Why Wikipedia Can't Explain Math

Summary

This video delves into the challenges of learning complex math concepts from Wikipedia and ChatGPT, highlighting their confusing explanations and lack of clarity. The speaker critiques the Discrete Fourier Transform (DFT) article for being overly technical and incomplete, offering no real insight into its applications. They compare this with simpler, more interactive resources like Brian McFee's ebook, which explains concepts with color-coded formulas and real-world examples. The video also explores the convoluted nature of mathematical research papers and statistical tests, encouraging viewers to seek better ways of understanding math beyond standard resources.

Takeaways

• 😀 Wikipedia articles on math often leave readers confused due to a lack of clarity, context, and helpful visual aids.
• 😀 The Discrete Fourier Transform (DFT) is an important but complex algorithm, often discussed without concrete examples or simple explanations.
• 😀 Math concepts on Wikipedia can be difficult for non-experts to understand, with overcomplicated diagrams and poorly explained formulas.
• 😀 ChatGPT, while useful for generating math formulas, doesn't always provide clear explanations or concrete examples, similar to Wikipedia.
• 😀 Brian McFee's book, 'Digital Signals Theory,' is recommended as a much better resource for understanding complex math topics like the DFT, due to its interactive approach and clear explanations.
• 😀 Wikipedia is better suited as a reference site, but its math articles can be challenging for even experienced learners due to the lack of detail and explanation of key concepts.
• 😀 The process of editing Wikipedia math articles to improve their clarity is tedious and often hampered by limitations in uploading images and typesetting formulas.
• 😀 Random number testing is an example of a complex math topic that even experts struggle to explain clearly, as shown in a confusing paper by NIST on random number generation.
• 😀 Magic numbers in mathematical formulas (constants with no explanation) contribute to confusion, as seen in the NIST tests for random number generators.
• 😀 A more user-friendly approach to teaching complex math concepts, like the NIST random number generator tests, would involve eliminating 'magic numbers' and making explanations clearer, as done in the author's simplified guide.

Q & A

What is the Discrete Fourier Transform (DFT), and why is it often confusing to learn from Wikipedia?

The DFT is a mathematical algorithm that converts a sequence of equally spaced samples into a same-length sequence of equally spaced samples in the frequency domain. It's confusing on Wikipedia because its definition is vague, uses jargon without context, and doesn't explain fundamental concepts like sine and cosine functions, which are essential for understanding the algorithm.

Why is the article on DFT criticized for being poorly written?

The Wikipedia article on DFT is criticized for using cryptic language, missing essential context, and presenting a formula without clearly explaining its components. It also references terms like FFT (Fast Fourier Transform) without introducing them properly and makes assumptions that the reader already knows other mathematical concepts.

What is the problem with how Wikipedia handles mathematical topics in general?

Wikipedia often fails to provide clear and digestible explanations of mathematical concepts. Many articles dive straight into technical formulas or advanced topics without adequate foundational explanations, making them inaccessible to non-experts or those without advanced mathematical backgrounds.

How does the author feel about learning math from Wikipedia or ChatGPT?

The author finds both Wikipedia and ChatGPT frustrating when learning math. While Wikipedia articles are often unclear or incomplete, ChatGPT's explanations tend to repeat the same abstract formulas without providing concrete examples or context, making it hard to grasp the underlying concepts.

What does the author recommend for better learning the Discrete Fourier Transform (DFT)?

The author recommends reading 'Digital Signals Theory' by Brian McFee, which provides a more approachable and interactive explanation of the DFT. The book uses color-coded formulas, interactive modules, and real-world examples, like applying the DFT to actual audio clips.

Why does the author criticize the NIST paper on random number generation testing?

The author criticizes the NIST paper for its lack of clarity and excessive use of 'magic numbers,' which are constants used in formulas without proper explanation. This makes the tests hard to follow and understand. The author also points out that many concepts in the paper are explained poorly, with no clear reasoning behind certain mathematical choices.

What is the issue with how Wikipedia handles images related to mathematical concepts?

The issue with Wikipedia's math-related images is that they often lack proper legends, explanations, or context. These images can be confusing and make it harder to understand the concepts they are supposed to illustrate. The author spent time improving an image for the DFT article, but the process of uploading it was tedious and cumbersome.

What is a 'magic number' in mathematics, and why is it problematic?

A magic number is a constant used in a mathematical formula without explanation or context. This makes the formula harder to understand and less intuitive. The NIST paper, for example, is filled with these magic numbers, which complicate the learning process for anyone trying to understand the statistical tests for random number generation.

What is the relationship between the Discrete Fourier Transform (DFT) and random number generation?

The DFT is sometimes applied to random number generation as part of tests to check for randomness. In the context of the NIST paper, the author highlights how certain statistical tests (like the Frequency Test) are used to analyze the randomness of sequences, and the DFT is applied to evaluate their properties. However, these tests often lead to confusing results and unclear explanations.

How does the author suggest improving the understanding of mathematical concepts and tests?

The author suggests making math resources more interactive and approachable. By simplifying concepts, explaining the reasoning behind formulas, and using practical examples (such as using JavaScript to visualize statistical tests), learners can better understand complex ideas. The author's own guide to randomness testing, for example, avoids magic numbers and makes the steps easier to follow.