Turkey has been in a long struggle of westernization. And unfortunately this has been blocked by the cold war policies. Its strategic location made Turkey the boiling pot in 1970-80 period and for some reason Kissinger preferred a green islamist and nationalist movement against communists left factions. And now this is the result.
Turkey is not european nor middle eastern. It is something different. Its westernization has been cut off but its founding fathers did make too big of an impact on people, still managed to keep its nerve endings touching to the civilized world view of the century, unlike all other surrounding countries in the middle east. You see democratic elections and leaders get democratically elected. Even this alone is much more than any other muslim state has to offer at the moment.
But of course, just like any other muslim state, there is a tendency for authoritarian leader figures. But I think this will change in time. What you are seeing in Istanbul and other cities now is; the need for democracy being realized by all the different elements of the society.
You don't see any single faction taking the leadership in these protests. It started with some pacifist environmentalists protesting the unlawful demolishing of a green space. Then police assaulted and beat these people up brutally. And now all the people are on the streets. Most of them don't even care about trees or green space. But they care about one thing in common, fundamental democratic rights of people. And they are out there because they know if they don't defend those rights now, it may be too late tomorrow.
And yes, the person they are opposing to have had 50% vote in elections. He is representing the majority. But protestors are not asking the majority to bow them, they are just asking the majority to elect someone who is not a sick dictator pushing them around, beat them up, threaten them with death and make a mockery of when they are simply excersiing their fundamental democratic rights. That shouldn't be too much to ask for, especially in a country claiming to be democratic, even more democratic than US or Eruope (that's what Tayyip Erdogan claims to be

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And I am hopeful for Turkey. I think it will bear more stability for Turkey, unlike others that have gone through the Arab spring. Turkey is lucky to have some type of institutionalized republican "power to the people" values. This luck will pay off at the end I think. The conservative religious majority will see the value to keep it in place, for stability and more prosperity and will find an alternative to their authoritarian dictator sooner than later.
So I guess we will see all together, if a muslim democracy is a possibility or not. This is the real test now. If they fail, than you can keep on with your hate mongering and declare muslims the barbarian mongols of the century. If they succeed, you should be happy because you will not be worried for your grand kids being have to deal with bunch of pissed off towel heads.
Personally, I wish success for turks...