Quantum Fables

Notes on
Experiment 01

Arjuna's Hesitation, and what the mathematics turned out to say.

Read the fable first

This page explains how the piece works, including the one thing it withholds while you are inside it. Knowing that in advance removes the only surprise the work has.

Read Arjuna's Hesitation, then come back.

Why the Gita gets pilot wave

The Gita is usually summarised as a book about choosing well. It is not. In the eighteenth chapter Krishna closes the argument by telling Arjuna the choice was never open. If from ego you resolve I will not fight, that resolve is vain, because your own nature will compel you. What you refuse through delusion, you will do anyway.

So Arjuna's paralysis is real and his branching is not. Krishna is not offering a menu. He is offering sight.

Pilot-wave mechanics says the same thing in different words. The outcome was always fixed by a variable you cannot see, and a guiding field carries the trajectory. What looks like chance is your ignorance of it.

You look for me across the field, Arjuna. But I am not across from you. I am the field, and the seeing of it. Krishna, in the fable

That line was written first, before any of the machinery, and it describes a guiding field. Most of the work on this experiment was making the machine agree with the sentence.

How the state is built

Four paths are two qubits. Choosing what the two axes mean is the authorial decision, and everything else follows from it.

settled unsettled engage withdraw FIGHT |00〉 SEEK |01〉 REFUSE |10〉 DOUBT |11〉
Fight and refuse are both settled and differ in whether you stay. Seek and doubt are both unsettled. Every choice is a rotation in this plane.

Here is the part the fable withholds. The state vector is not what Arjuna is. It is what he can see. His svabhava, his nature and therefore his path, is a hidden variable seeded before the first click and never sampled.

So the meter is not the odds of becoming. It is how clearly you see something already fixed. Your choices sharpen or cloud that. They do not move it, and we check that: five hundred arbitrary choices never shift the seeded path.

Measurement reveals. It never selects. Beginning again returns the same answer, and from the second visit the piece says so.

Four things we did not write

01The openness curve

Asking Krishna who he really is applies one Grover iteration, rotating the state toward the answer the field already holds. On four outcomes Grover is certain after one query, but only from perfect openness.

These are rounded means over every equally weighted sequence of the four questions, with immediate repeats included. They are not what every single reading will produce. After three questions, individual clarity ranges from 4.4 to 90.1 percent.

That is a theorem about a search algorithm. It is also the clearest statement of the teaching anywhere in the piece.

02A line that predicted its own mechanism

The teaching for the path of stillness was written early, long before this machinery existed.

Clarity is not forced.
It arrives when the noise softens.

That is a description of the table above.

03Interference

Amplitudes carry phase and the operators do not commute, so the order of your questions changes where you land. Duty and then the faces you love leaves you at fight 41.5 percent. Reversed, 30.9 percent.

Two ways of looking can also cancel, leaving you seeing less than before. The piece detects this and tells you when it happens.

04The wider field overshoots

The optional wider field uses three qubits and eight basis states. From perfect openness, standard Grover amplification raises the hidden state from 12.5 percent to 78.1 percent after one turn, then to 94.5 percent after two.

A third turn does not produce certainty. It overshoots and lowers the hidden state to 33.0 percent. Beginning from a field whose amplitudes already carry a shape leaves still more probability on the other states.

Checked, and claimed

The physics is checked. Evolution is unitary, so across two hundred thousand seeded random choice sequences the norm stays within 1e-15 of one. The meter reads the same array the reveal uses, so the shown odds and the real odds are one thing rather than two kept in agreement.

pnpm run test:quantum

  unitarity across 200,000 sequences ....... max |norm-1| 6.66e-16
  Born non-negativity ..................... pass
  order dependence ....................... pass
  Grover from uniform openness ............ clarity 1.000000
  mean after 3 uniform questions .......... 0.4814096
  three-qubit two-turn peak ............... 0.9453125
  three-qubit third-turn overshoot ........ 0.3300781
  fixed reveal and persisted destinations . pass

The decomposition is not checked, because it is not that kind of thing. Deciding these four paths factor into engage against withdraw, and settled against unsettled, is a claim about what the endings have to do with each other. A different pair of axes would be a different fable with the same four names.

Details

Adding ?reseed to the fable's address draws a new nature. Without it the piece remembers permanently, which is the point.

Reader state lives in localStorage. Nothing is sent anywhere and there is no analytics.

The four teachings are newly written and are not text of the Bhagavad Gita. Each ending separately offers a short traditional parallel from Annie Besant's 1922 fourth-edition translation. Those excerpts are public domain and link to the corresponding discourse on Wikisource. The imagery is synthetic.