{"id":146725,"date":"2013-09-20T12:00:15","date_gmt":"2013-09-20T16:00:15","guid":{"rendered":"\/gazette\/?p=146725"},"modified":"2019-05-31T16:22:42","modified_gmt":"2019-05-31T20:22:42","slug":"a-higher-plane","status":"publish","type":"post","link":"https:\/\/news.harvard.edu\/gazette\/story\/2013\/09\/a-higher-plane\/","title":{"rendered":"A higher plane"},"content":{"rendered":"\n\t
\"\"

Previous research has shown that young children and animals use geometric information in similar ways \u2014 to navigate environment and to recognize shapes. Harvard graduate student Moira Dillon worked with children of varying ages, including 4-year-old Helga Boros, to investigate her research. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d <\/p>

Rose Lincoln\/Harvard Staff Photographer<\/p><\/figcaption><\/figure>\n\n\t

\n\t\t\t\n\t\t\tScience & Tech\t\t<\/a>\n\t\t\n\t\t

\n\t\tA higher plane\t<\/h1>\n\n\t\n\t\t\t<\/div>\n\t\t\n\t
\n\t\t
\n\t\t\t
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\n\t\tPeter Reuell\t<\/p>\n\t\t\t

\n\t\t\tHarvard Staff Writer\t\t<\/p>\n\t\t\t\t\t<\/address>\n\t\t<\/div>\n\n\t\t

\n\t\t\tUniquely human geometric skills traced to evolution\t\t<\/h2>\n\t\t\n<\/header>\n\n\n\n
\n\n\n\t\t

Here\u2019s a short geometry test: How many straight lines can be drawn connecting two points on a flat plane? If you make two angles on a triangle smaller, does the third get larger or smaller? If you split a square diagonally, are the two resulting triangles the same size or different?<\/p>\n

If the answers \u2014 for the record, one, larger, and the same \u2014 seem obvious, they should be. The questions are examples of the innate understanding of abstract geometry that all humans possess, even if they\u2019ve never studied the subject. For researchers, however, the question is: Where does that knowledge come from?<\/p>\n

The answer, say Harvard scientists in Elizabeth Spelke\u2019s Laboratory for Developmental Studies, may lie deep in our evolutionary history.<\/p>\n

Previous research has shown that young children and animals use geometric information in similar ways \u2014 to navigate environment and to recognize shapes. In a study published last month in the Proceedings of the National Academy of Sciences<\/a>, researchers presented evidence that young children rely on the same abilities when exercising uniquely human abstract geometric skills, such as reading maps. The results suggest the innate understanding of abstract geometry among humans has origins in the evolutionary past.<\/p>\n

\u201cThere are two possibilities for the origins of this human-specific innate understanding of geometry,\u201d said graduate student Moira Dillon<\/a>, the first author on the study. <\/b>\u201cOne is that it\u2019s something that\u2019s completely new to humans; it\u2019s something we\u2019ve arrived at through our complex cognitive development. The other possibility is that it derives from existing geometric skills we\u2019ve inherited from other animals.\u201d<\/p>\n

Researchers in earlier studies were able to show that animals possess two basic geometric abilities: the ability to use distance and directional information to navigate their world, and the ability to use angle and length information to recognize shapes.<\/p>\n

Using tests similar to those used with other animals, as well as tests specifically designed to tap into young children\u2019s ability to read geometric maps, Dillon and her colleagues showed that children use the geometric abilities shared with other animals to understand uniquely human spatial symbols.<\/p>\n

Previous tests, Dillon said, demonstrated that children as young as 2\u00bd could relate the abstract geometry in a map to the real world, but it was unclear how. The new work revealed that young children, unlike animals, can flexibly use their geometric sensitivities \u2014 to distance and direction or to angle and length \u2014 to read maps.<\/p>\n

\u201cWhat we knew is that children \u2014 just like animals \u2014 use distance and directional information to navigate, and angle and length information to recognize shapes,\u201d Dillon said. \u201cWhat we now see is that children \u2014 unlike animals \u2014 can use one or the other type of geometric information flexibly when reading spatial symbols like maps, depending on what information is available to them in the environment.\u201d<\/p>\n

To uncover these intuitions and understand their origins, Dillon and her colleagues started by building two triangular rooms in the lab. One included only the sides of the triangle, with the corners removed, while the other included only the triangle\u2019s corners, with the sides removed.<\/p>\n

Children were presented with a map of the full triangle, and were asked to place a stuffed animal at a location marked by a dot.<\/p>\n

\u201cWhat we found was that children were relying either on their ability to navigate or their ability to recognize shapes,\u201d Dillon said. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d<\/p>\n

