Beating Asafa - Zeno's Paradox

Meet Asafa Powell, the 100m current record holder. If chased by a lion, he’ll make the first 100 meters in 9.74 seconds so find another partner for that dangerous backpacking trip to Africa...
EDIT: Since this post Usain Bolt has done it in 9.58 seconds.

Meet Maya, my 1.5 year old daughter (I have another 3.5 year old son named Yoav). When she runs, her feet twist inwards and her upper body leans forward in a scary angle, so an observer will probably define her running as a controlled crash.

Now here’s a scenario for you: a race between Asafa and my kid.
Let’s use round numbers.
Powell runs ten meters a second (I hope he won’t accidentally browse to this blog ‘cause he’ll probably kill me for that). My kid controlled-crashes one meter a second. Since my kid is in kindergarten, and Asafa is world famous, he foolishly agrees to grant her a ten meters lead. Ready. Set. Go!

1 second after the gun fires, the amused runner will close the lead, but my kid will manage to advance 1 meter in that time.
Current status: My 1.5 year old kid still has a 1 meter lead over the current record holder.

100 milliseconds later, the smiling Jamaican will pass this meter, but my daughter will manage to advance another 10 centimeters in that time.
Current status: My 1.5 year old kid still has a 10 centimeters lead over the current record holder.

10 milliseconds later, the optimistic sprinter will pass this small distance, but my 1.5 year old will manage to advance another 1 centimeter in that time.
Current status: My 1.5 year old kid still has a 1 centimeter lead over the current record holder.

1 millisecond later, the frustrated athlete will pass this tiny distance, but my cute underdog will manage to advance another 1 millimeter in that time.
Current status: My 1.5 year old kid still has a 1 millimeter lead over the current record holder.

Etc…

Can Asafa Powell ever catch up, or was he acting foolishly by agreeing to grant my daughter this lead?

~~~
p.s. Engraved on my tombstone: "I hope it’s not just 42…"

Counting Crows, Hunting Bugs - Hempel's Paradox

A new version of our product is just around the corner. We’ve just passed the code-freeze date, meaning no more writing code. The plan is to spend the next few weeks hunting down all those elusive bugs lurking viciously beneath the unsuspecting user interface. The rigorous checking and rechecking of all the features will probably prove to be a very boring task, so I came up with this alternative idea straight to the welcoming arms of escapism.

The Hempel's paradox is one example of a situation where inductive logic violates intuition. Let’s examine the hypothesis that all ravens are black. I must admit I’ve seen some gray crows in Israel, but I’m ready to ignore that and proceed with this example the Hempel’s way. While walking around in the world, every black raven observed should increase your belief in this hypothesis. No surprise there, but… this statement is equivalent, in logical terms, to the statement that all non-black things are non-ravens, so as it turns out, a red apple observed should also increase your belief in the hypothesis that all ravens are black. If you could see all the non-black things in the universe and ensure none of them is a crow, you could indeed conclude that the hypothesis is true. Since the number of non-black things is far, far larger than the number of crows, observing one more non-black non-raven thing can only make a very small difference to your degree of belief in the hypothesis compared to the difference made by observing one more black crow, but still, a red apple really does strengthen the hypothesis that all ravens are black.

With Hempel at my side I plan to call my new boss and inform her I’m staying home next week. She will probably expect me to validate ‘Our product contains no bugs’, but my strategy is to convince her I’ll check the equivalent ‘If there’s a software bug it’s not in our product’. I hope she’ll authorize this so I’ll be able to start the bug hunting on Sunday morning. I plan to begin by rigorously checking StarCraft. Wish me luck.

~~~
p.s. My husband was the first human on Mars and all I got was this lousy T-shirt.

The Vertigo and the Lion - Intuition Can Be Hazardous to Your Health

Sometimes, when a pilot flies at night with no visual reference, he gets disoriented, and his senses and intuition can cause him to think the instruments aboard his plane are wrong. He can be on a straight and level flight, but feel like he’s turning or even flying upside down. This dangerous phenomenon is called Vertigo. Pilots train for this condition and know that when their intuition disagrees with the instruments – they should trust the instruments.

Now consider this scenario: You are in Africa trying to hide from a lion. There are 3 small bushes with just enough space for one person/animal. You know the lion is waiting for you in one of the bushes (you don’t know which one) and your only hope is to pick a bush to hide in, hoping it’s lion-free. You randomly select bush #1 and start crawling at its direction hoping the lion is not there. Suddenly you see your friend crawling towards the bushes from the other side. He sees you are aiming for bush #1, so he can’t choose that bush even if it’s lion-free (no place for two people). You know he can see the lion from his angle but he can’t show you where it is because he’s afraid of making big sudden moves (or maybe he just thinks a satiated lion will give him a better chance). He aims for bush #3 (he’s sure it’s lion-free because he can see the lion from his angle), reaches it and hides there safely. So you are left with bush #1 and bush #2, one of them hides the lion.

Now, should you:
a. Stay with your original choice of bush #1.
b. Change your choice to bush #2.
c. It doesn’t matter – both bushes got the same probability for containing a hungry lion.
Please make your choice before reading on.

This was an example of how our intuition sucks. If you chose c - you are wrong, but take comfort in knowing you belong to the majority. If you chose b - you deserve to be eaten by a lion, please close your browser and book a flight to Congo. If you chose a - you are correct (this scenario is my weird inverted version of the Monty Hall problem). As you might have guessed, this problem is counter-intuitive so most people get it wrong.

While I can understand how evolution didn’t bother to equip us with intuition capable of avoiding Vertigo while night flying a high altitude super sonic metal machine, it seems like nothing short of a miracle that Homo sapiens has managed to get out of Africa in one piece with our fucked-up lion spotting intuition.

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p.s. If a tree falls in a forest and no one’s around, should you blame the Jews?