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According to Wolfram Alpha, there are enough IPv6 addresses to have one for every 1.5 square picometres of the Earth's surface. If we're talking about /64 subnets, then you can only have one per 27 square millimetres.

Based on current rates of growth and industry trends, how long will it be before the IPv6 space is exhausted?

(Deep breath)
When we have colonised the entire observable Universe (at a (hugely over)estimated one habitable planet per star), our descendants* will be able to own about three-quarters of a million cellphones each.**

Given how hard this transition is, would it be better to go directly to IPv8

If you mean we should skip a step while we're at it, we are: we're going straight from 32-bit to 128-bit, rather than 64-bit.

* In before "this is Slashdot".
** 715,925 cellphones should be enough for anyone!

Now they just need to do the same for economically relevant languages. The top developing countries currently are Brazil, India, and China (in no particular order) and none of them speak Spanish as a primary language.

Querying wolfram alpha, the most spoken languages in the world are:

1. Madarin - 1 Billion
2. English - 760 Million
3. Hindi - 490 Million
4. Spanish - 417 Million
5. Russian - 277 Million

So languages #1,3,and 5 all have a completely different character set (esp. Mandarin), while #2 and #4 share the basic roman character set (with a few symbols outstanding). I can see why they went Spanish. Also, many popular travel destinations (i.e., Central and South America, Spain, etc) have spanish signs where this would be useful.

I expect much more from this company... this is an Apple-like rollout, where the novelty and usability of the first release is outstanding but limited, but it's clear there's more to come. I can't wait for the FrenchEnglish.

Imagine instant subtitling!

the integral of 4sin(x)/x has to be solved with Taylor series, and I only got those in the second semester of university calculus

Fortunately (as is mentioned in the blog post), (working) knowledge of college level calculus is not actually required. You can pretty much plug and chug with wolfram alpha - it's got Mathematica baked into it.

I remember distinctively going over the Taylor Series for the sine function. In fact, we even did a Taylor polynomial expansion for sin(x)/x. This entire thing could be using Wolfram|Alpha in about 5-10 minutes if you take the time to get parenthesis correct.

err... Or you can just google for the answer...

The first result is Wolfram alpha.

Where, if you put in the integral, you can pick out the answer: http://www.wolframalpha.com/input/?i=integral+of+(4+sin+x)%2Fx

Click "Go on computing"

You get the question
http://www3.wolframalpha.com/Calculate/MSP/MSP110419dbee2916i2669300001475f9963d9ebb46?MSPStoreType=image/gif&s=38&w=468&h=156
and result:
http://www3.wolframalpha.com/Calculate/MSP/MSP110919dbee2916i26693000026ffbg47b13125if?MSPStoreType=image/gif&s=38&w=403&h=37

Which is bloody impressive.

90091/191605......
Which we know from the story maps to
goo.gl/spe....

Click "Go on computing"

You get the question
http://www3.wolframalpha.com/Calculate/MSP/MSP110419dbee2916i2669300001475f9963d9ebb46?MSPStoreType=image/gif&s=38&w=468&h=156
and result:
http://www3.wolframalpha.com/Calculate/MSP/MSP110919dbee2916i26693000026ffbg47b13125if?MSPStoreType=image/gif&s=38&w=403&h=37

Which is bloody impressive.

90091/191605......
Which we know from the story maps to
goo.gl/spe....

Here's what the whole thing looks like in Wolfram Alpha all at once: (9*10^4+3^4+10)/100/((2^8-10+4*6!+17^4+11!/5+integ(3x^5,x,1,9))(2*23^6-((2^28+4)/10-(22^4+3*70-sqrt(81))))(3*17^4-(sqrt(256)+31*30^2))(17*8!+93^2-10)(12*(11^2-6)/(5*pi)integ(4sin(x)/x,x,0,inf))-3) - Wolfram|Alpha

The 200 character limit in the input box is annoying, and it seems that you can't get around it by creating a URL manually. Managed to get it from 220 characters to under 200 by using valid shortened stuff like "integ" instead of "integral", and removing * and () where possible.

Wikipedia and WolframAlpha would beg to differ.