Although young children showed flexibility in their use of geometry when reading maps, there were still limitations: They were unable to relate the two geometric sensitivities to each other. Dillon said previous research has shown that by about age 12, children begin to integrate these two geometric sensitivities \u2014 relating distance information to angle information. Older children and adults therefore achieve the sort of abstract geometric knowledge that has long puzzled researchers.<\/p>\n

\u201cAdults, because they have a more advanced, mature abstract representation of geometry, can use both types of information at the same time,\u201d she said. \u201cBut because those intuitions are fully developed, it\u2019s difficult to look at adults and understand their origins.\u201d<\/p>\n

The challenge for researchers now is to understand how the ability to use geometry for navigation and shape recognition come together to form our abstract innate knowledge about the points, lines, and figures on the Euclidean plane.<\/p>\n

\u201cWe have to figure out what happens between age 4 and age 12,\u201d Dillon said. \u201cHow do we get from this incredible early ability to use symbolic geometry in maps to the later-developing, very abstract ability to reason about points and lines and the behavior of triangles when they\u2019re manipulated? We think we know now where these intuitions come from, but we\u2019re not sure how they come together.\u201d<\/p>\n\n\n<\/div>\n\n\t\t","protected":false},"excerpt":{"rendered":"

Research by scientists in Elizabeth Spelke\u2019s lab suggests our innate understanding of abstract geometry has origins in the evolutionary past. <\/p>\n","protected":false},"author":105622744,"featured_media":146728,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"gz_ga_pageviews":0,"gz_ga_lastupdated":"","document_color_palette":"crimson","author":"Peter Reuell","affiliation":"Harvard Staff 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Harvard graduate student Moira Dillon worked with children of varying ages, including 4-year-old Helga Boros, to investigate her research. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d ","mediaId":146728,"mediaSize":"full","mediaType":"image","mediaUrl":"https:\/\/news.harvard.edu\/gazette\/wp-content\/uploads\/2013\/09\/082213_dillon_1670_605.jpg","poster":"","title":"A higher plane","subheading":"Uniquely human geometric skills traced to evolution","centeredImage":true,"className":"is-style-full-width-text-below","mediaHeight":403,"mediaWidth":605,"backgroundFixed":false,"backgroundTone":"light","coloredBackground":false,"displayOverlay":true,"fadeInText":false,"isAmbient":false,"mediaLength":"","mediaPosition":"","posterText":"","titleAbove":false,"useUncroppedImage":false,"lock":[],"metadata":[]},"innerBlocks":[],"innerHTML":"<figure class=\"wp-block-image\"><img alt=\"\" height=\"403\" loading=\"eager\" src=\"https:\/\/news.harvard.edu\/gazette\/wp-content\/uploads\/2013\/09\/082213_dillon_1670_605.jpg\" width=\"605\"\/><figcaption class=\"wp-element-caption\"><p class=\"wp-element-caption--caption\">Previous research has shown that young children and animals use geometric information in similar ways \u2014 to navigate environment and to recognize shapes. Harvard graduate student Moira Dillon worked with children of varying ages, including 4-year-old Helga Boros, to investigate her research. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d <\/p><p class=\"wp-element-caption--credit\">Rose Lincoln\/Harvard Staff Photographer<\/p><\/figcaption><\/figure>\n","innerContent":["<figure class=\"wp-block-image\"><img alt=\"\" height=\"403\" loading=\"eager\" src=\"https:\/\/news.harvard.edu\/gazette\/wp-content\/uploads\/2013\/09\/082213_dillon_1670_605.jpg\" width=\"605\"\/><figcaption class=\"wp-element-caption\"><p class=\"wp-element-caption--caption\">Previous research has shown that young children and animals use geometric information in similar ways \u2014 to navigate environment and to recognize shapes. Harvard graduate student Moira Dillon worked with children of varying ages, including 4-year-old Helga Boros, to investigate her research. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d <\/p><p class=\"wp-element-caption--credit\">Rose Lincoln\/Harvard Staff Photographer<\/p><\/figcaption><\/figure>\n"],"rendered":"<header\n\tclass=\"wp-block-harvard-gazette-article-header alignfull article-header is-style-full-width-text-below centered-image\"\n\tstyle=\" \"\n>\n\t<figure class=\"wp-block-image\"><img alt=\"\" height=\"403\" loading=\"eager\" src=\"https:\/\/news.harvard.edu\/gazette\/wp-content\/uploads\/2013\/09\/082213_dillon_1670_605.jpg\" width=\"605\"\/><figcaption class=\"wp-element-caption\"><p class=\"wp-element-caption--caption\">Previous research has shown that young children and animals use geometric information in similar ways \u2014 to navigate environment and to recognize shapes. Harvard graduate student Moira Dillon worked with children of varying ages, including 4-year-old Helga Boros, to investigate her research. