W. H. Calvin, J. Theoret. Biol. 1983 throwing theory


William H. Calvin, "A Stone's Throw and its Launch Window: Timing Precision and its Implications for Language and Hominid Brains," Journal of Theoretical Biology 104, 121-135 (1983). See also http://WilliamCalvin.com/1980s/1983JTheoretBiol.htm.

copyright ©1983 by William H. Calvin and the Journal of Theoretical Biology
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This 'tree' is really a pyramidal neuron of cerebral cortex.  The axon exiting at bottom goes long distances, eventually splitting up into 10,000 small branchlets to make synapses with other brain cells.
William H. Calvin

University of Washington
Seattle WA 98195-1800 USA

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on the same topic, before and since.
Updates to the throwing theory can be found here.

A Stone's Throw and its Launch Window:

Timing Precision and its Implications

for Language and Hominid Brains


Department of Neurological Surgery, University of Washington, Seattle, Washington 98195, U.S.A.

(Received 15 July 1982, and in revised form 4 March 1983)

Did bigger brains for more precise throwing lead to language, much as feathers for insulation may have set the stage for bird flight? Throwing rocks even at stationary prey requires great precision in the timing of rock release from an overarm throw, with the "launch window" narrowing eight-fold when the throwing distance is doubled from a beginner's throw. Paralleled timing neurons can overcome the usual neural noise limitations via the law of large numbers, suggesting that enhanced throwing skill could have produced a strong selection pressure for any evolutionary trends that provided additional timing neurons. This enhanced timing circuitry may have developed secondary uses for language reception and production.

Judging from the delight which infants and young children take in throwing and hammering, and from right-handedness being strongest for such tasks, the neural machinery for rapid manual-brachial movements may have been under substantial selection at some time in evolution probably in hominid evolution, as these features are far more pronounced in humans than chimpanzees. Here I report that throwing spears or small rocks requires an unusual timing accuracy beyond the known accuracy of single neurons, and that the only known solution to the problem (the Law of Large Numbers) requires large increases in the numbers of neurons applied to the task. This emergent property of parallel timing circuits has implications not only for brain size but for brain reorganization, as another way of increasing the numbers of timing neurons is to temporarily borrow them from elsewhere in the brain, perhaps switching them into the throwing circuitry as one "gets set" to throw.

Spear throwing at large game is perhaps the most prominent mention of hunting in the archaeological record; while the neurophysiological timing arguments advanced here are applicable to spear throwing, primate ethology leads me to assume that such large game hunting surely had unrecorded antecedents such as rock throwing at small game. Discussions of hominid hunting often exclusively focus upon group hunting of big game but DeVore & Washburn (1963) note that "the hunting of small animals and defenseless young is much more likely to lie at the root of the human hunting habit". Hayden (1981) reports that "many of the (present-day nonagricultural) societies sampled here preferred small game, and presumably some terminal Paleolithic hunter/gatherers did too. This general emphasis on small animals, including rats, lizards, bats, mice, toads, and other choice morsels, raises numerous questions about the evolution of subsistence patterns and about the relative importance of small- and large game exploitation". Steward (1938) suggested a number of advantages associated with small game exploitation: small game do not range far and need not be pursued over long distances; some species occur in colonies and can be exploited in large numbers; small game reproduce rapidly, making overexploitation unlikely; some species also store quantities of seeds and other foods that can be raided and used too.

Even baboons successfully exploit small game. Strum (1981) reports that individual baboons prey upon birds and rabbits, catching some with a short chase but merely seizing most as they lie motionless in the brush; Thomson's gazelles require stalking and chasing. Chimpanzees also eat meat, at Gombe typically young colobus monkeys or bush pigs (Teleki, 1973, i981). The numbers are not. insignificant either: Busse (1977) estimates that 8-13% of the local colobus population is lost each year to chimpanzee predation. While chimpanzees often throw large objects during threat displays (Goodall, 1968), throwing as an aid to hunting has been reported in only one instance (Plooij, 1978) and there the thrown rock merely served to scare away adult pigs protecting a young pig from a group of predatory chimpanzees-essentially, as a variant upon threat displays rather than as an aimed missile. This provides one scenario (Calvin, 1982a, suggests another) for the invention of predation using thrown rocks, with threatening throws gradually converted into aimed throws as success is rewarded.

