Calculations Per Second per $1,000 (Log Scale)
Target 2045: 1.2e+26 ops/$1k
This saved paradigm stack is a hypothetical logistic model, not a validated forecast of computing or human cognition. For its fifth curve the start is twenty twenty and saturation year twenty sixty. Their midpoint is twenty forty, and the slope coefficient is ten divided by forty, or point two five. Ignoring the negligible numerical floor, the fraction of its ceiling is one over one plus exponential of minus point two five times year minus twenty forty. At twenty forty the fraction is one half. At twenty forty five it is about point seven seven seven three. Our bars use one thousand pixels per fraction unit, so five hundred pixels grows to seven hundred seventy seven point three. Saturation year twenty sixty still reaches only about ninety nine point three three percent, not an abrupt ceiling. Changing a ceiling scales that curve, but the overall envelope takes the maximum of all five curves rather than adding their capacities. With the fifth ceiling at ten to the twenty sixth, its twenty forty five contribution is about seven point seven seven three times ten to the twenty fifth. Lower it hypothetically to ten to the eighteenth, and its contribution becomes point seven seven seven three times ten to the eighteenth. The fourth curve is already about point nine nine nine seven four times ten to the eighteenth, so it becomes the envelope winner. At five hundred pixels per ten to the eighteenth, the fifth is about three hundred eighty eight point six five pixels and the fourth four hundred ninety nine point eight seven. This is a maximum selection rule, not a claim that separate technologies physically combine this way. The code samples integer years eighteen ninety through twenty sixty for its export, including both endpoints. That is one hundred seventy one samples. It also assigns fixed reference lines and threshold comparisons; they are not demonstrated biological equivalences or measured physical bounds. The native ceiling editor ranges from exponent three to thirty two in half-decade steps. One stored ceiling preset uses exponent thirty five, outside that input range, so the control can be clamped while the model retains a different value. Offline the external D three library is missing: chart initialization fails before the preset, mode and export handlers are bound. The original editor and graph do not initialize. This local narrated source explanation preserves that blocker and makes no prediction or biological claim.
How do successive logistic technology S-curves compose an accelerated computational envelope, and what physical bounds constrain them?
This interactive tool models Ray Kurzweil's hypothesis that long-term computational growth is an upper envelope formed by successive, overlapping technological paradigms rather than a single uninterrupted exponential curve. In the simulation, each paradigm—from mechanical tabulators to post-silicon substrates—follows an independent logistic sigmoid curve that rises rapidly and eventually flattens near a defined ceiling. The overall computational capacity at any given year is computed as the pointwise maximum (envelope) of all active paradigms, capped by a theoretical thermodynamic boundary known as the Landauer limit.
The simulator is an idealized conceptual demonstration rather than an empirical predictive model. The chosen thresholds—such as setting a single human brain capacity at 10^16 ops/$1,000, aggregate human brains at 10^26 ops/$1,000, and a flat Landauer ceiling at 10^35 ops/$1,000—are heuristic pedagogical values rather than measured engineering specifications. In addition, real-world paradigm shifts involve complex economic constraints, cooling architecture, interconnect latency, and software bottlenecks that are not captured by simple algebraic sigmoids.
Open the 'Preset Scenario' dropdown and select 'Moore's Law Silicon Saturation'. Observe the telemetry panel update: the 4th paradigm's ceiling drops to 1e16 and the 5th becomes 'Post-Silicon Stagnation' capped at 1e18 ops/$1k. As a result, the computed 2045 Projection decreases from 7.77e+25 down to 7.77e+17 ops/$1k, the Target 2045 badge reflects 'Target 2045: 7.77e+17 ops/$1k', and the calculated Human Brain Equiv year shifts from 1971 to 2022.
The Law of Accelerating Returns models technological progress through discrete technological epochs. Within any single epoch, technological capacity exhibits logistic growth: slow initial progress during early research, rapid exponential-like scaling during mainstream adoption, and eventual deceleration as the physical and thermodynamic limits of the substrate are approached.
In the simulator's implementation, each paradigm is evaluated using an algebraic sigmoid function: val = minVal + (maxVal - minVal) / (1 + exp(-k * (year - mid))), where k = 10 / (saturationYear - startYear) and mid is the midpoint between start and saturation years. The combined trajectory is calculated as the upper envelope over all active curves, yielding an accelerating macro-curve despite each micro-curve experiencing diminishing returns.
Concrete computing devices are physical systems governed by statistical mechanics and quantum thermodynamics. In 1961, Rolf Landauer demonstrated that logically irreversible operations—such as erasing or resetting a bit of information—dissipate a fundamental minimum quantity of heat into their environment equal to kT ln 2 joules per erased bit, where k is Boltzmann's constant and T is temperature. Information Processing and Thermodynamic Entropy (Stanford Encyclopedia of Philosophy)
Physical computing mechanisms cannot surpass theoretical energy, density, and communication bounds set by quantum mechanics and relativity. While the simulator represents the Landauer boundary as a horizontal ceiling of 10^35 operations per second per $1,000, actual limits in physical systems depend dynamically on operating temperature, logical reversibility, and materials architecture rather than an arbitrary static constant. Computation in Physical Systems (Stanford Encyclopedia of Philosophy)
Landauer's principle establishes that logically irreversible operations such as bit erasure incur a minimum thermodynamic dissipation of kT ln 2 heat into the environment.
Physical computation is subject to concrete substrate constraints, energy dissipation bounds, and physical limits of computability.