I agree with the sentiment -- learning *how* to learn and collecting those aha insights is the goal of education. But it depends so much on the professor to present material in this way -- I went to a good school and the difference in teaching quality between professors for the same subject was astounding. Academia rewards publications, not the praise of students.
Shameless plug, but I've been blogging at betterexplained.com with the goal of sharing the "aha" insights that make math & science enjoyable. Given your viewpoint, you might find it interesting.
(shameless plug)
I'm a nerd as well, and built an online calculator/spreadsheet for myself. It's a new take to an old problem: instant answers, inline units (MB, GB), and shareable results. Yes, it handles 850 * 77.1 and more.
I never thought I'd be arguing about Transformers on an internet forum, but here we are. I support you.
Guys, realize that you suspend your disbelief when watching a movie. Sure, alien robots could have evolved. Sure, they could fight. Sure, they could come to Earth and fight.
But make the body panels go somewhere! Make the mass roughly the same! (G1 Soundwave included... that bothered me even as a kid).
Inconsistencies beyond the realm suspended disbelief jolts you out of the illusion.
Star wars isn't "realistic" (or about as likely as transformers), but it's fine within that universe. But when they try to do crazy things like explain the force as being a physical property in your cells (ooh... can I have a force transplant?) the movie gets really bad really quick.
My.02
People often get stuck in a false dichotomy when choosing between a web and desktop app.
The simple answer is to use the web version for what it's good for (centralized updates, rapid development) and the desktop version for what it's good for (performance, offline access).
Some apps run a local webserver on a non-standard port (Yahoo Music Engine) to create a hybrid model. Javascript/HTML can be a very effective rapid prototyping tool.
For instacalc, I have an online version and downloadable gadgets to fill this need. I use both thunderbird (fast access to mail, offline access) and gmail (access from any computer) to read my email. The "secret" is letting a web app be a web app, and a desktop app be a desktop app. Use the right tool for the job.
Shameless plug -- I have a tool that can help you convert your yearly salary into dollars per hour. Thought you might find it useful for this discussion:)
"Switching to POST and denying GET: Forms can be trivially altered with DOM manipulation to forge POST requests."
I'm not an expert in CSRF (hadn't heard about it till this incident, which sparked my interest), but is this a problem? Do you know how this could be done?
The code is pretty straightforward. Basically, Google docs has an embedded script that will run a callback function, passing the function your contact list as an object. The embedded script presumably checks a cookie to ensure you are logged into a Google account before handing over the list.
Unfortunately, the script doesnt check what page is making the request. So, if you are logged in on window 1, window 2 (an evil site) can make the function call. Since you are logged in somewhere, the cookie is valid and the request goes through.
Also, if you check the object that is returned, you see fields for the contact's name, email and "affinity". Presumably, a higher affinity means a more-emailed contact, so it may be possible to know the relative weight of links.
Possible solutions
Google is run by smart people and I'm sure they'll have this fixed soon. A few suggestions appear to be popping up, all centered on making sure the user is on a Google.com page and not a random site:
Referrer blocking: Block all requests from sites not in the google.com domain. However, some people run referrer-blocking software. It may be the price they have to pay for security, but there could be other consequences.
Script checks: An idea I had was to check the window.location (just like you check the cookie) to make sure it's coming from a google.com domain. This is another way to see what page is making the request.
Challenge-response: Google pages (like Gmail) can have some token or unique, computed data that they submit with their requests. Random pages won't have access to this token when they make the function call.
(From user JRF on reddit): Include part of cookie in the request URL as a unique token that only a "real" Google page would know. Need to watch out for proxies/browser history (accessible from other pages) being able to access this unique data. May need to seed or salt it in a challenge-response system.
It's interesting thinking of fixes for this - do you have any other suggestions for how Google would fix this?