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d <\/p><p class=\"wp-element-caption--credit\">Rose Lincoln\/Harvard Staff Photographer<\/p><\/figcaption><\/figure>\n\n\t<div class=\"article-header__content\">\n\t\t\t<a\n\t\t\tclass=\"article-header__category\"\n\t\t\thref=\"https:\/\/news.harvard.edu\/gazette\/section\/science-technology\/\"\n\t\t>\n\t\t\tScience & Tech\t\t<\/a>\n\t\t\n\t\t<h1 class=\"article-header__title wp-block-heading \">\n\t\tA higher plane\t<\/h1>\n\n\t\n\t\t\t<\/div>\n\t\t\n\t<div class=\"article-header__meta\">\n\t\t<div class=\"wp-block-post-author\">\n\t\t\t<address class=\"wp-block-post-author__content\">\n\t\t\t\t\t<p class=\"author wp-block-post-author__name\">\n\t\tPeter Reuell\t<\/p>\n\t\t\t<p class=\"wp-block-post-author__byline\">\n\t\t\tHarvard Staff Writer\t\t<\/p>\n\t\t\t\t\t<\/address>\n\t\t<\/div>\n\n\t\t<time class=\"article-header__date\" datetime=\"2013-09-20\">\n\t\t\tSeptember 20, 2013\t\t<\/time>\n\n\t\t<span class=\"article-header__reading-time\">\n\t\t\t5 min read\t\t<\/span>\n\t<\/div>\n\n\t\n\t\t\t<h2 class=\"article-header__subheading wp-block-heading\">\n\t\t\tUniquely human geometric skills traced to evolution\t\t<\/h2>\n\t\t\n<\/header>\n"},"2":{"blockName":"core\/group","attrs":{"templateLock":false,"metadata":{"name":"Article content"},"align":"wide","layout":{"type":"constrained","justifyContent":"center"},"tagName":"div","lock":[],"className":"","style":[],"backgroundColor":"","textColor":"","gradient":"","fontSize":"","fontFamily":"","borderColor":"","ariaLabel":"","anchor":""},"innerBlocks":[{"blockName":"core\/freeform","attrs":{"content":"","lock":[],"metadata":[]},"innerBlocks":[],"innerHTML":"\n\t\t<p>Here\u2019s a short geometry test: How many straight lines can be drawn connecting two points on a flat plane? If you make two angles on a triangle smaller, does the third get larger or smaller? If you split a square diagonally, are the two resulting triangles the same size or different?<\/p>\n<p>If the answers \u2014 for the record, one, larger, and the same \u2014 seem obvious, they should be. The questions are examples of the innate understanding of abstract geometry that all humans possess, even if they\u2019ve never studied the subject. For researchers, however, the question is: Where does that knowledge come from?<\/p>\n<p>The answer, say Harvard scientists in Elizabeth Spelke\u2019s Laboratory for Developmental Studies, may lie deep in our evolutionary history.<\/p>\n<p>Previous research has shown that young children and animals use geometric information in similar ways \u2014 to navigate environment and to recognize shapes. In a study published last month in the <a href=\"http:\/\/www.pnas.org\/\">Proceedings of the National Academy of Sciences<\/a>, researchers presented evidence that young children rely on the same abilities when exercising uniquely human abstract geometric skills, such as reading maps. The results suggest the innate understanding of abstract geometry among humans has origins in the evolutionary past.<\/p>\n<p>\u201cThere are two possibilities for the origins of this human-specific innate understanding of geometry,\u201d said graduate student <a href=\"http:\/\/www.wjh.harvard.edu\/~mdillon\/Home.html\">Moira Dillon<\/a>, the first author on the study.<b> <\/b>\u201cOne is that it\u2019s something that\u2019s completely new to humans; it\u2019s something we\u2019ve arrived at through our complex cognitive development. The other possibility is that it derives from existing geometric skills we\u2019ve inherited from other animals.\u201d<\/p>\n<p>Researchers in earlier studies were able to show that animals possess two basic geometric abilities: the ability to use distance and directional information to navigate their world, and the ability to use angle and length information to recognize shapes.<\/p>\n<p>Using tests similar to those used with other animals, as well as tests specifically designed to tap into young children\u2019s ability to read geometric maps, Dillon and her colleagues showed that children use the geometric abilities shared with other animals to understand uniquely human spatial symbols.<\/p>\n<p>Previous tests, Dillon said, demonstrated that children as young as 2\u00bd could relate the abstract geometry in a map to the real world, but it was unclear how. The new work revealed that young children, unlike animals, can flexibly use their geometric sensitivities \u2014 to distance and direction or to angle and length \u2014 to read maps.<\/p>\n<p>\u201cWhat we knew is that children \u2014 just like animals \u2014 use distance and directional information to navigate, and angle and length information to recognize shapes,\u201d Dillon said. \u201cWhat we now see is that children \u2014 unlike animals \u2014 can use one or the other type of geometric information flexibly when reading spatial symbols like maps, depending on what information is available to them in the environment.