Why can’t blindfolded people walk in a straight line? My guess is: just math.

A study from about 2 years ago addressed a question that had (apparently) perplexed scientists since the 1920s. It got public attention when it was featured on a recent episode of Q.I. The study confirmed that when blindfolded, the average person can’t walk in a straight line for any considerable distance.  I cam up with my own answer (illustrated below).  It’s simple, and I have provided a computer simulation to illustrate its empirical soundness.

When your subject is blindfolded and asked to proceed forward in a straight line, they will make every effort to stay on course. Unfortunately, each time your subject takes a new step, there will be minor errors/deviations. Some will be caused by the unevenness of terrain, others by random muscle fluctuations, or nervousness caused by walking blindfolded, etc.  Therefore, at any given step, the range of possible locations your foot will land can be represented by a thin wedge:

‘Wedge of possibility’

It is important to realize here that any minor rotations from the ‘true’ (straightforward) path will be cumulative. In other words, if your subject rotates even 1 degree to the right, 1 degree to the right becomes the new ‘straight ahead’, at least for him.  The intuitive assumption we are tempted to make in such cases is that rotations to the left or right will, on average, cancel each other out.  However, that scenario would be extremely unlikely.

There are a range of possible total paths, from walking in a circle to the extreme left, to walking in a similar circle on the extreme right.  These cases would result if you always keep to the left or the right, respectively, of the above ‘wedge of possibility’. These two cases are extremely unlikely.

 

The (red) line in the middle indicates the intended straight line.  However, when you consider this straight line as a percentage of all possible paths (as represented by the yellow arc) it’s a very small proportion, and so its likelihood is also very small.  Even with very small errors/deviations at every step, their cumulative effect would, over a distance, be huge.

I created a simulation in Java which varies the “maximum angle of error” i.e. increases the ‘wedge of possibility’, and the “number of steps taken”, which, when run many times, replicates the same behavior exhibited by the subjects in the study.  This simulation doesn’t need to factor in handedness, evolutionary predispositions, or any other psychological or physiological factors.  Here are a few samples of its output (on the right).  Compare them to the blue and black paths in the original study (left).  The yellow and red lines indicate subjects who were not blindfolded.

Note the similarity of the two traversed paths. At any given point in the walk, the probability that your total journey will average out to a straight line is small, and gets smaller the longer you walk.  Without adjusting yourself from time to time (i.e. by orienting yourself to landmarks, etc), the vestibular (internal balance) sense is not accurate enough to tell you that you are actually rotating.  So you walk in ‘circles’, not by physiology, but by chance.