More interesting though, there is an parallel to the Interesting number paradox: If there is an uninteresting natural number (or day), there must be a smallest (earliest) uninteresting natural number (date), which would make it interesting of course. Therefor, all natural numbers (days) are interesting.

As it turns out, asking for the tensile strength of aluminum alloy does work. I guess "aluminum" is just too vague. It even gives the option to take it as a class of materials, allowing you to skirt around the problem of multiple alloys in order to make general calculations. It only provides the data in pascals unless you tell it otherwise, but it's trivial to convert from pascals to ksi. This link shows what I mean. I had to click once or twice, but it didn't exactly put me out of my way.

That's just under 3 micrograms of arsenic. According to our trusted interwebs source, wikipedia: "The acute minimal lethal dose of arsenic in adults is estimated to be 70 to 200 mg". In other words, each chip contains about 1/25,000th of the lethal dose, in a non-soluble form.

I'll think you'll be fine.

Well, I did the only sensible thing and entered it into WolframAlpha for analysis. So, at this point, I have determined that "fucking" is a very colloquial, informal intensifier with a Scrabble score of 17 that corresponds to the telephone keypad digits, 382-5464. I give up.

So long as you put the question mark in the right spot . . ..

http://www.wolframalpha.com/input/?i=first+post!

It appears that this functionality is not yet in WolframAlpha http://www.wolframalpha.com/input/?i=the+number+of+surface+area+of+football+fields+it+takes+to+hold+the+library+of+congress+printed+out+on+8.5x11%22+paper+with+1%22+margins&incParTime=true Perhaps we should demand this functionality?

woosh

s/in accordance with their religion//

I agree that this a violation of freedom, but this is a case of religion being subverted for political reasons, not a problem with the religion. Almost every religious group has had its fanatics at one time or another.

Admittedly I don't know a large fraction of the worlds Muslim population (something like 18.5%) but the Muslim folks that I know don't interpret their religion that way.

Oh you beat me to it!

http://www.wolframalpha.com/input/?i=%24741.66+*+inflation+rate+united+states+December+1976+to+November+2010

That's GDP. For federal budget it would be this, but that doesn't split it down to per-person detail. (You spend $15/year on the space program, for instance.)

http://www.wolframalpha.com/input/?i=usa+gdp+%2F+usa+population

Good catch. You're right, that is an error in my math of cubing 5 as an incorrect 75 and not the correct 125.

Still close though. :-)

Maybe we should mostly teach kids how to use the free equivalent (someday) of Wolfram Alpha?
    http://www.wolframalpha.com/
    http://www.wolframalpha.com/input/?i=5+*+5+*+5
    http://www.wolframalpha.com/input/?i=5+cubed

Of course, that might make it too easy to take things completely on faith: :-)
    http://www.wolframalpha.com/input/?i=weight+of+the+earth
"5.9742×10^24 kg"

Good catch. You're right, that is an error in my math of cubing 5 as an incorrect 75 and not the correct 125.

Still close though. :-)

Maybe we should mostly teach kids how to use the free equivalent (someday) of Wolfram Alpha?
    http://www.wolframalpha.com/
    http://www.wolframalpha.com/input/?i=5+*+5+*+5
    http://www.wolframalpha.com/input/?i=5+cubed

Of course, that might make it too easy to take things completely on faith: :-)
    http://www.wolframalpha.com/input/?i=weight+of+the+earth
"5.9742×10^24 kg"

Good catch. You're right, that is an error in my math of cubing 5 as an incorrect 75 and not the correct 125.

Still close though. :-)

Maybe we should mostly teach kids how to use the free equivalent (someday) of Wolfram Alpha?
    http://www.wolframalpha.com/
    http://www.wolframalpha.com/input/?i=5+*+5+*+5
    http://www.wolframalpha.com/input/?i=5+cubed

Of course, that might make it too easy to take things completely on faith: :-)
    http://www.wolframalpha.com/input/?i=weight+of+the+earth
"5.9742×10^24 kg"

Good catch. You're right, that is an error in my math of cubing 5 as an incorrect 75 and not the correct 125.

