T. Komplexify
Weizguyy Institute of Smart Axes
Abstract
In this article, we discuss the classic proof that girls are evil. The author will briefly discuss the origins of the problem and review the classic proof. The author then indicates a mathematical flaw in the argument, invalidating the statement. The article concludes with a revised and corrected statement of the result.
I. Introduction
I recently received an email discussing the differences between men and women from various mathematical and engineering points-of-view. Most of it was extremely funny, and sooner or later all shall certainly appear within the mathematico-humorist community, properly researched, and appended with standard references in the literature.
However, one portion of the email included a mathematical “proof” of the fact that girls are evil. This proof is doubtless familiar to many readers, having circulated a few times in mathematicians’ inboxes. However, for those readers unfamiliar with this well-known proof, we present it now.
II. Statement and classical proof of result
Theorem. Girls are evil.
Proof. It is axiomic in all cultures that girls require both time and money, and any man with either a deficiency in available “quality time” or “disposable income” knows that this a joint-proportion, whence
Similarly, it is has been proved that “time is money” [1], whence
Substitution yields
We also know that “money is the root of all evil” [2], whence
Substituting again yields
Squaring on the right-hand side of the equation yields
establishing the result. Q.E.D.
III. Identifying and resolving the flaw
The above “proof,” so-called, is widely known to mathematicians, leading to the widespread belief that girls are evil.
It will therefore come as a surprise to find that the proof above is flawed, and indeed, the result is incorrect. There is a subtle flaw in the above argument that seems to have escaped most diligent readers for quite some time. In the interest of correcting this mis-truth, which has improperly vilified girls as being evil, we present now the correct statement and its proof.
Theorem (Corrected). Girls are absolute evil.
Proof. Arguing as above allows us to conclude
However, let us more intently examine the consequences of money being the root of all evil. A moment’s thought shows that it is incorrect to conclude that
To see this, recall that evil is a inherently negative concept [3]. We cannot take square roots of negative quantities in the real world, lest we are will to assume that money is imaginary. (Graduate students in particular may choose to investigate this concept further [4].) Thus, we are therefore forced to conclude that
Substituting again yields
Squaring on the right-hand side of the equation yields
establishing that girls are absolutely evil. Q.E.D.
IV. Conclusion
We sincerely hope this clears things up.
V. Notes
- I. Walker, “Time is money, professor proves,” CNN.com (2002) May 29
- The Bible, King James Version (1611), I Timothy, Chapter 6, Verse 10
- cf. Q. Smith, “An Atheological Argument from Evil Natural Laws,” (1991) Section 2.
- This idea is explored somewhat in K. Marx, Das Kapital (1861).
The research reported in the paper has in part been suppressed by the National Silence Foundation.
Update!
In deference to the sudden influx of comments, I’ve provided a metacomment comment of sorts here.
LOL, Girls are cool dude!
http://www.web-privacy.pro.tc
Comment by Johnny SoMo — 01.5.2009 @
No, no, no. Your math is wrong. The square root of a negative number is i (the imaginary number) times the square root of it’s absolute value. Girls, therefore, are an imaginary evil.
Comment by A picky girl — 01.5.2009 @
You might want to re-read your source at #2. It reports the love of money is the root of all evil, not money itself.
Comment by Kim Siever — 01.5.2009 @
Well…women fought hard for being equal to men, so now I finally see why…
Women=Men
Girls ~ Women
Boys ~ Men
girls=boys
girls=evil
=> boys= evil also
q.e.d
Comment by Vlad — 01.5.2009 @
oh, reparate me for living through the extended version of this joke.
It was funny when twas created in the 1980s.
Comment by Reparate Me — 01.5.2009 @
Your reasoning for the absolute value is incorrect, though the final answer is correct. We cannot just introduce an absolute value because we can’t take the square root of a negative number. However, the square root function gives us the principle root (only the positive value), therefore sqrt( x^2 ) is equal to |x|. For example, if x = -3, then then x^2 = 9 and the principle square root of 9 is +3. This is why we need the absolute value. Many math professors are not aware of the principle square root convention of the square root function and most would initially reject it because it is not intuitive that one would be able to solve x^2 = k and arrive at two values. However, because the convention requires that sqrt(x^2)=|x|, then we do anyway.
