Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[sitnaltax]

Question:  mammals can "breathe" temporarily in a perfluorocarbon.  Would fish also be able to do so, or would they "drown" in an otherwise oxygen-rich environment?  (Ignore for a moment the density; fish would float straight to the surface in current PFCs.)

My uninformed biology-enthusiast speculation is yes. My best googling suggests that fish die if you take them out of water because their gills collapse, so there's not enough surface area to transfer oxygen. So in an appropriate-density environment, a fish would be fine. I'm making the unfounded assumption that gills and lungs transfer oxygen in fundamentally the same way, differing mostly in the way they're adapted to handle the density and oxygen concentration of water vs. air.

Like mammals, I can't speak to the longer-term effects for fish. You wouldn't have the "this thick fluid is damaging the delicate lung tissue" issue, though.

[Kirian]

Best unboxing video ever:  The newest Mersenne prime!

[Tables]

I already had that number memorised by the time that video came out. The short form, not the long form, obviously. Ah well, I still feel geeky.

As an aside, how would you round 0.095 to one significant figure? Would you leave the answer as 0.1 (which has 1 significant figure) or as 0.10 (which seems to have two significant figures, but shows the level of accuracy you get from rounding the previous number to one significant figure)?

[Witherweaver]

I already had that number memorised by the time that video came out. The short form, not the long form, obviously. Ah well, I still feel geeky.

As an aside, how would you round 0.095 to one significant figure? Would you leave the answer as 0.1 (which has 1 significant figure) or as 0.10 (which seems to have two significant figures, but shows the level of accuracy you get from rounding the previous number to one significant figure)?

It seems pretty obviously 0.1.  Rounding to 0.10 would exactly be rounding to two significant figures.  It doesn't matter how many significant figures you start with. 

[Kirian]

Depends on how you want to look at things.

For typical coursework, the correct answer is 0.1 rather than 0.10.  The second one indicates two significant digits, as WW notes.

Outside of the classroom, the correct answer is really 0.10.  You want to indicate for your customer/client/whatever that the measurements made were precise to the hundredths place, even though rounding would nominally chop it to the tenths place.  This is because rounding is addition/subtraction, and addition can generate an extra significant digit when there's a carry.

On the other hand, you can also easily write 0.09(5) and be done with it.

[LastFootnote]

I don't understand. If you're going to specify two significant digits (0.10), then why would you round it at all!? 0.095 is also two significant digits and is more accurate!

[Kuildeous]

On the other hand, you can also easily write 0.09(5) and be done with it.

0.45?

[Witherweaver]

On the other hand, you can also easily write 0.09(5) and be done with it.

0.45?

0.45!

[enfynet]

On the other hand, you can also easily write 0.09(5) and be done with it.

0.45?

0.45!

So, half of 0.9 is 0.45!?

[Witherweaver]

On the other hand, you can also easily write 0.09(5) and be done with it.

0.45?

0.45!

So, half of 0.9 is 0.45!?

Not quite, 0.45! is about .8856613803.

[Kirian]

I don't understand. If you're going to specify two significant digits (0.10), then why would you round it at all!? 0.095 is also two significant digits and is more accurate!

Well, here's the thing.  Significant digits are a fiction.  They're a shorthand for something much more useful, but rather than deluging chemistry students (and let's face it, this is almost always first introduced in chemistry) with yet another complex calculation, we simplify it.

The reality is that "one significant digit" has the same meaning as "+-~10%".  Two significant digits is +-~1%, and so forth.  These aren't exactly right, as 40 +- 5 is different from 90 +- 5, but they're close

So if you multiply 0.3 (1 sd) by 0.32 (2 sd), you get 0.096, but should only keep 1 sd.  0.1 and done, right?  Well...

The reality is that these measurements really "mean" 0.3 +- 0.05, and 0.32 +- 0.005.  Or, as bounds, 0.25 to 0.35, and 0.315 to 0.325.  If we multiply the bounds, we have a range in the final answer of:

0.25 x 0.315 = 0.07875 to 0.35 x 0.325 = .11375 = 0.09625 +- 0.0175

When chopped down to the maximum sd (2) from earlier, this is 0.096 +- 0.018

Now, here's where significant digits become a problem:

One sd is 0.1, which implies 0.1 +- 0.05
Two sd is 0.096, which implies 0.096 +- 0.0005
If we write 0.10, that implies 0.1 +- 0.005

The actual uncertainty is somewhere between the first and the third.  What to use, then?  Let's use the actual answer, 0.096 +- 0.018.  That eliminates our uncertainty with respect to... uncertainty.

--------

So what's the real problem here, then?  Well, there are two.

First, if you only have one significant digit in one of your measurements, you don't need to use significant digits anyway; your measurement is all but useless.  In reality, "one significant digit" means "using the wrong measuring implement."

