Nothing comes from nothing; nothing ever will. – Oscar Hammerstein
Boy, is that lyric ever wrong. (Bonus points, if you can name the song without Googling it.)
Recently, I read Charles Seife intriguingly titled book, Zero: The Biography of a Dangerous Idea and while I know it was recommended to me, I
cannot recall who provided me with the recommendation. I thought it was Ron Baker, but no, he has not read it. So, in a sense, even this review comes from nothing.
In this short, but fun read, Seife traces the history of the zero from its humble beginnings as an idea, through its use as a placeholder, to its current status as the only number capable of destroying everything (including temporarily disabling the USS Yorktown on the high seas. The humble zero shook the foundations of philosophy, caused arguments, even wars, and now is beginning to play its part in understanding the very origins and substance of the universe.
While I highly recommend reading the book, I did extract a few nuggets for reading here.
First, there are at least three ways that we can prove that something comes from nothing or to express it mathematically that 0 = 1.
Let a = 1 and b = 1; therefore b = a.
b2 = ab, Premise 1
a2 =a2, Premise 2
a2 – b2 =a2 – ab, subtract premise 1 from premise 2
(a + b) (a – b) =a(a – b), Factor
a + b = a, Divide both sides by (a – b)
b = 0 Subtract a from both sides
Since a = 1 and b = a, therefore 0 = 1.
Let a = (1 – 1) + (1 – 1) + (1 – 1)… = 0
Let b = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1)… = 1
The ellipses in the previous two equations indicate the infinite repetition of the parenthetical express. Therefore the two are arithmetically the same, they are just grouped differently, therefore a = b, therefore 0 = 1.
Proof C: (hat tip to Joe Santoro)
00 = 1, therefore 0 = 1.
Why is this so important? Well, because if you can prove that 0 = 1, you can then prove that 0 = anything, certainly any number. For an example of this simply replace the 1 that leads the Proof B, let b example with any whole number, fraction, or decimal number. (By the way, there are an infinite number of decimal numbers between any two whole numbers.) In short, proving that 0 = 1 is the ultimate in understanding the idea of subjective value – value is what the customer says it is.
What is fascinating about the book was learning that some of the foundational mathematical concepts that we accept today are based on this idea that 0 = 1. Calculus is based on the idea than we can compute the area of an irregular object as long as we allow our estimations to set 0 = 1. Had this been explained in this manner to me back in high school or college perhaps I would not have dreaded the course so much. I equated calculating the area under a curve to torture. Theory is important.
One last idea I had while reading this book was to create a new formula (tongue in cheek of course) for computing value. Seife clearly points out that calculating speed in the old “A train leaves New York” type word problems is not always as simple as distance = rate times time. What train moves at an absolute constant speed? Any train would begin slowly, speed up, slow down around curves and crossings, etc. It does no good to calculate speed at a constant rate, i.e., 140 mph for 3.5 hours. What was required for mathematicians was a higher degree of understanding. They achieved this through Newton’s calculus. (Remember 0 = 1.)
An example would be calculating the velocity of a falling object, which falls at 32 feet per second per second. After one second, the object is falling at 32 feet per second after two seconds it is falling 96 feet per second and so on. This is expressed as v = gt2/2 where v is velocity, g the force of gravity and t is time. As Seife puts it, “Rate times time equals distance is not a universal law; it doesn’t apply under all conditions.”
Look at the last sentence again and replace the word distance with value. See where I am going. Imagine a formula for a professional firm using the “falling object” model (which, by the way, while still wrong, is less wrong than value = rate x hours). It would look something like this — value = rate x hours2/2. Picture explaining this to a customer, “Well we bill you $150 for the first hour, than $300 for the second, $675 for the third, etc., since we spent a total of ten hours on your matter, our bill comes to $7,500, any questions.”
Again, while still wrong, the above is less wrong. What is needed is for professionals to make the leap that 0 = 1 (that value is subjective). VeraSage has been sounding the alarm on this for years. Dare I say Ron Baker = Issac Newton.
We now have the math! Worshipers of the ABH give up! We have proven you wrong again, this time with your own beloved mathematical formulae.