Wow! Reading Bambi Francisco’s CBS MarketWatch article, I see that Google chose to raise $2,718,281,828 in their IPO. Why such an irrational (wink, wink) number?
It turns out that 2.718281828… (…and an infinite number of digits after that) is ‘e’, the base of the natural logarithm. Because it can’t be expressed as a ratio of two numbers, it’s known mathematically as “irrational” — something some bankers might say about the way Google is going public. However, ‘e’ also happens to be “transcendental,” another fancy property of a number that means it can’t be expressed by a finite number of algebraic operations. Maybe Google is making a little wordplay — saying they expect to transcend expectations — to overcome or notably exceed ordinary limits.
Some more reading about ‘e’:
the constant e, at mathworld.wolfram.com
Ask Dr. Math: Why is "e" so important?
Ask Dr. Math: Compounding Interest and "e"
e: The Story of a Number, a book by Eli Maor
Comments (19)
I have “e” on my financial calculater (the venerable HP 12c).
It’s a big factor in determining the value of an annuity based on compound interest. Hence the appropriateness for a financial transaction like an IPO.
In calculating interest: i=prt (interest is the principal times the rate times the number of terms)
If an annuity compounds monthly and the annual interest rate is nominally 12 percent then the interest (i) is the principal times the annual rate divided by the number of payments) times the number of payments.
E^x (e to the x) is a way of determining the “effective” interest rate that applies when the principal is continuously compounded.
Here’s a myth to start: It’s also the source of the letter “e” in front of e*Trade…
Not to mention eBay
The author of the above comment is mistaken (or at the very least confused his terminology).
If:
i = interest accrued over t terms (i.e. the effective interest)
p = principal amount
r = rate of interest per term (as a multiplier — i.e. 1.07 means 7% interest)
t = number of terms
Then:
i = p * (r^t)
If you like, you could call the number (r^t) the “effective interest” and give it the letter “e”, but it’s not at all the same as the number e.
Links of the day
Giants rip catcher A.J. Pierzynski. This is a shame. Why aren’t women paid as much as men? In this politically incorrect post, the author suggests a reason. A dangerous surplus of sons. Is Asia going to become the center…
Just thought I’d also note that the Googleplex also has a building titled e (right next door to pi).
Hi, Jacob!
Check the “Ask Dr. Math: Compounding Interest and ‘e’ ” and “The Number e as a Limit” links above. You can use ‘e’ to calculate the result of continuous compounding (compounding with zero interval) because (1+(1/n))^n approaches ‘e’ as n goes to infinity.
Since I am a graduate of the University of Cambridge (BA, MA (Cantab.) Pure & Applied Mathematics) I don’t need lessons from “Dr. Math” :)
The point I have obviously failed to make above is that there is no reason to assume an infinite number of compounded interest terms.
In finance you need to know the “effective interest” for a fixed (i.e. finite) period. It is completely meaningless to ascribe meaning to a number arrived at after waiting an infinite amount of time.
If you read Dan Miller’s comment again you’ll see that he was talking about valuing an annuity and not working out a geometric progression.
Forgive me for being a pedant here.
I suppose I can see why investment bankers would want to know a quick way to do approximate calculations using a calculator.
I just hope that my tax bill isn’t worked out using the exponential approximation rather than the proper way I noted above.
I hate approximations :)
Who says financiers don’t have a sense of humour?
Two examples, both from Thursday’s announcements about forthcoming IPOs. In the first, Google announced that it was intending to raise $2,718,281,828 as a result of floating. 2.718281828 is, of course, the first 10 significant digits of the irrational …
http://24fridays.com/mt/archives/000721.html
The IPO value of google is “e” times one billion. That is awsome. [via]…
Google seeking to raise $e*10^9 via IPO
[via kottke] Peter Kaminski points out that Google set their IPO target at $2,718,281,828, which is the natural log value, “e.” Hi-freakin-larious. Who needs i-bankers to pull valuations out of the air when you’ve got a Googleplex of phd’s who can do i…
I’d like to take a turn at being pedantic. “I’m an incurable nitpick,” as somebody once said.
The original article is incorrect on one point and misleading on another. The number e can certainly be expressed as the ratio of two numbers, but at least one of these numbers must not be an -integer-. An irrational number is one that cannot be expressed as the ratio of two -integers-. Every number is equal to itself over 1.
“Trancendental” means that the number is not the root of a polynomial with integer (equivalently, rational) coefficients. (A number that is is called “algebraic.”) For example, the square roots of 2 and 3 are irrational, but they are not transcendental, because they are solutions to the equations x^2 – 2 = 0 and x^2 – 3 = 0, respectively. I’m not saying the author of the original post is incorrect, but what he says seems too unclear to be of much help in understanding the concept correctly.
I don’t know that irrational or even transcendental qualify as “fancy” properties. In set-theoretic terms, there are many “more” transcendental numbers than rational ones; the rational numbers are countable, as are the algebraic ones, in fact, but real numbers are not. Most real numbers are not algebraic.
Google Raising e*10^9
Peter Kaminski points out the previously unnoticed fact that the amount Google is raising in their IPO is a multiple…
Google Evil=3, Google Not Evil=4
How could a company that chose ‘e’ times 1 billion as the amount to raise prior to their IPO be Evil? There’s just too much geekiness inherent in that act, particularly when one considers the properties of ‘e’: 1)…
Irrational and Transcendental
Ever wonder how Google came up with its market valuation? It’s e-z! Take a look. Hat tip: Greg.org via Kottke….
Google is Full of Math Geeks
You can tell they’re a nerdy company when the amount of money they decided to raise in their IPO is the mathematical constant “e” times one billion. Very nerdy, indeed….
Peter Kaminski: Irrational? Transcendental!
Peter Kaminski: Irrational? Transcendental!…
Infinitely nerdy
Jesus, this is sooo nerdy: Google wants to raise the 1.000.000.000th of e (Euler’s number; the base of the natural logarithm). Via Kottke’s remaindered links….
I Heart Google
A string of recent moves by Google has solidified its place in my heart as the go-to company for innovating…
Is the sum of a rational and irrational number always irrational? What is the proof?(if true)