# Biggest

Psychic medium in white, touches and observes her crystal ball

In her mind, the people of the future, dependent on the resources we left them, will want to replace past constructions with the newly invented.

# Metamathematicians unite!

Observe that the quantum-information 2^10^120 in number, that is processed by all the quantum-bits of our universe, is very small compared to the numbers envisioned by its inhabitant mathematicians.

Suppose we formalize a self-reflective function, that boldly generates new generations of generalized mathematicians. Let the Biggest number the initial generation comes up with quantify the (financial?) mathematical resources the next virtual generation of mathematicians can work with to expand their Biggest number, and so on.

A claim on the endless power of mathematics circumvents the problem a straightforward list of record numbers would have. This list could always end, before the true Biggest number is found.
Not to miss any opportunity, we must assume that any Bigger (than infinite?) amount of resources is available for this most squandering project of all time.

The evolution of mathematics must have begun when someone counted a number on something like a hand. That hand may not even have had five fingers, we can't tell. We just propose to index past generations by negative numbers, and leave the values of their largest numbers Μ(-n) to historians.

Start with the zeroth mathematical generation of the present universe. Then Μ(0) might equal the number Beatrix Máxima from this article, constructed by Big finite recursions or by Bigger infinities (as appropriate). It is alright to be ambivalent about our universe's Μ(0) because the Beatrix Máxima is large enough to provide the livelihood of shamefully many next Big number enthusiasts for a long long time.
When that time resource has run out (at the next date 1) the next Biggest number Μ(1) is established, etc. We express these maths generations in terms of a function like Beatrix.

Beatrix(Μ) = Μ  (our universal Máxima)
Μ,a = Μa  (next maths' Biggest)
Μ,a,X = Μ..a  (recursion over Biggest)
Μ[A],X  (beyond any Biggest)

The next number of mathematicians is determined by the Biggest variable of the current generation, fed back to its meta-recursive system. Mind you, the metamathematical structure of each Beatrix-like system is adapted by each generation (let a Smullyan-like logician work this out).

Is the Biggest number forced to grow, or is there one that cannot be adapted? An axiomatic paradox, such as Kanamori's 0=1 where the whole process stops at a Point of No Return?
Have you counted in an infinite Armada of future mathematical Columbuses?
Have you always honoured the King of Spain, eh eh? All bound for Mu Mu land!

# Most fantastic epilogue

What if we postulate a thing so high (so Biggest) that it cannot be reached by any generator function of mathematicians xor logicians? A psychic paradox Ψ that lies wholy beyond?!
Cantor and Gödel, they both succumbed to it.

To be able to add 1 in succession unlimitedly, provides for a smooth mathematical operation, but fundamentally every next number would be a new guess. Actually the existence of numbers requires similar leaps of faith in the natural world as the assumption that leaps of Ω can be counted in the infinite realm. The Axiom of Infinity ω and the successor we call 2 are lookalikes.

We've seen Beatrix function very well with natural numbers a in its base, with the infinitary Ω and with the metamathematician's Μ, which could be finite or infinite (or something more advanced) depending on the mathematical fashion of the day.
The discrete and the infinite both merge into metamathematics, what will we think of next?

Beatrix(Ψ,Z) = Ψ.. = Ψ
              0.. = 0

Even if there was some Ψ that beats all of mathematics, Beatrix would iterate over it.

Catch the beat, and if she does: it's Bigggest and stays Biggest whatever.
But don't learn Ψ in maths, for fear it becomes less, a lesson for a less son.
In this it resembles the void, as we journey from zero to Zero
There's no end to this poem, …Ι ma dead 

by Giga Gerard

People can read this article plain or choose the hard & fast & open version.