How we know what babies know
Inferences about infant perception and cognition must be based on observable behaviors because babies can't talk, they don't follow instructions, and their physiological responses may reflect different psychological processes than those in adults (Blumberg & Adolph, Reference Blumberg and Adolph2023). But how to link observable behaviors with unobservable perception or cognition? A commendable feature of Spelke's (Reference Spelke2022) book is her celebration of Eleanor Gibson and Richard Held for their pioneering behavioral methods to test infant depth perception. Gibson focused on exploratory behaviors and devised the “visual cliff” to test infants' responses to an apparent drop-off (Gibson, Reference Gibson1988; Gibson & Walk, Reference Gibson and Walk1960). Held used psychophysical functions to index the development of stereoscopic depth perception and devised the “kitten carousel” to test the role of self-produced visual feedback from locomotion (Held, Birch, & Gwiazda, Reference Held, Birch and Gwiazda1980; Held & Hein, Reference Held and Hein1963).
Spelke's descriptions of Gibson's and Held's methods lay the foundation for her reliance on looking time to study infant cognition. Her arguments for innate avoidance of a drop-off lay the foundation for her claims about core knowledge. We take issue with these foundations on several counts. To really know what babies know requires more than rich interpretations based on lean looking-time behaviors. Standard looking-time procedures do not exploit the richness of infant behavior; infant exploration entails more than looking or not looking at a display; and standard looking-time procedures (and also Gibson's use of the visual cliff) are not psychophysical methods. Finally, Gibson's views about whether avoidance of the visual cliff is innate evolved over the course of her career.
Our comments are both biographical and intellectual. Like Spelke, we have unique insights into Gibson's work because all three of us were Gibson's doctoral students. However, we worked with Gibson at different periods in the evolution of her ideas – Spelke from 1973 to 1977, Schmuckler from 1983 to 1988, and Adolph from 1987 to 1993.
Spelke's cohort relied on looking-time methods (e.g., visual habituation, preferential looking). As in modern-day protocols, infants sit in a car seat or caregiver's lap while viewing a visual display, and researchers use group differences in looking duration to infer what infants know. The idea is that infants' “visual exploration” – here, defined by whether, not where, infants look at a display – can reveal perceptual sensitivity, learning over the course of multiple trials, or what infants knew prior to viewing the stimuli. Indeed, Spelke (Reference Spelke1976, Reference Spelke1979) innovated an influential cross-modal looking-time procedure in which babies hear sounds or touch objects that match one of two visual displays.
Over the ensuing decades when Schmuckler and Adolph were doctoral students, Gibson returned to the questions that fascinated her in the early 1960s with the visual cliff. In contrast to Spelke's looking-time era, now infants were out of the car seat moving around. The focus was on sensitivity to optic flow for balance and steering and perception of affordances for locomotion over challenging ground surfaces (e.g., Adolph, Reference Adolph1997; Adolph, Eppler, & Gibson, Reference Adolph, Eppler and Gibson1993; Gibson, Reference Gibson1997; Gibson et al., Reference Gibson, Riccio, Schmuckler, Stoffregen, Rosenberg and Taormina1987; Schmuckler & Gibson, Reference Schmuckler and Gibson1989). In these studies, apparatuses were not covered with safety glass; instead, babies' safety was ensured with netting or a researcher rescued infants when they fell. New apparatuses were built, new paradigms were developed, new tools were available for recording behavior, and thus new findings about perception, exploration, and action emerged. Some findings conflicted with Gibson's earlier work or called for new interpretations, including infants' behavior at the edge of a drop-off. Gibson willingly entertained these new findings and ideas, even if they conflicted with her prior interpretations. She would listen thoughtfully and say, “Well, dear, that's very interesting. Do more experiments to figure out what's going on.”
