Abstract—This work aims to finally fix a glaring issue in Andrei Tarkovsky’s final opus Offret (The Sacrifice) [1] namely, the inefficiencies of its final six minute shot.

THERE are perhaps a handful of directors whose oeuvres are as universally venerated as that of Andrei Tarkovsky. Who among us could find fault in the work of a man Ingmar Bergman called "The greatest, the one who invented a new language, true to the nature of film, as it captures life as a reflection, life as a dream [2]." And yet as one watches Offret, one error looms. This 1986 masterpiece of Swedish cinema is marred by its famous final sequence. In it, the paterfamilias, Alexander, burns the family's home to the ground in an attempt to honor an agreement with God to undo a nuclear apocalypse. In a single six minute long take, the family chases him as their house burns to the ground, splashing through and falling into the mud, occasionally collapsing in despair, and finally pushing him onto an ambulance that rolls away into the swamp. The family then watches as their house collapses onto itself in a glorious blaze, all the grandiose posturing of an aging academic conflagrated by a single act of faith.

As one watches this moving scene, one cannot help but think: Couldn't the family have captured and committed its crazed patriarch much more efficiently? The shot itself had to be re-done when a camera jammed during the first attempt, causing the crew to rebuild a perfect replica of the house from scratch to set fire to it a second time. Although nothing can be done at this point about the inefficiencies of the film's production, this paper seeks to optimize the paths the family takes as they rush to confront Alexander such that they may watch their home burn without the additional discomfort of getting their feet wet, as well as complete their task much faster.

I. Calculating Optimal Paths

Paths calculated using A* planning algorithm [3] overlayed onto the original footage. The heuristic used was Euclidean distance with cost calculated using [4] with wet areas being high cost and dry areas being low cost. In addition, paths were relaxed as proposed by Thorpe and Matthies[5].

Table 1

Percentage of path spent in water

Character	A*	Relaxed A*	Path in film	Straight line to goal
Marta	0%	1.2%	12.8%	8.2%
Victor	0%	1.3%	7.7%	21.8%
Julia	0%	1.1%	16.1%	9.7%
Adelaide	0%	1.0%	19.5%	10.0%

Table 2

Lengths of Paths

Character	A*	Relaxed A*	Path in film	Straight line to goal
Marta	76.7 m	72.8 m	72.0 m	70.7 m
Victor	63.3 m	60.2 m	61.8 m	58.0 m
Julia	84.3 m	80.5 m	79.6 m	77.6 m
Adelaide	82.7 m	78.6 m	79.3 m	76.1 m

II. Guaranteed Capture

Here results are shown of a pursuit algorithm that guarantees capture which is an extension of [6] and [7]. All actors are assumed to run at a human's optimal hunting speed of 3.3m/s [8]. Over 100 trials, Alexander was caught in an average of 16.3 seconds with a standard deviation of 4.5 seconds. The maximum time to capture was 28.0 seconds. In the film, Alexander runs free for a grand total of 5 minutes and 37 seconds before he is forced into the ambulance

III. Conclusion

The results of this paper confirm our suspicion that the final sequence of Offret contains a grave oversight when it comes to common-sense path planning. Clearly, Tarkovsky and his cast did not do even a cursory literary review. Otherwise, they would certainly have come across A* ([3] was published more than a decade prior to the release of the movie) and path relaxation ([5] was published more than a year before principal shooting began). As our pursuit and evasion results have shown, had the family employed even a simple surrounding technique, they would have caught Alexander an order of magnitude faster. Had the actors and director had the forsight to move in a more coordinated fashion, Tarkovsky may not have had to shoot this sequence twice [9], and even if he had, he would certainly have saved some money on film. These unfortunate oversights show yet again that the value of meticulous academic research trumps the brash, emotional decisions of even the greatest artists. As roboticists, scientists, and people of Reason, we continue to wonder: “Will they ever learn?”

The full paper with detailed results can be accessed here

IV. Works Cited

1. Andrei Tarkovsky. Offret. Svenska Filminstitutet (SFI), 1986
2. Paul Coates. Film at the Intersection of High and Mass Culture. Cambridge University Press. pp. 157–158, 1994.
3. Peter E. Hart, Nils J. Nilsson, Bertram Raphael. A Formal Basis for the Heuristic Determination of Minimum Cost Paths. Intelligence/sigart Bulletin - SIGART vol. 37. pp. 28–29, 1972.
4. Jack Bresenham. Incremental Line Compaction. The Computer Journal. vol. 25, no. 1, pp.116–120, February 1982
5. Charles E. Thorpe, L.H. Matthies. Path relaxation: Path planning for a mobile robot. Proc. AAAI. pp. 318–321, 1984.
6. Haomiao Huang, Wei Zhang, Jerry Ding, Dušan M. Stipanović, Claire J. Tomlin. Guaranteed Decentralized Pursuit-Evasion in the Plane with Multiple Pursuers. Proceedings of the IEEE Conference on Decision and Control. 2011.
7. Zhengyuan Zhou, Wei Zhang, Jerry Ding, Haomiao Huang, Dušan M. Stipanović, Claire J. Tomlin. Cooperative pursuit with Voronoi partitions. Automatica vol. 72, pp. 64–72, 2016.
8. Karen L.Steudel-Numbers, Cara M.Wall-Scheffler. Optimal running speed and the evolution of hominin hunting strategies. Journal of Human Evolution vol. 56, no. 4, pp. 355–360, April 2009.
9. Michal Leszczylowski. Regi Andrej Tarkovskij. Svenska Filminstitutet(SFI), 1988