Wednesday, December 3, 2014

Bernoulli Space

Daniel Bernoulli
The Bernoulli Space – A Mathematical Concept 

The Bernoulli space, is a mathematical concept for the transition from past to future with due consideration of uncertainty of the future developments. It is at the main focus of Bernoulli stochastic which represents the basis for reliable as well the exact predictions together with measurements.

The Bernoulli space does not seem to presume an ideal world, for instance, the example of physics on the basis of belief in truth and causality where in contrast, the Bernoulli space acknowledges human ignorance and cosmological pattern which could generate uncertainty and as a mathematical model of change, could be regarded as a means of obtaining accurate as well as reliable predictions.

The term `uncertainty’, before the introduction of the model, should be explained since it could have several inconsistent meanings in the daily speech which in everyday speech, uncertainty could be referred to determinate, though unknown facts or to the indeterminate future which is not known since it does not exist so far. The difference is obvious between the facts and future events, a fact which is specified and if considered has a fixed value.The future event on the other hand is indeterminate and hence may or may not take place.

Ignorance Related to True Value – Unknown 

Fact may be unknown though it is fixed while a future even may not be known or unknown since it is subject to randomness which could or not occur. From the point of unique interpretation, uncertainty is explained as the inability to predict the future development accurately and this inability is because of the ignorance related to the past as well as the randomness regarding the future.

The two elements of ignorance and randomness generate uncertainty and while describing uncertainty in a quantitative manner, both the sources need to be taken into consideration. Ignorance relates to the true value which is unknown it is only rarely that the true values of considered attributes are known though in general they are unknown.

Values are what is known but are not the true value and with the knowledge on `what is not’, it is possible to state a set of values which are true though may be unknown. This reflects the knowledge on `what is no’, or the ignorance of `what is’ and the larger the set, the larger would be the ignorance.

Randomness – Future Episodes

Randomness on the other hand refers to future episodes and reflects a natural tendency to take place and could be small or large based on the given situation. Over 300 years back, Jacob Bernoulli, the Swiss theologian as well as a mathematician was successful in quantifying randomness of a future event.

He related the occurrence of natural tendency of a future event with the help of degree of certainty of its occurrence, calling this degree probability and if the occurrence is impossible in a given event, there is no propensity with the degree of certainty, which is the probability that would be 0.

While on the other hand if the occurrence is certain in a given event, the propensity would be at the maximum with the degree of certainty being the value of one.

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