Some people say that thanks to Google all knowledge is 2 clicks away. This is as stupid to say as it is stupid to say that all eggs are in the fridge. Have you heard about egg-laying fridges or knowledge-producing clicking?
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The say the first million is the hardest. I'd say something different:
Most people will find it easier to earn a million than to find the sum of the digits of the first million numbers. No one wants to produce Bulgarian subtitles for the latest conspiracy theory documentary? Is this a conspiracy?
My blog-meter shows 0.714 visited pages per visit. Is this a conspiracy? There are creative directors in the most uncreative business of advertising. There are no such people in the universities and the high-tech companies, where the creativity rules. This is one of the advertising conspiracies, they want us to believe they have monopoly over creativity. And they are successful, as many people consider IheartNY product of a brain more creative than the brains of those who found that E = mcc or e^(iп) - 1 = 0. "Power is nothing without control," was Pirelli's motto. "Smarts is nothing without luck", is how John Atanasoff's life can be summarized.
According to Jane Smiley, author of Atanasoff's biography, the United States is the only country where patent applications are approved on item creation date basis (instead of patent application date basis). In any other country, Atanasoff would not have been recognized by the court as the creator of the first electronic digital computer because neither he nor Iowa State University (with whose funding Atanasoff created his computer) had ever applied for a patent. Atanasoff was doubly lucky: if Sperry had offered Honeywell a licensing agreement similar to the one signed with IBM (to use their patents for 10 million dollars), Honeywell would have agreed. But the people of Sperry were greedy and demanded 250 million. Honeywell refused and filed the famous lawsuit, which some people say was the most important patent case of the 20th century. From 2025 onwards all new cars sold in Europe will have to have a built-in system that prevents the engine from starting if there is more alcohol in the driver's breath than the legislated limit allows. Hence my idea for an anti-epidemic smart mask that in addition to viruses will retain alcohol fumes.
"There is no God but Allah and Muhammad is his messenger," cried out the Muslims, waved the green flag and succeeded in capturing the lands from India to France. Even if we have doubts about their faith, we cannot fail to admire its power, i.e. their readiness to die in the name of Allah.
"There is no greater God but Evolution and Darwin is its messenger," cry out today's believers. Even if we doubt the truth of their faith, we cannot fail to admire their pragmatism: as they wave the flags of Evolution, they head en masse to the vaccination points. Faith is dear, but life is dearer. The futurologists are strange creatures. They tell you that 20 years ago it was impossible to predict you'd carry in your pocket a computer more powerful than those of NASA were when you were born. Next minute they tell you that by 2040 the renewable energy will be at least 80% of all energy produced, if the unforeseen developments are ruled out.
There are always unforeseen developments, why should we rule them out? If there were no unforeseen developments, then 20 years ago I and the futurologists would have known that today we'd carry in our pockets computers more powerful than those of NASA were at the time of our birth. Which watch is smarter: the Swiss one (dozens of springs) or the Korean one (thousands of transistors and lines of code)? Which watch owner is smarter: the one with the mechanical watch (which costs thousands of Swiss francs) or the one with the Korean watch (which costs few hundred euros)?
