scientificamerican--2020-09-21--For Math Fans: A Hitchhiker's Guide to the Number 42

Everyone loves unsolved mysteries .
Examples include Amelia Earhart ’ s disappearance over the Pacific in 1937 and the daring escape of inmates Frank Morris and John and Clarence Anglin from Alcatraz Island in California in 1962 .
Moreover our interest holds even if the mystery is based on a joke .
Take author Douglas Adams ’ s popular 1979 science-fiction novel The Hitchhiker ’ s Guide to the Galaxy , the first in a series of five .
Toward the end of the book , the supercomputer Deep Thought reveals that the answer to the “ Great Question ” @ @ @ @ @ @ @ Everything ” is “ forty-two.
” Deep Thought takes 7.5 million years to calculate the answer to the ultimate question .
The characters tasked with getting that answer are disappointed because it is not very useful .
Yet , as the computer points out , the question itself was vaguely formulated .
To find the correct statement of the query whose answer is 42 , the computer will have to build a new version of itself .
That , too , will take time .
The new version of the computer is Earth @ @ @ @ @ @ @ , you ’ ll have to read Adams ’ s books .
The author ’ s choice of the number 42 has become a fixture of geek culture .
It ’ s at the origin of a multitude of jokes and winks exchanged between initiates .
If , for example , you ask your search engine variations of the question “ What is the answer to everything ?
” it will most likely answer “ 42.
” Try it in French or German .
You ’ ll often get the same answer whether @ @ @ @ @ @ @ Alpha ( which specializes in calculating mathematical problems ) or the chat bot Web app Cleverbot .
Since the first such school was created in France in 2013 there has been a proliferation of private computer-training institutions in the “ 42 Network , ” whose name is a clear allusion to Adams ’ s novels .
Today the founding company counts more than 15 campuses in its global network .
The number 42 also appears in different forms in the film Spider-Man : Into the Spider-Verse .
Many other references and allusions to @ @ @ @ @ @ @ , in the Wikipedia entry for “ 42 ( number ) .
” The number 42 also turns up in a whole string of curious coincidences whose significance is probably not worth the effort to figure out .
For example : In ancient Egyptian mythology , during the judgment of souls , the dead had to declare before 42 judges that they had not committed any of 42 sins .
The marathon distance of 42.195 kilometers corresponds to the legend of how far the ancient Greek messenger Pheidippides traveled between Marathon and Athens @ @ @ @ @ @ @ 490 B.C .
( The fact that the kilometer had not yet been defined at that time only makes the connection all the more astonishing . )
Ancient Tibet had 42 rulers .
Nyatri Tsenpo , who reigned around 127 B.C.
, was the first .
And Langdarma , who ruled from 836 to 842 A.D .
( i.e.
, the 42nd year of the ninth century ) , was the last .
The Gutenberg Bible , the first book printed in Europe , has 42 lines of text per column and is @ @ @ @ @ @ @ According to a March 6 Economist blog post marking the 42nd anniversary of the radio program The Hitchhiker ’ s Guide to the Galaxy , which preceded the novel , “ the 42nd anniversary of anything is rarely observed.
” An obvious question , which indeed has been asked , is whether the use of 42 in Adams ’ s books had any particular meaning for the author .
His answer , posted in the online discussion group alt.fan.douglas-adams , was succinct : “ It was a joke .
It had to be @ @ @ @ @ @ @ number , and I chose that one .
Binary representations , base thirteen , Tibetan monks are all complete nonsense .
I sat at my desk , stared into the garden and thought ‘ 42 will do.
’ I typed it out .
End of story.
” In the binary system , or base 2 , 42 is written as 101010 , which is pretty simple and , incidentally , prompted a few fans to hold parties on October 10 , 2010 ( 10/10/10 ) .
The reference to base 13 in Adams @ @ @ @ @ @ @ explanation .
In one instance , the series suggests that 42 is the answer to the question “ What do you get if you multiply six by nine ?
” That idea seems absurd because 6 x 9 = 54 .
But in base 13 , the number expressed as “ 42 ” is equal to ( 4 x 13 ) + 2 = 54 .
Apart from allusions to 42 deliberately introduced by computer scientists for fun and the inevitable encounters with it that crop up when you poke around a bit @ @ @ @ @ @ @ might still wonder whether there is anything special about the number from a strictly mathematical point of view .
The number 42 has a range of interesting mathematical properties .
Here are some of them : The number is the sum of the first three odd powers of two—that is , 21 + 23 + 25 = 42 .
It is an element in the sequence a ( n ) , which is the sum of n odd powers of 2 for n > 0 .
The sequence corresponds to entry A020988 in @ @ @ @ @ @ @ OEIS ) , created by mathematician Neil Sloane .
In base 2 , the nth element may be specified by repeating 10 n times ( 1010 ... 10 ) .
The formula for this sequence is a ( n ) = ( 2/3 ) ( 4n – 1 ) .
As n increases , the density of numbers tends toward zero , which means that the numbers belonging to this list , including 42 , are exceptionally rare .
The number 42 is the sum of the first two nonzero integer powers of @ @ @ @ @ @ @ 42 .
The sequence b ( n ) , which is the sum of the powers of six , corresponds to entry A105281 in OEIS .
It is defined by the formulas b ( 0 ) = 0 , b ( n ) = 6b ( n – 1 ) + 6 .
The density of these numbers also tends toward zero at infinity .
Forty-two is a Catalan number .
These numbers are extremely rare , much more so than prime numbers : only 14 of the former are lower than one @ @ @ @ @ @ @ , under another name , by Swiss mathematician Leonhard Euler , who wanted to know how many different ways an n-sided convex polygon could be cut into triangles by connecting vertices with line segments .
The beginning of the sequence ( A000108 in OEIS ) is 1 , 1 , 2 , 5 , 14 , 42 , 132 ... .
The nth element of the sequence is given by the formula c ( n ) = ( 2n ) !
/ ( n !
( n + 1 ) ! )
.
@ @ @ @ @ @ @ the density of numbers is null at infinity .
Catalan numbers are named after Franco-Belgian mathematician Eugène Charles Catalan ( 1814–1894 ) , who discovered that c ( n ) is the number of ways to arrange n pairs of parentheses according to the usual rules for writing them : a parenthesis is never closed before it has been opened , and one can only close it when all the parentheses that were subsequently opened are themselves closed .
For example , c ( 3 ) = 5 because the possible arrangements of @ @ @ @ @ @ @ is also a “ practical ” number , which means that any integer between 1 and 42 is the sum of a subset of its distinct divisors .
The first practical numbers are 1 , 2 , 4 , 6 , 8 , 12 , 16 , 18 , 20 , 24 , 28 , 30 , 32 , 36 , 40 , 42 , 48 , 54 , 56 , 60 , 64 , 66 and 72 ( sequence A005153 in OEIS ) .
No simple known formula provides the nth element @ @ @ @ @ @ @ amusing , but it would be wrong to say that 42 is really anything special mathematically .
The numbers 41 and 43 , for example , are also elements of many sequences .
You can explore the properties of various numbers on Wikipedia .
What makes a number particularly interesting or uninteresting is a question that mathematician and psychologist Nicolas Gauvrit , computational natural scientist Hector Zenil and I have studied , starting with an analysis of the sequences in the OEIS .
Aside from a theoretical connection to Kolmogorov complexity ( which @ @ @ @ @ @ @ the length of its minimal description ) , we have shown that the numbers contained in Sloane ’ s encyclopedia point to a shared mathematical culture and , consequently , that OEIS is based as much on human preferences as pure mathematical objectivity .
Problem of the Sum of Three Cubes Computer scientists and mathematicians recognize the appeal of the number 42 but have always thought that it was a simple game that could be played just as well with another number .
Still , a recent news item caught their attention .
@ @ @ @ @ @ @ sum of three cubes ” problem , 42 was more troublesome than all the other numbers below 100 .
The problem is stated as follows : What integers n can be written as the sum of three whole-number cubes ( n = a3 + b3 + c3 ) ?
And for such integers , how do you find a , b and c ?
As a practical matter , the difficulty in making this calculation is that for a given n , the space of the triplets to be considered involves negative integers @ @ @ @ @ @ @ , unlike the computation for the sum of squares .
For that particular problem , any solution has an absolute value lower than the square root of a given n. Moreover for the sum of squares , we know perfectly well what is possible and impossible .
For the sum of cubes , some solutions may be surprisingly large , such as the one for 156 , which was discovered in 2007 : Note that for some integer values of n , the equation n = a3 + b3 + c3 has no @ @ @ @ @ @ @ all integers n that are expressible as 9m + 4 or 9m + 5 for any integer m ( e.g.
, 4 , 5 , 13 , 14 , 22 , 23 ) .
Demonstrating this assertion is straightforward : we use the “ modulo 9 ” ( mod 9 ) calculation , which is equivalent to assuming that 9 = 0 and then manipulating only numbers between 0 and 8 or between −4 and 4 .
When we do so , we see that : In other words , the cube of @ @ @ @ @ @ @ = 8 ) , 0 or 1 .
Adding any three numbers among these numbers gives : You can not get a sum of 4 or 5 ( = –4 ) .
This restriction means that sums of three cubes are never numbers of the form 9m + 4 or 9m + 5 .
We thus say that n = 9m + 4 and n = 9m + 5 are prohibited values .
To illustrate how difficult it is to find solutions to the equation n = a3 + b3 + c3 , @ @ @ @ @ @ @ n = 1 and n = 2 .
For n = 1 , there is the obvious solution : Are there others ?
Yes , there is : That calculation is not the only other solution .
In 1936 German mathematician Kurt Mahler proposed an infinite number of them .
For any integer p : This proposition may be proved using the remarkable identity : An infinite set of solutions is also known for n = 2 .
It was discovered in 1908 by mathematician A. S. Werebrusov .
For any integer p @ @ @ @ @ @ @ equations by the cube of an integer ( r3 ) , we deduce that there are also infinitely many solutions for both the cube and double the cube of any integer .
Consider the example of 16 , which is double the cube of 2 .
For p = 1 , we get : Note that for n = 3 , as of August 2019 , only two solutions were known : A question that naturally follows is : Is there at least one solution for every nonprohibited value ?
To answer that @ @ @ @ @ @ @ nonprohibited values 1 , 2 , 3 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 15 , 16 ... ( A060464 in OEIS ) and examining them one by one .
If solutions can be found for all those examined values , it will be reasonable to conjecture that for any integer n that is not of the form n = 9m + 4 or n = 9m + 5 , there are solutions to the equation n = a3 + b3 + c3 .
The @ @ @ @ @ @ @ depends on the power of the computers or computer networks used , has produced an ever expanding body of results .
This work leads us back to the famous and intriguing number 42 .
In 2009 , employing a method proposed by Noam Elkies of Harvard University in [ [ OR : by American mathematician Noam Elkies in 2000 , German mathematicians Andreas-Stephan Elsenhans and Jörg Jahnel explored all the triplets a , b , c of integers with an absolute value less than 1014 to find solutions for n between 1 and @ @ @ @ @ @ @ concluded that the question of the existence of a solution for numbers below 1,000 remained open only for 33 , 42 , 74 , 114 , 165 , 390 , 579 , 627 , 633 , 732 , 795 , 906 , 921 and 975 .
For integers less than 100 , just three enigmas remained : 33 , 42 and 74 .
In a 2016 preprint paper , Sander Huisman , now at the University of Twente in the Netherlands , pressed on and found a solution for 74 : In 2019 @ @ @ @ @ @ @ in England settled the case of 33 : From that point , Douglas Adams ’ s number was the last positive integer lower than 100 whose representation as a sum of three integer cubes was unknown .
If there was no solution , that conclusion would provide a genuinely compelling rationale for the mathematical significance of 42 : it would be the first number for which a solution appeared possible but none had been found .
Computers tried but had been unable to crack the problem .
The answer came in a 2020 @ @ @ @ @ @ @ computational effort coordinated by Booker and Andrew Sutherland of the Massachusetts Institute of Technology .
Computers participating in the Charity Engine network of personal computers , calculating for the equivalent of more than one million hours , showed : The cases of 165 , 795 and 906 were also solved recently .
For integers below 1,000 , only 114 , 390 , 579 , 627 , 633 , 732 , 921 and 975 remain to be solved .
The conjecture that solutions exist for all integers n that are not of the form @ @ @ @ @ @ @ would appear to be confirmed .
In 1992 Roger Heath-Brown of the University of Oxford proposed a stronger conjecture stating that there are infinitely many ways to express all possible n ’ s as the sum of three cubes .
The work is far from over .
The difficulty appears so daunting that the question “ Is n a sum of three cubes ?
” may be undecidable .
In other words , no algorithm , however clever , may be able to process all possible cases .
In 1936 , for example @ @ @ @ @ @ @ can solve the halting problem for every possible computer program .
But here we are in a readily describable , purely mathematical domain .
If we could prove such undecidability , that would be a novelty .
The number 42 was difficult , but it is not the final step !
This article originally appeared in Pour la Science and was reproduced with permission .

