Good grief. Are you guys still arguing about that?

"A tsunami of deferred debt is about to hit homeowners no longer protected by a foreclosure moratorium"

This is from the Washington Post, so Google it if you're a subscriber. In addition, if I understand correctly, banks haven't been able to foreclose on properties where the owner died, so there should be a little bonanza of foreclosures coming up. Just saying.

Because your doctor could give a more customized treatment plan and "risk profile" for you, given that he or she presumably has more information about you. — Xtrix

Did you even bother to read the list of risks I presaged the enquiry with? Only around half of them were of a medical nature. So again, why would a doctor know anything about them?

How would I know what your numbers are? I know nothing about you. — Xtrix

I'm using me as an example. The point is you don't know anyone's numbers You only know the prevalence.

For someone who claims to care about statistics, this is pretty embarrassing. — Xtrix

Well, that would be disappointing for sure. So where have I gone wrong? Talk me through the correct process for risk analysis.

The absurdity of your argument can be demonstrated fairly easily by switching from this particular vaccine to the measles or smallpox or polio vaccines. Much easier to see the silliness there. — Xtrix

OK, go for it then.

Because if you can't produce figures for my risk then my decision is not risk based is it? — Isaac


Which is like saying we cannot calculate the risk of anything, if it isn't individualized to our specific situation. Which is nonsense. — Xtrix

Explain. In my experience this is exactly the case and always has been, so if you've been taught differently. Where exactly did you learn your statistics from?

If one wants to understand the risks involved in flying in an airplane, one can look up crash statistics. If one wants to understand the risks of a vaccine, one can look up the potential negative effects of the vaccine. — Xtrix

Again, you'll have to walk me through the maths here because it's clearly so advanced that I haven't come across it yet. How do we go from the prevalence of plane crash deaths or the prevalence of adverse responses to vaccination to a risk profile for some individual without any variables?

In this case, the COVID vaccines are extremely safe. It far outweighs the risks of being infected with COVID, and it helps stop the spread of COVID. — Xtrix

So you keep saying, yet I'm still not seeing how this is a response to any individual deciding not to take the vaccine.

We have an activity: x. The risk of dying or being harmed by x is shown to be extremely low statistically -- say, 1 in 10 million. You can further crunch the numbers if you'd like, but this is enough to tell anyone what they need to know about x. — Xtrix

This seems to be a repeat of the claim above. Talk me through the maths. How do you get from this prevalence figure to a relative risk?

First of all, "average" in terms of what? By what metric? — Xtrix

Average in terms of the mean. The mean probability from a probability distribution.

These numbers have nothing to do with "average" -- not the ones I'm talking about, regarding death from the vaccination. — Xtrix

So you're saying the risk figures for death from vaccination are not distributed about a mean? They're what? Absolute figures? Have no distribution at all? I don't understand how they could not have a distribution.

The risk of taking the vaccine can be calculated. Just as your risk of crashing in an airplane can be calculated as well. — Xtrix

Again, show me how.

How do we know the risk? Because we can calculate the number of flights and the number of crashes. — Xtrix

...which gives you the prevalence. We'd normally then run tests to discover variables and analyse the effect of each to come up with a risk profile for each multivariate, but you're saying we can do without all that somehow, but you're stopping short of explaining this new maths.

This is how we approach anything. — Xtrix

As I say, this is news to me. It's not how I've ever approached anything. Perhaps you could give me an example of a relative risk being calculated using prevalence of outcome alone

To say "Well the odds of a plane crashing only pertains to the AVERAGE person, after all, and I'm not average" is just an absurdity. — Xtrix

So if I don't fly my risk of dying in a plane crash is still the prevalence of plane crash deaths? It's an 'absurdity' to suggest that my not flying is a factor affecting my risk of dying in a plane crash even though it doesn't affect the prevalence of plane crash deaths? Is this more of this modern new method of statistical analysis that I've missed?

My point was that since the problem originated in China, and not with the anti-vaxxers, action against China should be given priority. — Apollodorus

First of all, what "action" is being taken against anti-vaxxers? If you mean complaining, hey, that's what this forum is for. If you mean coercing them into getting vaccinated, whether you like it or not, that is not against anyone. It is a public health action.

I still don't get why going after China matters. Getting information from them to help prevent future events, sure. You say for you that this isn't for revenge. Ok, but for many it is.

