Top 5 Math Mistakes of 2003
It has been a long time since I wrote a column here. I have been very lax in my web writing this past year, having been distracted by other interests. But, I am back at least for now as I have about 5 columns I feel I need to write before I believe the Math Mistakes site can feel complete and stand on its own.
In an effort to compensate for my relaxed attitude to this site over the past year. I am going to give you a list of the top five math related blunders or interesting headlines of the year.
1. The Gross Overestimation of Weapons of Mass Destruction in Iraq
This one may get me in trouble with my conservative friends, but it cannot be denied. The intelligence estimates about Hussein's biological and chemical weapons capacity were horribly overstated. The big question is, and we may never know the answer for years, is were the numbers fudged to make a case for going after Hussein?
The debate right now, and this will have quite a bit of debate during the upcoming election year, is if we knew then what we know now, should we have actually gone after Hussein in the first place? I think everybody is agreed that the world is better off without Hussein in power, but were we really justified? Was it worth the cost?
When historians in future generations look back at this "War on Terrorism", they will be asking the same questions.
2. The Gross Underestimation of Damage to the Columbia Shuttle Wing
NASA knew that a piece of foam from the booster rocket had hit the wing of Columbia on take off, but only a handful of the engineers considered it a serious threat to re-entry. Not enough to scrub the mission according to the higher ups. The final report blasted the "broken safety culture" and the bureaucracy in the upper levels of NASA for letting this get as bad as it did.
It resulted in the deaths of seven Astronauts.
3. Shortages that Were Not
Gross mismanagement is the word at Akron based FirstEnergy Corp. which has been singled out in all the reports as being the fault of the largest blackout in U.S. history last August, affecting eight States and two Canadian Provinces. Reports put the blame on overgrown trees that damaged power grid lines and alarms that sounded but did not work. Both of these are the fault of FirstEnergy. Their lack of action caused the whole infrastructure to fall like dominoes all down the line. There was not a shortage of electricity at all.
There was also not a real shortage of gasoline in Arizona last August, despite one of the three pipelines being shut down. Nevertheless a handful of stations that ran out of Premium, combined with news coverage, generated an unprecedented buying frenzy that cause 3 or 4 hour waits at the pump and gas prices exceeding $5 a gallon, when the usual price is around $1.50 a gallon. This caused a domino effect for gas buyers in neighboring California and New Mexico as well. The real cause of the gas shortage was panic buying by motorists who did not need to stock up. I do not have the numbers to back it up, but I would bet more gas was sold during the week long crisis than in any week of the rest of the year. Shortage creates demand.
Then just this month, we get a first ever shortage of flu vaccine. This crisis was generated entirely by the media who reported a worse than usual flu bug going around and a few children dying because of it. Now every parent wants their young children vaccinated for the flu, resulting in very long lines and normally abundant supplies of vaccine running out. Like the Arizona gas crisis, shortages create an even bigger demand. Some things the media forgot to mention (or if they did it was buried in the stories): 1. This years flu bug is the same that hit back in 1997, 2. children die from the flu every year -- even years when the flu season is not so bad -- but the odds of any child who contracts the flu actually dying is very very small, 3. the current flu vaccine was not designed to prevent the current flu that is making its way around, as happens some times the flu shot people guessed wrong as to what strain would hit this year, 4. Flu shots can themselves be dangerous, even deadly to some people, though the risk is very very small as well, 5. Unless you are in a high risk category, such as work in a profession where you are in contact with sick people, good hygiene habits can be as effective in prevention as a flu shot.
4. Radical Phone Changes
This is the year the telephone industry changed forever. Most of this change is the result of a Congressional mandate for cell phone companies to allow people to change companies and keep their existing number. This is a huge change which will spur competition primarily but secondarily could end the demand for more area codes, (the subject of my very first essay on this web site).
Meanwhile, there were major battles being fought in the long distance wars. Telecom USA, which most people don't know is a division of MCI, launched a new plan with 10-10-987 which boasts 39 cents a call and 3 cents for each minute. This is probably the cheapest plan out there for individual calls, unless your call is under 5 minutes. Then you are better off using another Telecom USA program 10-10-321 which they do not bother advertising anymore, but is still available. I use it to send fax's long distance for cheap.
The chart above compares cost per call for four long distance plans that do not require a monthly fee depending on call lengths. Notice that the length of the call can result in different price savings, but trying to determine which one is cheaper is very difficult and confusing.
The current battles over long distance will be dwarfed by the soon to be epic battles over cell phone plans, which are really just getting started. Now that people have the ability to move to other companies and keep their old phone and number, the competition will no doubt get much fiercer. They will spew out some really cheap sounding plans that in reality are not that cheap after all the fees you don't know about are tacked on. Like the above chart, the cheapest plan is going to vary from person to person depending on how they use their cell phone.
Another huge change this year was the creation of a national no call list. Many telemarketers cried foul as over 30 million people made their phone numbers off limits to telemarketing, but I believe the telemarketers are mistaken in their assessment. In reality, 30 million people who will never ever buy anything from a telemarketer have identified themselves as such, which should in theory make it easier for them to make sales to people that are likely to buy.
5. Proofs that May or May Not be Proofs
I'll finish with news from the world of pure mathematics. Keith Devlin wrote an interesting short piece for Discover magazine called "2003: Mathematicians Face Uncertainty".
This year three "proofs" were offered for famous unproven conjectures. One is a proof of the twin primes conjecture, which was widely accepted as complete until flaws were found. The jury is still deliberating but leaning towards accepting two others, a proof of the Poincaré Conjecture in Topology and a proof of Kepler's "cannon ball" conjecture. "What all three episodes reflect," writes Devlin, "is the complexity and abstraction of many modern proofs. Even experts find it almost impossible to be sure some arguments are correct."
This forces the Mathematical community to question the very nature of proof itself. Devlin Writes:
"So what is proof? There are two very different answers. One answer, which I will call the right-wing definition, is that proof is a logically correct argument that establishes the truth of a given statement. The other answer, the left-wing definition, is that a proof is an argument that convinces a typical mathematician.
"The right-wing concept of a proof is valid in the idealistic sense. The problem is that, except for trivial cases, it is not clear anyone has ever seen such a thing. ... The right-wing definition of a mathematical proof as an unrealistic ideal, unattainable in the real world. Actual mathematical proofs are all left wing. An argument becomes a proof when the mathematical community agrees it is such." - op. cit.
Ultimately, what these events demonstrate is that even pure mathematics, regarded by many to exist independent of humanity is still ultimately a human endeavor bound by human understanding.