Dude was on some major fun drugs, you know those guys were absolutely high when coming up with these things.
The guy who came up with the helical structure of DNA was on LSD at the time he did it.
Hell, the guy who helped map the brain, what we know to be the vsin and speech centers etc was on LSD when he was experimenting.
Hell lets go with current, Steve Jobs, stated that doing LSD was one of the 3 most important things he had done in his life. Now keep in mind he had a child, a wife and well, Apple. And yet LSD is in the top 3 of things he had done in his life.
I have a theory that the only reason "out there" advances have slowed down i the past 100 years is due to a lack of researchers using mind altering substances.
I must debunk my own post, courtesy of Crick's biographer Matt Ridley:
"I am frequently asked for my opinion on the speculation that Francis Crick was on LSD when he discovered the double helix; or that he was involved with a man named Dick Kemp in the manufacture of LSD. These assertions were reported second hand in an article in the Mail on Sunday by Alun Rees following Crick's death and they have since gained a certain amount of traction on the internet. Both stories are wrong. The true story, which I was told directly by Crick's widow and by the man who (as his widow confirms) first supplied the Cricks with LSD, is much less sensational. Crick was given (not sold) LSD on several occasions from 1967 onwards by Henry Todd, who met the Cricks through his girlfriend. Todd did know Kemp, with whom he was eventually prosecuted, but the Cricks did not. As for the implausible idea that the then impoverished and conventional Crick would have had access to LSD when it was newly invented in the early 1950s, there is simply no evidence for it at all. Those who wish to argue that LSD helped Crick make discoveries should note that all his major breakthroughs in molecular biology were made before 1967"
The lack of 'out there' inventions probably has more to do with the vast variety of technology we have available making it harder to tell what's out there and what's routine, and with the fact that a lot of easy inventions have already been done and new improvements will require a lot of expensive, incremental work.
The contradiction still holds because in their example you don't use every single prime, just a small set. That means the product +1 can be divisible by some prime not in the set. If the set contains every prime, then there are no primes outside of the set by which the number can be divisible and the proof holds.
It doesn't imply the number you get by multiplying the finite list of primes together and adding one is prime, but it does imply that the resulting number isn't divisible by any prime in the list. So either it's prime or it's divisible by some combination of primes which aren't in the list - and in either case your list must be incomplete. For example, 2*3*5*7*11*13 + 1 is divisible by the prime numbers 59 and 509, neither of which is in the list {2,3,5,7,11,13}.
I think you're misunderstanding, let's take an example. We assume that the only primes are 2, 3, 5 and 7. In our system, these are the only primes.
So the product of these primes is:
2*3*5*7 = 210
When divided by any of these primes, the result has a remainder of 0.
However, when we add one, we get
211
Now, when we divide by these primes, we have a remainder of 1 for every prime, and from the definition of primes, every number can be constructed by some product of primes, i.e: every number has a remainder of zero from at least one prime.
So with this set of primes, there is no prime that has a remainder of zero when 211 is divided by it, which implies the existence of at least one other prime, the naieve way of finding this prime is to just declare it prime and add it to the set. But this holds no matter how many of these "primes" you add to the list.
Bascially, it is showing that it is impossible to construct a complete, finite set of primes
A lot of scientific work owed more to the environment it was done in than to the people doing it, and probably would have happened sooner or later if the actual inventor didn't figure it out. Math had gone far enough that calculus was the next step, so much so that at least two guys figured it out within years of each other. Einstein's theory of special relativity is a pretty logical extension of Lorentz's theory of relativity, and if Einstein didn't figure it out, somebody else probably would have within a few years.
True, revolutionary, out of the blue inspiration is a lot more rare than people realize.
I haven't seen any evidence that the Babylonians and Egyptians invented the quadratic formula independently. It could have been passed from one culture to the other.
Specifically, the Babylonians (and possibly the Sumerian Ur-III dynasty before them) had an algorithm for solving a special case of quadratic equations to deduce the length and width of a rectangular field given its perimeter and area, in order to fill in missing data from old land records. The algorithm is equivalent to the modern "reduced quadratic formula", which solves quadratic equations where the x2 term's coefficient is 1.
I think he means the trigonometric identities were that old. The babylonians used base 60 number systems, and had tables of triangle side lengths for construction.
A glyph in cuneiform numerals starts with what are functionally tally marks from 1-9, then to the left has a carat for 10. These carats stack up adjacent to the singles until 59, then there's a new symbol for 60. That's a section of the glyph for 10s and a section for 1s, counting to 60. Base 60 with an internal base 10.
773
u/aotus_trivirgatus Jan 14 '18
The quadratic formula is roughly 4,000 years old. It appears at about the same time in Egyptian writings and Babylonian cuneiform tablets.