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Transforming towards global sustainability requires a dramatic acceleration of social change. Hence, there is growing interest in finding 'positive tipping points' at which small interventions can trigger self-reinforcing feedbacks that accelerate systemic change. Examples have recently been seen in power generation and personal transport, but how can we identify positive tipping points that have yet to occur? We synthesise theory and examples to provide initial guidelines for creating enabling conditions, sensing when a system can be positively tipped, who can trigger it, and how they can trigger it. All of us can play a part in triggering positive tipping points.

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Abstract. Humanity's situation with respect to climate change is sometimes compared to that of a frog in a slowly boiling pot of water, meaning that change will happen too gradually for us to appreciate the likelihood of catastrophe and act before it is too late. I argue that the scientific community is not yet telling the boiling frog what he needs to know. I use a review of the figures included in two reports of the Intergovernmental Panel on Climate Change to show that much of the climate science communicated to policymakers is presented in the form of projections of what is most likely to occur, as a function of time (equivalent to the following statement: in 5 min time, the water you are sitting in will be 2 ∘C warmer). I argue from first principles that a more appropriate means of assessing and communicating the risks of climate change would be to produce assessments of the likelihood of crossing non-arbitrary thresholds of impact, as a function of time (equivalent to the following statement: the probability of you being boiled to death will be 1 % in 5 min time, rising to 100 % in 20 min time if you do not jump out of the pot). This would be consistent with approaches to risk assessment in fields such as insurance, engineering, and health and safety. Importantly, it would ensure that decision makers are informed of the biggest risks and hence of the strongest reasons to act. I suggest ways in which the science community could contribute to promoting this approach, taking into account its inherent need for cross-disciplinary research and for engagement with decision makers before the research is conducted instead of afterwards.

Over the past 40 years, climate science has established with ever greater certainty that climate is changing as a result of human activity. Recently the Intergovernmental Panel on Climate Change (IPCC) concluded that the effect of human activity on climate is "unequivocal", and that climate change is already worsening extreme weather events across the globe (IPCC, 2021).The emphasis of physical climate science to date (summarized in successive IPCC Assessments) has been on quantifying the human influence on climate and its impacts over the coming decades (IPCC, 2021(IPCC, , 2022. The focus has been on projection of what is most likely to occur. But now the reality of climate change is beyond