# Time and Its Measure: Historical and Social Implications
## 2 The Social Implications of the Measurement of Time
### Engineering Applications
#### 2.1.5 Application to the World of Sport: Tokyo Olympics 1964  
In the 100 m freestyle race, two athletes (the German [PERSON] and the American [PERSON]) simultaneously crossed the finish line in 54.0 s. The (unofficial) automatic timing system was consulted to award the bronze. The two had the same time, even to the hundredth of a second, but [PERSON] was one thousandth of a second faster ([PERSON]: 54.060 s; [PERSON]: 54.061 s). After 35 min of discussion, the judges decided that it was enough, even if the electronic timing was not official, and they gave the bronze to [PERSON]. Does it make sense to measure time to the thousandth of a second in swimming competitions and use it to determine the rankings and national, continental and world records? During a 100 m freestyle competition, how much space does an athlete travel in 1/1000 th of a second? The space covered by two athletes in 0.001 s is equal to  
\[s=v_{m}\times t=1.8\times 0.001=0.0018\;\mathrm{m}\cong 2\;\mathrm{mm} \tag{2}\]  
where \(v_{m}\) is the average speed of the athlete during the race (that is, 1.8 m s\({}^{-1}\), equal to 100 m/54 s), and s is the space covered by the athlete during time \(t\). The FINA (Federation International de Natation) regulation in force from 2013 to 2017 with respect to sports facilities, particularly swimming pools, states [FR 2.2.1] the following:  
_\"Compared to the nominal length of 50.0 m, one tolerance of 0.03 m above and 0.00 m below is admitted on both back walls at any point from 0.3 m above to 0.8 m below the water surface. Such measurements should be certified by an appraiser or other qualified officer appointed or approved by the FINA Member of the country where the pool is located\"._  
Ultimately, if a tolerance of 0.03 m or 3 cm is allowed in the construction of an Olympic swimming pool, it makes no sense to discriminate the order of arrival of the athletes or the assignment of records with times measured to the thousandth of a second (time taken by the athletes to cover a distance of about 2 mm). In other words, a tolerance of 3 cm between one lane and another means that one lane could be 50.00 m long while another could be 50.03 m long. If the two athletes in the two lanes went exactly at the same speed of 1.8 m/s, they would travel the two lanes in two different times equal to  
\[\mathrm{S1}=50.00\;\mathrm{m};\mathrm{\upsilon}=1.8\;\mathrm{m}/\mathrm{s}; \mathrm{\leavevmode\
obreak\ }t1=S1/\mathrm{\upsilon}=27.778\;\mathrm{s}\]  
\[\mathrm{S2}=50.03\;\mathrm{m};\mathrm{\upsilon}=1.8\;\mathrm{m}/\mathrm{s}; \mathrm{\leavevmode\
obreak\ }t2=S2/\mathrm{\upsilon}=27.794\;\mathrm{s}\]  
Therefore, the two athletes, despite having the same skills (they travel 100 m at the same average speed), take a different time due to the different lengths of the lanes:  
\[\Delta\mathrm{t}=\mathrm{t2}-\mathrm{t1}=27.794-27.778=0.016\;\mathrm{s}\]  
It can therefore be concluded that the quantity being measured is the time taken by an athlete to travel 100 m (\(50+50\)). This time (i.e., the measurand) has an intrinsic variation (uncertainty) far greater than one thousandth of a second (0.016 s), and this is caused by the imperfect knowledge of the spatial reference (the length of the lane). These effects are not reduced for \"slower\" races, i.e., with respect to how much the distance is increased (200 m, 400 m, etc. ), since these distances are obtained by covering a 50 m lane several times. We should add that, although it is not easy, for the two outermost lanes, the effect of viscosity linked to the presence of the side walls, which, with their \"boundary layers\", slow down the two athletes who travel along these lanes, should be taken into account.