@Nasser I haven't encountered that before, but it's interesting. I'd guess that if no results are found they automatically fall back to "people that searched for 'lambert' also searched for 'orbit'" type searches and show the first of those that has any results.

@MichaelHale I use google search alot, much faster than searching all the books I have ;) and I've seen this so many times. This seems to be recent. I do not remember this many false positives before. May be google have so much $$ now they do not care about search any more.

But your theory sound possible. Google just recently started adding more AI to its search engine. it was in the news. I'll find a link

I think Google cares more about if the result helped you instead of if "lambert" was found specifically. If you add quotes around lambert in your search to make it exact then no results are found.

@MichaelHale yes. But I want to find a page with all the words. Then I have to do this "word1" "word2" "word3" to search for page that contains all 3 words?

I can't write "word1 word2 word3" as it will take this as one string.

This, for me, makes no sense. But what do I know about search. we are talking about google here.

Right. I'd guess that the more words in your query the less branching it does for related terms.

google.com/advanced_search

support.google.com/websearch/answer/136861?hl=en

I don't know of a multi-keyword query off the top of my head that gives bad results without quotes that I could try with quotes around each term.

site:www.braeunig.us "lambert" "problem"

@Nasser yes, I agree, Google is getting worse. They changed how the search terms are interpreted. In the past, I would often give a complicated Boolean-type query, and it worked fine. Now, it doesn't, and the reason is that your search terms are interpreted fuzzily. If something almost matches, that's good enough. The way to avoid it is to quote the search terms, but this is IMO inferior to the old way

Gives no results though, which is what you want I think.

@MichaelHale what do you mean by "Gives no results though"? Which one.

Quite often it will include results that are linguistically related but conceptually unrelated to your query. I find it very annoying to have to add a lot of "NOT x NOT y NOT z" to the end of the query to avoid Google's fuzzy logic.

"lambert" "problem" gives no results which shows that it is doing an exact-and search as you want.

I think the vast majority of searches Google receives are intended to be general. It's easier for technical people to remember to put quotes than for non-technical people to remember to put asterisks around terms to include related terms, for example.

You might be right. But a lot of the time Google generalizes a query to understand it as precisely the opposite of what you meant to search for. If you don't immediately realise it did this, you can waste a lot of time looking through the hits for the information you need and getting frustrated that they are all talking about something you explicitly did not want to know about. Highly specific/uncommon searches are now much more difficult to accomplish successfully.

@MichaelHale yes, but I did not use "". And having to use "" around each word is bad. And having to use advanced search each time is worst. I guess this is time for another one of my famous screen shots :)

The first search says that lambert was not on the page, this is fine and good. But the second search did not ! that is the problem for me. This again happens so many times. It must be like @OleksandrR. is saying, they changed something in the search algorithm. it is very frustrating to search for page with the words you want, they go to the page and find one of the words you wanted are not there.

I agree they should be consistent there and say it is missing in the second one too.

But I'm glad that searching for world war 2 also includes results for world war ii by default.

I think they don't say it's missing since they somehow inferred heuristically that "Lambert" has something to do with calculating orbits, which is what this page is about, and therefore it "must" be relevant. A classic example of Google returning results that are the opposite of what was asked for.

I think they are behaving reasonably to give that result for lambert and no results for "lambert". It would be nice if they saved you a search on the page by saying that result came from expanded results, but it seems they only list missing terms for multi-word queries.

A major problem with this is that if your search target is uncommon, but the thing you are not interested in is common, you have to exclude the common thing explicitly using NOT or minus prefixed to it. But this also excludes those pages that discuss both, which can be quite a few if the concepts are related but different. So you have a vast number of irrelevant results interspersed with a few relevant ones, if you're lucky, or no relevant results at all if you're unlucky.

I agree there are limitations to keyword based search technologies.

