Apr 2, 2021 02:06 AM
'Spacekime theory' could speed up research and heal the rift in physics
https://bigthink.com/surprising-science/...ime-theory
KEYPOINTS: The spacekime model is a 5D universe of 3D-space and 2D-complex-time, known as 'kime'. Our linear model of time may be holding back scientific progress. Spacekime theory can help us better understand the development of diseases, financial and environmental events, and even the human brain. This theory helps us better utilize big data, develop AI, and can even solve inconsistencies in physics... (MORE - details)
Is There A Fundamental Reason Why E = mc²?
https://www.forbes.com/sites/startswitha...207dc95773
EXCERPT: But why? Why does energy have to equal mass multiplied by the speed of light squared? Why couldn’t it have been any other way? [...] It’s a great question. Let’s investigate Einstein’s most famous equation, and see exactly why it couldn’t have been any other way... (MORE - details)
Mathematicians Find a New Class of Digitally Delicate Primes
https://www.quantamagazine.org/mathemati...-20210330/
INTRO: Take a look at the numbers 294,001, 505,447 and 584,141. Notice anything special about them? You may recognize that they’re all prime — evenly divisible only by themselves and 1 — but these particular primes are even more unusual.
If you pick any single digit in any of those numbers and change it, the new number is composite, and hence no longer prime. Change the 1 in 294,001 to a 7, for instance, and the resulting number is divisible by 7; change it to a 9, and it’s divisible by 3.
Such numbers are called “digitally delicate primes,” and they’re a relatively recent mathematical invention. In 1978, the mathematician and prolific problem poser Murray Klamkin wondered if any numbers like this existed. His question got a quick response from one of the most prolific problem solvers of all time, Paul Erdős. He proved not only that they do exist, but also that there are an infinite number of them — a result that holds not just for base 10, but for any number system. Other mathematicians have since extended Erdős’ result, including the Fields Medal winner Terence Tao, who proved in a 2011 paper that a “positive proportion” of primes are digitally delicate (again, for all bases). That means the average distance between consecutive digitally delicate primes remains fairly steady as prime numbers themselves get really big — in other words, digitally delicate primes won’t become increasingly scarce among the primes.
Now, with two recent papers, Michael Filaseta of the University of South Carolina has carried the idea further, coming up with an even more rarefied class of digitally delicate prime numbers. “It’s a remarkable result,” said Paul Pollack of the University of Georgia.
Motivated by Erdős’ and Tao’s work, Filaseta wondered what would happen if you included an infinite string of leading zeros as part of the prime number. The numbers 53 and …0000000053 have the same value, after all; would changing any one of those infinite zeros tacked on to a digitally delicate prime automatically make it composite?
Filaseta decided to call such numbers, assuming they existed, “widely digitally delicate,” and he investigated their properties in a November 2020 paper with his former graduate student Jeremiah Southwick.
Not surprisingly, the added condition makes such numbers harder to find. “294,001 is digitally delicate, but not widely digitally delicate,” Pollack said, “since if we change …000,294,001 to …010,294,001, we get 10,294,001” — another prime number.
In fact, Filaseta and Southwick couldn’t find one example in base 10 of a widely digitally delicate prime, despite looking through all the integers up to 1,000,000,000. But that didn’t prevent them from proving some strong statements about these hypothetical numbers.
First, they showed that such numbers are indeed possible in base 10, and, what’s more, an infinite number of them exist. Going a step further, they also proved that a positive proportion of prime numbers are widely digitally delicate, just as Tao had done for digitally delicate primes. (In his doctoral dissertation, Southwick achieved the same results in bases 2 through 9, 11 and 31.)
Pollack was impressed with the findings. “There are infinitely many possible things you’re allowed to do to these numbers and, no matter which you do, you’re still guaranteed a composite answer,” he said... (MORE)
Is the universe REALLY a hologram?
https://www.youtube-nocookie.com/embed/T4DAGabiGms
https://bigthink.com/surprising-science/...ime-theory
KEYPOINTS: The spacekime model is a 5D universe of 3D-space and 2D-complex-time, known as 'kime'. Our linear model of time may be holding back scientific progress. Spacekime theory can help us better understand the development of diseases, financial and environmental events, and even the human brain. This theory helps us better utilize big data, develop AI, and can even solve inconsistencies in physics... (MORE - details)
Is There A Fundamental Reason Why E = mc²?
https://www.forbes.com/sites/startswitha...207dc95773
EXCERPT: But why? Why does energy have to equal mass multiplied by the speed of light squared? Why couldn’t it have been any other way? [...] It’s a great question. Let’s investigate Einstein’s most famous equation, and see exactly why it couldn’t have been any other way... (MORE - details)
Mathematicians Find a New Class of Digitally Delicate Primes
https://www.quantamagazine.org/mathemati...-20210330/
INTRO: Take a look at the numbers 294,001, 505,447 and 584,141. Notice anything special about them? You may recognize that they’re all prime — evenly divisible only by themselves and 1 — but these particular primes are even more unusual.
If you pick any single digit in any of those numbers and change it, the new number is composite, and hence no longer prime. Change the 1 in 294,001 to a 7, for instance, and the resulting number is divisible by 7; change it to a 9, and it’s divisible by 3.
Such numbers are called “digitally delicate primes,” and they’re a relatively recent mathematical invention. In 1978, the mathematician and prolific problem poser Murray Klamkin wondered if any numbers like this existed. His question got a quick response from one of the most prolific problem solvers of all time, Paul Erdős. He proved not only that they do exist, but also that there are an infinite number of them — a result that holds not just for base 10, but for any number system. Other mathematicians have since extended Erdős’ result, including the Fields Medal winner Terence Tao, who proved in a 2011 paper that a “positive proportion” of primes are digitally delicate (again, for all bases). That means the average distance between consecutive digitally delicate primes remains fairly steady as prime numbers themselves get really big — in other words, digitally delicate primes won’t become increasingly scarce among the primes.
Now, with two recent papers, Michael Filaseta of the University of South Carolina has carried the idea further, coming up with an even more rarefied class of digitally delicate prime numbers. “It’s a remarkable result,” said Paul Pollack of the University of Georgia.
Motivated by Erdős’ and Tao’s work, Filaseta wondered what would happen if you included an infinite string of leading zeros as part of the prime number. The numbers 53 and …0000000053 have the same value, after all; would changing any one of those infinite zeros tacked on to a digitally delicate prime automatically make it composite?
Filaseta decided to call such numbers, assuming they existed, “widely digitally delicate,” and he investigated their properties in a November 2020 paper with his former graduate student Jeremiah Southwick.
Not surprisingly, the added condition makes such numbers harder to find. “294,001 is digitally delicate, but not widely digitally delicate,” Pollack said, “since if we change …000,294,001 to …010,294,001, we get 10,294,001” — another prime number.
In fact, Filaseta and Southwick couldn’t find one example in base 10 of a widely digitally delicate prime, despite looking through all the integers up to 1,000,000,000. But that didn’t prevent them from proving some strong statements about these hypothetical numbers.
First, they showed that such numbers are indeed possible in base 10, and, what’s more, an infinite number of them exist. Going a step further, they also proved that a positive proportion of prime numbers are widely digitally delicate, just as Tao had done for digitally delicate primes. (In his doctoral dissertation, Southwick achieved the same results in bases 2 through 9, 11 and 31.)
Pollack was impressed with the findings. “There are infinitely many possible things you’re allowed to do to these numbers and, no matter which you do, you’re still guaranteed a composite answer,” he said... (MORE)
Is the universe REALLY a hologram?
