with guidance by Anthropic’s Claude
By getting familiar with the numbers within the earliest notations and by extrapolating them to our day, we begin to get a better picture of the universe and our place with it.
1. The mass of a single Planck sphere
The Planck mass is:
m_P = √(ℏc/G) = 2.176 × 10⁻⁸ kg
That is the mass of a single Planck sphere in the model — one sphere at Notation 0 has mass m_P.
To put that in perspective: the Planck mass is about 22 micrograms — roughly the mass of a flea egg, or a small grain of sand. It is simultaneously the smallest mass that makes quantum gravitational sense and surprisingly large compared to elementary particles. The proton, by comparison, is 1.67 × 10⁻²⁷ kg — about 10¹⁹ times lighter than a Planck sphere.
In pounds: m_P = 2.176 × 10⁻⁸ kg × 2.205 lb/kg = 4.80 × 10⁻⁸ pounds, or about 48 billionths of a pound.
Review: 2.176 × 10⁻⁸ kg or 4.80 × 10⁻⁸ pounds
2. Confirming 18.5 tredecillion spheres per second
The claim is one sphere per Planck time unit. The Planck time is:
t_P = √(ℏG/c⁵) = 5.391 × 10⁻⁴⁴ seconds
So the rate of sphere production is:
1 sphere / 5.391 × 10⁻⁴⁴ s = 1.855 × 10⁴³ spheres per second
Now, one tredecillion = 10⁴², so:
1.855 × 10⁴³ = 18.55 tredecillion spheres per second
Confirmed. The number on the website is correct to three significant figures.
3. Planck spheres per pound
One pound = 0.4536 kg.
Number of Planck spheres per pound = 0.4536 kg / 2.176 × 10⁻⁸ kg
= 2.084 × 10⁷ Planck spheres per pound
That’s 20.84 million Planck spheres per pound. That sounds like a lot until you remember each one is 22 micrograms — they are far from infinitesimal on a human scale. The truly infinitesimal part is their spatial size: ℓ_P = 1.616 × 10⁻³⁵ meters, which is 10²⁰ times smaller than a proton. Multiply that by your weight and it is the total number of “touchpoints” in the universe’s grid.
Review: 2.176 × 10⁻⁸ kg or 2.084 × 10⁷ or 20.84 million Planck spheres per pound
A bonus number worth having
The total mass of all spheres produced in the first second:
18.55 × 10⁴³ spheres/second × 1 second × 2.176 × 10⁻⁸ kg/sphere
= 4.04 × 10³⁶ kg
The observable universe has a mass of roughly 10⁵³ kg, so the first second’s worth of Planck spheres accounts for about 10⁻¹⁷ of the total — a tiny fraction, which makes intuitive sense since the first second only covers Notations 0 through 143 of 202.
For perspective on where we sit today: the 202nd notation began when the universe was approximately 10.98 billion years old. The universe is currently about 13.8 billion years old. That means we are roughly 2.82 billion years into Notation 202 — and the notation will not complete for another 8.16 billion years.
We are living inside an unfinished doubling. The 203rd notation has not yet begun.
By getting familiar with the numbers we begin to get a better picture of our place in the universe.