# Throttled

Ewelina and I got throttled this month.

Not physically, but digitally, by our ISP - we reached our download limit of 40GB and so for the past few days our Internets have been very, very slooooooooooooooow.

This is annoying. I would switch ISPs, if they didn't all do the same thing. But as far as I know, there is no option in this silly country.

...

Update: My initial math was wrong. I fixed it.

Being throttled prompted another realization about why the Cloud being hyped as "more reliable" is just a load of marketing bunk. The argument goes something like this:

Consider the following events:

``````L = Laptop breaks
I = Internet breaks
C = Cloud service breaks
``````

L, I and C are all unrelated events, and since any one of these events is sufficient to keep our hypthetical user from getting anything done, we can calculate his odds of being interrupted as follows:

``````P(X) = 1 - (1 - P(L)) * (1 - P(I)) * (1 - P(C))
= 1 - (1 - P(I) - P(L) + P(L)P(I)) * (1 - P(C))
...
= P(I)+P(L)+P(C) - (P(L)P(I)+P(L)P(C)+P(I)P(C)) + P(L)P(I)P(C)
``````

(This is the odds that any of the events happens summed, minus the odds that any two overlap, plus the odds that all happen at once.)

The odds that a normal PC user cannot work are simply `P(L)` or, if he depends heavily on the internet, `P(L) + P(I) - P(L)P(I)` 1).

Now... no matter what the odds of each event, we know they are all non-zero. So we can reason as follows:

``````    P(L) < P(L) + P(I) - P(L)P(I)
=== 0 < P(I) - P(L)P(I)
=== P(L)P(I) < P(I)
=== P(L) < 1
``````

This final statement is true unless his laptop is already broken, which proves the rather obvious statement that depending on both the Internet and his laptop will be more error prone than depending on the laptop alone.

So... does the math magically do something different when we add the Cloud? Unfortunately, doing the math for the full statement above is tedious and really doesn't fit on my screen.

However! We've proven that depending on the Laptop and the Internet is less reliable than depending on just the Laptop. So let's restate the Cloud case as ((Laptop or Internet breaks) or (Cloud breaks)) and compare that with the case of just the (Laptop or Internet) breaking:

``````    P(LI) < P(LI) + P(C) - P(LI)P(C)
=== 0 < P(C) - P(LI)P(C)
=== P(LI)P(C) < P(C)
=== P(LI) < 1
``````

Which just happens to be the same reasoning as above - and it is also trivially true unless our poor user's Laptop or Internet are already broken.

So, to sum up: if your Laptop or Internet are already broken, the Cloud cannot possibly make things less worse. Otherwise, it will.

Tah dah!

EAT MY SCIENCE, CLOUD! You suck! :-P

...

Or, to put it another way, GMail is very annoying to use when my Internet connection is throttled... but my local Mailpile stays fast.

1) The case can actually be made that for many users the odds of being unable to work are more like `P(L) + P(W)/(1-P(I)) - P(L)P(W)/(1-P(I))` where W is the event "user wastes time on the Internet" and a flakey Internet connection is therefore good for productivity. But that is a somewhat different story.

Tags: life, tech