Everyone loves unsolved mysteries. Examples include Amelia Earhart’s disappearance over the Pacific in 1937 and the daring escape of inmates Frank Morris and John and Clarence Anglin from Alcatraz Island in California in 1962. Moreover our interest holds even if the mystery is based on a joke. Take author Douglas Adams’s popular 1979 science-fiction novel The Hitchhiker’s Guide to the Galaxy, the first in a series of five. Toward the end of the book, the supercomputer Deep Thought reveals that the answer to the “Great Question” of “Life, the Universe and Everything” is “forty-two.”
Deep Thought takes 7.5 million years to calculate the answer to the ultimate question. The characters tasked with getting that answer are disappointed because it is not very useful. Yet, as the computer points out, the question itself was vaguely formulated. To find the correct statement of the query whose answer is 42, the computer will have to build a new version of itself. That, too, will take time. The new version of the computer is Earth. To find out what happens next, you’ll have to read Adams’s books.
The author’s choice of the number 42 has become a fixture of geek culture. It’s at the origin of a multitude of jokes and winks exchanged between initiates. If, for example, you ask your search engine variations of the question “What is the answer to everything?” it will most likely answer “42.” Try it in French or German. You’ll often get the same answer whether you use Google, Qwant, Wolfram Alpha (which specializes in calculating mathematical problems) or the chat bot Web app Cleverbot.
Since the first such school was created in France in 2013 there has been a proliferation of private computer-training institutions in the “42 Network,” whose name is a clear allusion to Adams’s novels. Today the founding company counts more than 15 campuses in its global network. The number 42 also appears in different forms in the film Spider-Man: Into the Spider-Verse. Many other references and allusions to it can be found, for example, in the Wikipedia entry for “42 (number).”
The number 42 also turns up in a whole string of curious coincidences whose significance is probably not worth the effort to figure out. For example:
In ancient Egyptian mythology, during the judgment of souls, the dead had to declare before 42 judges that they had not committed any of 42 sins.
The marathon distance of 42.195 kilometers corresponds to the legend of how far the ancient Greek messenger Pheidippides traveled between Marathon and Athens to announce victory over the Persians in 490 B.C. (The fact that the kilometer had not yet been defined at that time only makes the connection all the more astonishing.)
Ancient Tibet had 42 rulers. Nyatri Tsenpo, who reigned around 127 B.C., was the first. And Langdarma, who ruled from 836 to 842 A.D. (i.e., the 42nd year of the ninth century), was the last.
The Gutenberg Bible, the first book printed in Europe, has 42 lines of text per column and is also called the “Forty-Two-Line Bible.”
According to a March 6 Economist blog post marking the 42nd anniversary of the radio program The Hitchhiker’s Guide to the Galaxy, which preceded the novel, “the 42nd anniversary of anything is rarely observed.”
A Purely Arbitrary Choice
An obvious question, which indeed has been asked, is whether the use of 42 in Adams’s books had any particular meaning for the author. His answer, posted in the online discussion group alt.fan.douglas-adams, was succinct: “It was a joke. It had to be a number, an ordinary, smallish number, and I chose that one. Binary representations, base thirteen, Tibetan monks are all complete nonsense. I sat at my desk, stared into the garden and thought ‘42 will do.’ I typed it out. End of story.”
In the binary system, or base 2, 42 is written as 101010, which is pretty simple and, incidentally, prompted a few fans to hold parties on October 10, 2010 (10/10/10). The reference to base 13 in Adams’s answer requires a more indirect explanation. In one instance, the series suggests that 42 is the answer to the question “What do you get if you multiply six by nine?” That idea seems absurd because 6 x 9 = 54. But in base 13, the number expressed as “42” is equal to (4 x 13) + 2 = 54.
Apart from allusions to 42 deliberately introduced by computer scientists for fun and the inevitable encounters with it that crop up when you poke around a bit in history or the world, you might still wonder whether there is anything special about the number from a strictly mathematical point of view.
Mathematically Unique?
The number 42 has a range of interesting mathematical properties. Here are some of them:
The number is the sum of the first three odd powers of two—that is, 21 + 23 + 25 = 42. It is an element in the sequence a(n), which is the sum of n odd powers of 2 for n > 0. The sequence corresponds to entry A020988 in The On-Line Encyclopedia of Integer Sequences (OEIS), created by mathematician Neil Sloane. In base 2, the nth element may be specified by repeating 10 n times (1010 ... 10). The formula for this sequence is a(n) = (2/3)(4n – 1). As n increases, the density of numbers tends toward zero, which means that the numbers belonging to this list, including 42, are exceptionally rare.
The number 42 is the sum of the first two nonzero integer powers of six—that is, 61 + 62 = 42. The sequence b(n), which is the sum of the powers of six, corresponds to entry A105281 in OEIS. It is defined by the formulas b(0) = 0, b(n) = 6b(n – 1) + 6. The density of these numbers also tends toward zero at infinity.
Forty-two is a Catalan number. These numbers are extremely rare, much more so than prime numbers: only 14 of the former are lower than one billion. Catalan numbers were first mentioned, under another name, by Swiss mathematician Leonhard Euler, who wanted to know how many different ways an n-sided convex polygon could be cut into triangles by connecting vertices with line segments. The beginning of the sequence (A000108 in OEIS) is 1, 1, 2, 5, 14, 42, 132.... The nth element of the sequence is given by the formula c(n) = (2n)! / (n!(n + 1)!). And like the two preceding sequences, the density of numbers is null at infinity.
Catalan numbers are named after Franco-Belgian mathematician Eugène Charles Catalan (1814–1894), who discovered that c(n) is the number of ways to arrange n pairs of parentheses according to the usual rules for writing them: a parenthesis is never closed before it has been opened, and one can only close it when all the parentheses that were subsequently opened are themselves closed.
For example, c(3) = 5 because the possible arrangements of three pairs of parentheses are:
( ( ( ) ) ); ( ) ( ) ( ); ( ( ) ) ( ); ( ( ) ( ) ); ( ) ( ( ) )
Forty-two is also a “practical” number, which means that any integer between 1 and 42 is the sum of a subset of its distinct divisors. The first practical numbers are 1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66 and 72 (sequence A005153 in OEIS). No simple known formula provides the nth element of this sequence.
All this is amusing, but it would be wrong to say that 42 is really anything special mathematically. The numbers 41 and 43, for example, are also elements of many sequences. You can explore the properties of various numbers on Wikipedia.
What makes a number particularly interesting or uninteresting is a question that mathematician and psychologist Nicolas Gauvrit, computational natural scientist Hector Zenil and I have studied, starting with an analysis of the sequences in the OEIS. Aside from a theoretical connection to Kolmogorov complexity (which defines the complexity of a number by the length of its minimal description), we have shown that the numbers contained in Sloane’s encyclopedia point to a shared mathematical culture and, consequently, that OEIS is based as much on human preferences as pure mathematical objectivity.
Problem of the Sum of Three Cubes
Computer scientists and mathematicians recognize the appeal of the number 42 but have always thought that it was a simple game that could be played just as well with another number. Still, a recent news item caught their attention. When it was applied to the “sum of three cubes” problem, 42 was more troublesome than all the other numbers below 100.
The problem is stated as follows: What integers n can be written as the sum of three whole-number cubes (n = a3 + b3 + c3)? And for such integers, how do you find a, b and c? As a practical matter, the difficulty in making this calculation is that for a given n, the space of the triplets to be considered involves negative integers. This triplet space is therefore infinite, unlike the computation for the sum of squares. For that particular problem, any solution has an absolute value lower than the square root of a given n. Moreover for the sum of squares, we know perfectly well what is possible and impossible.
For the sum of cubes, some solutions may be surprisingly large, such as the one for 156, which was discovered in 2007:
156 = 26,577,110,807,5693 + (−18,161,093,358,005)3 + (−23,381,515,025,762)3
Note that for some integer values of n, the equation n = a3 + b3 + c3 has no solution. Such is the case for all integers n that are expressible as 9m + 4 or 9m + 5 for any integer m (e.g., 4, 5, 13, 14, 22, 23). Demonstrating this assertion is straightforward: we use the “modulo 9” (mod 9) calculation, which is equivalent to assuming that 9 = 0 and then manipulating only numbers between 0 and 8 or between −4 and 4. When we do so, we see that:
03 = 0 (mod 9); 13 = 1 (mod 9); 23 = 8 = –1 (mod 9); 33 = 27 = 0 (mod 9); 43 = 64 = 1 (mod 9); 53 = (–4)3 = –64 = –1 (mod 9); 63 = (–3)3 = 0 (mod 9); 73 = (–2)3 = 1 (mod 9); 83 = (–1)3 = –1 (mod 9)
In other words, the cube of an integer modulo 9 is –1 (= 8), 0 or 1. Adding any three numbers among these numbers gives:
0 = 0 + 0 + 0 = 0 + 1 + (–1); 1 = 1 + 0 + 0 = 1 + 1 + (–1); 2 = 1 + 1 + 0; 3 = 1 + 1 + 1; 6 = –3 = (–1) + (–1) + (–1); 7 = –2 = (–1) + (–1) + 0; 8 = –1 = (–1) + 0 + 0 = 1 + (–1) + (–1)
You cannot get a sum of 4 or 5 (= –4). This restriction means that sums of three cubes are never numbers of the form 9m + 4 or 9m + 5. We thus say that n = 9m + 4 and n = 9m + 5 are prohibited values.
Searching for Solutions
To illustrate how difficult it is to find solutions to the equation n = a3 + b3 + c3, let’s see what happens for n = 1 and n = 2.
For n = 1, there is the obvious solution:
13 + 13 + (–1)3 = 1
Are there others? Yes, there is:
93 + (–6)3 + (–8)3 = 729 + (–216) + (–512) = 1
That calculation is not the only other solution. In 1936 German mathematician Kurt Mahler proposed an infinite number of them. For any integer p:
(9p4)3 + (3p – 9p4)3 + (1 – 9p3)3 = 1
This proposition may be proved using the remarkable identity:
(A + B)3 = A3 + 3A2B + 3AB2 + B3
An infinite set of solutions is also known for n = 2. It was discovered in 1908 by mathematician A. S. Werebrusov. For any integer p:
(6p3 + 1)3 + (1 – 6p3)3 + (–6p2)3 = 2
By multiplying each term of these equations by the cube of an integer (r3), we deduce that there are also infinitely many solutions for both the cube and double the cube of any integer.
Consider the example of 16, which is double the cube of 2. For p = 1, we get:
143 + (–10)3 + (–12)3 = 16
Note that for n = 3, as of August 2019, only two solutions were known:
13 + 13 + 13 = 3; 43 + 43 + (–5)3 = 3
A question that naturally follows is: Is there at least one solution for every nonprohibited value?
Computers at Work
To answer that question, mathematicians started by taking the nonprohibited values 1, 2, 3, 6, 7, 8, 9, 10, 11, 12, 15, 16 ... (A060464 in OEIS) and examining them one by one. If solutions can be found for all those examined values, it will be reasonable to conjecture that for any integer n that is not of the form n = 9m + 4 or n = 9m + 5, there are solutions to the equation n = a3 + b3 + c3.
The research carried out thus far, which depends on the power of the computers or computer networks used, has produced an ever expanding body of results. This work leads us back to the famous and intriguing number 42.
In 2009, employing a method proposed by Noam Elkies of Harvard University in 2000, German mathematicians Andreas-Stephan Elsenhans and Jörg Jahnel explored all the triplets a, b, c of integers with an absolute value less than 1014 to find solutions for n between 1 and 1,000. The paper reporting their findings concluded that the question of the existence of a solution for numbers below 1,000 remained open only for 33, 42, 74, 114, 165, 390, 579, 627, 633, 732, 795, 906, 921 and 975. For integers less than 100, just three enigmas remained: 33, 42 and 74.
In a 2016 preprint paper, Sander Huisman, now at the University of Twente in the Netherlands, pressed on and found a solution for 74:
(–284,650,292,555,885)3 + (66,229,832,190,556)3 + (283,450,105,697,727)3
In 2019 Andrew Booker of the University of Bristol in England settled the case of 33:
8,866,128,975,287,528)3 + (–8,778,405,442,862,239)3 + (–2,736,111,468,807,040)3
From that point, Douglas Adams’s number was the last positive integer lower than 100 whose representation as a sum of three integer cubes was unknown. If there was no solution, that conclusion would provide a genuinely compelling rationale for the mathematical significance of 42: it would be the first number for which a solution appeared possible but none had been found. Computers tried but had been unable to crack the problem.
The answer came in a 2020 preprint, the result of a huge computational effort coordinated by Booker and Andrew Sutherland of the Massachusetts Institute of Technology. Computers participating in the Charity Engine network of personal computers, calculating for the equivalent of more than one million hours, showed:
42 = (–80,538,738,812,075,974)3 + 80,435,758,145,817,5153 + 12,602,123,297,335,6313
The cases of 165, 795 and 906 were also solved recently. For integers below 1,000, only 114, 390, 579, 627, 633, 732, 921 and 975 remain to be solved.
The conjecture that solutions exist for all integers n that are not of the form 9m + 4 or 9m + 5 would appear to be confirmed. In 1992 Roger Heath-Brown of the University of Oxford proposed a stronger conjecture stating that there are infinitely many ways to express all possible n’s as the sum of three cubes. The work is far from over.
The difficulty appears so daunting that the question “Is n a sum of three cubes?” may be undecidable. In other words, no algorithm, however clever, may be able to process all possible cases. In 1936, for example, Alan Turing showed that no algorithm can solve the halting problem for every possible computer program. But here we are in a readily describable, purely mathematical domain. If we could prove such undecidability, that would be a novelty.
The number 42 was difficult, but it is not the final step!
This article originally appeared in Pour la Science and was reproduced with permission.