Action-at-a-distance Predation

However arrived at, action-at-a-distance predation would appear to be a major invention, made several times in evolution (archer fish spit accurately at flying insects). Like another important hominid invention, the carrying bag, rock throwing has often been ignored in evolutionary discussions because it does not leave behind characteristic, enduring evidence such as spear tips. Darlington (1980) observes that "modern evolutionists concentrate on what they can see and measure. This is good, but only up to a point. Some components of evolution that cannot yet be measured have probably been important too, and throwing may be one of them". Indeed, throwing could have permitted foraging hominids to expand their population because of the more widespread habitats of the small prey animals (Calvin, 1982a), which might have been one factor in the expansion of hominids outside of Africa during the Pleistocene.

A moving target is a complication which requires solving a more sophisticated three-body problem (Darlington, 1980; Calvin, 1983, p. 36); the thrower must not only compute the rock's trajectory but also the prey's. Surely such hunting started, however, with throwing at stationary targets from a distance at which the prey animal would tolerate the presence of a hominid. Because most prey animals are evolutionarily adapted only to such swift predators as carnivores and hawks, they will frequently tolerate slow approaches by a solitary primate (gazelle herds maintain a distance only when frequently preyed upon by baboons hunting in groups: Strum, 1981). If the hunter's body blocks the prey's view of the first half of the arm's pitching motion, then the startle response to the throw may have caused little target displacement by the time the stone arrives 600 msec later.

Most importantly, there is a faster-is-better aspect to throwing (faster means farther, more stopping power, etc). Is there a bigger-brain-is-better effect because larger brains allow faster throws? If so, then throwing success could select for encephalization trends in the genome via bigger-is-faster-is-better.

For almost flat trajectories distance achieved is proportional to initial horizontal velocity, as it is a question of how far the projectile travels in the fixed time that it takes to drop to the ground. Kinetic energy (KE) gives an estimate of the "stopping power" of the projectile; since it is a function of the square of the velocity, KE may quadruple when distance doubles. Learning to hit the same target at twice the distance thus carries with it the bonus of quadruple stopping power, enabling larger prey to be stunned. Though KE is also directly proportional to the rock's mass, one can easily make up for the KE of a larger stone with modest increases in a small stone's throwing velocity-and also gain distance. Thus one might expect a key invention to be the replacement of two-handed over-the-head throws of melon-sized rocks with rapid one-hand throws of rocks which fit in the palm of the hand (chimpanzees, with whom we share our brachiator's shoulder joints, can throw either way but with poor accuracy: Goodall, 1968, p. 203).

Faster throws require more rapid orchestration of muscles and thus morc precise timing-but the timing sequences produced by neurons have inherent fluctuations (Calvin & Stevens, 1967, 1968). Such neuronal limitations raise the question: how precisely must release be timed for the rock to hit the target, i.e., how tight is the launch window? Fortunately, one can answer this question from the physics rather than from kinesthetics: just as it is not necessary to fire rockets every ten minutes and see which ones hit the moon to determine a launch window, so too can we work backward from rock trajectories to the required precision in timing.

The overarm throwing style of children, like that of spear throwers, is perhaps more relevant to hominid origins than the complicated throwing style of modern-day expert pitchers (whose windup would surely startle the prey well before launch time). The rapid uncocking of the elbow generates the major component of the launch velocity, permitting one to ignore (for purposes of estimating timing precision limitations) the slower axial and shoulder motions.

Trajectory Computations

If one assumes that the elbow is 120 cm above the target, and that the hand rises towards the vertical with a 40 cm elbow-to-hand radius, then it is a simple matter to compute initial horizontal and vertical components of launch velocity for various angular velocities and release times along this arc. Releases-within 10 degrees before the top of this arc are examined here, in keeping with the relatively flat trajectories used by modern hominids at moderate distances. The hand often maintains contact with the rock for some time forward of the vertical position, but the question here is when the vertical component of velocity (to which distance is especially sensitive) is fixed bv releasing the grasp upon the rock; this is what corresponds to the "time of release" modeled here. The problem is essentially the same for throwing spears as small rocks.

Calculations explored a wide varietv of release times and other initial conditions; release time was varied in fine increments and the impact point computed with the throwing motion in a vertical plane. The results below are typical of low, direct trajectories approaching a rabbit-sized target. The throwing motion was assumed to be in the same vertical plane as the target; while rotation about the body axis also occurs, imprecision in the release time for this rotary motion is not serious because the angular velocity is so slow compared to that of the elbow uncocking.