\u201d<\/p>\n<p>To uncover these intuitions and understand their origins, Dillon and her colleagues started by building two triangular rooms in the lab. One included only the sides of the triangle, with the corners removed, while the other included only the triangle\u2019s corners, with the sides removed.<\/p>\n<p>Children were presented with a map of the full triangle, and were asked to place a stuffed animal at a location marked by a dot.<\/p>\n<p>\u201cWhat we found was that children were relying either on their ability to navigate or their ability to recognize shapes,\u201d Dillon said. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d<\/p>\n<p>Although young children showed flexibility in their use of geometry when reading maps, there were still limitations: They were unable to relate the two geometric sensitivities to each other. Dillon said previous research has shown that by about age 12, children begin to integrate these two geometric sensitivities \u2014 relating distance information to angle information. Older children and adults therefore achieve the sort of abstract geometric knowledge that has long puzzled researchers.<\/p>\n<p>\u201cAdults, because they have a more advanced, mature abstract representation of geometry, can use both types of information at the same time,\u201d she said. \u201cBut because those intuitions are fully developed, it\u2019s difficult to look at adults and understand their origins.\u201d<\/p>\n<p>The challenge for researchers now is to understand how the ability to use geometry for navigation and shape recognition come together to form our abstract innate knowledge about the points, lines, and figures on the Euclidean plane.<\/p>\n<p>\u201cWe have to figure out what happens between age 4 and age 12,\u201d Dillon said. \u201cHow do we get from this incredible early ability to use symbolic geometry in maps to the later-developing, very abstract ability to reason about points and lines and the behavior of triangles when they\u2019re manipulated? We think we know now where these intuitions come from, but we\u2019re not sure how they come together.\u201d<\/p>\n","innerContent":["\n\t\t<p>Here\u2019s a short geometry test: How many straight lines can be drawn connecting two points on a flat plane? If you make two angles on a triangle smaller, does the third get larger or smaller? If you split a square diagonally, are the two resulting triangles the same size or different?<\/p>\n<p>If the answers \u2014 for the record, one, larger, and the same \u2014 seem obvious, they should be. The questions are examples of the innate understanding of abstract geometry that all humans possess, even if they\u2019ve never studied the subject. For researchers, however, the question is: Where does that knowledge come from?<\/p>\n<p>The answer, say Harvard scientists in Elizabeth Spelke\u2019s Laboratory for Developmental Studies, may lie deep in our evolutionary history.<\/p>\n<p>Previous research has shown that young children and animals use geometric information in similar ways \u2014 to navigate environment and to recognize shapes. In a study published last month in the <a href=\"http:\/\/www.pnas.org\/\">Proceedings of the National Academy of Sciences<\/a>, researchers presented evidence that young children rely on the same abilities when exercising uniquely human abstract geometric skills, such as reading maps. The results suggest the innate understanding of abstract geometry among humans has origins in the evolutionary past.<\/p>\n<p>\u201cThere are two possibilities for the origins of this human-specific innate understanding of geometry,\u201d said graduate student <a href=\"http:\/\/www.wjh.harvard.edu\/~mdillon\/Home.html\">Moira Dillon<\/a>, the first author on the study.<b> <\/b>\u201cOne is that it\u2019s something that\u2019s completely new to humans; it\u2019s something we\u2019ve arrived at through our complex cognitive development. The other possibility is that it derives from existing geometric skills we\u2019ve inherited from other animals.\u201d<\/p>\n<p>Researchers in earlier studies were able to show that animals possess two basic geometric abilities: the ability to use distance and directional information to navigate their world, and the ability to use angle and length information to recognize shapes.<\/p>\n<p>Using tests similar to those used with other animals, as well as tests specifically designed to tap into young children\u2019s ability to read geometric maps, Dillon and her colleagues showed that children use the geometric abilities shared with other animals to understand uniquely human spatial symbols.<\/p>\n<p>Previous tests, Dillon said, demonstrated that children as young as 2\u00bd could relate the abstract geometry in a map to the real world, but it was unclear how. The new work revealed that young children, unlike animals, can flexibly use their geometric sensitivities \u2014 to distance and direction or to angle and length \u2014 to read maps.