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LoAmi

Numbers and Precision

37 posts in this topic

:: Grabs Mike ::

 

:: lets a furious Mike go and takes the microphone ::

 

I'll add my first 2c into the endless lot of simming tips on this forum.

 

Everyone who watched TOS remembers how Mr. Spock, in the classic episode "The Trouble with Tribbles," predicted that 1,771,561 tribbles are likely to exist on the station, assuming each tribble has a litter of 10 every 12 hours over a period of 3 days (and, no, I wouldn't have remembered that without Eric Weisstein's Excrucuatingly Detailed Star Trek Plot Summaries http://www.ericweisstein.com/fun.....html).

 

And, then, for those who preferred TNG, there was always Mr. Data, who would give every ETA down to seconds.  The first time when he didn't (and I can't remember what episode it was), Riker asked him why.  The answer involved that humans tend to become impatient with that kind of detail.  

 

Basically, it's boring.

 

The writers for Data and Spock assumed, as do many people, that, the more digits you put into a number, the more "accurate" it is, and the more "scientific" it sounds.  Of course, the logical Vulcan Spock, and the android Data should be as "accurate" as possible, right?

 

Well, not exactly.  There is a basic confusion going on here between "accuracy" and "precision."  

 

Saying something is "8.345679 km away" is just as accurate as giving the figure as "8.35 km."  The difference is that the former assumes that:

(1) you can actually *measure* the answer down to six decimal places

(2) that the answer is *precise* down to six decimal places (all error is in the sixth

and, finally, and most importantly for the sim:

(3) that the answer actually *matters* down to six decimal places.

 

For example, if I'm localizing another person, we can assume that he/she may move within, say, 10m in the amount of time it takes to give the figure.  So, "8.35 km" gives enough information to complete the task at hand.  However, a figure of "8.345679 km" assumes that the person will not even move 1 mm!  Add more decimal places, and you might even be limiting the answer for the location of a human to the size of a bacterium!  By adding in more decimal places to "sound scientific," you've managed not only to make your answer annoying, but also to make it wrong.

 

Back to Spock, given all his assumptions, his answer would be exact.  But, in the real world, there is an element of randomness associated with the timing of tribble reproduction.  "1.8 million" would have gotten the point across equally well, with better accuracy through less precision.

 

Similar issues arise when giving distances in space.  Remember, that the length of your starship is ~300m, and that your starship can travel many times its own length per second, even on maneuvering thrusters.  Giving a distance figure any more accurate than that is a waste of time.  (One notable exception here is precision shooting! -- but, wouldn't you rather be blowing something up than telling us exactly how far away it is and in what direction?)  Distance scales can get even more imprecise when you're at warp.  "4,765,945,321 km" is just as good as saying "4.77 trillion" when you can travel a few million km/s, but the latter is much easier to read.

 

Of course, the same logic applies to time measurements.  Unless the timing of your operation is the critical factor, that extra 10.3s over 2 hours that it will take you to get to your destination at warp 9 is really irrelevant.  By the time you're done reporting the ETA, the report is already inaccurate.

 

In sum: "Accuracy" tells whether the answer is right or wrong.  "Precision" tells you how well you know the answer.

 

[Precise and inaccurate: "The Earth is 1,356,323,387,986 mi from the sun."

Accurate and less precise: "The Earth is 93 million miles from the sun."

]

 

Now that I've beat this topic over the head with a stick, we return to regularly scheduled programming.

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:: Grabs Mike ::

 

:: lets a furious Mike go and takes the microphone ::

Why couldn't Ruca grab me instead?

 

LtJG (Mike) Van Roy

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:: Grabs Mike ::

 

:: lets a furious Mike go and takes the microphone ::

Why couldn't Ruca grab me instead?

 

LtJG (Mike) Van Roy

Silly Vanroy always turning serious stuff into funny stuff in a nice classy way goodjob and you might want to come Ruca is coming ;)

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1,771,561 tribbles are likely to exist on the station, assuming each tribble has a litter of 10 every 12 hours over a period of 3 days

It assumes more than that.

 

The first Tribble would have to actually be giving birth  - not just pregnant - to it's first litter when it was still in Uhura's hand.  That didn't happen.

 

We also know that tribbles are born pregnant.  Something in the womb must make them pregnant.  Therefore once a Tribble leaves the womb it can *be* pregnant, but it can't *get* pregnant.  They have one litter and that's it.  Mr. Spock's math assumes Tribbles are still getting pregnant and giving birth days after they would have lost the ability to do so.

 

Also, all of the Tribbles would have to still be alive, and we already know they weren't.

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Mr. Spock started rounding starting with Star Trek V

And if Mr. Spock learned to round, all the more so should STSF simmers!

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We also know that tribbles are born pregnant.  Something in the womb must make them pregnant.  Therefore once a Tribble leaves the womb it can *be* pregnant, but it can't *get* pregnant.  They have one litter and that's it.  Mr. Spock's math assumes Tribbles are still getting pregnant and giving birth days after they would have lost the ability to do so.

 

Not true! They can be born pregnant. But Spock never detailed exactly how their reproductive system works.

 

Its a possibility that tribbles in fact replicate a-sexually on a regular basis. Their own DNA may contain enough information for hundreds of different combinations, such as fur color (which seems to be the only distinction between them), and random chance as the tribble develops and various genes become dominant (remember this is an alien species...their genes may mutate and change every reproductive cycle, allowing different genes to dominate over others at different generations), can produce a very different looking tribble each time. They are born pregnant because this asexual reproductive cycle is active very early in their life cycle. While the tribble is only a fetus, its reproductive cycle has already begun and it is developing a baby tribble on its own. A zygote within a fetus, as it were.

