# 473: Math Is Not the Answer

- Show: [Embedded.fm](https://hardwarepodcasts.com/podcast/embedded-fm)
- Published: 2024-03-21
- Length: 1h 10m
- Episode: 473
- Page: https://hardwarepodcasts.com/podcast/embedded-fm/2024-03-21-473-math-is-not-the-answer
- Listen: https://embedded.fm/episodes/473

## Summary

Philip Koopman, a professor at Carnegie Mellon University and author of 'Understanding Checksums and Cyclic Redundancy Checks,' explains why empirical analysis and engineering trade-offs are superior to pure mathematics for selecting error detection algorithms. He details the critical differences between checksums and CRCs, highlighting how modulus choices (like mod 255 vs 256) drastically impact fault detection and how CRCs rely on XOR-based long division over Galois fields. Koopman also discusses the state of autonomous vehicle safety, arguing that statistical machine learning approaches struggle to meet the ultra-high reliability standards required for safety-critical systems.

## Chapters

- [0:07](https://hardwarepodcasts.com/podcast/embedded-fm/2024-03-21-473-math-is-not-the-answer#t=7) Introduction and Guest Background
- [9:03](https://hardwarepodcasts.com/podcast/embedded-fm/2024-03-21-473-math-is-not-the-answer#t=543) Checksums vs CRCs and Error Detection Basics
- [22:58](https://hardwarepodcasts.com/podcast/embedded-fm/2024-03-21-473-math-is-not-the-answer#t=1378) Modulus Choices and Fletcher Checksum Pitfalls
- [28:53](https://hardwarepodcasts.com/podcast/embedded-fm/2024-03-21-473-math-is-not-the-answer#t=1733) CRC Mechanics: Long Division and Galois Fields
- [39:01](https://hardwarepodcasts.com/podcast/embedded-fm/2024-03-21-473-math-is-not-the-answer#t=2341) TCP/IP Checksums and DualX Checksums
- [49:33](https://hardwarepodcasts.com/podcast/embedded-fm/2024-03-21-473-math-is-not-the-answer#t=2973) Empirical Analysis and Monte Carlo Simulations
- [1:01:21](https://hardwarepodcasts.com/podcast/embedded-fm/2024-03-21-473-math-is-not-the-answer#t=3681) Autonomous Vehicle Safety and Statistical Limits

## Topics

- [Embedded firmware](https://hardwarepodcasts.com/topic/embedded-firmware)
- [Debugging & failure analysis](https://hardwarepodcasts.com/topic/debugging-and-failure-analysis)
- [AI & machine learning](https://hardwarepodcasts.com/topic/ai-and-machine-learning)

## Most relevant to

established companies

## Mentioned

- Understanding Checksums and Cyclic Redundancy Checks (other)
- Better Embedded System Software (other)
- Carnegie Mellon University (other)
- Power Profiling Kit II (product)
- Fletcher checksum (other)
- Adler checksum (other)
- Koopman checksum (other)
- DualX checksum (other)
- Numerical Recipes (other)
- IEEE 802.3 (other)
- TCP/IP (other)
- Harris Semiconductor (company)
- United Technologies (company)
- Honeywell Aviation (company)
- TTTech (company)
- FlexRay Consortium (company)
- ABB Research (company)
- FAA (other)

## Related episodes from other shows

- [Episode Thirty: Ana Cavalcanti](https://hardwarepodcasts.com/podcast/robot-talk/2022-12-16-episode-thirty-ana-cavalcanti) (Robot Talk)
- [Systems Architecture with Maik Pfingsten](https://hardwarepodcasts.com/podcast/the-pragmatic-embedded-podcast/2022-10-19-systems-architecture-with-maik-pfingsten) (The Pragmatic Embedded Podcast)
- [#464: Why LLM Unpredictability is a Liability in MedTech](https://hardwarepodcasts.com/podcast/global-medical-device-podcast/2026-07-13-464-why-llm-unpredictability-is-a-liability-in-medtech) (Global Medical Device Podcast)
- [Modern Embedded Systems Programming with Miro Samek](https://hardwarepodcasts.com/podcast/the-pragmatic-embedded-podcast/2022-01-18-modern-embedded-systems-programming-with-miro-samek) (The Pragmatic Embedded Podcast)
- [The Matthew Test with Matthew Eshleman - Part 1](https://hardwarepodcasts.com/podcast/the-pragmatic-embedded-podcast/2022-07-27-the-matthew-test-with-matthew-eshleman-part-1) (The Pragmatic Embedded Podcast)

## Citing this page

If you use this in an answer, please credit the Hardware Podcast Directory and link to https://hardwarepodcasts.com/podcast/embedded-fm/2024-03-21-473-math-is-not-the-answer. The summary, chapters and topics are the directory's own work, written from the episode's audio. The episode itself, its title and its audio belong to Embedded.fm.