The Swiss watch is simple, you put it on your hand and forget about it. A Korean watch needs time and effort to set up, update, and connect to another smart and much more expensive device that also requires setup and updates. Therefore, a Korean watch wastes a lot of your time. On the one hand, the people with a lot of time seem smarter. On the other hand, if they dedicate their time to their watches, they don't seem so smart. On the one hand, the people with mechanical Swiss watches seem to earn more than enough and are therefore smarter. On the other hand, if they dedicate their money to Swiss watches and similar knick-knacks, they don't seem so smart. I think the smartest watch is the watch that does not say what time it is, but what to do with your time. The same goes for people: the smartest are not those who know what time it is, but those who: a) know what they spend their time on, and b) are happy about it. They definitely don't need watches for that. If I have seen further it is by standing on the shoulders of giants. Isaac Newton
If I have not seen as far as others, it is because giants were standing on my shoulders. Hal Abelson Find a positive integer X such that:
a) the set of its positive integer divisors can be partitioned into two disjoint subsets with equal sums of elements, and b) 2 and 3 are not divisors of X. P.S. Fausto Morales sent the following solution: Lowest Solution: 5391411025 Subset 1 = { 11 13 17 19 23 25 29 35 55 65 77 85 91 95 115 119 133 143 145 161 175 187 203 209 221 247 253 275 299 319 323 325 377 385 391 425 437 455 475 493 551 575 595 665 667 715 725 805 935 1547 1595 1615 1729 1771 1885 1925 1955 2093 2185 2233 2261 2275 2431 2465 2639 2717 2737 2755 2975 3059 3289 3325 3335 3451 3553 3575 3857 4025 4147 4199 4301 4669 4675 4807 5005 5075 5083 5225 5423 5525 5681 6061 6175 6325 6409 6545 7163 7315 7337 7429 7475 7735 7975 8075 8645 8671 8855 9367 9425 9775 10465 10925 11165 11305 11339 12155 12325 12673 13195 13585 13685 13775 15295 16445 16675 17017 17255 17765 19019 19285 20735 20995 21505 23023 23345 24035 24871 25025 25415 27115 28405 29029 29393 30107 30305 32045 32725 33649 35581 35815 36575 36685 37145 37961 38675 39767 42427 43225 43355 44275 44863 46189 46835 50141 51359 52003 52325 55825 55913 56525 56695 60697 60775 62491 63365 65569 65975 67925 68425 70499 76475 78793 79373 81719 82225 85085 86275 88711 88825 437437 4365515 5391411025 } Sum = 5399654400 Subset 2 = { 1 5 7 1001 1015 1045 1105 1235 1265 1309 1463 1495 95095 95381 96425 96577 103037 103675 104975 107525 115115 116725 120175 121771 124355 124729 127075 135575 139403 142025 145145 146965 147407 150535 151525 160225 164749 168245 177905 179075 183425 185725 189805 198835 212135 215441 216775 224315 230945 234175 250705 256795 260015 279565 283475 303485 312455 316825 323323 327845 352495 391391 393965 396865 408595 425425 443555 475475 476905 482885 493493 515185 551551 572033 575575 608855 621775 623645 667667 676039 697015 721259 725725 734825 737035 752675 823745 841225 852397 873103 889525 949025 975821 994175 1031849 1060675 1062347 1077205 1121575 1153243 1154725 1253525 1283975 1300075 1339481 1397825 1508087 1517425 1562275 1616615 1621477 1639225 1762475 1812239 1956955 1969825 1984325 2042975 2187185 2217775 2369851 2384525 2414425 2467465 2575925 2757755 2800733 2860165 3044275 3118225 3338335 3380195 3485075 3606295 3685175 4118725 4261985 4879105 5159245 5311735 5386025 5766215 6697405 7436429 7540435 8083075 8107385 9061195 9376367 9784775 10935925 11350339 11849255 12337325 12685673 13788775 14003665 14300825 16588957 16691675 16900975 18031475 19605131 21309925 21827575 24395525 25796225 26558675 28831075 30808063 33487025 37182145 37702175 40536925 45305975 46881835 56751695 59246275 63428365 70018325 82944785 98025655 154040315 185910725 215656441 234409175 283758475 317141825 414723925 490128275 770201575 1078282205 } Sum = 5399654400 Both subsets are of equal cardinalities (192 elements each). Perfect numbers like perfect men are very rare. René Descartes
Zumkeller numbers like good men are at least one in a dozen. Yours truly They say that the magic square in Albrecht Dürer's Melancholia is interesting because the painter's goal was to show the year of the sad event (death of his mother in 1514 AD) that provoked his melancholia. This worthy goal had several unintended consequences. The couples of symmetric quadruplets (first+ultimate and second+penultimate) form identical trapezoids, the second of which is rotated by 180 degrees. There is one more interesting thing: the sums of numbers on the numbered vertices of the two hexagons - blue (3+2+14+15) and red (10+11+7+6) - in the center of the square equal the magic constant of the square.  The strategy of keeping your doors open is a trap, Po Bronson writes. Why is it so? In the words of Bronson, failure’s hard, but success is far more dangerous. If you’re successful at the wrong thing, the mix of praise, money and opportunity can lock you in forever.
