An Infinite Problem
Jun 17, 2005
A few years ago on a Friday morning in late November a young man in late twenties summoned up enough courage and walked the few paces from the Moorgate tube station to London Wall area in the City of London to face his nemesis. The man had an honours degree in Philosophy and had been introduced to the world of investment banking only a few days ago by a headhunter friend of his over a pint of beer in a bar somewhere near Finsbury Square.
The company was, well, you know – the Investment Bank and the interviewer was a Ph.D. in Physics from the university across the Atlantic . The position was for a junior quantitative analyst within the equity derivatives trading team.
To date it is the most bizarre interview that we have ever heard of, bizzare and almost surreal. We are not privy to the exact transcript of the interview but have reconstructed the gist of conversation based on what has come down to us from our source.
The first question that the interviewer asked our young philosopher was: "How would you represent and declare real numbers in a C programme?"
The answer: "sorry, come again, please.¨
The question: "you know the C programme, the C computer language programme, right? In that, in how many ways can you declare a set of real numbers?"
The answer: "I am sorry, I don't have any knowledge of computer programmes."
To this the interviewer was a bit taken aback and said, "aren't you from _________ university?"
Yes, replied the candidate "but I did Philosophy".
The interviewer was speechless and said, "Oh my god, can't believe David sent me a philosophy major for this role!! And what was your minor?"
Our man, a bit rattled, blurted out, "I have actually done an honours degree in philosophy, not a major."
The question again (this time, more condescending tone): "look there has been a misunderstanding, this is a job that requires a very high degree of numeric skills and capability. We need a Physics or Computer Science major. You have to be playing with numbers and equations all the time to find solutions; Sorry, for your time, but this job is not for you."
The candidate immediately, cut him and said:"I'm afraid numbers can only add puzzles to life and can not solve any problem. If you are looking for solutions then numbers are not going to help you."
With a very agitated and a rather angry tone the interviewer said: "Excuse me? What do you mean? Are you out of your senses? In derivatives, numbers and equations are god and a computer programme is the way to reach the god. Bye, you know your way out." With this the man started to get up.
An innocent quip from the candidate, who was now all red in his face: "why is that so?"
Now, with sacrcasm and arrogance dripping like saliva from his mouth, half sitting, half standing, the interviewer says: "because if I integrate from zero to infinity my call payoff function and then take the expectation of it I will get the precise value of the call option up to the fourth decimal place. And that, I can assure you, is Latin and Greek to you!"
"Actually, sir, I did study a bit of Greek in my undergraduate course. Can I ask you a question?"
The interviewer said, "yeah, anything. Be quick, and let's walk to the door."
The candidate kept sitting, as if numbed by the experience and asked: "you just mentioned infinity. How would you define infinity. Or in a number sense, how would you quantify infinity?"
"Look, pal, what is this? Are you somehow trying to get even or something. Clearly there has been a mistake and I think"
"No, sir, please answer my question. What is infinity?"
With pure rage, the interviewer answered: "Well, infinity is a mathematical concept that signifies"
"My question, sir, is in your job how many numbers will it take to quantify infinity? A million, a billion, a trillion, a trillion trillion trillion?"
A stunned silence".A long, very long silence. The interviewer sat down. Rage, fury, frustration, all such emotions swirling in his head and the expression on his face clearly saying, how do you tell a five year old child that she is not capable of driving a car?
Anyway, our candidate soldiered on: "numbers are deceiving and as I said that add to our misery. Take the even numbers. They are half of all numbers and yet there are just as many even numbers as there are total numbers in this universe."
The interviewer almost groans: "and why are you asking me this question?"
The candidate replies: "Because every number, be it even or odd, has its even double. If you double any number you will get an even number. And this is the whole point of mathematical infinity. Infinity, is a whole that has as many parts as the whole."
The candidate continues: "And you mentioned infinity a little while ago and I think working with infinity is very dangerous."
For some mysterious reason the interviewer's attitude slowly changes towards this guy. He warms up and actually acknowledges the presence of another human being in the room. Perhaps, a past, dead and buried long ago inside him, comes alive. A past, where knowledge of mathematics was a pure delight rather than an excuse to make a fat bonus; a past where aimless gallivanting down the Harvard Square or sailing with your girlfriend on the Charles was worth much more than the Porsche and the five bedroom duplex in Knightsbridge.
