Hello – my name is Anik Malcolm, and this is a video explaining the incredibly elegant mathematics I found hidden within the sacred 21 million number, as displayed in my series of works titled ‘the whole entire universe’. I sincerely hope that it can astonish you the way it has astonished me in such a profound way! Even if you’re not into numbers, there is a simple beauty to it that is undeniable:)
My original idea was to create an artwork showing ‘21 million of something’, so that people, including myself, could actually SEE what 21 million looked like.
I mentioned this to my wife una, and she responded with ‘a cube of 21 million beads’. I loved this idea, as it both used the solid cube form so common in bitcoin, and also the bead which was one of the very first methods of exchange.
So I started putting it to practice. Clearly, 21 million was not a number that would cleanly fit into a cube – its cube root is in fact 275.8924176, impractical for a neat sculpture, so I thought I could round it up to the nearest whole number, 276, and take away the surplus.
276 cubed is 21,024,576. So to make a cube of exactly 21,000,000, I would make a cube 276 beads high, wide and deep, and remove the remaining 24,576.
As it is a cube we’re dealing with, I thought it would be most symmetrically pleasing to remove the same amount from each of the six sides – which would only be possible if 24,576 were divisible by 6. To my very great delight, 24,576 divided by six yielded exactly 4,096.
At this point i started getting quietly excited, as I felt I recognised that number.
Ok. So we can remove 4096 beads from each of the six faces of the cube to give us EXACTLY 21,000,000 beads, very cool indeed. And because it’s a cube, wouldn’t the neatest way to remove a layer of beads be in the shape of a square? My hands were actually shaking a little as I punched in ‘square root of 4096’ into my calculator – and to my utter disbelief, the result was exactly 64!! So, I could actually achieve a cube containing exactly 21,000,000 beads by means of removing six identical squares from its surfaces! What were the chances of that!!? They were VERY small indeed, as I’ll explain later.
But not only that. I felt that removing the exact same square of 64×64 would be visually boring, but recognised that 64 could be divided in half over and over again – and in fact exactly another five times before the squares became individual beads – absolutely perfect for the purposes of the cube. This repeated division by two yields the pattern you see in my works – one square of 64×64, then four squares of 32×32, then 16 squares of 16×16, down to 1024 squares of 2×2. This, to me is at the same time a visual representation of the halving mechanism so integral to the entire paradigm of bitcoin’s mechanics and function, but also the exponential growth that is a direct result of that halving. To me, it is a still life of Bitcoin itself – the most literal depiction of it that could be created, and in such an incredibly elegant manner. I can say this because I didn’t create it – I merely found it there waiting to be discovered in all its mathematical beauty.
One could say that you can find mathematical patterns anywhere if you look hard enough, and after having discovered this I looked VERY hard to see how common this pattern is, allowing for the same power-of-two halving pattern with a clean, round number like 21M. It turns out that this is the smallest number with which it is possible – the next smallest is 1.344 billion, after which it shoots into the trillions and quadrillions. The sheer size of the other numbers in the set, whether based on 64, 128, or further up the powers of two make it very obvious how
exceedingly unlikely it is that such mathematical elegance would apply to our sacred 21 million number, and how fortunate we are to be able to be able to see it so beautifully and symbolically.
My name is Anik Malcolm. I hope you’ve derived some of the pleasure that I have from this presentation. And who knows – maybe you can see a further pattern within that I had missed!