key step on the road from dictatorship to democracy.
In the event, voting went off peacefully. But the bombing showed that Indonesia's fledgling democracy still faces daunting challenges.
A tolerant face of Islam
The teenaged schoolgirls in Yogyakarta, in central Java, gave me a warm and very noisy welcome.
Identically clothed in neat blue dresses and white headscarves, they laughed and joked. One even sang a Maria Carey song.
It was a far cry from the prevalent Western image of a madrasa, or Muslim school.
The girls' school is part of the huge educational network run by Muhammadiyah, one of Indonesia's oldest and biggest Muslim grass-roots organisations.
Claiming a staggering 35 million members, Muhammadiyah runs schools, universities, clinics and charities across this far-flung country.
President Yudhoyono has a huge mandate for change
But only a few miles from the girls' school, I visited a very different madrasa.
This was infamous school founded in Ngruki by Abu Bakar Ba'asyir - the elderly cleric currently on trial in Jakarta as the alleged spiritual leader of Jemaah Islamiah.
Asked whether he condemned the Bali bombings, Wahyuddin - the man who runs the Ngruki school - said merely that he "disagreed" with them.
Americans attack Muslims, he said, so Muslims attack Americans. It was a case of action and reaction.
No one was attacking the Japanese.
The radical challenge
Back in the capital, I visited a bar which had been smashed up during Ramadan, the Muslim month of fasting.
There I met Hilmy Bakr Almascaty, one of the leaders of the Islamic Defenders' Front - the group which carried out the attack.
He made it clear that any bar or restaurant serving alcohol during the holy month was a legitimate target.
Islamic radicals like these pose a direct threat to Indonesia's centuries-old tradition of tolerance and moderation.
I began to wonder if the "silent majority" wasn't just a little too silent.
Abu Bakar Ba'asyir symbolises the radical Islamist challenge
I met one of the most articulate members of the new government, Defence Minister Juwono Sudarsono.
He links the rise of radicalism to the perception that corruption and social injustice are rife in south-east Asia.
But the government is reluctant to outlaw Jemaah Islamiah, for fear of upsetting Muslim sensibilities.
The smiling cleric
I went to the trial of Abu Bakar Ba'asyir in a makeshift courtroom in Jakarta.
There, at a distance, I saw the man who in many ways symbolises the radical Islamist challenge.
Sitting with a red and white keffieh draped around his shoulders, the elderly cleric smiled for the cameras.
Many Indonesian Muslims seem to regard him as a kindly old man who has no link whatever to Bali and the other bombings Indonesia has suffered.
One young radical I met at the trial said bluntly that the Bali attack had been carried out by the CIA - and that the trial was a CIA conspiracy.
In numbers, Indonesia's moderate mainstream - bolstered by groups like Muhammadiyah - dwarfs the radical fringe.
But I was reminded of the cryptic words of a former British prime minister.
"It's not enough to be nice."
Roger Hardy's programme on Indonesia - the third in a four-part series, "Islam's Furthest Frontier" - is broadcast on the BBC World Service on 21 February.