For a long time the interviewer looked at the young man sitting opposite him with a fondness that was quite disconcerting to the other party. Finally the interviewer said: "well, you are right; now that is pure philosophy and you know what I think what you are saying is crap ¡V but somehow I am starting to like it."
The interviewer continued on, this time rather gently and with some self-doubt: "in our world, in our Black-Scholes world, we only have finite integrals and the Ito's lemma. Simply can't escape them, so we make a virtue out of it. And you know what? " it all works; it works with such great degree of precision that we all make money, and make money for others "sometimes we lose, maybe big time (a rare grin)."
The candidate: "what is Black-Scholes?"
The interviewer genuinely let out a hearty laughter this time: "I'll tell you, if you promise me that you will never again go for an interview to any bank in the City."
"Well, Black-Scholes is the solution of a heat diffusion equation".oh, hang on, um..how do I explain a heat diffusion equation. Ok take another approach, say you wanted to buy something in the future and not now but you wanted to make the payment today, Black-Scholes will give you"
"So it is something like the equations in physics"
"Exactly! That's what all this is about."
"But this is not physics. It is social science. What you are doing here in this bank, or what anyone does in any other bank is social science."
The interviewer could have terminated this discussion and walked out of the room. There was no reason for this bizarre and unproductive job interview to go on any further. But it did. Call it the Friday effect, call it the Blackzhiemer's disease, the Global Head of Structuring and a Managing Director of a top tier bank was quite willing to engage a young philosopher in this discussion.
"So be it, but you know what physics has infiltrated this discipline and did so more than thirty years ago, so what the hell!"
"Even so, you make or lose money not because of your equations and numbers. You are simply lucky and someone else is unlucky. Someone has to lose for someone to make money - that is common sense, so where is the power of equations or numbers?"
"Go on, I like your crap"
“Physics or mathematics is all about abstractions. A priori truths. Two plus two is four and it will remain that way, even if you and I did not exist or even if this whole universe did not exits. Einstein’s laws (God knows what they are) will remain that way regardless of whether we or anyone else in this world exists or believes in it.”
“Not so true for endeavours and systems where human beings make things happen. If you go away, and your mates go away, then you does the buying and selling of whatever you do?”
“Actually, we don’t buy or sell anything, we simple structure……”
“OK, fine, so if you structure something, i.e. you build something then you influence that ‘something’, you and all others who are involved in that influence the ‘something’ and from start to finish change the nature of that ‘something’. Right?”
“You can say so.”
“Then where is the abstraction in it, Sir? Are these constructs that you deal in true a priori? Are the buying and selling of stocks, the lending of money by the banks and the running of the businesses in this world true a prori? No, they are not. They are dependent on the human beings who are engaged in these activities, and if these agents – human beings – were to be absent or move away to some other activity or change their method of operation to something else then these activities, businesses will become different. Right?”
No answer this time.
The candidate continued: “So my point is in social science, in banking, finance, whatever, the agents change and influence the activity and all action is contingent upon collective behaviour of the agents. The very fact that agents get involved in the activity alters the nature of activity significantly”. A bit of silence and then: “And of course, pure luck”.
The young man was quite animate now, as if this was a Ph.D. dissertation presentation: “Dinosaurs were unlucky, they got wiped out, Bill Gates was lucky he amassed billions, some stock brokers are luck they make money and some are unlucky and they lose”. “No equations or numbers there, sir, none at all”.
A brief pause and then the interviewer said: “Well, great I am happy I have heard something today that I have never heard before, or possibly ever hear again. At least not in a job interview.”
And then the interviewer with a finality: “But let me tell you pal, Black-Scholes as an abstraction, as a pure model constructed out of physics was true before I was born and shall remain true long after we are gone”.
The response: “But that I am sure has nothing to do with making or losing money or banking as an enterprise”.
The guy never got a job in that bank. We don’t know what happened to him. The interviewer, it is known with some degree of certainty, took a train that afternoon to Oxford to hook up with one of his old mates there. He got very drunk that weekend and returned to London the following Tuesday morning. Within a few months of this incident he left the bank and it is rumoured that he is now pursuing research in string theory in some west coast university in the States.
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