The mathematics of equality

[T]he data suggest that all humans are equal, as long as one is measuring the wrong thing with the wrong instrument. The same methodology also points to the unity of all beingness.

In Finnish / suomeksi: click here. More postings in a similar vein: WeirdMath.  

Derawi et al 2010 showed that it is possible to identify a person with nearly 80% accuracy by using just a simple accelerometer on a mobile phone. Peoples’ walking styles are different and consistent, and analysis of the gait can identify the person.

In this follow-up study we determined whether a test person can be identified from accelerometer data when the person only stares at the mobile phone. There were 34 test subjects. Part of the test (14 subjects) was a classical double-blind study, in which the participants had no idea what they were supposed to be doing. Part of the test (20 subjects) was a postmodern triple-blind study, in which the subjects did not know that they were participating (the phone was simply placed close to them without the subjects noticing anything).

The experiment was done by placing a pink Samsung Galaxy S2 on the table, and recording its accelerometer data with the AndroSense software. Data were stored at 50-millisecond intervals. The participants were asked to stare at the phone for 20 seconds. In the triple-blind test, logging was done for 20 seconds without telling the test subject. Eight-second samples of all measurements were taken for further analysis.

As a pilot, the test was extended to some animals, as well as other forms of sentient existence. It is unclear whether the pilot was double-blind or triple-blind, as the test subjects did not seem to understand the instructions they were given.

Figure 1: All data. The x-component of the accelerometer was used. To account for tilts, the data were normalized to zero by subtracting the average. An ANOVA test was run.

 

Figure 2: Four typical human profiles. It is not possible to statistically identify the test subjects. Age and gender do not affect the results.

 

Figure 3: Four animal profiles (dog, cat, cow, bug). The animals cannot be distinguished from one another, nor indeed from humans.

 

Figure 4: Other organic subjects: an apple, a tree, a woolen sock, and some navel fluff. Since the sock was dirty and the fluff was fresh, it can be reasonably assumed that all subjects were sentient. The profiles cannot be distinguished from the other test subjects.

 

Figure 5: The ANOVA test shows that the null hypothesis cannot be rejected for any subjects. There are no statistically significant differences between any of the subjects.

This means that a mobile phone’s accelerometer cannot determine who is staring at the phone. More fundamentally, the triple-blind test shows that the accelerometer cannot even determine whether the subject knows he is supposed to be staring at the phone. The experiment thus shows no differences whatsoever between people.

Extending the study to non-human subjects suggests that there is no statistically observable difference between for example an engineer, a cow, and navel fluff.

In summary, the data suggest that all humans are equal, as long as one is measuring the wrong thing with the wrong instrument. The same methodology also points to the unity of all beingness.