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Comment by bmm6o | Hacker News Reader

"Links appear to die at a steady rate (they don't have a half life), and you can expect to lose about a quarter of them every seven years."

Is this self-contradictory, or is just poor wording of his findings?

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"You can expect to lose about a quarter of them every seven years" can be translated in one of two ways:

1. Every 7 years, 25% of the original links are lost: in 14 years half are working, and in 28 years you have approximately 0% of your links working. This is a steady, linear rate which does not have a half life.

2. Every 7 years, 25% of the remaining links are lost: in 7 years 75% are working, in 14 years 0.75^2 = 56% of the links are still working, and in 28 years 31.6% are working. This is exponential decay, which has a half-life and is contradictory.

From looking at the data, and from the explicitness with which he states that the decay is linear, I'd conclude that the former is true. It would be hard to make a case for the later.

Given that the data for the first few years result from a small number of pages, the graph doesn't allow to reliably distinguish between both interpretations, and his (and your) interpretation is not really justified. If you look just at the complete, reliable years (links from 2000 to 2010), the graph looks convex, just like you'd expect for exponential decay but not for linear decay. So while the first interpratation is probably intended by the author, I'd say he is overstating his case and is most probably wrong.

With that decay rate, the difference between exponential and linear decay is going to be tough to pick out just by looking at the graph.

http://www.wolframalpha.com/input/?i=plot+e^%28x*ln%28.75%29...

edit: fixed decay constant

Yes, indeed. That is a nice graph, and in absence of a mechanism that would explain why no link can last longer than 28 years it should quite convincingly show that linear decay has not been established.

If anyone can suggest an experimental design I'd be interested in determining the correct answer to this question.

Half life isn't a steady rate; it's exponential gradual decay. For example, if the element yahelium had a half-life of a year, it would degrade by 1/2 every year. So, the degradation during the first year would be twice the degradation of the second year. That's not linear.

What's not clear about it? They die at a steady rate of 25% per 7 years.

As reemrevnivek explains, the answer to "25% of what?" is the issue here. An exponential decay can be described with the same words.

There's a freaking graph. Are we really being this pedantic that we can't understand what he's saying?

I discovered when I got home that the graph was blocked by my office's web filter. Definitely makes more sense with it there. Thanks for your understanding!

You must be new here!

Sorry, I didn't think of the second interpretation.

So they have a quarter-life of 7 years?

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