Well, Zenpundit had a thought provoking post, about what field of expertise might be best as a vertical thinking domain that would lead to productive horizontal thinking. Among his possible choices was physics, which is, of course, near and dear to my heart. Simply because of personal bias, I would have to say physics is the best domain to start from in terms of horizontal productivity (besides, physicists are known as being quite arrogant about the range of problems, like everything, they feel trained to tackle). But when I think about this seriously, it seems to make the most sense, at least to me.
Physics deals with fundamentals. It is the branch of science that looks to understand the quantities and phenomena that literally make up everything in the universe. In order to do high-level physics, mathematics, another field of study on Zen's list, is essential. So is mathematics a more important domain as far as making progress horizontally? I guess I swing back to physics only because, in the end, to solve real problems, one must have at least one eye that can see reality. One can also look at history when Isaac Newton, not a bad horizontal thinker/visionary, had to create calculus in order to solve a physics problem: gravity. I think one of the great examples of horizontal thinking in all of history was Newton's great leap that the force making an apple fall is the same as the force keeping the moon in orbit. That is not at all obvious to mere mortals!
Because physics is a science, it tackles problems through logic, common sense, observation, and experimentation. It studies the basic ingredients of the universe, energy, matter, and forces. And, it is built around the idea of finding the relationships, or interconnectedness, between all physical quantities for any physical system, no matter how simple or complex. It is the combination of these three features, mathematical preciseness and logic, fundamentals, and interconnectedness, that would allow a trained mind to expand on and attempt to tackle the most complex problems. It is the nature of a physicists mind to think we may be capable of a true 'theory of everything.' Now that is arrogance, but may turn out to not be that far-fetched an idea!
It appears that using physics as a 'training grounds' to horizontal breakthroughs is already playing out. The most intriguing areas in human thought right now tend to deal with complex systems. How is globalization going to affect both local and global societies and economies? What are the political, environmental, military, and socioeconomic consequences of global climate change? How do geopolitical hotspots, such as the Mideast, affect the global economy? What is the nature of terror organizations? Where does religion fit into the mix as far as East-West relationships? Now, in each of these examples, complexity reigns supreme because each big question being considered consists of multiple interacting agents that make up a given system. In complexity, the interrelationships between the quantities or principles are key to understanding how the system is going to evolve. This is the essence of what physicists do, and how they are trained to think and analyze problems. And, physicists have an advantage over mathematicians...not only are physicists trained in advanced mathematics and abstract thinking, but they are also trained as scientists, and are driven to always think in terms of basing conclusions on some type of real evidence - some kind of connection to the real world.
Already, domains of study such as economics have begun using mathematical analysis techniques developed by physicists to revolutionize economic theory. Econophysics is being born. Chemistry and biology are working at the molecular and atomic level, which is the realm of the physicist. Technology is driven by nanotechnology and electronics, the realms of physicists (both classical electromagnetic theory and quantum mechanics). Engineering in general is essentially applied physics. The exploding realm of computational science was given birth by theoretical physicists. And, going back to Newton, even the notion of using mathematical analysis of real systems began by addressing physics questions. Such mathematical analysis is now dominating areas such as network theory and complex systems, which includes social systems. Even modern areas of psychology, from a research perspective, are at the level of looking at information dispersal and signal processing in neural networks in terms of electrical pulses at the molecular level, which is a biophysical process.
In the end, physics, or at least a physicist's mentality and approach to problem solving, will likely lead to many horizontal breakthroughs in the future. However, I happen to believe certain issues cannot be thoroughly analyzed without some amount of historical analysis. Zen and I have had some amazing discussions over many years by taking historical features and precedents combined with technological and scientific advancements (which tend to throw off historical analogies, since the hyperspeed with which technology expands on a global scale is in fact creating situations with no historical analogs), so trying to attack some modern problems will require a mix of domains (i.e. consilient analyses), to be sure. New visions can also occur in unexpected ways, where accidental discoveries might trigger some new thought, or a creative mind that was trained in some field that is not directly related to a given problem. In the information age, some groups get it that it is imperative to build working teams of people triained in multiple disciplines, but much more of this will be needed in order to tackle the truly complex problems that affect the world presently.