Gunslingers, Bohr and epicycles

So one of my favorite anecdotes about Niels Bohr is that he used to duel with his students in classical western gunslinging style, and always win. He had a theory as to why this was – that anyone who has to act will be slower than someone who merely reacts. But one of the readers of the newsletter recently sent me an article from New Scientist that seemed to show that this was not true – and that science had disproven Bohr’s hypothesis.

Bohr, physicist and gunslinger

It is really interesting to observe how one reacts when something like this happens – a core data point or insight you like is disproven by research. So, what should you do?

My first instinct was to simply explain the result away, by looking at the design of the study. In the study the subjects did not use guns in gunfights, but instead used buttons:

Welchman pitted pairs of people against each other. The task? Lift your hand off a button, push two other buttons, then return to the first. There was no start bell. “Eventually one decides it’s time to move,” Welchman says. “The other player will then try to move as fast as possible.”

Read more:

So, the possible flaw here is obvious – pushing buttons is different from drawing a gun and firing it, since that is a much more complex action than that of the study. So there could be something about that complexity that made Bohr right, right?

This is how you end up with epicycles.

You amend and change your theory, find gaps between the study and the phenomenon and then suggest solutions that support your wanting the original insight to be true.

My second instinct – learned, to be sure – was to enjoy being wrong. If it is indeed not right that reaction is faster than action, then I was wrong and that meant that I had to think about how that affects other parts of my belief that there is value in waiting. Maybe the experiences I have had in practicing budo where Bohr’s insight has been so present were misinterpreted? And I remembered that in many samurai movies it is actually not action or reaction – but the swordsmen act on an external cue – a leaf falling to the ground, a cat moving and they act without acting as zen masters will teach you. Who cuts with the sword? Noone – the sword cuts and that is all there is.

That seemed to open an interesting revision of my thinking on waiting and made me interested in reading more, and this is the point at which it gets even more intriguing. As I did this – disappearing down the rabbit hole of Google Scholar – a different picture emerged.

A literature review of Bohr’s law

This is a list of the articles I found and the insights they contained.

Pinto, Y., Otten, M., Cohen, M.A. et al. The boundary conditions for Bohr’s law: when is reacting faster than acting?. Atten Percept Psychophys 73, 613–620 (2011).

This article outlines the boundaries of Bohr’s law and argues that it only holds for simple ballistic actions. So it holds, but for simpler actions, not more complex! See here.

Welchman, A. E., Stanley, J., Schomers, M. R., Miall, R. C., & Bülthoff, H. H. (2010). The quick and the dead: When reaction beats intention. Proceedings of the Royal Society of London. Series B: Biological Sciences, 277, 1667–1674. –

This is the study referred to in the New Scientist article, and imagine my confusion when it actually seemed to reinforce Bohr’s theory – this is the conclusion: “We placed pairs of participants in competition with each other to make a series of button presses. Within-subject analysis of movement times revealed a 10 per cent benefit for reactive actions. This was maintained when opponents performed dissimilar actions, and when participants competed against a computer, suggesting that the effect is not related to facilitation produced by action observation. Rather, faster ballistic movements may be a general property of reactive motor control, potentially providing a useful means of promoting survival.” and they also found that this is mirrored in how Parkinson affects its victims: “Faster movement speed for reactive movements has a parallel to known deficits in Parkinson’s disease. In particular, Parkinson’s patients are especially compromised in speed when making intentional, rather than reactive, reaching arm movements (Majsak et al. 1998).” and — again, this was true for simpler actions and not second actions (because intentionality infects the action?) – but then, at the end of the article, they write this: “As a general survival strategy, the evolution of a movement system capable of producing quick (and possibly dirtier) movements that support faster responses to the environment seems reasonable. However, within the context of a gunfight, a strategy based purely on reaction seems unlikely to increase evolutionary fitness as the advantage produced by reacting is far outweighed by the time taken to react to the opponent. Anecdotal reports suggest that Bohr tested his original idea with colleague George Gamow using toy pistols, with the ‘reactive’ Bohr apparently winning every duel (Cline 1987). Our data make it unlikely that these victories can be ascribed to the benefits associated with reaction. Rather, they suggest that Bohr was a crack shot, in addition to being a brilliant physicist.

