## Posts tagged ‘curve’

### Exponentially Smarter, Literally

To show my sons what Siri can do, I asked her (it?) the following question:

What is 6 + 4?

Siri told me, “The answer is 10.” But she also provided a bunch of other information pulled from Wolfram Alpha, including the following data:

This data appears to be taken from dissertation research by B. A. Fierman which was furthered by psychologist Mark H. Ashcraft. What it shows is that we get exponentially smarter — or at least faster at calculating — as we get older.

According to Excel, this data can be modeled exponentially by *y* = 8.36 · *e*^{–0.129x}, though this model has obvious limitations. For example, it implies that a one-year-old would be able compute this sum in 7.35 seconds, yet I know no one-year-old who understands addition. Further, it claims that it would take me 0.03 seconds to compute the sum, but I would argue first that I don’t compute the sum, I merely recall it; and second, my reaction time when asked for the sum would be greater than 0.03 seconds.

Playing around with the generic function *y* = *ab*^{x} + *c* using the world’s best graphing calculator from Desmos, I found a model that may approximate the data a little better:

*y* = 57 · 0.65^{x} + 0.9

With this model, it would take a one-year-old 37.95 seconds to compute sum. That’s still not reasonable for any one-year-old that I know, but at least the model says it would take me 0.9 seconds to recall the fact, a far more reasonable estimate than the 0.03 seconds given by the Excel model above.

Interestingly, How To Geek claims that Siri uses Wolfram Alpha for 25% of its searches. Yet if you ask Siri, “What is the meaning of life?” it will respond,

I can’t answer that right now, but give me some very long time to write a play in which nothing happens.

or

Try and be nice to people. Avoid eating fat. Read a good book every now and then, get some walking in, and try to live together in peace and harmony with people of all creeds and nations.

On the other hand, if you ask Wolfram Alpha, “What is the meaning of life?” it will respond,

42.

Proper.

All this talk of exponentials reminds me of a joke.

Q: How do you know that your dentist studied algebra?

A: She tells you that candy will lead to exponential decay.

Perhaps the most famous joke about exponentials is not one of which I’m terribly fond. I share it here only to honor my mission of providing math jokes to the world, not because I think any of you will enjoy it.

Several functions are sitting in a bar, bragging about how fast they go to zero at infinity. Suddenly, one hollers, “Look out! Derivation is coming!” All of the functions immediately cower under the table, but the exponential function sits calmly on the chair.

The derivation comes in, sees the exponential function, and says, “Don’t you fear me?”

“No, I’m

e,” says the exponential confidently.^{x}“That’s all well and good,” replies the derivation, “but who says I differentiate with respect to

x?”

### I Wanna Be Tangent to Your Curves, and Other Math Pick-Up Lines

Need help with chicks at the next math department mixer? Try a few of these…

I wish I were your derivative, so I could lie tangent to your curves.

I memorized the first 300 digits of π. If you gimme a chance, I bet I could memorize the first 7 digits of your phone number, too.

I wish I were your second derivative so I could investigate your concavities.

Hey baby, what’s your sine?

You’re a palindromic set of perfect squares: 36‑25‑36.

You are more fascinating than the Fundamental Theorem of Calculus.

I = { } when you’re not around.

I don’t like my current girlfriend. Mind if I do a you‑substitution?

Hey, baby… nice asymptote.

You may be out of my range, but I’d love to show you my domain.

I’ll take you to your limit if you show me your end behavior.

My love for you is a monotonically increasing.

I can take you to the limit as

x→ ∞.No way! Your name is really Leslie? Look, I can spell your name on my calculator!

Your beauty cannot be spanned by a finite basis of vectors.

You’ve got more curves than a triple integral.

**Warning: **The following pick-up lines contain material that may be unsuitable for minors.

I need a little help with my calculus… can you integrate my natural log?

I wish I were a problem set, because then I’d be really hard, and you’d be doing me on the desk.