Still close though. :-)

Maybe we should mostly teach kids how to use the free equivalent (someday) of Wolfram Alpha?
    http://www.wolframalpha.com/
    http://www.wolframalpha.com/input/?i=5+*+5+*+5
    http://www.wolframalpha.com/input/?i=5+cubed

Of course, that might make it too easy to take things completely on faith: :-)
    http://www.wolframalpha.com/input/?i=weight+of+the+earth
"5.9742×10^24 kg"

I never thought I'd use WA quite like this, but...

$32.10 per person will buy you a lot of pizza when you're ordering in bulk. That's about 2 large for every single man, woman, child, and baby in the USA.

> AC is not right. What i am saying is that if money is suppose to represent what you can buy, then "growth" means there must be a lot more "stuff" to buy/use etc. Yet earth is very finite. The idea of perpetual growth is as crazy as perpetual motion.

That is a provocative thought. Yet... When you invest in a stock it is like investing in a company. Over the years the value of the stock grows because the company itself grows (making more "stuff" or servicing more needs, in this service economy of ours) and also because the money the company generated in that interval gets invested in other companies that will, themselves, grow. The money you invested is fueling the coming into existence of more "stuff" to purchase.

So it is not a zero sum game. And yes, it is restricted to the reality of how much stuff there is the world. Unbelievably as it may be, the world GDP (= the total stuff available to buy)does grow exponentially. Developed countries grow at about 2% to 3% per year, developing countries grow 7%-10% per year. In total the real growth is around 3% to 5% (excepting a few recession years).

See
http://www.wolframalpha.com/input/?i=total+gdp+history
http://www.indexmundi.com/world/gdp_real_growth_rate.html

OK. so the mass of the moon is, oh about 7.346 x 10^22kg that's approximately 73459000000000000000 tonnes. If we extract, say, 1 million tonnes of stuff from the moon, that's about 1.3 x 10^-17 %, also known as a poofteenth of a percent.
According to my calculations, this will be enough to move the moon closer to us by about 4.76 x 10^-11 metres or approximately the diameter of a hydrogen atom.

Please don't make light of measles. It is deeply insensitive. You might try being positive instead. Give people the cure, and enjoy your instant celebrity. But beating up on people who have the answers, for no other reason than you can't accept that your child was born the way they were, is just plain evil. The people of India didn't ask for 125,565 of their people to die last year, but it happened and they're coping with that. Why on earth would you choose to make it harder than it already is by spreading junk science and FUD about the vaccine? Your passions could be towards assisting the people DYING EVERY FUCKING DAY FROM A COMPLETELY PREVENTABLE DISEASE, but instead you spend it on indulging your paranoia. And that's just sad.

How about Mercury to Gold? Mercury just needs to lose a proton and you have an isotope of gold. Specifically, Hg 196 to Au 195 will eventually yield stable platinum. Hg 198 will yield stable Au 197.

Out of curiosity, is the sound barrier here defined as the speed of sound on earth, or the speed at the temperature of air 23 miles up?

Mach one is determined by air pressure primarily and it does depend on altitude. Wolfram won't give me the answer below 0.1 bar of pressure. At 50000 feet the speed is pretty much the same as at sea level. I think 50k feet will be the point where the guy in free fall really starts to decelerate.

The speed of sound in a gas is actually almost entirely a function of temperature and the composition of the gas (70% Nitrogen, 29% Oxygen, 1% Other for air). Altitude mostly determines the temperature, but pressure is generally ignored when calculating the speed of sound in near-ideal gases.

Considering the nature of this jump, I would assume they've predicted his velocity throughout the entire fall based on the International Standard Atmosphere, with some safety factor to account for shifts in temperature due to weather, and established that he passes Mach 1 at some point in the fall based on the local temperature.

For interest, the lowest temperature below 23 miles (37 km) is -56.5 degrees Celsius in the tropopause which yields a=sqrt(k*R*T)=sqrt(1.4*287*(273.15-56.5))=295 m/s versus the typical 340 m/s you get at sea level (15 degrees Celsius). Not enormously different, but different enough.

I love Wolfram Alpha:

55mph for 300M

Out of curiosity, is the sound barrier here defined as the speed of sound on earth, or the speed at the temperature of air 23 miles up?

