Today’s post is by Dr. Tim Stafford. You can follow him on Substack as well.
The Two Marbles and the Hidden Difference
Imagine sitting at a table with a friend. They hold two identical plastic cups, and beneath each cup is a marble—one red, one blue.
You cannot see the marbles.
Your friend insists, “These marbles are different colors.”
You say, “Prove it.”
But they add a twist: “I want to convince you that the marbles are different—without ever showing you the colors.”
You scoff. That’s impossible, isn’t it? How can someone prove a difference if they’re forbidden to disclose what the difference is?
But your friend proposes a clever game:
- They lift both cups, peek, then replace them. You still see nothing.
- You close your eyes.
- While your eyes are shut, they may or may not swap the two cups.
- You open your eyes.
- You now challenge them: “Did you switch them or not?”
- They answer.
- You repeat this as many times as you like.
If the marbles are the same, your friend is just guessing. Over many rounds, they’ll eventually slip up. But if the marbles are different, your friend can track which is which—without ever showing you the marbles themselves.
After enough repetitions, you are convinced: the marbles are different, though you’ve never once seen their colors.
This is not deception. It’s conviction by design.
And that’s the architecture behind zero-knowledge proofs—and perhaps more surprisingly, it offers a lens through which to understand something ancient and sacred:
Faith—as the assurance of things hoped for, the conviction of things not seen (Hebrews 11:1).
What Is Faith, Really?
We must free the word faith from the tired and false dichotomy that equates it with blind belief or wishful thinking. In the Christian tradition—particularly in Hebrews—faith is a structured confidence:
“Now faith is the assurance of things hoped for, the conviction of things not seen.” (Hebrews 11:1)
This is not a psychological crutch. It is a way of knowing that is not dependent on sight, but on trust grounded in reliability. Faith is rational trust in a hidden truth—a trust earned not by proof in the strict sense, but by pattern, experience, and existential depth.
Faith is not what you have when proof is absent. It is the natural response to being encountered by a truth that refuses to disclose itself entirely—perhaps because it is too great, too holy, or too relational to be grasped like a scientific equation.
Zero-Knowledge Proofs: The Hidden Logic of Conviction
In modern cryptography, a zero-knowledge proof (ZKP) allows someone to convince another that they know a truth, without revealing the content of that truth.
It’s used in real-world applications:
- To prove you know a password without typing it out.
- To verify you’re over 18 without sharing your birthday.
- To confirm you possess some knowledge, identity, or credential without exposing it.
And it all rests on three properties:
- Completeness – If the statement is true, an honest prover will convince the verifier.
- Soundness – If the statement is false, no dishonest prover can consistently fool the verifier.
- Zero-Knowledge – The verifier learns nothing about the secret itself.
The two marbles game is a textbook illustration of this structure. The content (colors) remain hidden. But through repeated interaction, the truth is revealed in structure, not in substance.
You come to believe—not because you’ve seen the truth—but because you’ve watched the process, and the process has proven trustworthy.
Theology and the Logic of Hiddenness
This cryptographic insight opens a profound theological question:
Might faith function like a spiritual zero-knowledge proof?
That is: Can a person be rationally convinced of the reality of God without seeing God directly?
Let’s trace the parallels.
Faith (Hebrews 11)
- Conviction of what is not seen
- Trust grounded in relationship and history
- Hiddenness preserves human freedom
- Requires repetition and fidelity
- Meaning is existential, transformative
Zero-Knowledge Proof (ZKP)
- Verifier convinced without disclosure
- Trust grounded in protocol and repetition
- Secrecy preserves user privacy
- Requires multiple rounds and consistency
- Meaning is formal, verifiable
In both cases, conviction emerges not from what is seen, but from how one is engaged.
This is why the game works: the act of swapping or not swapping becomes a space of revelation. Likewise, God—hidden, veiled—can still be known through creation, conscience, Scripture, history, and inner encounter. These are not the full unveiling, but enough to reveal trustworthiness.
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The Philosophers: Kierkegaard, Augustine, and the Hidden God
Kierkegaard: The Risk of Relationship
Kierkegaard, father of Christian existentialism, insisted that faith must be risky. There can be no mathematical certainty in love. If God were laid bare like an equation, there would be no possibility of faith—only coercion.
“Without risk, there is no faith. Faith is precisely the contradiction between the infinite passion of the individual’s inwardness and the objective uncertainty.”
— Concluding Unscientific Postscript
Zero-knowledge proofs give us a structure for understanding this paradox: proofs that do not disclose, but still convince.
Augustine: The Logos Behind Logic
Augustine’s vision was that truth is not a construct, but a participation in divine reason—the Logos. When we encounter logical coherence, mathematical beauty, or moral clarity, we are not inventing truth—we are encountering God indirectly.
“The truth is neither in you nor in me, but above both of us.”
— Confessions, Book XII
Zero-knowledge proofs function in this same horizon: truths affirmed above the surface of disclosure. The logic works even when the content is hidden.
Why Hiddenness Is Not Absence
In an age obsessed with exposure, “transparency” becomes a false idol. We assume that only what is visible can be trusted.
But in both theology and cryptography, we are reminded: not everything true is visible. And not everything visible is trustworthy.
Faith, like a ZKP, asks: Can you see the pattern? Can you trust the integrity? Can you accept that truth, in some forms, does not need to be shown to be known?
What’s radical is that both cryptographers and mystics agree: the highest forms of trust occur where disclosure ends, and relational fidelity begins.
A Sacred Mode of Knowing
You never saw the colors of the marbles. But over time, you became convinced.
Not through exposure, but through encounter.
This is the deep logic of both zero-knowledge proofs and biblical faith: conviction without disclosure.
Not because God is absent, but because God refuses to become an object—something to be handled, proved, or reduced.
In faith, we are invited not into certainty-by-sight, but into relationship-by-trust. And it is there—beneath the plastic cups, in the repeated gesture, in the whisper behind the curtain—that the soul finds its conviction.
For Reflection (Blog Reader Addendum)
- Can something be fully trusted even if it is never fully revealed?
- Have you ever “known” something through a process rather than a proof?
- What are you asking God to reveal? And are you willing to trust what He chooses to hide?
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