How high can Google count? Very high it turns out but there is a limit.
Using the Google search box as a calculator, Google’s ceiling appears to be 2.00135558564^1023, which Google says equals 1.79769313 × 10^308.
Try 3^1023 and you get the search results page instead of a calculated result. The same holds true for 2^1024.
Increasing the number to 2.001355585641^1023 results in the same total, 1.79769313 × 10^308. So that appears to be where Google stops calculating.
Does that mean anything?
Not to me and probably not to anyone else, apart from a few computer scientists… but knowing that Google has a limit is somehow comforting.
If you want to find out all the latest news on tech why not subscribe to our RSS feed?
Thats the maximum size for a 32-bit Double precision floating point.
I imagine, since Google uses 64-bit systems, that their limit is much much higher, however I don’t feel like siting down and figuring out the maximum size for a say 16-byte double…
It’s not just a Google limit, 1.7976931348623157×10^308 is the highest possible value you can have for a 64-bit floating point under the IEEE 754 Standard (which almost everybody uses).
You can learn more about it here.
[...] Mathematical Limit Google’s Mathematical Limit How high can Google count? Very high it turns out but there is a limit.[offbeat news] [news] [world [...]
@Daniel:
32-bit double is an oxymoron. A ‘double’ is 64-bit. a float is 32-bit.
Btw, x86 processors that have FPUs can use 64-bit floating point numbers. So a ‘64-bit processor’ give it no advantage. The 64 in 64-bit processor refers to the size of the general purpose registers, not the floating point registers.
[...] Mathematical Limit Filed under: Uncategorized — recar @ 4:07 am Google’s Mathematical Limit How high can Google count? Very high it turns out but there is a limit.[offbeat news] [news] [world [...]
yeah.. what those smartguys said
As nanotechnology and molecular manufacturing evolve all the current limits in computing will cease to exist.
Sounds like someone was bored!
Assuming it can round down, which would explain why 2.001355585641^1023 got the same answer I got 2.001355585648338708999^1023 9’s repeating as the highest calculatable number, but that might be false too I didnt check my answer
More than a googol, but I was kinda hoping it would be a googolplex.
If they were using 64bit systems they could get a 128 quad precision (http://en.wikipedia.org/wiki/Quad_precision)
Interesting as well, the largest integer that Google will spit out is 4,398,046,511,104 = 2^42. Add one and you flip it over into floating point mode (for display, at least – see below). This is a bit surprising to me because it’s not a very natural boundary point – I’ve never heard of a compiler using 42 bit integers, have you? They must be doing 64 bit manipulations behind the scenes, but perhaps decided that anything over 2^42 was probably too large to care about displaying as an integer. Seems odd to me, though, I’d have thought the conversion would happen at the parse level, not the display level. After all, if you’re willing to display a 13 digit number fully, why not a 19 digit one?
Also interesting: 48 is the highest number k such that (2^k + 1) – 2^k = 1 according to Google’s calculator. I haven’t done the math; this might either be because they are using integers all the way up to 48 bits, or it may be that their floating point precision allows 1.0 to be resolved correctly all the way up to 48 bits (quick exercise that I’m not going to do right now: what would that tell us the FP precision is? 64, probably?). I could look more deeply into this, but it’s 3 AM here and I really should be doing some actual work…anyone know a sure-fire test to tell where the int/float cutoff is?
uhhhhhhh…
how about this googlers!
google calculater -> Life the universe and everything…. see what it says.
if you ask me… there is no limit since it can figure this out.
Why are people expressing this limit in terms of (2 + x)^1023? It’s quite clearly just anything approaching 2^1024. You can see this by adding together a string of 2^n + 2^(n-1) + 2^(n-2) + …. starting with 2^1023. With a little math, you’ll see that this approaches 2^1024. I tried it as far out as I was willing to bother, and google handled it everytime. So the answer is sum(n = 1023; n >= 0; n–) {2^n} –> 2^1024 – 1, or if you continue into negative exponentials, –> 2^1024.
Google may just use doubles for all internal calculations. If so they may have picked 2^42 as a cutoff for displaying integers as I believe that’s near the area where the first integer not representable as a double value is.
Interesting trivia: the x86 processor’s original floating point registers are actually 80 bits wide, and values are typically converted from and to 64-bit format on each load and store. So intermediate calculations can have precision higher than the results. Google is almost certainly using x86 processors, so I wonder if someone can come up with a Google calculation that reveals the presence of this extra intermediate precision? Or, the lack of it might indicate the use of other types of processors (or, more boringly, simply the use of other operating modes of x86…).
1 017) + (2^1 016) + (2^1 015) + (2^1 014) + (2^1 013) + (2^1 012) + (2^1 011) + (2^1 010) + (2^1 009) + (2^1 008) + (2^1 007) + (2^1 006) + (2^1 005) + (2^1 004) + (2^1 003) + (2^1 002) + (2^1 001) + (2^1 000) + (2^999) + (2^998) + (2^997) + (2^996) + (2^995) + (2^994) + (2^993) + (2^992) + (2^991) + (2^990) + (2^989) + (2^988) + (2^987) + (2^986) + (2^985) + (2^984) + (2^983) + (2^982) + (2^981) + (2^980) + (2^979) + (2^978) + (2^977) + (2^976) + (2^975) + (2^974) + (2^973) + (2^972) + (2^971) = 1.79769313 × 10308
OK now that we have discovered the highest possible number that google can count to –
Has anyone discovered the lowest possible number ?
rofl, ditto.
Haha! So it’s true, there’s no such thing as infinity. The universe’s largest number is 2.00135558564^1023
Our universe just got smaller….
I thought 42 was the ultimate answer to the life, universe and everything. No wonder they are using it.
(2^k + 1) – 2^k = 1
Surely, mathematically, the brackets in that are redundant since it’s an addition (of a negative number) not a multiplication? And any number k satisfies that, since it cancels algebraically too.
Or do I misunderstand you?
tite you are a nerd if you can figer out this shit
[...] template How high can Google count? Very high it turns out but there is a limit. scooby doo pronread more | digg [...]
That’s the best use of the word ‘figer’ I’ve ever seen. Fumbs up from me.
TRY THIS,
1.9^1024 and you will see the response is simply its value, i.e. = 2.77771303 × 10^285.
You wont find any search results !
You have forgot the lower limit, which is -1.79769313 x 10^308.
Looks like I am not the only one that’s bore.
10^308.2547155599167183999 round to 10^308.2547155599167184.
Note it cannot computer the 4, so the value will be 9 recurring, so we can assume it is less than the 4.
Maths:
2^x=10^308.2547155599167184
xlog 2=log (10^308.2547155599167184)
x=log (10^308.2547155599167184)/log 2
x=1024, therefore:
-2^1024
I think the interesting part, google makes this job unknown so we dont know exactly what is happening.. if google is counting or not.. is nofollow links work for someting or not.. so there is always a hope
can anyone solve z(z+1) over 10(z-7)
[...] read more | digg story [...]
[...] Others have found limits with Google’s calculator. For example, 2.00135558564^1023 is interpreted by Google’s calculator as 1.79769313 x 10^308. But increase that number by one eensy tiny amount to 2.00135558565^1023, and Google interprets it as a search, not a math problem. [...]