And, as I said, in my view China is a National Socialist dictatorship similar to Nazi Germany only about 17 times bigger and more dangerous. — Apollodorus

China may be a bad place, but I don't know what it means to say it is national socialist. Is it dangerous? I think significantly less so than the Soviet Union was. The US is just pissed that China thinks they deserve a place in the world on a par with us. They do a lot of the same things to project themselves out into the world that we have done or are still doing.

The point is you don't know anyone's numbers You only know the prevalence. — Isaac

"Anyone's numbers"? What would that look like, exactly? Give me an example.

Yes, we use statistics to calculate risk when engaging in an activity. That's assuming there are statistics on the activity. Statisticians are able to calculate probabilities on all kinds of activities based on the data.

If you play roulette, does the fact that the ball lands on black a little less than 50% of the time pertain to you when you make a bet? Or is there a more personalized number that you're looking for?

"No, I want MY odds of winning, not the prevalence of landing on black."

Saying "But I'm special" doesn't exempt you from the laws of probability, I'm sorry to say.

Talk me through the correct process for risk analysis. — Isaac

Let's talk concretely: the process of risk analysis for taking the COVID vaccine -- which is what we're actually discussing. What's the "correct process" in this case?

It depends on your motives, beliefs, goals.

(1) If you don't care (or don't believe) that taking a vaccine will help slow the spread of the virus, and thus be better for the community, the country and the world, then there's no need for risk analysis.

(2) If you believe it protects just you, that's one analysis.

(3) If you believe it protects both you and others, that's another analysis.

So, I'm arguing as if we agree on (3).

Using this as a premise, our goal should be to be vaccinated unless (a) it is dangerous (i.e., it causes suffering or death) or (2) otherwise goes against our goals. There's no reason to believe either, in my view, but what you're arguing about, mainly, is (a) -- and so I gave you (or Baker, I don't remember -- but you came into the conversation at that point) the statistics.

You're now arguing that the statistics aren't good enough, because they don't pertain to you -- why? Because you're "above average." Can you see the mistake in this?

We'd normally then run tests to discover variables and analyse the effect of each to come up with a risk profile for each multivariate, — Isaac

You can divide the statistics up in all kinds of ways. You can choose a parameter: the specific airline through time. How much time? A decade? The last year?

You can choose by country, and compare countries.

Yes, that's possible. What's the point? That we should do the same with vaccinations as well? Sure -- and don't you think this has been done? Are there specifics you'd like to look into? Which ones, exactly?

Because if what you're asking for is, "what's MY number"? I'm afraid that's not possible. Ever. You have general probabilities when it comes to almost any action in life. You can narrow down the range if you like, and select subgroups like ethnicity, sex, age, BMI, family history, history of vaccine reactions, allergies, etc. -- but even that won't be good enough to get you a specific number for YOU personally. You can claim this selection of data, customized for you, is still only generalities or prevalences.

So I really don't know what you're looking for, because it's a fantasy. You'll never receive it. What's happening here, I think, is that you're just afraid and are looking for absolute certainty. But maybe I'm wrong -- have you been vaccinated? But besides this, I really am at a loss as to what could be motivating you to press on like this. Just as we're talking here, the mandates are working, more people are being vaccinated, the death rates are finally coming down, few people have had to be laid off, and very few people have suffered from taking the jab.

Stop looking for reasons to continue to defend this stuff. It's a waste of your time.

"Anyone's numbers"? What would that look like, exactly? Give me an example. — Xtrix

The RR for lung cancer and smoking is 6.99 for men and 5.09 for women.

If you play roulette, does the fact that the ball lands on black a little less than 50% of the time pertain to you when you make a bet? — Xtrix

Yes.

Or is there a more personalized number that you're looking for? — Xtrix

No. To my knowledge none of the variables determining the fall of a roulette ball pertain to the individual betting. The game's designed that way.

Saying "But I'm special" doesn't exempt you from the laws of probability, I'm sorry to say. — Xtrix

What have the laws of probability got to do with it. I'm talking about heterogeneity in the probabilities themselves, not the laws governing them.

what you're arguing about, mainly, is (a) -- and so I gave you (or Baker, I don't remember -- but you came into the conversation at that point) the statistics. — Xtrix

I've not once suggested the vaccine is 'dangerous'.

why? Because you're "above average." Can you see the mistake in this? — Xtrix

No. That's why I'm asking you to explain. Are you suggesting that nobody is above average (or below it)? Otherwise I can't see why you'd find such a claim so obviously erroneous.

