The Future is Teddy Bear-shaped

In my work in foresight, I often quote the UK Government’s Department for Science’s cone of possibility.  The “cone of possibility” is mathematically justified because uncertainty grows monotonically with time as variance, entropy and model error accumulate. In quantum systems, however, uncertainty does not grow smoothly: interference, entanglement, and non-classical probability composition create structured, non-monotonic, and branching futures. This makes the “teddy bear” metaphor, proposed by my esteemed teachers, more accurate than a cone. This is because quantum futures have lobes, nodes, cancellations and asymmetries, which are features classical cones cannot represent.

From the UK Government’s Futures Toolkit

But the world we are entering is not classical. In a quantum-entangled, interference-patterned, and structurally complex, the cone was no longer enough.

1. The Classical Cone of Possibility: Why It Works

The UK Government’s Futures Toolkit uses the cone of possibility to illustrate how uncertainty widens over time. This is mathematically grounded in classical probability and dynamical systems.

1.1 Classical uncertainty grows monotonically

In classical systems, uncertainty propagation follows:

2(t)=02+i=1ni2t

where

• 02 is initial variance,
• i are model errors,
• and time tincreases uncertainty linearly or super-linearly.

This is the same principle behind diffusion:

⟨x2(t)⟩=2Dt

where D is the diffusion constant.

Uncertainty spreads smoothly. The cone widens smoothly.

1.2 Entropy increases with time

Classically, entropy S grows because microstate uncertainty grows:

S=kln⁡(t)

and (t)  the number of accessible microstates – increases with time.

This is the mathematical justification for the cone’s widening.

1.3 Errors accumulate, never cancel

In classical systems:

• errors add
• noise accumulates
• deviations amplify

There is no mechanism for destructive interference.

Thus the future is a convex, expanding set – exactly what a cone represents.

2. Why the Cone Fails in the Quantum Era

Quantum systems obey different rules. The future does not expand smoothly. It branches, interferes, collapses, and re-coheres.

2.1 Quantum probability is not additive

Classical probability:

P(A∪B)=P(A)+P(B)

Quantum probability:

P=∣A+B∣2

The cross-term 2R(AB\*) introduces interference, meaning:

• some futures cancel
• some futures amplify
• the “width” of the future is not monotonic

This alone breaks the cone.

2.2 Entropy is not a simple cone in quantum systems

Quantum entropy is governed by the von Neumann entropy:

S(ρ)=-Tr(ρlog⁡ρ)

But unlike classical entropy, quantum entropy:

• can decrease temporarily
• redistributes across subsystems via entanglement
• is constrained by strong subadditivity
• does not form a simple convex cone for N≥3subsystems 

This is a key result: quantum entropy vectors do not form a cone. Thus the future cannot be represented by a cone.

2.3 Quantum futures have structure

Quantum evolution is governed by:

∣ψ(t)⟩=e-iHt/ℏ∣ψ(0)⟩

This produces:

• lobes
• nodes
• oscillations
• interference fringes
• entangled branches

The geometry is non-convex and non-monotonic.

A cone cannot capture this.

3. Why the Teddy Bear Is More Accurate (Selin, Ramirez & Colleagues)

The “teddy bear” metaphor from A Festival of Futures argues that futures are not smooth, symmetric, or monotonic. They are:

• lumpy
• uneven
• multi-layered
• temporally complex
• structurally asymmetric

This aligns with quantum behaviour.

3.1 Quantum futures resemble biological structures

Quantum systems often form:

• dendritic branching
• clustered probability densities
• asymmetric lobes
• discontinuous regions of zero amplitude

These resemble biological or organic shapes — not cones.

3.2 Temporal complexity replaces linear time

Selin et al. argue that futures unfold across multiple temporalities:

• slow variables
• fast shocks
• tipping points
• feedback loops
• emergent patterns

Quantum systems exhibit the same multi-temporal behaviour.

3.3 The teddy bear captures non-monotonicity

A teddy bear has:

• bulges (constructive interference)
• hollows (destructive interference)
• asymmetries (entanglement structure)
• discontinuities (phase cancellations)

This is a better metaphor for quantum futures than a cone.

4. Classical Cones and Quantum Teddy

In foresight work, the classical cone remains valid for:

• macroeconomic modelling
• policy uncertainty
• classical stochastic processes

But as the world becomes more quantum-enabled – technologically, economically, and epistemically – the cone becomes insufficient.

Quantum futures require:

• non-linear geometry
• interference-aware modelling
• entanglement-sensitive scenario planning
• multi-temporal reasoning

The teddy bear metaphor is not whimsical. It is mathematically closer to the geometry of quantum uncertainty.

2 May 2026