Second, significant digits are best used when all values being used have similar uncertainties.  If we were multiplying 0.35 (0.345 to 0.355) and 0.47 (0.465 to 0.475), with typical sd usage the answer is 0.16 (0.155 to 0.165), and with properly described uncertainty, the range is 0.1604 to 0.1686, or 0.164 +- 0.004.  Those ranges overlap a lot better than the ranges we had in the other problem.

[ashersky]

So what's the real problem here, then?  Well, there are two.

It's that no one cares.

[Witherweaver]

So what's the real problem here, then?  Well, there are two.

It's that no one cares.

Only no one to one significant digit, though.  Could be anywhere in [-0.5,0.5) people caring.

[Awaclus]

So what's the real problem here, then?  Well, there are two.

It's that no one cares.

90-93% of people care far more than people think.

[silverspawn]

So what's the real problem here, then?  Well, there are two.

It's that no one cares.

90-93% of people care far more than people think.

73,3% of all statistics are made up!

[Awaclus]

So what's the real problem here, then?  Well, there are two.

It's that no one cares.

90-93% of people care far more than people think.

73,3% of all statistics are made up!

Are you referring to my 90 - 93% estimate?

It's just an estimation but its probably not far off, its not important to be precise to the second decimal point here

In case you've missed it: http://forum.dominionstrategy.com/index.php?topic=14521.0

[Tables]

I already had that number memorised by the time that video came out. The short form, not the long form, obviously. Ah well, I still feel geeky.

As an aside, how would you round 0.095 to one significant figure? Would you leave the answer as 0.1 (which has 1 significant figure) or as 0.10 (which seems to have two significant figures, but shows the level of accuracy you get from rounding the previous number to one significant figure)?

It seems pretty obviously 0.1.  Rounding to 0.10 would exactly be rounding to two significant figures.  It doesn't matter how many significant figures you start with. 

See, now that's interesting, because my intuition says 0.10 is the better answer here. You're still rounding to 1 sf, but the extra 0 implies an accuracy to within 0.005 either way - which is what you're actually within. The 0.1 answer has 1 sf but implies an uncertainty of 0.05, which is much larger than what you actually started with. On the other hand, it does only specify 1 significant figure, so I guess that it's a more true answer in the abstract sense - although usually less useful. So... I dunno. I can kinda see both sides though, I was wondering if there was an actual standard convention here.

I don't understand. If you're going to specify two significant digits (0.10), then why would you round it at all!? 0.095 is also two significant digits and is more accurate!

Same question but rounding 0.0952341245 instead then.

Edit: Now I think about it a little more though, considering that could also be rounded to 0.095 it doesn't really make much sense to use 0.10 over 0.95, even if 0.10 seems better than 0.1. Hmm. I think really this is just because rounding anything up to  the next order of magnitude just makes things horrible accuracy wise, most of the time. So yeah, 0.1 sounds like the best answer to me now, or at least it should be about 90-93% of the time.

[Witherweaver]

I already had that number memorised by the time that video came out. The short form, not the long form, obviously. Ah well, I still feel geeky.

As an aside, how would you round 0.095 to one significant figure? Would you leave the answer as 0.1 (which has 1 significant figure) or as 0.10 (which seems to have two significant figures, but shows the level of accuracy you get from rounding the previous number to one significant figure)?

It seems pretty obviously 0.1.  Rounding to 0.10 would exactly be rounding to two significant figures.  It doesn't matter how many significant figures you start with. 

See, now that's interesting, because my intuition says 0.10 is the better answer here. You're still rounding to 1 sf, but the extra 0 implies an accuracy to within 0.005 either way - which is what you're actually within. The 0.1 answer has 1 sf but implies an uncertainty of 0.05, which is much larger than what you actually started with. On the other hand, it does only specify 1 significant figure, so I guess that it's a more true answer in the abstract sense - although usually less useful. So... I dunno. I can kinda see both sides though, I was wondering if there was an actual standard convention here.

I mean, if you say 0.10 to one significant figure, that's not correct, you should be saying 0.1.  Saying 0.10 is giving two significant figures (by the regular school definition of significant figure).  Saying 0.100 would be three (though in this case you'd have 0.0950), etc.

[Limetime]

We shouldn't talk about significant digits, considering how short life is.

[Roadrunner7671]

I have a pro tip if you want to live a better life: don't mix grapefruit juice, flat club soda and tonic water then attempt to ingest it. It will end badly.

[enfynet]

A little something for Sunday brunch

[Witherweaver]

[Witherweaver]

So I was playing some Diablo III some time ago, and I noticed there was a name elite called "Alot" (i.e., from here).  It even looks a bit like the image in the comic.  It's pointed out as an Easter Egg:

http://www.diablowiki.net/Diablo_III_Easter_Eggs#Alot

They don't have a picture there, but:

[pacovf]

Hyperbole and a half is one of the funniest things on the Internet. So sad it's not updated anymore. Anybody know if the author is doing anything similar now?

[ashersky]

Is that Chumlee getting slapped?