Some seventeen years ago, before the novelty of e-mail had worn off, I forwarded around a funny message I got from my boss. My friend M— forwarded it to a bunch more people, and one of them sent a rebuttal that I found a little too pat. Moreover, his opening sentence, “Your math is off,” struck me as a little smug. So, notwithstanding the absurdity of the original e-mail, I decided to defend it to the death. (Actually, being in the wrong actually increased my motivation: as a lover of rhetorical finesse, I have a natural fondness for the quixotic job of advancing untenable positions.)
I present the transcript of this debate because I think it’s funny, and because everybody loves a good smackdown, right?
(A note on the title: of course the term “STEM” hadn’t been coined yet in 1997. But my title, you may find, is decent shorthand for the subtext of this debate.)
Knowledge vs. Money - a debate between strangers
From: Dana Albert
Sent: Friday, November 07, 1997 5:36 PM
Subject: FW: Equation
Check out this funny e-mail from my boss!
I think we could call this the rule of the VP level at (insert client here)...
Do you know too much?
We all know that:
Knowledge is Power and Time is Money.
And, as engineers learned in school:
Power = Work / Time
So, if Knowledge = Power, and Time = Money, then Knowledge = Work / Money
Solving for Money, we get: Money = Work / Knowledge
Thus, Money approaches infinity as Knowledge approaches ZERO, regardless of the Work done.
The Less you Know, the More you Make.
Sent: Monday, November 10, 1997 11:18 AM
To: Dana Albert
Subject: FW: Equation
Below is follow up from my friend—working on his PhD in Physics...
Subject: Re: Equation
Date: Sunday, November 09, 1997 8:22PM
Your math is off. You must assume that work is independent of knowledge for your math to be correct. Since knowledge and work are correlated money does not go to infinity. Work is probaly proportional to knowledge to some power greater than one (first order approximation).. i.e. work = C * (knowledge)^(1+n). Where C is a constant. So if we go back to the eq M = W/K. We get M= C* K^(1+n) / K, by substituting in the relation for work. Finally simplfying, we get: M = C*K^n. So we see that as Knowledge increases money, actually also does increase. All is good in the world still.
From: Dana Albert
Sent: Tuesday, November 11, 1997 7:16 PM
Subject: RE: Equation
I find your friend’s rebuttal to my boss’s treatise interesting. I will analyze the rebuttal in terms of the three branches of rhetoric: ethos (authority), logos (logic), and pathos (emotional feeling).
First, ethos: the fact that your friend is working on his Ph.D. in physics is not nearly as impressive as an actual degree in physics. All that being in graduate school means is that he already has an undergraduate degree and has passed some tests. Meanwhile, we can only speculate on the quality of his undergraduate education. I did immediately notice that your friend’s his message had punctuation errors (such as only one space after a period), spelling errors (such as “probaly”), and grammatical errors (such as the sentence fragment “Where C is a constant”). Suffice to say he doesn’t win huge points in the ethos category.
Moving on to pathos, we immediately see that he bases his rebuttal largely on equations. I was not moved.
Finally, his logic is based upon what I would call a faulty premise: that knowledge and work are correlated. Where did he ever get that idea? It is futile to build an argument on an axiom that is not generally accepted. An effective argument must not only have valid reasoning, but must also be built upon sound premises—thus his equations, nothing more than smoke and mirrors, evaporate.
Clearly all is not “good in the world still.”
Subject: I am a Rocket Scientist!
Date: Tuesday, November 11, 1997 4:35PM
Mr. Albert feels that my argument fails for three reasons: I do not have the authority to make such statements, my rebuttal did not stir his emotions, and that knowledge and work output were indeed uncorrelated.
Mr. Albert challenges my authority, citing my numerous typos, and my lack of education. In science, authority has no baring on the validity of an argument. Just as the church’s authority could not stifle Galileo’s heresy, Mr. Albert’s authority can not stifle my heresy. I would also note that he is not immune to typos himself: “I did immediately notice that your friend’s his message had punctuation errors”
Mr. Albert goes on to say that my argument fails to move him. Perhaps, Mr. Albert, my equations failed to move you, because as an English major you fail to understand them.
Finally, Mr. Albert rejects my assumption that work output and knowledge are correlated. I challenge him to reject the assumption the next time he is interviewing a potential employee.