Though one can envisage the launch window as the permissible time variation in the command given to a robot-like hand to release the rock, the thumb does not suddenly spring open to release the rock when a timer runs out. Letting the rock slip at the right moment is a more gradual process, but one whose parameters must cause it to pass precisely through the same narrow window. That physiological process's essential feature-a launch window appropriate to the angular velocitv achieved-can be temporarily represented using the simple timers discussed here.

Launch Window Narrowing

The target was either modeled as a 20 cm bucket at the target distance, where one examines the release time decrement necessary to advance the point of impact by 20 cm (but still land "inside the bucket"), or as a 10 cm vertical silhouette, where one examines the release time decrement needed to raise the impact point by 10 cm at the given distance. These two estimates of launch window are tabulated in Table 1; unless otherwise qualified, comparisons refer to the average of the two launch window estimates, equivalent to moving the impact point up to the front of the target and then along its top; the 10 x 20 cm target is thus called one standard rabbit.

Throwing distance was primarily a function of angular velocity, but fluctuated with variations in release time within the final 10 degrees. At 4 m, the release time can vary by 6-7 msec at a given angular velocity and still have the rock drop into the bucket. However, at an 8 m distance, the precision needs to be within 0-7 msec if one is still to land within the same 20 cm bucket. As Table I demonstrates, to hit a 10 cm silhouette (e.g., the front of the bucket) at a 4 m distance tolerates a release variation of 4-5 msec; summed with the bracket, one arrives at the total 11 msec launch window. The head of a larger animal (e.g., pig, gazelle, deer) is also about one standard rabbit. For targets smaller than a standard rabbit, even tighter launch windows would be expected.

An eight-fold decrease in total launch window occurs when the distance doubles, a 27-fold decrease when distance triples. Note that the more rapid orchestration of muscles for faster throws is not merely a speeding-up of the "motor tape"; it requires an even greater increase in the timing precision.

A 4 m throw seems a reasonable beginner's throw; a 11 msec requirement for neural timing is likelv within the capabilities of some mammalian synapses and repetitive firing processes. Although distance could be finetuned via angular velocity rather than release time, inertia prevents major modification of angular velocity as the top of the arc is approached; presumably one senses the angular velocity actually achieved in mid-arc and sets the release time accordingly. Though not encompassing all relevant factors, the permissible fluctuation in release time provides a convenient index of the overall precision required of the neural machinery, one capable

TABLE I Permissible fluctuations in rock release time
Distance Rock launch window (msec) to Impact Redundancy target For 20 cm For 10 cm kinetic multiplier (m) bucket silhouette energy N needed 4 6-7 4-5 1.0 1 5 3-1 2-3 1-3 4 6 1.7 1-4 1-7 13 7 1.0 0.9 2-1 33 8 0-7 0-7 2-5 64 9 0.5 0.5 3-0 118 10 0-3 0-4 3-7 245 11 0-2 0-3 4-7 464 12 0-2 0-2 5-7 743 13 0.1 0-2 6-7 1254 14 0.1 0.1 8-0 2297
The sum of the two launch windows narrows as the cube of the distance; the redundancy requirement ascends as the sixth power of distance. The launch window values are averaged over all trajectories where the angular velocity permits a launch with less than 10 degree elevation angle, e.g., the 8 m distance (0.71 msec window for a bucket averaging 14 possible trajectories) includes launches at 10 degree elevation using 4.1 rev/sec (0.99 msec window) and launches with an initially flat trajectory using 5.4 rev/sec (0.47 msec window). The redundancy multiplier N is the factor needed to maintain the necessary launch window via summating redundant timers, relative to whatever redundancy is utilized for the 11 msec sum of the two launch windows achieved for 4 m throws. Kinetic energy at impact ("stopping power") is not quite proportional to the square of the target distance because of the additional vertical contribution, from the drop from the trajectory's peak. The 0-10 degree elevation results tabulated here would, of course, be somewhat different if 0-20 degree releases were allowed. The essential features of launch windows narrowing nonlinearly as distance increases, and a 4 m throw's launch window which is near the "physiological" cellular noise limit, do not appreciably change when such greater elevations are allowed. One can, of course, throw faster and release past vertical if able to control the release time sufficiently accurately: these calculations only attempt to set upper bounds on the launch windows and show how they change with distance.

of being compared with known neuronal precision and the intrinsic mechanisms limiting it (Calvin & Stevens, 1967, 1968).

