1 00:00:02,040 --> 00:00:07,040 Speaker 1: Welcome to brain Stuff. From how Stuff Works, Hey, brain Stuff, 2 00:00:07,080 --> 00:00:10,440 Speaker 1: Lauren Vogelbaum. Here, counting to three is so easy a 3 00:00:10,520 --> 00:00:14,360 Speaker 1: salamander can do it. Seriously. Lab experiments have shown that 4 00:00:14,440 --> 00:00:17,599 Speaker 1: captive salamanders are able to distinguish between piles of two 5 00:00:17,640 --> 00:00:21,240 Speaker 1: fruit flies and piles of three. If you're not impressed, 6 00:00:21,239 --> 00:00:23,959 Speaker 1: when we understand, a human being who had never taken 7 00:00:23,960 --> 00:00:26,239 Speaker 1: a single math class would have no trouble doing the 8 00:00:26,280 --> 00:00:29,639 Speaker 1: same thing. Some single digit numbers like one, two, and 9 00:00:29,800 --> 00:00:32,680 Speaker 1: three are so small that our minds can recognize their 10 00:00:32,760 --> 00:00:35,600 Speaker 1: value without even needing to count. Put a tray of 11 00:00:35,640 --> 00:00:38,080 Speaker 1: three cookies in front of your average adult, and he 12 00:00:38,200 --> 00:00:41,440 Speaker 1: or she will immediately and intuitively know how many. There 13 00:00:41,479 --> 00:00:46,360 Speaker 1: are no fingers or calculators required. Yet as numbers grow bigger, 14 00:00:46,560 --> 00:00:49,600 Speaker 1: our ability to comprehend their values starts to break down. 15 00:00:50,080 --> 00:00:53,040 Speaker 1: The word billion gets tossed around a lot by economists 16 00:00:53,040 --> 00:00:56,200 Speaker 1: and politicians, but it's hard to appreciate just how large 17 00:00:56,240 --> 00:01:00,560 Speaker 1: that some is. For example, have any idea how long 18 00:01:00,600 --> 00:01:04,280 Speaker 1: a billion seconds is? Me? Neither or not until we 19 00:01:04,319 --> 00:01:06,960 Speaker 1: did the math. It's thirty one years, two hundred and 20 00:01:06,959 --> 00:01:10,360 Speaker 1: fifty one days, thirteen hours, and some thirty four point 21 00:01:10,560 --> 00:01:15,160 Speaker 1: nine minutes, not counting leap days and leap seconds. By 22 00:01:15,200 --> 00:01:18,600 Speaker 1: the commonly accepted definition we use today, one billion is 23 00:01:18,600 --> 00:01:22,720 Speaker 1: equal to eight thousand millions. Numerically, it's expressed as a 24 00:01:22,760 --> 00:01:27,280 Speaker 1: one with nine zeros behind it. One trillion is understood 25 00:01:27,280 --> 00:01:30,440 Speaker 1: to be a million millions, or a one with twelve 26 00:01:30,520 --> 00:01:33,600 Speaker 1: zeros behind it. And to put that in perspective, let's 27 00:01:33,640 --> 00:01:35,600 Speaker 1: say you've pulled an H. G. Wells and built a 28 00:01:35,640 --> 00:01:38,160 Speaker 1: functional time machine. If you ordered it to take you 29 00:01:38,319 --> 00:01:41,120 Speaker 1: one trillion seconds back in time, you'd get to hang 30 00:01:41,160 --> 00:01:44,560 Speaker 1: out with mammoths and sabertooth cats, because one trillion seconds 31 00:01:44,600 --> 00:01:47,080 Speaker 1: is the equivalent of thirty one thousand, five hundred and 32 00:01:47,120 --> 00:01:51,040 Speaker 1: forty six years. Okay, so a trillion is a one 33 00:01:51,120 --> 00:01:54,200 Speaker 1: followed by twelve zeros. The next order of magnitude is 34 00:01:54,240 --> 00:01:58,160 Speaker 1: a quadrillion, which contains fifteen zeros. And you may be 35 00:01:58,240 --> 00:02:01,320 Speaker 1: interested to know that a supercomputer that was recently unveiled 36 00:02:01,320 --> 00:02:04,120 Speaker 1: at the Oak Ridge National Laboratory in Tennessee can make 37 00:02:04,200 --> 00:02:08,480 Speaker 1: up to two hundred quadrillion calculations per second. It's roughly 38 00:02:08,520 --> 00:02:12,320 Speaker 1: a million times faster than the average laptop. But regardless, 39 00:02:12,560 --> 00:02:14,560 Speaker 1: if you took a pen, grab some paper, and wrote 40 00:02:14,600 --> 00:02:17,680 Speaker 1: down a nice, tidy row of one hundred individual zeros, 41 00:02:17,720 --> 00:02:20,040 Speaker 1: then put a one in front of them. The massive 42 00:02:20,080 --> 00:02:22,840 Speaker 1: figure you'll see before you is ten to the power 43 00:02:22,919 --> 00:02:26,520 Speaker 1: of one hundred. Mathematician Edward Kastner took a fancy to 44 00:02:26,520 --> 00:02:30,160 Speaker 1: this number in his nine year old nephew, Milton, came 45 00:02:30,240 --> 00:02:32,480 Speaker 1: up with a name for it, calling the super large 46 00:02:32,480 --> 00:02:36,160 Speaker 1: sum a Google. Many years later, a misspelling of this 47 00:02:36,320 --> 00:02:38,280 Speaker 1: term would be used as the name of the Internet 48 00:02:38,480 --> 00:02:42,040 Speaker 1: top search engine. As enormous as a Google is, at 49 00:02:42,120 --> 00:02:44,880 Speaker 1: least you can write it down numerically. By this, we 50 00:02:44,960 --> 00:02:47,359 Speaker 1: mean to say that you could, if you felt so inclined, 51 00:02:47,560 --> 00:02:50,880 Speaker 1: write a one followed by one hundred zeros. The same 52 00:02:50,919 --> 00:02:54,000 Speaker 1: cannot be said of a google plex. That, dear listener, 53 00:02:54,120 --> 00:02:57,160 Speaker 1: is a one followed by a google's worth of zeros. 