Rich descriptions of behavior provide critical evidence about what infants know
Behavior is infinitely rich. It is up to researchers – using the recording technologies and tools at their disposal – to decide how much of the richness to describe. For example, to demonstrate that conditioned responses need not be rigidly stereotypic, Gibson (Reference Gibson1952, Reference Gibson1991) described nine reactions in infant goats to an aversive conditioned stimulus (shock to foreleg) – including both flexing and extending the leg, walking forward and backward, and wheeling in circles. Her descriptions of behavior on the visual cliff were equally rich (Gibson & Walk, Reference Gibson and Walk1960; Walk & Gibson, Reference Walk and Gibson1961). One insightful observation was that animals only show fear when forced onto the safety glass: When placed on the deep side, lambs and kids freeze in defensive postures with front legs rigid and hind legs limp. But when deciding for themselves whether to cross, animals calmly explore the shallow side of the apparatus and peer over the edge of the deep side. Later work showed that human infants spend most of their time near the brink of the deep side, regardless of whether they cross or avoid, showing neutral or positive – not negative – facial expressions in either case (Adolph, Tamis-LeMonda, Ishak, Karasik, & Lobo, Reference Adolph, Tamis-LeMonda, Ishak, Karasik and Lobo2008; Kretch & Adolph, Reference Kretch and Adolph2017; Tamis-LeMonda et al., Reference Tamis-LeMonda, Adolph, Lobo, Karasik, Dimitropoulou and Ishak2008).
Rich descriptions are not colorful frills. Rather, the suite of behaviors can provide converging evidence. For example, infants' increased hesitation, exploratory looking and touching, displacement behaviors, refusal to walk, and use of alternative strategies all point to infants' perception that a deformable waterbed or steep slope does not afford walking (Adolph, Reference Adolph1997; Gibson et al., Reference Gibson, Riccio, Schmuckler, Stoffregen, Rosenberg and Taormina1987). Similarly, infants lean away from a looming object and toward an open aperture (Carroll & Gibson, Reference Carroll and Gibson1981) and blink in response to a looming object but not to a looming aperture (Schmuckler & Li, Reference Schmuckler and Li1998), providing converging evidence that infants perceive affordances for collision versus passage. Alternatively, behaviors can alter interpretations of the primary outcome measure, as when novice walkers explore the edge of a precipice, but walk over the brink nonetheless (Adolph, Reference Adolph1997; Adolph et al., Reference Adolph, Tamis-LeMonda, Ishak, Karasik and Lobo2008; Karasik, Tamis-LeMonda, & Adolph, Reference Karasik, Tamis-LeMonda and Adolph2016).
Looking time does not capture the richness of visual exploration
In standard looking-time paradigms (e.g., preferential looking, visual habituation, violation of expectation), the richness of infants' visual exploration is reduced to a single metric – accumulated duration of looking. In the 1970s, researchers were limited by available tools for recording duration of looks, and they could not record where on the display infants looked. But now eye-tracking technologies and video-annotation tools show that visual exploration is exceedingly rich – filled with looks of varying durations to various parts of a display. It is worthwhile to capture this richness. For example, Kellman and Spelke (Reference Kellman and Spelke1983) found that infants who are habituated to a partially occluded rod moving behind a box perceive one unified rod rather than two rod parts. But visual habituation relies on group data and is not sufficiently detailed or powerful to explain why infants perceive object unity for moving objects. Kellman and Spelke could only speculate. In contrast, richer eye-tracking data reveal that individual differences in visual exploration explain infants' perception of object unity: Infants who look at the visible parts of the moving rod during habituation subsequently dishabituate to two rod parts at test, whereas infants who visually explore the box or background do not (Johnson, Slemmer, & Amso, Reference Johnson, Slemmer and Amso2004).
Moreover, in standard looking-time studies, other behaviors babies emit are routinely ignored – pupil dilation, looks to caregivers, facial and manual gestures, vocalizations, postural changes, and so on. Looking-time researchers acknowledge that “surprise” at an “unexpected” event is merely shorthand for “longer looking” to displays researchers consider unexpected. But uninformed readers do not realize that behavioral indices of surprise such as infants' facial expressions – when included at all – often fail to provide converging evidence (Camras et al., Reference Camras, Ujiie, Mayake, Wang, Murdoch, Meng and Campos2002; Scherer, Zentner, & Stern, Reference Scherer, Zentner and Stern2004).
Finally, when infants act in the world with all the behaviors in their repertoires, possibilities for exploration are limitless (Gibson, Reference Gibson1988). Babies explore objects with their eyes, hands, and mouths. They explore ground surfaces by looking, touching, and testing various postures and forms of locomotion. Their every movement generates perceptual information.
