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Information Geometry Conflicts With Independence^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Counter-Example

#### 2.1. Two Parameters v and w

$f\left(u\right)$ | ${e}^{u}/(e-1)$ | $(8+6{u}^{2}-4{u}^{3})/9$ |

$A$ | $e-1=1.71828$ | $\frac{11}{6}log2+\frac{5}{6}log5-\sqrt{15}(arctan\frac{5}{\surd 15}-arctan\frac{1}{\surd 15})=0.05945$ |

$B$ | $1=1.00000$ | $\frac{89}{12}log2-\frac{25}{12}log5-\frac{\sqrt{15}}{6}(arctan\frac{5}{\surd 15}-arctan\frac{1}{\surd 15})-\frac{4}{3}=0.02909$ |

$C$ | $e-2=0.71828$ | $\frac{251}{24}log2+\frac{5}{24}log5+\frac{13\sqrt{15}}{12}(arctan\frac{5}{\surd 15}-arctan\frac{1}{\surd 15})-\frac{31}{3}=0.01636$ |

#### 2.2. One Parameter w

#### 2.3. Comparison of One and Two Parameters

#### 2.4. Science

Treatment of v should not influence inference about w | [Science] |

**science requirement**. Any observational consequence of information-geometry’s invariant volumes would be rejected by the informed scientist. If there were such consequence, then observation of width w could be used to infer something about location v, contrary to the intention of the formulation.

## 3. Conclusions

**Information geometry is not science**. It denies the independence of separate parameters even though such independence is a fundamental requirement of scientific inquiry. The assumption of a geometrical connection between distributions is unnecessary for science and it fails under test.

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Skilling, J.
Information Geometry Conflicts With Independence. *Proceedings* **2019**, *33*, 20.
https://doi.org/10.3390/proceedings2019033020

**AMA Style**

Skilling J.
Information Geometry Conflicts With Independence. *Proceedings*. 2019; 33(1):20.
https://doi.org/10.3390/proceedings2019033020

**Chicago/Turabian Style**

Skilling, John.
2019. "Information Geometry Conflicts With Independence" *Proceedings* 33, no. 1: 20.
https://doi.org/10.3390/proceedings2019033020