I was there in Copenhagen in 2009.

I remember the quiet conference hall and trains, filled with disappointment and despair as the international negotiations to address climate change unraveled. Rather than a detailed roadmap to a low-carbon future, nations "took note" (the technical United Nations term of agreeing something matters but not agreeing enough to sign it) of a two-page document filled mostly with platitudes. As I headed home, the indomitable, late climate scientist Stephen Schneider said to me, "Saving the world takes time. It's a long dance. We stumbled this time, but the dance goes on."

Fast-forward six years. On Saturday evening in Paris, 187 nations ratified a landmark climate accord known as the Paris Agreement. This 31-page document is a big, big deal. Here's why it matters and what we learned.

First, the bad news. Together, the voluntary commitments the world's nations agreed to probably aren't enough. The stated goal of the agreement is to keep global temperatures under 2 degrees Celsius (3.6 Farhrenheit) of warming since preindustrial times, but the best estimate of the actual agreement puts us on a trajectory of 2.7 C of warming.

The problem is, since carbon dioxide stays in the atmosphere for centuries, humanity only has a limited "carbon budget" of emissions that it can spend before warming above 2 degrees C is highly likely. Just from the gases already in the atmosphere, we are close to crossing 1 C already and have probably committed ourselves to 1.4-1.6 C of eventual warming. That doesn't leave a lot of wriggle room.

So why am I optimistic?

To start, for the first time in history, all nations were at the table and made commitments to reduce or slow their carbon emissions. This means that developing countries like China and India, who have a legitimate point that developed countries pulled themselves from poverty largely by burning fossil fuels, are committed to slowing the growth of their emissions and developing cleanly.

Second, and perhaps more importantly, the agreement has a "ratcheting" mechanism to update goals. In 2018, nations will meet to assess progress and new national targets will be declared in 2020 and reevaluated every 5 years thereafter. Each new target must be at least as ambitious as the previous one, effectively ratcheting down carbon emissions over time. This mechanism provides a path to reach a 2 C or lower world.

There are reasons to believe this frequent reevaluation will work. Many other pollution reductions quickly became cheaper than predicted due to technological innovation, and there's no reason to think that carbon pollution won't follow suit. (Solar power, for instance, is arguably 15 years ahead of schedule.) Adding to the sense of momentum, the Paris negotiations were accompanied by large pledges of public and private R&D investment in energy, spearheaded by Bill Gates. Combine this with the agreement's transparent emissions monitoring and it's not hard to see how frequent target updates could help us reach 2 C.

Finally, the most surprising thing about the talks was the emergence of widespread acknowledgement that 1.5 C of warming should be our target. Even if we are potentially committed to 1.4-1.6 C already, we could, in theory, still reach 1.5 C by ambitious cuts in emissions paired with technologies that take carbon dioxide from the atmosphere. These technologies are currently unproven, but with a major, global research push might be ready in time.

Small island states have long pushed for 1.5 C. The reason is simple: While it's nearly impossible to say what a "safe" amount of warming is — it's akin to asking how many cigarettes you can "safely" smoke — recent scientific evidence suggests that the lock-in point for a catastrophic rise in sea levels — ones that submerge islands from melting glaciers in Greenland and Antarctica — is above 1.5 C of warming.

It was also a remarkable display of alliance-building. For the first time, the small island nations were joined in Paris by the U.S. and E.U., leading to a powerful and ambitious negotiating block combining the most developed and most vulnerable nations. Led by the Marshall Islands, these nations make the moral case that climate change inaction will cause their entire nations to cease to exist. It's a huge testament to them that the agreement says warming should be kept "well below" 2 C and that the world should "pursue efforts" to keep it below 1.5 C.

In the end, saving the world is a long dance and won't happen in a few short weeks. But in years to come, Dec. 12, 2015, may be remembered as the day the world finally took the first step.