66 km^2 in miles^2 = 25.48 miles^2 66 km^2 in furlongs^2 = 1,630.89 furlongs^2 66 km^2 in rods^2 = 2,609,432.82 rods^2
Shameless plug: I made these using http://instacalc.com/beta/, a new tool I've developed. Feel feel to play around for all your conversion/calculation needs:)
Thanks for pulling this together. I whipped up a quick chart to help visualize the difference. It's amazing how many DSs were sold! Nearly double the PSP and almost 5x the PS3.
Based off pure revenue, Microsoft appears to take the lion's share with 30%. But as we all know, revenue and profit are quite different. You can play around with the numbers above to get a feel for who's coming out ahead - I may have a mistake in my formulas.
Thanks, totally agree. The lack of comments is pretty disturbing, esp. if this is a core routine. It's not immediately obvious if it works on 32- and 64-bit architectures, big or little-endian machines, etc. Although in this case, even if it were commented, the comment might look something like this
// Computes inverse square: 1/sqrt(x) // using Newton's method of approximating roots and a magic number as an initial guess. // See this master's thesis paper and the IEEE floating point spec on why I chose this number:...
The code is extremely clever. Net: It finds the inverse square root [1/sqrt(n)] using a great initial guess and one iteration of Newton's approximation method. It avoids excessive division, the square root operation, and multiplication, which are computationally expensive.
I'm not an expert, but heres how I understand it:
1. Background: Newton's method finds roots of any function ------
What does factoring an equation have to do with finding 1/sqrt(n)? A lot. Give me a number n. I now make the function
f(x) = 1/sqrt(x) - n
Notice that when you find an x where f(x) = 0, it means x is the inverse square root of n:
f(x) = 0 1/sqrt(x) - n = 0 1/sqrt(x) = n x = 1/sqrt(n)
In other words, I need to find the root of that equation. Newton's method lets you do this by picking a starting value, seeing how far off you are, and getting closer and closer with each iteration. There's more info online. With Newton's method, call your initial guess "g". An better approximation for the root is
guess_new = g - f(g)/f'(g)
In our case, f(x) = 1/x^2 - i (where i is the initial value, as seen in the code). We use the power rule to see that f'(x) = -2x^-3, and plug it into the guess_new equation above:
which is exactly what the code above has. If you keep plugging "guess_new" back in the equation, you can get closer and closer to the answer.
Here is a demo of multiple iterations to find inverse square: http://tinyurl.com/vh7hg/ Try plugging in different initial guesses (.2,.4,.8) to see how it converges. With me so far? Newton's method finds roots, and finds them fast if given a good guess.
2. Now our problem becomes: How can we make a good guess? ------
If we had a lot of time, we could just pick a random number and keep iterating using the method above. But that would be slow - we want a *good* guess.
Well, our best guess for the inverse square root is the inverse square root itself! What's a good way to get 1/sqrt(n)?
This is the first level of magic. Assume you have a number in exponent form, like this:
10^6 = 1 million
If you want to find the regular square root of 1 million, just divide the exponent by 2. sqrt(10^6) = 10^(6/2) = 10^3 = 1 thousand.
If you want the *inverse* square root, divide the exponent by -2 to flip the sign.
invsqrt(10^6) = 10^(6/-2) = 10^-3 = 1/thousand
Ok so far? Our goal is to divide the exponent of i (our number) by -2 to get a really awesome guess for Newton's approximation method.
3. Floats are stored in mantissa-exponent form ------
This is the key. Floating-point numbers have an explicit exponent and mantissa component. Theoretically, we could mask out the bits for the exponent and do division.
But division is expensive; the code uses another clever hack. Shifting bits is the same as dividing by 2 (or 4, 16, or any other power; the remainder is truncated, which is OK for an approximation).
So we can divide by 2 easily. And if we want a negative number, instead of multiplying by -1 (expensive), we can just subtract the number from "0" (cheap).
The program converts the floating point into an integer (using the pointer tricks), shifts the bits by 1 to halve the exponent, and subtracts from "0" (the magic number - hold on) to negate it.
4. Why the magic number 0x5f37...? ------
We can't just subtract from zero, there's too much going on. First, by shifting the bits we mave move some of the exponent bits into the mantissa. Also, there are different cases of odd/even exponents. The paper goes into lots of special cases, I didn't really understand them all first time around. But the magic number tries to minimize errors, and there can be several magic numbers used.