The success of the scientific worldview has been in large part due to the rejection of pathos and ethos, in favor of logos. While Mr. Albert certainly has pathos and ethos in abundance, it does not obscure the fact that he lacks logos. Mr. Albert defends his boss’s abuse of math and science in an attempt to prove that the less you know the more money you make. The argument is empirically false, and the argument should be rejected for that reason alone. I simply wished to point out where the logic of the proof collapsed.
From: Dana Albert
Sent: Tuesday, November 11, 1997 8:16 PM
Subject: RE: I am a Rocket Scientist!
I will continue to uphold the validity of my boss’s statement about money, knowledge, and work. This is fun.
The following sentence, committed by Mr. S—, I find comical: “In science, authority has no bearing on the validity of an argument.” Perhaps Mr. S— is quibbling on the definition of “valid,” which in strict logical terms can mean “correctly inferred or deduced from a premise.” I see no point in doing this: valid, in a normal context, means “(1) Well grounded; just: a valid objection. (2) Producing the desired results; efficacious.” Now, does Mr. S— really believe that authority has no bearing on the validity of an argument? If a doctor diagnoses sickle-cell anemia and the patient insists it’s just a cold, does the doctor back down? When a judge or attorney evaluates the merit of forensic evidence, whom does he call on: a forensics specialist, or an art historian? Perhaps Mr. S— is unimpressed by credentials, but he can hardly speak for the entire scientific community.
For Mr. S— to point out my typo is an excellent example of what in logic is called the “red herring fallacy.” While I did make a typo, pointing it out is irrelevant to the actual argument, which concerns my boss’s statement about work, knowledge, and money. I cited Mr. S—’s grammatical errors because I was attempting to evaluate his level of education. My level of education, on the other hand, does not figure in the validity of my boss’s argument. Meanwhile, since the quality of S—’s education is still very much in question and pertinent to our ongoing discussion, I did notice that in the very sentence in which Mr. S— points out my typo, he commits another punctuation error by neglecting to end his sentence with a period. Perhaps he wasn’t sure whether the period should go after the quotation mark or before it and just gave up. But I digress.
Mr. S— suggests that the failure of his equations to move me emotionally is due to the nature of my undergraduate education. On the contrary, elegant and conclusive math—such as that exemplified by my boss in his original statement—moves me almost to tears. Moreover, a solid argument can impress and persuade anybody, regardless of his or her background. To confine one’s audience to nerdy scientists seems pointless, given that my boss’s original statement had universal appeal to any of us weary cogs of industry.
I was surprised to see that Mr. S— returned to his ill-fated premise about knowledge and output being correlated. This assertion is arguable at best, and simply cannot stand up to ages-old, commonly accepted axioms such as “time is money” and “knowledge is power.” And yet his first attempt to support this assertion is a suggestion that I keep his assertion in mind when conducting job interviews. I can assure Mr. S— that when conducting job interviews, I actually keep in mind the fallacy of this assertion. When I interview an applicant, particularly one weighted down with extra degrees, I invariably have the following question in mind: “Okay, he’s got plenty of knowledge, but after such long residence in the ivory towers, will he work hard enough to finish his projects on time? Will he complete a variety of tasks, or get bogged down in his habit of perfectionism? Or will he decide that his job is a nuisance, and return to academia for another degree?”
Meanwhile, it appears that Mr. S—’s submersion in his graduate physics program has given him a skewed perception of “the success of the scientific worldview.” All around us are examples of science’s failure to persuade people. For example, it is scientific fact that smoking cigarettes causes lung cancer, yet millions of people begin doing it every day. Why? Is it because they refute the validity of the scientific findings? I doubt it. More likely it’s a clear example of scientific logos being overpowered by the pathos of cigarette ads showing beautiful sexy cool people smoking, combined with the ethos of the Marlboro Man and assorted smokers in the entertainment industry. Again, Mr. S— seems to confuse the prestige of his field with the realities of rhetoric.
Mr. S—, meanwhile, himself seems to try to infuse his argument with ethos by titling his message “I am a Rocket Scientist!” and repeatedly citing the strength of logos in science as if it were exemplified in his own arguments. Alas, it is not. For Mr. S— to claim that “Mr. Albert . . . lacks logos” is both incorrect and a good example of the logical fallacy called “ad hominem.” For Mr. S— to assert that my argument is illogical is one thing; to assert that I as a person “lack logos” is a personal attack. I will not dwell on this attack, since it is far more interesting to wonder what problems he has found in my logic. Incongruously, he attempts to support his attack on my logic by claiming that my boss’s statement about knowledge and money is empirically false. First of all, what does empirical evidence have to do with the quality of my logic? Dismissing the premises of an argument does not in itself do anything to evaluate the logic of conclusions that proceed logically from those premises.
