Uploaded June 2026 | Updated September 2026, 3 weeks ago
I made a $20,000 mistake. Ten years ago I made this YouTube series on Imaginary Numbers, that we turned into this book. But when I opened up the first box from our latest print run, I was horrified to see this low resolution image on the back cover.
I rushed to checked the files I sent our printer, and realized that we had miscommunicated - the printer had grabbed the incorrect cover file and used it on the full print run. After lots of stressful back and forth with our printer last week, I essentially got nowhere, and we’re left with a $20,000 bill and bunch of books with an error on the cover.
I’m very particular about the fit and finish of everything we put out - but as my team has pointed out to me, unless you’re looking for it, this is not that noticeable of an error. So, we’ve decided to offer these books at welchlabs.com/store at a discounted rate. This will help us recoup our printing costs - and you can pick up what is still by and large a great book on Imaginary Numbers at a great price.
I made a $20,000 mistake. Ten years ago I made this YouTube series on Imaginary Numbers, that we turned into this book. But when I opened up the first box from our latest print run, I was horrified to see this low resolution image on the back cover.
I rushed to checked the files I sent our printer, and realized that we had miscommunicated - the printer had grabbed the incorrect cover file and used it on the full print run. After lots of stressful back and forth with our printer last week, I essentially got nowhere, and we’re left with a $20,000 bill and bunch of books with an error on the cover.
I’m very particular about the fit and finish of everything we put out - but as my team has pointed out to me, unless you’re looking for it, this is not that noticeable of an error. So, we’ve decided to offer these books at welchlabs.com/store at a discounted rate. This will help us recoup our printing costs - and you can pick up what is still by and large a great book on Imaginary Numbers at a great price.
![Yann LeCuns $1B Bet Against LLMs [Part 1]](https://i.ytimg.com/vi/vmz5TJbTjdg/mqdefault.jpg "Yann LeCuns $1B Bet Against LLMs [Part 1]
Yann LeCuns $1B Bet Against LLMs [Part 1]")
![Learning To See [Part 9: Bias Variance Throwdown]](https://i.ytimg.com/vi/yLwZEuybaqE/mqdefault.jpg "Learning To See [Part 9: Bias Variance Throwdown]
In this series, well explore the complex landscape of machine learning and artificial intelligence through one example from the field of computer vision: using a decision tree to count the number of fingers in an image. Its gonna be crazy.
Supporting Code: https://github.com/stephencwelch/LearningToSee
welchlabs.com
@welchlabs")
![Self-Driving Cars [S1E3: AI Failure?]](https://i.ytimg.com/vi/yaYER2M8dcs/mqdefault.jpg "Self-Driving Cars [S1E3: AI Failure?]
PATREON: https://www.patreon.com/welchlabs
TWITTER: @welchlabs
MORE: http://www.welchlabs.com
CODE: https://github.com/stephencwelch/self_driving_cars
FURTHER READING + REFEERENCES
For a bayesian approach to the same reliability testing math: https://stats.stackexchange.com/questions/73645/how-do-you-derive-the-success-run-theorem-from-the-traditional-form-of-bayes-the
Rand Report: https://www.rand.org/pubs/research_reports/RR1478.html
Zeiler and Fungus 2013: https://arxiv.org/abs/1311.2901
WHO top 10 causes of death: https://www.who.int/news-room/fact-sheets/detail/the-top-10-causes-of-death
WHO injuries and violence facts: https://apps.who.int/iris/bitstream/handle/10665/44288/9789241599375_eng.pdf%3Bjsessionid=7558B4BDC59A52BB94AEC68A0AD79EE8?sequence=1
Bojarski et al: https://arxiv.org/abs/1704.07911
Dean Pomerleau: http://www.cs.cmu.edu/~bhamner/neuralNetworksProject/pomerleau_dean.pdf
Dean Pomerleau: https://www.ri.cmu.edu/pub_files/pub3/pomerleau_dean_1991_1/pomerleau_dean_1991_1.pdf
Dean Pomerleau: https://www.ri.cmu.edu/publications/life-in-the-fast-lane-the-evolution-of-an-adaptive-vehicle-control-system/
Nvidia End to End: https://arxiv.org/abs/1604.07316
Way ChauffeurNet: https://arxiv.org/abs/1812.03079
VIDEO REFERENCES
Amnon Shashua Talk: https://www.youtube.com/watch?v=GCMXXXmxG-I
NAVLAB: https://www.youtube.com/watch?v=rV0H7u6tmIk
MUSIC
https://www.premiumbeat.com/royalty-free-tracks/jazz-manouche-forever
https://www.premiumbeat.com/royalty-free-tracks/out-of-the-woods
https://www.premiumbeat.com/royalty-free-tracks/wanderer
SPECIAL THANKS TO
Tony Fast
Krish Ravindranath
Karthik Naga
Alex Mones
Michael Grabchak
- AND -
Sid Sarasvati
Ross Hanson
Vin Soma
Antoine Pintout
Jaewon Jung
Raphael J Vasquez
AJ Englehardt
Nate Fuller
Hitoshi Yamauchi")
![Imaginary Numbers Are Real [Part 6: The Complex Plane]](https://i.ytimg.com/vi/z5IG_6_zPDo/mqdefault.jpg "Imaginary Numbers Are Real [Part 6: The Complex Plane]
For full problem statement, check out:
http://www.welchlabs.com/blog/2015/10/2/imaginary-numbers-are-real-part-6-the-complex-plane
More information and resources: http://www.welchlabs.com
Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering.
Part 1: Introduction
Part 2: A Little History
Part 3: Cardans Problem
Part 4: Bombellis Solution
Part 5: Numbers are Two Dimensional
Part 6: The Complex Plane
Part 7: Complex Multiplication
Part 8: Math Wizardry
Part 9: Closure
Part 10: Complex Functions
Part 11: Wandering in Four Dimensions
Part 12: Riemanns Solution
Part 13: Riemann Surfaces
Want to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources.")