scientificamerican--2020-09-20--Ruth Bader Ginsburg's Death Is One More Terrible Blow in a Year of Loss

This year has been one of incredible loss .
We are approaching 200,000 deaths from the COVID-19 pandemic in the U.S. and nearly a million around the globe .
And on the streets , the killings of Black , Indigenous , Latinx individuals and other people of color—George Floyd , Breonna Taylor , Daniel Prude , Rayshard Brooks and many others at the hands of those sworn to protect us continues a long history of loss because of racism .
Last night the devastating loss continued with the death of Supreme Court Justice Ruth Bader Ginsburg .
Justice Ginsburg was @ @ @ @ @ @ @ a key vote in a closely divided court .
Along with the passing of Representatives Elijah Cummings of Maryland and John Lewis of Georgia , this latest loss feels like a body blow .
To those who believe , as I do , that the Fourteenth Amendment of the Constitution ’ s mandate of equal protection is at the heart of our democracy , the loss of these giants from public life brings even greater unease in a time of extraordinary uncertainty .
Justice Ginsburg would likely have played a pivotal role in @ @ @ @ @ @ @ court in the coming term .
A large proportion of those cases involve equal protection or civil rights by my reading .
Others involve government transparency , including a case concerning public information related to an Endangered Species Act biological opinion in which the Sierra Club is challenging the U.S .
Fish and Wildlife Service and National Marine Fisheries Service .
I and my colleagues at the Union of Concerned Scientists have filed an amicus brief supporting greater transparency in that case .
Justice Ginsburg would have also played a critical role in @ @ @ @ @ @ @ in future .
Given the long list of attacks on science we have tracked over the past three and a half years and an equally long list of regulatory rollbacks that have been vociferously disputed , it is highly likely some of those issues will ultimately reach the court .
Here are a few examples where Justice Ginsburg ’ s loss will be felt acutely : • There are several coming battles over regulations directly aimed at slowing global warming .
These conflicts include legal battles over fuel economy standards for cars and @ @ @ @ @ @ @ , grid modernization , holding companies accountable and likely many more issues .
• Regulatory rollbacks affecting clean air and water , toxic chemicals , endangered species , consumer product safety , and other public health and safety protections are all under court challenge as we speak .
How these battles play out may ultimately involve the nation ’ s highest court .
• The dramatic weakening of the U.S. ’ s overarching environmental law , the National Environmental Policy Act , raises issues of permitting oil and gas activities , including pipelines @ @ @ @ @ @ @ Defense activities and virtually all other federal actions .
The legal battle will be intense .
• The weakening of regulatory protections for political reasons rather than based on scientific evidence has resulted in many disputes in recent years .
They include attempts to alter how science is considered in making policy through rules , such as the so-called Strengthening Transparency in Regulatory Science rule proposed at the Environmental Protection Agency , as well as the way the costs and benefits of regulations may be calculated .
Ultimately , court action will result @ @ @ @ @ @ @ public health and safety protections .
• Members of the scientific community—including academic , governmental and civil-society organizations such as the Union of Concerned Scientists—are struggling to overcome a history of systemic racism .
Change will not come easily or without challenge as science , technology , engineering and mathematics ( STEM ) education and STEM career paths necessarily become more diversified and our institutions become more equitable .
These issues , too , will result in court battles .
Justice Ginsburg touched the lives of everyone in this country , whether we @ @ @ @ @ @ @ will be a loss—for women ’ s rights , civil rights , equal protection and wisdom in our democracy .
I close with a quote from the justice : “ Think back to 1787. Who were ‘ we the people ’ ?
...
They certainly were n't women ... they surely weren ’ t people held in human bondage .
The genius of our Constitution is that over now more than 200 sometimes turbulent years that ‘ we ’ has expanded and expanded .
”

