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The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

Uncertainty in Measurement: Significant Figures

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.

Expected Value

Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:

Uncertainty in Measurement: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...

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Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations

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Pessimistic outcome expectancy does not explain ambiguity aversion in decision-making under uncertainty.

C Ahrends¹, F Bravo², M L Kringelbach^3,4

¹Center for Music in the Brain, Department of Clinical Medicine, Aarhus University & The Royal Academy of Music Aarhus/Aalborg, Aarhus, Denmark. christine.ahrends@clin.au.dk.

Scientific Reports

|August 23, 2019

Summary

People avoid ambiguity due to caution, not pessimism. This study found that ambiguity aversion in decision-making is not driven by expecting the worst, but rather by general cautiousness.

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Area of Science:

Cognitive psychology
Decision science
Neuroeconomics

Background:

Ambiguity aversion is a common human trait, often linked to pessimistic beliefs about potential negative outcomes.
Understanding the psychological drivers of ambiguity aversion is crucial for decision-making models.

Purpose of the Study:

To investigate whether pessimistic prior beliefs explain ambiguity aversion.
To differentiate between the roles of outcome expectation and general caution in ambiguity aversion.

Main Methods:

Utilized two linked behavioral tasks (risk-taking and beliefs tasks) with 78 healthy participants.
Assessed participants' decisions under risk and ambiguity, and their subjective beliefs about outcomes.

Main Results:

Participants' beliefs in ambiguity conditions were not overly pessimistic, aligning closer to optimal decision-making than risk conditions.
Individual differences in pessimism did not correlate with ambiguity aversion.
Pessimism influenced outcome expectancy but not the aversion to ambiguity itself.

Conclusions:

Ambiguity aversion appears to stem from general caution rather than the expectation of negative outcomes.
Decision-making under ambiguity may involve different psychological mechanisms than previously assumed, emphasizing caution over specific negative outcome predictions.