# Wikipedia:Reference desk/Archives/Science/2009 January 2

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# January 2

## Electro magnetic theory

Find the vector magnetic field intensity in Cartesian coordinates at P2 (1.5, 2, 3) caused by a current filament of 24A in az direction on z axis extending from (i) z=0 to z=6 (ii) z=6 to z= infinity (iii) z= −infinity to z = infinity. (b) Given the electric scalar potential V=80z cos (x) cos (3 × 108 t) kV and magnetic vector potential A=26.7 z sin(x) sin(3 × 108 t) ax mWb/m in free space. Find fields E and H. —Preceding unsigned comment added by Antony salvin (talkcontribs) 04:57, 2 January 2009 (UTC)

Welcome to Wikipedia. Your question appears to be a homework question. I apologize if this is a misinterpretation, but it is our aim here not to do people's homework for them, but to merely aid them in doing it themselves. Letting someone else do your homework does not help you learn nearly as much as doing it yourself. Please attempt to solve the problem or answer the question yourself first. If you need help with a specific part of your homework, feel free to tell us where you are stuck and ask for help. If you need help grasping the concept of a problem, by all means let us know. Algebraist 05:07, 2 January 2009 (UTC)
OK, I've done it. Now what? Was there a question? Edison (talk) 05:49, 2 January 2009 (UTC)

## What the Fuck is Fermet's Last Theorum?

Correct me if I'm wrong, but isn't it something along the lines of.... a mathematical proof? A proof that was "solved" by a Princeton mathematician (But not really)? He apparently had to "solve" some other math problem as well (Taniyama's Conjecture?) to untheorumize this. I'm a little confused about the whole deal. I'm not sure if this is some profound E=mc2 thing or just some obscure mathematical property that only mathematicians enjoy tinkering around with.

Sorry about the colorful language, by the way. I'ts just that when I typed this into your search box, it came up empty. I've found almost every other thing I've searched for, no matter how obscure, so I was a bit upset. And I figured it couldn't be that obscure if a country boy like me has heard of it. But for the most part, you guys do a pretty good job. God bless, and thank you for your patience. Sincerely, --Sunburned Baby (talk) 05:22, 2 January 2009 (UTC)

