We measure on average 1.70 meters (about 5 feet 7 inches). A common height that seems normal in our human-scale world. Yet, when we compare it to the smallest and largest conceivable distances in the Universe, our size takes on a dizzying significance. What is the middle of infinities? Are we closer to the minuscule or the gigantic? The answer is less intuitive than it seems.
Let's start at the bottom of the scale: the infinitely small. The smallest known theoretical "piece" of space is the Planck length, approximately 1.6 × 10⁻³⁵ meters. At this size, we're no longer talking about atoms or even particles. The laws of physics as we know them simply cease to apply: space and time become grainy, as if losing their continuity. This is perhaps where the ultimate boundary of matter lies.
To give an idea, an atom measures about 10⁻¹⁰ meters, and its nucleus about 10⁻¹⁵ meters. In other words, an atomic nucleus is already about one hundred billion billion times larger than the Planck length. If we could enlarge a proton to the size of the Solar System, the Planck length would then be on the order of a virus. It is at this scale that physicists believe gravity and quantum mechanics converge.
At the other end of the spectrum lies the infinitely large. The observable Universe, meaning everything whose light has reached us since the Big Bang, has a radius of about 4.4 × 10²⁶ meters, or 46,5 billion light-years, or 92 billion in diameter. It is a colossal sphere of galaxies, void, dark matter and dark energy. And this is probably only a portion of the total Universe, much vaster, perhaps infinite.
Between the Planck length (10⁻³⁵ m) and the observable Universe (8.8 × 10²⁶ m), there exists a scale of 10⁶¹ orders of magnitude. In other words, we must multiply the smallest length by a 1 followed by 61 zeros to reach the largest. And the human being, with its 1.70 meters (about 5 feet 7 inches), lies somewhere between the two. But where exactly?
We notice that at the meter scale, we are about 10³⁵ times larger than the Planck length and about 10²⁶ times smaller than the observable Universe. In other words, our size is 35 orders of magnitude above the smallest and 26 orders below the largest. This means we are much closer to the gigantic than to the minuscule.
What matters is the logarithmic scale—that is, a scale where each step corresponds to a factor of 10—and we are then only slightly shifted toward the "large." If we were to look for the middle between the two extremes, it would be around 10⁻⁴ meters, or about 0.1 millimeters: the thickness of a human hair.
The thickness of a hair: this is therefore the middle of the two infinities, on a logarithmic scale, and something we can distinguish with the naked eye. We, with our 1.70 meters (about 5 feet 7 inches), are then about 17,000 times larger than this "center of the Universe of sizes."
The middle of infinities on a logarithmic scale: the hair.
Illustration image Pixabay
This vertigo of scales reminds us how limited our perception is. We live at a size where we perceive certain laws of physics, called "classical," where we can grasp objects, walk, breathe. From the subatomic quantum grain to galaxy clusters, we have our place in the midst of cosmic vertigo. Humanity is not lost between two extremes: it is a conscious link between nothing and everything.