Talk:Learning curve

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Comments
Suppose I need to acquire 100 units of knowledge between time 0 and time 1, 90 units between time 1 and time 2, 70 units between time 2 and time 3, 40 units between time 3 and time 4, and 0 units between time 4 and time 5. It follows that I need to have accumulated a total of 100 units by time 1, a total of 190 units by time 2 (i.e. 100 + 90), a total of 260 units by time 3 (i.e. 100 + 90 + 70), a total of 300 units by time 4 (i.e. 100 + 90 + 70 + 40), and a total of 300 units by time 5 (i.e. 100 + 90 + 70 + 40 + 0). Where the X axis represents time and the Y axis represents the total number of units that I need to have accumulated, we have a steep curve.

Assuming it takes more effort to acquire 100 units of knowledge than 0 units of knowledge, the implication is that a lot more effort has had to be expended during the first stage than the last.


 * The reverted paragraph speaks about a singe aspect: two opposite interpretations: "easy vs. difficult" learning. The alleged "third" meaning speaks about different interpretations of the "learning cirve". If you want to add it, do it in a separate seciton and provide a reference admissible in wikipedia. There are several meanings of the expression. You are welcome to add it as long as you provide valid references. `'mikka 22:31, 22 May 2007 (UTC)

New section duly added. I'm not sure what sort of reference you want though. Perhaps you can explain by referencing your own paragraph 'Over time ... difficult to climb'. 194.221.133.226 09:58, 23 May 2007 (UTC)
 * I am not sure what you mean. From your writing style I guess you are not a 8-year old boy and I assume you know what the term "reference" means: an indication to the source of the information you add to the article. I also gave you a link to wikipedia rules about which references are admissible, just click at the wikilink. Finally, the article already has examples how references are formatted. Please  explain in more detail what is is unclear to you. `'mikka 16:49, 23 May 2007 (UTC)

I wasn't sure whether you wanted a reference to a) an authoritative statement that the expression is sometimes used in the way I've described or b) an explicit example of its being used in this way. I'm not sure I can find an authoritative statement, as my knowledge of this usage is based on listening and discussing rather than formal research, but I've supplied an explicit example. I can also supply implicit examples, i.e. examples where to attribute any other meaning to the speaker would be to contravene the principle of charity; but perhaps this sort of evidence wouldn't be deemed sufficiently solid.

Incidentally, I'm not sure Dr Smith's comments support your contention that this is a "popular misapprehension" that has become "widespread", but I shan't take this any further.

I've tried to rewrite "my" paragraph so that it's more relevant to what goes before, but I'll leave it to you from now on, provided you retain my meaning. 194.221.133.226 13:33, 24 May 2007 (UTC)
 * Thank you for your contribution. Just like you, I find it different to provide a reference to a really authoritative source about the use/abuse of the term. I am not sure which part you object: "misapprehension" or "widespread". I may agree with the judgement "misapprehension", since it is not uncommon for words to change their meaning. But as for "widespread", there is no doubt. While the "correct" meaning may be found in many scientific articles dedicated specifically to cognitive science, in popular parlance I'd say 90% of usage is "incorrect". As for the reference you provided, unfortunately is is not very good, since the weblink refers to an IP address of storage, hence cannot be permanent. What is more, the document clearly gives a very strange definition: "Learning curve is the time it takes for a person to learn a new task and perform it competently". So I am removing it, sorry. Fortunately, this is a collaborative project, and I hope eventually someone will provide a good reference. I also modified/expanded your last change. `'mikka 17:01, 24 May 2007 (UTC)