Extending the distance while maintaining target size, however, greatly escalates the need for precision timing. To double the distance from 4 to 8 in with constant the target size, the permissible release error shrinks eight-fold due to such factors as the halving of the angle subtended bv the target and the need to double launch velocity, which shrinks the time scale. A 12 m throw (about two standard automobile parallel parking spaces') is also a modest distance for "action-at-a-distance to suggest a considerable degree of elaboration in neural timing mechanisms beyond those presently considered "physiological".

Redundancy in Neural Timing Circuits

One method for increasing the timing precision beyond that of the individually imprecise neurons is to use redundancy, a method whose use may be seen on the voyage of the Beagle where 22 chronometers were used to reckon longitude precisely from local noon. Enright (1980a,b) examines the properties of a simple neural circuit for decreasing the variability of a circadian oscillator, addressing the problem of individual pacemaker neurons' periods having a much larger standard deviation (SD) than the overall organism's circadian behavior. Essentially, the many primary timers in the first stage could feed a summating neuron; not until a critical number (e.g., 30%) of first-stage neurons have fired does the second-stage neuron discharge. Computer simulations show that the times to second-stage discharge varv much less than does the firing time of any first stage neuron: the resulting SD is reduced from the SD of the N primary timers by a factor of the square root of N. Clay & DeHaan (1979) show exactly this decline in SD when observing clumps to embryonic heart cells beating in culture: the more eiectricallv-coupled cells in the cluster, the morerhythmicthebeat. Even though theequivalentcircuit isquitedifferent from Enright's, the result is the same. Hence fine timing precision can be an emergent propertv of parallel neural circuits.

These are examples of the Law of Large Numbers (Feller, 1957, chapter 10), where ever more precise constants arise from increasing numbers of random events (such as half-life times from many random radioactive decays). Schrödinger (1944) called this the "order from disorder principle" and noted that there was a "N ^- 1/2rule": normalized fluctuations in a system of N units often vary as N ^-1/2, as might be expected from the central limit theorem. Thus the emergent N^-1/2 precision of the two exemplar circuits may serve as the typical case, from which departures to the rule are judged.

Thus, to reduce a 11 msec fluctuation range by eight-fold, one could use a suitable redundancy; it merely requires a 64-fold increase in the number of paralleled neurons over the original numbers (Table 1). Other mechanisms could, of course, contribute to narrowing the fluctuation range but a 11 msec range (about 2-3 msec SD if a normal distribution) is probably close to the limit of precision which could be attained within a single neuron from minimizing synaptic noise and firing mechanism sources when the timing interval is greater than 100 msec (Calvin & Stevens 1967, 1968).

That precision timing capabilities correlate with bigger brains can be seen from the animals with some of the largest brains (relative to body weight), which are the mormyriform fish (Bullock, Orkland & Grinnell 1977); they engage in precise timing for eiectrocommunication between individuals. Sonar in chiroptera and cetacca involves a high order of precision timing; they also have among the largest of mammalian brain/body ratios. Note, however, that this does not imply a backward correlation: all animals with big brains do not show present-day evidence of a precision timing skill exposed to selection pressure. The location of the extra timing neurons may be midbrain or cerebellum, as in the cases just cited, but there is also some likelihood that premotor cortex is involved in humans.

Secondary Uses of Timing Circuits

Hammering uses most of the same manual-brachial motions as does throwing. One might suppose that better circuitry for throwing would improve hammering skills; indeed, judging from female chimpanzee nutcracking skills (Boesch & Boesch, 1981), skillful hammering may have preceded precision throwing. While throwing is of primary interest in hominids because of its immediate exposure to selection pressures and long growth curve, the motor sequencing neural machinery is hypothesized to have additional secondary uses (Calvin. 1982a, 1983): language, memory, and motor mechanisms of the dominant hemisphere have many important interrelationships (Ojemann, 1982). In particular, motor sequencing lateralizations in the dominant hemisphere are thought to provide a possible foundation for language specializations. Ojemann & Mateer (1979) show that the core of the peri-Sylvian language cortex is a region involved with both phoneme discrimination and with oral-facial motor sequencing (as in mimicking a series of facial expressions. Deficits in manual sequencing with either hand are often associated with aphasia produced by strokes damaging this same general region of the dominant hemisphere (Mateer & Kimura, 1977, 1982), raising the issue of sequencer machinery shared by manual and oral-facial tasks (Cai%,in, 1982a; Ojemann, 1982).

