Beyond Einstein: In Search of the Ultimate Explanation

See: Beyond Einstein: In Search of the Ultimate Explanation

Plinko and the Galton(quincunx) Board

See Plinko Probability 2.02 

A working replica of the machine  

(following a slightly modified design.)

There is this randomness that seems to take hold over my thoughts regarding probability. The thoughts question how we can even know with certainty when something is going end in a result.  To know this before hand.

In a way this is what drew me to outcomes  seen and expressed as scenarios given in context of Game theory in terms of negotiation.  I would like to give a little shout out to the work John Baez is doing in that regard.

Predicting economic events with some certainty(?) and here the questions of Nassim Taleb and the Black Swan raises its head again. Fractal Antennas. A lot of things have elevated the discussion for me as to wonder how we have graduated  to a degree to a level of perception that was not so obvious before.

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

It also deals with Particle physics and collision processes as the link suggests at the bottom of this entry. So it seems we are getting some kind of hold on this probability and outcome in terms of what was a random act can now become specific and predictable.

If you get the opportunity to watch the latest show of Touch I thought it interesting,  as I see this fellow searching all over for a machine that is mechanical and not electronic,  to use for a project for Amelia.

What is capture in the picture here below is what made this interesting. While a fictional story,  Amelia is capable of being able to determine the randomness of a dropped ball,  even before the result is known. This kidnapping is somehow recognized as a necessary evil when taking Amelia. They want to teach another computer to be able track the neurons as she relays the pockets with which the balls drop as some underlying algorithmic process sequencing.

 

The idea for me while it is nice it is so plain that we could map such an abstract mind to have encompassed such probabilities. It is again with such forth sight that I came to such a vision as an  encompassing one, held above such statistics.  Natures way. If you must, a overlord position using the recognition of Powers of ten,  for as such a view is to contain,  all must contain such outcomes.

So this part of this post is not finished, as ideas will spring up as people and scientists talk about different things. For me,  it is about seeing these "abstract things" as viable entries into the recognizable as functions of our everyday lives.

See Also:

• TVO S James Gates on Does Reality have a Genetic Basis

• Plinko Sounds a Bit like the Galton Board

Fractals and Antennas and The Economy

 The intuitive framework has to recognize that you have already worked the angles and that such intuition is gathered from all that has been worked. This contradicts what you are saying. I am not saying it is right just that I have seen this perspective in development with regard to scientists as they push through the wall that has separated them from moving on. This then details a whole set of new parameters in which the thinking mind can move forward with proposals.

 
 I never quite could get the economy either, until I understood the idea of Fractals as a gesture of the underlying pattern of all of the economy in expression. Of course that is my point of view.  I might of called it the algorithm before.

 The idea here is that all thing are expression of the underlying pattern and you might call the end result psychology or sociology of thinking and life as a result.

 It seems that the accumulated reference of mind as a place in it's evolution is to see that all the statistical information is already parametrized by the judgements in which you give them personally?

 Ultimately this is the setting for which your conclusions guide your perspective, yet, it is when we look back, one can choose too, "guide their brain?"

If you did not pick it up, Benoit was able to reduce the economy too, and used an inductive deductive facility in regard to what is self evident. But I would point out what you might have interpreted as illusory in terms of the graph he sees on the board was instrumental to his penetrating the pattern in the economy.

Just raising the name of Nassim Nicholas Taleb and the idea of the Black Swan in relation to the basis of the economy Benoit raises deeper questions and does garner a look for me. I don't know what to expects is opening up the door to understanding more about such erudition's but they are with regard to the economy.

 Taleb was collaborating with Benoit Mandelbrot on a general theory of risk management Collaborations

A simple assumption about heads and tails, leads to bell curves and such?

Taleb, N. N. (2008) Edge article: Real Life is Not a Casino

So you are looking at both sides of the coin.

More on the Black Swan here.

 While these writings are disparate pieces, do they indeed come together under this post book review?? As a scientist and mathematics person are you not intrigued about "the pattern?" I was shocked.....yet is made sense.

Now Nassim adds dimension to the subject. "He calls for cancellation of the Nobel Memorial Prize in Economics, saying that the damage from economic theories can be devastating".

Game theory if you know how it works it is used in all types of negotiation.

• The Black Swan

See Also:

• Process Fractal vs Geometry Fractals

Rara Avis in Terris Nigroque Simillima Cygno

Statistical and applied probabilistic knowledge is the core of knowledge; statistics is what tells you if something is true, false, or merely anecdotal; it is the "logic of science"; it is the instrument of risk-taking; it is the applied tools of epistemology; you can't be a modern intellectual and not think probabilistically—but... let's not be suckers. The problem is much more complicated than it seems to the casual, mechanistic user who picked it up in graduate school. Statistics can fool you. In fact it is fooling your government right now. It can even bankrupt the system (let's face it: use of probabilistic methods for the estimation of risks did just blow up the banking system).THE FOURTH QUADRANT: A MAP OF THE LIMITS OF STATISTICS [9.15.08]  By Nassim Nicholas Taleb

Nassim Nicholas Taleb - What is a "Black Swan?"

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SEE Also:

• The Black Swan 
• Plinko Sounds a Bit like the Galton Board

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)
See also: Entheorizing

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

From Wikipedia, the free encyclopedia

  (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]

See Also:The Black Swan

In this article I talk about the Demarcation problem:

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

From Wikipedia, the free encyclopedia

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 . 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 . 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:

• Bagatelle
• Pachinko
• Plinko
• Payazzo
• Pazzo-lolo

External links

Wikimedia Commons has media related to: Galton box

• An 8-foot-tall (2.4 m) Probability Machine (named Sir Francis) comparing stock market returns to the randomness of the beans dropping through the quincunx pattern. from Index Funds Advisors IFA.com
• A simulation with explanations
• Another simulation from John Carroll University
• Quincunx and its relationship to normal distribution from Math Is Fun
• Dynamical turbulent flow on the Galton board with friction
• Animations for the Bean Machine by Yihui Xie using the R package animation

The Black Swan

"All swans are white" is a falsifiable claim – it could be proven wrong.

Black Swan, Claremont (Cygnus atratus), Tasmania, Australia

Even so, the statement all swans are white is testable by being falsifiable. For, if in testing many swans, the researcher finds a single black swan, then the statement all swans are white would be falsified by the counterexample of the single black swan. See:Inductive categorical inference

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]

Our major conclusion is simply a reaffirmation of the general statement that perceptual organization is powerfully determined by expectations built upon past commerce with the environment. When such expectations are violated by the environment, the perceiver's behavior can be described as resistance to the recognition of the unexpected or incongruous. The resistance manifests itself in subtle and complex but nevertheless distinguishable perceptual responses. Among the perceptual processes which implement this resistance are (1) the dominance of one principle of organization which prevents the appearance of incongruity and (2) a form of "partial assimilation to expectancy" which we have called compromise. When these responses fail and when correct recognition does not occur, what results may best be described as perceptual disruption. Correct [p. 223] recognition itself results when inappropriate expectancies are discarded after failure of confirmation. See:On the Perception of Incongruity: A Paradigm

See Also:

•  Book review: “Thinking, fast and slow” by Daniel Kahneman -