Switching to three decimals on the timer?

Nukoca

Veteran
Joined
Mar 11, 2009
Messages
414
Location
United States of America
Do you think that eventually the time people are getting will get so close that we'll need to switch to a timer that goes up to thousandths of a second?

There was that time when Yu Nakajima got 8.72 seconds twice.. there was probably a difference in the two times, however small they were.
 
Last edited:
A hundredth is probably enough. Then even your time to put down the puzzle will affect everything. It won't be fair to beat someone by a milisecond. It's bad enough to get beaten by 0.01
 
People are getting close times, but if you lose to some one by like a millisecond, it just encourages you to get better
 
Everyone seems to think 1/100 sec is a millisecond. I don't know why. It is surprisingly rare to see people talk about centiseconds.

Anyway I think all real puzzles have too much randomness to make timing to the nearest thousandth worthwhile. Because luck is always involved, I don't really see much of a reason to introduce thousandths - pretty much nobody is beating record by a few hundredths anyway. I wouldn't be opposed to including the thousandth decimal point in averages of 5 or means of 3, though (for instance: 15.01 (12.28) 15.02 15.04 (16.85) would be 15.023, not just 15.02), because rounding it to the nearest hundredth is actually getting rid of a little bit of data.

As for non-random events such as Magic or Master Magic, though, keeping track of thousandths might be a good idea. The same is true for non-random timed events in other sports, such as the 100m dash. If a hundredth of a second (the limit of current timing) can be an important difference, it means we're not being precise enough.
 
qq: significant figures? you can't be MORE precise than the timer =P so the millisecond part shld be rounded off. speaking of which I always lose marks in tests/quizzes/exams because significant figures....
 
qq: significant figures? you can't be MORE precise than the timer =P so the millisecond part shld be rounded off. speaking of which I always lose marks in tests/quizzes/exams because significant figures....

It's a lot more complicated than that. Here's why.

The way sigfigs are *supposed* to work (what they teach you in school) is that every measurement has an associated "error", which is basically the distance that the actual measurement is expected to be from the measurement you got. The implication is that when you give a specific number of digits you are saying that the error is a certain constant times the size of the smallest digit you gave. With the significant figures they teach you in middle and/or high school, you're taught that the number of significant figures doesn't change when you add things together, but one thing they might not tell you is that when you divide by a constant integer you can sometimes get more digits out of it. For instance if you have a measurement of 4.3 and you divide by exactly 10, it's okay to give 0.43, because dividing by 10 makes your measurement 10 times more accurate (as long as it is EXACTLY 10 and not something you measured to be 10). When you're taking an average of 5 or mean of 3, and you divide by 3, technically the best way to give the quotient would be 0.14 + 1/300. In real life it's okay to give an extra digit as long as people understand it only has 3 possible values (namely 0, 3, and 7). You actually can get more accurate numbers from taking an average than from a single measurement, because adding up the numbers doesn't change the number of digits you have, and then dividing by (say) 10 will give you a more accurate result and thus more digits.

Here's the thing - that isn't at all the whole story In more advanced scientific study, you have to explicitly give the error for every number you use. For instance, if you measure something to the nearest hundredth, the error is (believe it or not) 0.005/sqrt(12). But the error can be any nonnegative real number, so it's not okay to just give the right number of digits.

Now when you do operations on numbers that have associated errors, you also have to do the operations on the errors. When you add together two numbers with errors e1 and e2, the error of the sum is sqrt(e1^2 + e2^2) (really!). Adding N numbers with the same error will actually multiply that error by sqrt(N). When you divide two numbers it gets much more complicated, but if you divide a number by a constant (like 10) the error gets divided by that constant. So when you take the mean of N numbers, you add them up (multiplying the error by sqrt(N)) and divide by N (dividing the error by N), so the error you end up with is the original error divided by sqrt(N). As weird as it may sound, this means that the mean actually is more accurate than the original measured values. When you take an average of 100, for instance, the error is 1/10 of the original error - so even by the standards of scientific research, it's OK to add another decimal and still get a number that is not "too accurate".

My approach is to only take the mean value - what do I mean by that? When you measure (say) an 18.34, you actually might've measured any time from 18.335 to 18.345, but the accuracy isn't important, just the number that pops out. Every number is a mean value +- an error, and the mean values work just like normal numbers when you do arithmetic. So if you take the average of ten numbers you might end up with a mean value of (say) 17.396... but as it turns out the error is actually midway between the traditional error of a reported 17.40 and 17.396. If you don't give an error explicitly, you're going to be either over- or under-estimating the error no matter how many digits you give.

The point of all this is that the "significant figures" stuff you've learned does not give you the whole story, and in real life it is significantly more complicated, because research has higher standards of accuracy. Unless you're willing to report the error along with every time, I think the best practice is to give as many digits as are available - giving the mean value. It is possible that the error is so large as to make the last digit or two irrelevant, but in my opinion it's better to give it (and let the person who looks at the data disregard it if they think the error is so big it doesn't matter) rather than to decide yourself that it's irrelevant and not give other people the chance to see it.
 
Back
Top