Every minute counts

[The Baron]

PC Neil makes for a better suspect than Lechmere!


Paul thought he detected a faint breath, she could have been still alive when they examined here.

Both Paul and Lechmere didn't notice any Blood.

We Know PC Neil was there before the murder.

He may have started murdering her before he was interrupted, and after Paul and Lechmere went a way he came and finished her.



The Baron

[The Baron]

Fact: It is not proven, that Nichols was dead when Lechmere and Paul first examined her.


The Baron

[MrBarnett]

Of course, if ano killer heard Lechmere approaching, he may have swiftly pulled the clothing down, fearing that if the carman had caught sight of the wounds he would have screamed ‘Murder!’ at the top of his voice and alerted any copper in earshot.

[Simon Wood]

Hi Christer,

A dead "prostitute" was found in Bucks Row.

Bucks Row was infested with prostitution.

When was the last time a prostitute was discovered, dead or alive, in Bucks Row?

Simon

[Fisherman]

Hi Fisherman,

Well, maybe someone can be decapitated and stop bleeding a minute later, but as Nichols was not decapitated that doesn't really apply here.

Which vessels are opened up by decapitation? And which were opened in the Nichols case? Her head hung on by the spine only, and so the difference will not be that large, really.

And yes, I agree, clotting isn't going to stop the bleeding from a severed cartoid artery, that was just me mulling over ideas (if not very appropriate ones for this case, but we've both made that mistake).

True. Thank you for explaining the underlying reason.

Anyway, all I can say is that the probability distribution you're describing is the "logical inverse" of a cumulative one with respect to "not bleeding any more", meaning "after a cut everyone bleeds immediately, so 0% are not bleeding" then at some interval later (call that X) some percent stop bleeding, say 0.5% have stopped. Then another interval later and more have stopped bleeding, say we're at 1.05%, and so on, until we eventually get to the point where all cases (100%) have stopped bleeding. That means, the logical inverse cumulative probablity for bleeding starts at 100% and yes,I see what you mean, it then decreases until it reaches 0%. That decrease would be slowly at first, then it would tend to decrease more quickly, and then slow down again as we get into the range of rare long bleeders.

That's not the one that would be used, though, to compare the likelihood between the two theories. One uses the density function version, which is "what percent stop bleeding between 0 and X" and then what percent fall between X and 2X, and then between 2X and 3X, and so on. It's the same information, but it's not plotting the running totals (or in this case the running decrease), but rather the values between two successive multiples of your interval. It's the density function that is used to test questions like this (is Cross/Lechmere more or less likely than JtR as Other), not the cumulative distribution. The two distributions come from exactly the same data, they are just different ways to represent them, but the differences are fundamentally important with regards to making probabilistic inferences of this sort. I get where you're coming from, but inferentially speaking, the probabilities you're talking about are not the ones that you want.

And again, without us knowing what that density function looks like, there's no way for us to know which would be the more probable because it depends upon which side of the peak the two theories end up. But I am sure, that given how little of a time difference we're talking about, any difference in either direction is going to be so very small nobody would consider one more likely than the other in any real sense, only a purely mathematical one.

Anyway, I spend enough time at work lecturing on statistics that I'm not about to bore everyone here with it. I'll leave it to you to decide what you want to do with that though. It has got me wondering if there are any papers on this, but I doubt it as I can't imagine how one could ever obtain such data with enough knowledge of when a cut was produced and how long it took that wound to eventually stop bleeding since, well, that requires the participant to die. They don't sign up for such studies.

- Jeff

I am aware of how there are many ways to calculate probabilities. What you seem to be saying here is that all people are different kinds of bleeders and until we know what kind of a bleeder Nichols was, we do not know how long she was likely to bleed for. Correct me if I´m wrong.
However, this is something I have already admitted will have a bearing - individuals bleed individually.

But the overall picture is not changed by that. We know for certain that the bleeding will stop at some time, and therefore any minute of bleeding that is recorded as coming after another minute MUST be closer to the end of the bleeding. Consequentially, it must also be accepted that the later minute is a less likely one to occur, REGARDLESS of the disposition of the bleeder. There can be no arguing about that. We can never say "If we cut a person´s neck open, then that person is likelier to bleed in minute 8 than in minute 7. Instead, we can say that he or she is likelier to bleed in minute 7 than in minute 8.

In the discussion, we must work from the assumption that Nichols was a "normal" bleeder, meaning that there was nothing much that told her away from other bleeders. The fact that her blood was in a large clot as it was cleaned away seems to be in line with such a suggestion.