<\/p>\n<p>\u201cWhat we knew is that children \u2014 just like animals \u2014 use distance and directional information to navigate, and angle and length information to recognize shapes,\u201d Dillon said. \u201cWhat we now see is that children \u2014 unlike animals \u2014 can use one or the other type of geometric information flexibly when reading spatial symbols like maps, depending on what information is available to them in the environment.\u201d<\/p>\n<p>To uncover these intuitions and understand their origins, Dillon and her colleagues started by building two triangular rooms in the lab. One included only the sides of the triangle, with the corners removed, while the other included only the triangle\u2019s corners, with the sides removed.<\/p>\n<p>Children were presented with a map of the full triangle, and were asked to place a stuffed animal at a location marked by a dot.<\/p>\n<p>\u201cWhat we found was that children were relying either on their ability to navigate or their ability to recognize shapes,\u201d Dillon said. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d<\/p>\n<p>Although young children showed flexibility in their use of geometry when reading maps, there were still limitations: They were unable to relate the two geometric sensitivities to each other. Dillon said previous research has shown that by about age 12, children begin to integrate these two geometric sensitivities \u2014 relating distance information to angle information. Older children and adults therefore achieve the sort of abstract geometric knowledge that has long puzzled researchers.<\/p>\n<p>\u201cAdults, because they have a more advanced, mature abstract representation of geometry, can use both types of information at the same time,\u201d she said. \u201cBut because those intuitions are fully developed, it\u2019s difficult to look at adults and understand their origins.\u201d<\/p>\n<p>The challenge for researchers now is to understand how the ability to use geometry for navigation and shape recognition come together to form our abstract innate knowledge about the points, lines, and figures on the Euclidean plane.<\/p>\n<p>\u201cWe have to figure out what happens between age 4 and age 12,\u201d Dillon said. \u201cHow do we get from this incredible early ability to use symbolic geometry in maps to the later-developing, very abstract ability to reason about points and lines and the behavior of triangles when they\u2019re manipulated? We think we know now where these intuitions come from, but we\u2019re not sure how they come together.\u201d<\/p>\n"],"rendered":"\n\t\t<p>Here\u2019s a short geometry test: How many straight lines can be drawn connecting two points on a flat plane? If you make two angles on a triangle smaller, does the third get larger or smaller? If you split a square diagonally, are the two resulting triangles the same size or different?<\/p>\n<p>If the answers \u2014 for the record, one, larger, and the same \u2014 seem obvious, they should be. The questions are examples of the innate understanding of abstract geometry that all humans possess, even if they\u2019ve never studied the subject. For researchers, however, the question is: Where does that knowledge come from?<\/p>\n<p>The answer, say Harvard scientists in Elizabeth Spelke\u2019s Laboratory for Developmental Studies, may lie deep in our evolutionary history.<\/p>\n<p>Previous research has shown that young children and animals use geometric information in similar ways \u2014 to navigate environment and to recognize shapes. In a study published last month in the <a href=\"http:\/\/www.pnas.org\/\">Proceedings of the National Academy of Sciences<\/a>, researchers presented evidence that young children rely on the same abilities when exercising uniquely human abstract geometric skills, such as reading maps. The results suggest the innate understanding of abstract geometry among humans has origins in the evolutionary past.<\/p>\n<p>\u201cThere are two possibilities for the origins of this human-specific innate understanding of geometry,\u201d said graduate student <a href=\"http:\/\/www.wjh.harvard.edu\/~mdillon\/Home.html\">Moira Dillon<\/a>, the first author on the study.<b> <\/b>\u201cOne is that it\u2019s something that\u2019s completely new to humans; it\u2019s something we\u2019ve arrived at through our complex cognitive development. The other possibility is that it derives from existing geometric skills we\u2019ve inherited from other animals.\u201d<\/p>\n<p>Researchers in earlier studies were able to show that animals possess two basic geometric abilities: the ability to use distance and directional information to navigate their world, and the ability to use angle and length information to recognize shapes.<\/p>\n<p>Using tests similar to those used with other animals, as well as tests specifically designed to tap into young children\u2019s ability to read geometric maps, Dillon and her colleagues showed that children use the geometric abilities shared with other animals to understand uniquely human spatial symbols.