Can you please explain in layman's terms what an "IP address of storage" is and why the fact that it "cannot be permanent" is a problem? That will help me look for something better. (Incidentally, I totally agree that the definition given of "learning curve" is odd. It's the following sentence, about "steep learning curve", that's the important one. I put "Search for "learning curve"" simply because it's the glossary entry for "learning curve" that contains the relevant use of "steep learning curve".)
 * Please see the wikipedia policy about reliable sources for all future questions. The issue of permanence is because we want wikipedia be useful many years to follow. The reference in question is from a webpage whose addres starts not from www.something.dot.somethnig, but from digits, like in you signature, indicating that this is a temporary storage, not intended for access of others. It became visible most probably  becaause of the neglect of inexperience of their system administrator. `'mikka 21:49, 25 May 2007 (UTC)

You say, "But as for "widespread", there is no doubt. While the "correct" meaning may be found in many scientific articles dedicated specifically to cognitive science, in popular parlance I'd say 90% of usage is "incorrect"." You may well not doubt this, but unless you provide supporting references, your claim is, like mine, supported by nothing more than your own experience. A few misuses of a phrase in a single article, plus one man's observation of this misuse, don't constitute evidence that the mistake is popular or widespread. Therefore, I've provisionally removed "popular" and substituted "emerged in at least one place" for "become widespread". 194.221.133.226 10:13, 25 May 2007 (UTC)
 * No disagreement here. Only I took the liberty to remove "at least in one place", because it very strongly reminds a joke about a mathematician and sheep in Schotland `'mikka 21:49, 25 May 2007 (UTC)

Your last edit: You probably thought I removed your addition. In fact, I expanded it. Please re-read carefully the paragraph starting "A yet another specific..." `'mikka 21:49, 25 May 2007 (UTC)

Terrible joke, good edit.

Regarding my addition, I had indeed missed that you'd expanded on it in your "A yet another specific ... " paragraph, which is fine. So I've deleted the most recent version of my paragraph, which obviously duplicated what you'd written in the "A yet another specific ... " paragraph. Good grief. 194.221.133.226 10:58, 29 May 2007 (UTC)

Please link each of the 4 example scenarios in the lede to a learning curve. Gherson2 (talk) 18:43, 17 September 2010 (UTC)

my link removed
I guess I am not sure I understand why my link to my article Conquering the Learning Curve was removed & why it does not meet the guidelines. It is an article about the Learning Curve, that is what this page is. It is my interpretation on the Learning Curve & how it affects the way I learn. It is the Learning Curve explained so that it is easily understandable. There are many people who are afraid to learn something new & Conquering the Learning Curve is something that many people can relate to. The article is not an ad, promotion or a way to get external links to increase my page rank it is an link to an article I wrote about Conquering the Learning Curve & how it is not all that bad. Could some body please explain to me how & why it is not relevant? Lacurcio 18:13, 4 October 2007 (UTC)


 * The key here you uttered yourself is "It is my interpretation". Wikipedia is an encyclopedia which everyone can write, but only following basic rules. In this case the policies are "No original research" and "Reliable sources". Since you did not provide any proofs that you an expert in the area, your AssCon is not a reputable source for wikipedia. If "your interpretation" is based on some books or articles you have read, please cite these books. `'Míkka 21:39, 4 October 2007 (UTC)

Proposing merge
As this article and the one on "experience curve" addresses the same topic. A merge would (and redirect of experience curve to here, or vice versa) produce a more comprehensive article to the benefit of all Wikipedia readers. Editor br (talk) 11:36, 9 January 2009 (UTC)


 * That would be conditionally OK with me. I did the natural limits to learning section.  I feel the thrust of the experience curve page in representing learning as following formulas is problematic and incorrect, as learning is a discovery process.  For either a business or an ecology it's an accumulative exploration/adaptation process.  I'd also want it to include the relationship of learning to the physics of entropy and natural limits of systems generally, as the learning curve in that case being the path along which those limits are approached. I also left a note on it on the other discussion page.   --Pfhenshaw (talk) 01:31, 21 January 2009 (UTC)


 * Wishing to save time, avoid complicated discussion and ambiguity for readers I disambiguated the two pages by clarifying that this one refers primarily to learning curves as a measure of progress in learning as exploratory discovery and organizational development, which are non-deterministic. The other page largely refers to equations reflecting some of the common general features of such curves.  It seemed the easiest way at least for the moment. --Pfhenshaw (talk) 19:16, 30 January 2009 (UTC)

