Wowzer!! How's This For Being Totally & Utterly Misconstrued?

So this happened, and it's one of those rare things that when it does happen it reveals fascinating things about humans. I just joined a Mensa debating forum containing what seemed like a few select, intelligent people, and just as I was given access by the admin, a woman called Amber happened to start a thread with her opening statement - a statement that was definitely wrong.

So, maintaining politeness at all times, I made a statement that was definitely right and contrary to what she had reasoned, and subsequently a couple of people joined the thread to tell me how wrong I was. Then after explaining to them where they were going wrong, they were so shocked at what I was saying they accused me of being a troll and within 20 minutes the admin had banned me! By then there were about six contributors + Amber, all thinking I was saying what I was saying to wind them up, when actually I was explaining what are, admittedly counter-intuitive, but absolutely correct points.

It is fascinating when you meet people who are so confused that the opposite of their falsity (the truth) seems so bizarre that they mistake you for a trolling nutter who is not even worthy to remain in the group.

Those that want to know what the discussion was about will be pleased to know that I copy and pasted all the text before losing access to the group, and put the meat of it in this blog post I just created. It's a funny old world!

 

There is only one negative thing that comes from having frequent sexual encounters with multiple partners - there is more chance that sexually transmitted diseases will be passed on.

(Opening statement in a Mensa group. from a lady called Amber)

Realising that that is not just wrong, but the opposite of the truth, I responded with:

Actually, no, there is only one positive thing that comes from having frequent sexual encounters with multiple partners - there is less chance that sexually transmitted diseases will be passed on. 

Here is how the rest of the conversation went.

Amber: Do pray tell James how?

JK: Here’s how it works - the more people in the promiscuity pool, the more people having one night stands, which means those infected have a reduced chance of having sex, which equals a reduced chance of the infected ones passing on their infection. It is counter-intuitive, but many true things are.  It may seem intuitively that the more people you have in a pool of people who are having sex when one has an STD, the more people end up having STDs, but precisely the opposite is true! The more people you have in a pool of people who are having sex when one has an STD, the fewer people end up having STDs. It's a simple case of numbers - the more people in the pool, the greater the competition, so the greater likelihood that Mr. infected won't pass on his DNA.

Ronald:  Maybe this is true on the first go-round. However, that one person infects at least one other -- then you have two others with an infection to spread, and they infect two others... You begin to see the logical progression there?

JK: But that isn't correct, and here's why... I'll try to explain it in a bit more detail - first I'll show you with the mathematics, then I'll back it up with an analogy.

THE MATHEMATICAL REASON: Suppose you go for a night on the town full of people on the pull. That is what we've called the 'pool' - and it consists of, say, forty people; twenty are infected, twenty are uninfected, and you don't know which is which. This means you have a 50-50 chance of finding a safe partner. Now let's say that next weekend the same forty people are out, but it's the annual carnival, where an extra one thousand people are out on the pull. You now have about a 1/25 chance of finding a non-safe partner - hence, the more people you have in a pool of people who are having sex when a few are infected, the fewer people end up being infected. Further, you mustn't mistakenly think that every single person is going to get lucky - the pool won't facilitate everyone's success (mathematically it's almost impossible) - so by adding more to the pool you increase the number of safe people, and thereby reduce the chances that the infected people will get lucky and thus pass on their DNA.

THE ANALOGY: Think of it in terms of pollution - pollution is when a pernicious external force finds its way into a benign or neutral system (it could be ecological, physiological, or whatever). Having a smaller pool is analogous to increased pollution because (to put it bluntly) by not being in the pool the uninfected majority would diminish the chances of an overall de-pollution. Or if you prefer, the pollution rates are greater with a smaller pool. If you are one of the recklessly promiscuous people with a high probability of being one of the infected you add pollution to the pool every time you ingratiate yourself into it. If you are one of the infected, your chances of pulling are decreased by the greater numbers in the pool, because competition for mates becomes fiercer.

Let's now put this into practice by looking at your statement and seeing which way the logic takes us. You said: "Maybe on the first go-round. However, that one person infects at least one other -- then you have two others with an infection to spread, and they infect two others... You begin to see the logical progression there?"

Now then, you are right that one person infects at least one other, and you are right that you then have two others with an infection to spread. But looked at carefully you should be able to see that your statement vindicates me, not you. The reason is this; what would make the pool safer and less polluted - by making it smaller? No, that will only make it less safe and more susceptible to pollution. But if we do what I said the logic dictates and add more people to it, we make pollution less conducive - thus we have a safer pool.

Amber: James your scenario is unsound. It assumes that your small group will be heavily infected, and a large group will be strongly uninfected, thus diluting the infected group. But there's no valid reason to assume your starting assumptions.

