User blog comment:Vel!/Yudkowsky on googology/@comment-24.103.234.74-20140326023811

@FB100Z

After following your link and looking into the usage of the word crank, I concede that there is a distinction to be made between what cranks do and what googologist's do.

As I understand it from my reading, cranks lack basic knowledge of the subject they are claiming to be experts in, and refute well-established theorems using elementary and sometimes broken arguments simply because the result of the theorem "feels intuitively wrong". They also seem to have a track-record for inflated egos, interpreting the rejection of their ideas as proof that they are "too revolutionary" for the stupid experts, but the degree of megalomania varies between individuals. Cranks also seem to have an odd tendancy to insist that their ideas will not only be a revolution in their field of "study" but also to completely unrelated fields including physics, philosophy, meta-physics, religion, and the very way we live.

Googologist's on the other hand make no radical claims and are more or less in agreement with the results of set theory/computability theory. Rather than refute or reverse well established theorems, googologist's explore the consequences of those ideas to the nth degree ... and beyond ...

That being said there is such a thing as "crank googology". We've all seen it try to creep it's way into our community! Stuff like claiming there is a largest finite number (Ballium's Number is a spoof on that, but I've actually seen people who make the claim in seriousness), various nonsense involving infinity like infinitillion = 10^(3*infinity+3), pure gibberish masquerading as googolisms, either in a serious but flawed attempt to ape googology, or to actually lampoon it (it's a little hard to tell which), circular references, broken jumbles of functions and numbers claiming to be "the largest number in the world", salad numbers, trivial extensions,  broken notations, ill-defined ideas ... which we are assured grow really fast and yet defy a workable definition, or gems of illogic, like the idea that removing the decimal point in pi would make a number much larger than ''graham's number! sigh ... -_-''

The problem is that it is rather difficult for the non-expert to distinguish crank-googology from the real thing, given it's somewhat whimsical tendencies. From that point of view we can easily be accused of being cranks. I am pretty sure professional mathematicians can tell the difference, but none the less we would still get lumped with cranks as being somewhat loony.

I don't think it can be denied that googology is somewhat pathological, but it's hard to diagnose it's precise pathology. If it's not "crank" than what is it?

Where as cranks seem to be driven by a desire to bend and break mathematical results they don't like, googologist's are characterized by a curiousity to further explore mysterious mathematical results.

I believe that we might not be that different from stamp collectors, or people who try to become experts in some form of trivia. In this case we try to expand our knowledge of large numbers, and collect (or create) googolism's like a coin collector collects exotic coins.

So one key thing that characterizes us is an obsession to create the most complete picture of numbers as possible ... even though the numbers are literally infinite in extent. Where as such a state of affairs leaves most people saying "it's pointless", because it will "never be complete", we tend to see that as all the more reason to be fascinated and see just how far we can take things! This pathology to take something as far as it will humanly go is not limited to googology. It can be seen in a lot of human activities. Why did we go to the moon? To prove we could do it. Why do we have world records? To keep track of our progress towards impossible goals. Why do dare-devils risk their lives doing near-impossible stunts? Why would anyone want to row a boat around the globe when we have jet airplanes? ...

Lots of time this tendancy will come across as stupendously ludicrous/pointless and/or even dangerous. This will be especially true if there is no real incentive to take something to the absolute limit except for bragging rights. In our case, we would mostly be told it's pointless.

The closest characterization I could find for googologists is that we are eccentrics. The term eccentric has a much more positive connotation than crank.

An eccentric may appear to be "crazy" to the average person, but unlike the genuinely insane, an eccentric is not mentally impaired, and may in fact be over functioning. The key to the eccentric is not madness, but rather a simple refusal to completely obey the norm and instead define their own norm. The eccentric's pecularities are, almost by definition, benign and not terribly relevant. They can therefore function normally in society, and their odd habits can mostly be shrugged off of "oh he/she's just a little eccentric".

Cranks on the other hand are more than just merely eccentric. They insist on a radical upheaval of the current order of knowledge because they are convinced that the current model is, not just a little wrong, but completely broken at the foundation. They might write copiously, but scrutinizing the content of this writting will usually reveal an embarassing ignorance of the subject matter ... making refutation almost trivial even for the non-expert. It is for this reason, not the mere radicalness of their ideas, that they are so glibly dismissed. If their radical theory had even a slight amount of substance, experts would be much more offended. Instead they often are almost completely indifferent.

So what are googologists? Well I think the best way to describe us is that we're mathematical hobbyist's. Consider this: John Conway, the inventor of Chain arrow notation, and the game of life ... has little interest in these things. In fact he's even admitted that he found people constantly asking him about the game of life as annoying. Yet "the game of life" has become a popular subject among non-experts, "hobbyists". We may not be as bad as the cranks who send broken papers attempting to overturn well-established mathematics, but we would still be viewed as overindulgent amateurs, and not taken seriously.

While we are by no means experts, we differ from cranks considerably in our level of proficency. Where as a crank rarely has more than average knowledge in a subject (despite how much of an expert they claim to be), googologist's actually possess knowledge that ISN'T common knowledge. How many people know about epsilon-zero, let alone gamma-naught, SVO, and beyond? And this state of affairs is slowly changing. As the community gradually accumulates more knowledge we become more and more indistinguishable from the professionals. Already we can see the effects of this. There is an arms race going on and the bar for entry keeps being raised. It used to be sufficient to say your number was larger than Graham's Number, Bower's linear arrays used to be considered already quite powerful. Now days an order-type of w^w is quite a common benchmark ... for beginners! The upper-echelons have also been steadily climbing! It will be interesting to see where our community goes in the future ...

--Sbiis.ExE