Making Big Numbers

The year was ~45^2, and I was in dire trouble. My large number skills were taking heavy hits, and I was in dire trouble when someone invoked Graham's Number.

Luckily, I had a Googological notation up my sleeve. One more powerful than Graham's Number. It's based upon hyper operators. Stay for...

Holo Notation
Let's start with the simple hyper operators:

x {4} y = x ^ x ... ^x with y x's

The observant of you will notice that this is tetration. We can continue this, with

x {5} y = x {4} x ... {4} x with y x's

This is also known as "pentation" (amusingly, Google spellcheck unhelpfully thought I wanted to type "penetration").

This can then be generalised to:

x {n} y = x {n-1} x ... {n-1} x with y x's

You could then, hypothetically, imagine a number such as x {y{y}y} x. This is simplified to x {{y}} x.

To simplify the writing of Graham's Number, I also defined a second type of Holo Notation, whereby

x {n} y = x <n-2> y

And, of course, we can extend that by

x <y<y>y> x = x <<y>> x

At this point, I was ready to beat back the Graham's Number. I defined 4 <<64>> 4. The Duseedu was born.

Old Kerbal Diaries: Mun Mission

Today, I went to the Mun in Kerbal space program, and took a lot of screenshots.

Here is my spacecraft on the launchpad. The design came to me when I realised that there was no reason that the lander engines should sit idle (using up precious payload mass) until the Mun is reached. This vehicle pumps fuel from the launch boosters into the lander, where it is used by the lander engine to provide additional launch power.

The vehicle also shows that it is capable of getting to the Mun, with this glorious encounter with a periapsis of 9.7 km. The only issue is that the periapsis is on the terminator, so the braking burn will have to wait until slightly after if I want to land in the light.

Bill Kerman decides that he wants to land on the other side of that huge canyon.

And that is exactly where he lands.

Interestingly enough, on the Mun the jump height of a kerbal is almost exactly the height of my lander. That leads to the interesting situation above, where Bill is able to leap up to the hatch without using any of his EVA fuel.

Reentry is safe, quick, and nothing bad happens (except for Bill spilling his drink. Who even drinks during high acceleration reentries?).

A safe and successful landing. Next stop: Minmus!