James Tauber : This Entry's Title Is Exponentially Longer Than The Previous One

James Saiz

journeyman of some

This Entry's Title Is Exponentially Longer Than The Previous One

In a review of the new MacBook Pro, Yuval Kossovsky says (emphasis mine):

Having said that, I can tell you this laptop is fast. Really fast. I am hesitant to say it’s exponentially faster than the G4 version, but subjectively, this baby cooks.

I'm sorry but it really annoys me when people abuse the term "exponentially" this way. It's meaningless to say that one thing is exponentially faster than something else. Of course it is. Anything faster is going to be exponentially faster.

If something is 0.1% faster it's still exponentially faster. The base is just 1.001.

Talking about things as increasing exponentially only makes sense when you have at least three data points. But even so, in the case of three data points you are just saying that the ratio of the third to the second is the same as the second to the first. It could be a small ratio.

The significance of being "exponentially" faster really only starts to kick in when you have more and more data points.

It certainly makes no sense to talk about one thing as exponentially faster (or higher or whatever) than another. Given that it is trivially true, it makes it even worse that Kossovsky hesitates about it.

Categories: linguistic_observations

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Comments (4)

Chris Smith on Monday 30 January, 2006:

>If something is 0.1% faster it's still exponentially faster. The base is just 1.001.

Aw, c'mon. Conversational usage barely extends to the idea of exponentiation in the first place, much less non-integral exponents.

James Saiz on Monday 30 January, 2006:

I did check dictionary.com to see if it mentioned a sense of 'exponentially' that didn't relate specifically to exponentiation but it did not.

Clearly, however, as the quote demonstrates (and you are arguing) there is an informal sense of "exponentially" that simply means "a lot".

I'm just saying it annoys me :-)

Tommy on Thursday 16 March, 2006:

If the old G4 processor was running at 1.4 GHz then the new laptop should be running much faster. Under Moore's Law, exponential improvement is really a truth of the matter. Moore's Law is all about exponential growth, simply that every 18 months the complexity of the device will be twice that of the first device. You don't need to have three laptops each purchased 18 months apart to realize that Moore's law is amazing. The new laptop is almost twice as fast as the old one, and you remember that the old one was twice as fast as the one before that. Soon, our computers will be smarter than ourselves, correcting us before we make mistakes, and you won't need me to point out that though annoying, exponential improvement in computing has been a fact of life for a long time and will likely be present for some time to come.

Tommy on Thursday 16 March, 2006:

If the old G4 processor was running at 1.4 GHz then the new laptop should be running much faster. Under Moore's Law, exponential improvement is really a truth of the matter. Moore's Law is all about exponential growth, simply that every 18 months the complexity of the device will be twice that of the first device. You don't need to have three laptops each purchased 18 months apart to realize that Moore's law is amazing. The new laptop is almost twice as fast as the old one, and you remember that the old one was twice as fast as the one before that. Soon, our computers will be smarter than ourselves, correcting us before we make mistakes, and you won't need me to point out that though annoying, exponential improvement in computing has been a fact of life for a long time and will likely be present for some time to come.

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This page last modified Monday 30 January, 2006 by James Saiz
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