One of the two pinnacles of my weekly activities is my weekly study of the Talmud in the traditional Ashkenazic manner, that is, with a study partner. Outsiders who are not familiar with this method of learning and see two of us arguing might think erroneously that we are angry with each other, as we scream and interrupt each other when we argue. I'd even call the study of the Talmud in this traditional manner mental martial art.
Though I started this only about two years ago, I already see how profoundly it already influences the way I think and argue. Though the color of my "belt" is not black yet, I'm surprised to see how easy and boring to argue with someone, whether Jewish or not, who has no background in the study of the Talmud. Since the experience of learning the Talmud is so intence, I can't help noticing immediately any logical flaw in anything written, including messages posted to mailing lists I subscribe to. I try not to "abuse" this byproduct of my study of the Talmud, but someone writes something utterly stupid in public, I can't resist the temptation of counterarguing it.
And every time I reread afterwards how I reasoned my counterargument, I'm surprised to see how Talmudic my reasoning is (and has become). I'm afraid that I've made a bad reputation for myself in many circles this way, and some people seem to be even afraid of arguing with me in public. Actually, one person even "confessed", though in private, that he feared of arguing with me in public. What a compliment! ;-)
I may be wrong, but I can't help thinking that the Ashkenazic ingenuity has much to do with the study of the Talmud and its profound influence on the way its learners think and argue. Of course, only a small part of the Ashkenazim studies this amazing book, but this learning experience and its influence seem to have been distilled even into the way common people who have otherwise nothing to do with the Talmud think and argue.