What is the largest meaningful number?

Despite having more numbers than atoms in the universe, trying to prove that your integer is bigger than anyone else's integer has continued through the centuries. The biggest number referred to regularly is a googolplex (10googol), which works out as 1010 ^ 100.

metro.co.uk - Are we running out of numbers? - Metro UK

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The future really can be explained

It may be the answer for everything but we don’t think it’s the highest number you can think of (Illustration: Ella Byworth for Metro.co.uk)

What’s the biggest number you can think of?

A billion? A trillion? A quadrillion? A sextillion? A tredecillion? A googol? A googolplex?

There’s a schoolyard joke about infinity+1 being the largest number in existence.

The problem is that infinity+1 still equals infinity.

Infinityinfinity? Still infinity.

A bigger problem still is that infinity isn’t a number, it’s a concept.

And is it the biggest number you’re trying to think of or is just the name for the biggest number?

In Ancient Greece, mathematician Archimedes theorised that the biggest number we would ever need would be the total grains of sand in the Universe. Big numbers are represented in powers so 104 (sometimes displayed as 10^4) is 10x10x10x10 or 10,000 and this power kept increasing until Archimedes found his number.

The higher the factor, the bigger the number

He wasn’t one for small challenges and set the number at (108)8 or 1064. Despite his view that no bigger number would ever be needed, he kept multiplying and multiplying until he reached what has become known as the Beast number, (108^108)10^8

That’s one followed by 80 quadrillion zeros.

As a guide, there are said to be somewhere between 1078 and 1082 atoms in the observable universe, which is a tredecillion (1078) or just above. The number of atoms in the universe is not even 0.1% of the Beast number. Despite having more numbers than atoms in the universe, trying to prove that your integer is bigger than anyone else’s integer has continued through the centuries. The biggest number referred to regularly is a googolplex (10googol), which works out as 1010^100. To show how ridiculous that number is, mathematician Wolfgang H Nitsche started releasing editions of a book trying to write it down. It took him 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 (just under a sexdecillion) volumes of the book to fully portray the number of zeros. But he did it (though we assume he had a lot of automated help, we have asked). Even then, there is a bigger number that nobody knows the value of: Graham’s number holds the Guinness World Record for the biggest specific integer used in a published mathematical proof. It is to solve a problem in Ramsey theory around an n-dimensional hypercube (if you even understand that tiny piece of the theory, you’re doing better than us). Graham’s number is divisible by 3 and ends in a 7, its last 12 digits are 262464195387 but it can’t be expressed in a standard way and is too big to be worked out in full. But the issue with any of these numbers is that they’re not ‘sanctioned’ nor really that useful in everyday mathematics or measurement. The big conversation is around what ‘useful’ numbers should be called and who should be in charge of naming them. The name for the googol (10100) was first dreamt up by a nine-year-old nephew of a mathematician a century ago. ‘You can make up any names you like but the official ones are sanctioned under what we call the metre convention,’ Dr Richard Brown, head of metrology at NPL, the UK’s National Measurement Institute, tells Metro.co.uk.

‘That’s an intergovernmental treaty where member states agree on units.’

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The International Committee For Weights And Measures (CIPM) meets once every four years and is responsible for what the definite answer is to questions like ‘how much does a kilogram weigh?’

The definition of a kilogram was actually tweaked at the last summit.

The bigger numbers are used in maths but CIPM is more focused on real-world uses: The International System Of Measurements recognises kilo (1,000), mega (1m), giga (1bn), tera (1tn), peta(1015), exa (1018), zetta (1021) and yotta (1024) as prefixes. These prefixes can be used before any measurement – kilometre, megametre for example – but most understand them from the bytes of computing (megabyte, gigabyte).

And, Dr Brown believes, we might need something bigger:

‘The advent of things like quantum computing will soon move us to a stage where we need something that’s above a yottabyte. ‘Historically these things go up in ten to the power of three, so the next will be 10 to the power of 27.’ There are already many names travelling the internet for what this new prefix might be:

Xenottabyte? Shilentnobyte? Domegemegrottebyte? Brontobyte? Geobyte?

They’re all genuine suggestions.

