Readers Respond to the March 2023 Issue
COUNTER ARGUMENTS
In “Born to Count,” Sam Clarke and Jacob Beck present several experiments that they assert demonstrate that humans are born with an innate “number sense.” But not one of them indicates that the concept of, say, “eightness” is innate. What they instead show is that there is an innate inequality sense, an ability to distinguish which of two quantities is larger, provided that the difference between them is large enough.
JOEL SANET via e-mail
The various experiments Clarke and Beck describe demonstrate that young children have a concept of order. That is, they can put the elements of a set in order by some criterion. For example, a child may be able to put a golf ball, baseball, softball and soccer ball in order by size. The experiments do not show that these children can count.
ERIC KLIEBER via e-mail
It seems that the property of thought that the article describes might better be called “generalized quantity,” “comparative quantity” or “generalized cardinality.” The term “number” doesn’t seem appropriate for research on young children before they have developed either the ability to use a system of symbols or words associated with specific quantities or cardinalities—or at least before they know the sequence of number words “one, two, three …” or something equivalent.
In my own past research with young children, it seemed to me that their thinking about numbers was more closely related to Giuseppe Peano’s basic concept of “successor” than cardinality or quantity. For example, if a kindergartener responded “five” to the question “How old are you?” the child would certainly not be able to remember far back enough to be conscious of their four birthdays prior to their fifth. To that child, the most important thing about “five” is that it is the successor of “four.”
GEORGE E. GULLEN III Southgate, Mich.
THE AUTHORS REPLY: Arguments that seek to debunk the innate number sense are tempting, but they struggle to fully explain the evidence. Sanet and Klieber propose that young children merely represent inequality and order, respectively, not number. Yet neither proposal can explain young children’s ability to add and multiply, as described in our article. Meanwhile Gullen proposes that children merely represent generalized quantity. We were at pains to explain that the number sense is sensitive to properties that are unique to number, however—for instance, the description relativity isolated by Gottlob Frege.
Gullen observes that when children learn to use number words such as “one, two, three,” they gain a novel appreciation for the successor relation. We agree. But it is a non sequitur to conclude that children don’t represent number beforehand. Just as you can see how far away a tree is (thereby representing distance) before you learn to measure distance precisely with a ruler, you can see how many trees there are (thereby representing number) before you learn to count.
INEQUITABLE INNOVATION
In “The Eight-Billion-Person Bomb” [Observatory], Naomi Oreskes argues against cornucopianism, a theoretical framework that asserts that human ingenuity can overcome limited natural resources.
I would like to offer a point of confirmation that cornucopianism is misguided. On CBC Radio, I recently heard an interview describing the catastrophic effects of finding cobalt, a rare mineral needed for batteries, in the Democratic Republic of the Congo. To me, this illustrates one of the flaws of the cornucopians: they focus on benefits of innovations enjoyed by some while consciously or unconsciously overlooking negatives experienced elsewhere. This is a logical progression of the phenomenon of the past several centuries: global capitalism.
RICHARD “DICK” FAHLMAN Tla’amin Nation, British Columbia
NATURAL CAPITAL IDEA
In “Use Nature as Infrastructure” [Science Agenda, April], the editors lay out the reasons why policy makers should be putting nature on the nation’s balance sheet. The Biden-Harris administration wholeheartedly agrees. In January we released the National Strategy to Develop Statistics for Environmental-Economic Decisions, a historic effort to account for America’s natural assets in our national economic statistics.
We’re currently working to quantify the economic value of our natural capital, including the ocean and rivers that support our recreation and fishing industries, the forests that clean our air and water, the minerals that power our technology economy and drive the electric vehicle revolution, and much more. By expanding the national economic accounting system to include natural capital and by including services from ecosystems in benefit-cost and regulatory analyses, we will more accurately capture the links between nature and the economy—which will help guide policy and business decisions.
Both the Inflation Reduction Act and the Bipartisan Infrastructure Law include funding for nature-based solutions to climate change, such as protecting forests and restoring marshes to reduce greenhouse gas emissions, remove carbon from the atmosphere and lower the risks to people from extreme weather. President Joe Biden has taken additional action by signing executive orders that create a National Nature Assessment to better understand how nature is changing in the U.S.; quantify the impacts of climate change in the federal budget; and promote environmental services and opportunities for local economies across the country.
The Biden-Harris administration is working hard to maintain and invest in natural infrastructure. We’re making sure that ecosystem services are considered at every level of government decision-making.
ELI FENICHEL, HEATHER TALLIS, SOLOMON HSIANG and JANE LUBCHENCO White House Office of Science and Technology Policy
EDITOR’S NOTE: Fenichel was at OSTP when this letter was submitted. He is now at Yale University.
FUNDAMENTALLY WEIRD
British geneticist J.B.S. Haldane (1892–1964) would have been delighted to read “Primordial Soup,” by Clara Moskowitz. It raises the question of why the universe is so floridly strange and weird at all scales. At large scales, we see stars, galaxies, supernovae and black holes; at medium scale, we see molecules, DNA, proteins, molecular machinery and life itself.
And now the tiny, pristine sphere of positive charge of my physics education has become a sea of quarks and antiquarks with three valence quarks bobbing on its surface, all held together by gluons. I, too, am delighted.
JOHN COENRAADS Victoria, British Columbia
ERRATA
“A Hidden Variable behind Entanglement,” by Michelle Frank [April], incorrectly gave Emilio Segrè’s first name as “Emile.”
