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Now, let's assume that someone has tossed a coin twenty four times in succession, and we have video evidence that toss #'s 4, 9, 16, 21 and 24 landed on 'Heads'. Messrs. Cates, Wood, Marriott, Richards, et al. then come along and insist on the basis of conjecture that all 24 tosses landed on 'Heads'.
The thing is, when we look at London in 1888, we can pick two dates, and just look at events between those dates, but they are still just a part of a string of events.
If I flip a fair coin 1,000 times, I will probably get about 500 heads, and 500 tails, but I won't get exactly alternating heads and tails (well, I could, but I probably won't). I will probably have a long streak of alternating heads and tails, and also a long streak of just heads. I might get 20 heads in a row. If I then go up to you and say "Hey! I just flipped this coin and got heads 20 times in a row," you would probably be skeptical; however, if I said "I just flipped this coin 1,000 times, and in that 1,000, got a string 0f 20," that sounds perfectly plausible.
The fact is, that the coin does not remember what happened on the last toss, or the last 20 tosses, so they have no effect on the next toss.
What c.d. is suggesting, and correctly so, is that if an event were unlikely to occur in the first place, then an independent second occurrence of the same sort of event would be even more unlikely.
No, that is incorrect; if two events are entirely independent, then one has no effect on the other. If two people with murderous minds live in the same area, and don't know each other, nor communicate in any way, so that one has no more idea what the other is up to than anyone else in town, then one has to more effect on the other than the previous coin toss has on the next one.
If you claim that two killers can't live within close enough proximity for their "turf" to overlap, then I want to see evidence of this. Unless they belong to the serial killers' guild, I very much doubt this, and in fact, I suspect there are lots of reasons why big cities would attract killers, and the poorer sections, more than the wealthier ones.
Of course they occur! This is why no one, as far as I know, is actually discounting the the very real possibility of a multi-murderer 'Double Event'.
I'm going to assert once more that if it were not for the "double event" letter, the police at the time would have concluded that Stride and Eddowes were killed by two different people.
Several of Sutcliffe's victims were ... not prostitutes.... But he believed ... that they were prostitutes, and that is all that mattered.
Which I mentioned could have been the case with Eddowes, easily.
Exactly. But flip that around. They did happen but they are STILL statistically unlikely meaning that they are rare and we would not expect to see them with any sort of frequency. And doesn't that lead us to the question of probability?
That's called specifying an event before or after it happens. The odds of an event happening before it happens, and after it happens are apples and oranges, and I'm not even talking about the "duh" fact that anything that happened has a 100% chance of happening.
You are collecting a bunch of things that just happened, then saying "Show me another case where all those events came together." It's like throwing a dart at a wall, drawing a target around it, and then saying "Now, you hit it exactly where I did." Eddowes and Stride both had their throats cut. Fine. That was a pretty common method of murder when a lot of people bought birds whole at the market, shaved with straight razors, and small, concealable guns were prohibitively expensive, not to mention loud, in a quieter world. Eddowes was drunk and Stride wasn't, so that detail isn't important, but if they had both been intoxicated, you would probably include that in your list of significant coincidences. Stride may have had money on her. Eddowes definitely did not. So, that isn't important either. Right?
I am not asserting for a fact that JTR did not kill both women; I simply think it is less likely than other scenarios, and I think that because I think the "double event" letter is a hoax.
Serial killers don't repel one another, like magnetic poles; and I don't think they stake out turf, like gangs, although I don't really know, so the activities of one just don't affect another.
That leads us to Whitechapel. Is it possible that more than one killer was slitting throats and taking organs at that time. Sure. If so, would most people consider that to be quite unusual? I, for one, would say yes. I would want to see evidence to support that it was more than one man.
You are trying to have it both ways, I think-- or I am confusing two posters, which is possible.
On the one hand, you seem to be arguing that the slit-throat + abdominal mutilations, is so singular, that there can be just one perpetrator, then on the other that Stride must be considered a victim whether her abdomen was mutilated or not, because sometimes these killers get interrupted, and it's beyond us to know why, and then concluding that there is just one killer, whether Stride fits the pattern or not.