Given all of this and accepting that the pathologists were correct in saying that the third and fifth minute are likelier bleeding minutes than the seventh, the implication is easy enough to see. After that, Nichols may have had a gene from Queen Victoria and some sort of hemophilia (although it is contradicted by the clotted blood that was washed away) or some other condition that made her a different bleeder than the average one, and so that may have had an impact.

The conclusion, though, reasoning not from how we may b 2X or 3X:s, but instead looking at the general picture (which was what the pathologists must have done when making their call), becomes one where Lechmere is simply a likelier cutter than an alternative killer who must add time to the schedule.

[Fisherman]

Fiver, I will not comment on your posts, other than to say that we cannot claim something for true without having seen the whole material. It will inevitably go wrong if we do.

[Fisherman]

PC Neil makes for a better suspect than Lechmere!

If we look at the bleeding only, he makes for a viable suspect. Not a better one, though, since both pathologists kept the door open for a longer bleeding time than the 3 and 5 minute stages they said were the likeliest minutes of bleeding.

Paul thought he detected a faint breath, she could have been still alive when they examined here.

Both Paul and Lechmere didn't notice any Blood.

We Know PC Neil was there before the murder.

He may have started murdering her before he was interrupted, and after Paul and Lechmere went a way he came and finished her.

The Baron

Yes, you should work along that line, and tell us all about Neils exploits when you are ready.

[Fisherman]

Fact: It is not proven, that Nichols was dead when Lechmere and Paul first examined her.

The Baron

Fact: All of the investigations into the matter will nevertheless work from that assumption. You are welcome to revolutionize the world of Ripperology, though!

[Fisherman]

Hi Christer,

A dead "prostitute" was found in Bucks Row.

Bucks Row was infested with prostitution.

When was the last time a prostitute was discovered, dead or alive, in Bucks Row?

Simon

I´ll check the diaries and return to you, if I may? Oh, wait - there are no such diaries, are there?

"Infested with prostitution" has to stand for you, it is not something I invented.

I am saying that the business of the prostitutes was conducted to a large degree on the streets adjacent to the streets where they paraded in search of punters. I think that the assumption that they did not actively avoid Bucks Row is a reasonable one. The fact that there were always people saying "Not in my back yard" was always going to be a universal thing. The article you brought up, with a well lit, orderly street (even benefitting from the lamps outside the brewery in Bath Street, it seems), is not in line with what was said - Bucks Row was instead very dark, with only the odd lamp burning. It would have provided a very useful setting for prostitution in that regard, I´d say.

No diaries exist of the comings and goings of prostitutes, not for any street, and so proving that on my behalf will be as hard as you will find it to prove the opposite.

[JeffHamm]

I am aware of how there are many ways to calculate probabilities. What you seem to be saying here is that all people are different kinds of bleeders and until we know what kind of a bleeder Nichols was, we do not know how long she was likely to bleed for. Correct me if I´m wrong.
However, this is something I have already admitted will have a bearing - individuals bleed individually.

But the overall picture is not changed by that. We know for certain that the bleeding will stop at some time, and therefore any minute of bleeding that is recorded as coming after another minute MUST be closer to the end of the bleeding. Consequentially, it must also be accepted that the later minute is a less likely one to occur, REGARDLESS of the disposition of the bleeder. There can be no arguing about that. We can never say "If we cut a person´s neck open, then that person is likelier to bleed in minute 8 than in minute 7. Instead, we can say that he or she is likelier to bleed in minute 7 than in minute 8.

In the discussion, we must work from the assumption that Nichols was a "normal" bleeder, meaning that there was nothing much that told her away from other bleeders. The fact that her blood was in a large clot as it was cleaned away seems to be in line with such a suggestion.

Given all of this and accepting that the pathologists were correct in saying that the third and fifth minute are likelier bleeding minutes than the seventh, the implication is easy enough to see. After that, Nichols may have had a gene from Queen Victoria and some sort of hemophilia (although it is contradicted by the clotted blood that was washed away) or some other condition that made her a different bleeder than the average one, and so that may have had an impact.

The conclusion, though, reasoning not from how we may b 2X or 3X:s, but instead looking at the general picture (which was what the pathologists must have done when making their call), becomes one where Lechmere is simply a likelier cutter than an alternative killer who must add time to the schedule.

Hi Fisherman,

I'm afraid you're misunderstanding how one uses probability distributions to make inferences. The short version is that you're using the wrong distribution when you get into things like "the previous minute must be more probable than this minute" because you're making inferences from a running total distribution of probabilism, so you're counting all the previous times again, and again. What we're interested in is whether Cross/Lechmere is more likely than a JtR as Other, who is 30 seconds to a minute earlier. That requires a different set of probabilities. Basically, the probabilities don't act like you are describing them.