Looking time is not psychophysics: Open air or otherwise
Spelke implies that looking time involves psychophysics. Since the 1960s, psychophysics is associated with methods that link systematic variations in a physical dimension of the environment with the accuracy of perception (Cornsweet, Reference Cornsweet1962; Green & Swets, Reference Green and Swets1966). Many psychophysical methods do not require self-report by adult humans (as Spelke attributes to Helmholtz). Notably, Teller's (Reference Teller1979) “forced-choice preferential-looking” procedure is a psychophysical method appropriate for use with babies and other nonverbal animals.
Psychophysical methods are extremely powerful because the ground truth is the known physical dimension. In addition, they yield psychometric functions for individual participants. In contrast, standard looking-time procedures are weak methods because they are based on the reliability of human judgments (or computer-vision algorithms) with no external ground truth. They must rely on group data and therefore cannot allow conclusions about individual infants. Moreover, because preferential and cross-modal preferential-looking paradigms lead researchers to accept both novelty and familiarity preferences as evidence of discrimination, these paradigms incorporate a fundamental ambiguity in determining and interpreting infants' perceptual experiences (Hunter & Ames, Reference Hunter, Ames, Rovee-Collier and Lipsitt1988). Contrary to Spelke's claims, psychophysics and looking time are different beasts.
Spelke correctly credits Held for conducting psychophysical experiments with infants, but incorrectly credits Gibson for doing the same. Gibson did conduct “open-air” psychophysical studies with adults walking through fields judging distances among targets (Gibson & Bergman, Reference Gibson and Bergman1954), and she admired Teller's ingenious forced-choice psychophysical method (Gibson & Pick, Reference Gibson and Pick2000). However, Gibson never used psychophysics with infants in her own studies. To be sure, change in a visual display from habituation to test or contrasts between shallow and deep sides of the visual cliff are experimental manipulations. But they are not psychophysics.
The evolution of Gibson's ideas from depth perception to perceiving affordances
In her original studies, Gibson viewed the visual cliff as a test of depth perception, and she did indeed conclude that avoidance of the deep side was innate (Gibson & Walk, Reference Gibson and Walk1960; Walk & Gibson, Reference Walk and Gibson1961). Decades later, Gibson (Reference Gibson1991) retained her assumption of innateness, but reinterpreted her work in terms of perception of affordances (Gibson, Reference Gibson1997), and by the 2000s, she believed that avoidance of a precipice is learned (Gibson, Reference Gibson1997, Reference Gibson2002; Gibson & Pick, Reference Gibson and Pick2000).
So why do infants avoid falling at the edge of an impossibly high drop-off, steep slope, narrow bridge, wide gap, or narrow ledge? As both Spelke and Gibson propose, sensitivity to depth information might be available at birth or shortly thereafter. However, depth perception is only a necessary condition, not a sufficient one. Altricial animals require learning to perceive the difference between a step and a cliff, an incline and a steep slope, a walkway and a bridge, and so on – that is, they must learn to perceive affordances for locomotion (Gibson & Pick, Reference Gibson and Pick2000).
What do infants learn? Negative feedback from falling is not necessary, as Walk and Gibson (Reference Walk and Gibson1961) showed with dark-reared kittens that walked repeatedly onto the deep side of the visual cliff in the light and as Adolph (Reference Adolph1995, Reference Adolph1997, Reference Adolph2000) showed with human infants on slopes and gaps. Likewise, experience with drop-offs, slopes, or other such obstacles is not necessary. Rather, infants must learn to perceive the relations between the physical features of the environment and the current status of their bodies and skills (Gibson, Reference Gibson1997). Such relations change from moment to moment, so exploration is needed to generate the requisite information. Spelke's innate knowledge and fetal dreams in precocial animals cannot supplant real-time exploration and learning.
Conclusions
This commentary about Spelke's book is not merely a bunch of middle-aged, former students arguing about their mentor's legacy. It's about how to do developmental science. Spelke writes in her prologue, “To learn how infants think, we have to listen to what the infants in our studies tell us.” However, overly simplified behaviors provide only a crude narrative of what babies might know. For Gibson, the richness of behavior is key. She advised her students to observe infants with an open mind, and to “let the behaviors speak to you.” Thus, a critical lesson we learned in her lab is that the rich details of what babies do allow their voices to be heard more clearly.