A student in California suggested ‘hella’ in 2010 as the prefix for 1027 and got thousands of signatures for an online petition but this, nor any of the others above, have ever made it to the CIPM Dr Brown, on the other hand, already has a white paper submitted, waiting for discussion. Using the Greek and Latin works for nine (ennea, novem) and 10 (deka, decem) for inspiration, he worked his way backwards in the alphabet (zetta, yotta to come to letters that hadn’t been used yet

Ronna – to represent 10 27 or 1000 9

or 1000 Quecca – to represent 1030 or 100010

Dr Brown says this is just the start of the discussion around how we define bigger numbers. And it’s not just a conversation about what to the call them but what needing prefixes for bigger values means for everyday life. Big data strategist Paul Sonderegger has called this whole debate the ‘whateverbyte problem’ and sees it as irrelevant compared to the real issue: ‘Not only do we lack a name for that volume of data, we don’t know how to talk about its consequences,’ Sonderegger told Forbes. It’s estimated, as discussed earlier in the Future Of Everything series, that a brain’s size is up to 2.5 petabytes. If that’s the case, a single yottabyte has enough memory for around 400m brains. A single ronnabyte, or whatever it is finally called, would have space for around 4bn brains. A single queccabyte would have more than enough space for the entire knowledge of every person who has ever been born. ‘A yottabyte (1024) is still a huge measurement but it is still finite and we deal with practical measurement, not theoretical maths,’ Dr Brown says.

‘We’re always constrained by the size of things we can measure.

‘We’re never going to deal with things as big as Beast numbers or googols or stuff like that.’ While the etta/yotta/whatever debate is often around bytes, the CIPM doesn’t actually recognise the byte as a physical measurement as it doesn’t have a size.

‘It actually sits outside the International System of Units,’ Dr Brown says.

‘It’s obviously something we should consider because people in the area of computing are using our prefixes and we have to bear that in mind.

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‘But bits and bytes are not physical units but mathematical entities.’

Scientists, on the other hand, are more concerned with what the numbers do rather than worrying about what they are called: ‘I don’t know anyone who has used a googolplex,’ Dr Simon Foster, solar physicist at Imperial College, London, tells Metro.co.uk ‘My colleagues looking at the scale of the universe have never had a problem with numbers.

‘People simulating galaxies are not worried about running out of numbers.

‘How we communicate our science might eventually become an issue but it’s not a problem for the actual science.’ Rather than working our way towards infinitely big, Dr Foster thinks that experts would be better looking toward smaller and smaller numbers: ‘For quantum, it’s actually going the other way, with tiny numbers – pico (10-12) and nano (10-9) are useful as shorthand,’ he says. A negative factor means you divide rather than multiply so 10-3 (or 10^-3) would be 1/10/10/10 or 0.001.

But all these numbers have been around for a while.

If the new terms for 1027 (ronna) and 1030 (quecca) are adopted, they will be the first new prefixes since 1991. The next opportunity would be the meeting in 2022 but De Brown thinks 2026 is more realistic. ‘You don’t want to make changes that no one will use, you want to make sure that it’s right,’ he says. ‘A lot of interest is around the names of the prefixes but the bigger decision is: do you need to expand the system at all?’ If it ever does pass the rigorous tests, Dr Brown already has the name for 1033 up his sleeve: Bundecca, based on the Latin for 11, undecim.

B is the last letter not used as a prefix.

After that, we’re out of letters.

But are we really running out of numbers?

In coding, you really can run out.

If you use computer programming language JavaScript, the largest integer you can safely use on a 64-bit system is said to be 253-1, or 9,007,199,254,740,991.

Everything above that can be displayed as infinity.

In the real world, the names for numbers might be running out but numbers are infinite, despite what the schoolyard jokes about infinity +1 tell you. While mathematicians have developed theories around infinity and addition, until those are more widely agreed, we won’t run out of numbers, just names for them. The Future Of Everything This piece is part of Metro.co.uk's series The Future Of Everything. From OBEs to CEOs, professors to futurologists, economists to social theorists, politicians to multi-award winning academics, we think we had the future covered, away from the doom-mongering or easy Minority Report references. Every week, we explained what's likely (or not likely) to happen. Talk to us using the hashtag #futureofeverything. Though the series is no longer weekly, if you think we might have missed something vital to the future, get in touch: hey@metro.co.uk or Alex.Hudson@metro.co.uk Read every Future Of Everything story

metro.co.uk - Are we running out of numbers? - Metro UK

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