Hi, Jelle here. I'm currently helping the IoC organisation with the more mathematical parts and technical bits.

Quote from: Laume on January 05, 2015, 10:53:50 AM

I think this project sounds very interesting. If I understand correctly, anyone could pay me in any cryptocurrency,

Yes, this is true. The system will try to automatically find a way to convert from cryptocurrency X to cryptocurrency Y, using hybrid assets.
But this should be (mostly) hidden for the user. You just see: convert Doge to Flappy.

Quote from: Laume on January 05, 2015, 10:53:50 AM

and I would not have to rely on the services of a third party to exchange anything?

You don't have to rely on the services of a trusted third party. However, the exchange is going to be governed by a decentralised service consisting of many nodes. So this is similar in spirit to how Ethereum works.

Quote from: Laume on January 05, 2015, 10:53:50 AM

And this would in turn increase the security? How, exactly?

I think the bit of the white paper you are referring to here, tries to say that decentralized services are better than centralized.

Quote from: Laume on January 05, 2015, 10:53:50 AM

And doesn't this promote centralisation, if everyone uses this asset for their transactions?

I'm sorry if these questions are ignorant...I'm still new to the realm of cryptocurrencies.

I'll leave this one to the others to answer :-)

Don't worry about asking "ignorant" questions, it's up to us to make the story as clear as possible. Every question is welcome, this way we can learn what need to be explained better. So keep asking :-)