Mathematical Logic Finds Unexpected Application on Wall Street
In an unexpected development for the depressed market for mathematical logicians, Wall Street has begun quietly and aggressively recruiting proof theorists and recursion theorists for their expertise in applying ordinal notations and ordinal collapsing functions to high-frequency algorithmic trading. An ordinal notation system is used to name each ordinal in a certain initial subsequence of the countable ordinals; such systems have recently been applied by elite trading operations to the parameterization of families of trading strategies of breathtaking sophistication. Ordinal notation high-frequency trading algorithms, also called ordinal arbitrage systems, pit their strategies against similar algorithmic opponents on electronic exchanges for a few fleeting seconds, during which thousands of trades are executed, including exploratory trades that test the strategies of opposing human and machine traders.
The monetary advantage of the current strategy is rapidly exhausted after a lifetime of approximately four seconds–an eternity for a machine, but barely enough time for a human to begin to comprehend what happened. The algorithm then switches to another trading strategy of higher ordinal rank, and uses this for a few seconds on one or more electronic exchanges, and so on, while opponent algorithms attempt the same maneuvers, risking billions of dollars in the process.
The elusive and highly coveted positions for proof theorists on Wall Street, where they are known as trans-quantitative analysts, have not been advertised, to the chagrin of executive recruiters who work on commission. Elite hedge funds and bank holding companies have been discreetly approaching mathematical logicians who have programming experience and who are familiar with arcane software such as the ordinal calculator. A few logicians were offered seven figure salaries, according to a source who was not authorized to speak on the matter.
Qfwfq
Cornelius Fitzedward Pope II
Christian Marks
[...] for the depressed market for mathematical logicians, Wall Street has begun quietly and aggressively recruiting proof theorists and recursion theorists for their expertise in applying ordinal notations and ordinal collapsing functions to [...]
Sudden Demand For Logicians On Wall Street | JetLib News
May 27, 2010 at 2:01 AM
Well, I wouldn’t really say this is an area for “logicians” but for “set theoreticians” yet again, the border between this two are most of the times blurry.
Anyway, as an student of computational logic, we don’t even deal with ordinal algebra in our program. I only learn that many years before in a set theory lecture.
Sambatyon
May 27, 2010 at 3:12 AM
Sambatyon -
I would politely beg to differ as
a) Set theory is a branch of logic anyway; and, more importantly
b) Large countable ordinals are of huge importance to proof theorists in working out the complexity of proof-theoretic and subrecursive hierarchies.
I wrote my MSc thesis on this. Albeit about 16 years ago, so sadly I’m too far away from it to get one of those seven figure salaries. Unless they offer me £10000.01 a year (there’s definitely 7 figures there…)
Matt S
May 27, 2010 at 10:09 AM
Could you tell us more about these ordinal strategies?
Joseph Turian
May 27, 2010 at 3:19 AM
Reading between the lines here: Wall Street is increasing it’s use of high frequency trading. ie: The game which is already rigged in extreme favor of the house, is going to be even more rigged in favor of the house.
Individual investors attempting to trade markets are, as it stands now, ignorant of the odds. What’s coming down the road is a system that will suffer massive shortages of liquidity. Why? Because no fool will want anything to do with them.
popo
May 27, 2010 at 6:13 AM
Being the author of the Wikipedia article on ordinal collapsing functions (and a great part of that on large countable ordinals), I must say that I’m flabbergasted.
Ruxor
May 27, 2010 at 8:57 AM
Can you elaborate on why you are flabbergasted?
Dennis
May 27, 2010 at 12:11 PM
I would like to channel the Bobs from Office Space, and ask these financial companies: “What, exactly, is it that you do here?”
Jeremy
May 27, 2010 at 12:14 PM
Look for these very mechanisms to be banned by congress, the senate and possibly by presidential decree as the kind of “wealth creation without effort but strictly through gaming the system” which led us down the same path that derivatives did.
All of the gains were wiped out and everybody but the insiders got stuck with the multi-trillion dollar tab when the music stopped and we found out the chairs were rented and had all be repossessed.
These are the kinds of games which should be outlawed.
msbpodcast
May 27, 2010 at 1:04 PM
Yeah, but in the mean time, I’ll be steering my math degree toward set theory and mathematical logic – with an emphasis on proof and recursion theory.
If we’re playing another round of musical chairs, I want to end up with a chair when the music stops.