See Fermat's Last Theorem (note spelling). Algebraist 05:24, 2 January 2009 (UTC)
Also for future reference, Google Search (and possibly other search engines) would have spotted your incorrect spellings and offered the correct search term. See [1]. Abecedare (talk) 05:38, 2 January 2009 (UTC)
Wikipedia's inbuilt search does that also. Algebraist 05:48, 2 January 2009 (UTC)
Sometimes Wikipedia's search feature directs you to another article that doesn't exist. ~AH1(TCU) 17:04, 2 January 2009 (UTC)
But not in this case Nil Einne (talk) 05:37, 3 January 2009 (UTC)
As for whether it's profound, no, but it is surprising, easily understandable to non-mathematicians, and seems deceptively easy to prove. That's why you have heard of it and not of, say, the much more profound NP problem. --Bowlhover (talk) 07:10, 2 January 2009 (UTC)
On the other hand, the modularity theorem, which was considered intractable before Andrew Wiles proved a special case in his proof of Fermat's Last Theorem, is profound. However, you need a gound grounding in analytic number theory to even understand the statement of the modularity theorem, whereas Fermat's Last Theorem can be understood with schoolboy arithmetic. Gandalf61 (talk) 13:13, 2 January 2009 (UTC)
The theorem itself is very easy to understand - it's a simple statement:
"If an integer n is greater than 2, then the equation an + bn = cn has no solutions in non-zero integers a, b, and c."
So, for example, we know that 32+42=52 because 9+16=25 right? In that case, 'n' is 2 - and there are plenty of equations that fit. But it's a bit surprising that there are NO equations that work when 'n' is bigger than 2...not for any non-zero values of n, a, b and c ! Wow!
That's something that mathematicians had long SUSPECTED (because they never found any equations that worked for n>2 - and people had used computers to test that up to very large numbers) but they couldn't PROVE it. That's a big deal if you're a mathematician. It's very annoying to have something that simple that seems to be true - but you can't actually prove.
So - this guy Fermat (who was/is a very respected mathematician) scribbles a note in the margin of a book that says he's found a really cool proof - but he doesn't have room in the margin to write it down. Then he dies without writing the proof down anywhere. Since then, many, many mathematicians have tried to work out this simple and elegant proof. None of them succeed until just a few years ago when FINALLY someone manages to prove it - but the proof is long, horribly complicated and maybe there are only a handful of people on the planet who understand it. Worse still, it relies on several other recent proofs that are just as complicated and perhaps even harder to understand.
Did Fermat really come up with a simple/elegant proof? No. That's very unlikely indeed. Did he manage to prove it the way modern mathematicians have finally proved it? No - that's pretty much impossible. Most likely, Fermat made a mistake in his simple/elegant proof...or he had some other motive for writing that margin note.
But let me make this clear - the PROOF is hard to understand. The thing it proves is really, really simple.
The consequences of having the proof are that formal mathematics can now build on the fact that there are none of these Fermat equations - but practical sciences have been not been deeply affected either way - it's not a particularly useful piece of mathematics in itself. However, it's likely that some of the things learned along the way will eventually prove useful. This isn't as useful as e=mc2 (which is physics - not mathematics) - it's nowhere near as useful as (say) Pythagoras' theorem. What it is - is an incredible piece of mathematical reasoning - one of the most difficult things a mathematician has ever done - a stunning intellectual achievement.
IMHO, we should stop calling it "Fermat's Last Theorem" because it's really clear that Fermat did nothing to help solve the problem, and arguably (by making it seem that a simple proof existed) wasted more valuable mathematician's time than anyone else in history!
SteveBaker (talk) 13:47, 2 January 2009 (UTC)
Yes, it has wasted a lot of mathematicians' time, but it also likely intrigued and motivated many to enter the field in the first place. So in my subjective judgment the theorem and the romance that has surround the quest for its proof has been a net positive. What can take its place ? P = NP problem, "easy" Formula for primes ... Abecedare (talk) 10:00, 3 January 2009 (UTC)
Not only that, but, what with all the stuff invented to attack it, FTL has stimulated the creation of more interesting mathematics than any other problem I'm aware of. Algebraist 00:07, 5 January 2009 (UTC)
With respect, I believe there's a proof by negation approximately 8 lines in length which doesn't stretch beyond high school algebra (which, I believe, is entirely within Fermat's toolset) that involves expansion of the binomial theorem (n-inifically so, but it cancels out in the next step) midway, and I think one of those sum/difference of squares/cubes shorthands, and the rest is fairly boilerplate grade school proof. 98.169.163.20 (talk) 07:20, 3 January 2009 (UTC)
No doubt you would have included this proof here, but the margin was too narrow. - Nunh-huh 09:47, 3 January 2009 (UTC)
I suggest that we IMMEDIATELY start discussion on Village pump, proposing that wikipedia page margins be expanded. We cannot tolerate any more such losses! Abecedare (talk) 09:52, 3 January 2009 (UTC)
I don't think 98 is in danger of dying soon. I could of course be wrong Nil Einne (talk) 11:20, 3 January 2009 (UTC)
It was twenty years ago, my apologies but that's all I remember, beyond that those were the key statements of the proof. Slightly better then Fermat's margins. 98.169.163.20 (talk) 23:59, 4 January 2009 (UTC)
You probably mean this non-proof : Let n be prime, and let a,b,c have no common factor. If an+bn=cn, then a+b, a+wb, a+w2b, etc are all factors of cn (where w is a primitive nth root of 1). Let p be a prime factor of a+b. Then p also divides c. If p divides any other a+wkb, then p divides both a and b, so a,b and c have a common factor. Otherwise, from some other reasoning I can't remember, so I shall replace with handwaving for the purpose of this exposition, a,b and c still have a common factor. Q.E.D.. mike40033 (talk) 02:55, 5 January 2009 (UTC)

"If an integer n is greater than 2, then the equation an + bn = cn has no non-trivial solutions in non-zero integers a, b, and c."

Let a,b,c all equal 1.--72.200.82.14 (talk) 04:28, 5 January 2009 (UTC)

1+1≠1. Algebraist 04:33, 5 January 2009 (UTC)

## penetration of UltraViolet A rays in flesh

when a 5 mm diameter spot of UV A rays is placed on human body part(by a UV laser); what amount of energy(mJ/cm^2) of UV spot is required for 5cm penetration of uv rays in flesh? 123.201.1.238 (talk) 12:13, 2 January 2009 (UTC)crony

5 cm ? That's 2 inches. You'd need enough energy to vaporize most of the flesh above it. Are you sure you don't mean 5 mm penetration ? StuRat (talk) 16:40, 2 January 2009 (UTC)
5 mm penetration? You must be great with the ladies. ok... y'all can go back to answering the question seriously now. I will stop. --Jayron32.talk.contribs 21:40, 2 January 2009 (UTC)

## Solar cell production capacity

Hi

I have been unable to find any data on the worldwide solar cell production capacity ("how many square meters of solar cell can be produced per day (or per month or per year)?").

I am comparing various means of "green" energy production. Having arrived at the conclusion that covering almost all roofs with 10% efficient solar cells would provide enough electricity for a typical first-world nation, I wonder what it would take to actually do this. What would it take to produce hundreds of square kilometers of solar cell? What are the bottlenecks in solar cell production?

