wmc_e6 2018.10.12 | 歧路結節，開合解謎 Hidden Variables | 羅海德 Hector Rodriguez | 最後四天 open until 15 Oct 2018, 11:00 – 19:00 daily | The collaboration between artist Hector Rodriguez and mathematician Felipe Cucker results in “Entropic Envelope” (EE), the visualization of an image analysis process, and “Approximation Theory” (AT), visualized mathematics in prints and a video. AT interrogate the tyranny of our image culture. In EE, 3 film samples are subverted and re-invented as wave forms and visual turbulence.

**《The Entropic Envelope》**運用資訊理論技術視覺上呈現電影的時間流動，顯示影格之間圖像資訊量的改變。影格間差別越大，則觀眾可從中獲取更多的資訊，反之亦然。作品概念來自現象學傳統，包括埃德蒙德．胡賽爾及貝爾納．斯蒂格勒等著作。電影有如樂章般是具備時間性的，作品目的是展示現象學裡的「時間對象」及影像流的其中一種可能的數學範式。[示例欣賞]

**《Approximation Theory》**以影像展現數學中的「逼近理論」（或作「近似值」理論）。作品演算運用不同圖像庫現算，而每個圖像庫均有其獨特之處，或由程序生成的不同直線曲線組成，或由其他電影影格甚至中文大寫數字組成。透過把不同圖像加權重疊，程式能夠估算出任意影像的近似圖像並重構之。而重構質素則取決於圖像庫中圖像的數量以及質量，即圖像不同的形態。故此不同圖像庫會生成出不同特色的重構。此系列為羅海德及Felipe Cucker所共同創作。[示例欣賞] [更多參考]

The** Entropic Envelope**project (2016-16) uses information theoretic techniques to visualize the temporal flow of cinematic works. More specifically, it represents the amount of graphical information in each frame relative to previous frames. The basic idea of

*Entropic Envelope*was influenced by the phenomenological tradition, particularly the work of Edmund Husserl and Bernard Stiegler. A film, like a musical piece, is an essentially temporal object. The aim of this project is to provide one possible mathematical model of the concept of a temporal object or an image flow.

Watch on Vimeo one of the three films studied: Godard’s *Alphaville*

The* Approximation Theory *(2017) [demo on Vimeo: Part 3]

In *Approximation Theory*, an image contains more information if it is visually distinct from preceding frames in the movie. If it is very similar to previous images, its information content is low.

This project visualizes the mathematical idea of approximation. The methodology involves the choice of a set of fixed dictionaries or databases of images. Each dictionary has its own distinctive quality. For instance, some consist of linear or curved elements generated procedurally. Other dictionaries might consist of more complicated images, such as frames from movies or Chinese characters. Any other image can then be approximately reconstructed as a weighted superposition of all or some of the images in the dictionary.

The character of the approximation depends on two kinds of factors: qualitative and quantitative. The quantitative aspect has to do with the number of images used in the reconstruction. The qualitative aspect has to do with the character of the images in the dictionary, for instance whether they are linear or curved. Different dictionaries generate qualitatively different reconstructions.

The concept of approximation also appears in Hector Rodriguez’ Theorem series. The latest addition to the series, Theorem 9, is also included in this show.

This project is the collaboration between Felipe Cucker & Hector Rodriguez.