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How we know what babies know
Inferences about infant perception and cognition must be based on observable behaviors because babies can't talk, they don't follow instructions, and their physiological responses may reflect different psychological processes than those in adults (Blumberg & Adolph, Reference Blumberg and Adolph2023). But how to link observable behaviors with unobservable perception or cognition? A commendable feature of Spelke's (Reference Spelke2022) book is her celebration of Eleanor Gibson and Richard Held for their pioneering behavioral methods to test infant depth perception. Gibson focused on exploratory behaviors and devised the “visual cliff” to test infants' responses to an apparent drop-off (Gibson, Reference Gibson1988; Gibson & Walk, Reference Gibson and Walk1960). Held used psychophysical functions to index the development of stereoscopic depth perception and devised the “kitten carousel” to test the role of self-produced visual feedback from locomotion (Held, Birch, & Gwiazda, Reference Held, Birch and Gwiazda1980; Held & Hein, Reference Held and Hein1963).
Spelke's descriptions of Gibson's and Held's methods lay the foundation for her reliance on looking time to study infant cognition. Her arguments for innate avoidance of a drop-off lay the foundation for her claims about core knowledge. We take issue with these foundations on several counts. To really know what babies know requires more than rich interpretations based on lean looking-time behaviors. Standard looking-time procedures do not exploit the richness of infant behavior; infant exploration entails more than looking or not looking at a display; and standard looking-time procedures (and also Gibson's use of the visual cliff) are not psychophysical methods. Finally, Gibson's views about whether avoidance of the visual cliff is innate evolved over the course of her career.
Our comments are both biographical and intellectual. Like Spelke, we have unique insights into Gibson's work because all three of us were Gibson's doctoral students. However, we worked with Gibson at different periods in the evolution of her ideas – Spelke from 1973 to 1977, Schmuckler from 1983 to 1988, and Adolph from 1987 to 1993.
Spelke's cohort relied on looking-time methods (e.g., visual habituation, preferential looking). As in modern-day protocols, infants sit in a car seat or caregiver's lap while viewing a visual display, and researchers use group differences in looking duration to infer what infants know. The idea is that infants' “visual exploration” – here, defined by whether, not where, infants look at a display – can reveal perceptual sensitivity, learning over the course of multiple trials, or what infants knew prior to viewing the stimuli. Indeed, Spelke (Reference Spelke1976, Reference Spelke1979) innovated an influential cross-modal looking-time procedure in which babies hear sounds or touch objects that match one of two visual displays.
Over the ensuing decades when Schmuckler and Adolph were doctoral students, Gibson returned to the questions that fascinated her in the early 1960s with the visual cliff. In contrast to Spelke's looking-time era, now infants were out of the car seat moving around. The focus was on sensitivity to optic flow for balance and steering and perception of affordances for locomotion over challenging ground surfaces (e.g., Adolph, Reference Adolph1997; Adolph, Eppler, & Gibson, Reference Adolph, Eppler and Gibson1993; Gibson, Reference Gibson1997; Gibson et al., Reference Gibson, Riccio, Schmuckler, Stoffregen, Rosenberg and Taormina1987; Schmuckler & Gibson, Reference Schmuckler and Gibson1989). In these studies, apparatuses were not covered with safety glass; instead, babies' safety was ensured with netting or a researcher rescued infants when they fell. New apparatuses were built, new paradigms were developed, new tools were available for recording behavior, and thus new findings about perception, exploration, and action emerged. Some findings conflicted with Gibson's earlier work or called for new interpretations, including infants' behavior at the edge of a drop-off. Gibson willingly entertained these new findings and ideas, even if they conflicted with her prior interpretations. She would listen thoughtfully and say, “Well, dear, that's very interesting. Do more experiments to figure out what's going on.”
Rich descriptions of behavior provide critical evidence about what infants know
Behavior is infinitely rich. It is up to researchers – using the recording technologies and tools at their disposal – to decide how much of the richness to describe. For example, to demonstrate that conditioned responses need not be rigidly stereotypic, Gibson (Reference Gibson1952, Reference Gibson1991) described nine reactions in infant goats to an aversive conditioned stimulus (shock to foreleg) – including both flexing and extending the leg, walking forward and backward, and wheeling in circles. Her descriptions of behavior on the visual cliff were equally rich (Gibson & Walk, Reference Gibson and Walk1960; Walk & Gibson, Reference Walk and Gibson1961). One insightful observation was that animals only show fear when forced onto the safety glass: When placed on the deep side, lambs and kids freeze in defensive postures with front legs rigid and hind legs limp. But when deciding for themselves whether to cross, animals calmly explore the shallow side of the apparatus and peer over the edge of the deep side. Later work showed that human infants spend most of their time near the brink of the deep side, regardless of whether they cross or avoid, showing neutral or positive – not negative – facial expressions in either case (Adolph, Tamis-LeMonda, Ishak, Karasik, & Lobo, Reference Adolph, Tamis-LeMonda, Ishak, Karasik and Lobo2008; Kretch & Adolph, Reference Kretch and Adolph2017; Tamis-LeMonda et al., Reference Tamis-LeMonda, Adolph, Lobo, Karasik, Dimitropoulou and Ishak2008).