Timing and/or sequencing specializations seem quite important for both phonemic and motor aspects of language (Mateer & Kimura, 1977; Ojemann & Mateer, 1979; Ojemann, 1980, 1982) as well as for the dominant hemisphere's temporal-order judgments (Efron, 1963; Lomas & Kimura, 1976; Cowey & Weiskrantz, 1976; Sherwin & Efron, 1980; Bradshaw & Nettleton, 1981; Tallal & Newcombe, 1978; Tallal & Schwartz, 1980). This suggests that cortical circuits with timing specializations that are widely used in modern humans were perhaps originally selected via hominid throwing success. Redundancy might allow "language" timers to contribute to precision "motor" timing and vice versa; indeed, language timers might have evolved by utilizing the idle redundant timing circuits used for precision throwing inbetween throwing occasions.

Accustomed as we are to thinking of static cortical maps for various functions, timing specializations might contribute to different functions at different times. Certainly, redundancy suggests maps which could shrink. Suppose that cortical circuits with a 3 msec SD were routinely available but that a SD of 1 msec was needed: if the timing precision was initially accomplished by nine-fold redundancy, with some neural circuits then gradually tuning themselves up to 2 msec SD so as to reduce the need for redundancy to only four-fold, one might have a "cortical representation" shrinking by 55% over time.

The redundancy model would thus seem relevant to one of the working models for language representation in bilingual patients: to account for the cortical regions where only the first, or only the second, language seems to be represented, Ojemann (in Calvin & Ojemann, 1980) has suggested that it takes a large area of cortex to initially learn a language, but that the over-learned task then uses a much smaller area, the freed-up areas becoming available for the acquisition of the second language or other novelties. Fine-tuning of timing circuits reducing the need for redundancy would create just such a picture.

An individual's verbal abilities have an unusual relationship to the extent of cortical representation seen with stimulation mapping, with representation extending into parietal lobe only in individuals with below-average verbal IQ (Ojemann, 1980; Mateer, Polen & Ojemann, 1982). Such a counter-intuitive result might reflect an above-average need for redundancy in a brain with below-average abilities to fine-tune timing circuits.

Temporal lobe timing specializations?

The temporal lobe is a region of human brain which is unusually prone to seizure activity (as is motor strip), and one particularly refractory to improvements in anticonvulsants (which are often thought to augment inhibitory mechanisms). Because so much of our knowledge of the periSylvian region suggests specialization for timing and sequencing, it may be that the epileptic tendencies are a side-effect of, literally, "reverberating circuits" - that this region is a sympathetic oscillator (in the engineering, not the neurological, sense) which reproduces rhythmic interictal and ictal activity that might originate elsewhere. For example, from media] temporal structures damaged at bith by herniation (Wvler & Bolender, 1983).

While there are many alternative neural schemes (e.g., long-lasting synaptic potentials) of accomplishing the sustained activity for which such reverberating activity was classically postulated, some newer phenomena suggestive of reverberation have been discovered within a single neuron, typically along its axon (Goldstein & Rall, 1974; Howe, Calvin & Loeser, 1976; Calvin & Hartline, 1977; Calvin 1982b; Calvin, Devor & Howe, 1982). This self-re-excitation, where an impulse propagating into certain regions of axon will initiate a new impulse which propagates backwards, could serve to activate some axon terminals twice by axon reflex, with the interval fixed by conduction times. Precise timing in nervous systems is often associated with conduction delays over long distances (such as callosal pathways and the frontal-to-temporal-lobe arcuate fasciculus could provide): Re-excitation might well be one of the specializations evolved for establishing a precise timing loop tens to hundreds of msec long.

Precision timing for shorter periods may utilize the crossover time between the relative refractory period and the subsequent supernormal period in the axon: A second impulse traveling in the relative refractoriness of the first will propagate more slowly, though it will speed up (catching up with the first) when in the supernormal period. Thus, given sufficient propagation distance (and intrahemispheric distances seem sufficient in practice for many short starting intervals; see Kocsis et al., 1981), the second impulse will take up station at a fixed delay after the first (typically about 2 msec): The time between impulses arriving at the axon terminals will become fixed at that axon's crossover time. Indeed, many CNS neuron trigger zones have a special "double spike" mechanism, which initiates a second impulse at approximately this interval (Calvin, 1974, 1980). If different axons specialized in various crossover times, a whole family of specialized precision timers could be constructed. Though timers could be constructed with a variety of known cellular ionic mechanisms and pattern generating circuits as well (Kristan 1980), such specialized axon properties hold promise of high precision in timing.

