User blog comment:Ubersketch/How did you get into googology?/@comment-32213734-20181124124403

In 1987, when I was 5, I read about googol and numbers up to decillion. Few years later I learned about googolplex. When I learned about exponentiation (I was about 7), I thought that we can continue sequence "addition, multiplication, exponentiation, ..." When I learned about tetration, I already knew what it is.

Circa 1998 I came up with idea of linear notation. I called it "theory of operations": "operation #0" is + 1; "operation #1" is addition; "operation #2" is multiplication; "operation #3" is exponentiation; "operation #4" is tetration; etc. Then "operation (1,0)" of n and 2 is "operation #n" of n and 2; then "operation (1,1)" of n and 2 is "operation (1,0)" of n and n; then "operation (1,0,0)" of n and 2 is "operation (n,0)" of n and 2; etc. But I failed to define uniform rules (maybe, because addition, multiplication and higher "operations" are defined different ways - this was the cause why Bowers started his BEAF from exponentiation, not from addition), and I threw this business. Anyway, it didn't seem very useful to me. I don't remember, did I consider array of two or more dimensions. Maybe.

In 2004 I started to use internet.

In 2006 I returned to this topic. This time I considered multi-dimensional arrays and beyond. I tried to imagine arrays as large as I could (multi-trimensional, multi-quadrumensional, ...) I don't remember exactly, how far I went (I think, not so far). I again found out that rules for addition and exponentiation are different. I started to use modified functions (as I remember, n0 = n instead of n1 = n, or something like), and I was slightly disappointed that I need to use some new functions instead of familiar exponentiation. I never tried to make up and name big numbers, because I wanted "simple" and "natural" system, but I was not sure about my system, I understood that few different rules can be, and I could not choose the "right" rules. And I was more interested in large arrays than numbers, and even fast-growing functions.

In 2011 I read about ordinals in Wikipedia. I was hooked, but I didn't understand anything.

In Semptember or October 2016 I read about ordinals in Wikipedia one more time. Surprisingly, I started to understand something. But there was little information about large ordinals (such as Bachmann-Howard ordinal and larger). I started to search about large ordinals in internet. I found a forum, where was a competition, whoose number is bigger, then Googology Wiki, then Bowers' site. When I saw BEAF I thought like "wow, somebody published it, cool". I read List of googolisms, and it was very interesting.

Then I thought: "Why we use ω + 1, ω2, ω2, ωω, but we do not use ω↑↑ω, ω↑↑↑ω, ..., {ω, something}?" (here {} is BEAF). So, I tried to make up array notation for ordinals. I tried different versions of the notation, and I compared it with Veblen function. I wrote few dozens of sheets of paper of ordinal lists and calculations.

In June 2017 I felt that I already can share my ordinal array function with others. I registrated on this site and started to post blogs here. So, I'm here because of ordinals. I think, you know the rest.