What is the ratio of Tourism to Culture when influencing a civilization?
In Civilization 5, Culture is described as your defense, while Tourism is your offense in the game of influencing other civilizations. When you generate Tourism, you generate it 2 points at a time. I've found that, even when you're generating as little as 4 points of Tourism, you can find some (culture-poor) civilizations where your influence is rising. It seems unlikely that even a small, culture-poor civilization would generate a mere 4 points of Culture per turn.
So: how many points of Tourism does it take to overcome X points of total Culture? Does it matter whether the Culture was generated recently? Or does Tourism compare against Culture-per-turn rather than total Culture?
Culture and Tourism match up 1:1, and their numbers are considered over all time; that is, if your opponent has earned, say, ten thousand total points of culture since the start of the game, you need to have ten thousand points of tourism against them to become dominant. If the tourism/culture indicates that your influence over another civ is rising, then you are generating more tourism against them than they are generating culture.
Note, however, that even when you are only showing four points of tourism in the bar at the top, you may be generating more against specific civilizations; open borders, trade routes, religion, social policies and more can give you tourism bonuses against specific civilizations that are not reflected up there.
You can get a pretty good feel for all this by opening the Culture Overview. Just click the Tourism indicator on the top bar, and you should see a window like this (you may need to flip over to the Influence by Player tab):
In this window, you can see, for each civilization, what level of influence you have, what your Tourism multiplier is against them, how much total net tourism that's resulting in per turn, and how it's trending. More interestingly, you can hover over the Tourism and Culture bars in the middle section to see the current net totals of each, and also if the trend is "Rising", you can hover over that arrow to see an estimate of how long it will take to reach the "Influential" level, assuming your tourism rate and their culture rate remain constant.
Furthermore, even if you're not making a play at a Culture Victory yourself, this information is still useful; hit the Select Player dropdown, switch to another player, and you can see how well their tourism is doing, both against you, and against other civilizations.