You can choose a parameter: the specific airline through time. How much time? A decade? The last year?

You can choose by country, and compare countries.

Yes, that's possible. What's the point? That we should do the same with vaccinations as well? Sure -- and don't you think this has been done? — Xtrix

Yes, it has been done.

if what you're asking for is, "what's MY number"? I'm afraid that's not possible. Ever. — Xtrix

Yes. That's the point I'm making.

if you can't produce figures for my risk then my decision is not risk based is it? — Isaac

You understand the use of conditionals, yes.

"Anyone's numbers"? What would that look like, exactly? Give me an example.
— Xtrix

The RR for lung cancer and smoking is 6.99 for men and 5.09 for women. — Isaac

Great -- but that's not what you were asking for, when discussing "MY numbers."

If this counts as the kind of number you want, fine -- then simply divide the vaccine data into men and women, and compare rates of death. They'll be exceedingly low in both groups -- but at least you'll have what you wanted.

What have the laws of probability got to do with it. I'm talking about heterogeneity in the probabilities themselves, not the laws governing them. — Isaac

I'm not talking about laws of probability, I'm talking about actual probability. Namely, that there were 150 (roughly) strokes out of 10,000,000 cases studied. That's 150/10,000,000. That's a 0.000015% chance of stroke, using that size. You could look up the statistics for death around the world out of 6 billion shots given and see what you find. Looking for something more specific? Fine -- look at that, too.

If you're looking for statistics specifically for you, that makes no sense. I have no idea what that means if it doesn't mean removing yourself from probabilities. If the probability of having a stroke is .000015%, that pertains to you as well -- as much so as a roulette wheel.

I've not once suggested the vaccine is 'dangerous'. — Isaac

So you agree the vaccines are safe. Fantastic.

So what's the problem?

Are you suggesting that nobody is above average (or below it)? Otherwise I can't see why you'd find such a claim so obviously erroneous. — Isaac

Above average for what? As human beings? When you say that the probabilities or prevalence applies to an average, and so doesn't apply to you because you're above average, what exactly are you talking about? -- and how do you know? Are you talking about height? Weight? Chess skill? IQ?

You've already acknowledged the vaccines are not dangerous. So I'm failing to see the relevance of even discussing this.

if what you're asking for is, "what's MY number"? I'm afraid that's not possible. Ever.
— Xtrix

Yes. That's the point I'm making.

if you can't produce figures for my risk then my decision is not risk based is it?
— Isaac

You understand the use of conditionals, yes. — Isaac

The numbers still apply to you, as they apply to everyone, despite not having an individualized number. If that's what's required in order to count as "risk based," then there's never any risk based analysis. When you want to weigh the risk of flying in an airplane --" sorry, it's just prevalence, and doesn't pertain to me, because there's not a number risk number for me specifically."

It's really an absurd position, if you look at it. What's the risk of taking Tylenol to you? Is there zero risk? No -- there's some risk. It's just miniscule. If you had liver disease, then perhaps it's not so miniscule. But there's a number to that subset as well, and we're in the same predicament and can make exactly the same claims: well yes, that's the prevalence within that subset, but what about ME? And so on. It's chasing a fantasy. It's like the idea of limits in calculus -- you'll never get there, but that's not the point.

you offered roughly nothing, and called my comment shallow rhetoric?

I've already mentioned that the evidence is the ground authority. And we'd be fools not to learn from it. — jorndoe

And you still have nothing to offer to those damaged by the vaccines and their close ones.
All you can offer is the standard rhethoric of risk, luck, and large populations. This is shallow.

All the evidence in the world changes nothing for those damaged by the vaccines and other medical treatments.

Here, I posted a thread on this quite a while back, but it generated little interest: https://thephilosophyforum.com/discussion/10157/how-to-come-to-terms-with-being-an-expendable-cog-in-the-system

The larger organization operates in big numbers.
From its perspective, it's acceptable if a medical treatment has serious side-effects for a certain % of the population.
From its perspective, it's acceptable if a governmental measure during the pandemic leads to job loss for a certain % of the population.

For the larger organization, some losses are acceptable. It goes further: it expects that those who are that loss -- those who end up losing jobs in a pandemic because the government doesn't allow their industry to operate, or those who end up with permanent negative effects of a medical treatment -- nevertheless continue to trust the larger organization as if all was well.

