## Plinko Sounds a Bit like the Galton Board

This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth. (Einstein to Thornton, 7 December 1944, EA 61-574)

So nature has it’s way in which it may express itself, yet, to settle on how such selections are parametrized in expression is to “know in advance” what you are looking for. How to approach it for the simplest summation of that event that may help one to arrive at a conclusion. So this procedure has done that.

The search looks at a class of events called jets plus missing energy – proton collisions that result in a shower of hadronic particles plus a stable, neutral particle that escapes detection – and ignores events that show signs of electrons or muons.See:Keep it simple, SUSY

 This CMS event display from October 2010 captured a collision that produced very energetic jets – showers of particles that leave energy deposits in the detectors – and an exceptional amount of missing energy, represented by the blue line at the bottom left. Experimentalists and theorists are continuing to analyze collision events such as this one in search of new physics.(Image courtesy CMS/CERN.)

Both the theorists and the experimentalists looked only at the pile of tokens that landed in a particular slot at the bottom of the Plinko board. While the experimentalists had a set of guidelines about how the tokens should have gotten there and excluded any tokens that didn’t follow the rules, the theorists didn’t care as much about that. They were primarily concerned with the mass of the initial particles, the mass of the final particles and the ratio between them.

When the initial massive particles decay into lighter ones, the total energy must be conserved. Sometimes this energy goes missing; if the missing energy adds up to a certain amount, it could mean that a supersymmetric particle carried it away without being detected.See:Keep it simple, SUSY

So the coordination in thought process is to know what events help us to distinguish where such events allow for missing energy to be in evidence,  so as to direct our attention to that amount of energy that is missing.

This has been known for quite sometime, as to the dimensional significance of new areas of probability concerns, as to extend our rationalizations on extra dimensions of a space, that we have been to this point limited on explanations and sought after by those looking to explain the abstract world that as yet remains unseen other then in this venue.

Naysayers comment loudly on abstraction in mathematical explanations but it helps one to be able to know what space we are talking about so don’t let them persuade you into thinking it’s not worth the time or expense  of theoretical thought to venture into such areas as being irresponsible action around scientific thought.

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# Black swan theory

(Redirected from Black Swan theory)

A black swan, a member of the species Cygnus atratus, which remained undocumented until the eighteenth century

The Black Swan Theory or Theory of Black Swan Events is a metaphor that encapsulates the concept that The event is a surprise (to the observer) and has a major impact. After the fact, the event is rationalized by hindsight.

The theory was developed by Nassim Nicholas Taleb to explain:

1. The disproportionate role of high-impact, hard to predict, and rare events that are beyond the realm of normal expectations in history, science, finance and technology
2. The non-computability of the probability of the consequential rare events using scientific methods (owing to the very nature of small probabilities)
3. The psychological biases that make people individually and collectively blind to uncertainty and unaware of the massive role of the rare event in historical affairs

Unlike the earlier philosophical “black swan problem“, the “Black Swan Theory” (capitalized) refers only to unexpected events of large magnitude and consequence and their dominant role in history. Such events, considered extreme outliers, collectively play vastly larger roles than regular occurrences.[1]

The demarcation problem (or boundary problem[1]) in the philosophy of science is about how and where to draw the lines around science. The boundaries are commonly drawn between science and non-science, between science and pseudoscience, between science and philosophy and between science and religion.[2] A form of this problem, known as the generalized problem of demarcation subsumes all four cases.

After over a century of dialogue among philosophers of science and scientists in varied fields, and despite broad agreement on the basics of scientific method,[3] the boundaries between science and non-science continue to be debated.[4]

Hind sight dictates that the solution for consideration is parametrized by the selection and location where such events might be identified to help discern that such location exist in space

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# Bean machine

The bean machine, as drawn by Sir Francis Galton

The bean machine, also known as the quincunx or Galton box, is a device invented by Sir Francis Galton to demonstrate the central limit theorem and the normal distribution.

The machine consists of a vertical board with interleaved rows of pins. Balls are dropped from the top, and bounce left and right as they hit the pins. Eventually, they are collected into one-ball-wide bins at the bottom. The height of ball columns in the bins approximates a bell curve.

Overlaying Pascal’s triangle onto the pins shows the number of different paths that can be taken to get to each pin.

A large-scale working model of this device can be seen at the Museum of Science, Boston in the Mathematica exhibit.

## Distribution of the balls

A working replica of the machine (following a slightly modified design.)

If a ball bounces to the right k times on its way down (and to the left on the remaining pins) it ends up in the kth bin counting from the left. Denoting the number of rows of pins in a bean machine by n, the number of paths to the kth bin on the bottom is given by the binomial coefficient ${n\choose k}$. If the probability of bouncing right on a pin is p (which equals 0.5 on an unbiased machine) the probability that the ball ends up in the kth bin equals ${n\choose k} p^k (1-p)^{n-k}$. This is the probability mass function of a binomial distribution.
According to the central limit theorem the binomial distribution approximates normal distribution provided that n, the number of rows of pins in the machine, is large.

## Games

Several games have been developed utilizing the idea of pins changing the route of balls or other objects:

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### 3 Responses to Plinko Sounds a Bit like the Galton Board

1. Phil Warnell says:

Hi Plato,Nice piece which coincides with my own. I particularly like your bean machine; wished I had one of those myself. The interesting thing about the standard interpretation of QM is to have a bean going through both slits to interfere with itself. This never made sense to me as what does it mean to have something interfere with itself? The closest analogy I’ve been able to associate with this was with peas rather than beans and yet all one gets in the end is split pea soup; that is no insight to be gained with that 😉"If the price of avoiding non-locality is to make an intuitive explanation impossible, one has to ask whether the cost is too great."-David Bohm et al. “ Physc. Rep. 144, 321” (1987)Best,Phil

2. Plato says:

Hi Phil,It was more the Black Swan theory, as to the thoughts I am getting from what you are writing. I wanted to point toward it to help extend the thinking you may have about theories in general and the case of the Thomas Young experiment.The entanglement issue is the one that has a long history, which leads me to what you may have thought,"This never made sense to me as what does it mean to have something interfere with itself? "Best,

3. PlatoHagel says:

Hi Phil,It was more the Black Swan theory, as to the thoughts I am getting from what you are writing. I wanted to point toward it to help extend the thinking you may have about theories in general and the case of the Thomas Young experiment.The entanglement issue is the one that has a long history, which leads me to what you may have thought,\”This never made sense to me as what does it mean to have something interfere with itself? \”Best,