Contemplating Impossibility

If you had asked me about this idea 10 years ago, I would have told you it's completely uninteresting to me.

Now it literally keeps me up at night.

The world of Mentalism is an unending wealth of deeply disturbing questions packaged within the wrapping of "fun" and "entertainment."

In actuality, however, it points straight to the deepest mysteries of life.

This is just one tiny thread in its rich tapestry.

Archimedes

In my estimation Archimedes was the single greatest intellect in all human history.

He dealt with massive questions that wouldn't be answered for 1500 years after his death.

Or so we thought.

Turns out he had many of the answers that were believed to be discovered centuries after his life came to an end.

He invented the "method of exhaustion" to compute the area of a circle. This approach is nearly indistinguishable from the Calculus "invented" by Sir Isaac Newton in the 1600's.

Archimedes also dabbled a field of mathematics called "combinatrics" which deals with the question of "how many ways can these finite pieces be joined together?"

Think of it like the question of "How many ways can a Rubik's Cube be mixed up?" In his day the toy was called the "Stomachion" and I find it so interesting that I used my 3D printer to create my own version:

Now, there's an interesting detail here: finite pieces.

From a very limited number of parts you can create near-infinite arrangements and relationships.

This brings us to another detail: Archimedes also dealt with Infinity. Real Infinity. Capital "I" Infinity.

Big I Infinity is a terrible thing to deal with. All sorts of beasties come out to play when you invite Infinity to the party.

Imagine you had an infinite number of whole numbers increasing by one increment. 1, 2, 3, 4, 5, and so on to real Infinity.

Now imagine you doubled each number in the sequence to Infinity. 2, 4, 6, 8, 10, etc. to Infinity.

Now you can have two Infinities of different amounts.

These genies are released into the world of mathematics and they wouldn't be properly put back in their bottles until the 1900's.

Or, so we thought.

Archimedes not only demonstrates his awareness of the issue, but shows how he can compute with Infinity in a way that goes unnoticed for 2000 years.

Stunning.

While Infinity is mind blowing in itself, smaller infinity or Potential infinity, is still worthy of our respect.

Let us look to the humble deck of playing cards in order to appreciate our insignificance.

From the world of combinatrics, we could ask, "How many ways can you arrange a deck of cards?"

Your first instinct might be to think: There are 13 values and 4 suits. Multiply them together and you get 52. But that feels a little low. So you multiply by 52 again: 2704.

Better.

Still not there.

The real number is genuinely so big your mind can't comprehend it.

Even if I put it in human terms, you still won't be able to appreciate it.

I'm still going to try.

Lifetimes

Imagine I shuffle the cards once a second every second I'm alive. Let's say I live 80 years instead of my real lifespan that I may or may not know already down to the second.

Also assume that I'm competent enough to start shuffling cards when I was 5 years old.

(Which I was, because I did.)

Imagine that I don't eat, sleep, or do anything else for 75 years.

Just one shuffle after another.

At this point, the more pedantic of you might be wondering if I account for leap year. No. No, I do not. This is already difficult enough without being silly about it.

Stop distracting me.

So for 75 years every day and night I shuffle cards. Never missing a beat. One every second. A new shuffle. A new order.

Oh, that's right, we're also assuming that I never repeat a sequence.

My entire life is devoted to shuffling.

How many lifetimes would I live before I exhaust the possibilities?

The answer?

34, 102, 052, 752, 809, 013, 432, 969, 996, 979, 707, 000, 000, 000, 000, 000, 000, 000, 000, 000 lifetimes.

Each of those is spent shuffling nonstop.

That's how many ways you can shuffle a deck of cards without repeating a sequence.

When you pick up a deck of cards and absentmindedly give them a mix, it is not just a once in a lifetime chance. It's a once in 34,102,052,752,809,013,432,969,996,979,707,000,000,000,000,000,000,000,000,000 lifetimes chance that THAT arrangement of cards comes into existence.

And then gone again the instant a single card is moved.

Is it Infinite possibility? No. There is a very real limit to the potential arrangements. Is it functionally infinite?

Absolutely.

You literally couldn't make a meaningful dent in the potential in 100 lifetimes.

The takeaway?

You have near infinite potential in nearly infinite areas of life.

And you'll never even get close to making use of any of it.

Your potential is worth nothing.

The only thing that matters is what you create with it.

For all that CAN be, it is only that which IS that makes a difference in the world.

Turn your potential kinetic.

After all, you only have one life to live.

This is why I am drawn deeper and deeper into the mysteries of playing cards.

Written & posted by Jonathan on March 8, 2021.
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A painting of Mentalist Jonathan Pritchard in the old world magic poster style.

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