No mention of pollution or climate change? The trend for climate change been observed since the 1950's. 99% of Scientists agree that it's really happening, and it will have a major impact on how livable our planet is.
This paper[1] looks at things from the perspective of cumulative CO2 emissions, as they have a roughly linear relationship with the temperature increase. For example, over the period of 1870 to 2012 we added about 1,430 (+- 70) GtCO2 to the atmosphere, and we're already observing a +0.8°C mean global temperature increase:
> Taking into account CO2 emissions prior to 2014, the remaining emissions quota (from 2015 onwards) associated with a 66% probability of keeping warming below +2°C is estimated to be 1,200 (900–1,600) GtCO2. This +2°C quota will be exhausted in about 30 (22-40) ‘equivalent emission-years’ at the 2014 emission level (40.3 GtCO2 yr^-1). Owing to inter-annual and decadal variability, the actual year when +2°C will be reached is uncertain. The remaining quota associated with a 50% probability of committing to 2 °C of warming is estimated to be 1,500 (1,100–1,900) GtCO2 (Table 1), corresponding to 37 (27–47) equivalent emission-years at the 2014 emission level.
So, within the 40 year timeframe mentioned in the link, and assuming (optimistically) that we've reduced global CO2 emissions to 2014 levels (recall: global emissions have been growing by 2.5% each year for the past decade.), we'll have hit a 50% chance of having locked in > +2°C of warming.
I don't think that a linear relationship between temperature and CO2 level is a safe bet. The climate is pretty chaotic, it seems unlikely that such a simple relationship is true in general. It seems entirely possible that we'll hit some kind of runaway effect at some point that completely breaks the linear relationship.
Anyway, I'm not a climate scientist and there are a number of people who claim that 1000 GtCO2 lead to 2 degree warming, so your 1500 GtCO2 seem only a little optimistic. However, just reducing CO2 production is not enough. We have to completely stop, because CO2 takes basically forever to sequester from the atmosphere, and every degree of warming we cause increases the likelihood that we leave the "safe" linear-relationship territory.
> Taking into account CO2 emissions prior to 2014, the remaining emissions quota (from 2015 onwards) associated with a 66% probability of keeping warming below +2°C is estimated to be 1,200 (900–1,600) GtCO2. This +2°C quota will be exhausted in about 30 (22-40) ‘equivalent emission-years’ at the 2014 emission level (40.3 GtCO2 yr^-1). Owing to inter-annual and decadal variability, the actual year when +2°C will be reached is uncertain. The remaining quota associated with a 50% probability of committing to 2 °C of warming is estimated to be 1,500 (1,100–1,900) GtCO2 (Table 1), corresponding to 37 (27–47) equivalent emission-years at the 2014 emission level.
So, within the 40 year timeframe mentioned in the link, and assuming (optimistically) that we've reduced global CO2 emissions to 2014 levels (recall: global emissions have been growing by 2.5% each year for the past decade.), we'll have hit a 50% chance of having locked in > +2°C of warming.
[1] -- Friedlingstein et al - nature geoscience, 2014 -- pdf version http://www.globalcarbonproject.org/global/pdf/Friedlingstein...