Coincidence in Unimaginable Scales of the Universe

March 27, 2025 - Reading time: 7 minutes

This story is created for the YouTube video with the title "Coincidence in Unimaginable Scales of the Universe".

In our world, a few numbers describe the sizes of the most important objects and phenomena. Among them are the sizes of a proton, DNA, a human, the Moon, the Earth, the Sun, the Solar System, the Galaxy, and the observable Universe - only a dozen numbers. Any coincidences among these numbers should spark interest because the number of possibilities is limited. One cannot dismiss strange events as mere play of chance or numerology without first examining the total number of random occurrences. And for a set of just a dozen numbers, meaningful coincidences typically indicate an underlying fundamental regularity.

Here is the list of the major scales in this universe, as we perceive them:

• Planck length 1.6 x 10^-35 meters
• Proton size 0.8 x 10^-15 meters
• Carbon Atom 1.5 x 10^-10 meters
• Diameter of Human DNA 2.5 x 10^-9 meters
• Human height 1.8 x 10⁰ meters
• Diameter of the Earth 12.9 x 10⁶ meters
• Diameter of the Sun 1.4 × 10⁹ meters
• Solar System size 1.5 x 10¹⁵ meters
• Galaxy size 9.5 x 10²⁰ meters
• Diameter of the observable Universe 8.8 x10²⁶ meters

Humans cannot easily grasp scales like 10^{-35} or 10^{26}. Such extreme numbers go against our intuition. Even the number of grains of sand on Earth is estimated to be around 10^{18}, which is much smaller than the size of the Universe in meters.

The smallest size known to humans is called the Planck length. It is an unimaginably small distance. It has a value of the order of 10^-35. This is the scale at which all existing theories break down. Science does not yet know what can happen beyond the Planck length. It can be assumed that this number reflects the physical size of the smallest information quantum.

According to theoretical physicist John Wheeler (1911-2008), every time we see an equation with a constant that reflects this size, it is a sign of the presence of the smallest quantum. As we recall, a "bit" is the fundamental unit of information measurement. Wheeler said,

"It's from a bit… Formulas with this magnitude reflect a part of physics that we have learned to translate in terms of information theory. Tomorrow we will learn to understand and express all of physics in the language of information".

He proposed that all objects in the Universe should be viewed as secondary, originating from carriers of an abstract and fundamental entity - information. Therefore, the true foundation of the physical world is information itself, not matter. Our Universe is a simulation constructed from these informational bits. As we've explored on our channel, the simulation hypothesis offers a compelling explanation for several phenomena we've observed.

In the human world, computers are made up of logic gates, the fundamental building blocks of digital circuits. These gates perform basic logical operations on binary inputs (0 or 1) and enable computers to store information. A modern computer can contain billions of logic gates.

A typical logic gate in an integrated circuit can be as small as 10^{-7} meters. If a microchip measures 10^{-3} meters in size, one can estimate the number of logic gates it contains as follows: 10^(-3)/10^(-7) = 10000.

In reality, the number of logic gates in a microchip can be much larger, as microchips come in various shapes and sizes. A single computer may contain multiple microchips.

What if the Planck length is the size of a logic gate from which everything in the universe is built, as some theorists suggest? It can be viewed as the size of a single pixel on a computer screen. This is just a hypothesis. We do not know this for sure.

But there is one thing we know for certain about information. The smallest carrier of biological information known to humans is DNA. It is a complex molecular system that contains genetic data for the functioning of an organism. Can DNA be akin to a microchip composed of logic gates at the scale of the Planck length?

Then you can ask this question: How many Planck scales are required to build the diameter of a single human DNA molecule (akin to a microchip)? Let's calculate: (2.5 x 10^-9 / 1.6^-35) ~ 1.6*10^(26)

Does this number remind you of anything? Yes, it's approximately the number of meters in the diameter of the observed Universe, which is 8.8x10²⁶. Or even more precisely - this is roughly how many heights of an average human (1.8m) are required to cover the diameter of this Universe. A difference of a few factors between these numbers is not significant when dealing with unimaginably large values spanning many orders of magnitude.

Here, we observe an astonishing cosmic coincidence in the magnitudes of numbers that are most essential to our perception of the Universe. The number of Planck-scale 'logic gates' required to encode the binary information of DNA is approximately the same as the number of length units humans use to describe the diameter of the observable Universe. If a human represents a fundamental unit of the Universe's mind, then this coincidence between the Planck scale and DNA cannot be merely a product of random chance.

We had only 10 numbers spanning about 60 orders of magnitude. A huge discrepancy was possible - one ratio could have been infinitely larger than another or smaller by many orders of magnitude. Yet, we found a match between these two simple ratios at the level of orders of magnitude. Isn't this stunning?

A skeptic might object, saying, 'People use many different numbers. One can always find numbers with similar coincidences!' But this is precisely our main point: the number of possibilities - the most important scales used to describe the smallest and largest things in the Universe - is very limited. We are concerned only with coincidences that are meaningfully related to the most essential numbers for humanity..

Somehow, the minimum and maximum scales of the Universe, along with those associated with the information of biological systems like humans, seem to reveal a hidden structure. It is an echo of a grand design, connecting humans to both the smallest and largest scales of existence. The Universe is speaking to us through the language of mathematical patterns, and we are here to decode them.

by Dr. S. V. Chekanov

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This is a full transcript of the video https://youtu.be/hBZsl65aueU?si=fDtyPzSIascRCEjj created by the DesignedWorld YouTube team using the book "The Designed World of Information: Unveiling the Incredible Realm Beyond", by Dr. Sergei V. Chekanov, 466 pages, ISBN: 9798990642836; Hardcover 9798990642843, eBook ISBN 9798990642829; Book webpage: https://ermislean.org/designed-world/