54 00:02:57,680 --> 00:03:00,400 Speaker 1: No matter how tiny your handwriting is, you'll never be 55 00:03:00,480 --> 00:03:02,960 Speaker 1: able to jot down all those zeros. There are more 56 00:03:03,080 --> 00:03:05,360 Speaker 1: zeros in a googleplex than there are atoms in the 57 00:03:05,400 --> 00:03:08,600 Speaker 1: observable universe. The only way to commit this figure to 58 00:03:08,639 --> 00:03:12,320 Speaker 1: paper is by using exponential notation. Written out that way, 59 00:03:12,360 --> 00:03:15,520 Speaker 1: a googleplex is ten to the tenth to the one 60 00:03:16,840 --> 00:03:19,120 Speaker 1: and If you think a google plex is big, get 61 00:03:19,120 --> 00:03:21,080 Speaker 1: a load of Skews number, which is ten to the 62 00:03:21,080 --> 00:03:24,160 Speaker 1: tenth to the tenth to the thirty four. This one 63 00:03:24,240 --> 00:03:27,639 Speaker 1: derives its name from Stanley Skews, a South African mathematician 64 00:03:27,639 --> 00:03:30,320 Speaker 1: with an interest in prime numbers. You may know that 65 00:03:30,400 --> 00:03:32,760 Speaker 1: a prime is any number that can only be divided 66 00:03:32,760 --> 00:03:36,200 Speaker 1: by itself and by the number one, and therefore three 67 00:03:36,280 --> 00:03:39,120 Speaker 1: is a prime, but four is not, because it's divisible 68 00:03:39,160 --> 00:03:42,160 Speaker 1: by two. To make a long story short, Skews was 69 00:03:42,160 --> 00:03:45,119 Speaker 1: studying a mathematical function that's been used to give rough 70 00:03:45,240 --> 00:03:48,080 Speaker 1: estimates of how many primes there are between zero and 71 00:03:48,480 --> 00:03:52,240 Speaker 1: any number you might care to name. Excuse introduced his 72 00:03:52,240 --> 00:03:54,880 Speaker 1: eponymous number to the world in a nineteen thirty three 73 00:03:54,880 --> 00:03:57,720 Speaker 1: paper and the words of one colleague. This was, at 74 00:03:57,720 --> 00:04:00,880 Speaker 1: the time, at least the largest number has ever served 75 00:04:00,920 --> 00:04:05,280 Speaker 1: any definite purpose in mathematics. It's since lost that distinction 76 00:04:05,320 --> 00:04:08,480 Speaker 1: to still bigger sums like Graham's number and the monstrous 77 00:04:08,600 --> 00:04:11,760 Speaker 1: tree three. Both of these are way too vast for 78 00:04:11,800 --> 00:04:14,840 Speaker 1: the human mind to grasp, yet each is finite and 79 00:04:14,920 --> 00:04:19,120 Speaker 1: mathematically useful in its own way. Before wrapping up this discussion, 80 00:04:19,320 --> 00:04:22,200 Speaker 1: let's take a step back to acknowledge a smaller figure. 81 00:04:22,600 --> 00:04:27,600 Speaker 1: In January, matth enthusiast Jonathan Pace identified what is, to date, 82 00:04:27,839 --> 00:04:32,000 Speaker 1: the biggest known prime number, named M seven seven two 83 00:04:32,200 --> 00:04:36,760 Speaker 1: three seven. It contains more than twenty three million digits 84 00:04:37,120 --> 00:04:40,640 Speaker 1: twenty three million, two hundred thousand, four hundred and twenty 85 00:04:40,680 --> 00:04:43,760 Speaker 1: five of them to be exact. As such, it is 86 00:04:43,839 --> 00:04:46,600 Speaker 1: nine hundred and ten thousand, eight hundred and seven digits 87 00:04:46,680 --> 00:04:50,000 Speaker 1: larger than the previous record holder. To be sure, this 88 00:04:50,120 --> 00:04:52,760 Speaker 1: prime number isn't in the same league as the Google, 89 00:04:52,839 --> 00:04:55,960 Speaker 1: the google Plex, or Skews number, but if you wrote 90 00:04:55,960 --> 00:04:58,039 Speaker 1: it out in its entirety at a rate of five 91 00:04:58,080 --> 00:05:01,599 Speaker 1: digits per inch, the whole thing would seed seventy three miles. 92 00:05:01,600 --> 00:05:05,039 Speaker 1: That's a hundred and eighteen kilometers in length. Sounds like 93 00:05:05,040 --> 00:05:12,960 Speaker 1: a surefire way to get finger cramps. Today's episode was 94 00:05:13,000 --> 00:05:15,800 Speaker 1: written by Mark Mancini and produced by Tyler Clang. For 95 00:05:15,839 --> 00:05:18,359 Speaker 1: more on this and lots of other math magical topics, 96 00:05:18,480 --> 00:05:32,400 Speaker 1: visit our home planet, how Stuff Works dot com.