@MichaelHale the problem is not with the idea of a keyword search. It arises because Google considers keywords only partly relevant to the results and tries to infer your possible meaning from the context of the search and what other people have searched for, what is discussed in the hits, and so forth. When it happens that the desired query is expressed exactly by the keywords used and cannot easily be expressed in another way, this broader interpretation becomes an inconvenience, at the least.

So then you put quotes around the terms, right?

@MichaelHale doesn't always work. Google always considers (for example) "linear" close enough to "nonlinear" that it will include results for "linear" even if you have "nonlinear" in quotes unless you specifically add -"linear". But then you can't see any pages that discuss "linear and nonlinear". If "nonlinear" is a highly specialized topic, these pages might be the only ones that exist, so there are no useful hits.

The result is that you have to either wade through a sea of irrelevance looking for something that might not even exist, or get nothing at all from the beginning. This is frustrating for obvious reasons, but doubly so since in previous years Google made things much easier by taking queries literally.

I'm still very confused. You can search for nonlinear to see results for nonlinear and linear and you can search for nonlinear -linear to see results for only nonlinear. But you're asking "What if I want to see results for term A and not term B, when all pages that talk about A also talk about B?"

Consider the case of two searches, one very common, and one uncommon to the point where you don't know whether anyone has even discussed or thought about this before. In technical fields Google can often consider these two related since they use "similar" search terms even if conceptually they are not the same at all. When term B pages outnumber term A pages by a million to one, you have a million term A pages to look through before you find your desired one term A and term B page.

You mean a million term B pages? Search engines knew to prioritize results that contain two search terms above results that contain one search term well before Google.

Of course, the problems are vastly compounded when the search is based on a phrase rather than a particular word because it is difficult to anticipate what false context Google will infer to surround your query in that case.

So then you put quotes around it to prevent expansion.

@MichaelHale yes, I meant term B, sorry. Anyway the point is that one only ever searched for term A, but Google interpreted it as if it was a search for term A OR term B which is not what you wrote but Google thought was related. This interpretation is not easy to undo and it is not solved by prioritization, which is based on a variety of factors

@MichaelHale this makes the problem orders of magnitude worse because now you have to imagine every possible phrasing of your search term that includes it while excluding whatever Google imagined that you might have meant.

Anyway this is perhaps not a common use case, so you could be forgiven for not having experienced it. When you do, you'll know my (our) frustration!

I think I'm getting more confused. Now it seems to me like you are saying that the default behavior should be to find pages that include only the search terms and no other words at all.

@MichaelHale agreed. That should be the default. Or at least there should be an option to switch off heuristics altogether.

So if I search for Mathematica, it should exclude all pages that include the word "the"?

@MichaelHale if you search for Mathematica, you get pages that are about mathematics, because Mathematica could be a misspelling of mathematics. Did you want a million mathematics pages or did you want your Mathematica page? (Actually Mathematica is a relatively common search term and a single word so this situation does not exist in practice. But it does happen for less common terms.)

@MichaelHale not exclude. But it shouldn't include pages that do NOT include the search term.

But it only does that if it thinks you probably made a typo or if no results are found, right?

@MichaelHale of course few/no results will be found if your query is highly specialized and uncommon! The problem arises exactly because in these cases Google can assume you really meant to make a related very common search.

Ok, I understand the situation you are describing, but I can't think of an example.

I just made up "Harry Botter" as a potential less popular book that has nothing to do with Harry Potter, and the results seem entirely reasonable.

Well, fortunately, these examples are (perhaps by definition) not very common. Unfortunately the only approach I've found that works to address the situation is to give up and try a conceptually related query that it is less easy for Google to misconstrue

@MichaelHale not a great test since more than likely "harry botter" doesn't really exist and even if it does then you are not looking for some very specific information about it. The problem is only evident when you are seriously searching for something and will know for sure whether you found it or not.

Well, if you find an example I will try to help you, and if we can figure out a way to automate making it better we can sell it to Google.

@MichaelHale next time I have an example I'll be sure to let you know. I would like to give you one now but can't quite recall what gave me problems in the past. When you encounter this problem, though, it is really infuriating, uncommon as it may be.

