"Hinge of History" Refuted

Epistemic status: 100% confident.

Introduction

Is the present the hingiest time in history? The answer to this question is enormously important to altruists, and as such has attracted the attention of many philosophers and researchers: Nick Beckstead, Phil Trammell, Toby Ord, Aron Vallinder, Allan Dafoe, Matt Wage, Holden Karnofsky, Carl Shulman, and Will MacAskill. I attempt to answer the question through a novel method of hinginess analysis.

Flawed Hinginess Measures

To determine whether one era of history is hingier than another, we must have some way to measure hinginess. The naive method used by many previous researchers is to simply count the number of hinges in each time period. There are several problems with this idea.

Suppose that a heavy door is held up by two hinges. Replacing these with four hinges, each half the size, would double the number of hinges. However, since the range of motion of the door is the same in each case, the hinginess has not changed.

Taken to its conclusion, a naive hinge count leads to the absurd conclusion that the hinginess of the world is dominated by its insect population. It is estimated that the world contains on the order of ​1 million billion ants; each ant has six legs, with each leg containing three hinges. Even disregarding the antennae and mandibles and necks of ants, we end up with an estimate of 1.8*10​¹⁶ hinges belonging to ants, which dwarfs all of humanity's hinges by orders of magnitude.¹ Despite the fact that ant joints are millions of times less hingey than some other hinges, many people believe that underground ant colonies contribute the vast majority of the world's hinginess-- the so-called "underfoot myth". In reality, the proportion is much smaller, which we will examine in the next section.

Estimating the total mass or volume of hinges is not much better. While past hinges were limited to natural materials, advances in materials science have allowed us to manufacture hinges of many different metals: "copper, brass, nickel, bronze, stainless steel, chrome, and steel" (source), allowing for much better quality, more hingey, hinges of the same mass or volume. A reasonable hinginess measure should take into account the number of hinges in the universe, but also the hinginess capacity of each individual hinge.

Estimating Hinginess

I claim that hinginess of a given hinge depends on three factors, and can be estimated as scale * tractability * neglectedness:

• Scale: How big a door can the hinge swing, and through what distance?
• Tractability: When carrying this door, how low is the hinge's friction torque, compared to the torque required to twist the hinge off-axis? (In short, how good of a hinge is it?)
• Neglectedness: How long has the hinge functioned without maintenance?⁵

Some hinges rank poorly in scale and are not very neglected (e.g. ant tarsal joints), while others are large in scale and very neglected (e.g. the doors of ancient temples). Similarly, some hinges are very tractable (e.g. in a precision-engineered bank vault) while some are intractable (a living hinge, like that on a plastic ketchup bottle lid, is only a few times easier to open than to twist or break). This is summarized in the table below.

Hinginess in the Past

Despite the low neglectedness of animal joints, they accounted for most of the hinginess in the world between the Cambrian explosion and the rise of agriculture. The reason is that there were simply no other hinges.⁴

The "underfoot myth" notwithstanding, insects account for comparatively little hinginess, mostly due to their small scale and neglectedness.²

Hinginess in the Present

We examine three sources of present hinginess: animal joints, door hinges, and large artificial structures.⁷ All calculations can be found at this Guesstimate.

Animals

The biomass of large animals today is significantly larger than during prehistory; humans comprise 0.06 gigatons of carbon, and livestock 0.1 Gt C, while previous to human influence, total mass of mammals was only 0.04 Gt C (source) and fish about 0.8 Gt C, almost none of which consists of large fish. Overall, we are fairly confident that the hinginess from animal joints is higher than at any time in the last several million years. Tractability of animal joints is often low compared to manmade hinges; top human athletes routinely suffer knee injuries that limit their performance. With ordinary door hinges about an order of magnitude more tractable, animals contribute relatively little to the world's hinginess.

Doors and Artificial Structures

We use two Fermi estimates to determine the hinginess contributed by residential doors, and find that it is probably larger than the hinginess from animals (details are in the Guesstimate model).

Some artificial structures have massive doors, with hinges that must withstand large forces-- most notably, water locks for canals and rivers. The original Panama Canal lock gates weigh about 662 t * 9.81 m/s² = 6.5*10⁶ N and swing through a distance of about 25 m, for a scale of 1.6*10⁸​ N m.³ They are well-engineered and lubricated, so tractability is likely about 4x that of residential doors. The gate hinges also have not been replaced in ~100 years. Because they undergo regular maintenance, we estimate their neglectedness at 50 years, giving the twelve gates of the Panama Canal a hinginess of about 8.1 * 10¹² N m y​, equal to that of millions of residential doors. However, there are few structures as large as the Panama Canal, so we estimate that large structures contribute less than 10% of the hinginess of the world today.