With various long- and short-interval precision timers, "Get set" might constitute synaptically switching the appropriate precision timers into parallel with the throwing circuitry, and "Go" would initiate this preset orchestration of the many muscles whose final relevant act is the precise release of the stone when the launch window is reached.

Since 4 cm of the tip of the human temporal lobe mav be surgically amputated with minimal deficit detectable, the issue of redundancy is unavoidable. The throwing theory suggests that it could be parallel redundancy for precision timing. rather than as a redundant backup system. Backup systems, when more than a few layers deep, are rarely exposed to selection pressures but, at least in the throwing theory, more parallel timing continues to be exposed to natural selection for harder and farther throws. Faster and faster continues to be better and better.

As for the cerebral location of the timing specialization, logical candidates are anterior temperal lobe and the premotor areas of posterior inferior frontal lobe; these are also typically the locations where brain lesions interfere with the neuropsvchologists' finger-tapping task (C. Dodrill, personal communication).

Hominid Evolution

The throwing theory for encephalization must be viewed from the essential background of Miocene and Pliocene developments, particularly hominoid reproductive strategy and the carry-while-gathering aspect of bipedality, as in the theorv recently put forward by Lovejoy (1981). Possible Pleistocene interrelationships between handedness, tool-making, and language are discussed by Montagu (1976) and Calvin (1982a, 1983). In particular. Lee (1979, appendix E) has noted how throwing could give rise to a need for the carrying bag, a key hominid invention.

Though the throwing theorv suggests a continuous selection pressure. punctuated evolution may mean that such selection pressures operate most rapidly and effectively upon small, geographically isolated, inbreeding populations near the time of speciation (see Mayr, 1982; Eldredge & Tattersall, 1982), rather than upon established species with large and widespread numbers to buffer and stabilize the genome via a well-stirred gene pool. Thus, even if the main population did not rely upon throwing for subsistence, throwing's usefulness in marginal habitats could have episodically shaped the genome.

One of the final steps in hominid evolution has been the tripling of hominid brain volume in the last several million vears (Jerison, 1973; Holloway, 1976; Cronin et al., 1981). As Lovejoy (1981) notes, most other important hominid features may have been well-established before the great encephatization; with the exception of language, they may not be parallel developments with brain enlargement. And, important as they are to humans, it has been difficult to see how bipedalism, tool-making, problem-solving intelligence, culture, altruism, and the two-parent family could have rapidly driven encephalization: each occurs to some degree in various smaller-brained animals without having produced a notable growth spurt. Many hominid inventions such as carrying bags and fire-starting do not have a growth curve associated with them; each may incrementally advance hominid capabilities, but they typically lack the bigger-is-faster-is-better characteristics which could have repeatedly selected for ever faster (and perhaps ever bigger) brains.

The association of handedness with the speech hemisphere has long caused speculation about the role of hunting and tools in the evolution of language (Montagu, 1976); indeed, Annett's (1970) data shows that it is the ballistic skills which are strongly right-handed, not the fine motor skills (throwing and hammering are about 89% right-handed in the population, vs 77% for threading needles), emphasizing the common hemispheric localization for ballistic skills and language. It would appear from the present throwing calculations and redundancy assumptions that throwing could have an immediate use (harder and farther throws) for increases in brain size produced by genetic mutations and permutations, raising the possibility that it provided a "fast track" for encephalization.

Thus a bigger brain could have been under continuing selection for several million years based on ever-improving throwing skills, with the size requirement escalating in power-law relationship to precision. Unlike hypertrophy with use, there is no reason to presume that such enlargement is restricted to the part of cerebral cortex used for timing sequences - a simple genetic tendency towards global enlargement of neocortex seems a more likely postulate. Such a simple scheme for larger brains is neoteny, with selective slowing of some developmental rates retaining the juvenile brain/body size ratio (Gould, 1977) as well as some of the behavioral plasticity of juveniles. By arresting somatic growth at - by ancestors' standards - a juvenile form, adults would come to have the larger juvenile brain/bodv ratio. Nonspecific enlargement suggests that selection for throwing success could enhance other cortically-based abilities as a by product or exaptation, e.g., increasing intelligence in general and language in particular, because of shareable timing-sequencing circuits. In this sense, perhaps bigger brains for hominid precision throwing promoted human intelligence and language, much as feathers for reptilian thermoregulation are thought (Ostrom, 1974) to have set the stage for bird flight.