So if you -- yes, you -- end up being the unfortunate one who lost their job because of the measures; if you end up being the one permanently paralyzed by the vaccine:

How do you still trust the government, the medical system?

How do you make sense of the damage that you yourself suffer, presumably for the wellbeing of others?

The government and the medical system expect you to view yourself as an expendable cog in the system. As such, how do you still trust them? — baker

Either way, you've been given plenty of information by now, but oddly brush it off with a hand wave. Are you looking for something else altogether...? — jorndoe

I get the feeling that Baker is arguing for the sake of argument. But I see absolutely no substance to it— just the appearance of disagreement and contradiction. Other than “pro-vaxxers are mean in communicating and overly enthusiastic,” which is sometimes true, I see nothing. — Xtrix

Oh for fuck's sake. Do you have plastic flowing in your veins or what?!

My consolation is: some people are unlucky. — Xtrix

Now sit down and think long and heard about what "luck" means in terms of science.

Chance is the end of science. We do science in order to overcome chance.

Either way, you've been given plenty of information by now, but oddly brush it off with a hand wave. Are you looking for something else altogether...? — jorndoe

I get the feeling that Baker is arguing for the sake of argument. But I see absolutely no substance to it— just the appearance of disagreement and contradiction. Other than “pro-vaxxers are mean in communicating and overly enthusiastic,” which is sometimes true, I see nothing. — Xtrix

I mean, really. What is wrong with you?!


Must you yourselves suffer strokes from the vaccine in order to even begin to have empathy for iatrogenic diseases?

You think people should be consoled by a reference to luck?!

Oh for fuck's sake. Do you have plastic flowing in your veins or what?! — baker

That kind of sounds contemptuous.

My consolation is: some people are unlucky.
— Xtrix

Now sit down and think long and heard about what "luck" means in terms of science.

Chance is the end of science. We do science in order to overcome chance. — baker

If you want to talk about the philosophy of science, we can. Until then, let's not pretend anything you've just said is simple and uncontroversial. It isn't. The idea of what we "do" when we're "doing" science isn't known. Ideas about the scientific "method," and whether it even exists, is a big subject on its own. And so on.

Good to keep in mind before giving advice to people about "sitting down and thinking long and hard" about science. I wouldn't even mind your condescension if you had done anything to earn it. So far, you simply haven't made a strong argument about anything when it comes to this issue.

Yes, when running experiments, we sometimes try to overcome chance. When I say, "some people are unlucky," that has nothing to do with science, it's a simple matter of probability. I was referring to the 150 or so people who suffered strokes, out of 10,000,000. I would say that's unlikely, and so those people are fairly unlucky to be in that group of people who have suffered from it. That's a judgment call -- perhaps it's not "unlucky". That's a colloquial term. But more precisely: it's highly improbable.

I mean, really. What is wrong with you?! — baker

Interesting way of communicating from someone who feels entitled to give others lectures about the importance of communicating well. Doesn't mean the advice is wrong, of course -- it just means you're a complete hypocrite.

The same cynical attitude, the same threats, the same simplificationism, the same not listening, the same diversions. — baker

Hmm....sound like anyone we know?

Must you yourselves suffer strokes from the vaccine in order to even begin to have empathy for iatrogenic diseases?

You think people should be consoled by a reference to luck?! — baker

Of course I have empathy for these people, as I've said repeatedly and which you ignored. You asked for consolation...what can I possibly give for consolation? It doesn't make the choice to take a vaccine stupid, it means it was a good decision and you got very unlucky. It's the same thing if you reverse the issue, and someone spends $1,000 bucks for a 0.000015% chance of winning $100,000 and does, indeed, win. That doesn't mean the decision a wise one -- it means they were incredibly lucky.

That has nothing to do with empathy. That's an attempt to offer "consolation." My only consolation, in general, is the idea that you made a good decision despite a negative outcome. That's very difficult for most people to understand, because almost everyone is results-oriented -- we see this is poker as well, and other areas involving probability.

But speaking of empathy...what is your consolation for the 4.5 million people who have died of COVID while you talk up the minuscule risk involved in the vaccines? What about the 95%+ of hospitalizations among the unvaccinated in the US? Where's your empathy and consolations for them -- a far, far larger group than those who have suffered from strokes?

Interesting to be such an advocate for one group while entirely ignoring another, larger group with far higher rates of fatality.