Comment by Kevin — 01.5.2009 @
Thou hath misquoted mine agents. Correctly:
“THE WANT OF money is the root of all evil”
Comment by God — 01.5.2009 @
I always knew it! hahahaha
Comment by Pablo Q. — 01.5.2009 @
On the issue of willingness to assume that money is imaginary, in the current day where governments use paper money not backed by any asset it is in fact imaginary. Or rather the value of it is imagined. Then we must also consider the velocity of money (http://en.wikipedia.org/wiki/Velocity_of_money) which creates economic activity that is not truly there. I’m not an academic so I can’t really elaborate more, but that’s my two cents.
Comment by John — 01.5.2009 @
So sad but true
Comment by Michael Goodale — 01.5.2009 @
Don’t you need to square both sides of second to last equation, otherwise the equality doesn’t hold. So what you would really have is girls^2 = abs(evil).
Comment by adam a — 01.5.2009 @
Actually, “THE LOVE of money is the root of all evil.” So you have some recalculating to do. Look it up. It’s in the bible.
Comment by ted — 01.5.2009 @
WOW, hilarious. The twist ending is priceless. I thought for sure this was a girl writing to disprove this.
Comment by pianowow — 01.5.2009 @
money is not the root of all evil
the love of money is the root of all evil
therefore the love of girls equals the love of evil
i’m not sure where that leaves us heteros…
Comment by mark — 01.5.2009 @
A small revision from an English Major and a Girl. The correct quote is “the love of money is the root of all evil.” Thus substituting Love for Money as your operative object in the sentence. If you carry through the equation it then falls apart, unless you carry through the phrasing. Thence the love of girls = the love of money…. Heterosexuality = Evil. You may have just mathematically ended the reproduction of the human race with that equation. Just remember fellows. Check your sources and refine your data before running a proof. Poor scientific method if you ask me.
Comment by Vasi — 01.5.2009 @
you fail
Comment by not funny — 01.5.2009 @
If this is the case then all boys are devils – they run after evil !!
Comment by mehak — 01.5.2009 @
Technically the Bible quote is that “the love of money is the root of all evil.”
Comment by Anonymous — 01.5.2009 @
Actually, you will find that “the *love* of money is the root of all evil”[1] – which is an important distinction (else collections every Sunday would be seem to be evil). This makes the substitution of money with the root of evil invalid and therefore both proofs are incorrect.
1. As my Grandmother reminded me whilst I was showing her the proof.
Comment by Nick — 01.5.2009 @
Actually, chinese proverb would dictate that time > money, so girls would be greater than evil…
Comment by Christie — 01.5.2009 @
At the risk of pooping on a great classic joke, I object to “money is the root of all evil”. I think that’s BS to be honest. Money is just a medium of exchange, and wealth is the root of better quality of life, not evil.
Comment by Edward — 01.5.2009 @
I’m sorry, your proof is flawed. Your mistake is that money is the ROOT of all evil, not the SQUARE ROOT. Therefore if girls = money x time, and time = money, girls = (money)(money). If money is the root of all evil, then money = evil = 1 (the root of all numbers). Therefore girls = 1 x 1, which means girls = 1. Therefore, girls are #1.
Comment by Nan — 01.5.2009 @
Saw this done by Simon Singh 3 years ago in NYC. but it was to prove that teletubbies are evil.
Comment by sueb — 01.5.2009 @
I’m not a bible thumper, but your logic is flawed. There is nothing intrinsically evil with money, its just paper. 1 Timothy 6:10 says for the LOVE of money is the root of all evil. Therefore, money does not equal the square root of evil.
Comment by jdpressley — 01.5.2009 @
Brilliant, brilliant, BRILLIANT!
