"Chaos" (The Movie) And The Pigeonhole Principle - An Interesting Goof

***Caution: Spoiler Ahead***

While reading the list of goofs in the movie Chaos, I noticed that nobody had pointed out this important mathematical goof in the movie. At around 1:13:00 time in the movie, note this set of dialogs

1. "...about a billion dollars..."
2. "Now. If you look at all the transactions, no 2 amounts are the same, and none of them are over 100 dollars"
3. "...less than 100 dollars, from, say, 10 million accounts, no reflex"

According to the Pigeonhole principle, it's not possible to make about 10 million transactions, each less than 100 dollars, such that no two transactions have the same amount [assuming the least count is 1 cent]. It's only possible if transaction limit is 100,000 dollars.

However, if 10 million transactions [all withdrawals] are made such that no two amount to the same, then the minimum amount withdrawn would be ((10,000,000)*(10,000,001)/2) cents - about 500,000,000,000 dollars- far, far more than 1 billion dollars.

Pigeonhole Principle - Also known as Drichlet's Box / Drawer Principle

It's unfortunate that the people behind Chaos overlooked this important mistake -especially when they were trying to make a movie that apparently is so dependent on mathematics and Chaos Theory.

Finally, to withdraw 1 billion dollars such that no 2 withdrawals amount to the same, we need at least about 450,000 withdrawals [starting from 1 cent, 2 cent, 3 cent and so on till about 450,000 cents].

A Goof In The Movie "Crimson Tide"

Are the top web search engines correspondingly related to the top web browsers?

I should begin by admitting that this idea sprung up in my mind (probably) as a repercussion of my watching the movie "Chaos" today morning (there isn't much of a direct relation between the movie and this idea though).

This is pretty straightforward- the current top web search engines (Google Search, Yahoo Search, Live/MSN Search, Ask.com Search- in that order) bear resemblance to the current top web browsers (Windows Internet Explorer, Mozilla Firefox, Apple Safari, Opera Browser- in that order again) in some striking ways- apart from a broad similarity in their current market shares.

I'll list those here

1) Google Search and Windows Internet Explorer- Both these market leaders are zippy (a clean install of IE 7 runs and renders fast- and most of the complaints of IE 6 or IE 7 being slow or heavy are a result of bad add-ons or wrong settings). Both are lightweight- IE is the least resource consuming browser on Windows operating system, when stacked up against the other 3 in question here- while Google Search is the lightest web search engine out of the 4 being considered here.

2) Yahoo Search and Mozilla Firefox- Both these powerhouses pack large number of useful features, and both "get the work done", although in the process of achieving this, they tend to be heavier than their more popular rivals.

3) Live/MSN Search and Apple Safari- Slick looks mark their main resemblance, as is the tremendous promise both of them hold. Both are expected to gain market share at the expense of their larger rivals.

4) Ask.com Search and Opera Browser- "Innovation" and "Innovative features" are the hallmarks of both of them. Each one of them is an underdog, fighting for survival, constantly innovating in the process. Each of them provides innovative features and tools not to be found (yet) elsewhere.

I can even add AOL Search and Netscape Browser/Navigator here- with feature richness but undue bloat characterising them both.

The important and unresolved point, however, is- does this correspondence have something more than what meets the eye (something scientific, some patterns maybe)? Or is it merely a consequence of an unsettled mind watching a movie as confounding as "Chaos"?

If we are able to identify some common characteristics in the products and services talked about in this post (which caused them to attain their respective positions in the market), we shall be a step closer to identifying and listing "Rules for Success".

P.S.- Identification of these "Rules for Success" is an area of my interest, and I have put significant time and energy into it.

Microsoft Silverlight forces the web browser process to run at 'Above Normal' priority

I felt like puking after what I just noticed- I had downloaded and installed Microsoft's Silverlight runtime on my computer a day back. Today I was browsing the web on 2 browsers together- Opera and Mozilla Firefox. When I opened www.microsoft.com in Firefox the website threw up a Silverlight based animation [whereas it used JPEG or Flash/SWF while I had not installed Silverlight]. The animation slowed down my computer [Intel Celeron M 1.5 GHz based laptop] significantly and perplexed me.

On analyzing what was wrong, I noticed that firefox.exe process was running at 'Above Normal' priority, and manually trying to lower it to 'Normal' simply failed- firefox.exe would automatically [and immediately] switch back to 'Above Normal' priority [but that's only if Silverlight is active- as soon as the tab having www.microsoft.com was closed, Firefox could again be switched to 'Normal' priority- so I conclude that it was Silverlight which forced Firefox to run at 'Above Normal' priority].

However, to me there is something else that is far more important- a Flash animation running in parallel in Opera browser slowed down immediately [and significantly] when Silverlight got activated in Firefox, whereas the Silverlight animation running in Firefox appeared to run faster [relative to the Flash animation].

To me, nothing else is more important than what I wrote in bold above. With this [yet another] wicked tactic, Microsoft gives a user not 1 but 2 false impressions:-

1) Silverlight is made to look better than it is- by forcing the process to run at 'Above Normal' priority, Microsoft is essentially fooling users by the apparent performance of Silverlight

2) Flash based animations running in other browsers are made to look slower than they actually are- user gets an impression of poor performance of Flash, compared to a parallel running Silverlight animation

Also, this is going to impact performance of other browsers as well [which a user runs in parallel]. And because this has not been documented anywhere, nor is the user informed about this, users will unknowingly develop false impressions of speed and performance of other runtimes and other browsers. This is nothing short of pathetic!

Personally I feel that Microsoft deserves to be sued for such a lame and desperate act- this act is an admittance on Microsoft's part that it lacks the engineering talent required to produce a high performance runtime that can equal, let alone better, Adobe's Flash.

My 2 cents for Microsoft:-

"Real men triumph without cheating."

(Microsoft does possess the talent to decipher what I meant...)