@OleksandrR. @MichaelHale I'll start collections of such google search false positives, including the one I showed above. I created a new VISIO document and will keep adding more as I find more. I find such examples all the time. When I collected many will ping you both :)

@MichaelHale this is not the best example, but try e.g. high speed linear optocoupler. "high speed" "linear optocoupler" does not really help. This gives an idea of the difficulties but the situation can be worse in other cases.

@OleksandrR. I run your example. yes, this is what I mean. I would have expected both these results below to show same number of hits. But they do not?

with no quotes around each word, it found over 4 million pages. with quote around each word, it found only 75 thousand pages.

@Nasser well, what I meant is really that "high speed linear optocoupler" is a monolithic concept, i.e. a linear optocoupler with a fast response time or wide bandwidth. The individual words or groupings thereof do not mean the same thing and produce many irrelevant hits.

For instance Google produces a "high linearity optocoupler".

So I see the first result and then I change it to high speed linear optocoupler -"high linearity" Does that help? Do you have an example of a page that you think should be first in that query?

@Nasser by the way, the "about x hits" can be severely incorrect. It should be regarded only as an order-of-magnitude guess because Google does not collate all the results in one go.

@MichaelHale would this search help you to show me a high speed linear optocoupler that one can buy or a circuit for it that someone has designed? No, you get a lot of "high speed optocoupler" and "linear optocoupler" and people asking for whether anyone else knows of a high speed linear optocoupler?

But I still say there are false positives. Will start a collection.

The third result is "Optocoupler Selection Guide" with a table of different performance characteristics. Does that not help find one?

@MichaelHale of course if one is looking for an optocoupler the first place one looks is in the selection guides and on Digikey and whatever. And finding nothing suitable, then what?

Lol. Then I guess build something better.

@MichaelHale Wolfram Alpha? :) (more AI !)

No, I mean build a new circuit component, not another website.

@MichaelHale but typically I don't want to waste my time building a component myself when someone has designed it already and sells it but Google just can't find it. (By the way, in that selection guide there was not a single high speed linear optocoupler.)

If you already know someone that has designed it and sells it then why do you need Google?

@MichaelHale well how do I know that? The point of using Google is surely to find out, is it not?

I don't know much about optocouplers, but if someone searches for "fast processors" it's not Google's fault if no one is selling 10 GHz ones.

@MichaelHale you should bear in mind that this is just an example. I don't really care about high speed linear optocouplers. It is just something that is not unreasonably obscure and that I can imagine someone wanting, that nonetheless is rare enough that Google can't find it.

Right, so how do you decide if Google can't find it or it just doesn't exist?

@MichaelHale I just found another false hit. I used your "" method. (will use that from now on actually). Please see

and the third link had false positive. It picked "Version:10" as the same as "Version 10" even though I used exact search term with quotes. I selected LAST WEEK only also.

Well I could make it myself if I was desperate, so yes it exists because it solves a real problem that someone will have encountered before. If I wanted to solve it as well, it would be useful to me to see how someone else did so, before possibly wasting my time with unsuitable designs.

@Nasser I get different results. You could try DuckDuckGo.

is DuckDuckGo better than google? Never tried it, but heared of it.

Oh, I didn't see last week constraint.

sorry, forget to mention the last week constraint first.

@MichaelHale apart from that, designing it to make sure it worked properly would entail considerable effort. If I don't know if someone else has done that before and want to find out, then "oh well Google says probably not" is not really an acceptable answer.

I think they allow ":", "-", etc as substitutes for " " in exacts searches.

Right, so you find an electronics forum and ask people.

People that have been reading industry and research journals for a while would be able to tell you where the cutting edge is.

@MichaelHale I want to thank you for the the quotes around each word method. I have been using google all this time, thinking it will find pages with ALL the words that I enter. It turned out it find pages with ANY of those words. silly me. I know use "" around each word. Most of my searches are looking for pages with ALL the words I want. NO wonder I was having such hard time with search finding what I want.

