Imagine · for everyone, from age ten upward
What if far away could become next door?
This page has no equations. It has the real question we work on every day, drawn so you can play with it — and an honest label on every single idea, so you always know what is measured, what is being studied, and what is only ours to wonder about.
Space is enormous, and rockets have to cross all of it
A spacecraft moves by pushing itself through every kilometre between here and there. Even at astonishing speed, the nearest other star takes tens of thousands of years.
A rocket is a brilliant machine for crossing space. It is still crossing all of it.
A thousand pages — or one fold
Imagine a book with a thousand pages. Normally you reach page 1000 by turning every page. But the pages are not far apart because of the paper — they are far apart because of how the book is bound.
This is a picture to think with, not a description of space. Bending paper is easy; nobody has shown that space has a binding you can change.
What if distance is a result, not a thing?
Take away the empty space and keep only dots and the relationships between them. Now 'far' means weakly related and 'near' means strongly related. Slide the control and watch which dots become neighbours — none of them move.
Computational idea. Not physical evidence. This is a graph on a screen, and a graph is mathematics.
Move through it, change it, or change who you are next to
Only the first of these three is transportation as we know it. The other two happen inside the model: links change, or a traveler's list of relationships changes while the traveler itself sits perfectly still.
1 · Traversal
The traveler crosses every bit of the path. This is how travel works today.
2 · Change adjacency
Nothing moves. The links themselves change, so the modeled separation shrinks.
3 · Relational address
The traveler stays exactly where it is on screen. What changes is who it is related to.
Ideas 2 and 3 are not real transportation and are not teleportation. They are edits to a mathematical model of relationships.
What makes one state of reality allowed to become another?
Instead of asking how something moves, we ask what the rules permit. Between state A and state B there is a whole landscape of possible routes — some cheap, some expensive, some forbidden.
Same start. Same finish. Different routes, different costs — and some routes the rules may simply not allow.
Being the same at both ends is not enough
Here are states our model actually generated. Every filled dot passes the same 'is it still the same thing?' test. Colours show which dots you can actually walk between using allowed steps — and sometimes there is no way across at all.
A picture of a mathematical state space, not of places. Nothing here moves through space, and nothing here is evidence about the world.
If every road causes the same damage, a better road cannot help
If every road to the same place causes the same damage, choosing a better road cannot help. The rules themselves must change so the route matters. Here are three routes from A to B in one of our toy models — same start, same finish, three different results.
Toy model / not physical transportation
The requested toy example. The identity cost of moving in y depends on where the state already sits in x, so the order of the moves changes the endpoint result.
Interpolate both coordinates together. · endpoint ΔI 0.500 · path length 1.414
Move the first coordinate fully, then the second. · endpoint ΔI 1.000 · path length 2.000
Move the second coordinate fully, then the first. · endpoint ΔI 0.000 · path length 2.000
All three routes start at A and finish at B. Under a constant coupling their accumulated identity response would be identical. Here it is not, and the difference is the whole point.
We proved to ourselves that with the simplest possible rule — damage grows in fixed proportion to how far you move — every route costs exactly the same. That is a dead end, and knowing it is dead is progress. The smallest change we have found that reopens the question is letting the cost of a move depend on where you already are. See the working.
Toy model / not physical transportation. These are lines on a mathematical plane, and the 'damage' is a number our own model computes.
Failure is data
This is the loop every scientist uses, and the one we follow here. The most valuable thing we can do to our own idea is try hard to destroy it.
- step 1
Imagine
Ask a question nobody has answered yet.
- step 2
Write a rule
Turn the question into exact mathematics.
- step 3
Simulate
Let a computer follow the rule honestly.
- step 4
Try to break it
Attack our own result on purpose.
- step 5
Keep what survives
Whatever survives the attack, we keep.
- step 6
Ask a better question
Then start again, one step smarter.
When an experiment fails here, we keep it, publish it and give it a number. A failed test is not a bad day — it is the part of science that actually tells you something.
Four outcomes, from likely to wildly speculative
Every card below is conditional. Read the label on each one: they are not equally likely, and the last one is not remotely established.
Better ways to describe shape from structure
Mathematics that turns a web of relationships into a geometry already exists and is useful today.
New tools for networks and information
If our observables behave well, they could help describe traffic, brains, materials or any other network.
Clues that help with quantum gravity
Several serious research programmes ask whether space emerges from something more basic. Our toys sit beside them, not above them.
Nothing amplifies for free
In our computational toy models a small nudge can set off a huge response — but the extra work always comes from somewhere: the medium never returns to normal, or it was loaded with energy beforehand and gets drained. These are mechanisms inside equations we wrote, not claims about matter.
A real mechanism that changes effective separation
The distant, speculative end game: some physical way to change the relationship rather than out-run the distance. We have no evidence that nature allows this.
A simulation can only surprise us if we did not secretly put the answer into its rules
The easiest way to fool yourself with a computer model is to build the answer into the setup and then act amazed when it comes out.
Negative controls · plain language
A simulation can only surprise us if we did not secretly put the answer into its rules
Suppose we build a model where a thing’s identity and its position are stored as two separate lists of numbers, and we let ourselves edit either list freely. Then we run the model and announce that position changed while identity stayed the same. That is not a finding. It is a restatement of how we set up the lists.
So before believing anything we compute, we run the same test on models designed to fail. We tie identity and position together and see whether the effect survives. We shuffle the structure while keeping the numbers, and see whether the effect was about structure at all. We add rules that make shortcuts expensive, and see whether the shortcut still exists. A result only counts if it beats the versions we rigged against it.
Rigged to succeed
Independent identity and position. Always works. Tells us nothing.
Rigged to fail
Identity and position wired together. If the effect survives here, it is interesting.
Shuffled
Same numbers, scrambled structure. Separates real structure from lucky magnitudes.
When a result is guaranteed by the way we wrote the model, we label it EXPECTED BY CONSTRUCTION and it is not allowed to count as a discovery.
This is why several of our own results are labelled EXPECTED BY CONSTRUCTION and are not allowed to count as findings.
The most speculative picture we are willing to draw
If — and it is an enormous if — relationships could be changed in the world and not only in a model, then reaching somewhere far would not be about going faster.
We do not know if nature allows this
The dream: change the relationship, not the speed.
Speculative. Not demonstrated physics. No experiment on this site provides any evidence that this is possible.
Curious people welcome — including the ten-year-olds
Every model here is open, seeded and reproducible. You can run the same experiment we ran, get the same numbers, and then try to break them.
This whole page, in four lines
- What we tried
- We asked whether distance could be a result of relationships, and built small computer models to find out.
- What happened
- In our models, changing relationships changes the measured separation — and we can measure exactly how much it costs.
- Why it matters
- It gives us a precise, testable way to ask an old question about what space really is.
- What it does NOT prove
- It does not show that real space works this way, and it does not make any kind of travel possible.
“Nothing is possible unless we have thought it.”
Thought opens the possibility. Testing decides what survives.