<\/p>\n<p>Previous tests, Dillon said, demonstrated that children as young as 2\u00bd could relate the abstract geometry in a map to the real world, but it was unclear how. The new work revealed that young children, unlike animals, can flexibly use their geometric sensitivities \u2014 to distance and direction or to angle and length \u2014 to read maps.<\/p>\n<p>\u201cWhat we knew is that children \u2014 just like animals \u2014 use distance and directional information to navigate, and angle and length information to recognize shapes,\u201d Dillon said. \u201cWhat we now see is that children \u2014 unlike animals \u2014 can use one or the other type of geometric information flexibly when reading spatial symbols like maps, depending on what information is available to them in the environment.\u201d<\/p>\n<p>To uncover these intuitions and understand their origins, Dillon and her colleagues started by building two triangular rooms in the lab. One included only the sides of the triangle, with the corners removed, while the other included only the triangle\u2019s corners, with the sides removed.<\/p>\n<p>Children were presented with a map of the full triangle, and were asked to place a stuffed animal at a location marked by a dot.<\/p>\n<p>\u201cWhat we found was that children were relying either on their ability to navigate or their ability to recognize shapes,\u201d Dillon said. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d<\/p>\n<p>Although young children showed flexibility in their use of geometry when reading maps, there were still limitations: They were unable to relate the two geometric sensitivities to each other. Dillon said previous research has shown that by about age 12, children begin to integrate these two geometric sensitivities \u2014 relating distance information to angle information. Older children and adults therefore achieve the sort of abstract geometric knowledge that has long puzzled researchers.<\/p>\n<p>\u201cAdults, because they have a more advanced, mature abstract representation of geometry, can use both types of information at the same time,\u201d she said. \u201cBut because those intuitions are fully developed, it\u2019s difficult to look at adults and understand their origins.\u201d<\/p>\n<p>The challenge for researchers now is to understand how the ability to use geometry for navigation and shape recognition come together to form our abstract innate knowledge about the points, lines, and figures on the Euclidean plane.<\/p>\n<p>\u201cWe have to figure out what happens between age 4 and age 12,\u201d Dillon said. \u201cHow do we get from this incredible early ability to use symbolic geometry in maps to the later-developing, very abstract ability to reason about points and lines and the behavior of triangles when they\u2019re manipulated? We think we know now where these intuitions come from, but we\u2019re not sure how they come together.\u201d<\/p>\n"}],"innerHTML":"\n<div class=\"wp-block-group alignwide\">\n\n\n\n<\/div>\n","innerContent":["\n<div class=\"wp-block-group alignwide\">\n\n","\n\n<\/div>\n"],"rendered":"\n<div class=\"wp-block-group alignwide has-global-padding is-content-justification-center is-layout-constrained wp-block-group-is-layout-constrained\">\n\n\n\t\t<p>Here\u2019s a short geometry test: How many straight lines can be drawn connecting two points on a flat plane? If you make two angles on a triangle smaller, does the third get larger or smaller? If you split a square diagonally, are the two resulting triangles the same size or different?<\/p>\n<p>If the answers \u2014 for the record, one, larger, and the same \u2014 seem obvious, they should be. The questions are examples of the innate understanding of abstract geometry that all humans possess, even if they\u2019ve never studied the subject. For researchers, however, the question is: Where does that knowledge come from?<\/p>\n<p>The answer, say Harvard scientists in Elizabeth Spelke\u2019s Laboratory for Developmental Studies, may lie deep in our evolutionary history.<\/p>\n<p>Previous research has shown that young children and animals use geometric information in similar ways \u2014 to navigate environment and to recognize shapes. In a study published last month in the <a href=\"http:\/\/www.pnas.org\/\">Proceedings of the National Academy of Sciences<\/a>, researchers presented evidence that young children rely on the same abilities when exercising uniquely human abstract geometric skills, such as reading maps. The results suggest the innate understanding of abstract geometry among humans has origins in the evolutionary past.<\/p>\n<p>\u201cThere are two possibilities for the origins of this human-specific innate understanding of geometry,\u201d said graduate student <a href=\"http:\/\/www.wjh.harvard.edu\/~mdillon\/Home.html\">Moira Dillon<\/a>, the first author on the study.<b> <\/b>\u201cOne is that it\u2019s something that\u2019s completely new to humans; it\u2019s something we\u2019ve arrived at through our complex cognitive development. The other possibility is that it derives from existing geometric skills we\u2019ve inherited from other animals.