Now, let's assume that someone has tossed a coin twenty four times in succession, and we have video evidence that toss #'s 4, 9, 16, 21 and 24 landed on 'Heads'.
If I flip a fair coin 1,000 times, I will probably get about 500 heads, and 500 tails, but I won't get exactly alternating heads and tails (well, I could, but I probably won't). I will probably have a long streak of alternating heads and tails, and also a long streak of just heads. I might get 20 heads in a row. If I then go up to you and say "Hey! I just flipped this coin and got heads 20 times in a row," you would probably be skeptical; however, if I said "I just flipped this coin 1,000 times, and in that 1,000, got a string 0f 20," that sounds perfectly plausible.
The chance of landing entirely 'Heads' on 20 sequential tosses of a single coin is 1-in-1,048,576.
The chance of landing entirely 'Heads' on ... let's say ... 30 sequential tosses of a single coin is 1-in-1,073,741,824.
What c.d. is suggesting, and correctly so, is that if an event were unlikely to occur in the first place, then an independent second occurrence of the same sort of event would be even more unlikely.
No, that is incorrect; if two events are entirely independent, then one has no effect on the other.
It most certainly iscorrect!
The chance of landing a 'Twelve' on one toss of a single pair of dice is 1-in-36. The chance of landing a 'Twelve' on two sequential tosses of a single pair of dice - each toss being independent of the other - is 1-in-1,296.
Have you even bothered to follow any of the prompts - i.e. the white quote prompt arrows - from my first post earlier today? I don't believe you have!
Registered Deaths of Female Adults (Ages 20 - xx) throughout England, Classified as 'Murder', by way of 'Cut'/'Stab': 1881-1890
---
In Accordance with the Forty-Forth through Fifty-Third Annual Reports of the Registrar-General of Births, Deaths, and Marriages in England:
Registered Deaths of Female Adults (Ages 20 - xx) throughout England, Classified as 'Murder', by way of 'Cut'/'Stab': 1881-1890 (Click Image, to Enlarge in flickr)
The white prompt (arrow), for those of you that don't know, will take you directly to the post, from which the quotation is taken. This is why we should all learn to use the 'Quote' function: i.e. for the convenience of those that would like to see a quoted statement within the context, in which it was made, without having to scroll through dozens of posts in order to find it.
The above quotation is taken from post #86 in its respective thread. My participation in the discussion at hand continues through post #158:
As I do not wish to be involved in a 'Double Event' debate, I shall not be returning; unless, as was the case, just yesterday, my statistical analysis is misrepresented, by posters that either don't bother to read it, or simply don't understand it.
But I would ask that you read at least as far as post #116:
That Two Independent Murders, of Female Adults, by way of 'Cut Throat', would Occur; within the depicted Color-Shaded Circular Region, and during a particular One-Hour Period:
- Perceptual Probability: 0.000006386608%
- Perceptual Chance: 1 -in- 15,657,764.58
- Perceptual Odds: 15,657,763.58 -to- 1
- Odds, which are, in fact, equivalent to the odds of 23.90037 sequential tosses of a coin, landing entirely on 'Heads'.
- Odds, which are, in fact, equivalent to the odds of 9.24593 sequential tosses of a single die, landing entirely on '1'.
If you claim that two killers can't live within close enough proximity for their "turf" to overlap, then I want to see evidence of this. Unless they belong to the serial killers' guild, I very much doubt this, and in fact, I suspect there are lots of reasons why big cities would attract killers, and the poorer sections, more than the wealthier ones.
"If you claim that two killers can't live within close enough proximity for their "turf" to overlap, ..."
Dear God!
Where, oh where have I come within a million light years of making such a claim?
If you can't be bothered to read my posts, then please don't attempt to counter the points that I have made therein.
Eddowes and Stride both had their throats cut. Fine. That was a pretty common method of murder when a lot of people bought birds whole at the market, shaved with straight razors, and small, concealable guns were prohibitively expensive, not to mention loud, in a quieter world.
"That was a pretty common method of murder …"
No it wasn't!