In “The Sisterhood of Species,” by Barbara Natterson-Horowitz, the box “Under Pressure” incorrectly depicts the right atrium of the heart. The corrected illustrations can be found at https://www.scientificamerican.com/article/what- scientists-are-learning-about-womens- health-from-other-female-animals
COUNTER ARGUMENTS
In “Born to Count,” Sam Clarke and Jacob Beck present several experiments that they assert demonstrate that humans are born with an innate “number sense.” But not one of them indicates that the concept of, say, “eightness” is innate. What they instead show is that there is an innate inequality sense, an ability to distinguish which of two quantities is larger, provided that the difference between them is large enough.
JOEL SANET via e-mail
The various experiments Clarke and Beck describe demonstrate that young children have a concept of order. That is, they can put the elements of a set in order by some criterion. For example, a child may be able to put a golf ball, baseball, softball and soccer ball in order by size. The experiments do not show that these children can count.
ERIC KLIEBER via e-mail
It seems that the property of thought that the article describes might better be called “generalized quantity,” “comparative quantity” or “generalized cardinality.” The term “number” doesn’t seem appropriate for research on young children before they have developed either the ability to use a system of symbols or words associated with specific quantities or cardinalities—or at least before they know the sequence of number words “one, two, three …” or something equivalent.
In my own past research with young children, it seemed to me that their thinking about numbers was more closely related to Giuseppe Peano’s basic concept of “successor” than cardinality or quantity. For example, if a kindergartener responded “five” to the question “How old are you?” the child would certainly not be able to remember far back enough to be conscious of their four birthdays prior to their fifth. To that child, the most important thing about “five” is that it is the successor of “four.”
GEORGE E. GULLEN III Southgate, Mich.
THE AUTHORS REPLY: Arguments that seek to debunk the innate number sense are tempting, but they struggle to fully explain the evidence. Sanet and Klieber propose that young children merely represent inequality and order, respectively, not number. Yet neither proposal can explain young children’s ability to add and multiply, as described in our article. Meanwhile Gullen proposes that children merely represent generalized quantity. We were at pains to explain that the number sense is sensitive to properties that are unique to number, however—for instance, the description relativity isolated by Gottlob Frege.
Gullen observes that when children learn to use number words such as “one, two, three,” they gain a novel appreciation for the successor relation. We agree. But it is a non sequitur to conclude that children don’t represent number beforehand. Just as you can see how far away a tree is (thereby representing distance) before you learn to measure distance precisely with a ruler, you can see how many trees there are (thereby representing number) before you learn to count.
INEQUITABLE INNOVATION
In “The Eight-Billion-Person Bomb” [Observatory], Naomi Oreskes argues against cornucopianism, a theoretical framework that asserts that human ingenuity can overcome limited natural resources.
I would like to offer a point of confirmation that cornucopianism is misguided. On CBC Radio, I recently heard an interview describing the catastrophic effects of finding cobalt, a rare mineral needed for batteries, in the Democratic Republic of the Congo. To me, this illustrates one of the flaws of the cornucopians: they focus on benefits of innovations enjoyed by some while consciously or unconsciously overlooking negatives experienced elsewhere. This is a logical progression of the phenomenon of the past several centuries: global capitalism.
RICHARD “DICK” FAHLMAN Tla’amin Nation, British Columbia
NATURAL CAPITAL IDEA
In “Use Nature as Infrastructure” [Science Agenda, April], the editors lay out the reasons why policy makers should be putting nature on the nation’s balance sheet. The Biden-Harris administration wholeheartedly agrees. In January we released the National Strategy to Develop Statistics for Environmental-Economic Decisions, a historic effort to account for America’s natural assets in our national economic statistics.
We’re currently working to quantify the economic value of our natural capital, including the ocean and rivers that support our recreation and fishing industries, the forests that clean our air and water, the minerals that power our technology economy and drive the electric vehicle revolution, and much more. By expanding the national economic accounting system to include natural capital and by including services from ecosystems in benefit-cost and regulatory analyses, we will more accurately capture the links between nature and the economy—which will help guide policy and business decisions.
Both the Inflation Reduction Act and the Bipartisan Infrastructure Law include funding for nature-based solutions to climate change, such as protecting forests and restoring marshes to reduce greenhouse gas emissions, remove carbon from the atmosphere and lower the risks to people from extreme weather. President Joe Biden has taken additional action by signing executive orders that create a National Nature Assessment to better understand how nature is changing in the U.S.; quantify the impacts of climate change in the federal budget; and promote environmental services and opportunities for local economies across the country.
The Biden-Harris administration is working hard to maintain and invest in natural infrastructure. We’re making sure that ecosystem services are considered at every level of government decision-making.
ELI FENICHEL, HEATHER TALLIS, SOLOMON HSIANG and JANE LUBCHENCO White House Office of Science and Technology Policy
EDITOR’S NOTE: Fenichel was at OSTP when this letter was submitted. He is now at Yale University.
FUNDAMENTALLY WEIRD
British geneticist J.B.S. Haldane (1892–1964) would have been delighted to read “Primordial Soup,” by Clara Moskowitz. It raises the question of why the universe is so floridly strange and weird at all scales. At large scales, we see stars, galaxies, supernovae and black holes; at medium scale, we see molecules, DNA, proteins, molecular machinery and life itself.
And now the tiny, pristine sphere of positive charge of my physics education has become a sea of quarks and antiquarks with three valence quarks bobbing on its surface, all held together by gluons. I, too, am delighted.
JOHN COENRAADS Victoria, British Columbia
ERRATA
“A Hidden Variable behind Entanglement,” by Michelle Frank [April], incorrectly gave Emilio Segrè’s first name as “Emile.”
In “The Sisterhood of Species,” by Barbara Natterson-Horowitz, the box “Under Pressure” incorrectly depicts the right atrium of the heart. The corrected illustrations can be found at https://www.scientificamerican.com/article/what- scientists-are-learning-about-womens- health-from-other-female-animals
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