User talk:MrSolis

Antihydra

Hi, I rolled back your recent change to Antihydra because it seems like you removed a ton of content there. Feel free to add your proofs if you'd like, but no need to remove the transition table and so much of the description. Sligocki (talk) 03:35, 17 February 2025 (UTC)

Explaining Myself

Sligocki Hello,

I appreciate your criticisms of the changes I have made to one of your pages. I would like to explain my thought process behind the changes so that we may come to an agreement on what should and should not be changed. I will review each section of your article to explain why I did what I did.

1. The lead section: I wanted to be brief. Perhaps I was being too brief.

2. Turing Machine: No other individual Turing Machine page has a transition table, only its inline form. If you look at the pages for the 5-state busy beaver winner and Hydra, the other two TM pages that I have made significant changes to, you can infer that I intend for these to be the final (or semi-final, for unsolved machines) versions of these pages. That means I want consistency across every individual Turing Machine page and a clear structure. If you prefer that I not edit the table out, let me know so that I can add one to the 5-state busy beaver winner and Hydra (and any other TM pages I decide to modify) pages. I also omitted the names mxdys and Racheline in my version. Is that a problem? I did not think that was a problem because I had cited your blog post where they are mentioned. If it is a problem, I will not omit their names in my second edit to the page.

3. Analysis: You will notice that I did not use the preferred and more useful rules in my version. That is intentional. I noticed that the page "Hydra function" just says "The Hydra function is Collatz-like function whose behavior is connected to the the unsolved halting problems for the Cryptids Hydra and Antihydra". Aside from the obvious grammatical errors, this article does not explain how the function H(n) = floor((3*n)/2) is connected to Hydra and Antihydra except for the name, which feels circular. It also does not explain why that matters. After Antihydra, I was planning on changing that article so that these questions could be answered.

4. Biased Random Walk: I have two separate points on why I changed it.

The first and more important one, is that the probability analysis is simply incorrect. The probability of the random walker b going down from n to -1 is not (1/2)^(n+1). The simple argument for why is that (1/2)^(n+1) is the probability that the random coin lands on the same face n+1 times in a row. Consider the situation where b = 5, and you are given a coin to flip. It if lands on heads, b increases by 2; if tails, decreases by 1. If you had to get b to -1 without getting heads a single time, then the probability would be (1/2)^6 (assuming independent random flips where heads and tails each have a 1/2 probability). However, if you just had to get b to -1 you could still win if you get heads on your first flip and then get eight tails in a row. You could win even if b rose to 10^(20) if you are lucky enough. These situations are not very likely to happen, but they make a non-zero difference.

My second point is that I did not entirely remove this section from the wiki; I had moved it to the Hydra page in the Trajectory section and corrected it, along with giving a proof for why my analysis is true there. I did not want to include basically the same thing in two separate pages, so in my Antihydra edit I basically just said "read the Hydra article".

If you still do not believe me when I say that (1/2)^(n+1) is incorrect, I would like you to make and run a program based on this pseudocode:

trials = [some large integer]
fakeInfinity = [some other large integer]

integer reachedMinusOneCount = 0
integer startingValue = 1 // THIS IS N

for (integer i = 0; i < trials; i++)
     integer walk = startingValue

     while(walk > -1 AND walk < fakeInfinity)
        integer flip = [either 0 or 1, chosen randomly]
        if (flip equals 0)
            walk = walk - 1 // Getting a 0 is tails here
        else
            walk = walk + 2 // Getting a 1 is heads here

     if (walk equals -1)
        increment reachedMinusOneCount

probability = (reachedMinusOneCount)/(trials)
output(probability)

If you alter startingValue and run the program, you will find that probability is greater than (1/2)^(n+1) and closer to what I got.

5. Simulation: I included the part where after 2^(31) rule steps we have b = 1073720884 in my Trajectory section. I thought that if the average uninformed reader was curious about the "20940 (0.002%)" error, they could check for themselves, so I removed that part. Again, the same problematic (1/2)^(n+1) probability shows up, which I saw no issue with removing.

I sincerely apologize for making drastic changes to your article and not elaborating on why before I did that. I would like for you to respond with what precisely I did wrong so that I do not make unwanted changes in the future. MrSolis (talk) 15:30, 17 February 2025 (UTC)

Thanks for your efforts in improving the wiki! Are you on the discord server? It might be easier to discuss wiki changes there since that's where most people are active. Peacemaker II (talk) 17:00, 17 February 2025 (UTC)

User:Peacemaker II, No, I am simply curious as to exactly where I went too far. MrSolis (talk) 17:05, 17 February 2025 (UTC)