As they now stand I feel that they function well as two standalone, but linked articles. I will remove the merge tags. -- Alan Liefting (talk) - 21:48, 1 November 2009 (UTC)

Ah ha moments should be a new page
an "ah-ha moment" or "breakthrough" representing "S" curve learning There should be a new page about ah-ha moments... (perhaps linked to breakthrough disambiguations page...) Google finds lots of them. Now how about the opposite of ah-ha moments... Jidanni (talk) 18:17, 21 July 2009 (UTC)
 * an "Uh-uh moment"? Jidanni (talk) 09:27, 8 January 2010 (UTC)

proposed image
not a big wikipedia user, but curious if one of the more interested page-participants on would be interested in an image illustrating the learning curve. the basic idea is a 'graphical representation of....', anyone else find it odd that we then don't have a simple example of this graphical representation?

"Learning Curve" has no meaning
The fundamental problem here is that the expression "learning curve" has crept into our langauage and it actually has no meaning, definition, entymology, source or reference. As such it is open to interpretation. My anecdotal experience concludes that the word "curve" now gets added to the word "learning" in popular usage, and the user has no idea of what they are actually trying to say. —Preceding unsigned comment added by 81.159.22.75 (talk) 01:02, 19 January 2011 (UTC)
 * I'm going to have to disagree with you. "Learning curve" means the graph of increasing ability over time, and I've pretty much never heard it used any differently. It has become a pretty cliché term, but not in any way that makes it hard to define. &mdash;Mu Mind (talk) 19:51, 20 November 2011 (UTC)

can someone please rewrite the most read section...
"In the former case, the "steep[ness]" metaphor is inspired by the initially high rate of increase featured by the function characterizing the overall amount learned versus total resources invested (or versus time when resource investment per unit time is held constant)—in mathematical terms, the initially high positive absolute value of the first derivative of that function. In the latter case, the metaphor is inspired by the pattern's eventual behavior, i.e., its behavior at high values of overall resources invested (or of overall time invested when resource investment per unit time is held constant), namely the high rate of increase in the resource investment required if the next item is to be learned—in other words, the eventually always-high, always-positive absolute value and the eventually never-decreasing status of the first derivative of that function. In turn, those properties of the latter function dictate that the function measuring the rate of learning per resource unit invested (or per unit time when resource investment per unit time is held constant) has a horizontal asymptote at zero, and thus that the overall amount learned, while never "plateauing" or decreasing, increases more and more slowly as more and more resources are invested."

This sounds like this was written by someone who took their first calculus class without ever taking any English ones. Can we please get a rewrite?--24.191.102.86 (talk) 02:27, 2 December 2012 (UTC)

I agree that this entire section is plain wrong. ALL learning curves (of a finite body of knowlege) are asymptotic to 100% proficiency : STEEP means you initially learn quickly, SHALLOW (or LONG) means you learn slowly. Current footnote 7 "Laparoscopic Colon Resection Early in the Learning Curve" .. has it right. Alanf777 (talk) 23:43, 5 March 2013 (UTC)

I rewrote the section, emphasizing the most common mis-interpretation (steep is bad), and providing a different summary of the referenced encyclopedia article. Do NOT revert without consensus in TALK. Alanf777 (talk) 20:21, 14 March 2013 (UTC)

Lede

 * This word Lede does not exist; what is propably ment is Lead (paragraph), the opening paragraph of an article, right? – Detlef Lindenthal (talk) 14:49, 30 August 2020 (UTC)

The second sentence of the lede makes no sense either. If an example is needed, I'd use draughts (aka checkers) vs chess.