Comment by Rem — 01.5.2009 @
Actually the Bible says the
“*love* of money is a root of *all kinds* of evil” in 1 Tim 6:10
(emphasis mine)
cs
Comment by seb — 01.5.2009 @
The criticism of the traditional argument is flawed. Women are obviously complex; so, we can take the root of evil since it is defined over the complex space.
Comment by NF — 01.5.2009 @
Further: it’s axiomatic that money is imaginary. How else do you explain the complete vanishing of literally trillions of monetary units in the American meltdown? If it was real, the release of energy caused by such vanishing would vaporize half the planet.
Since money is imaginary, it’s perfectly acceptable for it to be the root of an inherently negative concept.
Comment by Flinthart — 01.5.2009 @
I’d disagree on the original, for a completely different reason, and that reason follows into the new model, I’m afraid. The fact that girls require both time and money in no way equates that girls = time X money. Rather, it equates that girls = time + money. In such a case that said male is lacking in either time or money, it would then be proportional to something like girls = .5 time + 1.5 money, since time = money and can be exchanged on a one for one basis. Now, SHOULD time further = something with the numeric value of 2, the entire theorem works well to be either girls = time X money or girls = time + money, assuming no substitutions are made for time/money inequalities, in which case, the entire thing fails again. In any other numeric denomination, time X money does not equate to time + money, and therefore, you either have a finite answer for the value of time, and by extension money…or a flawed construct. Don’t you just hate a girl that can do math?
Comment by BLyons — 01.5.2009 @
I can spot a much more significant flaw.
If women = time AND money, then the appropriate mathematical phrasing would be women = (time + money), not women = (time)(money). So if time = money, the correct formula is women = 2(money).
Further proof that men just don’t understand women…
Comment by Indigo — 01.5.2009 @
It stands to reason if “true evil” is to be represented mathematically as
” – Evil” (negative evil) then the result of |evil| means that girls are the OPPOSITE of evil, or GOOD!
Comment by Yanni — 01.6.2009 @
you always delete first comments for calling you out on a joke stealing?
Comment by SueB — 01.6.2009 @
The flaw in this proof remains unexamined by the author:
Quote
“Proof. It is axiomic in all cultures that girls require both time and money”
The key word in this phrase is “and”
Therefore:
Girls = Time + Money (’+’ being the universal sign for ‘and’)
not Girls = Time x Money (’x’ being the sign for ‘times’)
Subsequently, the rest of the equation falls.
Comment by John — 01.6.2009 @
Awesome
Comment by Mark Jackson — 01.6.2009 @
Ignoring all the other flaws stated already, the whole point of your article to prove that the method most *mathematicians believe* is flawed, is incorrect. If evil is an inherently negative concept, then it means that the negativity is implied by the symbol, and denoting it with a negative would imply cancellation, and result in a positive result. Consider (-10), for example. (-10) is an inherently negative concept, and if we write it with a preceding negative as -(-10) we end up with 10, a number that is no longer negative. This means that -evil = good, and your result finishes with girls = good (an incorrect deduction from the statements used). This indicates that your method is incorrect, and the original one is fine as it is.
Comment by Anonymous — 01.6.2009 @
that is a sterotype. not all girls look for guys with money.this was probably just made up by some angry guy who got dumped. the person who wrote this=evil. for saying this about girls
Comment by wtf — 01.6.2009 @
@BLyons:
The reason girls = time x money is that if a girl costs $300 a day, and you have her for 10 days, then she has cost you a total of 10 * 300 (time * money) = $3,000.
Comment by Anonymous — 01.6.2009 @
Since you didn’t actually explicitly write -evil, your proof is still flawed in the sense that it’s an algebraic manipulation, and you don’t actually take the square root of evil.
If money = sqrt(evil) = evil^(1/2)
then money^2 = (evil^(1/2))^2
and by laws of exponentiation, money^2 = evil^((1/2)*2) = evil^(2/2) = evil
and we end up with evil without absolute values regardless, without problems since we never computed sqrt(evil).
Comment by Anonymous — 01.6.2009 @
Oh lord you ruined the joke at the end by being too strict with using sqrt(x^2) = |x| instead of sqrt(x^2) = x.