This is from the Washington Post, so Google it if you're a subscriber. In addition, if I understand correctly, banks haven't been able to foreclose on properties where the owner died, so there should be a little bonanza of foreclosures coming up. Just saying. — frank

I've wondered about this in Australia. Apparently something like one third of all mortgage holders are right on the edge in regards to being able to service their mortgage. Governments payments to secure jobs will end when we come out of lock-down and "life returns to the new normal", so many people will be economically affected by that which may lead to defaults and foreclosures and if house prices suddenly declined (amazingly they've risen more in the last year than at any time since the late eighties) and margin calls are made, or if interest rates rise, then there would likely be a huge number of defaults. Would the banks foreclose on all those (which would cause property prices to plummet causing even more defaults in a vicious feedback loop) or would they instead assume ownership of the properties and become the new order of landlords?

Would the banks foreclose on all those (which would cause property prices to plummet causing even more defaults in a vicious feedback loop) or would they instead assume ownership of the properties and become the new or — Janus

I think the banks would try to work with people until the economy is rolling again. That's what's happening here.

That would be ideal, the alternative of massive numbers of foreclosures would seem to be likely to crash the economy. What measures are the banks taking there?

That would be ideal, the alternative of massive numbers of foreclosures would seem to be likely to crash the economy. What measures are the banks taking there? — Janus

The banks would rather give people time to recover than end up with a glut of foreclosures, so they take the initiative to connect people with the various funds set aside for covid recovery and work with people to create affordable payment schedules.

:ok:

Interesting to be such an advocate for one group while entirely ignoring another, larger group with far higher rates of fatality. — Xtrix

You should know better.

There is less fault with the anti-vaccers, becuse their stance is a reaction, a revolt against the normalization of scientism, against capitalist exploitation, against being ruled by aged adolescents with advanced degrees.

Every day, I turn on the news and I see people in their 40's, 50's, 60's and older, high politicians, people with advanced degrees, money, and political power who have the emotional maturity of adolescents and who are enforcing a culture of plebeian mediocrity upon everyone.

Interesting way of communicating from someone who feels entitled to give others lectures about the importance of communicating well. Doesn't mean the advice is wrong, of course -- it just means you're a complete hypocrite. — Xtrix

I can't say that I'm not glad to see that scientism and capitalism are digging their own grave. Granted, at an enormous cost to human life and to the planet, but still, a grave.

Great -- but that's not what you were asking for, when discussing "MY numbers."

If this counts as the kind of number you want, fine -- then simply divide the vaccine data into men and women, and compare rates of death. They'll be exceedingly low in both groups -- but at least you'll have what you wanted. — Xtrix

You asked for an example. You know what an example is, right?

If the probability of having a stroke is .000015%, that pertains to you as well -- as much so as a roulette wheel. — Xtrix

So there are no variables involved at all? Strokes are a random event, like the roulette ball? Do you have any supporting evidence for this. It's not my area of expertise, but I thought strokes had physiological causes.

So you agree the vaccines are safe. Fantastic.

So what's the problem? — Xtrix

Literally everything I've written over the last200 pages, but by all means don't let what I actually write get in the way of your little avatar of me against whom you're arguing, it's a fantastically grotesque golem and you seem to be having enormous fun fighting it, I wouldn't want to get in the way.

Above average for what? — Xtrix

The variables which influence the probabilities we're talking about. But I see from your roulette wheel example, that you're of the opinion that probabilities are not influenced by variables at all and that every event we might discuss is basically random like a roulette wheel. That would explain why you're having so much trouble understanding this. Of course it wouldn't explain why you bother, say, putting a seatbelt on. If your risk of dying in a car crash just is exactly the prevalence of car crash deaths then there's little point, you can't do anything about it, it's just random, like the roulette wheel...

When you want to weigh the risk of flying in an airplane --" sorry, it's just prevalence, and doesn't pertain to me, because there's not a number risk number for me specifically." — Xtrix

Well yes. The prevalence of dying in a plane crash as a measure of risk definitely doesn't apply to me if I don't fly. It doesn't apply to me if I only choose the safest airlines, it doesn't apply to me if fly six times a day, it doesn't apply to me if refuse to put the seatbelt on when instructed, it doesn't apply to me if I'm elderly, frail, or otherwise compromised... I'm delighted to have found such an unusual view of risk, but I'm struggling to see how it's maintained in the face of such obvious evidence to the contrary. The prevalence is a sum of the effects of all the variables, any individual will have their own unique measure in each variable, only the average in all variable will have a risk approximate to the prevalence. At least that's how it's normally done. You've yet to walk me through this new maths of your. So please...you have the prevalence of an event, your claim is that you can go directly to a calculation of the individual risk of that event without measuring any variables at all. This would turn the whole field of risk analysis on it's head, you do realise what a game-changing piece of mathematics you've stumbled on here?