Austin
May 27, 2010 at 3:56 PM
this would be like some cosmic joke except it’s actually funny. thanks.
vlorbik
May 27, 2010 at 2:31 PM
Examples? I’m stumped; despite having studied these topics on and off over the years, and having a rather vivid imagination, I still can’t see the connection between large ordinals and trading.
Now, logic and trading,that’s a whole nuther matter … clearly, mining data to auto-discover structure, e.g. markov logic nets or whatever, yeah, duhh. Or maybe even somehow applying JH Conway’s “numbers and Games” .. maybe .. But ordinals? ?? I’d like to see at least a hand-waving example of the utility.
linasv
May 27, 2010 at 3:31 PM
You can outlaw what you like the reality is that those who can do those who can’t teach.
Chris. Harding
chris harding
May 27, 2010 at 6:24 PM
At least what teachers ‘do’ isn’t morally dubious.
B0ris
June 19, 2010 at 2:24 AM
[...] Mathematical Logic Finds Unexpected Application on Wall Street In an unexpected development for the depressed market for mathematical logicians, Wall Street has begun quietly and [...] [...]
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May 27, 2010 at 8:17 PM
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May 27, 2010 at 8:44 PM
Not a surprise to anyone who has read the excellent “Accelerando” by Charlie Stross, I suspect. This is pretty much his take on “Economics 2.0″.
Chris Harris
May 28, 2010 at 8:31 AM
After posting (with a link here) on this today, I had a thought: what if a writer on mathematics, like Steve Strogatz whose columns at the times have been so fun and instructive this year, were to approach this topic? I wrote him at Cornell and he replied that his Times column has been shut down, though he agreed that this is a critical topic for mathematicians to be leading a discussion upon.
Brian
May 28, 2010 at 11:14 AM
[...] Mathematical Logic Finds Unexpected Application on Wall Street The monetary advantage of the current strategy is rapidly exhausted after a lifetime of approximately four seconds–an eternity for a machine, but barely enough time for a human to begin to comprehend what happened. The algorithm then switches to another trading strategy of higher ordinal rank, and uses this for a few seconds on one or more electronic exchanges, and so on, while opponent algorithms attempt the same maneuvers, risking billions of dollars in the process. [...]
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May 28, 2010 at 12:02 PM
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May 28, 2010 at 12:41 PM
In light of all the other insanities we are so eager to embrace it is comforting that logician/mathematicians have not been forgotten. rm
Richard Rhoads
May 28, 2010 at 2:16 PM
[...] In all seriousness, if you can get past the geek-speak, this is very interesting. Wall Street is recruiting math wizards to assist with interpreting information from a new high-frequency trading algorithm. The job titles will be “transquantitative analysts” (try to say that three times fast). These very coveted positions are not being advertised. Rumor has it that the salary for these new positions will be in the seven figures, but that is not from a reliable source. Since I have an advanced degree from university in math and I study physics on the weekends, I find this fascinating. I think this new algorithm sounds brilliant. This new way of interpreting information could take some of the risk out of the billions of dollars that are traded. If you would like to read more nitty gritty details about this, just click here! [...]
This Is The Geekiest Thing You’ll Read All Day - Programming Blog
May 28, 2010 at 3:19 PM
I have a paper on a result I’ve found with regards to using ordinal numbers for an explicit form of Avery’s constant. I wonder if Wall St. would prefer me to not to publish it before I speak with them … maybe they could make a better offer than Springer-Verlag?
icarus
May 29, 2010 at 5:25 AM
A simple model, like a five-card poker hand with three rounds of betting and a potential discard at every round might use the obvious five-digit base 52 number as a quick representation of a hand. It can be conveniently passed around the code, used for comparisons, or stored in a database. However, there are only about two and a half million distinct hands, so if the model contains a bunch of arrays indexed by the five-card hand, the difference between two and a half million versus 52 to the fifth be comes important fairly early in the design of the model. Throw in a sprinkle of recursion due to multiple discards and it is the difference between doing it on your laptop versus running it on a cluster.
A lot of simulations and models are built from combinatorial sets generated recursively. Often there are logical relations among the generators that induce equivalence relations within the enumeration of such sets. The brain-dead example might be an ordered set of items where all permutations are admissible but under certain circumstances the order of some of the items is irrelevant, under all others the order is relevant. A computational model will very often contain an array with the exact cardinality of the recursively specified set. No repetitions and no gaps. Furthermore, a fast algorithm mapping an observation (say, a collection of market triggers) to a unique index in that array is usually required. That part of the model might be keeping track of the frequency of occurrence of each of these distinct patterns of activity, for example. The model requires not only an accurate enumeration of complex recursion, it needs a fast map from local data (the observation) to an index uniquely representing that combination in the model.
