Reproduced here from my LinkedIn post
Tribute to Sir Francis Galton and The Dance of Chance -- a new Galton Machine,
The Galton Machine was invented by Sir Francis Galton in 19th century (1894). It demonstrates the binomial and normal distribution represented by Bell Curve or Gaussian Curve. Sir Galton was most curious mind of nineteenth century. He was explorer, geographer, meteorologist, geneticist, psychologist and eugenicist, but his most outstanding quality was 'empiricism' , his passion to count and quantify everything and reduce it to statistics, e.g. computing the additional years of life enjoyed by the Royal Family and the clergy because of the prayers offered up for them (the surprising result being a negative number), or correlating the number of a painter‟s brush strokes needed for a portrait (approx. 20.000) with the hand movements that went into the knitting of a pair of socks (Pearson, 1930). Galton introduced new statistical concepts like regression and correlation to analyze the large amounts of data he accumulated (Obituary, 1911; Forrest,1974; Gillham, 2001). He also introduced the idea of the percentiles as a criterion for the measurement of the distribution of quantitative parameters (Enciclopedia Italiana, 1950).
Galton Machine:
Lets start with video, please check following link to visualise Galton Machine
https://youtu.be/epq-dpMJIxs
You will see that as ball falls, it will hit pin and thereafter bounce on left or right. If there are N rows of pins, then ball bounces N times and finally enter bin at bottom (that represents 9 sigma). The position of the bin into which ball falls has binomial distribution. You will notice how most balls fall into central, evidence that most things have tendency to 'regress to mediocrity'.
The binomial distribution of balls can be represented through equation.
Where:
If the number of rows of pins is large enough, this would approximate a normal distribution due to the central limit theorem.
IFA is working on option pricing algorithm , has developed Probability machine (named Sir Francis) comparing stock prices to randomness of balls dropping through the quincunx pattern.
https://youtu.be/AUSKTk9ENzg.
Medina et el use Galton Machine to show main concepts of Markovian-Stochastic motion of only one particle.
Source:
Tribute to Sir Francis Galton and The Dance of Chance -- a new Galton Machine,
The Galton Machine was invented by Sir Francis Galton in 19th century (1894). It demonstrates the binomial and normal distribution represented by Bell Curve or Gaussian Curve. Sir Galton was most curious mind of nineteenth century. He was explorer, geographer, meteorologist, geneticist, psychologist and eugenicist, but his most outstanding quality was 'empiricism' , his passion to count and quantify everything and reduce it to statistics, e.g. computing the additional years of life enjoyed by the Royal Family and the clergy because of the prayers offered up for them (the surprising result being a negative number), or correlating the number of a painter‟s brush strokes needed for a portrait (approx. 20.000) with the hand movements that went into the knitting of a pair of socks (Pearson, 1930). Galton introduced new statistical concepts like regression and correlation to analyze the large amounts of data he accumulated (Obituary, 1911; Forrest,1974; Gillham, 2001). He also introduced the idea of the percentiles as a criterion for the measurement of the distribution of quantitative parameters (Enciclopedia Italiana, 1950).
Galton was one of the pioneers to “mapping” methods. He developed "beauty map"
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| of British Isles, based on how many pretty women he countered, (giving London the highest score and Aberdeen the lowest.) Today Galton‟s “beauty-map” is still a relevant topic , evidenced in study done by Swami & Hernandez (2008) who compiled a more empirical beauty-map of London. They investigated association between wealth and attractiveness, and compared their findings to
Galton‟s original beauty-map.
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Lets start with video, please check following link to visualise Galton Machine
https://youtu.be/epq-dpMJIxs
You will see that as ball falls, it will hit pin and thereafter bounce on left or right. If there are N rows of pins, then ball bounces N times and finally enter bin at bottom (that represents 9 sigma). The position of the bin into which ball falls has binomial distribution. You will notice how most balls fall into central, evidence that most things have tendency to 'regress to mediocrity'.
The binomial distribution of balls can be represented through equation.
Where:
- x is the bin position e.g. x=0 could be treated as the left-most bin, and x=N could be treated as the right-most bin.
- P is the probability of x
- p is the probability of bouncing right (if x=0 represents the left-most bin). In an unbiased machine: p = 0.5.
- N is the number of rows of pins i.e. the number of times a ball bounces.
If the number of rows of pins is large enough, this would approximate a normal distribution due to the central limit theorem.
IFA is working on option pricing algorithm , has developed Probability machine (named Sir Francis) comparing stock prices to randomness of balls dropping through the quincunx pattern.
https://youtu.be/AUSKTk9ENzg.
Medina et el use Galton Machine to show main concepts of Markovian-Stochastic motion of only one particle.
Source:
- M. Nuñez, A. L. Villa, C. A. Vargas, A. Medina, "Stochastic Trajectories of Beads in the Galton-Board", Applied Mechanics and Materials, Vols. 110-116, pp. 299-309, 2012
- Swami, V. & G. Hernandeza, E. (2010). A beauty-map of London: Ratings of the physical attractiveness of women and men in London‟s boroughs. Personality and Individual Differences, 45, 361–366
- Wikipedia (2010), http://www.wikipedia.org/
- http://www.statisticalconsultants.co.nz/blog/the-galton-box.html
- https://youtu.be/gOgv6_S9S7o (excellent 15 minute video on Binomial distribution)
- Obituary (1911). Sir Francis Galton D.C.L. D.Sc F.R.S. Journal of the Royal Statistical Society, Vol. 74, 3, 314-320
- Obituary: Sir Francis Galton, F. R. S. (1911a). The Geographical Journal, 37, 3, 323-325
- Gillham, NW. (2001). A Life of Sir Francis Galton: From African Exploration to the Birth of Eugenics. New York: Oxford University Press. 416pp.
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Galton 2011 revisited: A bibliometric journey in the footprints of a universal genius
Juan Gorraiz*, Christian Gumpenberger and Martin Wieland
