safety Article A National Pragmatic Safety Limit for Nuclear Weapon Quantities Joshua M. Pearce 1,2,3, * ID and David C. Denkenberger 4,5 1 Department of Electronics and Nanoengineering, School of Electrical Engineering, Aalto University, FI-00076 Espoo, Finland 2 Department of Materials Science & Engineering, Michigan Technological University, Houghton, MI 49931-1295, USA 3 Department of Electrical & Computer Engineering, Michigan Technological University, Houghton, MI 49931-1295, USA 4 Tennessee State University, 3500 John A Merritt Boulevard Nashville, Nashville, TN 37209, USA; ddenkenb@tnstate.edu 5 Alliance to Feed the Earth in Disasters (ALLFED), 23532 Calabasas Road, Suite A, Calabasas, CA 91302, USA * Correspondence: pearce@mtu.edu; Tel.: 906-487-1466 Received: 15 February 2018; Accepted: 6 June 2018; Published: 14 June 2018   Abstract: This study determines the nuclear pragmatic limit where the direct physical negative consequences of nuclear weapons use are counter to national interests, by assuming all unknowns are conservatively optimistic. The only effect considered is nuclear winter (“nuclear autumn” in the low weapons limits) and the resultant effects on the aggressor nation. First, the ability of low nuclear weapon limits is probed for maintaining deterrence in the worst-case scenario of attacking the most-populous nation. Second, the ability of aggressor nations to feed themselves is assessed without trade and industry resultant from a nuclear attack causing “nuclear autumn” (10% global agricultural shortfall). Third, the best-case wealthy aggressor nation with abundant arable land is analyzed for starvation and economic impacts given 7000, 1000, and 100 nuclear weapons scenarios. The results found that 100 nuclear warheads is adequate for nuclear deterrence in the worst case scenario, while using more than 100 nuclear weapons by any aggressor nation (including the best positioned strategically to handle the unintended consequences) even with optimistic assumptions (including no retaliation) would cause unacceptable damage to their own society. Thus, 100 nuclear warheads is the pragmatic limit and use of government funds to maintain more than 100 nuclear weapons does not appear to be rational. Keywords: nuclear weapons; nuclear proliferation; nuclear winter; national survival; futures; nuclear safety; atomic bombs; global catastrophic risk; existential risk; nuclear war 1. Introduction In the past, the size of the nuclear weapons arsenal for a given nation was determined through a military and policy analysis of deterrence and the ability to fund the stockpile [1–4]. There is a broad literature on this subject with many viewpoints both for and against building up nuclear weapons capabilities [5–10]. Although nuclear weapons inventories are in slow decline in Russia and the U.S., eight of the nine nuclear states continue to produce new or modernized nuclear weapons [11]. Realizing there are fundamental limits to safety, previous work has looked at the implications of “close calls” including technical glitches, misinterpretation of military exercises, inadvertent nuclear war (where one side believes it is being attacked), accidental nuclear detonation, escalation of convention war and other accidental potential paths to nuclear Armageddon [12–14]. In addition, Safety 2018, 4, 25; doi:10.3390/safety4020025 www.mdpi.com/journal/safety