3X+1 is an unexpectedly weird math problem

Thanks. I'll check their site also for sale pricing. Silver Asiatic

The Amazon audible version was $35. I think I have the VHS version someplace. If I see the audio one on sale, I will post it but you have to be around that day. Another good one by same author is Science and Religion. jerry

I wish they would notify me when those go on sale. I'm digging into the roots and origins of science. That course shows that science emerged from theism and Christianity specifically. I saw it listed for around $99, which seems too much for just audio. I look on EBay for Great Courses also and there are hundreds. But a used copy of that one is still $60 which is probably a very good deal but it seems a lot for audio and no book. A few people have old VHS versions for around $30 and that just seems crazy. Especially because as you say they offer brand new DVD sets for $20 to 30. The one on Quantum Theory you posted looks good also. Silver Asiatic

I am waiting for the price to drop on the History of Science, ancient to 1700

All the history of science courses are good. I like the more modern era ones better since more has happened since 1700. They go on sale every 4-6 weeks. Some times at very low prices. They also have a program where you can stream hundreds of video courses for a yearly fee. I have that but will get those courses that show up at about $20/$30 per 24/36 lectures when they are on sale. Normal prices are 70% off list but have seen them occasionally at 90% off list. The History Science prior to 1700 is only on audio so not on their yearly streaming. It is probably available on Audible. But doesn’t come with a course book. They recently on The Great Courses, last week, had all audio courses on sale. jerry

But another way is The Great Courses. I recently purchased a course for less than a dollar a lecture

I am waiting for the price to drop on the History of Science, ancient to 1700. That one was highly recommended to me. A very excellent Great Courses I completed was Daniel Robinson on the nature of Consciousness. I was shocked to discover he is a Thomist-realist with tremendous knowledge of contemporary ideas on consciousness. Dr. Robinson recently passed away - R.I.P. Silver Asiatic

Fell apart at the end by promoting Brilliant. We can all waste time in various ways and maybe Brilliant is one. But another way is The Great Courses. I recently purchased a course for less than a dollar a lecture, called Great Thinkers, Great Theorems. If you are interested in mathematics, this is the best one I’ve seen. Three lectures just on Euclid. He did not use any numbers. Question- how does one define a right angle with no numbers. https://www.thegreatcourses.com/courses/great-thinkers-great-theorems jerry

H, there are as yet no generally accepted proofs. KF kairosfocus

At collatz.com, Franz Ziegler offers a proof of the Collatz Conjecture (3n+1). Is this proof valid? Why or why not? hoosfoos

Fascinating! Barry Arrington

Yes, indeed, this is an interesting problem, as was noted here earlier. Your linked case, for 3 illustrates how the process looks for the ladder of powers of 2 and once this hits, goes to the 421 loop: 3, 10, 5, 16, 8, 4, 2, 1,… KF kairosfocus