Since you can't be bothered to follow my quote prompts, I'll follow one of them for you, and then scroll to the next post:
Registered Deaths of Female Adults (Ages 20 - xx) throughout England, Classified as 'Murder', by way of 'Cut Throat': 1881-1890
---
In Accordance with the Forty-Forth through Fifty-Third Annual Reports of the Registrar-General of Births, Deaths, and Marriages in England:
Registered Deaths of Female Adults (Ages 20 - xx) throughout England, Classified as 'Murder', by way of 'Cut Throat': 1881-1890 (Click Image, to Enlarge in flickr)
Registered Deaths of Female Adults (Ages 20 - xx) throughout England, Classified as 'Murder', by way of 'Cut Throat' 1881: 3 1882: 0 1883: 2 1884: 5 1885: 3 1886: 3 1887: 9 1888: 15 1889: 6 1890: 7
- Year, in which We are Most Interested (i.e. 1888): 15.00
Registered Deaths of Female Adults (Ages 20 - xx) throughout England, Classified as 'Murder', by way of 'Cut Throat': 1881-1890 (Click Image, to Enlarge in flickr)
What c.d. is suggesting, and correctly so, is that if an event were unlikely to occur in the first place, then an independent second occurrence of the same sort of event would be even more unlikely.
No, that is incorrect; if two events are entirely independent, then one has no effect on the other.
It most certainly iscorrect!
The chance of landing a 'Twelve' on one toss of a single pair of dice is 1-in-36. The chance of landing a 'Twelve' on two sequential tosses of a single pair of dice - each toss being independent of the other - is 1-in-1,296.
"... if an event were unlikely to occur in the first place, then an independent second occurrence of the same sort of event would be even more unlikely."
Admittedly, this was poorly written. It should read as follows:
... if an event were unlikely to occur in the first place, then two independent occurrences of the same sort of event would be even more unlikely.
Clarification without the numbers:
If a goalkeeper were to score a goal in a football match, then the event would be regarded as being remarkable.
If a goalkeeper were to score two goals in a football match, - each goal being independent of the other - then the event would be regarded as being extraordinarily remarkable.
In a recent match against Chelsea, a Stoke City forward inadvertently put the ball into his own net, not once, but twice - each own goal being independent of the other. A single own goal, would have been noteworthy. The double own goal, in this instance, was noted in media headlines throughout Britain.
Getting back to the goalkeeper …
What if he were to score three goals during the course of a single match - each goal being independent of the other?
The event would have to be regarded as being exceedingly extraordinarily remarkable. But what if we could somehow temper or 'rationalize' that remarkability by viewing two of the three goals as being somehow connected or dependent upon each other? Granted, no two goals in a football match are ever dependent upon each other, but what if we were to learn that this goalkeeper was the designated penalty kicker for his team, and that two of the three goals that he scored were in fact successful penalty kick conversions? That would certainly temper or 'rationalize' the exceedingly extraordinarily remarkable nature of his feat.
Cut-throat murder of post-adolescents was uncommon in late-Victorian Britain. There were a total of fifteen registered deaths of female adults classified as 'Murder' by way of 'Cut-Throat' throughout England, in the whole of 1888. Three of the fifteen occurred within a six-hour period in London's metropolis. We know that at least one of them was independent of the other two, meaning that at least two persons independently committed cut-throat murder during the course of this fateful six-hour period. That in itself is extraordinarily remarkable.
If we were to assume that each of the three was independent of each of the other two, meaning that not just two, but three persons independently committed cut-throat murder during the course of this fateful six-hour period, then the occurrence would have to be viewed as being exceedingly extraordinarily remarkable.
The two murders that may or may not have been independent of each other occurred within a forty-five minute period, and within a 900-yard (straight-line) range. They both involved the uninhibited outdoor slaughter of a vagrant Spitalfields dolly-mop, to which there were no witnesses, in which there was no notable degree of struggle, and in which there was no attempt to conceal corpus delicti.
The fact that the Brown murder in Westminster occurred where and when it did does not serve to make the notion of a multi-perpetrator 'Double Event' less remarkable and more believable. It serves to make it more remarkable and less believable. Period!
Your football match example is lost on me, because I have no idea how American football is played, let alone European football.