I suggest moving the diagram in Common Terms to the lede, and putting the "steep is bad" misinterpretation as the second sentence in the lede. Then move the "power law" to the "models" sevtion .. and move and rewrite the current second-sentence of the lede into the common terms !!?? Alanf777 (talk) 20:43, 14 March 2013 (UTC)

EDIT BOLDLY -- I rewrote the lede, with a nice new diagram, and replaced the "common use" section with a specific "product review " section, and another diagram. I'll add a diagram of an S-curve later. Alanf777 (talk) 02:15, 15 March 2013 (UTC)


 * Note : I left in a lot of the phrasing of the original version. eg "the increase is ... sharpest" rather than "greatest". I also left the notepad/vim example alone. For now. Alanf777 (talk) 02:44, 15 March 2013 (UTC)

EDIT VERY BOLDLY -- I re-re-wrote the lede, with lots of diagrams. I also expanded another section to emphasise and include the history of Wright's and Henderson's work -- with a view to merging this article and the learning curve effects article. I put all the figures in the lede .. I don't know how to spread them out. I made bigger pictures so that the text would be more readable .. but now they are too faint. I'll upload new, more legible versions when I get the time. Alanf777 (talk) 01:16, 17 March 2013 (UTC)
 * I'm not going to put any more work into the diagrams unless there's consensus on my additions (or no comments at all within a week or so) Alanf777 (talk) 03:42, 17 March 2013 (UTC)


 * You might want to read WP:LEDE Darrell_Greenwood (talk) 01:26, 17 March 2013 (UTC)
 * I just did ... and (apart from formatting) I think I met all the requirements. If you have any specific complaints please comment here. eg I COULD compress it into four paragraphs (eg combine the sentences on axes), but IMHO that would make it less readable. Alanf777 (talk) 02:14, 17 March 2013 (UTC)
 * I would be tempted to move your present lede down to after the table of contents to become an Introduction and write a one or two paragraph lede to replace it. I find the present lede with diagrams too large, busy and spread out, but it may be just me. Darrell_Greenwood (talk) 19:18, 17 March 2013 (UTC)
 * That would work. Anyone? Bueller ? Alanf777 (talk) 21:22, 17 March 2013 (UTC)
 * I've figured out how to put figures into a table, so I can bunch them together. I used a table, because I couldn't figure out how to adjust the PADDING of a gallery (the gap round the picture). Some CSS foo, no doubt, but I'm not sure where to put it. Alanf777 (talk) 23:51, 17 March 2013 (UTC)


 * Is it polite to inform previous contributors (of 3,4,5 years ago) that there's been a change, and to invite review? Alanf777 (talk) 02:22, 17 March 2013 (UTC)
 * Probably not necessary, I just looked at Contributors (<100) and Watchers (54) and most, if not all, registered editors appear to be watching the changes. Darrell_Greenwood (talk) 19:41, 17 March 2013 (UTC)

I'm contemplating a reorganization, following Darrell_Greenwood's suggestion.
 * 1. A short lede with a couple of diagrams (revised figs 1 and 2)
 * 2. The present Learning curve in psychology and economics -- maybe with the last sentence moved into the the broader interpretations or another detailed section : maybe as TWO sections, or as subsections -- psychology and economics
 * 3. An examples section -- basically my current lede, and ending with the sentence from Learning curve models (which can be deleted) -- referring to experience curve effects.
 * 4?. In Culture -- keeping it higher in importance because that's why most people will come here -- although in most wiki's it's put in last place.
 * 5. Broader interpretations of the learning curve
 * 6. General learning limits

Alanf777 (talk) 04:26, 19 March 2013 (UTC)

History
Ben Zimmer has a much better history than the current article : http://www.visualthesaurus.com/cm/wordroutes/a-steep-learning-curve-for-downton-abbey/ -- I'll augment the current version with references to zimmer. Alanf777 (talk) 07:36, 17 March 2013 (UTC)