Comment by Jack — 01.6.2009 @
Ummm, no, you have to perform the same on both sides of the equation, so you have to square on the left as well as the right, therefore, you could have girls=evil where as girls^2 = |Evil|.
Comment by sierraslidr — 01.6.2009 @
Holy crap — thousands of airhead Xians race to poopoo this dumb old sexist joke not on the basis that it is sexist or even not very funny (and fairly lame) but so they can make apologies for the existence of currency. Before money famines and poverty were limited to local natural disasters and harsh weather with respect to those who suffered it; the norm in human history had always been resources are shared collectively and so is the labor and if you didn’t share you were an outcast; now famine and poverty through the invention of capital are exported globally. Water, food, justice, and freedom are commoditized and given price tags that violently refuse those who cannot afford them the benefit of their consumption; to rebel against this theft of the common rights of humans is labeled theft by an illegitimate muscle that all the true thieves pay protection money too, the government. Money is an assault on human dignity, is inherently a symbol of callousness and indifference to the condition of fellow humans, and guilds the chains of those around the World who make its products. Wage slavery is sick. Money is still the root of all evil. Property is theft. Capitalism is criminal. RESISTANCE IS FERTILE!
Comment by JackSparrow — 01.6.2009 @
His name is Robert Paulson.
Comment by Robspierre — 01.6.2009 @
oh man…
Comment by bandit — 01.6.2009 @
problem: money is the root of evil. Therefore money = sqrt(evil), therefore, using the same substitution, girls = evil ^ 4.
In other words, girls are beyond any ability of us to comprehend as evil.
Comment by PtrN — 01.6.2009 @
Ok….lets just pare this one down to the bare essentals of mathmatical reason
1. Mathematician
2. Girlfriend
3. You’ve never had one……..
Comment by James Banks — 01.6.2009 @
Resistance is fertile?
Comment by 1 of 4 — 01.6.2009 @
>@BLyons:
>
>The reason girls = time x money is that if a girl costs $300 a day, and you >have her for 10 days, then she has cost you a total of 10 * 300 (time * >money) = $3,000.
>
>Comment by Anonymous — 01.6.2009 @
Well, this ‘proof’ only proves that geek know nothing about women and prefer to use hookers…
Comment by Delphi — 01.6.2009 @
I agree with your math. They are always telling us how to dress etc… The story in the bible goes that adam was shown a perfect women (She could drive and clean and would be quiet when asked) So he asked god what is that going to cost me so god said an arm and a leg so adam replied what can i get for a rib?
Comment by Suits — 01.6.2009 @
What’s really funny is that men have one less rib (or at least one severely less developed) than women because that’s where we came from. According to Genesis: //v.21 “And then the LORD God caused a deep sleep to fall upon the man, and so he slept, and then He took one of his ribs and then He closed flesh in its place.”
LMAO
Comment by Stormy — 01.6.2009 @
You run under the assumption that any girl has a negative value of evil. I deem this hypothesis unproven to my satisfaction, as if all girls are evil, then evil in that senseinherently positive. Buy hypotheses aside, we can still get your result by changing the order of operations, as is allowed in a ring we have the following:
girls = sqrt(evil)^2 = sqrt(evil^2) = |evil|
Of course, this assumes that all the variables mentioned in this proof are elements of a ring (probably the real numbers), something which could be strongly argued. However, if we assume that evil, money, time, and girls are real then this proof holds.
-Kyle Baxter
Comment by Kyle — 01.6.2009 @
How many people have to feel self important by correcting this person on biblical verse. Once is enough already!
Comment by Exhausted — 01.6.2009 @
In any event, women may or may not be evil – but they sure can be nasty. God Bless them.
Comment by kennylibido — 01.6.2009 @
These comments are so close, but don’t carry through.
First, define G = girls, T = time, M = money, E = evil and is always a negative quantity, and the function L(x) = Love of x.
