Estimating the amount of unique elements in a set and counting the amount of unique elements in a set are very different things. Cool method, bad headline.
They’re not very different things; the terms are used interchangeably in most contexts because in the real world all counting methods have some nonzero error rate.
We talk about ‘counting votes’ in elections, for example, yet when things are close we perform ‘recounts’ which we fully expect can produce slightly different numbers than the original count.
That means that vote counting is actually vote estimating, and recounting is just estimating with a tighter error bound.
I kind of think the mythology of the ‘countless stones’ (https://en.wikipedia.org/wiki/Countless_stones) is a sort of folk-reminder that you can never be too certain that you counted something right. Even something as big and solid and static as a standing stone.
The situations where counting is not estimating are limited to the mathematical, where you can assure yourself of exhaustively never missing any item or ever mistaking one thing’s identity for another’s.
> the terms are used interchangeably in most contexts
Counting and estimating are not used interchangeably in most contexts.
> because in the real world all counting methods have some nonzero error rate.
The possibility that the counting process may be defective does not make it an estimation.
> We talk about ‘counting votes’ in elections, for example, yet when things are close we perform ‘recounts’ which we fully expect can produce slightly different numbers than the original count.
We talk about counting votes in elections because votes are counted. The fact that the process isn't perfect is a defect; this does not make it estimation.
> That means that vote counting is actually vote estimating, and recounting is just estimating with a tighter error bound.
No. Exit polling is estimation. Vote counting is counting. Vote recounting is also counting, and does not necessarily impose a tighter error bound, nor necessarily derive a different number.
> The situations where counting is not estimating are limited to the mathematical, where you can assure yourself of exhaustively never missing any item or ever mistaking one thing’s identity for another’s.
So like, computers? Regardless, this is wrong. Estimating something and counting it are not the same thing. Estimation has uncertainty, counting may have error.
This is like saying addition estimates a sum because you might get it wrong. It's just not true.
True - for (relatively) small numbers. For large (huge) numbers estimation is usually considered to be equivalent to counting, and the result is sometimes represented using the "scientific" notation (i.e. "floating-point") rather than as an integer. For example, the mole is an integer whose value is only known approximately (and no one cares about the exact value anyway).
This doesn't justify estimation to be equivalent to counting even if some mathematicians consider them to be the same. Floating points are for estimation. Integers are for counting. The two are not the same, not even for large numbers.
Actually, my understanding is that it is an estimation because in the given context we don't know or cannot compute the true answer due to some kind of constraint (here memory or the size of |X|). An approximation is when we use a simplified or rounded version of an exact number that we actually know.
For someone who's pretty well-versed in English, but not a math-oriented computer scientist, this seems like a distinction without a difference. Please remedy my ignorance.
jameshart|1 year ago
We talk about ‘counting votes’ in elections, for example, yet when things are close we perform ‘recounts’ which we fully expect can produce slightly different numbers than the original count.
That means that vote counting is actually vote estimating, and recounting is just estimating with a tighter error bound.
I kind of think the mythology of the ‘countless stones’ (https://en.wikipedia.org/wiki/Countless_stones) is a sort of folk-reminder that you can never be too certain that you counted something right. Even something as big and solid and static as a standing stone.
The situations where counting is not estimating are limited to the mathematical, where you can assure yourself of exhaustively never missing any item or ever mistaking one thing’s identity for another’s.
samatman|1 year ago
Counting and estimating are not used interchangeably in most contexts.
> because in the real world all counting methods have some nonzero error rate.
The possibility that the counting process may be defective does not make it an estimation.
> We talk about ‘counting votes’ in elections, for example, yet when things are close we perform ‘recounts’ which we fully expect can produce slightly different numbers than the original count.
We talk about counting votes in elections because votes are counted. The fact that the process isn't perfect is a defect; this does not make it estimation.
> That means that vote counting is actually vote estimating, and recounting is just estimating with a tighter error bound.
No. Exit polling is estimation. Vote counting is counting. Vote recounting is also counting, and does not necessarily impose a tighter error bound, nor necessarily derive a different number.
> The situations where counting is not estimating are limited to the mathematical, where you can assure yourself of exhaustively never missing any item or ever mistaking one thing’s identity for another’s.
So like, computers? Regardless, this is wrong. Estimating something and counting it are not the same thing. Estimation has uncertainty, counting may have error.
This is like saying addition estimates a sum because you might get it wrong. It's just not true.
lupire|1 year ago
Koshkin|1 year ago
YoshiRulz|1 year ago
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davidmurdoch|1 year ago