Software

The program is an attempt to bring the problem of randomness closer together. It's called "RANDOM 50", it's free to download.

It offers the following options:

1) Theoretical calculations of the probability of randomly extracting many white balls in succession from a set of 100 half white balls and black mats.

(2) Real random extraction tests.

3) Analysis arbitrary construction of letters of the alphabet and random and intelligent reconstruction of a biblical text.

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The program presented here is an attempt to bring the problem of randomness really close together. It is called "A CASO 50", it can be downloaded free of charge, and it performs four functions.

 

FIRST FUNCTION

An algorithm calculates the theoretical number of attempts required to randomly extract some white balls in succession (without black balls) from a set of 100, half white and half black balls. The calculation is simple: at each extraction, the probability of extracting a white ball is:

white balls/(white balls + black balls)

At the first extraction you have: 50/100 = 0.5. The average number of draws is calculated as a reciprocal probability: the first draw takes on average 2 attempts to get a white ball.

When there is only one white ball left between 50 black balls, the probability of extracting it is:

1/51 = 0.0196078431372549

 and the average number of extractions necessary to obtain it by chance is 51. You can have fun seeing how many names pop out when you climb up with the number of white balls extracted in succession (without black balls). For large numbers, the result is in exponential form.

 

SECOND FUNCTION

The algorithm draws 50 white balls and 50 black balls randomly scattered in a 10 x 10 matrix. On the right of this matrix, there is a list box with numbers from 1 to 50. Above the list box, there is a button with the inscription "BALLS." Clicking this button randomly redistributes the black and white balls. Clicking on a number tells the algorithm to start random extraction of white balls for the chosen name. Be careful to click names over 15 white balls: you risk staying in front of the screen from a few tens of minutes to a few billion years! To avoid this unpleasant situation, the algorithm stops every 15,000 draws and asks whether to continue or block the attempt (recommended). If you repeatedly click on the same number of balls, the algorithm calculates and presents the number of attempts, the number of draws of the last effort, the average number of draws made and the theoretical number of draws. In this way it will be possible to verify that by making many attempts for the same amount of balls, the average number of attempts approaches the theoretical number until it becomes equal, demonstrating the correctness of the calculations.

 

THIRD FUNCTION

Under the right list box, there is a key with the word "LETTER." Clicking this key, you get the random distribution of 25 black balls and 75 white balls in the usual matrix 10 x 10. The letters of the alphabet appear in the list box on the right. Repeatedly click on the "LETTER" button to see if you can get a random arrangement of black balls that looks like a letter of the alphabet. Clicking on a note in the list box will see how a modest intelligence like mine can get the desired letter in a fraction of a second.

 

FOURTH FUNCTION

Poetry. Writing poems requires some skills that are rarely found all together in a single individual: inspiration, intuition, sensitivity, literary culture, mastery of language. Not having these qualities, to complete my computer tests on randomness I borrowed "A Silvia" by Giacomo Leopardi, a poem that, despite my cold rationality, struck me since high school for the deep feelings it expresses. So, I took this poem and broke it up into single words or into small groups of words (note 1) that I included in a matrix. Then I wrote two algorithms: the first mixes the elements of the model and recomposes them at random, the second neatly recomposes the components of the matrix according to their order.

 

The conclusion is simple: an ordered reconstruction of the randomly obtained poetry is extremely unlikely (I would say impossible), and in reality, in nature, there is no poem written by chance, but they all have their own author.