
The $25B eigenvector (2006) [pdf] - onecooldev24
https://www.rose-hulman.edu/~bryan/googleFinalVersionFixed.pdf
======
cs702
An oldie but a goodie. IMHO, this paper, along with Larry and Sergei's
original work[0], _should be_ part of every Linear Algebra course. Few things
get students to pay attention like the mention of ungodly amounts of money!

[0]
[http://ilpubs.stanford.edu:8090/422/1/1999-66.pdf](http://ilpubs.stanford.edu:8090/422/1/1999-66.pdf)

~~~
konschubert
_Unasked for, arrogant rant:_

Do you mean in school or in university?

Because if somebody is taking linear algebra in university and still didn't
understand that this is an extremely important topic, then he should maybe go
back to school or take a gap year or something to improve his general
education.

From a university lecture in linear algebra, I expect that it carries me
through as many important topics as possible while giving me the tools to form
a good formal and intuitive understanding.

The motivation part should be solved by that time.

~~~
mindcrime
Ya know, I get what you're saying and I am somewhat sympathetic to this
position. But I think you're being a bit harsh. It's easy to talk about
"understand(ing) that this is an extremely important topic" when you _already
know_. But how many high-school kids really know anything about Linear Algebra
or understand much at all about how/where it's used? Heck, rewind time a bit
and ask if _you_ really understood that when you were first starting college.
And if you did, realize that you are probably the exception.

 _From a university lecture in linear algebra, I expect that it carries me
through as many important topics as possible while giving me the tools to form
a good formal and intuitive understanding._

Sure and unless your goal is to do pure mathematics research, part of that is
providing some motivation in terms of understanding applications. There's
nothing wrong with a class on LA (or any other topic as far as that goes)
spending some time motivating study of the topic by showing how it can be
useful... even explaining how it might used to make millions or billions of
dollars.

~~~
zitterbewegung
When I took math in college there was no motivating examples for nearly
everything. I had to complete my CS courses to understand nearly a quarter of
the actual applications of what I learned in my math class. The only reason
that I even know more applications right now is the fact that I am trying to
teach myself SMT solving and ML. Why can't we have a math book that has
motivating examples applicable to everyone? Or if that is too hard then just
one for Computer Science?

Right now in nearly every Math book that is bought by a College student or
High School student has motivations in Phyaics. So a person could go through
HS, get their Undergraduate degree in CS and then never figure out how math
could be useful in their job at all. When students ask "when am I going to use
this" you have already failed in teaching your students how to apply this.

Once they have reached this point either they will have a really bad
impression of math and just give up OR they will believe whatever you say
after words and get rewarded ten years down the line.

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s-c-h
I am curious to know what major innovations in search engines happened since
the page rank algorithm, or were there only incremental improvements?

Also is search considered a solved problem?

~~~
saagarjha
> Also is search considered a solved problem?

I certain wouldn't, since I still encounter things that I _know_ are on the
internet but Google can't find. It's possible that the next advance won't be
actually indexing the web but rather figuring out what the user _wants_ rather
than what they _requested_.

~~~
osrec
Google does this to some extent. Recently I've found that Google uses my past
queries to make cogent suggestions for my next search (essentially to predict
what I want next based on prior info). Eg, if I've just searched for "sully",
then a short time after type "t" into Google, the first suggestion is Tom
Hanks. I've only noticed this in the last few months.

~~~
leggomylibro
My favorite example of this is the Bullet physics library.

Google eventually learned to give me documentation in response to stuff like
'bullet collision', but for awhile it was big on youtube links and gun ranges.

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dboreham
Well...pretty much everything important turns out to be an eigenvector.

~~~
tw1010
That has less to do with some mysterious fact about eigenvectors, and more to
do with the fact that linear algebra is incredibly incredibly well studied and
understood; with octopus arms sticking into every special case of applied
mathematics imaginable. Give it a few decades and "everything" will be some
other (today obscure) mathematical idea.

~~~
comicjk
At least one part of the universe really does seem to prefer linear algebra:
quantum mechanics. Every quantum state is a linear combination of
eigenvectors, and that's unlikely to change within a few decades (it would be
a revolution analogous to the discovery of quantum mechanics itself).

~~~
tw1010
I would argue that the reason QM is expressed in linear algebra is also not a
mysterious property of LA, but because that is what was part of the physicists
curriculum when the field was developed.

~~~
comicjk
Physicists would have preferred to do it with calculus -indeed, intro QM is
usually taught with calculus, not with linear algebra. But you can't go very
far without talking about operators and eigenstates. Linear algebra fits the
underlying physical phenomenon. People have tried to develop nonlinear
versions of quantum mechanics, with no success so far. In particular, if
quantum mechanics was not exactly linear, then a quantum computer would be
able to solve NP-complete problems in polynomial time!

