I think the likelihood of AI killing all humans is bigger than the likelihood of climate change killing all humans.
Nevertheless I think that we should worry and act much more about climate change than about AI.
Allow me to explain.
Both AI and climate change will, in this century, force changes to basically every aspect of the lives of basically every single person on the planet. Some people may benefit, some may not. The impact of both will be drastic and irreversible. I expect the year 2100 to look very different from 2000.
Climate change will lead to billions of people to suffer, and to many deaths. It will destroy the current livelihoods of many millions of people. Many people will be forced to leave their homes, not because they want to, but because they have to in order to survive. Richer countries with sufficient infrastructure to deal with the direct impact of a changed climate will have to decide how to deal with the millions of people who want to live and who want their children not to die. We will see suffering on a scale never seen before, simply because there have never been this many humans on the planet.
But it won't be an existential threat to humanity (the word humanity has at least two meanings: 1) the species as a whole, and 2) certain values we associate with humans. Unfortunately, I only refer to the first meaning. The second meaning will most certainly face a threat). Humanity will survive, without a doubt. There are enough resources, there are enough rich and powerful people, to allow millions of us to shelter away from the most life threatening consequences of climate change. Millions will survive for sure. Potentially at the costs of many millions lives and the suffering of billions. Whole food chains, whole ecosystems may collapse. Whole countries may be abandoned. But humanity will survive.
What about AI? I believe that AI can be a huge boon. It may allow for much more prosperity, if we spread out the gains widely. It can remove a lot of toil from the life of many people. It can make many people more effective and productive. But history has shown that we're not exactly great at sharing gains widely. AI will lead to disruptions in many economic sectors. If we're not careful (and we likely aren't) it might lead to many people suffering from poverty. None of these pose an existential threat to humanity.
But there are outlandish scenarios which I think might have a tiny chance of becoming true and which can kill every human. Even a full blown Terminator scenario where drones hunt every human because the AI has decided that extermination is the right step. Or, much simpler, that in our idiocy we let AI supervise some of our gigantic nuclear arsenal, and that goes wrong. But again, I merely think these possible, but not in the slightest likely. An asteroid hitting Earth and killing most of us is likelier if you ask my gut.
Killing all humans is a high bar. It is an important bar for so called long-termists, who may posit that the death of four or five billion people isn't significant enough to worry about, just a bump in the long term. They'd say that they want to focus on what's truly important. I find that reasoning understandable, but morally indefensible.
In summary: there are currently too many resources devoted to thinking about the threat of AI as an existential crisis. We should focus on the short term effect of AI and aim to avoid as many of the negative effects as possible and to share the spoils of the positive effects. We're likely to end up with socializing the negative effects, particularly amongst the weakest members of society, and privatizing the benefits. That's bad.
We really need to devote more resources towards avoiding climate change as far as still possible, and towards shielding people and the environment from the negative effects of climate change. I am afraid we're failing at that. And that will cause far more negative impact in the course of this century than any AI will.
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