Anyway, I do this for work and don't want to spend my off hours doing it too. Just letting you know that it doesn't work the way you are describing, but feel free to continue if you wish.

- Jeff

[MrBarnett]

We are presented with two options: Nichols’ was a ‘normal’ bleeder or she suffered from the rare condition of haemophilia. Queen Victoria’s name is thrown in to emphasise the unlikelihood of the latter.

Were there no more common reasons why a woman of Polly’s background might have fallen outside of the ‘normal bleeder’ range?

https://pubs.niaaa.nih.gov/publications/arh21-1/42.pdf

“Blood clotting, or coagulation, an important physiological process that ensures the integrity of the vascular system, involves the platelets, or thrombocytes,4 as well as several pro- teins dissolved in the plasma. When a blood vessel is injured, platelets are attracted to the site of the injury, where they aggregate to form a tem- porary plug. The platelets secrete several proteins (i.e., clotting factors) that—together with other proteins either secreted by surrounding tissue cells or present in the blood—initiate a chain of events that results in the formation of fibrin. Fibrin is a stringy protein that forms a tight mesh in the injured vessel; blood cells become trapped in this mesh, thereby plugging the wound. Fibrin clots, in turn, can be dissolved by a process that helps prevent the development of thrombo- sis (i.e., fibrinolysis).

Alcohol can interfere with these processes at several levels, causing, for example, abnormally low platelet numbers in the blood (i.e., thrombocy- topenia), impaired platelet function (i.e., thrombocytopathy), and dimin- ished fibrinolysis. These effects can have serious medical consequences, such as an increased risk for strokes”

[Fisherman]

We are presented with two options: Nichols’ was a ‘normal’ bleeder or she suffered from the rare condition of haemophilia. Queen Victoria’s name is thrown in to emphasise the unlikelihood of the latter.

Were there no more common reasons why a woman of Polly’s background might have fallen outside of the ‘normal bleeder’ range?

https://pubs.niaaa.nih.gov/publications/arh21-1/42.pdf

“Blood clotting, or coagulation, an important physiological process that ensures the integrity of the vascular system, involves the platelets, or thrombocytes,4 as well as several pro- teins dissolved in the plasma. When a blood vessel is injured, platelets are attracted to the site of the injury, where they aggregate to form a tem- porary plug. The platelets secrete several proteins (i.e., clotting factors) that—together with other proteins either secreted by surrounding tissue cells or present in the blood—initiate a chain of events that results in the formation of fibrin. Fibrin is a stringy protein that forms a tight mesh in the injured vessel; blood cells become trapped in this mesh, thereby plugging the wound. Fibrin clots, in turn, can be dissolved by a process that helps prevent the development of thrombo- sis (i.e., fibrinolysis).

Alcohol can interfere with these processes at several levels, causing, for example, abnormally low platelet numbers in the blood (i.e., thrombocy- topenia), impaired platelet function (i.e., thrombocytopathy), and dimin- ished fibrinolysis. These effects can have serious medical consequences, such as an increased risk for strokes”

I prefer not to speculate but instead treat her as anybody else. To work from any other angle would be a preconception. When Chapman was discussed, all sorts of conditions were bandied about, some of them pro a late TOD, others against it. The fairest way to do it - in my opinion - is to work from the presumption of normality until something else can be established.

[Fisherman]

Hi Fisherman,

I'm afraid you're misunderstanding how one uses probability distributions to make inferences. The short version is that you're using the wrong distribution when you get into things like "the previous minute must be more probable than this minute" because you're making inferences from a running total distribution of probabilism, so you're counting all the previous times again, and again. What we're interested in is whether Cross/Lechmere is more likely than a JtR as Other, who is 30 seconds to a minute earlier. That requires a different set of probabilities. Basically, the probabilities don't act like you are describing them.

Anyway, I do this for work and don't want to spend my off hours doing it too. Just letting you know that it doesn't work the way you are describing, but feel free to continue if you wish.

- Jeff

As long as I am totally certain that every minute in a bleeding is less likely than the minute before, I will continue. And who misunderstands all of this is an open question. That´s not to say that I am qualified in the field of statistics, but some things are so self-evident that no such qualifications are necessary. Polly Nichols was not as expected to bleed in minute seven as she was in any of the preceding minutes, period. She could not be, it would be in direct conflict with the laws of nature. To be able to bleed in minute seven, you MUST have been bleeding in minute 1-6. And whether you WILL bleed or not in minute seven is an open question until that minute comes around.
Ergo, the six first minutes are given, while the seventh is not. Maybe you stop bleeding after minute six, maybe you go on to bleed after it. But the logic of what I am saying cannot be challenged as far as I can see. If we call it "theory X" or "theory Y" is of little interest to me. All I know is that any theory that claims that a bleeding in minute seven can be as likely or likelier than a bleeding in minute six, generally speaking, must be bonkers.