JK: Amber, I'm afraid you're mistaken - what I've said is not to do with forecasts about the difference between a small and large group's infection rate. It is to do with more people lowering the probability that the infected ones will get the chance to pass on their infection.

Ronald: But if you pick 20 random people from the population and have sex with one, or pick 1,000 people at random from the population and have sex with one, your odds of encountering an STD are exactly the same.

JK: This is another mistaken approach because it requires an assumption based on no background information. But with the above example you do have background information - you know that the people entering the pool are low risk entrants because they are not promiscuous. I have explained this in my last post - the logic is correct, and its veracity is self-evident because it is based on mathematical facts.

Ok, look, you mustn’t think of the non-promiscuous people having lower probability than the promiscuous people, because you’re forgetting my original claim – that an increased pool of promiscuous people would reduce the spread of infection. That’s the point – we are saying the whole pool is now promiscuous, so you cannot simply imagine that it is only the infected people who are promiscuous.

The reality is, the pool is full of promiscuous people, and the more people that enter it the less likely that infected people will spread their infection. Pretend you are one new person in the pool, and you have been sexually cautious in the past. It's great for the pool that you've decided to become promiscuous. Your presence in the pool is good on two counts (probabilistically): if you pull an uninfected partner you divert that partner from a potentially more precarious tryst; if you pull an infected partner you divert that partner from giving it to someone who might spread it at a more proliferated rate than you. Rinse and repeat that cycle every weekend! ;-)

It's not just that the individual's chances of safe sex are greater, it is also the case that a larger pool = the less likely that infected people will spread their infection! It's a 100% mathematical fact of conditional probability. You keep mistakenly assuming that every single person in the pool is going to mate every single time, when I've already said that's not the case.

Louis: "having frequent sexual encounters with multiple partners - there is less chance that sexually transmitted diseases will be passed on" says James Knight. I think we have a troll in the midst, only an attention-seeker would make such a ridiculous claim. 

JK: Yes, it could be that I'm just trying to seek attention from a bunch of people I've just met and with whom I'm only ever going to have the weakest of social ties, or it could be that, in actual fact, everyone who has contributed to the thread thus far is not quite yet seeing why what I've said is right. I believe that what I’ve said already in this thread more than comprehensively conveys the truth of my claim. I grant you, though, it is somewhat counter-intuitive, and is perhaps akin to a circuit board epistemology where one sudden eureka light can light up the whole situation, leaving you wondering how you missed it to begin with. I suppose these things require a bit more wrestling with precisely because they are counter to our intuitions. Our minds have not evolved to accept counter-intuitive notions very easily - and when one considers things like, say, monotonic voting systems, 0.999 denoting a real number that can be shown to be 1, water being heavier in liquid form than in solid form, the Monty Hall problem, and things of that nature that confound the more intuitive feelings, one understands why a crowd can pull together and argue in the opposite direction.

The picture makes sense to me because, as I said, I imagined a heuristic model in which infection was seen in terms of pollution. In this instance the pollution model meant that a counter-intuitive notion was quite clear. What I've argued is not incorrect - perhaps it requires you to gather it together in a different way - but whatever works for you really. Once you think of it in terms of economics it's fairly obvious really - that if you are a frivolously promiscuous individual with a high probability of causing infection, you are going to pollute the partner pool every time you enter into it with the intention of promiscuity — and for the good of the pool you should be discouraged, just as anybody causing pollution should be discouraged. Therefore, the corollary of that - arguing with the signs reversed - is that that if you are a very circumspect individual with less propensity for promiscuity and a low probability of infection then you are going to improve the quality of the partner pool every time you enter into it. Evidently, in the case of the latter, that’s the opposite of causing pollution, and it would make the pool less polluted - the more of these types, the merrier - for precisely the same reasons that pollution should be discouraged.

Amber: Your whole argument is surely set on the faulty assumption that there's a reliance on the external forces diluting more than helping it spread, is it not?

JK: No Amber, it has precious little to do with the extent to which external forces dilute, it is to do with rates at which infected people copulate, and an increase in pool size reducing the rate, where everyone in the pool is equally promiscuous. More people in the pool, more competition, less success for the infected ones. Hence, my above comment. If you keep increasing the pool further, you will keep diminishing the chances of one of the infected ones pulling a mate, because statistically more of the safer people will pull (this is the nature of probability). You'll keep making the pool safer by adding more fresh promiscuity to it, because those additions will increase the competition further, and continue to lessen the probability that one of the infected will get to pass on his or her DNA on any given night! The competition means that they will pull less frequently. Which means they will get the chance to pass on their infection less frequently. Add even more to the pool and this infrequency is more probabilistic, and so on.

Louis: Yep definitely trolling.

JK: Or in other words, Louis, you don't have a comeback because this conversation is over your head, so you resort to crass, baseless accusations. Look it's fine if you don't get it - like I said, some counter-intuitive things require a bit more of a lateral approach, but if you think about it carefully you will be able to arrive at the same conclusion I have.  

