Tuesday, September 15, 2026
Saturday, September 12, 2026
Von Neumann and the Collatz Conjecture
He famously said that: "Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin."
I wonder if he knew about the Collatz Conjecture when he said that.
On his Wikipedia page, I read:
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At times he could be ignorant of the standard mathematical literature, finding it easier to rederive basic information he needed rather than chase references.
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So it's possible, even likely, he did not know about it.
The Collatz Conjecture definitely involves a deterministic process, and I say it produces random numbers.
Here is my informal proof of that: given any number, there is no algorithm for determining how many iterations it will take the Collatz Conjecture process to reach 1. There is also no algorithm or equation you could use to find the maximum value of the iterations. Small changes in the initial value produce drastically different results, which is a hallmark of chaos theory.
In this way, the process is akin to rolling dice. The overall and final results can be calculated beforehand, but the specific and intermediate results are unknowable.
If something is deterministic but unpredictable, it is effectively random.
Thursday, September 10, 2026
icky history
I try to keep things family friendly here. Sometimes that is not possible. People often shit and piss themselves when they die, so various warrior cultures developed a tradition of fasting before battle. This has obvious downsides.
Cannibalism of slain enemies was common across Polynesia. If there was nothing left to eat, stealing shit from the guts of a dead warrior was proof you were in the battle.
During WW2 in the Pacific, US troops sometimes took ears, teeth, and other body parts from dead Japanese soldiers as grisly souvenirs.
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In the May 22, 1944 issue of LIFE magazine, a striking and controversial image was featured as the “Picture of the Week.” It showed 20-year-old Natalie Nickerson of Phoenix, Arizona, gazing at a human skull — reportedly of a Japanese soldier — that she had received from her boyfriend, a Navy lieutenant serving in the Pacific
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The Japanese mutilated the dead too.
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The Ear Mound, or Mimizuka, in Kyoto is a memorial burial mound for the severed noses of Korean and Chinese victims killed during Toyotomi Hideyoshi's invasions of Korea in the late 16th century.
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A plaque, which was later removed, stood in front of the Ear Mound in the 1960s with the passage, "One cannot say that cutting off noses was so atrocious by the standard of the time." Most guidebooks do not mention the Ear Mound, and only a few Japanese or foreign tourists visit the site.[10] The majority of visiting tourists are Korean—Korean tour buses are often seen parked near the Ear Mound.[citation needed]
In 1982, not a single Japanese school textbook mentioned the Ear Mound.
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But sure, let's all get extra pissed off about Confederate monuments...
Tuesday, September 8, 2026
conjecture: can all primes greater than 2 be written in the form 2n + 3?
All primes greater than 5 end in either 1, 3, 7, or 9. If n is an integer, 2n + 3 will always be odd, but not necessarily prime. If we further require that n not be a multiple of 3, we eliminate all odd multiples of 3 since 2n + 3 will always be a multiple of 3 if n is a multiple of 3. We can also require that n be an integer whose last digit is not 1, because in those cases, 2n + 3 will always have 5 as the last digit. Likewise, if the last digit of n is a 6, the last digit of 2n + 3 will be 5.
If the conjecture is true, then it makes sense that 1 cannot be written form 2n + 3 since it is not prime. Also, it intuitively makes sense that all other primes would be some combination of the two smallest primes.
Let's make a table
n 2n + 3 prime?
0 3 yes
1 5 yes
2 7 yes
4 11 yes
5 13 yes
7 17 yes
8 19 yes
10 23 yes
13 29 yes
14 31 yes
17 37 yes
19 41 yes
20 43 yes
22 47 yes
23 49 no
25 53 yes
28 59 yes
29 61 yes
32 67 yes
34 71 yes
35 73 yes
37 77 no
38 79 yes
40 83 yes
43 89 yes
44 91 yes
For larger primes, we know that because of the possible last digits, the result of subtracting 3 will always be an even number, and so the result can always be written in the form of 2n.
I have a hunch I'm missing something but feel I'm on the right track. Could this be a new primality test? It may even be a way to find the next largest prime. It seems the conjecture occasionally returns a perfect square or a semiprime instead of a prime number.
The largest known prime number is 2^136279841 − 1. That's not really relevant for the conjecture, but I thought I'd put it here. The prime numbers used for RSA and other modern cryptography are in the range of about 2^300, which has roughly 100 digits.
Let's try n = 100,000.
2n + 3 = 200,003
200,003 is prime.
n = 1,000,000
2n + 3 = 2,000,003
2,000,003 is prime.
n = 5,000,000,000
2n + 3 = 10,000,000,003
10,000,000,003 = 13 × 769231
Well, looks like I have to think about this some more.
Saturday, September 5, 2026
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