Question: There are lots of articles written about trying to imagine a 4th dimension of space, but what would it be like to live in a universe with a 2nd dimension of time?
The short answer: We simply don’t know. This question is a bit more complicated than talking about different spacial dimensions because we experience 3 dimensions of space, and so we can use what we know about life in one dimension (and how it changes when you have two dimensions) to make inferences about what 4 or more dimensions would be like. But it would be extremely difficult to imagine how things behave in 2 or 3 dimensions if we lived in a one dimensional universe (we would have nothing upon which to base our inferences). This is exactly the problem that we have with our 1d view of time. Consequently, much of what will be discussed is HIGHLY theoretical, if not blatant guesswork.
And now for the long answer:
A universe with two dimensions of time would be super confusing and probably a little bit lonely. Any sensible person will tell you that relationships require commitment. And, for the most part, commitment is simple in a universe that only has one dimension of time: you plan on meeting someone, and you meet them; you say that you’ll be there, and you're there. However, in a universe that has two dimensions of time every person-- every star, every galaxy, every particle, every everything--moves through two different times: t1 and t2. Obviously, these two times can't proceed at the same rate (otherwise, it would be exactly the same as if the universe had only one dimension of time). Since everything is moving through two different times, it makes it very hard to keep any commitments.
To illustrate this point, let’s talk about meeting a significant other (who we’ll call Bob). When you meet Bob on Earth, it's because you're at the same coordinates in space during an overlapping period of time. However, if you and Bob experienced time differently, then Bob could die and be dead for 86,000 years a second after you meet him. Poor Bob. The problem is, if you and Bob are moving through different time coordinates at different rates, you might remain in the same place but you won't remain in the same time. To put the problem plainly: “unless your loved ones are all on the same world-lines you're destined never to see them again.”
Of course, there would be many other problems in a universe with two dimensions of time. Namely, with 2 time dimensions we couldn’t say anything useful about the "future."
One of the most fundamental parts of science (and life in general) is observation and inference. We look around us and, based on the state of things, determine with some measure of accuracy what will happen in the future. For example, if you cross a street when a car is coming, you’ll probably get squashed. With two dimensions of time, you simply can't do that. Maybe you’ll start to cross the street and, a second after you do, the car is 5 miles down the road. Or maybe it will squash you. It's impossible to say which will occur because it's impossible to make any reliable predictions or inferences with two dimensions of time. (However, it's safe to say that certain physicists are working on it, as many believe we are missing a crucial dimension of time and ANOTHER dimension of space, which would hypothetically make the universe 6 dimensional.. at least by their calculations.) And no prediction or inference means no science or knowledge. Sad face.
Of course, there are a million other hypotheticals that I could take into consideration (like: what if you developed a double consciousness and were able to essentially "read" the future in order to make decisions in the past? In such a universe, with so many people constantly changing the past, could you ever really read the future in any useful way?). With so many hypotheticals, I could easily turn this post into a book (what if a universe had 2 time dimensions but only one space dimension? What if a universe with 2 time dimensions only had one living being in it?). But I think it would be a waste of time for me to go over all the hypotheticals, as I'm sure a lot of people are more than capable of coming up with their own...and please post them if you do. I truly look forward to reading them : )