Random events (1962)

and order random events is number effect indeed can that large be overall of events are various know of predictable of which such the occur with yet very unpredictably dr. Hume just told you what this film is about he wrote a sentence to explain what we want to show you and then he kept the sentence up into individual words put the slips of paper into a hat and drew them out in a random order and read them to you in this random order here's the sentence before it was scramble random events are events weaker with no order that is unpredictably and yet the overall effect of a very large number of such events can be very predictable indeed who's going to start well let's use a random event to decide heads or tails tails heads you lose you start here are random events occurring naturally see the needle hear the clicks this is a Geiger counter and this contains a radioactive material polonium every time the Geiger counter clicks it means that an atom of polonium has changed into an atom of lead except that there are some extra flex because of cosmic rays I said that these clicks are random events what does that mean it means that there's no order to them I can't predict when the next one will occur even if I measure the time between clicks very accurately for a large number of clicks I will still not be able to predict when the next one will occur that's what I mean by a random event here's a picture from your textbook a graph of the activity of a sample of polonium plotted against time in days you can see that the activity that is the number of radioactive disintegrations in the sample decreases as time goes on the activity at the start is one hundred percent it's only one half as much at the end of 138 days at the end of another 138 days it's half of what it was at the end of the first 138 days it's down to one quarter of its original activity and this goes on every 138 days sees the activity cut in half this length of time is called the half-life of polonium all radioactive substances behave in this same way some have very short half-lives here's helium 6 a radioactive isotope of helium it has a half-life of eight tenths of a second some have very long half-lives here's uranium 238 half-life is four and one half billion years as you can see if a graph of activity is plotted in terms of half-life times it is identical for all radioactive substances this is a law a law of radioactive disintegration a description which fits the behavior of a great variety of substances and allows us to predict their activity at any time in the future how can this predictable behavior emerged from the random unpredictable behavior that dr. Ivy showed you well we'll come back to radioactivity later but first we're going to investigate some other examples of random behavior would you care to predict where the next marble will go the same no I'll try a few more unpredictable isn't it there are 100 marbles in here I'll drop them all most in here maybe that's the slot that the marbles are most likely to go into I'll mark the way that the marbles are distributed here I'll put the marbles back in the tube now I'll do it again you can see that the distribution is not going to be the same this time there are most marbles in this slot perhaps now I might guess that the marbles are more likely to go into the slots here but that's all it would be a guess I still haven't made enough observations of the behavior of this apparatus to make reasonable predictions about what will happen so I'm going to take some statistics on the apparatus that is I'm going to observe what the behavior is in a systematic way I'm going to drop a hundred marbles many times and each time got a graph like this of the distribution and dr. Hume will help well let's get to work here are the ten distributions we found in 10 tries you can see that they're all different I'll put three of them together so you can compare them now you can see the sort of fluctuations that there are between them this graph shows the next thing that we did we added together these ten distributions and we divided by 10 to make this graph the same size as these graphs this is now the average distribution for the 10 tries one way of looking at this is that this is the distribution we would have found if we drop the thousand marbles all at once in the apparatus except that we couldn't because the apparatus won't hold a thousand marbles all at once then we did this again dropped a hundred marbles ten times we got another thousand marble distribution and once more there it is these three are hundred marble distributions and these three are thousand marble distributions you can see that the fluctuations here are much smaller than the fluctuations here if we drop the million marble to the time in the apparatus then we probably wouldn't be able to see any fluctuations tall each of these graphs is a frequency distribution and the point of taking a lot of statistics for the apparatus is to get the best approximation that we can to the true frequency distribution for the apparatus the average of these three will be reasonably close to the true frequency distribution here it is the average now that I have this I can make predictions statistical predictions about the behavior of Miss a parade us you can see that the frequency here is about twice that of the frequency here this means that the probability of a marble going in this slot is about twice that of a marble going in this slot it didn't go in either one you must realize that a single marble still behaves unpredictably to say that the probability of a marble going in here is twice that of a marble going in here just means that if I drop a very large number of marbles twice as many of them will go in here as go in here and as you've seen very large number means just that you've seen how to find the frequency distribution for a simple pinball machine what about this machine it has 16 squares of cardboard mounted so that they can spin around one face is white and the other face black now the light scattered from these squares can be read on a light meter over there and the results projected on the screen right now half of the squares are white and half of them are black and the reading is 8 now dr. ivy is going to turn the squares around so that they are all white side out now yes no we've made the scale on the meter so that reads directly the number of white squares facing out the reading now is 16 now we better check up on the ball black reading the reading is zero no white squares facing out dr. Ivy is going to start the square spinning now with a fan he has to help some of them along by hand I want them to end up facing out so he's sliding a screen across the back the reading is 8 now we're going to do this again several times and just show you the results five 11 796 tan and you might expect that the most probable result would be eight corresponding to half black and half white but we get considerable fluctuation from them sex well we'll have to do this a large number of times in order to get a proper frequency distribution I don't think I have the strength well don't worry about that because for this machine I can calculate the frequency distribution I'll show you when I spin one of these cards around it comes out either black or white and I can't predict which I can't see any reason why it should come up white instead of black so first of all I assume that these two alternatives are equally probable now these squares spend quite independently of each other so the final result is the overall effect of 16 independent random events how do I calculate the probabilities of the 17 different possible results there is only one