Buried deep in our subconscious, there still lays the belief that our political leaders are collective Daddies and Mummies who will – in the last instance – guarantee our safety. Sure, they might screw us over when it comes to hospital waiting lists, or public transport, or taxing the rich, but when it comes to resisting a raw existential threat, they will keep us from harm. Last week in Copenhagen, the conviction was disproved. Every leader there had been told by their scientists – plainly, bluntly, and for years – that there is a bare minimum we must all do now if we are going to prevent a catastrophe. And they all refused to do it.

To understand the gravity of what just happened, you need to know a few facts about global warming that, at first, sound odd. The world's climate scientists have shown that man-made global warming must not exceed 2C. When you hear this, a natural reaction is – that's not much; how bad can it be if we overshoot? If I go out for a picnic and the temperature rises or falls by 2C, I don't much notice. But this is the wrong analogy. If your body temperature rises by 2C, you become feverish and feeble. If it doesn't go back down again, you die. The climate isn't like a picnic; it's more like your body.

Two degrees is bad: 2C means we lose much of the world's low-lying land, from the island-states of the South Pacific to much of Bangladesh to swathes of Florida. But at every step up to and including 2C, if we reduce our emissions, we can stabilise the climate at this new higher level. If we go beyond 2C, though, the situation changes. The earth's natural processes begin to break down – and cause more warming. There are massive amounts of warming gases stored in the Siberian permafrost; at 2C, they melt and are released into the atmosphere. The world's humid rainforests store huge amounts of warming gases in their trees. Beyond C, they lose their humidity and begin to burn down – releasing them too into the atmosphere.

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These are called "tipping points". Because of them, the world gets warmer and warmer beyond 2C. They stand at the climate's Point of No Return, beyond which there lies only warming. We are only 6C away from the last ice age; we are setting ourselves on course to go that far in the opposite direction.

So what do we need to do to stay this side of 2C? There is a very broad, rock-solid scientific consensus that we need a cut of 40 per cent in the most polluting countries' emissions by 2020 if we are going to have even a 50-50 chance of doing so. Then, by 2050 we need an 80 per cent cut from everyone. The fact we are only aiming for a 50 per cent goal of avoiding calamity is a sign of how far we have already made a terrible compromise with fossil fuels – but our leaders are refusing to aim even for those odds.

There was plenty of disgrace to go around in Copenhagen. The world's worst per capita warmer is the US, yet its President turned up offering a pathetic 4 per cent cut by 2020 – and once you factor in all the loopholes his negotiators demanded, he was actually demanding the right to a significant increase in US emissions. He caved to the oil and gas lobbies who virtually own the Senate. It was – apart from anything else – a terrible betrayal of his own country's national security. In 2004, a leaked Pentagon report warned that unchecked global warming would ensure "disruption and conflict will be endemic ... [and] once again, warfare would define human life."

Similarly, the Chinese Premier Wen Jiabao behaved appallingly. His country is the single largest overall emitter of gases, albeit with a far larger population, and much more need for development. Yet he vetoed the 80 per cent target by 2050, and refused to allow other countries to carry out basic checks to ensure China was carrying out the smaller cuts they were committed to. Again, he is betraying his own people: most of China's population depend on rivers that flow down from the Himalayan glaciers, yet they are rapidly disappearing. His name will be cursed in the Chinese history books.

The European Union was hardly better. They sat inert, refusing to make any larger offer to get the ball rolling. Only President Lula da Silva of Brazil came out boldly with an ahead-of-the-curve offer – but his heroism was met with awkward silence and avoided glances from the other leaders.

So here's the situation. There is no deal. The world's leaders refused to agree to limit our emissions of warming gases. The most they could agree was to officially "note" the scientific evidence about 2C – with no roadmap to keep us this side of it. You get a sense of how valuable this "noting" is when you look at the things the conference also "noted": the hard work of the airport security staff, and the quality of the catering in the Bella Centre. It seems impossible, but our leaders really did give the stability of our climate the same status as their praise for Danish sandwiches.

I am normally somebody who supports incremental change. Most progress happens by inches. But with this problem, we can't wait patiently knowing we'll prevail in the next generation. The tipping points will make that too late. You can't defuse a ticking bomb slowly year after year. You either defuse it fast, or it blows up in your face.

Our leaders were given the scientific facts, and they have responded by trying to haggle with the facts about the atmosphere. Imagine a 50-a-day smoker who goes to his doctor and is told he must stop immediately or he will develop lung cancer. He says: "I'll tell you what, doc – I'll cut down to 40-a-day, I'll eat a salad every lunchtime, and I'll slap on a few nicotine patches. How does that sound?" That's the official response to global warming.

Where does this leave us all? At least we know now: scientific evidence and rationality are not going to be enough to persuade our leaders. The Good Daddy isn't in charge. Nobody is going to sort this out – unless we, the populations of the warming-gas countries, make them. Politicians respond to the pressure put on them, and every single politician at Copenhagen knew they would get more flak at home – from their corporate paymasters and their petrol-hungry populations – for signing a deal than for walking away.

There is only one way to change that dynamic: a mass movement of ordinary democratic citizens. They have made the impossible happen before. Our economies used to be built on slave labour, just as surely as they are built on fossil fuels today. It seemed permanent and unchangeable, and its critics were regarded as deranged – until ordinary citizens refused to tolerate it any more, and they organised to demand its abolition.

The time for changing your light-bulbs and hoping for the best is over. It is time to take collective action. For some people, that will mean joining Greenpeace or Friends of the Earth or the Campaign Against Climate Change and helping them pile on the pressure. But those who can go further – by taking non-violent direct action – should do so. Every coal train should be ringed with people refusing to let it pass. Every new runway should be blockaded. The cost of trashing the climate needs to be raised.

It works. Look at Britain. Three years ago, eight new coal power stations were being planned, and the third runway at Heathrow was all but inevitable. A few thousand heroic young people took direct action against them. Now all the new coal power stations have been cancelled, and the third runway is dead in the water. Here in the fifth largest economy in the world, they have stopped coal and airport expansion. Politicians felt the heat. That was done by a few thousand people. Imagine what tens or hundreds of thousands could do.

There need to be parallel movements to this in every country on earth (and a much bigger one in Britain). Copenhagen had one value, and one value alone. It has shown us that if we don't act in our own self-defence now, nobody else will.

You can hear Johann being interviewed about what happened in Copenhagen on Air America by clicking here.

j.hari@independent.co.uk