User blog comment:PsiCubed2/Back to Googology: a reminder as to why this wiki was opened in the first place/@comment-11227630-20181012084451/@comment-30754445-20181012112231

There's nothing wrong with "guesses" as long that:

(1) They are clearly labeled as such.

(2) They are educated guesses by people who have at least an inkling of an understanding regarding the subject matter they're guessing about.

(3) They do not contradict already established knowledge.

The problem is that 99% of the "guesses" we see here nowadays are like "guessing" that:

354987927349812x784651727386186312 = 25754197249827310909873523974198498144

For the record, I just punched in random digits and made sure that the answer looks sort-of reasonable. But is it actually correct? Not very likely.

Of-course, the above can be checked (and most likely disproven) in seconds with a calculator. But lets say we didn't have calculators. Would you waste your time to try and "verify" the above equation, had you known that I've simply mashed random digits on my keyboard?

My point is simply this:

If you don't yet know how to do something, don't take wild guess. The odds of your post even remotely making sense, in such a situation, are practically nil.

If you don't know how to multiply numbers, it is pointless to just take a shot in the dark.

If you don't know the basics of how even the most basic OCFs work, don't attempt to create a notation that reaches Psi(Psi_I(0)).

If you are not well-versed in proof theory and set theory, don't "guess" your way through Inaccessibles and Mahlos and Weakly Compacts.

And if you don't know how the ordinals below Z2 work (which, currently, no person alive does) then don't pull an ordinal table out of your ass and pertend it to be an actual work of mathematics.

Now, I agree with you doing actual googology is difficult. Part of the problem, is that this site have attracted some people (not you) who are not willing to put in the effort. It became a playground for people who pertend to do googology, rather than people who do actual work. We've actually had people who don't know what a function is, who then proceeded to "use functions" in their "notation".

I'm sorry, but the fact that subject is hard, is not an excuse to talk nonsense.

And on a related note:

I think that the days where the main interest of googology was "to define the biggest number you can" are long over. Breaking records today is simply not as interesting as it was in the days of Bowers and Saibian and Bird, because we already know the universal recipe: you take a really powerful ordinal notation from the mainstream literature and plug it in the FGH. End of story. How is this in any way interesting?

In my view, it is far more interesting to explore and research the vast googological world we've already discovered. How do we compare numbers from different notations? Can we make our notations simpler? Can we find interesting mathematical problems that have googological answers? Is it possible to create a practical and universal "standard notation" that goes (say) up to epsilon-0?

Is BB(5) really 4098? Can we get better bounds for the solution of Graham's problem? Can we get better bounds for Friedman's n(3)? What about TREE(3) or SCG(13)?

What lies between computable and the uncomputable? What's the general structure of  ordinal landscape up to Z2? How should we define the FGH for w1_ck and beyond?

Can we find better ways to visualize ordinals and/or numbers? How would you visualize e0? gamma-0? The BHO? How would you explain these concepts to the layman?

Is there a simple way to extend all our googological constructs from integers to real arguments? Can we have continuous fundamental sequences? Continuous tetration? What are the implications of the fact that a Taylor series is defined with ordinary powers, to the analysis of googological functions?

These are just a few of the interesting questions that we can ask about googology, which have absolutely nothing to do with the old "defining the largest number" challenge.