Infinity, or not?

I heard someone ask recently;
"What is the biggest number?".

Googol X Googolplex to the power of Grahams Number? Perhaps?

Apparently, 'Grahams Number' currently holds the record, as proved in the 1980 edition of Guiness World Records. Being too large to communicate, calculate or indeed even write down. They say that every atom in the visible universe could have a zero written on it and there just wouldn't be enough atoms to complete the task of writing down, fully, Grahams Number.

The question should be, is there really any real use for such a large number?

Specific integers known to be far larger than Graham's number have since appeared in many serious mathematical proofs (e.g., in connection with Friedman's various finite forms of Kruskal's theorem).

Perhaps, if you had a spaceship capable of Inter-Galactic travel, the mile counter would need to go to such high numbers. But even then, I would heartily recommend that your spaceship's counter be set to measure Light Year's instead, far more usable for spaceship servicing purposes.

So, infinity...

I particularly like the idea of The Infinite Monkey Theorem. A single monkey tapping away at a keyboard for 14 billion years could supposedly and accidentally tap out on a type writer the complete works of Shakespeare ~That's one tired monkey! Given an infinite universe and an infinite amount of monkeys doing the same job, the task would be completed an infinite amount of times.

Improbable? Of course! but still possible within the constraints of the 'infinite' universe.

The Infinite Hotel or Hilbert's Paradox of the Grand Hotel, is a good way to describe the nature of the concept of infinity. A hotel with infinite amount of rooms should never get fully booked. and even if it did, there would always be more, because it's infinite. Of course.

If I were to take three of my mates to this hotel, to hear that they were fully booked, you could argue;

infinity+3=infinity
Just as;
infinity+infinity=infinity
There is just no moving away from the number of 'infinity' once it has been added to an equation. Even if one, two, three or indeed an infinite amount of people were to leave the hotel, it remains the same;
infinity-3=infinity
infinity-infinity=infinity (or 0 ~there are many paradoxes)

I believe, that the biggest or largest 'real' number, has to be related to the smallest and most abundant thing in the known universe, which is probably a quark - or if future science allows, could be something even smaller than that, as they too have to surely be made of something.

Now, once you've counted them all, there surely is no need for a bigger number? Even though theoretically there could be.

Therein lies the wall of necessity, once you've counted ALL of the smallest things in our visible universe there can be no bigger number. So in my humble view, that then is the largest number (that we should care about anyway), and not infinity.

To imply infinity, is to imply an infinite Universe. To do that (as is the true nature of being a scientist), we would have to have travelled to the very edge of all matter to determine if there indeed is an edge or not, thereby proving or disproving 'infinity' either way. Until then, its all mumbo jumbo at the 'Hotel Infinity' LOL

All sky view of the Visible Universe

I may still be 'pro' to some ideals of the infinity concept, barring paradoxes of course.

Ideals like; there may be identical planets to ours, with identical people like us and even someone identical to me or you. Put aside any theory of parallel universe's and the like and consider this;

Given that the total matter (building blocks of everything in the universe) available to us is finite and certainly countable, there can only be so many ways that these building blocks can be put together before you start seeing duplicates. And then duplicates of duplicates of duplicates.

So;

In a simple universe example, where only two different atoms exist. In sets of four there can only be 16 different variations of the set's of four containing only two different atoms. hence any further additions to the 16, will inevitably be identical to at least one of the original sixteen sets;

2 to the 2 to the 2

With this formula in mind, we could effectively evaluate, that given that we can calculate the amount of different building blocks available in the visible universe, we can run the exponential of itself twice then divide by the diameter of the visible universe, thus giving us an estimated distance of how far we would have to travel to find an 'almost' identical version of oneself, on an 'almost' identical planet. I'll forgo the math on that one lol

While sounding somewhat far-fetched, the current understanding of our visible universe is easily large enough to accommodate such a formula.

Our Earth, for instance, is an incandescent, almost invisible to outsiders, irrelevant little piece of rock orbiting a very very average star of 400 Billion stars in our Galaxy alone, while our Galaxy is one of many Billion's just like it in the Virgo Supercluster, which also is one of Billions of clusters of Galaxy's within our known universe.

Virgo Supercluster

The distance that is calculated from this formula, is of course farther away than any human can currently travel, or indeed comprehend, thus making the exercise pointless per say, but still important to differentiate the term 'infinity' from actual real math.

Maybe one day we will be able to travel said distance. And maybe we will want to know if there is an identical 'me' out there. Although also improbable.

This is not infinity. This is just simple math.

It was said recently by a man who's name I forget, "Infinity, may or may not exist. God, may or may not exist. But what remains true, is that neither Infinity nor God have a place in Mathematics".