Thanks in advance —Preceding unsigned comment added by 81.11.170.174 (talk) 15:39, 2 January 2009 (UTC)

Check out Photovoltaics and Deployment of solar power to energy grids - and look especially at the references at the bottom of both articles. SteveBaker (talk) 15:43, 2 January 2009 (UTC)
Thank you, I found the total peak power produced by all solar cells produced in 2007 by the largest solar cell manifacturers in one of those references. It's not a surface/year, but I can calculate what I want to know from power/year just as well. —Preceding unsigned comment added by 81.11.170.174 (talk) 16:17, 2 January 2009 (UTC)
To answer your question about "bottlenecks", there are two main constraints to the take-up of PV. One is that the return on investment is rather low compared to other energy-saving measures available to households, e.g. extra insulation, solar water heating, condensing boilers. The other is that PV only generates electricity in daylight hours, so a form of storage is necessary. The usual method in domestic installations is to connect to the grid, so an inverter must be incorporated in the system, and not all jurisdictions allow for net metering, so again it may not be seen as cost-effective. Itsmejudith (talk) 17:28, 2 January 2009 (UTC)
Also, solar cells gradually lose power over their lifetimes and ultimately have to be replaced (which is costly). The business of sending unused electricity back to the grid during daylight and pulling it back at night is only working well right now because so few people do it. There could well be problems down the line when everyone (including the electricity generators themselves) have an excess of daylight power and a terrible lack of nighttime capacity. In a sense, all we're doing it pushing the storage problem back onto the electricity companies - which isn't exactly fair if 'net metering' prohibits them from charging us for the privilege of doing that. Hopefully, we end up with hydrogen powered cars or something - so we use excess daylight power to generate hydrogen and fall back on something else for nighttime supply. Certainly in a scenario where some country decided to do what our OP suggests, there would be a major 24 hour cycle storage issue. SteveBaker (talk) 19:36, 2 January 2009 (UTC)

One main bottleneck is the process of purifying the silicon. Polypipe Wrangler (talk) 04:16, 3 January 2009 (UTC)

## DNA math

I need to know how many different combinations in human DNA are there before you actually get a human. I once was given this number and would like to know if 1) it is accurate,and 2) how that number would be arrived at (DNA = number times 10 to the 87th power)

I don't know what the number would be. As for how to calculate it:
Let n be the number of nucleotides in human DNA.
Let m be the number that you can change while keeping them human.
The number of possible strains of human DNA is 4^m*nCm
The number of possible strains that length is 4^n.
The fraction of strains at that length that result in a human is (4^m*nCm)/(4^n)=nCm/4^(n-m)
I don't know how high that would be, but I suspect it would be something more like one in 10^(10^(20)) — DanielLC 18:36, 2 January 2009 (UTC)
Our article on human genetic variation says "on average two humans differ at approximately 3 million nucleotides". The article goes on to say "Most of these single nucleotide polymorphisms (SNPs) are neutral, but some are functional and influence the phenotypic differences between humans. It is estimated that about 10 million SNPs exist in human populations, where the rarer SNP allele has a frequency of at least 1%". Even if there are only two alleles for each site, this gives 210 million possibilities, or about 103 million. There is a big assumption in this calculation that sites can vary independently. But it still looks as if 1087 is a big underestimate. Gandalf61 (talk) 18:58, 2 January 2009 (UTC)
You are also neglecting the effect of indels and copy number variations. Not every human has exactly the same number of base pairs in their DNA - current research indicates that features such as indels and copy number variation may have as much, if not more, effect on the differences between two humans than SNPs do. -- 128.104.112.113 (talk) 20:20, 4 January 2009 (UTC)
Not withstanding the indel issue, this is impossible to calculate because m is entirely subjective. What does "keeping them human" mean? There will be many thousands (if not millions) of possible nucleotide substitutions that would result in spontaneous abortion. Do they count, after all the outcome is still a human (albeit a dead one). How about those that result in terrible congenital malformations, where the child survives until birth, but dies shortly after? Or how about those that live to 1, 2, 5, 10, 15yrs but with zero quality of life? Where do you draw the line? And how do you quantify those changes that result in early miscarriage, because 99.9% of the time they will never even be seen. Rockpocket 20:34, 4 January 2009 (UTC)

## pittuitay tumors

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--Milkbreath (talk) 14:10, 3 January 2009 (UTC)

