Go Back   EcoModder Forum > Off-Topic > The Lounge
Register Now
 Register Now
 


Reply  Post New Thread
 
Submit Tools LinkBack Thread Tools
Old 01-18-2021, 03:50 AM   #1 (permalink)
Master EcoModder
 
freebeard's Avatar
 
Join Date: Aug 2012
Location: northwest of normal
Posts: 18,380
Thanks: 5,047
Thanked 6,077 Times in 4,866 Posts
A zeroth-order approximation

I thought I'd found a solution to the problem of 'rules of thumb' rubbing thin-skinned individuals the wrong way. But the upshot was that the thread in Aerodynamics was locked. I choose to share here instead to spare the feelings of the last poster.

en.wikipedia.org/wiki/Order_of_approximation

Quote:
Usage in science and engineering
In formal expressions, the ordinal number used before the word order refers to the highest order of derivative in the series expansion used in the approximation. The expressions: a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth are used as fixed phrases. The expression a zero order approximation is also common. Cardinal numerals are occasionally used in expressions like an order zero approximation, an order one approximation, etc.

The omission of the word order leads to phrases that have less formal meaning. Phrases like first approximation or to a first approximation may refer to a roughly approximate value of a quantity.[1][2] The phrase to a zeroth approximation indicates a wild guess.[3] The expression order of approximation is sometimes informally used to mean the number of significant figures, in increasing order of accuracy, or to the order of magnitude. However, this may be confusing as these formal expressions do not directly refer to the order of derivatives.
So don't say rule of thumb when there is a nerdier expression available.

__________________
.
The difference between science and screwin' around, is writing it down.
Adam Savage
_________________
  Reply With Quote
The Following 2 Users Say Thank You to freebeard For This Useful Post:
Ecky (01-18-2021), redpoint5 (01-18-2021)
Alt Today
Popular topics

Other popular topics in this forum...

   
Old 01-18-2021, 11:05 AM   #2 (permalink)
EV convert
 
oil pan 4's Avatar
 
Join Date: Jul 2011
Location: NewMexico (USA)
Posts: 9,059

Sub - '84 Chevy Diesel Suburban C10
SUV
90 day: 19.5 mpg (US)

camaro - '85 Chevy Camaro Z28

Riot - '03 Kia Rio POS
Team Hyundai
90 day: 30.21 mpg (US)

Bug - '01 VW Beetle GLSturbo
90 day: 26.43 mpg (US)

Sub2500 - '86 GMC Suburban C2500
90 day: 11.95 mpg (US)

Snow flake - '11 Nissan Leaf SL
SUV
90 day: 141.63 mpg (US)
Thanks: 215
Thanked 2,965 Times in 2,308 Posts
We could start a hurt feelings sub forum to aerodynamics.
It's really a good thing I didn't bother to notice that one till after it was locked.

Last edited by oil pan 4; 01-18-2021 at 11:18 AM..
  Reply With Quote
Old 01-18-2021, 01:26 PM   #3 (permalink)
Master EcoModder
 
freebeard's Avatar
 
Join Date: Aug 2012
Location: northwest of normal
Posts: 18,380
Thanks: 5,047
Thanked 6,077 Times in 4,866 Posts
I took me a while to figure out why there was no Quick Reply field. My first reaction? Sorry, not sorry; let's take it to The Lounge, where you-know-who doesn't go.

I will point out that zeroth order would be a Wild *ss Guess. First order is more appropriate for Rule of Thumb. What it comes down to is the significant digits. 4000 vs 3900 vs 3914 or 0.1 vs 0.01 vs 0.001, etc. So zeroth order has one significant digit that could be off by an order of magnitude.
__________________
.
The difference between science and screwin' around, is writing it down.
Adam Savage
_________________
  Reply With Quote
The Following User Says Thank You to freebeard For This Useful Post:
Ecky (01-18-2021)
Old 01-18-2021, 04:03 PM   #4 (permalink)
Tyrant-at-large
 
Vman455's Avatar
 
Join Date: Feb 2012
Location: Champaign, IL
Posts: 1,806

Little Red - retired - '05 Honda Civic EX
90 day: 49.03 mpg (US)

Pope Pious the Prius - '13 Toyota Prius Two
Team Toyota
SUV
90 day: 54.18 mpg (US)
Thanks: 189
Thanked 1,596 Times in 846 Posts
To use the topic that provoked this as an example, I would equate "rule of thumb" in this context with "zeroth-order approximation." If I measure a 5% fuel economy improvement on my already low-drag, CVT, electric-assist (all of which are differences from the cars which generated the RoT) car from a change and I assume that means I improved drag 10%, I have no basis on which to guess that. Maybe my car actually needs a 20% improvement in drag to get a 5% fuel economy improvement at 55mph, in which case increased resolution of the 10% guess doesn't improve its accuracy--it's still just a guess. I have absolutely no way of knowing on my car specifically without measuring something else to corroborate or disprove, and I could be way off as a result.

