Since leaving university, I have tried to find any excuse to
use the mathematics that I learned there in everyday life, even if a lecturer
did tell us that it would be difficult. It always makes me think back to when I
would use maths as procrastination from maths during exam season.
A set is defined to be a collection of well defined distinct
objects, often being of numbers, for example:
{0,1,2,3}.
You can have a set containing anything though. Another
example would be the set containing the years that Liverpool have won the
Premier League, ∅.
This is the empty set, and is a subset of every possible set. Now let’s
consider a set S. The power set of S, written P(S), is a set itself containing
every possible subset of S. If you found that sentence harder to unscramble
than an egg I do not blame you, so it is best that I give an example: If
S
= {1,2,3},
P(S)
= {∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} }.
I used to think as a power set as every possible
crossover between the elements in the set, as if they were films to be made,
but we’ll come back to this later.
When I was younger I had no objection to superhero
movies. Being a child who was easily entertained and subsequently thought that
every film I saw was the greatest thing ever, I quite obviously enjoyed them.
There came a point though where they just began to annoy me, with their
somewhat copy and paste storylines and somebody defying all probability yet
again. There are a few exceptions to the rule of course, The Dark Knight and
Deadpool to name a couple, but on the whole, they are usually not for me. I thought, at what point will they run out? A quick Google search when I was meant to be
revising for my final exams found that there are around 947 of them (although I
copy and pasted the superheroes list straight from the marvel website, deleting
any duplicates and it came out closer to 1250, so we’ll just play it safe
here and stick to 947).
Scrolling through this giant list made for a good
laugh. Some superhero names are pretty cool, but then again you put two cool
words together and hey presto! Any 10-year-old could nail it: Black Panther,
Hawkeye, Steel Serpent and my favourite... Mathemaniac. Not sure what
Mathemaniac’s superpower could be though, maybe he can total the price of his
weekly shop before he gets to the checkout or something. The cool names are
short lived though. There are 10 superheroes or villains that start with ‘Mr.’
and 8 that start with ‘Captain’. Then there are some that must have been thought up at 5-to-5 on a
Friday with names like; Bloke, which accurately describes him I suppose but the
naming here is about as lazy as Garfield and Homer Simpson holidaying in The
Maldives together; Giant Man, which suggests he may be a giant man, but who can
really be sure, and; Hindsight Lad, I am not making this up. I can only imagine
this is some guy walking around in a cape who keeps telling people he meets at
checkouts or in locker rooms that he wishes he travelled more or that he
bet on Leicester City to win the Premier League. But we are just getting
started. Those are just the lazy names. All of these names only strengthened my annoyance towards most
superheroes as I continued this list. There are;
Spider-Ham, a joke in The Simpsons Movie and not surprisingly, as a comic too;
Xavin, what is he Xavin, his face? 3-D man, or as I like to refer to him, Man.
Then the final 3 sound like a Pokémon evolution line, being Namar, Namora and
Namorita.
Insults aside, let us have the set S being the set
containing the approximate 947 marvel superheroes. You can call the set
anything, but ‘S’ is easy as it stands for superhero, although the word
superfluous is a better fit.
S
= {Ant-Man, Banshee, Bloke, Hindsight Lad, Iron Man…}
When you have a set of elements, you can see that
all the elements in its power set can be divided into how many elements each
set has. To easier visualise this, consult the examples below. Assume we have
some set X of 4 or more elements. The number of subsets of X that contain
themselves 2 elements can be found with the formula below. This formula does
not change, no matter how big X is.
We can repeat this to find the number of subsets of
size 3, 4, 5, up to any number you want. When you add up all of these
quantities, they sum to 2n
elements in the power set of X, or in our example, S. As we are looking at
film crossovers though, we will minus 1 as the empty set ∅ would be a film containing no
superheroes, but this will make no noticeable difference to our outcome, as 2n
in the case of S, is going to get more out of hand than a wet bar of soap.
Now we see that there are just under half a million 2-character
crossovers between all marvel characters, which let’s assume you can watch 8
films a day, would total a time of over 153 years to watch them all. 3 and 4-character
crossovers increase each time up until 473 and back down again in the shape of
a standard deviation correlation, so just how many can we get?
I
have been watching a lot of maths and science based, very interesting videos on
YouTube recently on a channel called ‘Vsauce’. Here is the video, entitled ‘How Many Things Are There?’, which caught my attention most.
In
the video, Michael approximates the possible number of thoughts that our
universe could have before a googol (10100) years has past and there
is no usable energy left in the universe. First he takes the approximate mass of the
universe, 3.4 x 1060kg and the fastest possible computing limit due to
the speed of light and the uncertainty principle (called Bremermann’s limit) 1.36 x 1050bits
sec-1 kg-1. Using these he simulates making the universe into a universe sized supercomputer that estimates that for the 3.154 x 10116
seconds that the universe has left, there are 1.458 x 10227 thoughts
that could be thought. This is assuming that each thought takes about 1
sentence, or 800 bits worth of information. This is an interesting result when
it comes to the amount of superhero movies there could ‘possibly’ be…
So now we just need to plug in the numbers. 2n-1 gives the number of crossover films for a group of superheroes of size n, which we
find to be in the case of n=947 is
5.80866
x 10281,
making them literally unthinkable. Thanks for reading.
No comments:
Post a Comment