To paraphrase: a field of corn will absorb all CO2 in the first square meter of the atmosphere. Constantly churning air currents replenish the C02 in the "static" corn field... the corn grows, increasing biomass above and below the surface. Carbon captured!
My shallow understanding is that the bacteria and microbes in the first ~1" of top-soil assist plant-life by transporting/transforming raw organic matter, minerals, and trapped gases (released by decaying organic matter trapped in the soil) into usable forms of energy (sugar?) for the plant.
At the end of a season, left-over corn husks may be turned into the soil (ideally while they are still green?) Plant a fast growing cover crop (clover, oats, rye, etc.) and the elemental gases released will be especially trapped in the soil and released at a slower rate than if left exposed to the elements. A nitrogen fixing cover will also supply additional energy to the system... either way, the bacteria, microbes, and mycorrhizae in the soil help plants convert raw elements into usable energy.
> Can anyone comment on the viability of solving the global carbon dioxide problem by sequestering it in topsoil, as Dyson proposes in the video?
Dyson mentions no-till methods. Tilling the soil (intentionally) disrupts this layer to release trapped NPK but disturbs soil life in the process. Natural ecosystems are no-till--wherein gaseous carbon and "embodied energy" is released at a slower rate. The flow of energy through the system determines the health and state of the system.
Both approaches make sense from my perspective. They have different dynamics, goals, and time-scales: (annually-productive) intensive agriculture systems and (perennially-productive) broad-acre forest farms and silvo-pastures. On the one hand you have vegetables, and the other raw materials like wood and fiber. Chopping and dropping understory plants, or letting cows/sheep/goats do the work; coppicing/pollarding trees allowing for new trees to take their place while the old roots slowly decay in the soil... all no-till methods which produce a yield with historical and cultural precedents. The economics are different?
Dyson also mentioned that current climate models (whenever this was recorded) did not reflect the carbon and embodied energy stored in soil and biomass. I would think it is now possible to better model these natural processes. (From field to forest, how much carbon does a mature forest consume in it's lifetime? How much energy does it take to maintain this system in a healthy state so carbon is continuously captured/cycled... how can society/culture incentivize healthy land-stewardship? This seems like it would require some sort of inverse-cobra incentive/maneuver.)
Tangentially, I think his point is that humans are a keystone species. We can intervene, or not, in natural systems, but to do so we need to identify and understand appropriate, human-scale leverage points.