1. Redefining the Hyperoperation Sequence / Hyperoperation Tree?
   1. Why? and Backstories
   2. Support
   3. Afterwords
   4. Update

Redefining the Hyperoperation Sequence / Hyperoperation Tree?

All the technical stuff are in this pdf I linked below because I did not had the time to implement Mathematics display on the blog site still (may consider swapping out the base to something better in the future).

Link to pdf download here: HyperopetationTree

Anyways now I’ll talk about the back story of it:

Why? and Backstories

It has always been clear to me that multiplication is not actually “actually” repeated addition, else why would 5*0 be 0 if we are repeatingly adding a number to 5 for 0 times?

So I’ve had at least a dozen of informal mental session thinking about this, and a few attempts trying to solve it.

All these old thoughts came together yesterday (after I designed a Nerf Rival magazine mechanism which I call Tridact-Helion), so I took my still-charging iPad to bed and started working (on bed).

Next day at school. since we’ve already finished all the syllabus, math lessons are now just to do work on your own, I worked on the extremely awkward ABCD keyboard of my nspire CX II-T CAS (seriously it gave me a headache) to make a python function for the Omega. And carried work to home and so on and so forth coming to what I have now.

If you want a look to the note I used to work it all out, here’s the link: Thought

But warning it is extremely messy because I did a lot of writing on bed either upside down or with straight arms.

I actually haven’t really read through even the wiki page for hyperoperation sequence even though I knew it when I was in middle school. I don’t know but the page is and was really unappetizing to me. So hopefully, I did not accidentally rediscover what is already being done. I mean, hyperoperation is niche, right?

My hope for it is that, if a hardware design can perform Omega and other functions (which is not yet found) really fast, maybe computer calculations can get faster?

I thought to think of it like a relationship or constraint because ideas from (quantum) annealing taught me any system with enough constraints can be solved (not really the exact wordings but same idea).

Support

These are the Python functions I use to calculate numerical results for Omega:

def  u(a):
    return  a+1

def  Omega(vars,subs):
    #print("vars:", vars)
    if  len(vars) == 1:
        return  u(vars[0])

    for  _  in  range(vars[-1]):
        new_vars = vars[:-1]
        new_subs = subs[:-1]
        #print("new:",new_vars)
        vars[subs[-1]] = Omega(new_vars,new_subs)

    return  vars[subs[-1]]

subs are basically the letter subscripts, but instead of a, b, c, … use 0, 1, 2, …
subs should be 1 item less in length than vars

Example use:

Omega([0, 1, 6, 2], [0, 0, 1])
36

(it is the same as Omega_(4aab) (a=0, b=1, c=6, d=2)

Afterwords

If you decided to work more on this topic and have some discoveries, or you have knowledge in this area that I can learn, please tell me about it.
You can e-mail me at the address qty@qty10.tech
And I will probably be responding with another e-mail due to erroneous security settings (and no there isn’t an attack vector, it’s just that I am not sure how to get certificate for a mailbox that is out of my control).
or send a message through any of the social link in my About Me Page that has a instant message feature (except moegirlpedia I never check it).

Update

Also I want to note that what I felt from this function thingy, perhaps calculation resources are “wasted” during exponentials? Like we could’ve done a geometric series as well in the same time. (I feel like this is not true but it’s just an idea).