Tolerance Simulator — Find the Bug
Before you build anything, see what happens when a hole is cut too big. Drag the slider to set your small-hole tolerance, then drop a penny and see what happens.
⟁ Live Sorter Simulator
What This Is
Every computer program in the world relies on conditional logic — the ability of a machine to look at a piece of data, ask a question about it, and decide what to do next. In programming, this is an IF/THEN/ELSE statement.
A vending machine sorts mixed coins instantly without cameras or lasers — it uses a physical algorithm. Coins roll down a ramp over a series of holes. The machine asks: "Is this smaller than this threshold?" If TRUE, it drops. If FALSE, it rolls to the next question.
The Real Numbers — Why This Is Hard
A US dime measures 17.91mm across. A US penny measures 19.05mm across. The gap between them is only 1.14mm.
A tolerance of +1.5mm — which sounds small and safe — is actually larger than the entire gap between these two coins. Built that way, a penny can squeeze through a hole meant only for dimes.
| Object | Diameter | Gap to Next Size |
|---|---|---|
| Dime | 17.91mm | 1.14mm to Penny |
| Penny | 19.05mm | 5.21mm to Quarter |
| Quarter | 24.26mm | — |
The Flowchart of Gravity
A flowchart is a map of an algorithm. A diamond represents a decision (True/False); a rectangle represents an action. Your ramp is a 3D version of this exact flowchart.
[ INPUT: Mixed Objects ]
│
▼
/───────────\
/ IS IT SMALL? \
\ (< threshold) /
\───────────/
│ │
(TRUE) │ │ (FALSE)
▼ │
[ BIN 1: SMALL ] │
▼
/───────────\
/ IS IT MEDIUM? \
\ (< threshold) /
\───────────/
│ │
(TRUE) │ │ (FALSE)
▼ │
[ BIN 2: MEDIUM ] │
▼
[ BIN 3: LARGE ]
Order matters. If the questions were asked largest-first, every object would get caught by the first question — exactly the bug you can test in the simulator above.
The Full Module — Reading Mode
What This Is
Every computer program in the world relies on conditional logic — the ability of a machine to look at a piece of data, ask a question about it, and decide what to do next based on the answer. In programming, this is called an IF/THEN/ELSE statement. If you dump a handful of mixed coins into a standard vending machine, it sorts them instantly without cameras or lasers — it uses a physical algorithm. The coins roll down a ramp over a series of holes, and the machine asks a physical question at each one: is this object smaller than this threshold? If true, it drops through; if false, it rolls on to the next question. You're going to engineer a physical logic board that executes a sequential sorting algorithm using nothing but gravity, geometry, and careful measurement.
A Tolerance Correction
A first pass at this project used real US coins with a flat 1.5mm tolerance added to every hole size. That doesn't actually work, and the reason is the whole engineering lesson of this module. A US dime measures 17.91mm across. A US penny measures 19.05mm across. The gap between them is only 1.14mm — smaller than a flat 1.5mm tolerance. Built that way, a penny would be able to squeeze through the hole sized for a dime, which is exactly the failure this project's troubleshooting normally warns against, except caused by a measurement error in the plan itself rather than the builder. This guide recommends washers instead, since the builder gets to choose generous, foolproof gaps rather than being constrained by the accidents of US currency sizing, and provides a corrected, much tighter coin tolerance as an alternative for anyone who wants the history and familiarity of real currency.
The Concept
When a computer sorts a list of numbers from smallest to largest, it runs an algorithm that compares two pieces of data at a time, asking: is A smaller than B? A sorting machine asks a series of physical questions, and the order of those questions matters as much as the questions themselves. If you roll three sizes of object over a large-sized hole first, everything falls in — the machine fails because the logic is out of order. To sort correctly, the algorithm must process data from the smallest threshold to the largest: is it smaller than the small threshold (smallest objects drop, others continue), then is it smaller than the medium threshold (medium objects drop, the largest continues), then else — the largest object reaches the end of the track. This sequence prevents data from being miscategorized, exactly how software engineers structure code to prevent bugs.
The Flowchart of Gravity
A flowchart is a map of an algorithm. In computer science, a rectangle represents an action, and a diamond represents a decision — a true or false question. A physical sorting ramp is a three-dimensional version of this exact flowchart. Every hole cut into the ramp is a decision diamond: if the object is smaller than the hole, the answer is true and it drops; if the object is larger, the answer is false and it rolls across the gap to the next question.
Why Order Matters — The Deeper Lesson
This project's real lesson isn't actually about coins or washers — it's about a principle that shows up constantly in real software: the order conditions are checked in can change whether a program works at all, even when every individual condition is written correctly. A programmer who checks conditions in the wrong order produces exactly the bug visible on a poorly-ordered ramp: everything gets caught by the first matching rule, even data that should have kept going. This is one of the most common real bugs in actual software, made physical and visible through gravity and cardboard.
The Arts-as-Attention Pass
An engineer who builds a machine without documenting the logic has built a puzzle, not a tool. After testing the ramp with a mixed handful of sorting objects, the builder must translate the physical machine back into the abstract language of computer science: drawing the flowchart that exactly matches the built machine, labeling each decision diamond with the precise millimeter measurements of the holes cut, and writing a brief explanation of why the holes must be ordered from smallest to largest. The final test is handing the manual and a handful of sorting objects to a friend — if they can operate and understand the machine using only the written documentation, the Arts-as-Attention pass succeeds.
Field Engineering: Step by Step
Build It For Real
Materials
Recommended Washer Sizes
| Size | Suggested Diameter | Gap to Next |
|---|---|---|
| Small | 12mm | 6mm to Medium |
| Medium | 18mm | 7mm to Large |
| Large | 25mm | — |
Complete Project Checklist
Phase 1 — Mathematics & Tolerances
- Decided: washers (recommended) or real coins
- Three distinct sizes of data gathered and measured precisely in mm
- Tolerance calculated for the small and medium holes
- Verified the small tolerance hole is strictly smaller than the medium object, with real margin
- Verified the medium tolerance hole is strictly smaller than the large object, with real margin
- Tested numbers in the live simulator before cutting anything
Phase 2 — Engineering the Algorithm
- Cardboard ramp base cut
- Node 1 (smallest hole) cut precisely
- Node 2 (medium hole) cut precisely, further down the track
- Guide rails installed to prevent data from derailing
- Pitch of the ramp adjusted to allow smooth, controlled rolling speed
Phase 3 — The Arts-as-Attention (Documentation)
- Machine tested successfully with all three sizes
- Algorithmic flowchart drawn in notebook, featuring diamonds for decisions
- Tolerances and measurements labeled on the flowchart
- Paragraph written explaining why sequential ordering is necessary
- Tested successfully by a friend using only the written manual