Recent Trends in Hinginess

Since the human population, livestock population, and world real estate market have all increased roughly monotonically, the present is also more hingy than the recent past.

Hinginess in the Future

While magnetic bearings exist, humanity currently does not use magnetic bearings as hinges. Such a hinge has the potential for extremely high tractability compared to all current hinges, because magnetic bearings have no mechanical friction, only tiny eddy current losses. However, recall that tractability is also proportional to the torque required to twist the door off of its hinges, which is much lower for magnetic bearings than for other types of hinges. So, designers must increase the force aligning the door to its hinges to achieve high tractability, and thus high hinginess.⁶ If future civilization can solve this "alignment problem", the universe's hinginess could quickly increase to almost unimaginable levels.

On the other hand, it is possible that humanity fails to reach its ultimate hinginess potential. If humanity goes extinct, the hinginess of the universe will increase at first (due to increasing neglectedness), but then decrease as this neglect causes the tractability of hinges to fall to zero. (If large animals survive, the hinginess of the world will eventually return to the pre-human baseline). Even in this case, it is possible that prior to extinction, humanity could construct extremely durable hinges in geologically stable locations that can remain tractable for millions of years. Even a single such hinge could potentially result in a combination of scale, neglectedness, and tractability that outweighs the total hinginess of the present.

Conclusion and Future Work

Due to the increase in hinginess from humans, livestock, large structures, and especially residential doors, it is likely that the present is more hingey than any time in the past. However, a trend of increasing hinginess is likely to continue into the near future, and in the far future, several possibilities exist for hinginess to increase far beyond current levels, possibly even if humanity goes extinct.  This conclusion could change with unexpected evidence of abiotic hinges, if extraterrestrial intelligence is common, or with further analysis of the hinge alignment problem.

Further applications of this novel method of analysis could include determining the impact of charities through seismography.

[1]    Insect joints have differing morphology, with some insects having additional hinge-type joints in place of the ant's ball-and-socket joints, or in the wings. However, ants are by far the most numerous insects and likely account for most of the world's hinges.

[2]    The joints of ants are extremely small in scale since they need support only a few milligrams each, and low in neglectedness because they are made of living tissue and undergo constant repair. To preempt possible criticism, periodical cicadas are likely not hingier than ants. Though they live for 13 or 17 years as nymphs, during which time they have legs with hinge joints, they also undergo constant repair and are no more neglected than the joints of ants.

[3]    The gates in the newer canal locks are larger, but slide rather than swing open. Also, the gates can only open when water level is equal on both sides, so they are not supporting the weight of a large mass of water. The scale of the hinges could be even smaller, because the gates are hollow and buoyant.

[4]    We assume that naturally occurring, abiotic hinges do not exist. If they do exist, they probably account for the vast majority of past and present hinginess, since they are likely found on many millions of planets throughout the universe and have been neglected for millions or billions of years. Similarly, if extraterrestrial life is common, there could be millions of times more hinginess from aliens than Earth animals. However, there is currently no evidence for either type of hinges.

[5]    This simple sentence belies some ambiguity. Consider a hinge that has lasted for 100 years, but was oiled every year. Is its neglectedness 1 year, or 100? The neglectedness of hinge joints of animals is even more difficult to evaluate: "The hinge joint is made up of two or more bones with articular surfaces that are covered by hyaline cartilage and lubricated by synovial fluid. Stabilization of each hinge joint is by muscles, ligaments, and other connective tissues, such as the joint capsule." (source) The synovial fluid alone consists of several types of cells, which sit in a complex bath of chemicals replaced at different rates. We estimate that the joints of large animals have neglectedness comparable to the rate of progression of rapidly progressive osteoarthritis in humans, about 1 year. The neglectedness of insect joints is even more uncertain, but insect joints are small enough in scale that this does not affect our conclusion.

[6]    Currently, magnetic bearings require components external to the hinge to produce the strong magnetic fields required for hinginess. Continuous improvements to current magnetic bearings would gradually solve the "outer alignment" problem. Achieving "inner alignment", where the magnetic hinge requires no external power or equipment, will likely be far more difficult, but these compact, passive hinges can potentially operate at larger scale and accrue far greater neglectedness, increasing their hinginess.

[7]    We make no attempt to quantify the hinginess of the dating app Hinge.