 

Then, after the tribble gives birth it will restart its reproductive cycle and become pregnant with yet another tribble embryo.

 

Remember that the danger of the tribbles was only if you overfed it. So its likely to assume that their reproductive cycle also engages when they have excess energy stored. If this is true, and the tribble is ready to reproduce even as only a fetus, then the excess energy from the mother tribble to her fetus would allow that fetus to also contain excess energy and would therefore become pregnant.

 

Sound good??

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You point out yourself that the difference in the number of decimal places given is one of precision not accuracy, but why would we assume that Spock or Data wouldn't give an answer as precisely as possible?  Both were anal.  And indeed, as time went on, Data did learn that that degree of precision is not necessary (and is annoying) to state, so he stopped.  

 

Do the writers do it to make characters sound more scientific?  Of course.  But the distinction between precision and accuracy isn't necessary.  So in defense of the scientific-sounding writers we can simply say that Vulcans and Androids prefer to state full precision when it appears in a number.  

 

Do starships make noise in vacuum?  Do firey explosions exist in a vacuum?  Should a starship grind to a halt when it's engines stop?  Should every planet visited have Earth's gravitational constant and atmospheric pressure?  (Kudos to Enterprise for finally having a pressure-different species!)  And why oh why should the good guys be attractive and the bad guys ugly?  And the uglier they are, the badder they are.  And should all single alien women be thin with long legs?  

 

It's Star Trek.  We love it.

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And should all single alien women be thin with long legs?  

Why stop at single aliens?

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You point out yourself that the difference in the number of decimal places given is one of precision not accuracy, but why would we assume that Spock or Data wouldn't give an answer as precisely as possible?  Both were anal.  And indeed, as time went on, Data did learn that that degree of precision is not necessary (and is annoying) to state, so he stopped.

To answer your first point, Spock, in the tribble episode, gave answers *more* precisely than possible, sacrificing accuracy.  He had to make too many assumptions in order to justify the answer.  Basically, what he was doing was a back-of-the-envelope type of calculation, or an order of magnitude estimate.  In order to be correctly stated, his answer couldn't have been any more precise than the data he put in (estimates/averages themselves).  Spock's character should have been more attuned to being correct than showing off that he could do rapid mental arithmetic.

 

Data can be excused a little on ETAs, as long as he gave them before they actually started going into warp - when they were both precise and accurate (but still annoying).  If the ETA were given in transit, by the time he said "and 6.5s," it would no longer be true *and* it would still be annoying.

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why oh why should the good guys be attractive and the bad guys ugly?  And the uglier they are, the badder they are.

Because ugly people ARE evil.

 

JUST KIDDING  ::D:

 

Star trek is all about putting reality away for an hour or two, and it's good to do so every now and then.

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Yes, but the Tribble episode, he should have rounded and be more accurate than precise. See, they are trying to tell us that they are smarter than we are and that is not true.

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And why oh why should the good guys be attractive and the bad guys ugly?  And the uglier they are, the badder they are.  And should all single alien women be thin with long legs?  

Well it is the easy way to identify evil for it is a simple metaphor when you think of evil did you ever think of evil as being attractive or repulsive. There is also some flaw in you statement aswell for there were several attractive villians in  Star Trek to throw off the viewer are the evil or do they have cause for what that are doing take Khan and Shinzon for example :D

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Doesnt anybody care about my tribble theory? :cry:

I do. Just in a different way. :wink:

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Doesnt anybody care about my tribble theory? :cry:

OK - if you really want a comment.  

 

I always did think that tribbles reproduced asexually.  They might have a sexual reproductive mode as well, but there is no evidence for it.  Some yeasts can operate like this, and bacteria have a sexual recombination (but not reproduction!) process (conjugation).

 

There are real cases where genes do things like turn themselves on and off, skip generations, and even move around on the genome (transposons).   Random reshuffling of alleles (gene variants) happens too (think of "crossing over" in meiosis).  Tribble genetics don't have to be all that complicated to explain the variations in fur color.  I recall something about tribbles being prey on their native planet (limiting their reproduction along with a lower food supply). Having offspring with multiple fur colors might help them survive (random camouflage?).

 

I'm not sure I understand the energetics argument.

 

Either way, a very large number of tribbles is still a system that has some noise (randomness) in it.  So, I still find it hard to believe that you could predict their reproduction down to the last one tribble.

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Star trek is all about putting reality away for an hour or two, and it's good to do so every now and then.

Amen!  (And with popcorn).  

 

And as I say often... It's Star Trek, not Shakespeare.  :D

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Reality?  When did reality come into this?  Some of us have fun making up plausible sounding explanations for things.

 

Anyway, the point of my original post still stands.  Unnecessarily stating numbers with lots of digits is  annoying.  (And, this time, in parentheticals: It also happens to be wrong most of the time).

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Anyway, the point of my original post still stands.  Unnecessarily stating numbers with lots of digits is  annoying

 

I totally agree Loami. My calculator does it all the time.

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I say we change LoAmi's post counter to say "Around 290, give or take" to make him happy.

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I say we change LoAmi's post counter to say "Around 290, give or take" to make him happy.

woah woah woah, going a little far with being exact aren't we dumbass? Just leave it at,

 

"somewhere in the hundreds...maybe".

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"somewhere in the hundreds...maybe".

ROFL!!  Very good!

 

Or perhaps...  "A lot."

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No, "too many"

 

The alternative, "needs a life" would be equally descriptive.

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Or mabye it should be, "Somewhere" or even better "a number between one and infiniti"  :D    ::D:

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Why couldn't Ruca grab me instead?

 

LtJG (Mike) Van Roy

Aww.. ::grabs::

 

::grins::

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