This year has been one of incredible loss. We are approaching 200,000 deaths from the COVID-19 pandemic in the U.S. and nearly a million around the globe. And on the streets, the killings of Black, Indigenous, Latinx individuals and other people of color—George Floyd, Breonna Taylor, Daniel Prude, Rayshard Brooks and many others at the hands of those sworn to protect us continues a long history of loss because of racism.
Last night the devastating loss continued with the death of Supreme Court Justice Ruth Bader Ginsburg. Justice Ginsburg was a longtime champion of civil rights and a key vote in a closely divided court. Along with the passing of Representatives Elijah Cummings of Maryland and John Lewis of Georgia, this latest loss feels like a body blow. To those who believe, as I do, that the Fourteenth Amendment of the Constitution’s mandate of equal protection is at the heart of our democracy, the loss of these giants from public life brings even greater unease in a time of extraordinary uncertainty.
Justice Ginsburg would likely have played a pivotal role in in a host of cases before the court in the coming term. A large proportion of those cases involve equal protection or civil rights by my reading. Others involve government transparency, including a case concerning public information related to an Endangered Species Act biological opinion in which the Sierra Club is challenging the U.S. Fish and Wildlife Service and National Marine Fisheries Service. I and my colleagues at the Union of Concerned Scientists have filed an amicus brief supporting greater transparency in that case.
Justice Ginsburg would have also played a critical role in deciding which cases the court would hear in future. Given the long list of attacks on science we have tracked over the past three and a half years and an equally long list of regulatory rollbacks that have been vociferously disputed, it is highly likely some of those issues will ultimately reach the court. Here are a few examples where Justice Ginsburg’s loss will be felt acutely:
There are several coming battles over regulations directly aimed at slowing global warming. These conflicts include legal battles over fuel economy standards for cars and trucks, restrictions on greenhouse gas emissions, grid modernization, holding companies accountable and likely many more issues.
Regulatory rollbacks affecting clean air and water, toxic chemicals, endangered species, consumer product safety, and other public health and safety protections are all under court challenge as we speak. How these battles play out may ultimately involve the nation’s highest court.
The dramatic weakening of the U.S.’s overarching environmental law, the National Environmental Policy Act, raises issues of permitting oil and gas activities, including pipelines, major development projects, Department of Defense activities and virtually all other federal actions. The legal battle will be intense.
The weakening of regulatory protections for political reasons rather than based on scientific evidence has resulted in many disputes in recent years. They include attempts to alter how science is considered in making policy through rules, such as the so-called Strengthening Transparency in Regulatory Science rule proposed at the Environmental Protection Agency, as well as the way the costs and benefits of regulations may be calculated. Ultimately, court action will result as communities around the country lose key public health and safety protections.
the way the costs and benefits of regulations may be calculated. Ultimately, court action will result as communities around the country lose key public health and safety protections. Members of the scientific community—including academic, governmental and civil-society organizations such as the Union of Concerned Scientists—are struggling to overcome a history of systemic racism. Change will not come easily or without challenge as science, technology, engineering and mathematics (STEM) education and STEM career paths necessarily become more diversified and our institutions become more equitable. These issues, too, will result in court battles.
Justice Ginsburg touched the lives of everyone in this country, whether we know it or not. Her passing will be a loss—for women’s rights, civil rights, equal protection and wisdom in our democracy.
I close with a quote from the justice: “Think back to 1787. Who were ‘we the people’? ... They certainly weren't women ... they surely weren’t people held in human bondage. The genius of our Constitution is that over now more than 200 sometimes turbulent years that ‘we’ has expanded and expanded.”


scientificamerican--2020-09-20--We Need to Do More Research on Honesty

We Need to Do More Research on Honesty

Last year , I published a book about honesty , exploring what it means to live a more honest life .
I examined my own struggles with honesty , and did my best to translate academic research about honesty and apply it to everyday life .
Through interviewing many researchers and reading dozens of studies about ethics , deception , moral character , secrecy , and self-delusion , I learned that we know quite a bit about lying and the reasons people lie in a variety of relationships .
But we know far less about the reasons people are honest @ @ @ @ @ @ @ philosopher , honesty is stunningly neglected , ” says Wake Forest University philosophy professor Christian B. Miller , author of The Character Gap : How Good Are We ?
“ Almost no work about honesty has been done in philosophy in the last 50 years .
It ’ s been largely overlooked.
” And yet , he says , when you ask people what they consider to be the most important virtues , a great majority will include honesty .
Courage , patience and kindness may also top the list .
Humility , @ @ @ @ @ @ @ not so much .
But can you imagine anyone ever leaving honesty off the list ?
So why don ’ t we know more about what motivates people to be honest ?
To disclose , to say the true thing , to correct false information , to speak up ?
One answer is that in thinking about honesty , we ’ ve mostly been tuned into deception .
By “ we , ” I mean you and me , and I also mean philosophers and scientists .
First of all , lying , @ @ @ @ @ @ @ intent to deceive people , has been on full display in the form of Donald Trump for the past several years ( though he is certainly not the only elected official to practice deception with regularity ) .
We ’ ve also had a front-row seat watching personalities like Lance Armstrong and Elizabeth Holmes weave their tangled webs .
As citizens of the world , we ’ re obsessed with lying and lies right now—what ’ s real , what ’ s fake , and what ’ s deliberate and deceitful manipulation ?
@ @ @ @ @ @ @ wasn ’ t on purpose .
Not exactly .
There has been a surge of research over the past 15 years in psychology , organizational behavior , behavioral economics and related fields on lying and unethical decision-making .
Starting around 2005 , investigators developed and refined new methods to examine when and why people lie and cheat to earn money .
“ Examples include the now classic matrix and die-rolling tasks where people lie about their performance to earn extra money for themselves , and sender-receiver deception ‘ games ’ where people lie @ @ @ @ @ @ @ for themselves , ” says Taya Cohen , associate professor of organizational behavior and theory at Carnegie Mellon University ’ s Tepper School of Business .
By allowing or provoking people to lie in controlled experiments—methodology that Cohen herself has used in much of her research—researchers can observe , measure and track these behaviors .
“ This means that lying and cheating can be operationalized in a way that isn ’ t restricted to people 's hypothetical decisions or recalled past behaviors , ” Cohen says .
From these and other types of @ @ @ @ @ @ @ great deal about how and why people lie .
We lie when we think we can get away with it .
We lie more in groups , especially if we see other people lying , or we ’ ve been exposed to a bribe .
We lie when the lie—even a lie of self-interest—feels justifiable ( it ’ s only a little bit of extra money ) .
We lie less if we ’ re reminded to be honest or if we have high moral character or score highly on measures of guilt-proneness @ @ @ @ @ @ @ lies often are related to preserving some sort of identity , and we lie to protect our reputation , the reputation of someone we support or the reputation of a group to which we belong .
In relationships , we lie to spare feelings or avoid awkward situations ( but we get really irritated when our romantic partner does the same ) .
We lie to ourselves as well , consistently believing we are smarter than we are .
Children are also more likely to lie if they ’ ve been lied to @ @ @ @ @ @ @ re afraid the truth will look like a lie .
And of course , we lie on social media , even if the lies look more like “ reshaping ” the truth .
These are all extraordinarily helpful findings , with relevant takeaway for nearly any group : bosses , teachers , parents , friends , spouses , voters ( especially voters ) .
If we understand what motivates and fosters deception , we can better curb those things in ourselves .
I argue in my book that living a more honest life @ @ @ @ @ @ @ instead of simply noticing everyone else ’ s .
For me personally , this has meant paying more attention to what I ’ m saying and constantly examining my motivations .
This started as a more reactionary endeavor ( to notice when I was lying ) , but morphed into a far more proactive one ( to continually think about truth ) .
Though both are in service of the same thing—being a more honest person—I have noticed that they don ’ t feel the same .
This is because they aren ’ @ @ @ @ @ @ @ or in research .
If you set out to study what makes people tell lies , you tend to keep coming up with the same questions to investigate .
But if you set out to learn what makes people tell the truth or have the courage to speak up , you will inevitably come up with a different set of questions to investigate .
And that could do two things : ( 1 ) connect the dots between related research that wasn ’ t previously linked to honesty since the work didn ’ @ @ @ @ @ @ @ 2 ) create an entirely new body of philosophical and scientific research on honesty .
“ There is so much opportunity for more research about honesty , ” Miller says .
“ And it ’ s not just an academic matter .
There is an obvious real-world relevance and need.
” This is exactly what ’ s behind the Honesty Project , a $ 4.4 million grant from the John Templeton Foundation to study honesty that Miller and a team of researchers ( including Cohen ) at Wake Forest and Carnegie Mellon were @ @ @ @ @ @ @ a three-year timeline that involves funding competitions for Ph.D. academics studying the philosophy and science of honesty , and a conference at the end of the project .
Miller will serve as project director ( he previously directed the Character Project ) and team members have their own research they will conduct as well .
Wake Forest psychology professor William Fleeson will study how to cultivate honesty across the political divide .
This is particularly interesting to me because I ’ ve noticed that in our current climate of political polarization , the @ @ @ @ @ @ @ all the people on the other side are just lying .
Even as a person who has engaged with honesty a lot and written a book about it , I still feel this way whenever I hear anything Donald Trump is saying .
That he lies is a fact .
But are all the people who support him liars who don ’ t care about honesty ?
That ’ s an interesting question .
Cohen ’ s recent research has been focused on honesty in difficult conversations , particularly the idea that we @ @ @ @ @ @ @ at the same time .
Through her work with Emma Levine at the University of Chicago , she ’ s found that we often think being honest with people will be much harder and socially disastrous than it is ( in fact , people find that being honest strengthens relationships and social connections more than they expect ) .
She has plans to do more research on honesty and disclosure in difficult situations , hoping to discover concrete , actionable tips that people in organizations can use .
Though letters of intent for @ @ @ @ @ @ @ Cohen is already hearing from investigators in fields as diverse as political science and computer science .
One of the aims of the project is to see what researchers are working on that can be brought into the fold , particularly primary investigators early in their career ( the project will give preference to those who are within 10 years of receiving their Ph.D. ) .
The hope is that through this more specific focus on the virtue of honesty—the virtue we hold as one of the most important virtues , or even @ @ @ @ @ @ @ about what motivates people to be honest , how honesty impacts relationships , groups and institutions , and how we can better cultivate honesty as individuals and members of groups and families .
Candidly , my hope is even bigger .
I believe that through pouring substantial intellectual and financial resources into the study of honesty , we can be better at everything from disease prevention to racial reconciliation to climate change .
Naturally , I ’ m quite eager to see what these investigators turn up and ultimately present at the 2023 @ @ @ @ @ @ @ thing though : Honesty carries with it an amazing power .
It ’ s not just a shield against deception ; it ’ s a way to change the world .

