Is 34% far or slightly smaller than 100%?

[Ki_Ryn]

Is 34% "far" or "slightly" smaller than 100%?

I'm looking for a number of opinions on the question reproduced below as I'm currently in a disagreement regarding the results. The observed density of matter (both luminous and dark) is roughly 34% of the critical density needed for a flat universe. That part is not under dispute. What is under dispute is which answer (a or b) follows from this fact.

1. How does the observed density of matter (both luminous in stars and galaxies, and "dark") in the Universe compare with the critical density?

a) The density of luminous and dark matter is currently far smaller than the critical density.

b) The density of luminous and dark matter is currently slightly smaller than the critical density.

(Sorry about the poll getting cut off in the middle. I don't see a way to edit it. Hopefully this whole question, here in my post, can be seen. The poll text was meant to be the same as what is quoted above.)

 

[lindsayg]

It's a third.

Get two pies. Give your friend a whole pie. Give yourself a third of a pie.

Are you getting 'far less' or 'slightly less' pie than your friend?

 

[AUMathTutor]

In the physical sense of the word, I do not believe any physicist would say that 0.34 << 1. When physicists say "far less than", they mean "several orders of magnitude less than". As in, 0.0001 << 1.

 

[Razzor7]

In the physical sense of the word, I do not believe any physicist would say that 0.34 << 1. When physicists say "far less than", they mean "several orders of magnitude less than". As in, 0.0001 << 1.

But at the same time, no one would consider 34% only slightly less than a whole.

 

[Mapes]

Both arguments are valid dependent on the conventions to which the reader is accustomed. Why not simply say "less," give the values, and let the reader make his or her own decision as to whether it's a staggering or insignificant difference?

 

[uart]

Both arguments are valid dependent on the conventions to which the reader is accustomed. Why not simply say "less," give the values, and let the reader make his or her own decision as to whether it's a staggering or insignificant difference?

I'm guessing that the OP was given these options as part of a multiple choice exam and is in dispute with the marking. Is that correct Ki.

Yes it's certainly a fairly imprecise question. To my mind, whether 34% (of) is "far smaller" or "somewhat smaller" or "slightly smaller" really depends on the inherent variability in the thing being measured.

For example, with the 1/3 of the pie versus the whole pie example given previously by linsayg, that example is more or less assuming a fixed sized pie. Imagine a world where pies varied greatly in size from say 10^(-6) meter diameter through to 10^(+6) meter diameter. Now let's say you and your friend both acquired a pie and you found yours to be 10cm diameter and your friends pie was 30cm diameter. Under these high variability conditions you might well be surprised at just how similar are the size of these two pies.

Personally I wouldn't be too thrilled about receiving OP's original options in a multiple choice exam question. If I had to say one or the other I'd probably go with slightly smaller (though I'd prefer to say somewhat smaller).

 

[Mapes]

Ah, I didn't consider that; I assumed that Ki_Ryn was drafting a report or article and was disputing a word choice with coauthors. (Just to show you what's on my mind these days!)

 

[Ki_Ryn]

You're correct in that these were options on a test. Thank you for the input.

 

[lindsayg]

In the physical sense of the word, I do not believe any physicist would say that 0.34 << 1. When physicists say "far less than", they mean "several orders of magnitude less than". As in, 0.0001 << 1.

Actually, good point. Since the question relates to something as HUGE as dark matter, being of the same order of magnitude makes it only 'slightly less'. At A level and uni (although to be fair I dropped out after a year) we were taught that getting an answer to the correct order of magnitude was the next best thing after actually getting it right. AFAIR..

But yes, it's badly worded. Very ambiguous. Just see the different interpretations put on it in one short thread here.



ps: I guessed it was a test - do I win a pie?

 

[ParisAsta]

I know this has already been answered..

But please professors who teach this subject, please do not use this question if you are teaching a bunch of noobs on the subject. I got this question and well I got it right, but only after reading the responses here, so thanks for you help.

 

[Pinu7]

34 to 100 is comparable.

1 to 50000 is probably uncomparable.

Far or slightly left is much more subjective.