However, I suppose if what you are saying is that if a remarkable event, like an unassisted triple play in baseball, happens, it is somehow less likely to happen again during the same game. That just isn't true. Leaving aside variables like the fact that some teams sometimes have such remarkable pitchers, that they never allow enough base hits to create the opportunity for unassisted triple plays, something that is required for an unassisted triple play is a quick, and quick-thinking infielder, and someone who can accomplish it once can accomplish it again, but also, a pitcher who is "off," and walks a lot of batters could create lots of triple play opportunities.
Events, even uncommon ones, don't know to space themselves out in time. Something may be so uncommon, that on the average, it happen once every hundred years, but that doesn't mean it will happen exactly every hundred years. It can happen two days in a row, or even twice on the same day, and still average out to once every hundred years.
One thing that is tricky about statistics and probability, having to do with multiple events, is that when you are betting on two occurrences to happen together before they happen, that changes the odds for you, but it doesn't effect the odds of each event.
If we go to a ball game together, and during the first inning, bet on whether there will be an unassisted triple play, the odds will be whatever they are (I have no idea how to figure them, but I'm sure someone does). If there is an unassisted triple play, and we bet again on the next inning, the odds will not change due to the previous triple play.
However, if we bet before the game starts, on whether it will be a game with two unassisted triple plays, that is an entirely different thing from two different bets over plays in different innings.
I realize the foundation of your argument isn't that cut-throat murders don't happen, or don't happen on the same night, but that it is so unlikely for anyone to be a cut-throat murderer, that it is unlikely for two to be in the same area at the same time.
I disagree. I disagree with your assessment of the rarity of people with murderous intent, and I also disagree with your idea that murderers somehow naturally distribute themselves like predatory wild animals that establish hunting territories.
However, I suppose if what you are saying is that if a remarkable event, like an unassisted triple play in baseball, happens, it is somehow less likely to happen again during the same game. That just isn't true.
That is NOT what I am saying!
I am arguing on the basis of 'Joint' probability, whilst you are attempting to counter on the basis of 'Conditional' probability.
If the chance of an unassisted triple play occurring during a nine-inning game of baseball is deemed to be 1-in-1,000, then the chance of two unassisted triple plays occurring during the same nine-inning game of baseball - each triple play being independent of the other - would be deemed to be 1-in-1,000,000. Period! No if's, and's or but's.
This assessment is based upon the concept of a joint probability of two independent outcomes, and would be made prior to the onset of the game.
If the chance of a cut-throat murder occurring within London's inner East End during the calendar year 1888 was deemed to be 1-in-1,000,000, then the chance of two cut-throat murders occurring within London's inner East End during the same calendar year - each cut-throat murder being independent of the other - would have been deemed to be 1-in-1,000,000,000,000. Period!
Accordingly, this assessment would have been made at the onset of the calendar year, i.e. 1888
If we go to a ball game together, and during the first inning, bet on whether there will be an unassisted triple play, the odds will be whatever they are (I have no idea how to figure them, but I'm sure someone does). If there is an unassisted triple play, and we bet again on the next inning, the odds will not change due to the previous triple play.
I disagree. I disagree with your assessment of the rarity of people with murderous intent, and I also disagree with your idea that murderers somehow naturally distribute themselves like predatory wild animals that establish hunting territories.
Huh ???????
I would suggest that you spend more of your time studying this case, and less of your time posting to these boards.
I am arguing on the basis of 'Joint' probability, whilst you are attempting to counter on the basis of 'Conditional' probability.
Yes, because you are multiplying. You use multiplication when calculating a conditional variable, like "what is the probability that I will fall and break my ankle on a day where there is also a solar eclipse." I multiply the probability of a solar eclipse and the probability of falling and breaking my ankle.
If I'd picked another event, like my brother falling and breaking his leg, rather than a solar eclipse, it wouldn't matter. It might feel uncanny, though, because the two events are similar, rather than unrelated, like a solar eclipse and a broken ankle.
But that isn't the situation here, because we aren't looking at events before they happen. We are looking at them after they happen.
