Curing cancer is obviously positive progress. No-one who has cancer would prefer 19th century medicine.
Spending less than 1 hour a day focusing on food seems less clear-cut. It's really good not to starve or think you might starve, and we are really lucky that we don't have to spend most of the day meeting our basic nutritional needs. There also seems to be a risk that we put not enough thought into taking care of and fulfilling our biological needs, because we can. We can't escape food, sex, exercise and other meatspace needs, and attempts to do so often become pathological. If we have to eat, shouldn't we be taking our time and trying to enjoy the full rich experience of doing so?
Similarly, visiting Machu Picchu and being back by Monday seems like a double-edged sword. Maybe it would be worth spending more time in Peru. Does the short stay really allow time to absorb the history of the Incas and how it fits into the present-day culture of people living in the area? In the 19th century, the vast majority of the people living in the United States couldn't visit Europe. But those who did went on a tour for several months to a year, visiting many countries and cities and staying long enough to learn a bit about the language and lifestyle. Were they missing out by not being able to go in a day, take photos in the right places, and get back a few days later?
To know if a number less than 100 is a prime, you just need to remember that 7 x 13 = 91. This is the only number than seems like it might be prime, but isn't. All other composite numbers are multiples of 2, 3, 5 or 11 (easy to check quickly) or 49, widely known to be 7 x 7.
Secondly, if you are factoring large numbers, and you have quickly checked for division by 2, 3 and 5, you should then take the number modulo 1001. 1001 = 7 x 11 x 13, the next few primes, so you can use modulo 1001 to check for divisibility by all of these.
It's easy to reduce modulo 1001, similarly to reducing modulo 11. 1000 is -1 modulo 1001, 1000000 is 1 modulo 1001, etc. So 31,415,926,535,897 = 31 - 415 + 926 - 535 + 897 mod 1001
These two tidbits are numerical 'coincidences', but they're also related. Remember how 7 x 13 = 91? Well 1 / 11 = 0.0909090909... so 1000 / 11 = 90.9090.., just below 91, and repeating every two digits. Add one one-thousandth of itself and you get 90.9999999 = 91.
Curing cancer is obviously positive progress. No-one who has cancer would prefer 19th century medicine.
Spending less than 1 hour a day focusing on food seems less clear-cut. It's really good not to starve or think you might starve, and we are really lucky that we don't have to spend most of the day meeting our basic nutritional needs. There also seems to be a risk that we put not enough thought into taking care of and fulfilling our biological needs, because we can. We can't escape food, sex, exercise and other meatspace needs, and attempts to do so often become pathological. If we have to eat, shouldn't we be taking our time and trying to enjoy the full rich experience of doing so?
Similarly, visiting Machu Picchu and being back by Monday seems like a double-edged sword. Maybe it would be worth spending more time in Peru. Does the short stay really allow time to absorb the history of the Incas and how it fits into the present-day culture of people living in the area? In the 19th century, the vast majority of the people living in the United States couldn't visit Europe. But those who did went on a tour for several months to a year, visiting many countries and cities and staying long enough to learn a bit about the language and lifestyle. Were they missing out by not being able to go in a day, take photos in the right places, and get back a few days later?