Mach one is determined by air pressure primarily and it does depend on altitude. Wolfram won't give me the answer below 0.1 bar of pressure. At 50000 feet the speed is pretty much the same as at sea level. I think 50k feet will be the point where the guy in free fall really starts to decelerate.

http://www.wolframalpha.com/input/?i=the+meaning+of+life

Assuming that's a normal "US" billion, and assuming it's a journal of historical data going back a few years, I don't think it's unreasonable to think there could be information in there on a couple of hundred thousand people each of whom has been track for an average of at least 6 months. So, approximately and with some guesses, that's around 55 records per prisoner per day. 1 update every 30 minutes? That sounds about right, maybe a little on the low side if anything.

What is surprising is that they were running some sort of database process that maxxed out at 2 billion records, and that it just stopped once it hit that limit rather than failing over to a backup process. But then, this is a government IT contract, so maybe it's not too surprising.

"to lift 1000 grams (1 kg), you need about 163 grams (~0.16 kg) of helium"
150 tons = 150,000 kg
150,000 * 163 = 24,450,000 grams of helium needed
24,450,000 grams of helium = 137,000 cubic meters
"A billion cubic metres - or about half of the world's reserves"
2 billion / 137,000 = 14,598.5

14,598.5 airships before we run out of the current reserves. I think we're good. (Except for that last half airship, it'll be kinda screwed.)

"to lift 1000 grams (1 kg), you need about 163 grams (~0.16 kg) of helium"
150 tons = 150,000 kg
150,000 * 163 = 24,450,000 grams of helium needed
24,450,000 grams of helium = 137,000 cubic meters
"A billion cubic metres - or about half of the world's reserves"
2 billion / 137,000 = 14,598.5

14,598.5 airships before we run out of the current reserves. I think we're good. (Except for that last half airship, it'll be kinda screwed.)

"to lift 1000 grams (1 kg), you need about 163 grams (~0.16 kg) of helium"
150 tons = 150,000 kg
150,000 * 163 = 24,450,000 grams of helium needed
24,450,000 grams of helium = 137,000 cubic meters
"A billion cubic metres - or about half of the world's reserves"
2 billion / 137,000 = 14,598.5

14,598.5 airships before we run out of the current reserves. I think we're good. (Except for that last half airship, it'll be kinda screwed.)

"to lift 1000 grams (1 kg), you need about 163 grams (~0.16 kg) of helium"
150 tons = 150,000 kg
150,000 * 163 = 24,450,000 grams of helium needed
24,450,000 grams of helium = 137,000 cubic meters
"A billion cubic metres - or about half of the world's reserves"
2 billion / 137,000 = 14,598.5

14,598.5 airships before we run out of the current reserves. I think we're good. (Except for that last half airship, it'll be kinda screwed.)

Civilizations thrive and prosper if there are plenty of cheap resources and energy available. The more of it the better. Right now we're heading for a shock in energy prices, so any creative idea, initiative is certainly welcome. "Depopulation" (whatever that means) has a dark side as well. Just watch Japan in the coming decades. They certainly aren't having lots of children. If they don't build a population of robots/cyborgs, whatever to support them, in a few decades they will have a crippled economy full of old people. While I can be accused of not looking at the big picture here (like centuries), the best thing we can do is to maintain the population level. And while efficiency is certainly welcome in places (why the hell is the US using so much energy with almost identical living standards?), we will not need less, but more cheap energy in the future.

Geek Fail. That page uses the scale from the Next Generation, while Ensign Chekov would obviously have answered using the scale from the original series. By the original series scale, it would take just under 34 days.

This number is a prime: http://en.wikipedia.org/wiki/Palindromic_prime in base 2.
In decimal it is: 6830770643

1.1 times the number of people alive today

The question is not whether the meat industry is the primary cause of antibiotic resistance. It's whether it contributes, and what to do about that. There are certainly other factors (you mentioned hospitals several times) that also contribute. We need to look at those factors as well, absolutely. I never said we shouldn't. But if the meat industry is creating a potential health crisis (which no one knows for sure if it is or not), they're not off the hook just because hospitals are creating a potentially bigger threat. Society has to deal with both problems.

The point would be to reduce antibiotics usage overall, which I'm sure you would agree with. If a European-style ban is not working, and actually makes things worse, then I agree that that's not the solution. Maybe we should be looking at what makes so many animals sick to begin with, instead of whether to ban antibiotics or not.