5. What's the result? ------
The result is that you get a great initial value to
Interesting - are there any associations of home schoolers?
Consider this: If a parent is great at Chemistry, but you aren't, maybe you send your kids to their class. In exchange, you teach a weekly class on your subject of expertise. Maybe the home schoolers chip in to rent a room/equipment from the public school, esp. for a class like Chem.
Parents can pick what classes to send kids to, kids get to socialize. Not as formal as regular school, but perhaps has some of the benefits.
This is all theoretical of course; networking gurus can add in the effect of TCP headers, etc. to get a real throughput rate. Feedback is very welcome, thought you'd find this useful.
Slashdot Mirror
Yep, you did it right: 900 GB/month in KB/sec. Of course it depends on how long your "month" is (30 days or 365/12).
I agree with the sentiment -- learning *how* to learn and collecting those aha insights is the goal of education. But it depends so much on the professor to present material in this way -- I went to a good school and the difference in teaching quality between professors for the same subject was astounding. Academia rewards publications, not the praise of students.
Shameless plug, but I've been blogging at betterexplained.com with the goal of sharing the "aha" insights that make math & science enjoyable. Given your viewpoint, you might find it interesting.
Great reply. So many people love to naysay without taking 3 seconds to see that problems can be worked around.
(shameless plug)
I'm a nerd as well, and built an online calculator/spreadsheet for myself. It's a new take to an old problem: instant answers, inline units (MB, GB), and shareable results. Yes, it handles 850 * 77.1 and more.
Thought you might find it useful.
Oh, it's only about 10^32 years. How old is the universe again? =)
B uXm58c3VuIHBlciBzZWNvbmQ9IDEwXjQ1fHNlY29uZHMgPSByM iAvIHN1biBwZXIgc2Vjb25kfHI0IHNlY29uZHMgaW4geWVhcnN 8fA&s=sssssss&v=0.9
http://instacalc.com/?d=&c=biA9IDUwfHBob3RvbnMgPS
I never thought I'd be arguing about Transformers on an internet forum, but here we are. I support you. Guys, realize that you suspend your disbelief when watching a movie. Sure, alien robots could have evolved. Sure, they could fight. Sure, they could come to Earth and fight. But make the body panels go somewhere! Make the mass roughly the same! (G1 Soundwave included... that bothered me even as a kid). Inconsistencies beyond the realm suspended disbelief jolts you out of the illusion. Star wars isn't "realistic" (or about as likely as transformers), but it's fine within that universe. But when they try to do crazy things like explain the force as being a physical property in your cells (ooh... can I have a force transplant?) the movie gets really bad really quick. My .02
People often get stuck in a false dichotomy when choosing between a web and desktop app.
The simple answer is to use the web version for what it's good for (centralized updates, rapid development) and the desktop version for what it's good for (performance, offline access).
Some apps run a local webserver on a non-standard port (Yahoo Music Engine) to create a hybrid model. Javascript/HTML can be a very effective rapid prototyping tool.
For instacalc, I have an online version and downloadable gadgets to fill this need. I use both thunderbird (fast access to mail, offline access) and gmail (access from any computer) to read my email. The "secret" is letting a web app be a web app, and a desktop app be a desktop app. Use the right tool for the job.
Yeah, it's pretty mind-blowing. 350 mph is 500 feet per second!
Shameless plug -- I have a tool that can help you convert your yearly salary into dollars per hour. Thought you might find it useful for this discussion :)
http://tinyurl.com/328b3d
FYI, I put your numbers into a calculator here:
http://tinyurl.com/ydzspv
You can play around with different refresh rates, color depth, etc.
Thanks for the comment. I had wondered about POST requests as well, but a few sources seem to say that POST requests can be forged using Javascript.
t tacks_or_how_to_avoid_exposing_your_gmail_contacts .html
http://getahead.ltd.uk/blog/joe/2007/01/01/csrf_a
"Switching to POST and denying GET: Forms can be trivially altered with DOM manipulation to forge POST requests."