Last year, I published a book about honesty, exploring what it means to live a more honest life. I examined my own struggles with honesty, and did my best to translate academic research about honesty and apply it to everyday life. Through interviewing many researchers and reading dozens of studies about ethics, deception, moral character, secrecy, and self-delusion, I learned that we know quite a bit about lying and the reasons people lie in a variety of relationships.
But we know far less about the reasons people are honest.
“From my perspective as a philosopher, honesty is stunningly neglected,” says Wake Forest University philosophy professor Christian B. Miller, author of The Character Gap: How Good Are We? “Almost no work about honesty has been done in philosophy in the last 50 years. It’s been largely overlooked.” And yet, he says, when you ask people what they consider to be the most important virtues, a great majority will include honesty. Courage, patience and kindness may also top the list. Humility, too, perhaps. Chastity, probably not so much. But can you imagine anyone ever leaving honesty off the list?
So why don’t we know more about what motivates people to be honest? To disclose, to say the true thing, to correct false information, to speak up?
One answer is that in thinking about honesty, we’ve mostly been tuned into deception. By “we,” I mean you and me, and I also mean philosophers and scientists. First of all, lying, or saying untrue things with the explicit intent to deceive people, has been on full display in the form of Donald Trump for the past several years (though he is certainly not the only elected official to practice deception with regularity). We’ve also had a front-row seat watching personalities like Lance Armstrong and Elizabeth Holmes weave their tangled webs. As citizens of the world, we’re obsessed with lying and lies right now—what’s real, what’s fake, and what’s deliberate and deceitful manipulation?
For honesty researchers, the deception focus wasn’t on purpose. Not exactly. There has been a surge of research over the past 15 years in psychology, organizational behavior, behavioral economics and related fields on lying and unethical decision-making. Starting around 2005, investigators developed and refined new methods to examine when and why people lie and cheat to earn money. “Examples include the now classic matrix and die-rolling tasks where people lie about their performance to earn extra money for themselves, and sender-receiver deception ‘games’ where people lie to other participants to earn extra money for themselves,” says Taya Cohen, associate professor of organizational behavior and theory at Carnegie Mellon University’s Tepper School of Business. By allowing or provoking people to lie in controlled experiments—methodology that Cohen herself has used in much of her research—researchers can observe, measure and track these behaviors. “This means that lying and cheating can be operationalized in a way that isn’t restricted to people's hypothetical decisions or recalled past behaviors,” Cohen says.
From these and other types of studies, we’ve learned a great deal about how and why people lie. We lie when we think we can get away with it. We lie more in groups, especially if we see other people lying, or we’ve been exposed to a bribe. We lie when the lie—even a lie of self-interest—feels justifiable (it’s only a little bit of extra money). We lie less if we’re reminded to be honest or if we have high moral character or score highly on measures of guilt-proneness or honesty-humility.
In organizations, our lies often are related to preserving some sort of identity, and we lie to protect our reputation, the reputation of someone we support or the reputation of a group to which we belong. In relationships, we lie to spare feelings or avoid awkward situations (but we get really irritated when our romantic partner does the same). We lie to ourselves as well, consistently believing we are smarter than we are. Children are also more likely to lie if they’ve been lied to. We even lie if we’re afraid the truth will look like a lie. And of course, we lie on social media, even if the lies look more like “reshaping” the truth.
These are all extraordinarily helpful findings, with relevant takeaway for nearly any group: bosses, teachers, parents, friends, spouses, voters (especially voters). If we understand what motivates and fosters deception, we can better curb those things in ourselves.
I argue in my book that living a more honest life starts with confronting our own deception, instead of simply noticing everyone else’s. For me personally, this has meant paying more attention to what I’m saying and constantly examining my motivations. This started as a more reactionary endeavor (to notice when I was lying), but morphed into a far more proactive one (to continually think about truth). Though both are in service of the same thing—being a more honest person—I have noticed that they don’t feel the same.
This is because they aren’t the same, either in practice or in research. If you set out to study what makes people tell lies, you tend to keep coming up with the same questions to investigate. But if you set out to learn what makes people tell the truth or have the courage to speak up, you will inevitably come up with a different set of questions to investigate. And that could do two things: (1) connect the dots between related research that wasn’t previously linked to honesty since the work didn’t focus on deception, and (2) create an entirely new body of philosophical and scientific research on honesty. “There is so much opportunity for more research about honesty,” Miller says. “And it’s not just an academic matter. There is an obvious real-world relevance and need.”
This is exactly what’s behind the Honesty Project, a $4.4 million grant from the John Templeton Foundation to study honesty that Miller and a team of researchers (including Cohen) at Wake Forest and Carnegie Mellon were awarded in August. The project has a three-year timeline that involves funding competitions for Ph.D. academics studying the philosophy and science of honesty, and a conference at the end of the project. Miller will serve as project director (he previously directed the Character Project) and team members have their own research they will conduct as well. Wake Forest psychology professor William Fleeson will study how to cultivate honesty across the political divide. This is particularly interesting to me because I’ve noticed that in our current climate of political polarization, the people on one side tend to think all the people on the other side are just lying. Even as a person who has engaged with honesty a lot and written a book about it, I still feel this way whenever I hear anything Donald Trump is saying. That he lies is a fact. But are all the people who support him liars who don’t care about honesty? That’s an interesting question.
Cohen’s recent research has been focused on honesty in difficult conversations, particularly the idea that we cannot be both kind and honest at the same time. Through her work with Emma Levine at the University of Chicago, she’s found that we often think being honest with people will be much harder and socially disastrous than it is (in fact, people find that being honest strengthens relationships and social connections more than they expect). She has plans to do more research on honesty and disclosure in difficult situations, hoping to discover concrete, actionable tips that people in organizations can use.
Though letters of intent for proposals are not due until November, Cohen is already hearing from investigators in fields as diverse as political science and computer science. One of the aims of the project is to see what researchers are working on that can be brought into the fold, particularly primary investigators early in their career (the project will give preference to those who are within 10 years of receiving their Ph.D.).
The hope is that through this more specific focus on the virtue of honesty—the virtue we hold as one of the most important virtues, or even the most important one—we can learn more about what motivates people to be honest, how honesty impacts relationships, groups and institutions, and how we can better cultivate honesty as individuals and members of groups and families.
Candidly, my hope is even bigger. I believe that through pouring substantial intellectual and financial resources into the study of honesty, we can be better at everything from disease prevention to racial reconciliation to climate change. Naturally, I’m quite eager to see what these investigators turn up and ultimately present at the 2023 conference. I do already know one thing though: Honesty carries with it an amazing power. It’s not just a shield against deception; it’s a way to change the world.