And so on. It's chasing a fantasy. It's like the idea of limits in calculus -- you'll never get there — Xtrix

So we should never start? That seems a little daft. So assessing someone's risk for lung cancer you'd just take the prevalence of lung cancer deaths and say "that's it", yes? If another doctor said "what about the variables like smoking, sex, obesity, history, age..." you'd say "that's just chasing a fantasy, you can't get a truly individualised risk so don't even bother starting"?

you can't get a truly individualised risk so don't even bother starting"? — Isaac

I trust nobody is stoping you from trying to calculate your individual risk. Don't ask others to calculate it for you though. We don't give a rat's ass.

I trust nobody is stoping you from trying to calculate your individual risk. Don't ask others to calculate it for you though. We don't give a rat's ass. — Olivier5

Still having trouble with the actual line of argument I see.

if you can't produce figures for my risk then my decision is not risk based is it? — Isaac

Do you understand the point of this sentence at all? It's in the form if A then B right? So if A is the case, then B follows. How do you get out of that the notion that I think A ought or ought not to be the case? Talk me through the thought process that lead you from reading a perfect clear use of a conditional to a notion that I'm advocating for one of the elements in it.

Let me try to make it clearer. If I say "if you can't produce your ID then I can't let you in", am I suggesting that you ought to produce your ID? No. You could simply not produce your ID and I not let you in.

Or try "if you don't give me a pencil, I can't write my name", you might well still not give me a pencil and I not write my name, yes? Nothing in the line of argument advocates for you (or anyone ) providing me with personalised risk data, it is an argument claiming that without personalised risk data, the decision is not really about risk.

if you can't produce figures for my risk then my decision is not risk based is it?
— Isaac

Do you understand the point of this sentence at all? — Isaac

I do. You are asking others to do your homework for you. But nobody cares about you enough to give you these numbers...

I do. You are asking others to do your homework for you. But nobody cares about you enough to give you these numbers... — Olivier5

So, no then.

One last try. If I say "if you don't shoot me, then I'll live to see another day" am I asking you to shoot me?

You don't even understand what you are saying, and you don't understand what I am saying either.

One last try. If I say "if you don't shoot me, then I'll live to see another day" am I asking you to shoot me? — Isaac

So your question was rhetorical. Drumroll.

It still manifests bad faith. Because you are a scientist, you must know that no measurement can be perfectly precise; there's always a margin of error. And you must know that the risks taken by one particular individual are impossible to measure. Therefore you should know that you are asking for the impossible. Twice. That's a bit much, even rhetorically.

you are asking for the impossible. — Olivier5

When people speak of risk-based decision making, they are not talking of perfect estimates of risks across the whole demographic. They are speaking of basing their decisions on the best estimate of risks one can get at any given time.

the best estimate of risks — Olivier5

Is the prevalence of deaths from COVID the best estimate of risk available for any individual? Is the national R0 value the best available estimate of an individual's risk of transmission? Are global deaths to date the best available estimate of future global mortality risk? Is the current economic and social impact the best available estimate of future economic and social impact?

No, no, no, and no. And yet they're brought up again and again as if they were counter arguments to risk-based strategies.

Risk analysis is not perfect, but it's a damn sight more complex than the naïve presentation of national prevalence statistics we see posted here masquerading as serious analysis.

A thought experiment

Imagine a person (X1) has a knife, one big enough to kill, he kills a person. Someone (X2) finds the murder weapon, the knife. X2 makes two copies of the knife and gives one to another dude (X3). X2 uses the knife to off a person and X3 does the same. A person (X4) finds the X2's knife and another chap (X5) finds X3's knife. The process of copying the knives each one of these murderers leave behind is reiterated and so are the murders. The question is: What killed these people? People or knives?

Risk analysis is not perfect, but it's a damn sight more complex than the naïve presentation of national prevalence statistics we see posted here masquerading as serious analysis. — Isaac

You play hard to please. The data is never good enough for you.