Why do Black Holes and Blockchain Use the Same Math?

On the foothills of the Himalayas, a science enthusiast named Samsara had one goal: to protect his family’s secret Mo:mo recipe. While stargazing, he imagined hiding it inside a black hole, where nothing escapes once it goes in.

But there was a catch, putting something into a black hole might mean getting trapped yourself, like a lost astronaut in the movie Interstellar. That sparked an idea, what if he could recreate the security of a black hole using math, but without the risk?

Samsara had been taking online Cryptography class during which he discovered blockchain technology, a system where, once data is added, it can’t be changed or erased. It reminded him of a black hole: once something enters, it’s there forever.

He realized both systems use mathematics to protect information, making it nearly impossible to access or tamper with and got inspired to use it to hide his secret recipe.

But how do black holes and blockchains actually work and why do they seem so similar?

Let’s explore.

Black Hole

Before we can understand the connection between black holes and information, we need to understand what black holes actually are, and what happens when information falls into them.

What is Black Hole?

A black hole is a region of spacetime where gravity is so strong that nothing—not even light—can escape from it once past the event horizon. This point of no return is what makes black holes so fascinating and terrifying.

Black holes aren’t cosmic vacuum cleaners, they are more like cosmic information processors. When matter falls into a black hole, it doesn’t simply disappear. Its information is thought to be encoded on the event horizon, according to the holographic principle.

Hawking Radiation & The Information Paradox

In the 1970s, physicist Stephen Hawking made a groundbreaking discovery: black holes aren’t completely black. They emit a faint thermal radiation, now known as Hawking radiation, due to quantum effects near the event horizon. This led to a shocking paradox:

If black holes eventually evaporate through Hawking radiation, what happens to all the information that fell in? Is information truly destroyed, or is it somehow preserved?

If the black hole disappears, does the information vanish too? That would violate a core law of quantum mechanics: information cannot be destroyed. This dilemma known as the black hole information paradox has puzzled physicists for decades.

The Holographic Principle

A compelling solution to this paradox is offered by the holographic principle, proposed by physicist Leonard Susskind. It suggests that all the information inside a black hole is actually encoded on its two-dimensional surface, not within its three-dimensional volume.

In other words, the event horizon acts as a kind of hologram that perfectly encodes all the information that ever fell into the black hole. This leads to the Bekenstein-Hawking entropy formula, which states that a black hole’s entropy is proportional to the area of its event horizon, not its volume.

Where:

• S is the entropy of the black hole
• k is Boltzmann’s constant
• A is the area of the event horizon
• ℓₚ is the Planck length

Unlike ordinary objects, the entropy of a black hole is proportional to its surface area, not its volume. That’s like storing the content of a book not in its pages, but as a pattern on its cover

This formula marks the beginning of a deep and surprising connection between gravity, thermodynamics, and information theory, a connection that will soon echo in how we think about cryptographic hashes and blockchains.

Information

Now that we’ve explored black holes and their mysterious relationship with entropy, let’s take a moment to understand what information means mathematically.

Claude Shannon: The Father of Information Theory

In 1948, mathematician Claude Shannon published A Mathematical Theory of Communication, essentially founding the field of information theory. He was also the pioneer who connected Boolean algebra with logic circuits, laying the foundation for digital computing.

Shannon’s breakthrough was to treat information not as vague meaning, but as measurable uncertainty. According to him, the more surprising or unpredictable a message is, the more information it contains. A message that is completely predictable contains no new information.

Example:

Flipping a fair coin has 1 bit of entropy — there’s a 50/50 chance
(surprise exists), so it’s unpredictable. But if you always flip
"heads", then it contains zero bits of entropy you already know
the outcome (no surprises).

Shannon Entropy: Measuring Information

To quantify this concept, Shannon introduced a measure called entropy. Shannon entropy quantifies the amount of uncertainty or randomness in a system. It’s calculated based on the probability distribution of possible states.

High entropy corresponds to high unpredictability, which means more information content. For example, a string of random characters has high entropy, while a string of the same character repeated has low entropy.

High Entropy

Xf7@q!Zp#9tL\*mR2 -> Hard to predict, high information content

Low Entropy

Aaaaaaaaaaaaaaaaa -> Easy to predict, low information content

Information Entropy vs Physical Entropy

Remarkably, this mathematical concept of entropy is deeply connected to the physical concept of entropy in thermodynamics. Both measure disorder or unpredictability in a system. This connection is not just an analogy it’s a fundamental relationship that links information theory to physics.

When physicists like Hawking and Bekenstein calculated the entropy of black holes, they were essentially calculating how much information a black hole can encode. Similarly, when we calculate the entropy of a message, we’re determining how much information it contains.