scientificamerican--2020-09-18--Jaws: Classic Film, Crummy Science

Jaws: Classic Film, Crummy Science

The blockbuster film Jaws has been a perennial favorite here on Martha ’ s Vineyard since its release 45 years ago .
The epic 1975 feature film , shot on the Vineyard in iconic places like the picturesque fishing village of Menemsha , pits a fictional seaside tourist town called Amity against a villainous great white shark whose fearsome triangular teeth—300 of them—bite and kill unsuspecting townspeople and summer visitors enjoying the local Atlantic Ocean waters .
Jaws played recently at a COVID-safe drive-in theater here , allowing viewers to scream in the privacy of their own cars .
The @ @ @ @ @ @ @ psyche of audiences—and ocean swimmers—creating a larger-than-life fictional movie monster that evoked perpetual fear of the great white shark .
However , the Jaws phenomenon also triggered admiration and awe of these magnificent marine animals in the wild , as well as a push for more scientific field research into their natural history .
Studies in recent decades have sought to demystify the demon shark in Jaws and to create a more nuanced view of this apex predator atop the marine food chain : white sharks eat seals , sea lions , dolphins @ @ @ @ @ @ @ humans are not part of their normal diet .
Ironically , the human threat to sharks is far greater than the shark threat to humans .
Each year , fishermen kill , directly or indirectly , an estimated 100 million sharks of all kinds worldwide , the majority for shark fin soup or meat .
Many deaths also occur after white sharks are snagged in commercial fishing gear .
Jaws author Peter Benchley later regretted the man-eating portrayal of the fictional white shark in his best-selling book and the more dramatic , bloodthirsty @ @ @ @ @ @ @ .
With his wife Wendy , he became an avid conservationist , working with environmental groups and research scientists on behalf of oceans and sharks everywhere until his untimely death in 2006 .
“ When Jaws came out , it was a scary movie that terrified a lot of people , ” said Wendy Benchley .
`` Peter would not have written it the way he did once he knew more about sharks , ” she said .
“ He wrote it with the knowledge he had at the time .
It was @ @ @ @ @ @ @ treatise.
” “ The book and film exaggerated the white shark ’ s behavior .
The white shark in the film was far larger than normal—about 25 feet—while the largest animals in the wild are typically 15 to 18 feet , ” says Greg Skomal , a fisheries biologist and well-known shark expert with the Massachusetts Division of Marine Fisheries .
“ They had it satisfying hunger by consuming humans .
They don ’ t do that .
White sharks did not evolve with humans as prey or food , ” he said @ @ @ @ @ @ @ vindictive , attacking the boat and going after the captain .
White sharks certainly don ’ t do that .
It became this epic battle between the shark and the people chasing after it.
” When Jaws came out , “ relatively little was known about the white shark .
We know a lot more now about white shark ecology , distribution and natural history , ” says Skomal .
Studies of the white shark species , Carcharodon carcharias , show its critical role in keeping the marine ecosystem in balance , exerting @ @ @ @ @ @ @ help hold other ocean species in check .
In the Atlantic Ocean waters off New England , shark attacks on humans are “ incredibly rare events , ” says Skomal , especially when compared to other water dangers , like riptides and boating accidents .
“ Many more people drown than are attacked by sharks , ” he said .
Nonetheless , when attacks do occur , they draw incredible publicity .
In July , a wetsuit-wearing 63-year-old woman swimming in the chilly Gulf of Maine waters was killed by a great white @ @ @ @ @ @ @ s history .
In September 2018 , a 26-year-old man boogie boarding off Massachusetts ’ Cape Cod was killed by a shark , the first shark attack fatality in the state since 1936 .
Worldwide , there were 105 confirmed shark attacks on humans in 2019 , including five deaths , according to the International Shark Attack File , based at the Florida Museum of Natural History .
It documented 64 unprovoked attacks on humans worldwide , significantly lower than the five-year average of 82 incidents annually .
The U.S. leads the world @ @ @ @ @ @ @ in 2019 .
Of those , Florida had the most , with 21 , followed by Hawaii with nine .
In New England , the only 2019 fatality occurred in Rhode Island .
The Shark Attack File also documented 41 provoked attacks globally in 2019 in which humans “ initiated interaction with a white shark in some way.
” Although shark attacks are few in number and relatively stable year over year , white sharks in Atlantic coastal waters appear to have increased in number .
“ From the best available data , @ @ @ @ @ @ @ Eastern seaboard of the U.S. are rebounding after years of heavy exploitation , ” said Skomal .
Populations went down in the 1970s and 1980s with the expansion of commercial and recreational fishing that targeted big fish .
But federal conservation regulations , starting in the 1990 ’ s , provided strong protections for white sharks from fishing .
White sharks feed on seals , which have been protected since 1972 by the federal Marine Mammal Protection Act .
Seal populations have also grown in number in Atlantic coastal waters , with higher @ @ @ @ @ @ @ the Gulf of Maine in summer and fall months .
“ That provides a forage base that has drawn white sharks closer to shore , ” said Skomal .
One sign of sharks in the vicinity is the presence of seals they may be following for food .
“ Don ’ t swim where there is a high density of seals , ” says Skomal .
He advises swimmers to stay in shallower water , avoid turgid waters , or swimming when it is dark or getting dark .
Some scientists say the @ @ @ @ @ @ @ dusk , he said .
The Massachusetts Division of Marine Fisheries , working with the Atlantic White Shark Conservancy , has tagged more than 220 white sharks with acoustic or satellite-based tracking devices .
Acoustic tagging has led recently to novel protection for Cape Cod beachgoers .
At selected beaches , lifeguards armed with acoustic receivers can track in real time the proximity of tagged white sharks nearby , says Skomal , leading to temporary beach closures to swimming as needed .
To promote safety and awareness of white sharks , the conservancy @ @ @ @ @ @ @ , also has a popular app called Sharktivity , developed with state and local officials , that provides alerts about sightings of white sharks in the Cape Cod area .
Using satellite-based tagging technology to study seasonal migration patterns of white sharks in the western Atlantic , Skomal and colleagues have shown the animals are more widely distributed than previously thought .
“ They were thought to be largely coastal in nature .
But we ’ ve discovered them in the open ocean diving to depths as deep as 3,000 feet , ” @ @ @ @ @ @ @ early fall , white sharks are found in coastal waters as far north as Newfoundland , moving south for the late fall , winter and spring months to coastal waters off the southeastern U.S. , from North Carolina to the Gulf of Mexico .
Working with researchers from the Woods Hole Oceanographic Institution and Massachusetts Institute of Technology , Skomal found that during this time some white sharks also head further out into deeper waters of the open Atlantic , going as far east as the Azores .
In a 2017 paper in @ @ @ @ @ @ @ scientists noted that “ our findings extend the known essential habitat for the white shark in the North Atlantic beyond existing protection , with implications for future conservation.
” “ We now have relatively robust white shark populations on both coasts ” of the U.S. and in “ hot spots ” around the world , said marine conservation biologist Austin Gallagher , chief executive and lead scientist at Beneath the Waves , a nonprofit research and conservation organization .
“ We need to find ways of coexisting with them , ” he said @ @ @ @ @ @ @ the natural history of the white shark and how best to avoid encounters with it .
According to the International Shark Attack File , about half of shark attacks on humans are related to surfing or board sports , with one fourth involving swimmers or waders .
Its Web page provides additional safety advice for reducing the risk of shark bites .
Jaws was an important motivator for many people to go into marine science .
“ Jaws inspired me to do what I ’ m doing today .
I thought the Jaws @ @ @ @ @ @ @ job .
I was always fascinated by sharks and the ocean , ” says Skomal .
“ It ’ s an entertaining film to this day.
” Gallagher , who was not alive when Jaws premiered in 1975 , saw the film when he was about eight years old .
“ Jaws is one of my favorite movies , ” he says .
“ I look back on it as a motivating factor for pursuing a career as a scientist .
A lot of us saw ourselves as Matt Hooper.
” “ People @ @ @ @ @ @ @ with sharks , ” said Wendy Benchley , who continues to promote ocean conservation through speaking , writing and serving on the boards of nonprofits like Beneath the Waves and WildAid .
She ’ s beginning to think about special events celebrating the 50th anniversary of Jaws as a way to increase public awareness of marine environmental issues , from plastic pollution to overfishing .
“ People need to be more aware that the ocean is in deep trouble , ” she said .
As for Jaws , the beautifully written thriller and @ @ @ @ @ @ @ ’ s audiences .
It ’ s worth rereading or seeing it again—I just did—and appreciating it as a popular work of fiction that magnifies the power of the great white shark .
The suspenseful opening scenes of the movie—with that pounding , fear-inducing music—feature a young woman hopping into the ocean water for a nude midnight swim and , yes , right into the jaws of a menacing great white shark .
Okay .
You can scream now .
Or feel a little squeamish when her bloody remains are found washed up @ @ @ @ @ @ @ never read or seen Jaws , where have you been ?
And what are you waiting for ?
It ’ s time for a shot of adrenaline .
But see the film ’ s man-eating shark monster for what it is : a fictional characterization in a seaside scary movie , not a portrait of the great white shark ’ s behavior in nature .