To get an intuition of why quantum mechanics looks the way it does, Scott
Aaronson is extremely helpful:
[https://www.scottaaronson.com/democritus/lec9.html](https://www.scottaaronson.com/democritus/lec9.html)

~~~
eigenstuff
I think the main reason for the initial focus on calculus in intro QM is more
to do with making sure you have a solid grasp of the ugly, complicated, hard
way of doing things before diving into the more elegant, easy way (once armed
with an appreciation of all the whacky machinery under the simplified
proverbial hood). I recall my intro classical mechanics had a similar approach
on a few topics, and my professor explicitly said this was the reason for it.
That and the elegant way is generally more abstract, and it's important to
have the foundation the abstraction was built on first.

The link you posted looks interesting and fun to read, I'm looking forward to
going through it after work. Thank you!

~~~
comicjk
I'm not a fan of the teaching method where you do something the hard way first
so you'll appreciate it, but I was a pretty lazy student so that's
understandable. Maybe it works for most students.

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amelius
Sadly, this seems to be the last thing we've ever heard about the search
algorithm of Google. It tells nothing about topics like modern natural
language-processing (which defines a different, non-global, ordering of search
results, based on the query). How much of the basic algorithm is still in
effect?

~~~
endymi0n
From everything that is publically known, assume PageRank to still exist and
be one tensor feature on the RankBrain algorithm.

[https://searchengineland.com/faq-all-about-the-new-google-
ra...](https://searchengineland.com/faq-all-about-the-new-google-rankbrain-
algorithm-234440)

Although there haven't been any major announcements, from daily anecdotal
evidence I can confirm it's still a major factor to get you into the front
pages.

I'd say the major changes since deprecating PageRank in practice are 1\. Much
higher dependence on CTR and bounce rate once you start showing up in the
SERPs 2\. Much higher influence of a notion of "trust" on links (not just the
quantity, but mainly the quality counts now, too much quantity without quality
can actually hurt) 3\. PageRank much more disconnected from domain level. A
few years ago, you could rank with pretty much anything if your DomainPop was
high enough. By now, Google got much smarter about different folders that
don't have anything to do with what it's ranking your main site for and it's
harder to get them ranking. On the bright side, they also got smarter about
the negative SEO influence of subdomains or domain changeovers, which won't
cost you as dearly.

So TL;DR: PageRank still exists, but it's been reduced to an input vector.

~~~
SamPutnam
For example: "2 or 3 years ago links was 80-90% of what it took to get
something ranked, Panda has changed that in an insane way. Here's the test
example. Go to Google and search for 'best time to visit Tahiti'. You'll find
my little site, VisualItineraries up there, #1 for that, ahead of TripAdvisor,
Lonely Planet, USA Today, all these other sites. These other sites have
between 10,000 and 250,000 domains linking to them. My site has under 100. I
rank #1 for that. Now in case you think it's internal link, anchor text, or
page title match. Here's the other proof. Do a google search for 'when should
I go to French Polynesia'. The only word in that that matches the page title
or any anchor text is the word 'to' \- (and it's a) stop word - that's not
going to count. VisualItineraries.com is #1 for that too.

source:
[https://www.youtube.com/watch?v=7RvRUt9ejkw](https://www.youtube.com/watch?v=7RvRUt9ejkw)

~~~
PuffinBlue
I've found this too. My tiny little site sits at number one (for most people
in English) for most combinations of 'why was Margaret Thatcher hated?'

It out ranks national news papers and all sorts of huge sites, as it should
really the info in the post is pretty comprehensive and sourced.

Somehow Google worked that out for itself based on way more than the old page
rank back link weighted algorithm.

------
davesque
The resources already linked from this thread are surely superior but, as a
shameless plug, I wrote a blog article recently on this very topic as it was
presented in my linear algebra course at CU Boulder:
[https://thought.place/articles/2017/7/22/pagerank/](https://thought.place/articles/2017/7/22/pagerank/)

------
chepeadan
Click bait title. You can say the same about sums and multiplication, they are
at the basis of most trillion dollar technologies :P

~~~
jamez1
This isn't about eigenvectors in general, it's about a single eigenvector that
Google built. The title is accurate, their search product is giving you access
to query the eigenvector

------
cdibona
This post has happened before, it'll happen again:
[https://news.ycombinator.com/from?site=rose-
hulman.edu](https://news.ycombinator.com/from?site=rose-hulman.edu)

------
Fej
This article is from 2006. It's interesting but I'd hazard a guess that it's
hardly relevant to what Google is doing now.

~~~
N_A_T_E
Google has always spoken about adjustments to pagerank and they have been
visible but I assume the core concept still applies. Maybe someone with more
inside knowledge can comment?

~~~
saagarjha
Nice try, Bing.

But in all seriousness, Google is notoriously tight-lipped about how PageRank
works, so I doubt we're going to get any more information than this. I'd love
to proven wrong, though!