We now see that information, randomness, and entropy are not just abstract but are foundational forces in both physics and computation. And the same math that helps us measure information loss in black holes also powers the security of cryptographic systems, like hash functions and blockchains.

Hash Function

Now we’re ready to make a connection between black holes and modern cryptography. The key lies in understanding what cryptographers call hash functions: the digital equivalent of black holes.

What is a Hash Function?

A hash function is an algorithm that takes an input (or “message”) of any length and produces a fixed-size output, called a hash or digest. A good cryptographic hash function like SHA-256 (which stands for Secure Hash Algorithm, 256 bits) has several critical properties:

• One-way function: It’s computationally infeasible to reverse the process i.e. you cannot determine the original input just by looking at the hash.
• Deterministic: The same input always produces the same hash output.
• Avalanche effect: A small change in the input creates a dramatically different output hash.
• Collision resistant: It’s extremely difficult to find two different inputs that produce the same hash output.

Does any of this sound familiar? A one-way function that transforms inputs in an irreversible way, yet somehow preserves the information? That’s exactly what black holes do with physical information!

Why Hash Functions Work

Hash functions act as information compressors. They take an arbitrarily large input and encode it into a compact, fixed-size output.

That’s conceptually similar to how a black hole’s surface (its event horizon) encodes all the information about what has fallen into it, regardless of how much or how complex that information is.

The strength of hash functions comes from mathematical complexity. Behind the scenes, they use a series of non-linear, irreversible operations (mixing, shifting, rotating, and scrambling data) in a way that’s easy to compute forward, but nearly impossible to undo.

Even with today’s most powerful technology (and yes, I’ll rewrite this part if quantum computers take over the world), finding a message that maps to a specific SHA-256 hash would take longer than the age of the universe.

This leads us to a beautiful analogy: Hash functions are like trapdoors - easy to fall through, but impossible to climb back up.

Once data goes in, it gets compressed, scrambled, and sealed. You can verify it was there, but you can’t reconstruct it. Just like with a black hole, you might see the resulting gravitational imprint, or the encoded information on its horizon, but the original configuration of matter is lost to you.

Blockchain

Now that we understand hash functions, let’s see how they’re used in blockchain technology, systems that preserve and secure information not with locks and keys, but with math, entropy, and irreversibility.

What is a Blockchain?

At its core, a blockchain is a distributed ledger that records transactions across many computers. Each block in the chain contains a batch of transactions, and critically, a hash that links it to the previous block.

This structure gives blockchains their most important property, once information is added to the blockchain, it becomes extremely difficult to alter. This is because changing any information in a block would change its hash, which would invalidate all subsequent blocks. To fix one block, you’d need to recompute the hashes of every subsequent block across every copy of the ledger on the network. It’s computationally infeasible.

Merkle Trees

Blockchains use a data structure called a Merkle tree to efficiently verify the integrity of large datasets. In a Merkle tree, transaction hashes are paired and hashed again, with this process repeating until there’s just one hash—the Merkle root.

This allows someone to verify that a specific transaction is included in a block without downloading the entire blockchain, they only need a small set of hashes from the Merkle tree. This is conceptually similar to the holographic principle, where the surface encodes information about the volume!

Immutability Through Mathematics

The chain structure combined with hash functions creates a system where information, once added, is secured through pure mathematics rather than through physical security or human trust.

This immutability is not absolute but probabilistic as it becomes exponentially more difficult to alter information the deeper it is in the blockchain, much like how it becomes increasingly difficult to extract information from a black hole as time passes.

Mathematical Similarities: Black Hole vs Blockchain

Entropy as a Unifying Concept

In both systems, entropy plays a crucial role. For black holes, entropy represents the maximum amount of information that can be contained within. For blockchains, the entropy in hash functions ensures that the system remains secure, and that information cannot be tampered with or reversed.

Information Conservation

Perhaps the most profound similarity is how both systems deal with information conservation. Quantum mechanics suggests that information cannot be destroyed, only transformed even in black holes. Similarly, blockchains preserve information indefinitely through their distributed ledger structure.

The Final Verdict

Samsara is at peace because his Mo:mo recipe is safe, and along the way, he uncovered powerful ideas from math and physics.

Through his journey, we’ve seen how the mathematics of information connects two seemingly different worlds: black holes and blockchains. The next time you use a digital signature, verify a cryptocurrency transaction, or ponder the mysteries of a black hole, remember that you’re witnessing the same fundamental principles at work. It’s yet another reminder of how math quietly shapes the reality around us.

But, here’s a final thought What if the universe itself is a kind of blockchain, and everything we discover is just us slowly decoding the information it has already hashed?