So yes, maybe we should leave the topic.

[Fisherman]

Doing it the backwards way would also implicate Lechmere as he likelier cutter; if we assume that four minutes of bleeding is the likeliest outcome and if we assume that Lechmere was the cutter and cut Nichols at 3.45, then the bleeding should "ideally" have stopped at 3.49. Instead, it kept bleeding some five minutes longer if the nine minute estimation is correct.
Squeezing in another killer before Lechmere means that we are removed even further away from the likeliest scenario. An alternative cutter fit in at 3.44 prolongs the already stretched scenario by a minute, an alternative cutter using his knife at 3.43 adds two minutes, a cutter at 3.42 adds three minutes and so on. And Lechmere was certain that there was noone up at Browns as he turned into Bucks Row, so we will be looking at more than one minute going by that information.

Whichever way we look on it, if the pathologists are correct, then Lechmere is the likeliest killer as far as I can see. Admitting, as I must, that a killer cutting Nichols a minute only before Lechmere would not be much different in terms of timing, he would still be unlikelier.

Plus, there is the not unimportant fact that much as we know for certain that Lechmere was in place, we know no such thing about that alternative killer. He must remain speculation only, whereas we have a flesh and blood suspect who has many more things pointing towards himself than the blood evidence only. In that sense, there is a huge gap for that alternative killer to cover - even after we´ve confirmed that he was there...

[JeffHamm]

Doing it the backwards way would also implicate Lechmere as he likelier cutter; if we assume that four minutes of bleeding is the likeliest outcome and if we assume that Lechmere was the cutter and cut Nichols at 3.45, then the bleeding should "ideally" have stopped at 3.49. Instead, it kept bleeding some five minutes longer if the nine minute estimation is correct.
Squeezing in another killer before Lechmere means that we are removed even further away from the likeliest scenario. An alternative cutter fit in at 3.44 prolongs the already stretched scenario by a minute, an alternative cutter using his knife at 3.43 adds two minutes, a cutter at 3.42 adds three minutes and so on. And Lechmere was certain that there was noone up at Browns as he turned into Bucks Row, so we will be looking at more than one minute going by that information.

Whichever way we look on it, if the pathologists are correct, then Lechmere is the likeliest killer as far as I can see. Admitting, as I must, that a killer cutting Nichols a minute only before Lechmere would not be much different in terms of timing, he would still be unlikelier.

Plus, there is the not unimportant fact that much as we know for certain that Lechmere was in place, we know no such thing about that alternative killer. He must remain speculation only, whereas we have a flesh and blood suspect who has many more things pointing towards himself than the blood evidence only. In that sense, there is a huge gap for that alternative killer to cover - even after we´ve confirmed that he was there...

Hi Fisherman,

It does not necessarily follow that a killer a minute before Cross/Lechmere would be unlikelier, and while I agree the difference between them would be small, it is entirely possible for Cross/Lechmere to be the less likely.

Again, let's say we have 0.1% of the cases stop bleeding in under 1 minute. And 0.4% stop bleeding between minute 1 and 2, and 1 % between minute 3 and 4, etc. So working backwards, it would be the later killer that is more probable than the earlier one at these short intervals.

If I extended my above example series, it would reach a point where the later killer does become less likely, but we would need to know at what point that happens, not just pick a number. This is what I'm trying to explain to you, without knowing the density function of the probabilities, we can make no inferences about which would be more likely.

I like your idea of trying to use this information. It is a good one in principle, though it may be we have too little information to really do it properly, the general gist of it is sound. However, the nature of the probabilities you're employing are the wrong tool, and it does your good idea no benefit. Probabilities, and the inferences we can make from them, are not the sort of thing where intuition is very helpful, and very often what appears to be "common sense tells me this is correct" turns out to be very very wrong.

Anyway, I'm trying to help you develop your idea not tear it down or suggest the data you're looking at couldn't provide some interesting ways to look at things. Because I do think it might be possible to develop something. Because of that, I think it would be better if it was done using the proper tools (which is what the probabilities are, tools to inform us). Sadly, I rather suspect there will not be a study that will provide us with those probability distributions, making it hard to turn the idea, which is good in principle, into an actual analysis. But, I could be wrong, and there could be information that one could use, or adapt, to give a suitable estimate of the distributions. I would, as I say, be highly surprised if, after all of that, the differences between the times associated with Cross/Lechmere and JtR as Other end up being at all different from each other. But that's only my prediction, it remains to be tested, and I would be interested in seeing how it turns out should you pursue this.

- Jeff