Oddly enough, combining blankets is not commutative. Sometimes blankets A + B make you warmer than B + A.
Take 7 distinct numbers out of the numbers {1,2,...,9} and use them to fill in every circle so that the products of the numbers on every horizontal and vertical line are equal. This was the easy part. The hard thing to do is to find several different approaches to the right solution (embodied in the different first questions you may ask when you start thinking about the problem).  "People say that dog is man's best friend," said the dog, "but are silent about whether man is dog's best friend."
Once upon a time I wrote some program but later found it did lots of needless calculations. I removed the respective part of the program, but instead of running faster it slowed down. When I complained to a friend of mine, who had been programming for decades, he looked down on me the way the Great Incas had been looking down on their subjects and said, "This is what usually happens."
Come to think of it, this is what usually happens not only to our programs but to ourselves. Oh, how often our efforts to remove the needless things from our lives lead us to needless situations. Wishing to remove the needless weight we damage our muscles and tendons and are getting hernias. Wishing to spend the needless money we meet people we do not need to know, do things we do not need to do and waste our time. At the end we learn the hard way that out of all imaginable things time is never needless. I have a friend who does not know I am a synesthete and is amazed by my ability to compare music to movies or Irish whiskey to Bulgarian white wine. He told me more than once that comparing apples to oranges is a forbidden operation.
Not only am I synesthete, but I am also interested in math. That is why I know one can compare objects of different type. One can even add and multiply them. It’s elementary, my dear Watson, 5 apples plus 3 oranges equals 8 pieces of fruit. 5 jackets times 5 trousers equals 25 different suits. The fact that we think does not necessarily mean we don't have to learn how to think. Same with breathing, once we start practicing sports, yoga, or singing, we learn our "old" breathing doesn't work and we need to learn to breath correctly.
For every n > 0, it is possible to partition the set of the first 2n + 1 primes into two disjoint subsets with equal sums of elements.
Somebody asked the famous American mathematician John Forbes Nash where did the idea that aliens communicate with him come from. "Where my other ideas come from," Nash replied. His beautiful mind led him to the Nobel Prize in economics, but was not beautiful enough to make him realize that of all his ideas thе one about the aliens was impossible to prove.
It is better to make your own point than to follow other people's lines of reasoning.
... hard to hide and easy to hate.
In an essay called "Roberta", from his book Chronicles of a liquid society, Umberto Eco tries to explain why we are angry when athletes succeed with the help of chemistry, but think it is OK when artists use it for creative purposes. It is elementary, Eco writes, in sports we are interested in the person behind the result, in arts we are interested in the result, not the person. Trying to leave nothing unexplained, Eco gives the following examples:
> if football was firing balls into the goal by a cannon, football would lose all interest; > if a monkey could write The Divine Comedy, then the book would still be miraculous. If we are willing to think a little more, we can reach other conclusions about: Football In football we are interested in the goals, not the persons, which is why we watch football regularly, but read biographies of football stars once every 10 years. Art Think about supply and demand! If monkeys could write books like The Divine Comedy, then (due to the abundant supply) no one would think that their writings are divine. It is comparatively easy to make clever guesses; indeed there are theorems like "Goldbach's Theorem", which have never been proved and which any fool could have guessed.
G.H. Hardy Was G. H. Hardy's guess that it is comparatively easy to make clever guesses a clever guess? I have already shared my doubts. Now, instead of discussing Goldbach's Conjecture I'll turn to Ramanujan. If it was easy to make clever guesses, then why was not Hardy able to instantly guess the mathematical brilliance of Ramanujan, but needed Littlewood to discuss in detail Ramanujan's first letter with? Not only was G. H. Hardy's guess not clever, but also it was not original. It is said someone mentioned Goldbach's conjecture to Gauss and the math wizard replied it was nothing special and he could generate within seconds two or three similar conjectures. No one mentioned any such conjectures, which makes me think no conjectures were provided (or if they were, they were not particularly interesting to be remembered). |
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