Okay, I’ll rephrase my answer to read ‘the 1,339,724,852 completed census forms for the 2010 census of the PRC’.
Once upon a time, McDonald’s kept track of the exact total number of burgers served at all their outlets. (Or claimed to, anyway.) This number was prominently posted on the signs (scroll down for pic) at each store (rounded to millions, then later billions, but presumably they kept an exact count somewhere). At all their stores, these signs were updated periodically.
McDonald’s apparently eventually gave up on that.
When I was in chem class at college, I once sat down and counted out for myself how many atoms of [sup]12[/sup]Carbon are in exactly 12g of the stuff. It took me a few days. When I was done, I attempted to actually write down the number, but my pen ran out of ink.
I don’t think you have enough constraints…
If you include manufacturing, things like cigarettes or gum or something. But those are still sort of rough numbers.
If you are talking a single set of something large enough to require physical handling, and counted very accurately, what about coins?
The US mint alone, for instance, produces billions every year and I suspect the accuracy of counting exceeds most other items…
I would ask this guy.
30 million paper clips. I do not know how accurate the count is; whenever you are directly counting something one by one you are going to have errors.
Great.
There are lots of physics experiments where you individuality count photons one by one. Geiger counters count decay products that go through there tubes one by one. You don’t have to run an experiment for very long to get trillions of photons counted one by one.
The problem with counting very large quantities is that it’s difficult to postulate a situation in which it’s vital to know exactly how many there are. For example, in what situation would it be essential to determine that there were 31,287,989 of something instead of 31,287,988?
There is no substantive distinction between these examples. In the first the set is “Faces on Mt Rushmore” and in the second the set is “People in China”. There is no qualitative difference. The only difference is one of accuracy: because there are so many people in China, the count is not going to be accurate.
If there were about 1,339,724,852 faces on Mt Rushmore, then applying your further condition to your Mt Rushmore example would disqualify it. Once more you would be in a position where the set being counted would be (as you put it) “defined by the count”: there wouldn’t be exactly that many faces on Mt Rushmore, because you would miss a few.
You are hobbling your own question by attempting to exclude any count which might be inaccurate, which effectively limits the possible answers to those low enough to have a significant chance of being precise.
Yes, that’s exactly the sort of answers I’m interested in.
So something that was counted, and the count was accurate because it was verified in some manner? Pretty severe limits. If there were an alternative method to counting such weighing the items, it wouldn’t have made sense to count any significant number in the first place. And if they were weighed first they’d violate your rule about not defining the set. It has to be some low number which had to be counted twice, or more to verify the count.
I would venture that counting coinage would certainly rank up there in terms of being large numbers of physical objects counted accurately. If we wanted to apply some constraints so that the number had some meaning then we would use the Government Mint records of coins circulated in a particular time period. (We would not use all the coins counted by all the banks over a time period. This figure would have no real meaning and many coins would be counted more than once.)
However, I would hesitate to call it counting in the strictest sense. Coin counting machines measure the mass and divide by a known unit mass. The Mint would have a manufacturing run where the number of coins stamped from blanks is actually the result of a calculation. They would then (probably) adjust this figure by doing a count of coins rejected as not meeting standards.
I guess the whole question is one of definition as to what it means to count and how tightly one wants to apply constraints or define precision.
I’m sure this will be beaten, but to start off with something I think will fit the OP’s constraints: After VERY carefully defining what is and is not an island, there are 253 islands in Lake Winnipesaukee.
After very carefully defining what is a ship and what is merely a boat, On 12 October 2012 there were 283 ships in the world’s finest navy.
North Korea has that many ships?
For years I used to count my pennies by hand. At least 1400 each time I handed them into the bank. Unfortunately I don’t remember the exact amount.
There is an ongoing effort to catalog stars. Not just count them, but exactly locate them and measure what we can. So the one’s that have been “counted” (cataloged) are not only uniquely known, but often named. Carl Sagan used to famously state how many stars there are. But this may fail the OP’s criteria…no single person is looking through a telescope counting “1-star, 2-stars, etc.”
Counted individually, and then verified by a second count? Paper ballots in elections. Since the OP allows multiple counters, we can range from individual polling booths (several thousand) to full national elections (in the millions).
You can question the accuracy - but these are hand counted, watched by scrutineers from both parties, and frequently re-counted. I don’t know how you’re going to get anything more trustworthy as a hand-count.
Then your answer should stay at four. You can determine the presence of four objects by looking at them all at once without the need for a counting and recording system. For some people, this answer might be five or six.
Any larger number requires a system of counting and recording, and none of these systems are fool-proof. Human and mechanical error all make it impossible to be 100% certain.
Three! THREE STARS! Ah hahahahahahah!
50,000 items wouldn’t be counted one by one. They’d be split up into groups of some smaller where the count would be verified for each group, and then the total based of the number of groups, one of which may be smaller than the rest. I don’t think you have to go to single digits to get a verified count either. Dioptre may be onto something with paper ballots. Not every set of ballots counted produced an accurate result, but some of them must have. Identifying which ones and the counts will be difficult though. However, even in that case the counts may be based on subtotals.