Logic puzzle 6. The counterintuativeness of science

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The scientific method has fallen into disrepute recently among the Great unwashed and even some "scientists" . After the enlightenment everybody beleived that science would solve all the worlds problems. Then after the war the post modernist movement came along and told us that science that did not have all the answers.

Relativistic truth was the phrase of the day. You have your truth, i have mine. I can't assume mine is "better" than yours, its just different.

This principle was further cemented by the advent of quantum physics and uncertainty principle.

"Do you have a point?" i hear you cry. I'm getting there, be patient.

The concept of relativistic truth caused a fundamental shift in the public perception (or misconception) of the scientific method which is alive and well to this day. That is that the scientific method is based on trying to prove a hypothesis.

Its not.

The scientific method is based on trying to DISPROVE a hypothesis. It takes a supposition and tests it to se if it can be shown to be false NOT to see if it can be shown to be true.

"thats semantics" i hear you cry. "its the same thing"

But it is not. Its very different. Try this experiment yourself. For once i'm going to give you the answer straight away. Try it on your friends and family. See what results you get. You might find you surprise yourself. I guarentee your friends and family will surprise you.




I have 4 cards laid on the table in front of you. Each has a letter on one side and a number on the other. What you see is the following

[ A ] [ 7 ] [ 3 ] [ D ]




Now i will offer you a "rule" (or hypothesis if you will). This might be true or false

A card with A on one side has 3 on the other

Now riddle me this. What are the minimum card / cards you would need to turn over in order to prove / disprove the rule. Which ones.


Think about the answer, get it clear in your head, then read on...

 

If you are reading this without makeing a guess at the above, shame on you! Go back and put the effort in!















Chances are most people pick either A or 3 or both. That is because they are trying to prove the hypothesis (that the A card has a 3 on the other side.)

The correct answer is A and 7.

Why? Well it stems from the human tendancy to try to prove the rule rather than disprove it. If A has a 4 on the reverse the rule is untrue. If the 7 has an A on the reverse the rule is untrue. If the 3 has a w on the other side it means nothing (the rule was simply that A always has 3 not vice versa.) It is, as i said, counterintuative.

If you got this right then pat yourself on the back you clever sausage. Now go try it on the great unwashed. If you, with your scientific brain got it wrong (and i did) what chance to the others have?


I hope you found this interesting. If not i'm sorry for wasting 5 minutes of your life. But consider this the next time you read a study or see a news story. Is it trying to prove the hypothesis or disprove it. Is it good science or bad science.

Regards
Robert

 

Yep, i'm hooked, more

 

Ok. Heres one more to keep you going for the weekend. This is an interesting insight into how our brains process statistics and how the media can twist us.

There is a horrible and rare disease going around. It affects one in 10,000 people but is always fatal. There is a test for this disease which is 99% accurate, that is, it gives an accurate readout 99% of the time.

Along with the rest of the population you take this test and to your horror it comes back positive, saying you have the disease!

You are sad and worried!:empathy: There there.

So what are the odds you'll get to see the next rugby world cup?

Enjoy the migraine

Regards
Robert

 

OK, maybe I'm thick, but if you turn over A and there is a 3 on the other side then the rule is true.
If you turn over A and there is not a 3 on the other side the rule is false.
Why turn any others over?
Turning over 7, well, no matter what is on the other side this has no bearing the the rule that was presented other than if it's an A. So if you turn over the 7 and there is, say, the letter D (or anything else for that matter other than an A) this doesn't prove or disprove the rule.
Am I wrong?

Steve

 

Rugby????
You mean Football game?
Well.....I don't think the incidence of the disease is relevant. Whether the disease affects 1 in 10 or 1 in 10,000 the fact remains that he was tested positive for it, which is accurate 99% of the time, i.e., 1 out of 100 is inaccurate.
My take on this is he has 99 chances in 100 that the test results were correct and, depending on how quickly the disease terminates him, he should sell his tickets.
Steve

 

Hey steve. Thanks for playing.

I'm afraid you are wrong on both. With the cards you said

Which is correct. With the key phrase being "other than if its an A" As you say if the 7 card had an A on the other side you have disproved the rule. In other words if you only turn the A card over you have not proved the rule because it may still be false (if the 7 has an A). For it to be a rule it has to apply universally. If, as you say, the 7 card has anything other than an A it neither proves nor disproves the rule.

This is called confirmation bias. The weighting of evidence which supports the rule over that which could disprove it.

With me?

Robert

 

Well done for having a crack (since my gouty boy mark let me down) but wrong again i'm afraid. This is called the representiveness heuristic (google it if you don't beleive me) and is solves using something caled Baye's therorum.

Look at it thus. The test is 99% effective. Therefore regardless of the true result it offers an incorrect result 1% of the time.

In a disease which affects 1 in 10,000 people lets say we test them all. 1%, which is 100 people will get an incorrect result telling them they have the disease. However only 1 of these will actually HAVE the disease. Theirfore if you are one of that 100 people you will actually only have a 1% chance of missing the next series of Spooks.

Slightly less actually because that presumes that the sick person is going to get the correct result and be positive result # 101. There is a chance that the sick person will get the wrong result and be told they are healthy in which case it would be 1 in 100.

Its clever init.

Regards
Robert

 

Hi Robert:
Thanks, I get it.
I "out-thought" myself not taking into consideration that there were "just" those four cards, period....hmmmmmmm.

And thanks for explaining the second puzzle......just one thing, what are "spooks"? haha
Steve

 

Ah. Sorry, for some reason i thought you were a limey. That explains the whole football thing!

Spooks is quite simpky the best drama series ever shown on the tube.

 

Hello Again Robert.
I did google representiveness heuristic ......I started reading it and, well, I guess I needed a nap! I think I'll print it and start reading it again tonight instead of taking Ambien. HAHAHA
Not a limey!
I live in Green Bay, Wisconsin....home of the Green Bay Packers!
GO PACK!

Steve