Terms of use : http://www.visualthesaurus.com/terms/ -- does wiki count as "academic/fair use" ? I'll try asking for permission (been there, done that). Alanf777 (talk) 07:47, 17 March 2013 (UTC)
 * I added their required attribution to the ref. I thgink that's enough if this is a "scholarly" work. Alanf777 (talk) 21:51, 17 March 2013 (UTC)

Help! Can someone remind me how to make multiple REF links to the same article? Alanf777 (talk) 08:06, 17 March 2013 (UTC)


 * WP:REFNAME Darrell_Greenwood (talk) 17:44, 17 March 2013 (UTC)
 * thanks. Alanf777 (talk) 21:51, 17 March 2013 (UTC)

Reorganization in Progress
I'm doing this in my sandbox. Please don't make any other changes until I've finished. (A couple of hours from:) Alanf777 (talk) 19:30, 20 March 2013 (UTC)

DONE !! I'll edit the diagrams over the next couple of days). Alanf777 (talk) 21:34, 20 March 2013 (UTC)


 * I'm using "R" (a SHALLOW learning curve!!) to generate the new diagrams. Sample at User:Alanf777 Alanf777 (talk) 23:35, 23 March 2013 (UTC)
 * Done !!! Alanf777 (talk) 06:53, 24 March 2013 (UTC)

In computing
I don't think this section (added by anonymous 112.79.36.36) is relevant. It just says that something else (grid computing) has a steep learning curve. Grid computing itself doesn't use learning curves.

It certainly doesn't merit being the first section, so I moved it (in two steps: copy, delete).

I vote for deletion. Alanf777 (talk) 20:08, 12 February 2014 (UTC)
 * No objections. Deleted. Alanf777 (talk) 01:16, 21 February 2014 (UTC)

Moore's Law is not a learning curve
Under the examples right now there is the following sentence: "One of the best-known examples of a learning curve with Exponential Growth is Moore's law.[16]" This is wrong. Moore's law has nothing at all to do with a Learning Curve. Moore's law describes a phenomenon in the Information Technology field. For various reasons (not relevant here) there has been a predictable increase in the density, and hence computing power of the chips (e.g. CPUs for computers) that drive digital devices. There is a curve and it is exponential but it has nothing to do with learning.


 * I think Moore's law is a perfect example of a learning curve, that will inevitably top out and take on the normal shape of a sigmoid path starting with small steps and ending in small steps. Granted the name "Moore's law" will have to change as the back of the exponential shape breaks, but till then it's a quintessential example of what a learning curve is.  Perhaps we should add World GDP as a learning curve, another perfect example, of a slightly wiggly centuries-long steady exponential process of learning how to expand the world economy's ability to make money.  That would then raise the question of whether "making money" needs other

learning curves for "using money" given how vast the negative and unsustainable side-effects of just "making money" for greed alone seem to be.JessieHenshaw (talk) 19:43, 20 May 2017 (UTC)

I mean I guess you can say it's indirectly related to learning in the sense that the increases are due to continuing improvements to our knowledge about hardware but that is nothing like the learning curve concept. I'm removing that sentence. Oh the reference that supported it was just a boiler plate article about Moore's law. There was no mention of "learning curve" or "learning" anywhere in that article except someone was talking about "learning curve" in a comment. --MadScientistX11 (talk) 14:47, 6 April 2014 (UTC)

This discussion is pretty dead but if it ever comes alive again this article has some clear thinking on the subject. Themumblingprophet (talk) 01:53, 2 June 2020 (UTC)

Dr. Novarese's comment on this article
Dr. Novarese has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"I have just one remark on this article: how is learning measured? Learning involve a change, so I cannot understand most of the graphs. To my knowlege learning curve show errors or correct answers (and not "learning") as a function of the experience (or number of repetition)."

