Why are Normal Distributions Normal?

Abstract

It is usually supposed that the central limit theorem explains why various quantities we find in nature are approximately normally distributed—people's heights, examination grades, snowflake sizes, and so on. This sort of explanation is found in many textbooks across the sciences, particularly in biology, economics, and sociology. Contrary to this received wisdom, I argue that in many cases we are not justified in claiming that the central limit theorem explains why a particular quantity is normally distributed, and that in some cases, we are actually wrong. <l type="tab"><li> <b>1</b> <it>Introduction</it> </li><li> <b>2</b> <it>Normal Distributions and the Central Limit Theorem</it> <l type="tab"><li>   <b>2.1</b> <it>Normal distributions</it> </li><li>   <b>2.2</b> <it>The central limit theorem</it> </li><li>   <b>2.3</b> <it>Terminology</it> </li></l> </li><li> <b>3</b> <it>Explaining Normality</it> <l type="tab"><li>   <b>3.1</b> <it>Loaves of bread</it> </li><li>   <b>3.2</b> <it>Varying variances and probability densities</it> </li><li>   <b>3.3</b> <it>Tensile strengths and problems with summation</it> </li><li>   <b>3.4</b> <it>Products of factors and log-normal distributions</it> </li><li>   <b>3.5</b> <it>Transforming factors and sub-factors</it> </li><li>   <b>3.6</b> <it>Transformations of quantities</it> </li><li>   <b>3.7</b> <it>Quantitative genetics</it> </li><li>   <b>3.8</b> <it>Inference to the best explanation</it> </li></l> </li><li> <b>4</b> <it>Maximum Entropy Explanations</it> </li><li> <b>5</b> <it>Conclusion</it> </li></l>