Ruedi: If I understood James Knight correctly, I think his argument works as long as he can keep the sample population expanding at a faster rate than the infection rate. That's not really a feasible approach - sooner or later, the population will reach infinite or somewhere near that, and at that point, the infection risk will catch up and neutralize earlier gains

JK: Hi Ruedi, thanks for an attempt at least at some kind of sensible engagement. I think you nearly got it right when you said "his argument works as long as he can keep the sample population expanding at a faster rate than the infection rate", but then you go off track by saying "That's not really a feasible approach - sooner or later, the population will reach infinite or somewhere near that, and at that point, the infection risk will catch up and neutralize earlier gains."

No, no it won’t. You're missing the vital component in the equation, which is increased competition. As the percentage of infected people is reduced (or equivalently we add more uninfected) there is less chance that they have sex because competition is greater. This could even eventuate in a situation where there is only one infected person who as the group increases in size never gets look in and is thus squeezed out, never seeing intercourse. If you keep adding fresh blood to the pool it is likely you will have a situation where the infected percentage actually goes down as they die off and fail to breed new germs by passing them on. How do I know that? Because that is exactly what happens in biological evolution where alleles get fixed in a population in evolution and others die out. What my pollution model shows is that there exists some critical value of the percentage of the infected where it starts to increase – it’s what’s call the tipping point; on one side of the tipping point the infected percentage goes down and on the other side it goes up – we just need more and more fresh blood to ensure the infected percentage continues to diminish.

Louis: I just cannot believe you've got us all engaging in dialogue about a ludicrous claim that more people in a pool where because of sexual activity diseases will spread makes it more safe than when there are less people in the pool. I'm still calling troll.

JK: Ah, still nothing to contribute except this tiresomely narrow philosophical pez dispenser analysis, Louis - I've all but given up on you guys. I'm not sure I can say much more to convince if you don't already get it by now. I'm reminded of the obvservation by Charles Babbage about having an opponent who strikes him as so confused that he is difficult to understand - "I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question". Ho hum!

I'll have one last crack and then I'm outta here. What you guys have done is erroneously made an assumption that assumes that the probability of infected person copulating is a constant whereas I have repeatedly told you that this decreases with the percentage of uninfected persons in the pool due to competition factors. This in itself would lead to a reduction in the rate of increase of the percent infection; however the absolute numbers infected would still increase.

I haven’t even needed to do this yet as the mathematics justifies it alone – but if I wanted to present more of the real life model I could factor in the disabling effects of the infection - that is the infection causes a loss of the ability to breed the infection - hence infected people are going to drop out of the copulatory pool (when most people find out they have an infection they wilfully remove themselves from casual sex). The infected population is subject to, not one, but two competing rates; not just the rate of increase of new blood but also the rate at which they fall out of the "germ breeding" pool. This means that as the number of uninfected people increases the rate at which the infected persons can spread the infection is less than their disablement rate. Hence their population involved in breeding the germ reduces. If this continues they will die out completely.

It is not that being infected significantly affects competition, it is being in a group in which more members are added - it's not just the infected people who are having less sex - almost everyone in the pool is having less sex (on average) - but because the uninfected new blood astronomically dwarfs the infected, the rate at which the infected's sex drops is more significant than the rate at which the uninfected's sex drops - because remember we are showing that the infection is getting diminished in the pool.

There really isn't much more I need to say in this conversation except that everything you need to establish my opening remark - that with more new people in the pool there is less chance that sexually transmitted diseases will be passed on - is contained in this discussion.

(End of discussion)

After that discussion thread, which I'm glad I saved now, I found I could no longer access the thread or the group, which means I must have been banned - a truly odd thing to happen given that everyone else was getting the wrong end of the stick, and I was actually the only one getting the right end of it. It's a crazy situation to encounter people so unable to grasp the truth that to them the truth seems crazy, and the messenger a troll. I suppose one is reminded of Nietzsche and the quote about those who were seen dancing being thought to be insane by those who could not hear the music.

Anyway, after my ban, I decided to do a bit of research to see if anyone had undertaken any studies on this matter - and to my (not that much of a) surprise I found that a guy called Michael Kremer has a 54 page paper that goes into all the ins and outs of why what I said above is the case.

There's a lot of text to sift through, which I sped-read earlier before wring this blog post - but the first equation on page 16 and the surrounding text is most germane to the discussion above  The first equation on page 16 gives us the value of the rate of change of infection (the Y with a dot over it), with the tell tale being the minus sign where the "Y dot" is equal to the rate of increase of infection minus the death rate of the infected.  

I wish I could have survived just an extra few hours so that people in the group could have seen the proof, rather than them all thinking I'm some kind of trolling nutter who was just there to wind them up. Like I said, it's a funny old world!