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Novarese has expertise on the topic of this article, since he has published relevant scholarly research:


 * It would be good to add a discussion of the units of measure used. I think learning curves curiously are always "proxy measures" and just about never graph measures of "learning".  One of the best examples I know of is the learning curve of education, that presents students with a similarly large challenge in the first months of every higher grade with larger reading and performance demands, which most master by the end of the year.  That's a conceptual model of a staircase sigmoid curve, with successively bigger steps, but I think is summarizes the long view of learning curves very well.JessieHenshaw (talk) 19:54, 20 May 2017 (UTC)


 * Reference : Novarese, Marco & Lanteri, Alessandro & Tibaldeschi, Cesare, 2010. "Learning, Generalization and the Perception of Information: an Experimental Study," MPRA Paper 28007, University Library of Munich, Germany.

ExpertIdeasBot (talk) 16:02, 12 July 2016 (UTC)

Phantom Figure 8
Hi, The "Examples and Mathematical Modeling" section of learning curve article refers to a "fig 8" that is supposed to describe experience and proficiency graphed logarithmically. I cannot find this graph by either visually scanning the article or by using ctrl+F. Could someone find and add this graph?

Economicactvist (talk) 13:51, 28 April 2017 (UTC)

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Back in the day...
when I went to business school, the learning curve looked like this: https://i.imgur.com/doKGSc1.jpg

When did this change? I didn't get the memo. soibangla (talk) 17:40, 5 April 2019 (UTC)

How can you draw a graph when the two axes have no scale?
To the best of my knowledge, learning as described in Wikipedia ("Learning is the process of acquiring new understanding, knowledge, behaviors, skills, values, and preferences." (from Wikipedia's "learning" article, referenced in the "learning curve" article)) is (too) hard to quantify in an objective / verifiable way, therefore validation/falsification of a measurement is close to impossible. The same for experience ("Experience is the first person effects or influence of an event or subject gained through involvement in or exposure to it." (from Wikipedia's "experience" article, referenced in the "learning curve" article). I think that what is meant in the article is not "experience" but "competence" (in a human resource context defined as: "Competence is the set of demonstrable characteristics and skills that enable, and improve the efficiency of, performance of a job." (Wikipedia), in a more general setting I suggest replacing "a job" by something like "an intended behavior")).

So what do the graphs show?

To be informative, the graph should show, on one axis, the result of an effort, e.g., for carambole billiards, the average number of points, "caramboles" per turn, and on the other axis the effort, in the billiards example, e.g., the hours spent at the table, training. Given the meaning commonly attached to "a steep learning curve", the effort should be the vertical axis.

To put it differently: in the graphs in the article, as well as in the text, "learning" should be replaced by something like "investment in learning", and "experience" should be replaced by a "competence"in a broad sense, i.e., not the narrow HR sense, referring to a job.

For comparing the steepness of learning curves, some norm has to be invented. For example, to play chess at top 10 world level on average requires an investment of 12.000 hours (assumption, just for the example), to play carambole billiards at top 10 etc. 16.000 hours, and for tennis this in 10.000 hours. So the learning curve for carambole billiards is the steepest. This is, of course, in the lies, big lies and statistics realm, since other elements play a role (how are the figures for club-level average play? how is this influenced by the number of people that are active in the sport (at the given level), etc. etc.

In other words: to be of any meaning, the model used has to be very rigorously defined. I'd say ;-) — Preceding unsigned comment added by Willeeuwis (talk • contribs) 18:06, 5 May 2020 (UTC)

Labeling of axes in graphs
Proposed labeling of axes for graphs in this article: Attaining a small amount of proficiency requires much cumulative effort when there is a steep learning curve.
 * Vertical axis: Cumulative effort
 * Horizontal axis: Proficiency

As said by JavaLatte:
 * The term is often used about situations where somebody has to work very hard for a fixed period of time, for example "His first day in his new job was a steep learning curve". it's the amount of effort that's important

There can be a vast difference between (progressive) cumulative effort and "experience."
 * ''A lot of people in business say they have twenty years experience, when in fact all they really have is one year’s experience, repeated twenty times.

- 2601:156:1:9D10:65FA:3974:F767:6C08 (talk) 16:43, 6 May 2020 (UTC)