Whether dealing with lost packets when using Wi-Fi, or getting your credit-card details securely to an online store, most consumer technology couldn't work without some ingenious solutions to common problems.
And when Google decides to change its search algorithm - as it did with Hummingbird last week, it can make or break whole companies.
Here are just five which you couldn't live without.
Pagerank – how Google calculates search resultsThe broad strokes of how Google's search algorithm works have been public for over fifteen years, though the exact way it organises search results remains the company's most closely guarded secret.
PageRank is the system at the heart of it all, and the key invention behind Google's rapid dominance of internet search. Ten years ago, when competitors relied on human-maintained indexes of webpages, it allowed the company to assess the value of websites automatically - a massive advantage as the web grew exponentially.
The algorithm works by looking at every link to and from every page on the internet. A link to a page is, in effect, a vote for that page's validity, because it means that someone thought that whatever was on that page was worth sharing. So the more inbound links a page has, the higher its PageRank is.
But then it adds a second measure: links from pages which have a high PageRank themselves confer a higher PageRank. So being linked to by Stanford, the Google creators' alma mater, is significantly more valuable than being linked to by Stanford's, the map shop.
On top of PageRank are myriad tweaks and adjustments to improve the results further. Some of those, such as the decision to punish 'link farms', vast networks of sites which link to each other in an effort to boost their PageRank , are directly connected to the core algorithm.
Others, like the company's attempts to leverage what it knows about users based on their previous searches to deliver personalised results, were bolted on later.
But as the demands we make of search have got ever more intensive, the company has been forced to adapt. The most recent update to the algorithm, Hummingbird is "a new engine built on both existing and new parts", according to Danny Sullivan of the search blog Search Engine Land.
Hummingbird was built to deal with the fact that increasing familiarity with search, as well as the rise of voice control, mean that we now ask Google actual questions, rather than just typing in relevant words.
In the future, new problems will require further tweaks, but the position of PageRank at the heart of it all seems secure.
Public key cryptography - keeping credit card data securePublic key cryptography is the name for a broad collection of algorithms which lie at the heart of nearly every form of security online. Using what is perhaps best described as 'magic maths', public key cryptography lets people encode data with a key which cannot then decode it.
If Alice has a piece of information which she needs to get to Bob without anyone else seeing it – maybe a credit card number which she's using to buy a computer with, or perhaps evidence of state wrongdoing which she's leaking to a national newspaper – she has to encrypt it.
Way back in history, the only way to do this would be to use a shared secret: a cipher which both Alice and Bob know, but no-one else does. That's how encryption all the way up to the second world war worked.
But the obvious problem is that Alice and Bob can't use open channels to agree on their cipher. That's fine if they can meet in person to swap codes, but less effective if Alice is a consumer and Bob a multinational corporation.
Public key cryptography means that Bob can tell the world his public key, and let them know that anything encoded with that will be readable by him and only him. Alice sees the public key, locks up her credit card data using it, and then sends that packet on the way.
Only Bob, using a second, private, key can decrypt the data and read the number.
Unfortunately, doing all of this every time is pretty hard on a computer's processor, so another step, where both Alice and Bob use their keys together to generate a shared secret, is frequently added in most practical uses of public key encryption. That shared secret can then be used in old-fashioned symmetrical ciphers. But it all comes back to the public and private keys.
Correcting errorsCDs are temperamental beasts. When they were introduced, they were hailed as being a resilient replacement for vinyl and cassettes, but as anyone who has tried to play a carelessly preserved album found in their car's glovebox can attest to, that's only half true.
Still, it could a lot worse. When you're storing data using microscopic pits on a sheet of metal covered with a thin layer of plastic, it's quite a feat to read every single pit correctly, a feat only compounded by later generations of optical media, which shrink the pits still further.
Error correction lies at the heart of that reliability, thanks to the use of a cunning algorithm which lets CDs be readable even with quite a lot of damage to the data stored on them.
In hugely simplified form, imagine the data on a CD as a grid of 1s and 0s. Like this:
101If there's an error reading the CD, one of those 0s may turn into a 1. Without error correction, there's no way to tell if that's happened, and no way to fix it.
The simplest way to correct errors is to add another load of data. Each row and column is counted up, and if there's an even number of 1s, another 1 is added on the end. If there isn't, a 0 is added instead:
1011Now, if one of the 0s is misread, the player can check with the error correction codes, and tell that there's been a mistake – and even, assuming there's not too much damage, what the real value should be.
Suppose the bottom right 0 is read as a 1: by reading the error correction code for that row, the player can tell that there's one too many 1s. It can then cross-check with the error correction codes for each column, and spot that there are also too many 1s in one column as well.
Now the player knows where the error is, and can carry on with those sweet tunes.
Error correction isn't just used by disc drives, though. Nearly every electronic device which gets data from one place to another will have some error correction on it, from WiFi to DSL. Even ISBN numbers on the back of books have error correction: the final digit serves the role.
Protecting passwordsSometimes, it's really important to check that the file you have been given is exactly the one you expected. Maybe you are worried it's been tampered with, or just want to check that a large download finished without corruption. One way to do that is to look at its hash.
There isn't really one algorithm which can be used to make 'hashes' of data: any process which can take information and spit out something which fulfils a few criteria will do.
A good cryptographic hash function will give the same output every time it's given the same input; the hash will change if the message changes; it would be nearly impossible to work backwards from the hash to the message; and it would be nearly impossible for two messages to have the same hashes.
But there's a much more important use for hashing data than just checking files: password protection.
As is painfully obvious these days, not many organisations can guarantee they won't lose your data. That's particularly problematic if it's your password they've lost, because — well, you don't have a different password for every service, do you?
These days, companies shouldn't be keeping passwords in plaintext at all. Instead, when a user types in their password for the first time, the site should hash the password, and only keep that.
Every time they come back to log in, it can take another hash, and compare it to the one on file. If they match, the password's correct. But now, if the site's hacked, the only thing which gets lost is a table full of hashes which can't be reverse engineered into passwords, so everyone is happy.
(Technically, site owners should be salting their hashes - an oh-so-cute term which means adding a little bit of extra data into the password hash to prevent it being reverse engineered.)
Perlin noise: generating landscapes in gamesGames are just big bags of algorithms. There's art, music, writing, direction, design and playtesting too, but a lot of algorithms.
Take procedurally generated terrain, the favoured way of filling in the vast expanses of games like Minecraft or Dwarf Fortress. It's not enough just to generate random noise, and apply it to a landscape, because if you do, you end up with something which is too random: all noise, no pattern. Instead, you want terrain which demonstrates the same fractal nature as the real world, with mountains, hills, boulders and pebbles all having effects on different scales.
That's what Perlin noise can do. It's a simple enough algorithm: generate some random noise at a load of different frequencies, smooth it out, and then add them together. But when you do, you go from this:
Or consider trying to get enemies to take an intelligent route through a map. The obvious way to do it is easy enough: consider every possible route, then take the shortest one from A to B. But that's so computationally intensive that it's unusable in most situations.
Instead algorithms like the A* search can be used.
How it works is tricky to explain (essentially, it finds a path by always taking the step where the number of steps already taken plus the number of steps in a straight line to the destination is lowest), but it is entrancing in action.
• In August 2011, a rogue algorithm lost its owners $440m on the stock market before it was eventually shut down.
This article originally appeared on guardian.co.uk