You can pick another event that occurred the night of the Stride/Eddowes murders, and ask "what are the odds?" and calculate them as conditional probability, but it's nonsense, because you didn't specify them beforehand.
It's like the lottery. If 100 people buy 100 raffle tickets, each person has only a 1:100 chance of winning, but someone will win, so expressing awe at the winner's luck after the fact is nonsense. That's true as well if there are 1,000,000 tickets.
Don't you think I know that?
Apparently not.
I would suggest that you spend more of your time studying this case, and less of your time posting to these boards.
If two people with murderous minds live in the same area, and don't know each other, nor communicate in any way, so that one has no more idea what the other is up to than anyone else in town, then one has no more effect on the other than the previous coin toss has on the next one.
I share Colin's frustration with all this junk about coin tossing. The original argument was made by Mike Richards, among others, who claimed that the totally independent third murder that night (a domestic incident in a completely different part of London) did indeed have a bearing on the likelihood of Stride and Eddowes being killed by two men acting independently rather than the one man known fondly as "Jack", who appeared to be picking on the local unfortunate population. The argument went that the fact this other murderer picked this particular night out of all the available nights in 1888 to do his missus in made it somehow more believable that a third man chose the same night to kill Stride, shortly before "Jack" killed Eddowes, just a 15 minute walk away.
Colin and I, among others, have merely pointed out how backwards this argument is, because on the vast majority of nights in 1888, nobody in the whole of England was murdering any adult women by knife. Sept 30 was exceptional for featuring two such killers in different parts of London. What cosmic forces are supposed to have conjured up a third man because the second was going to prove this to be a night like no other? Surely anyone can see how three independent killers would merely make this night far more of an exception than the two we already have?
The recent 'close shave' asteroid, coming within a mere 17,000 miles of Earth, made it an exceptional day, without the completely coincidental meteor over Russia just hours earlier. But we know both happened and were unconnected events. If anyone tried to argue that the coincidental asteroid made it somehow a likely proposition, or an even likelier one, that there were two unconnected meteors which exploded in roughly the same time and space, explaining the widespread damage to windows and the variety of injuries to people below, you would rightly think they were nuts.
I'm going to assert once more that if it were not for the "double event" letter, the police at the time would have concluded that Stride and Eddowes were killed by two different people.
You can assert it as much as you like, but it won't make it true. The police at the time considered Dear Boss and the 'double event' postcard to be most likely the work of a hoaxer, and that view only strengthened over time. Apparently the police, like the author, had no problem with the concept of one man killing both women, but the former kept an open mind and routinely investigated Stride's associates for any evidence of involvement.
You are collecting a bunch of things that just happened, then saying "Show me another case where all those events came together."
Nobody has done anything of the sort. The whole point is we don't know what happened, in terms of what caused those two events, and some are using pure unadulterated speculation to argue that it's 'not bloody likely' that they were connected, despite fully documented examples of genuine double events among known repeat offenders, where certain aspects of the crimes are so remarkably similar to Stride/Eddowes that they cry out to be compared. That is why it is perfectly reasonable to ask for another example - just one would be nice - where two men acting independently managed to produce a similar night's work.
Eddowes and Stride both had their throats cut. Fine. That was a pretty common method of murder when a lot of people bought birds whole at the market, shaved with straight razors, and small, concealable guns were prohibitively expensive, not to mention loud, in a quieter world.
No - not 'a pretty common method' when you look at Colin's murder stats for adult women in the whole of England. Just 9 in 1887, and just 15 in 1888, with 5 of the murdered Spitalfields unfortunates making up a third of the total.
Eddowes was drunk and Stride wasn't, so that detail isn't important, but if they had both been intoxicated, you would probably include that in your list of significant coincidences. Stride may have had money on her. Eddowes definitely did not. So, that isn't important either. Right?
I know you were not addressing me, but we don't know that Eddowes was drunk, or even appeared drunk, when her killer encountered her. And we don't know who had money and who didn't when they met their killer. All we know is that they had none when found murdered.
