Tag: Archimedes

Beyond Straight Lines
Do these two statements contradict each other?
1. The shortest distance between two points is a straight line. ~Archimedes
2. There are no straight lines in nature. ~Antoni Gaudi
Archimedes is arguably one of the smartest human beings to have ever lived, and I mean that with absolutely zero hyperbole. He’s most commonly known for shouting “Eureka!” as he got into a bath as he realized the amount of water displaced from the tub was equal to the volume his body occupied, and for the water screw which is still in use today in many places.
In the late 90’s a book sold at auction for $2,000,000 was discovered to be a palimpsest containing 7 treatise written by Archimedes, and two are the only known copies of those works in the world. Researchers also discovered that Archimedes was not only familiar with the concept of infinity, but he outlines seven types of infinity. SEVEN.
1. On a geometric plane it can extend in both directions to infinity
2. There can be an infinite number of points on this plane
3. The number of straight lines drawn between two points are infinite
4. There are infinite numbers of curves possible between any two points
5. etc. etc.
It’s a fascinating story, and if you’d like to learn more about it, you can check out the Archimedes Palimpsest Organization.
This from a man who lived from 287 – c. 212 BCE.
Abstract Reasoning
What made his mind so unbelievably powerful was his ability to use logic and reason to intuit solutions in the abstract mathematical world. His strength was using his imagination to reason his way towards understanding universal truths.
With this approach, he was able to discover timeless truths about the world, and build his understanding on rock solid foundations built on logic & reason. It’s an incredibly powerful ability to pull order from absolute chaos. This is the way of fighting entropy and decay; find answers that are beyond the mere considerations of this broken-down world we live in; truth lives in a universe beyond the scope of time & space. This is the world of First Principles.
But, What About the World of Gaudi?
Antoni Gaudí was an architect born in 1852, and died in 1926. His buildings look like Dr. Seuss drawings brought to life, and they’re absolutely gorgeous. If you’d like to see examples of his work, click here for a Google image search.
His work “Sagrada Família” in Barcelona looks like a sand castle brought to life, and it will be finished 100 years after his death. It’s a testament to the enduring power of his work.
He recognized that in the world of nature, there are no straight lines. Even the unerring line of the horizon is actually a curve so large it only appears straight to us.
And there lies his genius.
Gaudi lives in the realm of nature. In the real world. Archimedes lives in the realm of abstract mathematics.
The world that human beings live in never moves in a straight line. It’s curved. It’s messy. It’s pure chaos.
The World of Chaos
This fundamental truth about the world we live in is the reason why the most elegant, simple answers lack mathematical beauty. They twist, they turn.
In the real world, indirect is more effective than the direct.
Success is usually the byproduct of aiming at something else. The straight line approach is often the longest way to get somewhere.
Training Artificial Intelligence
There’s a fascinating exploration in the world of AI that shows us this counter intuitive truth.
Researchers built systems that were allowed to play inside their environment without any specific goal or outcome; it was given free reign to discover what it could do on its own.
Later, researchers would establish a specific goal and see how long it would take the system to achieve it. After that, they would increase the difficulty by introducing a variety of obstacles and challenges.
The AI system took longer in the second case to achieve the goal, but was still able to do what was asked of it.
The Wrinkle
Here’s where things got interesting: AI systems built specifically to complete the task were almost completely unable to accommodate the simplest obstacle or challenge.
The most direct approach (design the tool to do the task) wound up being the least effective when presented with anything other than an optimal environment. The roundabout solution (design the tool to play on it’s own) takes more time & resources, but winds up being profoundly effective even in the face of insurmountable difficulty.
Our World
You might live in a perfect fairy tale world, but I sure as hell don’t. I face challenges, obstacles, and frustrations every day.
That’s why the direct approach rarely works in any context; whether it’s in relationships, a physical confrontation, business plan, marketing, or any other situation involving humans.
In ideal situations, yes, the abstract world of logic & reason will serve you well. But, we live in a crazy, chaotic swirl of doubt and uncertainty.
That’s why success is often the result of trying something else.
Want to make tons of money? Don’t focus on making money. Focus on solving peoples’ problems; the money will follow.
Want an amazing romantic partner? Don’t focus on finding someone. Focus on being an incredible person who has a lot to offer, and your match will show up.
Real World Success
Whatever you want to do in life, don’t aim at it. Look to what naturally creates that successful outcome, and then focus all your energy on that.
Live in the beautiful, organic, curvy world of Gaudi, not the world of Archimedes (no matter how much you love clean lines).
May 13, 2021
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.

March 8, 2021