Rich descriptions are not colorful frills. Rather, the suite of behaviors can provide converging evidence. For example, infants' increased hesitation, exploratory looking and touching, displacement behaviors, refusal to walk, and use of alternative strategies all point to infants' perception that a deformable waterbed or steep slope does not afford walking (Adolph, Reference Adolph1997; Gibson et al., Reference Gibson, Riccio, Schmuckler, Stoffregen, Rosenberg and Taormina1987). Similarly, infants lean away from a looming object and toward an open aperture (Carroll & Gibson, Reference Carroll and Gibson1981) and blink in response to a looming object but not to a looming aperture (Schmuckler & Li, Reference Schmuckler and Li1998), providing converging evidence that infants perceive affordances for collision versus passage. Alternatively, behaviors can alter interpretations of the primary outcome measure, as when novice walkers explore the edge of a precipice, but walk over the brink nonetheless (Adolph, Reference Adolph1997; Adolph et al., Reference Adolph, Tamis-LeMonda, Ishak, Karasik and Lobo2008; Karasik, Tamis-LeMonda, & Adolph, Reference Karasik, Tamis-LeMonda and Adolph2016).
Looking time does not capture the richness of visual exploration
In standard looking-time paradigms (e.g., preferential looking, visual habituation, violation of expectation), the richness of infants' visual exploration is reduced to a single metric – accumulated duration of looking. In the 1970s, researchers were limited by available tools for recording duration of looks, and they could not record where on the display infants looked. But now eye-tracking technologies and video-annotation tools show that visual exploration is exceedingly rich – filled with looks of varying durations to various parts of a display. It is worthwhile to capture this richness. For example, Kellman and Spelke (Reference Kellman and Spelke1983) found that infants who are habituated to a partially occluded rod moving behind a box perceive one unified rod rather than two rod parts. But visual habituation relies on group data and is not sufficiently detailed or powerful to explain why infants perceive object unity for moving objects. Kellman and Spelke could only speculate. In contrast, richer eye-tracking data reveal that individual differences in visual exploration explain infants' perception of object unity: Infants who look at the visible parts of the moving rod during habituation subsequently dishabituate to two rod parts at test, whereas infants who visually explore the box or background do not (Johnson, Slemmer, & Amso, Reference Johnson, Slemmer and Amso2004).
Moreover, in standard looking-time studies, other behaviors babies emit are routinely ignored – pupil dilation, looks to caregivers, facial and manual gestures, vocalizations, postural changes, and so on. Looking-time researchers acknowledge that “surprise” at an “unexpected” event is merely shorthand for “longer looking” to displays researchers consider unexpected. But uninformed readers do not realize that behavioral indices of surprise such as infants' facial expressions – when included at all – often fail to provide converging evidence (Camras et al., Reference Camras, Ujiie, Mayake, Wang, Murdoch, Meng and Campos2002; Scherer, Zentner, & Stern, Reference Scherer, Zentner and Stern2004).
Finally, when infants act in the world with all the behaviors in their repertoires, possibilities for exploration are limitless (Gibson, Reference Gibson1988). Babies explore objects with their eyes, hands, and mouths. They explore ground surfaces by looking, touching, and testing various postures and forms of locomotion. Their every movement generates perceptual information.
Looking time is not psychophysics: Open air or otherwise
Spelke implies that looking time involves psychophysics. Since the 1960s, psychophysics is associated with methods that link systematic variations in a physical dimension of the environment with the accuracy of perception (Cornsweet, Reference Cornsweet1962; Green & Swets, Reference Green and Swets1966). Many psychophysical methods do not require self-report by adult humans (as Spelke attributes to Helmholtz). Notably, Teller's (Reference Teller1979) “forced-choice preferential-looking” procedure is a psychophysical method appropriate for use with babies and other nonverbal animals.