Wasn't it you who observed on another thread that the victims apart from MJK were roughly the same age, in their forties, so she was arguably too young to appeal to the same killer? And Eddowes was arguably too thin, because the others had more meat on them? Is that not entirely circular, and just like the argument Mike makes for the killer always mutilating, therefore Stride cannot be one of his, because such a killer couldn't have failed even once, no matter how many times he killed?
Seeing a pattern that is only created by taking certain victims out of the equation will inevitably give you a nice, neat and above all consistent killer, who is demonstrably only targeting women of a certain age and build, or in circumstances which will definitely allow him to mutilate them. But is he real, and does he even sound real? Has there ever been a killer so exacting in his requirements, and so lucky or skilled in the execution? And what about all the loose ends piling up? All the victims who don't fit such a tightly perceived pattern, who then require separate murderers to be found for them?
Isn't this just as precarious as seeing less defined patterns across a greater number of the murders, involving a human being who is not acting in a vacuum but depends on each victim and the people around him for his successes? There is one man who could fairly be accused of having had the means, motive and opportunity in spades to kill any one of these women who make up the 1888 statistical 'extras'. But he gets eliminated in favour of God knows who, for God knows what motive, whenever the pattern doesn't match exactly with someone's personal design for him.
We are all seeing patterns here, one way or another. It's just that some of these patterns are becoming so restrictive that soon we will have a mercy killing "Jack", with Chapman his sole victim, because she was already on the way out. With no other victims fitting the pattern and three London murders in one night as the guide, as many killers as it takes can be conjured up to account for the rest.
I am not asserting for a fact that JTR did not kill both women; I simply think it is less likely than other scenarios, and I think that because I think the "double event" letter is a hoax.
I don't see how one would follow from the other. Assuming you are right about the postcard being a hoax, its author couldn't be expected to know either way; they would merely be assuming a connection, just like so many others did. Could be right, could be wrong. The claim can have no possible bearing on the reality.
Nothing is rarer than something that is unique.
Precisely - which is again why you need to find just one other case like this one, where two such crimes turned out to be committed by two offenders acting independently. Or are you indeed arguing for something that would be unique?
The original argument was made by Mike Richards, among others, who claimed that the totally independent third murder that night (a domestic incident in a completely different part of London) did indeed have a bearing on the likelihood of Stride and Eddowes being killed by two men acting independently rather than the one man known fondly as "Jack",
His point was just that JTR was not the only person in Victorian London who ever cut a throat, nor was it an idea that came to JTR out of nowhere.
What cosmic forces are supposed to have conjured up a third man because the second was going to prove this to be a night like no other? Surely anyone can see how three independent killers would merely make this night far more of an exception than the two we already have?
I don't believe in cosmic forces, and I don't think that three killers in one night, or two killers, makes much of a difference one way or another, because unlikely things do happen. The killer Mike Richards brought up has no bearing on the likelihood of one, or two killers for Stride and Eddowes; it only shows that it is possible because throat-cutting was something JTR didn't own a patent on.
No - not 'a pretty common method' when you look at Colin's murder stats for adult women in the whole of England. Just 9 in 1887, and just 15 in 1888, with 5 of the murdered Spitalfields unfortunates making up a third of the total.
I did. It looks like murders in general were up in 1888. It also looks like we disagree on "common." I guess I meant relative to today, and unconsciously, relative to the US. To me, though, even "30%" is common, considering how rarely one reads about throat-cut murders anymore.
Wasn't it you who observed on another thread that the victims apart from MJK were roughly the same age, in their forties, so she was arguably too young to appeal to the same killer? And Eddowes was arguably too thin, because the others had more meat on them? Is that not entirely circular,
I just made observations, not arguments, and I think I was pretty careful to state that they were not arguments. I'm not sure why you think they were circular. If I predicated anything on them, it was only to show that another theory was just as easy to whip up as some other one.
Or are you indeed arguing for something that would be unique?
My comment about uniqueness was directed as someone else's oxymoronic assertion that two events would be somehow unique to a greater degree than one.
Why is a double event so unbelievable? The only reason Stride is being discounted is lack of mutilation, nothing else. I'm sure there must be another serial killer who's killed twice or more in one night, I can't think at the moment (phone ringing) can anyone throw any of these at me while I get this?
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