So – in essence – reaction is faster than action, but for some reason the authors now introduce the idea that reaction may be advantageous but the time taken to react may counter-act that? So, they write “We demonstrate that reactive movements are associated with faster execution times, and that this quickening of movement does not appear to relate to having another human as a model for one’s own action. We suggest different cortical processing routes for the control reactive versus intentional movements, and argue that faster movement dynamics may constitute a basic property of reactive movement production.” so reaction is faster than action, but then they suggest there is a time taken to react? The key to this is in this paragraph: “We found that execution times were quicker by an average of 21 ms when participants reacted to their opponent’s movement (figure 2a; t9 = 4.406, p = 0.002), an improvement of around 9 per cent. This ‘reactive advantage’ was most pronounced for the first movement of the three-button press sequence (figure 2b,c), quickening responses by around 14 per cent of the mean movement execution time. Moreover, the advantage was maximal when participants moved approximately 200 ms after the opponent (electronic supplementary material). However, as the reactive advantage in movement execution (mean = 21 ms) was less than the participant’s reaction time to the movement of their opponent (mean = 207 ms), reactors rarely beat initiators“.

And this is interesting: there are two time measurements here: one that looks at how fast we react to the other persons action and the one for how fast we then move once that reaction has been observed. We should speak of reaction time (time to react) and reaction movement time, then. Not clear cut to put it mildly. Bohr could just have replied that the time to react is cut by gunslingers because they practice and make it “second nature” – something a made up exercise engaged in for 1 hour only will never become.

Obhi, S. S., & Haggard, P. (2004). Internally generated and externally triggered actions are phyiscally distinct and independently controlled. Experimental Brain Research, 156, 518–523.

Neuro-imaging research that shows that there is “peripheral physiological support for previous neuroimaging work suggesting that internally generated actions are preceded by greater levels of preparation than externally triggered actions. The present findings also raise the interesting possibility that the motor system processes these two classes of action separately even though the motor output required is the same.” – So reaction is different than action.

Oscar Martinez de Quel & Simon J. Bennett (2014) Kinematics of Self-Initiated and Reactive Karate Punches, Research Quarterly for Exercise and Sport, 85:1, 117-123, DOI: 10.1080/02701367.2013.872222

So it turned out that there is even research into the budo-aspect of this, and this study found the following: “Kinematic analyses indicated reactive movement had shorter time to peak velocity and movement time, as well as greater accuracy than self-initiated movement. These differences were independent of participant skill level although peak velocity was higher in the karate practice group than in the no-karate practice group. Reaction time (RT) of skilled participants was facilitated by a specific stimulus. There was no effect on RT or kinematic variables of the different type of auditory cues.” Reactive karate punches are faster AND more accurate than self-initiated movement. Note that the authors think reaction time had to do with the stimulus – something that actually points to a weakness in the study in New Scientist, even if that reference seems very suspect having read the study.

Wakatsuki Tsubasa, Yamada Norimasa, “Difference Between Intentional and Reactive Movement in Side-Steps: Patterns of Temporal Structure and Force Exertion” Frontiers in Psychology Vol 11:2020 DOI=10.3389/fpsyg.2020.02186 ISSN=1664-1078

Yet another study confirming Bohr’s law. This time for complex movement. “The execution time was significantly shorter in the reactive movement condition than in the intentional movement condition (772 vs. 715 ms, p = 2.9 × 10–4). We confirmed that Bohr’s law was applicable not only in hand-reaching tasks but also in whole-body movement.”

Shuji Mori, Yoshio Ohtani, Kuniyasu Imanaka, “Reaction times and anticipatory skills of karate athletes” Human Movement Science, Volume 21, Issue 2, 2002, Pages 213-230.

A really interesting study that shows that Karate masters have honed greater anticipatory skills than novices – not directly relevant to Bohr, but a clue to some of what I felt was happening in practice. At this point I think I was starting to nerd out, so closed out the brief literature review.


So what is the conclusion of this – except to beware of epicycles?

  • First, reaction is faster than action across different studies.
  • Second, the time it takes to react is key to the reactors advantage.

What the Karate-study suggests is that we can make huge cuts in the reaction time, freeing the speed advantage in reaction and that the conclusion about gunslingers being at a disadvantage is not as clear cut as the New Scientist-article indicates – which highlights another risk in thinking: the allure of mythbusting. If fashioning epicycles is bad, our tendency to accept mythbusting also needs to be kept in check – especially since we dislike being wrong!

Bohr’s come back would be that comparing the time to react for a made up action engaged in for only 1 hour with the time to react for something you can have practiced for hours, and made into second nature, is simply wrong – and he could have pointed to the studies above of karate masters.

The conclusion of the article referred to in New Scientist, then, begs the question of if practice matters, or simply never tested that. And this gives us a valuable new insight – waiting favors the prepared – the one who has practiced. That is a nice conclusion!

This brings me back to strategies for being wrong – I started with explaining away the result (bad) and then went on to accept it and try to adjust (slightly better), but the real value for me was to go look deeper. Now, think about how rarely we have the time to do this – and what that says about our opinions and views. It is a great argument for holding our views lightly!