I'm not an expert in CSRF (hadn't heard about it till this incident, which sparked my interest), but is this a problem? Do you know how this could be done?
I posted this on reddit which broke the story earlier, and on my blog. Thought you might find it useful.
. txt
Quick follow-up. On digg someone posted the un-obfuscated code: http://www.cc.gatech.edu/~achille/contacts-source
How it works
The code is pretty straightforward. Basically, Google docs has an embedded script that will run a callback function, passing the function your contact list as an object. The embedded script presumably checks a cookie to ensure you are logged into a Google account before handing over the list.
Unfortunately, the script doesnt check what page is making the request. So, if you are logged in on window 1, window 2 (an evil site) can make the function call. Since you are logged in somewhere, the cookie is valid and the request goes through.
Also, if you check the object that is returned, you see fields for the contact's name, email and "affinity". Presumably, a higher affinity means a more-emailed contact, so it may be possible to know the relative weight of links.
Possible solutions
Google is run by smart people and I'm sure they'll have this fixed soon. A few suggestions appear to be popping up, all centered on making sure the user is on a Google.com page and not a random site:
Referrer blocking: Block all requests from sites not in the google.com domain. However, some people run referrer-blocking software. It may be the price they have to pay for security, but there could be other consequences.
Script checks: An idea I had was to check the window.location (just like you check the cookie) to make sure it's coming from a google.com domain. This is another way to see what page is making the request.
Challenge-response: Google pages (like Gmail) can have some token or unique, computed data that they submit with their requests. Random pages won't have access to this token when they make the function call.
(From user JRF on reddit): Include part of cookie in the request URL as a unique token that only a "real" Google page would know. Need to watch out for proxies/browser history (accessible from other pages) being able to access this unique data. May need to seed or salt it in a challenge-response system.
It's interesting thinking of fixes for this - do you have any other suggestions for how Google would fix this?
Here's some more helpful conversions:
:)
66 km^2 in miles^2 = 25.48 miles^2
66 km^2 in furlongs^2 = 1,630.89 furlongs^2
66 km^2 in rods^2 = 2,609,432.82 rods^2
Shameless plug: I made these using http://instacalc.com/beta/, a new tool I've developed. Feel feel to play around for all your conversion/calculation needs
Thanks for pulling this together. I whipped up a quick chart to help visualize the difference. It's amazing how many DSs were sold! Nearly double the PSP and almost 5x the PS3.
Good catch, thanks. I should have combined it company-wide in the beginning, I was focused on just the next-gen consoles.
I updated the numbers and it actually looks like Sony actually pulled in the most revenue overall!
sony = ps3 + ps2 + psp = 254,150,000
microsoft = xbox360 = 200,000,000
nintendo = wii + nintendo_ds + gba = 236,900,000
Surprising, huh? Of course, the ps2 sales may be cannibalizing possible ps3 sales.
I plugged in the numbers into an editable chart (shameless plug for my site! :)
xbox360 = 500k * 400 = 200,000,000
ps3 = 200k * 600 = 120,000,000
wii = 500k * 250 = 125,000,000
ps2 = 500k * 129 = 64,500,000
nintendo_ds = 600k * 129 = 77,400,000
psp = 350k * 199 = 69,650,000
Based off pure revenue, Microsoft appears to take the lion's share with 30%. But as we all know, revenue and profit are quite different. You can play around with the numbers above to get a feel for who's coming out ahead - I may have a mistake in my formulas.
The code is extremely clever. Net: It finds the inverse square root [1/sqrt(n)] using a great initial guess and one iteration of Newton's approximation method. It avoids excessive division, the square root operation, and multiplication, which are computationally expensive.
.4, .8) to see how it converges. With me so far? Newton's method finds roots, and finds them fast if given a good guess.