\u201d<\/p>\n<p>Researchers in earlier studies were able to show that animals possess two basic geometric abilities: the ability to use distance and directional information to navigate their world, and the ability to use angle and length information to recognize shapes.<\/p>\n<p>Using tests similar to those used with other animals, as well as tests specifically designed to tap into young children\u2019s ability to read geometric maps, Dillon and her colleagues showed that children use the geometric abilities shared with other animals to understand uniquely human spatial symbols.<\/p>\n<p>Previous tests, Dillon said, demonstrated that children as young as 2\u00bd could relate the abstract geometry in a map to the real world, but it was unclear how. The new work revealed that young children, unlike animals, can flexibly use their geometric sensitivities \u2014 to distance and direction or to angle and length \u2014 to read maps.<\/p>\n<p>\u201cWhat we knew is that children \u2014 just like animals \u2014 use distance and directional information to navigate, and angle and length information to recognize shapes,\u201d Dillon said. \u201cWhat we now see is that children \u2014 unlike animals \u2014 can use one or the other type of geometric information flexibly when reading spatial symbols like maps, depending on what information is available to them in the environment.\u201d<\/p>\n<p>To uncover these intuitions and understand their origins, Dillon and her colleagues started by building two triangular rooms in the lab. One included only the sides of the triangle, with the corners removed, while the other included only the triangle\u2019s corners, with the sides removed.<\/p>\n<p>Children were presented with a map of the full triangle, and were asked to place a stuffed animal at a location marked by a dot.<\/p>\n<p>\u201cWhat we found was that children were relying either on their ability to navigate or their ability to recognize shapes,\u201d Dillon said. \u201cIf they were presented with a room that only had sides, they used the distance information to navigate, and when they were presented with a room that only had corners, they used the angle information they use to recognize shapes.\u201d<\/p>\n<p>Although young children showed flexibility in their use of geometry when reading maps, there were still limitations: They were unable to relate the two geometric sensitivities to each other. Dillon said previous research has shown that by about age 12, children begin to integrate these two geometric sensitivities \u2014 relating distance information to angle information. Older children and adults therefore achieve the sort of abstract geometric knowledge that has long puzzled researchers.<\/p>\n<p>\u201cAdults, because they have a more advanced, mature abstract representation of geometry, can use both types of information at the same time,\u201d she said. \u201cBut because those intuitions are fully developed, it\u2019s difficult to look at adults and understand their origins.\u201d<\/p>\n<p>The challenge for researchers now is to understand how the ability to use geometry for navigation and shape recognition come together to form our abstract innate knowledge about the points, lines, and figures on the Euclidean plane.<\/p>\n<p>\u201cWe have to figure out what happens between age 4 and age 12,\u201d Dillon said. \u201cHow do we get from this incredible early ability to use symbolic geometry in maps to the later-developing, very abstract ability to reason about points and lines and the behavior of triangles when they\u2019re manipulated? We think we know now where these intuitions come from, but we\u2019re not sure how they come together.\u201d<\/p>\n\n\n<\/div>\n"}},"jetpack-related-posts":[{"id":118073,"url":"https:\/\/news.harvard.edu\/gazette\/story\/2012\/09\/finding-our-way\/","url_meta":{"origin":146725,"position":0},"title":"Finding our way","author":"harvardgazette","date":"September 24, 2012","format":false,"excerpt":"Elizabeth Spelke, a professor of psychology, discussed research on how humans develop navigational skills in an event at the Barker Center.","rel":"","context":"In "Health"","block_context":{"text":"Health","link":"https:\/\/news.harvard.edu\/gazette\/section\/health\/"},"img":{"alt_text":"","src":"https:\/\/news.harvard.edu\/wp-content\/uploads\/2012\/09\/092012_spelke_073_605main.jpg?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/news.harvard.edu\/wp-content\/uploads\/2012\/09\/092012_spelke_073_605main.jpg?resize=350%2C200 1x, https:\/\/news.harvard.edu\/wp-content\/uploads\/2012\/09\/092012_spelke_073_605main.jpg?resize=525%2C300 1.5x"},"classes":[]},{"id":412653,"url":"https:\/\/news.harvard.edu\/gazette\/story\/2025\/07\/mounting-case-against-notion-that-boys-are-born-better-at-math\/","url_meta":{"origin":146725,"position":1},"title":"Mounting case against notion that boys are born better at math","author":"Christy DeSmith","date":"July 3, 2025","format":false,"excerpt":"Elizabeth Spelke studies French testing data, finds no gender gap until instruction begins","rel":"","context":"In "Science & Tech"","block_context":{"text":"Science & Tech","link":"https:\/\/news.harvard.edu\/gazette\/section\/science-technology\/"},"img":{"alt_text":"Elizabeth Spelke","src":"https:\/\/news.harvard.edu\/wp-content\/uploads\/2025\/07\/120224_Elizabeth_Spelke_07.jpeg?