As an aside, I don't only blame industry for these problems. Industry is simply keeping up with demand. One of the articles I read said that in America alone, *nine billion* animals are raised for slaughter each year. That's a staggering number. Industry isn't doing this for fun - that's just how much meat Americans eat. It means that even if 99% of animals are treated reasonably well, which I doubt is true, an appalling 90 million animals are mistreated every year (plenty of fodder for journalists and activists who are looking for industry abuses). Also, the study you mentioned that said that factory farming scales (environmentally speaking) better than other methods doesn't negate the fact that the meat industry is having a huge negative impact on the environment. It takes enormous amounts of food and energy (and fossil fuels) to raise nine billion animals, and they are going to produce an enormous amount of waste, no matter how they're raised. The problem seems to be that raising (and killing) nine billion animals per year is always going to be messy, inefficient, cruel, and bad for the environment. It's the law of truly large numbers again.

The primary solution is that Americans simply need to drastically reduce meat consumption (on average, we each ate over 250 lbs of cow, chicken, and pig in 2005 - http://www.wolframalpha.com/input/?i=united+states+meat+consumption). Policies regarding antibiotics and so on are just band-aids, and probably mostly useless, as you point out.

It's analogous to a hypothetical increase of gas mileage from 20 to 25 mpg in automobiles. That's great, and a big improvement, but it pales in comparison to the potential efficiency of public transportation, alternative fuels, or even carpooling. One gas guzzler may be better than another gas guzzler, but it's still a gas guzzler with a big, bad footprint.

I want to thank you for your thoughts from "the inside", by the way. I do appreciate hearing the other side of the story, even if I disagree with your assessment.

WolframAlpha needs to be updated now. Did a search on 60 million rotations per minute to find out the period (1×10^-6 seconds), and I noticed this bit of info: ~~ 3 × fastest induced angular velocity (steel ball 0.8 mm diameter suspended in vacuum) (~~ 2×10^7 rpm )

60 million rotations per minute - Wolfram|Alpha

...I'd give a number, but didn't have a calculator handy that could handle 2^(15*365.25*24*2)...

Sure you do.

http://www.wolframalpha.com/input/?i=2^%2815*365.25*24*2%29

7.38... × 10^79164

Protons from an accelerator do move at "about the speed of light", though. Also, protons at the speed of sound are boring: the molecules of hydrogen gas at 20C are going three times as fast.

Perhaps it only needs to get up to 600 MPH before the Scramjet takes over.

Well, unless something is taking over, this is just a big artillery piece: escape velocity is rather higher than mach 10.

No, it's a complex way to publish 147,846,528,820 keys ( http://www.wolframalpha.com/input/?i=40+C+20 ).

  The initial input to the algorithm is a 40-bit random integer, selected so that the binary representation contains exactly 20 zeros and 20 ones. These bits are then used to select rows in the matrix.

I honestly think you might be hobbling these young professionals in a sense. Have them show their work at least. Most free solutions to math problems never show the work, you have to shell out hundreds of dollars for that.

http://www.wolframalpha.com/input/?i=integrate+(1%2Bx%5E3)%2F2%5Ex

Click on "show steps".

That doesn't account for two things:

1) A friend who's willing to do the test for them.
2) Wolfram Alpha

If you let people be networked, they can, with a little information/practice, answer any question fairly quickly and efficiently. Quick - integrate x*e^(2*x^2). Graph it. Differentiate it. Do Taylor expansion to approximate it. If you can't find it on the internet, a case of beer will likely get you someone who already took the course, had the notes and the books, willing to text you back during it with the answers.

What you suggest will catch the dumbasses who look on the paper of the person next to them. It does nothing to solve the problem here, which is that networked devices can make cheating really easy and effective.

You don't know about wolfram alpha, do you? Let me educate you...

Question 4) Integrate x*sin(x), graph this curve. If you were to express this as a Taylor expansion, what would the first three terms be?

See the problem now? If you can't pass calculus with a tool like that, you're not ever going to pass any math class. Between the ability to do each part of the integral separately, and the ability to google "integration by parts", if you are connected to the internet, you pass everything.