## How many species are there?

Our Species article doesnt say. Well it gives a patheticly large possible range. Surely you can do better? Willy turner (talk) 22:47, 2 January 2009 (UTC)

new species are being discovered all the time, so it's impossible to give an exact number. These pages discuss it in detail [2] [3] [4] —Preceding unsigned comment added by 82.43.88.87 (talk) 00:14, 3 January 2009 (UTC)
Well... no. The thing is, it's impossible to know exactly how many species there are. New ones are discovered all the time while others go extinct. It's a big planet, and we simply don't know its contents well enough. (That said, maybe someone can be a little more exact than "between 2 and 100 million species", but I'm betting that not by much.) -- Captain Disdain (talk) 00:15, 3 January 2009 (UTC)
(Doh! Edit conflict)... I was going to say:
• Not really. The problem is that taxonomy is a human classification system (we do love to pigeon-hole things!), and by virtue of that, the rules surrounding definition of species, as well as higher and lower taxonomic levels, are pretty much arbitrary. See my recent edits and the associated discussion on the mycology of pityriasis versicolor for an example of how this makes life really difficult in medicine. Counting species is like counting grains of sand on a beach, by a committee, that can't agree on what a grain of sand actually is, and what size shell fragments should be before they're too big to be sand, and if the really small bits are sand or perhaps they should be called sub-sand, and if grains of sand should be differentiated by colour, or when they should stop for a cup of tea, or what type of tea to have, and whether there should be biscuits or cakes with the tea .... Mattopaedia (talk) 00:29, 3 January 2009 (UTC)
Well summarized, I concur with Mattopaedia. It's roughly arbitrary to define a species. I recall being taught in 7th grade science that "breeding capability" was the definite and indisputable indication of species boundaries, but since then, I have learned that it is significantly more subtle. See Species problem for discussion. Nimur (talk) 01:39, 3 January 2009 (UTC)
A related phenomenon are ring species: There are multiple populations of a species, and they can all interbreed (sustainably, i. e. the offspring can interbreed again, not like a mule which is the offspring of a horse and a donkey) with geographically neighbouring populations, but if you take two populations from different ends of the geographical distribution range, they cannot interbreed. Icek (talk) 08:57, 3 January 2009 (UTC)
The precise definition of "species" is certainly a problem - but just look at what you're asking here: I mean, sure, it's unlikely that there are more than a dozen large land animals that we don't know about - but that's a negligable fraction of the species on earth. Look at a single grain of dirt under a microscope and you'll see hundreds and hundreds of bacteria - all sorts of different kinds - more than you could easily count in an hour. If you live somewhere where there are a lot of people then maybe all of the little animals and plants (and other things) that you are looking at have been classified and named - but probably nobody did the necessary testing to see if they are all unique "species" or not...but probably that level of testing hasn't been done on all of them. Now consider that we haven't looked at grains of dirt from (say) every square mile of the earth's surface and classified every little squiggly dot that we see - we haven't looked at drops of water from every square mile of ocean and classified all of the diatoms, algae, bacteria and other little critters - we haven't taken air samples everywhere and done the same thing. We haven't looked at all of the species of gut flora in every kind of animal that we know. We're finding new species at the bottom of half-mile-deep coal mines - in deep ocean trenches and thermal vents - under the ice at the south pole there are lakes of liquid water with who-knows-how-many tiny animals and plants. The problem is simply immense - and we've barely scratched the surface of counting them all. There was a documentary on TV the other day about a bunch of cave divers exploring a cave in some god-forsaken place - they said that they expect to find a dozen new species of fish/insects/amphibians in practically every cave they visit! So it's not surprising that we have no real clue as to how many species there are. There could easily be another billion species living two miles underground where we've never even drilled - let alone started to count species. SteveBaker (talk) 13:09, 3 January 2009 (UTC)
I would say "Go to Wikispecies where you may find out all about species." but at the moment it is just a list of Latin names in need of people who can give translation and description to these latin names (stuff like Elephant and Fungus are not available on search yet but are all listed by latin with pictures). ~ R.T.G 13:29, 3 January 2009 (UTC)
The problem is, there are so many species of plants, animals, and microorganisms we haven't even discovered! There are also many species going extinct every year, some before we even discover them, so we might never know for sure. ~AH1(TCU) 15:39, 3 January 2009 (UTC)
The article on Bacteria says there are 9000 known species but probably between 10,000,000 and 1,000,000,000 species still to be discovered. This helps to show why the estimates are so confused. --Maltelauridsbrigge (talk) 20:23, 3 January 2009 (UTC)
One problem is that a large fraction of species seems to be beetles. --76.167.241.238 (talk) 00:23, 4 January 2009 (UTC)
As the British Geneticist J.B.S. Haldane famously said when he was asked "What has the study of biology taught you about God?", he replied "I'm not sure, but he seems to be inordinately fond of beetles." SteveBaker (talk) 06:37, 4 January 2009 (UTC)
When we look at the biodiversity,we find that there are nearly 2500000 species of organisms currently known to science. More than half of these are insects(53.1%) and another 17.6% are vascular plants. Animals other than insects are 19.9%(species) and 9.4% are fungi, algae, protozoa, and various prokaryotes. This list is far from being complete. Various careful estimates put the total number of species between 5 and 30 million. Out of these only 2.5 million species have been identified so far.