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/news.harvard.edu\/wp-content\/uploads\/2025\/07\/120224_Elizabeth_Spelke_07.jpeg?resize=350%2C200 1x, https:\/\/news.harvard.edu\/wp-content\/uploads\/2025\/07\/120224_Elizabeth_Spelke_07.jpeg?resize=525%2C300 1.5x, https:\/\/news.harvard.edu\/wp-content\/uploads\/2025\/07\/120224_Elizabeth_Spelke_07.jpeg?resize=700%2C400 2x"},"classes":[]},{"id":227698,"url":"https:\/\/news.harvard.edu\/gazette\/story\/2017\/07\/research-may-provide-the-tools-to-create-better-schools\/","url_meta":{"origin":146725,"position":2},"title":"Research may provide the tools to create better schools","author":"gazettejohnbaglione","date":"July 7, 2017","format":false,"excerpt":"Harvard and MIT study reveals that cognitive science field experiments are critical to understanding human learning and education.","rel":"","context":"In "Science & Tech"","block_context":{"text":"Science & Tech","link":"https:\/\/news.harvard.edu\/gazette\/section\/science-technology\/"},"img":{"alt_text":"","src":"https:\/\/news.harvard.edu\/wp-content\/uploads\/2017\/07\/122413_spelke_elizabeth_110_605.jpg?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/news.harvard.edu\/wp-content\/uploads\/2017\/07\/122413_spelke_elizabeth_110_605.jpg?resize=350%2C200 1x, https:\/\/news.harvard.edu\/wp-content\/uploads\/2017\/07\/122413_spelke_elizabeth_110_605.jpg?resize=525%2C300 1.5x"},"classes":[]},{"id":69496,"url":"https:\/\/news.harvard.edu\/gazette\/story\/2001\/11\/toddling-toward-the-birth-of-knowledge\/","url_meta":{"origin":146725,"position":3},"title":"Toddling toward the birth of knowledge","author":"gazetteimport","date":"November 29, 2001","format":false,"excerpt":"Elizabeth Spelke was surprised to discover how much infants know about whats going on around them. The newly tenured professor of psychology was just as surprised by their limits. In some situations, counting, for example, babies act more like monkeys, rats, or pigeons than humans.","rel":"","context":"In "Campus & Community"","block_context":{"text":"Campus & Community","link":"https:\/\/news.harvard.edu\/gazette\/section\/campus-community\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":58815,"url":"https:\/\/news.harvard.edu\/gazette\/story\/2004\/07\/which-comes-first-language-or-thought\/","url_meta":{"origin":146725,"position":4},"title":"Which comes first, language or thought?","author":"harvardgazette","date":"July 22, 2004","format":false,"excerpt":"\"Infants are born with a language-independent system for thinking about objects,\" says Elizabeth Spelke, a professor of psychology at Harvard. \"These concepts give meaning to the words they learn later.\" Because languages differ in how they approach objects, many scientists suspected that children must learn the relevant concepts as they\u2026","rel":"","context":"In "Health"","block_context":{"text":"Health","link":"https:\/\/news.harvard.edu\/gazette\/section\/health\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":59346,"url":"https:\/\/news.harvard.edu\/gazette\/story\/2005\/09\/born-to-add\/","url_meta":{"origin":146725,"position":5},"title":"Born to add","author":"harvardgazette","date":"September 22, 2005","format":false,"excerpt":"In experiments, 5-year-olds, who had no real experience using number symbols, \"added\" two arrays of dots and compared them to a third array. When researchers replaced the third array of dots with beeps, the kids integrated the sight and sound quantities easily. The children performed all these tasks successfully, without\u2026","rel":"","context":"In "Science & Tech"","block_context":{"text":"Science & Tech","link":"https:\/\/news.harvard.edu\/gazette\/section\/science-technology\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/posts\/146725","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/users\/105622744"}],"replies":[{"embeddable":true,"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/comments?post=146725"}],"version-history":[{"count":1,"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/posts\/146725\/revisions"}],"predecessor-version":[{"id":277417,"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/posts\/146725\/revisions\/277417"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/media\/146728"}],"wp:attachment":[{"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/media?parent=146725"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/categories?post=146725"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/tags?post=146725"},{"taxonomy":"format","embeddable":true,"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/gazette-formats?post=146725"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/news.harvard.edu\/gazette\/wp-json\/wp\/v2\/series?post=146725"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}