The blockbuster film Jaws has been a perennial favorite here on Martha’s Vineyard since its release 45 years ago. The epic 1975 feature film, shot on the Vineyard in iconic places like the picturesque fishing village of Menemsha, pits a fictional seaside tourist town called Amity against a villainous great white shark whose fearsome triangular teeth—300 of them—bite and kill unsuspecting townspeople and summer visitors enjoying the local Atlantic Ocean waters. Jaws played recently at a COVID-safe drive-in theater here, allowing viewers to scream in the privacy of their own cars.
The movie took a deep dive into the psyche of audiences—and ocean swimmers—creating a larger-than-life fictional movie monster that evoked perpetual fear of the great white shark. However, the Jaws phenomenon also triggered admiration and awe of these magnificent marine animals in the wild, as well as a push for more scientific field research into their natural history.
Studies in recent decades have sought to demystify the demon shark in Jaws and to create a more nuanced view of this apex predator atop the marine food chain: white sharks eat seals, sea lions, dolphins, porpoises and many types of fish—but humans are not part of their normal diet. Ironically, the human threat to sharks is far greater than the shark threat to humans. Each year, fishermen kill, directly or indirectly, an estimated 100 million sharks of all kinds worldwide, the majority for shark fin soup or meat. Many deaths also occur after white sharks are snagged in commercial fishing gear.
Jaws author Peter Benchley later regretted the man-eating portrayal of the fictional white shark in his best-selling book and the more dramatic, bloodthirsty depiction in the Oscar-winning Steven Spielberg film. With his wife Wendy, he became an avid conservationist, working with environmental groups and research scientists on behalf of oceans and sharks everywhere until his untimely death in 2006.
“When Jaws came out, it was a scary movie that terrified a lot of people,” said Wendy Benchley. "Peter would not have written it the way he did once he knew more about sharks,” she said. “He wrote it with the knowledge he had at the time. It was a first novel, not a scientific treatise.”
“The book and film exaggerated the white shark’s behavior. The white shark in the film was far larger than normal—about 25 feet—while the largest animals in the wild are typically 15 to 18 feet,” says Greg Skomal, a fisheries biologist and well-known shark expert with the Massachusetts Division of Marine Fisheries. “They had it satisfying hunger by consuming humans. They don’t do that. White sharks did not evolve with humans as prey or food,” he said. “The Jaws shark even seemed vindictive, attacking the boat and going after the captain. White sharks certainly don’t do that. It became this epic battle between the shark and the people chasing after it.”
When Jaws came out, “relatively little was known about the white shark. We know a lot more now about white shark ecology, distribution and natural history,” says Skomal. Studies of the white shark species, Carcharodon carcharias, show its critical role in keeping the marine ecosystem in balance, exerting top-down forces on the food web that help hold other ocean species in check.
In the Atlantic Ocean waters off New England, shark attacks on humans are “incredibly rare events,” says Skomal, especially when compared to other water dangers, like riptides and boating accidents. “Many more people drown than are attacked by sharks,” he said.
Nonetheless, when attacks do occur, they draw incredible publicity. In July, a wetsuit-wearing 63-year-old woman swimming in the chilly Gulf of Maine waters was killed by a great white shark—the first such death in Maine’s history. In September 2018, a 26-year-old man boogie boarding off Massachusetts’ Cape Cod was killed by a shark, the first shark attack fatality in the state since 1936.
Worldwide, there were 105 confirmed shark attacks on humans in 2019, including five deaths, according to the International Shark Attack File, based at the Florida Museum of Natural History. It documented 64 unprovoked attacks on humans worldwide, significantly lower than the five-year average of 82 incidents annually. The U.S. leads the world in unprovoked shark attacks, with 41 in 2019. Of those, Florida had the most, with 21, followed by Hawaii with nine. In New England, the only 2019 fatality occurred in Rhode Island. The Shark Attack File also documented 41 provoked attacks globally in 2019 in which humans “initiated interaction with a white shark in some way.”
Although shark attacks are few in number and relatively stable year over year, white sharks in Atlantic coastal waters appear to have increased in number. “From the best available data, it appears that white sharks on the Eastern seaboard of the U.S. are rebounding after years of heavy exploitation,” said Skomal. Populations went down in the 1970s and 1980s with the expansion of commercial and recreational fishing that targeted big fish. But federal conservation regulations, starting in the 1990’s, provided strong protections for white sharks from fishing.
White sharks feed on seals, which have been protected since 1972 by the federal Marine Mammal Protection Act. Seal populations have also grown in number in Atlantic coastal waters, with higher densities in Massachusetts off Cape Cod and the Gulf of Maine in summer and fall months. “That provides a forage base that has drawn white sharks closer to shore,” said Skomal.
One sign of sharks in the vicinity is the presence of seals they may be following for food.
“Don’t swim where there is a high density of seals,” says Skomal. He advises swimmers to stay in shallower water, avoid turgid waters, or swimming when it is dark or getting dark. Some scientists say the sharks are more active at dawn or dusk, he said.
The Massachusetts Division of Marine Fisheries, working with the Atlantic White Shark Conservancy, has tagged more than 220 white sharks with acoustic or satellite-based tracking devices. Acoustic tagging has led recently to novel protection for Cape Cod beachgoers. At selected beaches, lifeguards armed with acoustic receivers can track in real time the proximity of tagged white sharks nearby, says Skomal, leading to temporary beach closures to swimming as needed. To promote safety and awareness of white sharks, the conservancy, which is based in Cape Cod, also has a popular app called Sharktivity, developed with state and local officials, that provides alerts about sightings of white sharks in the Cape Cod area.
Using satellite-based tagging technology to study seasonal migration patterns of white sharks in the western Atlantic, Skomal and colleagues have shown the animals are more widely distributed than previously thought. “They were thought to be largely coastal in nature. But we’ve discovered them in the open ocean diving to depths as deep as 3,000 feet,” says Skomal.
In the summer and early fall, white sharks are found in coastal waters as far north as Newfoundland, moving south for the late fall, winter and spring months to coastal waters off the southeastern U.S., from North Carolina to the Gulf of Mexico. Working with researchers from the Woods Hole Oceanographic Institution and Massachusetts Institute of Technology, Skomal found that during this time some white sharks also head further out into deeper waters of the open Atlantic, going as far east as the Azores. In a 2017 paper in the Marine Ecology Progress Series, the scientists noted that “our findings extend the known essential habitat for the white shark in the North Atlantic beyond existing protection, with implications for future conservation.”
“We now have relatively robust white shark populations on both coasts” of the U.S. and in “hot spots” around the world, said marine conservation biologist Austin Gallagher, chief executive and lead scientist at Beneath the Waves, a nonprofit research and conservation organization. “We need to find ways of coexisting with them,” he said, including educating the general public about the natural history of the white shark and how best to avoid encounters with it. According to the International Shark Attack File, about half of shark attacks on humans are related to surfing or board sports, with one fourth involving swimmers or waders. Its Web page provides additional safety advice for reducing the risk of shark bites.
Jaws was an important motivator for many people to go into marine science. “Jaws inspired me to do what I’m doing today. I thought the Jaws marine biologist Matt Hooper had a great job. I was always fascinated by sharks and the ocean,” says Skomal. “It’s an entertaining film to this day.”
Gallagher, who was not alive when Jaws premiered in 1975, saw the film when he was about eight years old. “Jaws is one of my favorite movies,” he says. “I look back on it as a motivating factor for pursuing a career as a scientist. A lot of us saw ourselves as Matt Hooper.”
“People, and especially children, are fascinated with sharks,” said Wendy Benchley, who continues to promote ocean conservation through speaking, writing and serving on the boards of nonprofits like Beneath the Waves and WildAid. She’s beginning to think about special events celebrating the 50th anniversary of Jaws as a way to increase public awareness of marine environmental issues, from plastic pollution to overfishing. “People need to be more aware that the ocean is in deep trouble,” she said.
As for Jaws, the beautifully written thriller and heart-pumping film hold up well for today’s audiences. It’s worth rereading or seeing it again—I just did—and appreciating it as a popular work of fiction that magnifies the power of the great white shark. The suspenseful opening scenes of the movie—with that pounding, fear-inducing music—feature a young woman hopping into the ocean water for a nude midnight swim and, yes, right into the jaws of a menacing great white shark. Okay. You can scream now. Or feel a little squeamish when her bloody remains are found washed up on shore.
If you’ve never read or seen Jaws, where have you been? And what are you waiting for? It’s time for a shot of adrenaline. But see the film’s man-eating shark monster for what it is: a fictional characterization in a seaside scary movie, not a portrait of the great white shark’s behavior in nature.


scientificamerican--2020-09-22--Color-Changing Ink Turns Clothes into Giant Chemical Sensors

A new color-changing ink could aid in health and environment monitoring—for example , allowing clothing that switches hues when exposed to sweat or a tapestry that shifts colors if a dangerous gas enters the room .
The formulation could be printed on anything from a T-shirt to a tent .
Wearable sensing devices such as smart watches and patches use electronics to monitor heart rate , blood glucose , and more .
Now researchers at Tufts University 's Silklab say their new silk-based inks can respond to , and quantify , the presence of chemicals on or around the body @ @ @ @ @ @ @ like a protective ‘ cocoon ’ for biological materials ” means the necessary sensing and color-changing compounds can be added to the ink without losing their function , says Fiorenzo Omenetto , a biomedical engineer at Silklab and senior author of a new paper on the technology published in July in Advanced Materials .
The researchers improved on an earlier iteration that worked with inkjet printers , thickening the ink with the chemical sodium alginate to make it viable for screen printing , and then added various reactive substances .
With the new @ @ @ @ @ @ @ print a large number of reactive elements onto large surfaces , ” Omenetto says .
The team made the ink by breaking down raw silk fibers into constituent proteins , which the researchers suspended in water .
Next they mixed in various reactive molecules and analyzed how the resulting products changed color when exposed to alterations in their environment .
When printed on fabric and worn , pH indicators , for example , could convey information about skin health or dehydration ; lactate oxidase could measure a wearer 's fatigue levels .
The @ @ @ @ @ @ @ , but the researchers also used a camera-imaging analysis to continuously monitor the color variations and create a database of values .
“ In the case of a T-shirt , the wearer ‘ paints ’ the shirt [ through ] exercise—with colors correlating to the acidity distribution of their sweat , ” Omenetto says .
The ink could also be adapted to track environmental changes in a room , he says , or to respond to bacteria and follow disease progression .
Mechanical engineer Tyler Ray of the University of Hawaii at Mānoa @ @ @ @ @ @ @ study , notes that most of today 's wearable monitors are rigid and fairly bulky .
The new ink technology has “ the potential to transform consumer wearables from recreational novelty devices into body-worn , clinical-grade physiological measurement tools that yield physician-actionable information , ” he says .
But “ one of the challenges with any colorimetric approach is the effect various environmental conditions have on accuracy , such as lighting ... or the camera used.
” Future work needs to address these issues .

A new color-changing ink could aid in health and environment monitoring—for example, allowing clothing that switches hues when exposed to sweat or a tapestry that shifts colors if a dangerous gas enters the room. The formulation could be printed on anything from a T-shirt to a tent.
Wearable sensing devices such as smart watches and patches use electronics to monitor heart rate, blood glucose, and more. Now researchers at Tufts University's Silklab say their new silk-based inks can respond to, and quantify, the presence of chemicals on or around the body. Silk's ability to “act like a protective ‘cocoon’ for biological materials” means the necessary sensing and color-changing compounds can be added to the ink without losing their function, says Fiorenzo Omenetto, a biomedical engineer at Silklab and senior author of a new paper on the technology published in July in Advanced Materials.
The researchers improved on an earlier iteration that worked with inkjet printers, thickening the ink with the chemical sodium alginate to make it viable for screen printing, and then added various reactive substances. With the new ink, they can now “easily print a large number of reactive elements onto large surfaces,” Omenetto says.
The team made the ink by breaking down raw silk fibers into constituent proteins, which the researchers suspended in water. Next they mixed in various reactive molecules and analyzed how the resulting products changed color when exposed to alterations in their environment. When printed on fabric and worn, pH indicators, for example, could convey information about skin health or dehydration; lactate oxidase could measure a wearer's fatigue levels. The changes are visible to the naked eye, but the researchers also used a camera-imaging analysis to continuously monitor the color variations and create a database of values.
“In the case of a T-shirt, the wearer ‘paints’ the shirt [through] exercise—with colors correlating to the acidity distribution of their sweat,” Omenetto says. The ink could also be adapted to track environmental changes in a room, he says, or to respond to bacteria and follow disease progression.
Mechanical engineer Tyler Ray of the University of Hawaii at Mānoa, who was not involved with the study, notes that most of today's wearable monitors are rigid and fairly bulky. The new ink technology has “the potential to transform consumer wearables from recreational novelty devices into body-worn, clinical-grade physiological measurement tools that yield physician-actionable information,” he says. But “one of the challenges with any colorimetric approach is the effect various environmental conditions have on accuracy, such as lighting ... or the camera used.” Future work needs to address these issues.


scientificamerican--2020-09-22--Powerful New Observatory Will Taste Neutrinos' Flavors