Psychophysical methods are extremely powerful because the ground truth is the known physical dimension. In addition, they yield psychometric functions for individual participants. In contrast, standard looking-time procedures are weak methods because they are based on the reliability of human judgments (or computer-vision algorithms) with no external ground truth. They must rely on group data and therefore cannot allow conclusions about individual infants. Moreover, because preferential and cross-modal preferential-looking paradigms lead researchers to accept both novelty and familiarity preferences as evidence of discrimination, these paradigms incorporate a fundamental ambiguity in determining and interpreting infants' perceptual experiences (Hunter & Ames, Reference Hunter, Ames, Rovee-Collier and Lipsitt1988). Contrary to Spelke's claims, psychophysics and looking time are different beasts.
Spelke correctly credits Held for conducting psychophysical experiments with infants, but incorrectly credits Gibson for doing the same. Gibson did conduct “open-air” psychophysical studies with adults walking through fields judging distances among targets (Gibson & Bergman, Reference Gibson and Bergman1954), and she admired Teller's ingenious forced-choice psychophysical method (Gibson & Pick, Reference Gibson and Pick2000). However, Gibson never used psychophysics with infants in her own studies. To be sure, change in a visual display from habituation to test or contrasts between shallow and deep sides of the visual cliff are experimental manipulations. But they are not psychophysics.
The evolution of Gibson's ideas from depth perception to perceiving affordances
In her original studies, Gibson viewed the visual cliff as a test of depth perception, and she did indeed conclude that avoidance of the deep side was innate (Gibson & Walk, Reference Gibson and Walk1960; Walk & Gibson, Reference Walk and Gibson1961). Decades later, Gibson (Reference Gibson1991) retained her assumption of innateness, but reinterpreted her work in terms of perception of affordances (Gibson, Reference Gibson1997), and by the 2000s, she believed that avoidance of a precipice is learned (Gibson, Reference Gibson1997, Reference Gibson2002; Gibson & Pick, Reference Gibson and Pick2000).
So why do infants avoid falling at the edge of an impossibly high drop-off, steep slope, narrow bridge, wide gap, or narrow ledge? As both Spelke and Gibson propose, sensitivity to depth information might be available at birth or shortly thereafter. However, depth perception is only a necessary condition, not a sufficient one. Altricial animals require learning to perceive the difference between a step and a cliff, an incline and a steep slope, a walkway and a bridge, and so on – that is, they must learn to perceive affordances for locomotion (Gibson & Pick, Reference Gibson and Pick2000).
What do infants learn? Negative feedback from falling is not necessary, as Walk and Gibson (Reference Walk and Gibson1961) showed with dark-reared kittens that walked repeatedly onto the deep side of the visual cliff in the light and as Adolph (Reference Adolph1995, Reference Adolph1997, Reference Adolph2000) showed with human infants on slopes and gaps. Likewise, experience with drop-offs, slopes, or other such obstacles is not necessary. Rather, infants must learn to perceive the relations between the physical features of the environment and the current status of their bodies and skills (Gibson, Reference Gibson1997). Such relations change from moment to moment, so exploration is needed to generate the requisite information. Spelke's innate knowledge and fetal dreams in precocial animals cannot supplant real-time exploration and learning.
Conclusions
This commentary about Spelke's book is not merely a bunch of middle-aged, former students arguing about their mentor's legacy. It's about how to do developmental science. Spelke writes in her prologue, “To learn how infants think, we have to listen to what the infants in our studies tell us.” However, overly simplified behaviors provide only a crude narrative of what babies might know. For Gibson, the richness of behavior is key. She advised her students to observe infants with an open mind, and to “let the behaviors speak to you.” Thus, a critical lesson we learned in her lab is that the rich details of what babies do allow their voices to be heard more clearly.
Acknowledgments
The authors wish to thank Mark Blumburg and Catherine Tamis-LeMonda for their helpful comments on previous versions of this commentary.
Financial support
This commentary was supported by NICHD grant R01-HD33486 and DARPA grant N66001-19-2-4035 to K. E. A., and a Natural Sciences and Engineering Research Council of Canada Discovery Grant to M. A. S.
Competing interest
None.