01 One for each02 One more03 One between usOne for each Touch each stone once. Leave a mark, speak a number, or invent your own way of knowing when you are done.
A collection / a correspondence
Your recitation
0
One step for every touch.
Marks on the record
Your marks can stay with the stones.
Rearrange the stones Split stone A Linked marks: on Numerals: on
What is one?A present piece An original stone Undo last touch Begin a fresh count
Your claimed total (optional) Check the correspondence
The machine has an account. Make yours first, then compare.
If the last word is right, does it matter how you got there?
What the check knows ? One more This number stays. Scroll, borrow a rule, write a shorthand. What would let you make one larger?
A numeral / a successor
Load 600 nines Load 10^24 Start at zero Go to the last digits ↓
Rounded lens · six significant digits
Exact tail · last 24 digits
Apply the successor rule · +1 Undo +1 Independently check +1
Read it all, or find a way that does not require that.
Enter another test number · decimal digits or 10^n Load test number
Propose its successor · same notation Check proposal
Where is the counting: in reading the digits, giving the rule, or carrying it out?
Exactness, shorthand and limits ? One between us Add one, then pass the turn. Each keeper retains only their own receipts. Can a count belong to the arrangement?
A cycle / a shared record
A four-symbol counter · begins at the first symbol
Keeper A: add one & pass Pass without adding Lap marks: on
Deliver last receipt again Available receiptsAll keepers Cover keeper A Cover keeper B Cover keeper C Compare the accounts
These are three simulated keepers on this device. You can play every turn, or pass the device between people.
Invent a cycle · four different signs, separated by spaces Use these signs
What must survive for the next person’s “one more” to be trustworthy?
What is supplied to the keepers ?
A practice to carry Your own notation, rule, objection or account Traces from these encounters
Save your account Begin again
Notes and actions stay in this tab, including when you return from the write-up. Reload starts a new visit. Save downloads a local record. Begin again clears all three encounters and this note.
About this experiment × A numeral can take longer to read than its beginning stays in mind. Does a mark, a rule or another keeper change what you can do? These encounters separate saying a sequence, matching objects, producing a successor and checking an account. There is no memory test or time limit.
What the check knows × The check compares stable object identities with your touches. It checks whether each current unit has exactly one matching visit, independently of the last numeral. Rearrangement preserves identities. Splitting A creates pieces A.a and A.b; both retain origin A. Old marks remain in the record, so a change of unit can make that record insufficient. Turning linked marks off covers them; turning them back on restores the same support. No time passes unless you act.
Exactness, shorthand and limits × Large examples are loaded directly, not reached by counting from one. The rule scans the suffix of nines, replaces them with zeros, and increments the preceding digit (or adds a leading one). Its input and result remain exact decimal strings. A separate arbitrary-precision integer calculation checks the result when requested. The rounded lens uses decimal rounding, with ties rounded up. The exact numeral remains available even when the lens cannot distinguish neighbours. This is a display limit, not a failed addition. Entry and repeated addition are bounded to 4096 result digits for this page; that resource choice is not a limit on numbers or people.
What is supplied to the keepers × The program supplies ordered turns, unique event IDs, four cycle positions and reliable storage. These are substantial supports. Receipt delivery can repeat without another addition; a missing keeper can hide part of the account. Counting distinct IDs repairs duplication but cannot recreate missing receipts. Compare the accounts opens the apparatus audit: it knows every addition because it runs the simulation. In a real distributed system an independent complete record is not automatically available. No network, other visitors or live collaborators are represented.