Glad to help.

@MichaelHale well, this is really an apology for Google's inability to interpret the search term correctly. If I put "fast" or "wideband" instead of "high speed" then all the problems are solved and I quickly get here

Varying the search terms also yields many alternative designs. It is really just the misunderstanding of the term "high speed" that leads to problems because of the high frequency with which "high" and "speed" appear other than in that phrase.

@OleksandrR. I agree with you that AI and fuzzy logic has no place in search engine. I do not like a search engine to guess what I might have meant. (other than suggesting correction to spilling errors of course, which I have many). FYI, Google hired an AI company not long ago bits.blogs.nytimes.com/2014/01/28/… "Google Buys A.I. Company for Search, Not Robots"

@Nasser I don't mind it in the common case, to be honest. Even if I don't find it terribly useful most of the time, it can make simple searches more straightforward occasionally. The big problem I find is that, now that this has become the norm, we can't go back to the old situation where queries were understood literally, so searching very precisely has become more difficult than it needs to be.

@OleksandrR. I agree. We need a new search engine, with non of fuzzy, AI type of search. May be this is a chance for some new search engine to take over. At least they could have an option (use AI in search or not), but this might make it harder for google to implement both at the same time.

I don't think it was any easier to filter false positives from "high speed linear optocoupler" queries in the mid-90s.

@MichaelHale well, as I said, this was probably not the best example. It was just one that I came up with quickly. When I have a better one I'll let you know.

bye @MichaelHale and @OleksandrR. got to go finish my long HW. Thanks both for the feed back. was useful.

@Nasser yes, there might be implementation problems that Google chose to circumvent by interpreting all queries broadly. I wouldn't find it nearly as annoying if it wasn't the case that Google of 5 years ago was generally more useful to me than Google of today. But, such is life... have a good evening!

Later, @Nasser. @OleksandrR. Maybe today you are doing more advanced things.

@MichaelHale that is a good point and probably true to some extent. On the other hand when the behavior was first changed I was less than enthusiastic about it from the start since I knew it would lead to problems of this nature.

So when is #$%$%^v10 coming?

could someone please try this in their M? something strange has happend. I run this before and it gave the correct numerical values. Now it does not. So I deleted my answer until I find why. This is the code:

The answer I got before, which is the correct answer is the same as Bill's answer here:

b == 2.6 || b == 0.1 || b == -0.0666667

I have no idea what happened. Using V 9.01 on windows.

@Rojo based on history of M releases, my guess is middle of summer to early winter. So, few months from now.

@Nasser You define m and then call Eigenvalues on mat. Perhaps your correct answers arise from prior definitions laying around somewhere?

Simple mistake. :)

What question?

sorry, this mathematica.stackexchange.com/questions/46417/…

I need to find out why FindRoots gets different result from Det and the symbolic based method.

@MarkMcClure It is the guess value!  Different guess values gives different answers. That is why I do not like to use FindRoot if I am not sure the region where the root is. So I think I'll keep my answer deleted :) When I guess `b=2` I get
{{b -> 0.1}, {b -> 2.29643}, {b -> 2.6}}

But many times, Mathematica NSolve can't set of nonlinear equations, so I use FindRoot. I had this on a HW I am working on. NSolve could not solve 3 very non-linear equations (Lambert problem related), so had to use FindRoot

@Nasser That makes sense. I think that's just the nature of FindRoot. It works best when you've got some sense of an approximation to the solution.

@Rojo #$%$% if I know.

@MarkMcClure In your SE profile, the link to your home-page is dead. Was this done on purpose?

@halirutan Thanks! Our school's IT department has forced us to migrate to Google Sites. I've been using the new site for a couple of semesters now but the school only just finally killed the old server. I'll update soon but, unfortunately, much of my old stuff doesn't really translate over to Google Sites very easily. Thanks again for pointing that out.

Done. The little Julia set image over on the right of the page is generated by the WolframCloud.