So, really, that’s what we are talking about here, in practical terms, isn’t it? Some ass-kicking recursive enumerations and computationally efficient passage to their denumerate sets. Not to belittle Cantor, but a familiarity with the infinite prepares you for the many traps referred to by the ancients as “effective computability”.
PlutoReturns
June 3, 2010 at 2:59 PM
Как хорошо было Адаму: когда он произносил что-нибудь умное, он был уверен, что до него никто этого не говорил.
What a good thing Adam had. When he said a good thing, he knew nobody had said it before. (С) Twain
Надеюсь, Вы поняли к чему я об этом……
Twain
June 15, 2010 at 5:23 AM
With the exception of dart throwers, market players are trying to relate a dependent variable (price at some not-too-distant future time) to a sea of independent variables (recent price history, interest rates, etc). Mathematicians build algorithms which attempt to compute dependent from independent. They do this for WallStreet companies who can afford them. But as algorithms grow old their value declines. So higher-level algorithms which produce new and increasingly profitable low-level trading algorithms are needed. Mathematical logicians do this.
Those of us who are old enough to have worked with punched-card programs have seen programs represented as integers (an integer is a very simple ordinal). Remember columns of digits 0…9, eighty columns per card, and a couple of hundred cards per program? That deck of cards coded/defined our program as an enormous integer/ordinal — for two hundred cards the ordinal was about 10^16000 (a sixteen thousand digit integer).
So the high-priced mathematical logicians employed by Goldmacher&Company are creating functions from ordinals to ordinals which might decode into a sequence of winning trading strategies. There is more, but I’ll leave that to the next contributor.
wRichardStark
June 16, 2010 at 10:37 AM
The justifications for Wall Street’s existence are that it enables liquidity and leads to valuations that more or less correctly reflect value. Other systems can’t do that. When I sit listening to my (ideological) capitalist friends talking to my (ideological) socialist, this is the argument that even seems convincing to the socialist. But if Wall Street fails to provide liquidity and some kind of efficient valuation, it quickly ceases to be useful. Extremely fast (super human) technical trading is aimed precisely at exploiting the market structure itself, not the values of the companies being traded. So it can not do anything but reduce liquidity (by keeping more of us out of the market) and further decouple the financial markets from actual markets (for stuff that companies make and do).
The right solution (which will not be one of the government’s regulatory moves) is to radically slow the trading down, not speed it up. There is no reason, vis a vis, liquidity and valuation, that a particular firm’s stock should be traded more that once a day. A blind auction, once or twice a day (say scheduled in tranches occurring throughout the day) would help refocus Wall Street to the problems it is meant to solve.
Drew
June 20, 2010 at 9:52 PM
if true, amazing!
Federico Gobbo
June 21, 2010 at 11:39 AM
I’m pretty sure you’re actually talking about experts in ordinal optimization, which makes perfect sense in a HFT shop. I don’t think, for example, the ordinal calculator is useful for doing this, though it might be. The two wikipedia links just give me a headache; I don’t even know what they mean.
I might write a blog on the subject. HFT is actually pretty simple.
Scott Locklin
August 18, 2010 at 1:33 AM
Yes, please write that blog post.
Joseph Turian
August 19, 2010 at 1:34 AM
Ordinal optimization, although interesting, is not what was intended-see http://www.mafeco.fr/?q=node/230#comment-1303 and the reply http://www.mafeco.fr/?q=node/230#comment-1317
Anonymous
August 19, 2010 at 12:44 PM
[...] Marks in his post here, said Wall Street is waking up to mathematical logicians. Ok so he says Wall Street need someone [...]
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Cary
September 13, 2011 at 9:23 PM
[...] behavior other algorithms can’t predict, the math involved gets very tricky. In May 2010, Christian Marks claimed that financiers were hiring experts on large ordinals—crudely speaking, big [...]
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August 8, 2012 at 7:00 AM
[...] The monetary advantage of the current strategy is rapidly exhausted after a lifetime of approximately four seconds–an eternity for a machine, but barely enough time for a human to begin to comprehend what happened. The algorithm then switches to another trading strategy of higher ordinal rank, and uses this for a few seconds on one or more electronic exchanges, and so on, while opponent algorithms attempt the same maneuvers, risking billions of dollars in the process. Christian Marks [...]
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