Technorati tags: Science, Education, Community, Radio, Canberra, Australia
Technorati tags: Science, Education, Community, Radio, Canberra, Australia
Technorati tags: Science, Education, Community, Radio, Canberra, Australia
[Canberra Times 6 April. This is a re-post of an earlier version scrubbed up for publication]
Coming out of my kitchen cupboard at the moment is a terrible smell. A miasma of rotting potatoes threatening to inflict upon me some awful disease. At least, that’s what I might think if I believed the old theory that foul smells can spread disease.
Now we could all chuckle, thinking patronising thoughts about how quaint it is for anybody to believe such a thing. We know that infection is caused by microbes, and no one is going to contact Yellow Fever from a smell.
Still, you can see the logic. I went to a swamp. Thick gloopy anaerobic mud, and it smelled disgusting. Next week I fell sick. Ergo the smell infected me with Yellow Fever. Here we have an example of false logic, which is what I want to talk about in this story.
You know what’s missing in the story above. The smell is associated with the swamp, but I forgot to mention the mosquitos.
Aristotle might’ve known about Yellow Fever, but he’s very unlikely to have known of its connection to mosquitos. He mightn’t have known much about disease, but he sure knew logic, so once learning his mistake he would probably say the Greek equivalent of non causa pro causa, otherwise known as the fallacy of false cause.
A variant is reductio ad absurdum, which literally means “reduce to absurdity”. A body builder might say if some muscle is good, then lots of muscle must be really good. In fact, if I bound myself up in so many layers of muscle that I can hardly move, I must be the pinnacle of health. Yet body builders can be so focused on muscle development aided by steroids and diet restrictions, they die of heart failure.
Meanwhile, Aristotle has been scratching out on parchment a catalogue of the forms of false logic. Some wag titled this his Sophistic Refutations, probably in the hope of making it sound impressive. Here’s my interpretation.
The General to the Particular: Violent spectators have been a problem at English soccer matches, therefore English soccer fans are hooligans.
The Particular to the General: People find football entertaining, therefore I find football entertaining.
Irrelevant Conclusion: There are a few variants of this, but they all revolve around unrelated causes: Ad Hominem, against the man; Ad Misericordiam, an appeal to pity; Ad Populem, “most people say…”; Ad Vericumdiam, an appeal to authority (Rod says…); Ad Ignorantiam, in the absence of evidence; Ad Baculum: agree with me or else.
Circular Argument: Paula is bad because she is racist. She’s racist because she’s bad.
Many Questions: Have you stopped beating your wife? Is actually two questions posing as one.
False Cause: The miasma theory of disease.
Non Sequitur: Sue is wrong, therefore Bill must be right. Actually they’re both wrong. (Perhaps Rod is right.)
Strictly speaking the Sophistic Refutations are about formal logic, which leaves no room for intuition or judgement based balance of probability. Circumstantial evidence is not permitted. Unfortunately in the real world, pure logic is limited because are forced to operate on imperfect information. We don’t have all the data, and we don’t understand all the mechanisms, so often we can only guess that A causes B.
In other words, in science you need logic and evidence. Understanding false logic only gives you a clue to the traps to avoid when drawing conclusions. Science has had to invent methods to overcome the little logic traps nature sets for us. Deep breath, here’s one – smoking.
I remember great aunt Betty’s withered hand holding a Capstan cigarette, but did that kill her? Or perhaps it was old age. Perhaps it was because she had polio. To say with confidence that A causes B, we need to control the variables. We need to untangle what’s significant amid the confounding noise.
Betty is only one case, and we can’t run her life again as a non-smoker to see the result. Instead we try to find a large number of people like her, and use statistics and say that on the balance of probabilities, we think smoking is a cause of early death.
Ultimately this story comes down to a question of what is inherently knowable. I don’t know that logic will solve this problem, but I do know that without it we are left with a smelly miasma of diseased science.
Sadly, all we’ve achieved with all this is to help cull failed ideas, and the Nobel Prize is not yet ours. We still haven’t covered the creative spark, the flash of insight that generates truly great discoveries. Where that comes from is a bit of a mystery, and formal logic is probably not a good place to find it.
Technorati tags: Science, Education, Community, 
ERadio, Canberra, Australia
Technorati tags: Science, Education, Community, Radio, Canberra, Australia
(Canberra Times 23 Feb 2009) If you wanted a computer to identify glasses of beer, you could use fuzzy logic as part of the solution. It would incorporate rules such as “we’re in a pub, and beer is often served in pubs”, and “that’s Katie holding the glass, but she doesn’t like beer”.
Feeding these parameters in allow it to compute an answer more like what a human would give, and the result would be something like “that probably is a beer”. Of course we haven’t solved the problem of how the computer knows you’re in a pub in the first place.
Fuzzy logic is now used in many consumer applications such as the face recognition feature in cameras. Using rules about shapes, light, and colour, it will attempt to make sure any faces in the frame are in focus.
Like computers, bureaucracies also tend to find fuzzy logic difficult, and perhaps their reliance on computers tends to reinforce this. When is a person considered to be “young”? What age between zero and 25 would you chose, and what if the person is 14 years, 11 months, and 29 days old? Or perhaps you recall the GST chicken that attracts GST only when served above room temperature – whatever that is.
The result of all this is an arcane maze of complicated rules. You receive a pension if you are over 30, have assets less than $100,000, income under $50,000, live in a rural area, and do not also receive this other pension with equally twisted rules.
In fact the situation becomes so complicated, that sometimes the rules themselves become internally inconsistent. So by one chain of logic you must satisfy condition X, and by another chain, you must not.
Surprisingly, computers can help here in an unexpected way. Such errors are created by humans, but when forced to translate them into the zero-and-one logic of computers, their inconsistencies are exposed.
Another way in which human logic and computer logic differs is in a technique called “chunking”. Imagine you wanted to know how many sheep are in a paddock. One way is to force them through a gate, and count them as they go.
That’s probably what a computer would do. But that’s also quite tedious, and do you really need to know exactly? Another way is to “chunk” them into sets of say, ten. You’d figure out how many sheep occupy a certain space, then multiply it across the whole paddock. From that you estimate so-many sheep per hectare, and then how many sheep are on the whole farm.
Counting sheep seems simple and benign enough, but what about something a bit more challenging. Imagine you are on a battlefield, and being charged by several dozen ugly hairy warriors who mean to do you harm. You’re carrying a bow and arrow, but don’t have time to evaluate the enemy all at once, so you make a snap assessment. You chose the first target, and make all the calculations you need to take him down.
This is a kind of computational chunking, which tells you in the shortest possible time where to direct your energy. Ignore the mob directly ahead – they’re furthest away. Ignore those on the right because your comrades have them covered. For the moment, just focus your attention to those on your left.
This strategy helps manage complexity by breaking a large problem into pieces. It applies simplified logic that glosses over detail when there is not enough time or information to go deeper. Scientists, decision makers, and artificial intelligence systems all do this because it’s simply not possible to fully analyse every problem.
Now back to that beer, and the correct answer will be obvious when I tell you. That is, if that is a beer in your hand, I am pleased to see you.
That is not just me trying to be funny, because I’ve just done something you will never see a computer do. Not only have I made a joke, I have reframed the question. I certainly don’t expect to see a computer do that in my lifetime. And furthermore, after all this logic, I will enjoy that beer.