I'm not an expert, but heres how I understand it:
1. Background: Newton's method finds roots of any function
------
What does factoring an equation have to do with finding 1/sqrt(n)? A lot. Give me a number n. I now make the function
f(x) = 1/sqrt(x) - n
Notice that when you find an x where f(x) = 0, it means x is the inverse square root of n:
f(x) = 0
1/sqrt(x) - n = 0
1/sqrt(x) = n
x = 1/sqrt(n)
In other words, I need to find the root of that equation. Newton's method lets you do this by picking a starting value, seeing how far off you are, and getting closer and closer with each iteration. There's more info online. With Newton's method, call your initial guess "g". An better approximation for the root is
guess_new = g - f(g)/f'(g)
In our case, f(x) = 1/x^2 - i (where i is the initial value, as seen in the code). We use the power rule to see that f'(x) = -2x^-3, and plug it into the guess_new equation above:
guess_new = x - (1/x^2 - i)/-2x^-3
guess_new = x(1.5 - ix^2)
which is exactly what the code above has. If you keep plugging "guess_new" back in the equation, you can get closer and closer to the answer.
Here is a demo of multiple iterations to find inverse square: http://tinyurl.com/vh7hg/ Try plugging in different initial guesses (.2,
2. Now our problem becomes: How can we make a good guess?
------
If we had a lot of time, we could just pick a random number and keep iterating using the method above. But that would be slow - we want a *good* guess.
Well, our best guess for the inverse square root is the inverse square root itself! What's a good way to get 1/sqrt(n)?
This is the first level of magic. Assume you have a number in exponent form, like this:
10^6 = 1 million
If you want to find the regular square root of 1 million, just divide the exponent by 2.
sqrt(10^6) = 10^(6/2) = 10^3 = 1 thousand.
If you want the *inverse* square root, divide the exponent by -2 to flip the sign.
invsqrt(10^6) = 10^(6/-2) = 10^-3 = 1/thousand
Ok so far? Our goal is to divide the exponent of i (our number) by -2 to get a really awesome guess for Newton's approximation method.
3. Floats are stored in mantissa-exponent form
------
This is the key. Floating-point numbers have an explicit exponent and mantissa component. Theoretically, we could mask out the bits for the exponent and do division.
But division is expensive; the code uses another clever hack. Shifting bits is the same as dividing by 2 (or 4, 16, or any other power; the remainder is truncated, which is OK for an approximation).
So we can divide by 2 easily. And if we want a negative number, instead of multiplying by -1 (expensive), we can just subtract the number from "0" (cheap).
The program converts the floating point into an integer (using the pointer tricks), shifts the bits by 1 to halve the exponent, and subtracts from "0" (the magic number - hold on) to negate it.
4. Why the magic number 0x5f37...?
------
We can't just subtract from zero, there's too much going on. First, by shifting the bits we mave move some of the exponent bits into the mantissa. Also, there are different cases of odd/even exponents. The paper goes into lots of special cases, I didn't really understand them all first time around. But the magic number tries to minimize errors, and there can be several magic numbers used.
5. What's the result?
------
The result is that you get a great initial value to
Interesting - are there any associations of home schoolers?
Consider this: If a parent is great at Chemistry, but you aren't, maybe you send your kids to their class. In exchange, you teach a weekly class on your subject of expertise. Maybe the home schoolers chip in to rent a room/equipment from the public school, esp. for a class like Chem.
Parents can pick what classes to send kids to, kids get to socialize. Not as formal as regular school, but perhaps has some of the benefits.
I've whipped up a calculator to estimate download time:
Download Time CalculatorThis is all theoretical of course; networking gurus can add in the effect of TCP headers, etc. to get a real throughput rate. Feedback is very welcome, thought you'd find this useful.
But wait, this is slashdot... don't we have a polite way to tell users to read the manual? =)
There is also mysql_escape_string which can clean up quotes for you.
not to nitpick, but GPS uses triangulation as well =)
"How come" does sound colloqial, but I consider it shorthand for:
If the members of mensa are so clever, how [did it] come [about that] there are so many of them?
I really enjoy martial arts, from karate (mainly stand-up striking) to jiu jitsu (groundwork, grappling).