Many years ago, 1986, in the first year of electronic engineering at the University of Padua, in the laboratory hours of one of the most fundamental, difficult and blocking exams, Physics I, there was a wonderful laboratory experiment that awaited the representatives of the "best youth" of Italy, the flower of the students, the aspiring members of the technological intellighèntsia of the country, and it was none other than the experimental proof of Gauss's law of large numbers, the curve which took its name from the illustrious German mathematician and that has influenced statistics and thought so much, perhaps the mathematical concept with the greatest impact today, there is in fact no statistical analysis, subatomic physics or marketing study that does not make use of it, if only implicitly, and not there are countless fields of application in the technological field, in insurance... no concept is as pervasive in everyday life.
The "Gaussian" had to be highlighted directly, in empirical, concrete tests, conducted by students divided into pairs, in a wonderful and vast laboratory specifically structured for this purpose.
Each pair of students had a test bench at their disposal which, when a button was pressed, generated an electrical impulse which gave a pre-set amount of energy, calibrated in a very precise way, starting a trolley which moved on an air bearing, within At the other end of the bench was a speed gauge, also extremely accurate, of the trolley.
The idea was that while in an "ideal" world there should have been one and only one final speed of the trolley, in this world, due to random variations in friction, air density, temperature, fields surrounding magnetic forces, the movement of the air due to the students themselves, and who knows what else, the speed samples of the trolley should have differentiated from each other with perfectly random rules, and therefore subject to Gauss's law.
The samples were then analyzed by extracting the mean and the standard deviation, these values were used to generate the descriptive gauss curve of the experiment and, both the (relative number or percentage of) samples and the curve itself, on a sheet of graph paper , according to the professor, it would have been impossible to contain the astonishment and emotion in seeing that the Gaussian curve fit perfectly, or rather: "like-a-condom-on-a-standard-size-bird-LOL" ( cit. laboratory technician), the trend of the relative number/percentage of random samples: once again Gauss's law would materialize and the chaos would prove to be manageable.
A curve like the one shown in the figure had to come out... and the relative number of random samples detected should have been found in the immediate vicinity of the Gauss curve.
The task assigned to the students was laborious but considered extremely simple, simple to the point that it was practically not possible to plan more than two tests in the entire semester preceding the exam, just enough time to become familiar with the measuring benches and take an adequate number of samples.
To prevent abstention from this instructive and pleasant activity, with the usual decidedly non-Montessorian frown, it had been clarified since the first days of the course that it was considered a fundamental prerequisite for access to the exams, translated into simple and understandable of the charming lab technicians and/or senior students: “do these fucking speed tests on the super cool benches that-with-the-face-that-it-happens-you-have-in-all-probability-you-unworthy-of, draw WELL the Gaussian that will emerge from the samples (of trolley speed ed.), I-recommend-on-pink-graphed-paper-A3-sheet-done-well-don't-draw-rubbish-hindsight-we-don't-admit/they-will-not-admit-at-all-at-exam, deliver the work to john-doo-never-heard-before-and-never-you-will-see-him-again, get this stranger to sign the precious exam access doc and get the hell out of here forever!" .
It is worth remembering that in those years PCs and smartphones did not exist, and that in order to calculate a Gaussian starting from a set of raw samples, students had the only possibility of acquiring, at their own expense, one of the few habd-calculators on the market that put This function is available, as far as I know only expensive HP hand-calculators, and then carry out a laborious manual entry of all the samples taken, extremely rigid procedures, where if you were wrong even one value among several dozen samples taken you had to start all over from scratch.
I felt lucky: I was paired with one of the best and most serious students of our group of friends: Pietro P and I brought a precious HP calculator as a dowry, which had been given to me by my father years before, and which obviously I had never used until that moment.
(To be continued:
https://www.marco-fornaro.com/en/blog-detail/post/207047/la-gaussiana---episode-2
)