There emerges from this view of our brain, with its relentless reorganization and enlargement for ever more precise pitching, some glimpses of the neural foundations on which we construct our utterances and think our thoughts. The brain may have begun precisely uncocking the elbow while hammering nuts in the tropics. Overextended on the Ice Age frontiers, however, our ancestors staved off starvation according to their inborn throwing abilities. Faster and faster was always better and better. Those with bigger and better organized brains survived with the aid of the Law of Large Numbers; eventually even their babies came to hammer and throw instinctively.

From such an evolutionary ratchet jacking up brain size, there arose unbidden our own brain of unbounded potential. In basketball to tennis, this mosaic brain expresses its ancient pleasure in precisely timing a sequence. Transcending its origins, our brain can now create novel sequences using grammar and music, even contemplate how our enlarged consciousness evolved and is evolving.

Barbara Isaac was kind enough to share with me her manuscript on the anthropological background of throwing. I thank George A. Ojemann, Joan S. Lockard, Daniel K. Hartline, Catherine Mateer, A. O. Dennis Willows, Judi L. Smith, Katherine Graubard, John L. Dubois, Robert B. Pinter and John Z. Young for particularly useful discussions and the Friday Harbor Laboratories for ambience. Partially supported by research grant NS 04053 from the National Institutes of Health. The author is an affiliate of the Child Development and Mental Retardation Center at the University of Washington.


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Trajectory Calculations

The pre-release path was modeled as a circular arc of 40 cm in a vertical plane (the hand and forearm rotating about the elbow at 120 cm above the ground) as in dart-throwing. One may appreciate the relative contributions of elbow motion and the other motions by attempting to throw with the elbow locked -- and comparing the distance achieved with that accomplished by a dart-throwing motion using only forearm rotation about the elhow. If one allows elbow motion superimposed upon an additional horizontal-only velocity contributed by shoulder and body motion (its magnitude was taken as equal to the lesser of the tangential velocity at launch or 5 m/sec), then the bucket launch windows are 6.1 msec at 6 m and 0.3 msec at 12 m. No corrections were made for wind or air resistance; they will further increase the need for precision releases, as will smaller targets.

It might be argued that other pre-launch trajectories would be easier for the hominid to produce; indeed, no claim is made that the circular arc is optimal. Yet the narrow launch windows are a consequence of the physics, not the physiology. Working backwards from trajectories which bracket the target shows that, however the body accomplishes it, the throw must become many-fold more accurate in its timing to double the distance of a beginner's throw. And, while current kinesthetic measurements may not suggest sub-millisecond timing precision, the fact that humans accomplish such throws shows that they are somehow satisfying the launch window imposed by Newtonian physics. An analogous situation would be where a primate could only time to 20 msec precision in an experimental setting and would therefore be predicted to miss the target when swinging from one tree to another. The fact that they seldom fall to the ground says that the experimental design was insufficient to reveal the precision that the natural behavior elegantly demonstrates, which is one reason why primate ethologists prefer the jungle to the zoo.

The BASIC program lines which demonstrate the relevant trajectory phvsics for initial conditions and impact point are:

10 'A = elbow to hand throwing arc, B = rev/sec, YEL = elbow elevation

20 'VXPUSH = horizontal velocitv of elbow, TO = time of release

30 'first find vertical and horizontal velocities, initial positions

40 VY0 = 2*PI*A*B*COS(2*PI*B*TO)

50 VX0 = 2*PI*A*B*SIN(2*PI*B*TO) + VXPUSH

60 Y0 = YEL - A*SIN(2*PI*B*T0)

70 X0 = A*(1 - COS(2*PI*B*T0))

80 'find time of flight and distance

90 TF = (VY0/G) + SQR((2*Y0/G) - (VY0/G) ^2)

100 XF = X0 + VX0*TF

where terrestrial gravitational acceleration G = 9.8 meters/sec/sec.

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