Let us use a simpler proof to elucidate Mr. S—’s mistake. Assume this premise: it is raining outside. Assume also this premise: if it rains, Mr. Jones will carry his umbrella. If we assume these premises to be true (i.e., it is raining, and Mr. Jones does carry his umbrella when it rains), then we arrive at the logical conclusion that Mr. Jones is therefore carrying his umbrella. I believe this is a classic example of inductive reasoning, called (if memory serves), “modus tollendo ponens.” Now, if we discover that we were mistaken about the rain—that it is in fact not raining—does that mean we were being illogical when we concluded that Mr. Jones was carrying his umbrella? Of course not. Our logic was impeccable; we were simply wrong about one of the premises. For Mr. S— to state that my premise is the point “at which the logic of the proof collapsed” suggests that he aspires to an understanding of logical proof which he has not yet achieved.
This brings us to what apparently is the last possible foundation of his argument: his assertion that knowledge and output are interrelated, and that this statement is empirical fact. Even when I take into consideration Mr. S—’s lack of experience in the corporate world (immersed as he is in academia), I still must believe that examples of knowledge without output are all around him. What about the tenured professor who hasn’t published in three decades, who recycles the same rote lecture year after year? What about the grad student who has read every single book on his subject and still hasn’t started on his doctoral thesis, and never will? What about all those who finally get their Ph.D.s, only to take dead-end jobs in the service sector, letting their nine years of education slowly fall to oblivion? Meanwhile, we see other examples of output without knowledge, such as the factory worker who knows almost nothing about the textile industry but is nonetheless capable of sewing more than 500 elastic waistbands a day. Clearly, Mr. S— is unwise to base his entire argument—and his condemnation of my logical ability—on such a problematic assertion as knowledge and output being interrelated to a significant degree.
I hope that clears up the matter.
Subject: Re: Equation (fwd)
Date: Wednesday, November 12, 1997 1:44PM
I’ve been busy researching the correlation between knowledge and wages, but I offer the insights of C—, a fellow graduate student.
Date: Wed, 12 Nov 1997 11:36:23 -0700 (MST)
Subject: Re: Equation (fwd)
I find this entire discourse fairly meaningless in light of one error. Even if we accept the premises that knowledge is power, and that power is equal to work divided by time, the conclusion that these two relationships obey the laws of communicability is fallacious. The original author has fallen into a fairly common trap in the sciences. As with the infamous “Intensity” definition in optics, the true meaning of power depends upon the specific context, or less generally, discipline of science in which it is used.
Since an astronomer uses “intensity” to mean “watts per square meter” and a radiometric scientist uses “intensity” to mean “power per steradian” (the true SI definition), can we state that the ratio, area divided by solid angle, is a meaningless quantity and should thus be discarded? Of course not. As I see it, there are two definitions of power in play. As a businessman might use the term, power is the ability to wield influence over others. Fortunately, the science definition is more exact. It is presented appropriately in the original document, power = work/time. You may disagree with the former definition, but my fundamental point is undeniable: business power cannot be made equivalent to science power.
You may attribute any typos in this document to my telnet settings (which do not properly justify and update the window as I edit) rather than to how much attention I paid to spelling back in the sixth grade. Thank you.--~--~--~--~--~--~--~--~--
From: Dana Albert
Sent: Wednesday, November 12, 1997 5:40 PM
Subject RE: Equation (fwd)
I find C—’s assessment to be refreshingly clear and conclusive. With surgical precision, he has gotten right to the crux of the matter: the inappropriate merger of mathematical equations with abstract aphorisms.
However, I can’t help but point out that the original treatise (“the less you know, the more you make”) is meant as comedy—and, like other examples of the comic genre, depends upon its good-natured audience to gloss over the certain things (in this case the math/aphorism incompatibility). If the director of “Trading Places” had been hung up on the impossibility of a panhandler becoming a successful Wall Street trader, the movie never would have been made. In like fashion, if Mr. C— had responded directly to the knowledge/money treatise, he would have spoiled our fun. I much prefer the protracted debate in between, especially when my opponent is off in the weeds. ; )