Source equations
1. G = T*M
2. T = M
3. L(M) = sqrt(E) (for all E)
Sub 2 into 1 gives
4. G = M^2 or M = sqrt(G)
Sub 4 into 3,
5. L(sqrt(G)) = sqrt(E)
Square both sides of 5,
6. L^2(sqrt(G)) = sqrt(E^2)
Since E is defined as being a negative quantity,
7. L^2(sqrt(G)) = i*E
But L is a simple scalar function. To see this, take the observation “I love you twice as much as yesterday but only half as much as tomorrow” [5]. In other words, love as a function of time is
8. L(T) = a*T for some scalar ‘a’.
From subbing (2) into (1) we get
9. G = T^2 or T = sqrt(G)
Sub 9 into 7 gives us
10. L^2(sqrt(G)) = L(sqrt(G))*L(sqrt(G)) = L(T)*L(T) = i*E
Now insert 8 into 10
11. (a*T)*(a*T) = a*(a*T^2) = L(L(T^2)) = i*E
Sub 9 back in for T^2 and get
12. L(L(G)) = i*E
Or, the love of love of girls is imaginary evil. In other words, taking into account all of the comment points about “love of” and the square root of a negative (evil) is imaginary, we come to the inevitable conclusion:
There’s nothing wrong with loving lesbian pornos.
Refs
[5] http://www.scrapbook.com/quotes/doc/27125/67.html
Comment by DL — 01.7.2009 @
Maybe the ladies wouldn’t cost so much money if our society paid them equal wages for equal work.
Comment by Anonymous — 01.7.2009 @
hi all, i may not fully disagree, but girls are okay and good to bear uptill they are not “girlfriend” of any boy. The theorem “Girls are evil” as stated above becomes true when the girls becomes the “girfriends” of any boy, and the moment that girfriend becomes the WIFE of same boy then the second theorem activated “Girls are absolute evil” (aawww… that unlucky chap).
Cheers!!
AB
Comment by ab — 01.8.2009 @
Dont listen to the girls comments cause they are all evil .
Girls = Evil = manipulate = erasig the throuth = proof of they are all evil .
Comment by Root of all Evil — 01.8.2009 @
Uh… gang? “The LOVE of money is the root of all evil”…
Comment by Jon — 01.13.2009 @
Next time I read the posts first, so as not to be a total Nimrod.
Comment by Jon — 01.13.2009 @
Haha I think the equation works but doesn’t that mean it is also true for children? Which is why I believe we need to eat the children before they grow up
Comment by JonR — 01.13.2009 @
Did anyone mention that it is…
Love of Money is the root of all evil.
My god such basic sloppiness.
You should read the source material before
staring your proofs!
Comment by IReadItAll — 01.16.2009 @
then why don’t you kill the girls if they are so evil… who wants to throw a stone at them first? do it, if you are an angel!
Comment by Lisa — 01.16.2009 @
hey, that means that I’m a devil if I like girls… Girls are cool, man!
Comment by jason kenny — 01.16.2009 @
Something that has also escaped the community of mathematicians is that if girls equal time and money, then the equation would be g = t + m, no g = t x m.
Comment by Justin — 01.17.2009 @
If “girls equal time and money,” then the correct math is girls = time + money.
BUT pay attention, people… the proof says “girls REQUIRE time and money.” That just means that girls are a function of time and money. It’s like reading the sentence “the area of a rectangle requires the length of its base and the length of its altitude” and concluding “area of rectangle = base + altitude.”
In fact, the rest of the VERY SAME sentence says that if EITHER time=0 OR money=0, then girls=0, which is definitely NOT TRUE if girls = time + money.
And P.S. “IReadItAll” clearly didn’t, did he?
Comment by Marvin the Paranoid Android — 01.17.2009 @
I prefer the first proof, the second proof is flawed because he just decides to make the evil positive rather than dealing with the negative case seperately. There’s also no reason why evilness can’t be rated on a positive scale anyway.
Comment by Anonymous — 02.3.2009 @
going to be harsh on my own sex, but i completely agree!
Comment by opinion of a girl — 02.24.2009 @
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