way to get all black or all white so these two meter readings are equally probable and they're certainly not very probable but look at the arrangement of squares right now the probability of this particular arrangement is exactly the same as that for all black for all light but the meter reads the overall effect and can't tell the difference between this arrangement and any other with ten white and six black so the probability of a particular meter reading depends on the number of different ways the reading can be produced there are 16 different ways of getting one white or one black so these two meter readings are equally probable and 16 times more probable than this you may be able to go on now and calculate how many different ways there are getting two white or two black there are 120 different ways now I'm already off scale here but I plotted this frequency distribution before and here it is to a much reduced tail you can see that the ones that I was calculating before hardly show here at all and that the eight is the most probable perhaps you can try working this out for yourself but you must remember that when you do make a calculation of this sort that you should do experiments to check it now over here I have a similar machine with spinning squares here there are 256 cards in the same area the overall effect of this one is made up of a much larger number of independent random events what about a frequency distribution for it for 16 cards a reading of eight is more probable than the others for 256 cards a reading how eight is very much more probable than any other reading in fact it is so much so that I can almost say with certainty what the result will be when I spin the cards I predict a reading of eight let's try it checks my prediction let's do it again 88 eight again the fluctuations are very much smaller here this reading is predictable that's why we said in the beginning that the overall effect of a large number of random events is very predictable now at last we're in a better position to talk about this law of radioactive decay that we started with first of all what does it mean to talk about activity it should mean that a sample of radioactive material has a definite predictable number of disintegrations in a certain length of time how conductors you speak of a predictable number of disintegrations in a certain length of time when the disintegrations are random I'll show you with this it's a Geiger counter which displays the number of counts here I'll start it 1 2 3 4 5 as you can see the time between counts is not predictable when there are 10 counts then a 1 comes up in the tens column and the unit column starts over now I'm going to move the radioactive polonium here closer to the detector this will increase the number of counts the unit calm is still random but much faster than before the tens column is pretty random but watch the hundreds cough 600 700 800 900 these are quite regular there is some fluctuation this fluctuation would be even smaller if I took a thousand counts at a time this is just the law of large numbers I can never say what the time interval between single counts will be but i can say fairly accurately what the time interval for a large number of counts will be well that's how we get the activity to plot on this graph now why does the activity decrease in this particular way for all radioactive substances this too fits the idea that disintegrations are random events perhaps I can simulate this behavior with a sort of game here are 60 dice think of them as atoms a rather small sample compared to the vast numbers of atoms in any piece of radioactive material suppose that the fives represent atoms that have just disintegrated I'll pile them up here the chance of a 5 turning up is just the same as any other number it happens at random and is independent of what comes up on any of the other dice these represent the activity in the time interval of the first throw they are no longer the same atoms they were before they disintegrated so that they are eliminated from now on now i'll throw again the chance of any one of these dice coming up five is exactly the same as it was on the last throw I'm piling these up beside the first row this time there are fewer atoms disintegrating is one more now I'm going to go on doing this throw after throw and you'll see what I get extra I still have a few dice left that I'm trying to get five sweat but i'll stop here this is a an activity time graph for this dice game and I want you to compare it with the activity graph for a radioactive substance the dice graph isn't smooth there are sizable fluctuations which are bound to occur because I had only a small number of dice but the general trend is exactly the same for booth so it looks as if the law of radioactive disintegration is the same as the law of chance for these dice I mentioned the law of chance for the dice but I better say it again the chance of any one of the dice turning out five is exactly the same on every throw this means that the chance of an atom exploding in any one time interval is the same as in any other it doesn't change whatever as time goes on Adams unlike people do not have a greater chance of disintegrating as they get older the chance always stays the same perhaps you can calculate for yourself what the half-life of these dice should be on this experiment it looks as though it is about four throws so far we've used one particular natural phenomenon radioactivity to illustrate random events that's because the random nature of the individual disintegrations is apparent orderly behavior is observed for a radioactive substance only it's the time for a large number of counts is used as a measure of activity now you observe orderly behavior in the measurements that you make for instance you measure light intensity with a light meter the needle doesn't jump around in an unpredictable way does the orderly behavior that you observe always arise because of random events this question can only be answered by doing experiments many experiments these show that sometimes the order that we observe does have at the roots randomness which is not apparent but this isn't always true sometimes experimental results indicate some sort of order at the roots how can we tell when randomness underlies orderly behavior here is orderly behavior every time these squares spun around the reading was 8 it's clear that the order here comes from randomness but I could not tell by watching the meter alone but this was true now suppose that I masked off all of the squares here except 16 the light going to the meter would decrease and I'd have to use a more sensitive meter but the point of this is that I could then tell by watching the meter alone that there was randomness it would be just like the machine with 16 squares there would be observable fluctuations you know that very large numbers of photons arriving at a light meter produce the reading is the arrival of a photon a random event to tell us it would be necessary to cut the number of photons arriving at the meter down to a much smaller number and of course use a much more sensitive detector experiments like this have been done this film shows an oscilloscope which is connected to a very sensitive light detector you can see the Pips caused by the arrival of individual photons and you can see from the intervals between them that there is evidence of randomness we see order in the world around us order that enables us to make measurements for instance measurements of light intensity with a light meter often this order arises from random events such large numbers of random events that the most probable thing is the thing we always observe