Put another way: If the RoT was a first-order approximation, we would have to know that drag improvement between 5%-14% on any car results in 5% fuel economy improvement, and we simply don't know that. The friction wasn't with the terminology; it's with the concept.
__________________

  Reply With Quote
Old 01-18-2021, 05:09 PM   #5 (permalink)
Master EcoModder
 
freebeard's Avatar
 
Join Date: Aug 2012
Location: northwest of normal
Posts: 18,380
Thanks: 5,047
Thanked 6,077 Times in 4,866 Posts
I'd say the concept is meta to the content.

Like the programmer at the airport that kept counting his luggage and coming up one short. (Off-by-one error joke)

en.wikipedia.org/wiki/Order_of_approximation#Colloquial_usage
Quote:
These terms are also used colloquially by scientists and engineers to describe phenomena that can be neglected as not significant (e.g. "Of course the rotation of the Earth affects our experiment, but it's such a high-order effect that we wouldn't be able to measure it" or "At these velocities, relativity is a fourth-order effect that we only worry about at the annual calibration.") In this usage, the ordinality of the approximation is not exact, but is used to emphasize its insignificance; the higher the number used, the less important the effect. The terminology, in this context, represents a high level of precision required to account for an effect which is inferred to be very small when compared to the overall subject matter.
__________________
.
The difference between science and screwin' around, is writing it down.
Adam Savage
_________________
  Reply With Quote
Old 01-18-2021, 05:13 PM   #6 (permalink)
Growin a stash
 
Join Date: Jun 2014
Location: Austin TX
Posts: 645
Thanks: 361
Thanked 228 Times in 172 Posts
Quote:
Originally Posted by freebeard View Post
let's take it to The Lounge, where you-know-who doesn't go.
Voldemort?



(Harry Potter reference)
__________________


2015 Nissan Leaf S, 164 mpge
  Reply With Quote
The Following 2 Users Say Thank You to ME_Andy For This Useful Post:
Ecky (01-18-2021), freebeard (01-18-2021)
Old 01-18-2021, 08:20 PM   #7 (permalink)
Somewhat crazed
 
Piotrsko's Avatar
 
Join Date: Sep 2013
Location: 1826 miles WSW of Normal
Posts: 1,574
Thanks: 153
Thanked 431 Times in 367 Posts
Systematic wild a##ed guess?

I ve seem him here, with a zero looked at couple of posts, BTW.

So much for a working ignore function.
  Reply With Quote
The Following User Says Thank You to Piotrsko For This Useful Post:
freebeard (01-18-2021)
Old 01-18-2021, 09:27 PM   #8 (permalink)
Master EcoModder
 
Ecky's Avatar
 
Join Date: Dec 2011
Location: Vermont
Posts: 4,201

Gaptooth (retired) - '00 Honda Insight
Team Honda
Gen-1 Insights
90 day: 54.26 mpg (US)

Such Fit - '07 Honda Fit Sport
90 day: 41.27 mpg (US)

Connect - '15 Ford Transit Connect XL
90 day: 20.32 mpg (US)

K-sight - '00 Honda K-sight
Team Honda
90 day: 41.29 mpg (US)
Thanks: 2,005
Thanked 1,777 Times in 1,149 Posts
I appreciate this. I'm going to start using this in common, everyday speech.
  Reply With Quote
The Following User Says Thank You to Ecky For This Useful Post:
freebeard (01-18-2021)
Old 01-19-2021, 12:31 AM   #9 (permalink)
Master EcoModder
 
freebeard's Avatar
 
Join Date: Aug 2012
Location: northwest of normal
Posts: 18,380
Thanks: 5,047
Thanked 6,077 Times in 4,866 Posts
I just like to say 'zeroth'.
__________________
.
The difference between science and screwin' around, is writing it down.
Adam Savage
_________________
  Reply With Quote
Old 01-19-2021, 11:03 AM   #10 (permalink)
Somewhat crazed
 
Piotrsko's Avatar
 
Join Date: Sep 2013
Location: 1826 miles WSW of Normal
Posts: 1,574
Thanks: 153
Thanked 431 Times in 367 Posts
Well it does cause a certian academic aura to your conversation.

  Reply With Quote
Reply  Post New Thread


Thread Tools




Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, vBulletin Solutions Inc.
Content Relevant URLs by vBSEO 3.5.2
All content copyright EcoModder.com