Neutrinos are the oddballs of the subatomic particle family .
They are everywhere , pouring in from the sun , deep space , and Earth and zipping through our bodies by the trillions every second .
The particles are so tiny that they seldom interact with anything , making them extremely elusive and hard to study .
Moreover , though neutrinos come in different types , or flavors , they can switch from one type to another as they travel near the speed of light .
These weird behaviors , scientists believe , might point toward insights about the history @ @ @ @ @ @ @ physics .
After nearly six years of excavation , a gigantic neutrino laboratory is taking shape in the rolling hills of southern China , about 150 kilometers west of Hong Kong .
The Jiangmen Underground Neutrino Observatory ( JUNO ) will be one of the world ’ s most powerful neutrino experiments , along with the Hyper-Kamiokande ( Hyper-K ) in Japan and the Deep Underground Neutrino Experiment ( DUNE ) in the U.S .
Using two nearby nuclear power plants as neutrino sources , JUNO will aim to learn more about these @ @ @ @ @ @ @ How do the masses of the three known types of neutrinos compare to one another ?
Though researchers know the particles have a small amount of mass , the exact amount is unknown .
Existing evidence shows that two of the flavors are close in mass and that the third one is different .
But scientists do not know if that third type is heavier or lighter than the others : the former scenario is called the “ normal mass ordering , ” and the latter is named the “ inverted mass ordering.
@ @ @ @ @ @ @ is a key parameter for researchers to determine , says theoretical physicist Joseph Lykken of the Fermi National Accelerator Laboratory in Batavia , Ill. “ In fact , all kinds of other things depend on the answer to that question , ” he adds .
For instance , the answer can help scientists better estimate the total mass of neutrinos in the universe and determine how they have influenced the formation of the cosmos and the distribution of galaxies .
Even though neutrinos are the lightest of all known matter particles , there @ @ @ @ @ @ @ that they must have had a big effect on the way ordinary matter is distributed .
Understanding how neutrino masses are ordered could also help explain why the particles have mass at all , which contradicts earlier predictions .
More than 650 scientists , nearly half of whom are outside China , have been working on JUNO , which was first proposed in 2008 .
Later this year or in early 2021 researchers will start assembling the experiment ’ s 13-story-tall spherical detector .
Inside , it will be covered by a total @ @ @ @ @ @ @ 20,000 metric tons of specially formulated liquid .
At 700 meters below the ground , once in a blue moon , an electron antineutrino ( the specific type of particle that is produced by a nuclear reactor ) will bump into a proton and trigger a reaction in the liquid , which will result in two flashes of light less than a millisecond apart .
“ This little ‘ coincidence ’ will count as a reactor neutrino signal , ” says particle physicist Juan Pedro Ochoa-Ricoux of the University of California , Irvine @ @ @ @ @ @ @ phototube systems for JUNO .
As neutrinos arrive at the detector from the nuclear power plantsseveral kilometers away , only about 30 percent of them will remain in their original identity .
The rest will have switched to other flavors , according to Jun Cao , a deputy spokesperson for JUNO at the Institute of High Energy Physics ( IHEP ) at the Chinese Academy of Sciences , the project ’ s leading institution .
The observatory will be able to measure this percentage with great precision .
Once operational , JUNO expects @ @ @ @ @ @ @ day .
To have a statistically convincing answer to the mass ordering question , however , scientists need 100,000 signals—which means the experiment must run for years to find it .
In the meantime JUNO will detect and study neutrinos from other sources , including anywhere between 10 and 1,000 of the particles from the sun per day and a sudden influx of thousands of them if a supernova explodes at a certain distance from Earth .
JUNO can also catch the so-called geoneutrinos from below Earth ’ s surface , where radioactive @ @ @ @ @ @ @ 232 go through natural decay .
So far studying geoneutrinos is the only effective way to learn how much chemical energy is left down there to drive our planet , says geologist William McDonough of the University of Maryland , who has been involved in the experiment since its early days .
“ JUNO is a game changer in this regard , ” he says .
Though all the existing detectors in Japan , Europe and Canada combined can see about 20 events per year , JUNO alone should detect more than 400 @ @ @ @ @ @ @ is dealing with a flooding issue that has delayed the construction schedule by two years , says Yifang Wang , a JUNO spokesperson and director of IHEP .
Engineers need to pump out 120,000 metric tons of underground water every day , but the water level has dropped significantly .
It is not uncommon to run into flooding issues while building underground labs—an issue also experienced by the Sudbury Neutrino Observatory in Ontario .
Wang believes that the problem will be solved before construction is completed .
JUNO should be up and running @ @ @ @ @ @ @ Wang says .
Toward to end of this decade , it will be joined by DUNE and Hyper-K .
Using accelerator-based neutrinos , DUNE will be able to measure the particle ’ s mass ordering with the greatest precision .
It will also study a crucial parameter called CP violation , a measure of how differently neutrinos act from their antimatter counterparts .
This measurement could reveal whether the tiny particles are part of the reason the majority of the universe is made of matter .
“ JUNO ’ s result on the @ @ @ @ @ @ @ the best possible discovery and measurement of CP violation , ” Lykken says .
The former experiment , along with the other neutrino observatories in development , could also reveal something scientists have not predicted .
The history of neutrino studies shows that these particles often behave unexpectedly , Lykken says .
“ I suspect that the combination of these experiments is going to produce surprises , ” he adds .

Neutrinos are the oddballs of the subatomic particle family. They are everywhere, pouring in from the sun, deep space, and Earth and zipping through our bodies by the trillions every second. The particles are so tiny that they seldom interact with anything, making them extremely elusive and hard to study. Moreover, though neutrinos come in different types, or flavors, they can switch from one type to another as they travel near the speed of light. These weird behaviors, scientists believe, might point toward insights about the history of the universe and the future of physics.
After nearly six years of excavation, a gigantic neutrino laboratory is taking shape in the rolling hills of southern China, about 150 kilometers west of Hong Kong. The Jiangmen Underground Neutrino Observatory (JUNO) will be one of the world’s most powerful neutrino experiments, along with the Hyper-Kamiokande (Hyper-K) in Japan and the Deep Underground Neutrino Experiment (DUNE) in the U.S. Using two nearby nuclear power plants as neutrino sources, JUNO will aim to learn more about these particles and answer a fundamental question: How do the masses of the three known types of neutrinos compare to one another? Though researchers know the particles have a small amount of mass, the exact amount is unknown. Existing evidence shows that two of the flavors are close in mass and that the third one is different. But scientists do not know if that third type is heavier or lighter than the others: the former scenario is called the “normal mass ordering,” and the latter is named the “inverted mass ordering.”
The mass ordering of the neutrino is a key parameter for researchers to determine, says theoretical physicist Joseph Lykken of the Fermi National Accelerator Laboratory in Batavia, Ill. “In fact, all kinds of other things depend on the answer to that question,” he adds. For instance, the answer can help scientists better estimate the total mass of neutrinos in the universe and determine how they have influenced the formation of the cosmos and the distribution of galaxies. Even though neutrinos are the lightest of all known matter particles, there are so many of them in space that they must have had a big effect on the way ordinary matter is distributed. Understanding how neutrino masses are ordered could also help explain why the particles have mass at all, which contradicts earlier predictions.
More than 650 scientists, nearly half of whom are outside China, have been working on JUNO, which was first proposed in 2008. Later this year or in early 2021 researchers will start assembling the experiment’s 13-story-tall spherical detector. Inside, it will be covered by a total of 43,000 light-detecting phototubes and filled with 20,000 metric tons of specially formulated liquid. At 700 meters below the ground, once in a blue moon, an electron antineutrino (the specific type of particle that is produced by a nuclear reactor) will bump into a proton and trigger a reaction in the liquid, which will result in two flashes of light less than a millisecond apart. “This little ‘coincidence’ will count as a reactor neutrino signal,” says particle physicist Juan Pedro Ochoa-Ricoux of the University of California, Irvine, who co-leads one of the two phototube systems for JUNO.
As neutrinos arrive at the detector from the nuclear power plants 53 kilometers away, only about 30 percent of them will remain in their original identity. The rest will have switched to other flavors, according to Jun Cao, a deputy spokesperson for JUNO at the Institute of High Energy Physics (IHEP) at the Chinese Academy of Sciences, the project’s leading institution. The observatory will be able to measure this percentage with great precision.
Once operational, JUNO expects to see roughly 60 such signals a day. To have a statistically convincing answer to the mass ordering question, however, scientists need 100,000 signals—which means the experiment must run for years to find it. In the meantime JUNO will detect and study neutrinos from other sources, including anywhere between 10 and 1,000 of the particles from the sun per day and a sudden influx of thousands of them if a supernova explodes at a certain distance from Earth.
JUNO can also catch the so-called geoneutrinos from below Earth’s surface, where radioactive elements such as uranium 238 and thorium 232 go through natural decay. So far studying geoneutrinos is the only effective way to learn how much chemical energy is left down there to drive our planet, says geologist William McDonough of the University of Maryland, who has been involved in the experiment since its early days. “JUNO is a game changer in this regard,” he says. Though all the existing detectors in Japan, Europe and Canada combined can see about 20 events per year, JUNO alone should detect more than 400 geoneutrinos annually.
Right now the experiment is dealing with a flooding issue that has delayed the construction schedule by two years, says Yifang Wang, a JUNO spokesperson and director of IHEP. Engineers need to pump out 12,000 metric tons of underground water every day, but the water level has dropped significantly. It is not uncommon to run into flooding issues while building underground labs—an issue also experienced by the Sudbury Neutrino Observatory in Ontario. Wang believes that the problem will be solved before construction is completed.
JUNO should be up and running by late 2022 or early 2023, Wang says. Toward to end of this decade, it will be joined by DUNE and Hyper-K. Using accelerator-based neutrinos, DUNE will be able to measure the particle’s mass ordering with the greatest precision. It will also study a crucial parameter called CP violation, a measure of how differently neutrinos act from their antimatter counterparts. This measurement could reveal whether the tiny particles are part of the reason the majority of the universe is made of matter. “JUNO’s result on the neutrino mass ordering will help DUNE make the best possible discovery and measurement of CP violation,” Lykken says. The former experiment, along with the other neutrino observatories in development, could also reveal something scientists have not predicted. The history of neutrino studies shows that these particles often behave unexpectedly, Lykken says. “I suspect that the combination of these experiments is going to produce surprises,” he adds.
Editor’s Note (9/24/20): This story has been edited after posting to correct the figure for the amount of water engineers must pump out of the experiment site daily. It has also been updated to specify the distance between the two power plants and the experiment’s detector.