Apr

10

Randomness, from Jeff Watson

April 10, 2011 |

 I've been thinking a lot about randomness lately. Trying to define randomness, I presume that it can only be defined negatively, as in the absence of any discernible or systematic patterns. I believe that complete randomness can only be disproved and not proven; but a test will only detect a single pattern or a group of related patterns. I would appreciate any thoughts on randomness in a philosophical vein as there might be a few meals lying right under our noses.

Gary Rogan writes:

Just some random thoughts on the subject. Randomness signifies the lack of an informational connection between the process that generates one even and any other event. There are two kinds of connections: the specific knowledge of one process knowing what the other one is doing, and the inherent construction similarity between the processes. Imagine that you need to pick 100 random events. You could pick 100 individuals, put them in separate rooms and let them pick a number each. They will satisfy the lack of the first type of connection, but not the second. Their picks will not be truly random because human beings of any kind have enough similarities to not satisfy the second, yet their picks will be more random than if they were together as a group. So the trick is to find processes that have not connection to each other and no preferences to generate any particular number within the rules of what's acceptable. 

George Parkanyi adds: 

Randomness seems to be overlaid on some kind of order – a basic framework within which seemingly unconnected events then play out to set up our environment and our experiences. Kind of like a board game - a basic set of rules with additional random elements, say dice, shuffled cards and individual decisions that ensure that no two games will ever be played exactly the same way. The game overall works toward a predictable outcome (someone winning), but the means of getting there will never be the same for any two plays. 

Mark Schuetz writes: 

Apologies if Rumsfeld's quote has become hackneyed, but I think it describes one facet of randomness well.

"There are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know."

Some always think of randomness as "known unknowns": everything was determined by some underlying process or fits some probability distribution. Depending on one's definition of randomness, perhaps there are more "unknown unknowns" than meets the eye: a truly random event or series of events might not determined by some underlying logical process and a descriptive probability distribution might not exist or might be impossible to know.

Russ Sears adds:

Randomness is a major topic in Abstract Algebra, and studying it almost became my career after grad school. Not sure if I can do it justice now, as I have been away from the subject for so long. However, in sequence of numbers (most events/things can be numbered), if there is no way to discern step t+delta from t even by narrowing its probability down then by most definitions it is random. For practical matters to "create" something that is random it is really a matter of hiding the pattern so that these probability distributions can not be discovered. You do this by the size of the numbers involved. In other words it is deterministic (it really can be discerned by cause and events ) but the numbers involved make it impossible to do so either because the measurement of the determining factors are impossible to categorized with enough accuracy to determine (think lottery ball drawings or weather/chaos) or because the "code" is varied and on such a large scale that only those with the "key" can decipher it.


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10 Comments so far

  1. Wang Yuanhang on April 10, 2011 1:21 pm

    you are thinking randomness in Laplace sense. if you slightly move away from the limit, you could fit your observation to a large function space, if there is no fit, it is complete random with respect to the part of function space you define the ‘complete randomness’ against? otherwise there is pattern or ‘limited predictability’, i.e. chao.
    problem for market is the underlying structure that generates observation is in constant flux.

  2. jl on April 10, 2011 11:12 pm

    Turn on your radio, tune to an empty channel, listen. That is randomness.

  3. jeff Watson on April 11, 2011 9:06 am

    Radio noise on an empty channel(AM radio as FM radio is full quieting in most receivers) is far from random. You hear the oscillations from RF from the sun, you hear pulses from quasars, there’s electrical noise like 60 cycle hum, motor noise, generation noise, different pops and clicks from high voltage sources like ignition switches, noise from the earth’s own ionosphere, RF echoes from the big bang, and RF produced by magnetic flux. All of these produce harmonics that fall within the broadcast band and can be detected with a sensitive radio. In fact, there’s a certain orderliness to RF noise that scientists are examining for clues to origins of the universe and other mysteries.

  4. Andre Wallin on April 11, 2011 11:50 am

    There is randomness for the individual, but not the whole. And in the long run all numbers and individuals are equal.

  5. anonymous on April 11, 2011 4:18 pm

    I know the site is not a big fan of NNT’s work (Black swan). However he makes a very good point stating that one should try to be ‘robust’ to randomness. This applies more to the ‘known unknowns’. We know a crash can occur in the stock market, but how much it goes down is unknown, so dont overleverage. Same goes for buying a house with a mortgage especially if there is only one breadwinner in the family whose job is tied to a large corporation. No job = no income for an unspecified period of time, therefore you can be unduly harmed by your leverage. To be robust, perhaps you would have your own small business with multiple customers, none of which accounting for a significant portion of your business. My point (or actually NNT’s point) is randomness is going to happen no matter how we define it. Try to put yourself in a position where randomness won’t harm you (at the minimum, hopefully you can position yourself where it will help you). Obviously one could walk across the street and be accidentally killed and there is no way to be robust to that except to live life to the fullest every day.

  6. Andre Wallin on April 11, 2011 6:22 pm

    we only care about randomness because of our greed and fear. if we look at the whole, who cares about randomness? logically this is correct, but emotionally it is very hard if not impossible.

  7. Andre Wallin on April 11, 2011 6:29 pm

    in terms of the speculator, who puts positions at certain numbers all of a sudden there is selfishness attached to the numbers because there are people or computers behind those numbers. one must be and remain the whole and identify the greed and fear in each number through a price distribution and trajectory and what numbers mean in the human psyche 666 on sp500 for instance.

  8. Precision and Exactness, From Enola Gay « on April 11, 2011 7:33 pm

    […] When I’m applying nail polish, I care about accuracy and precision. When I’m playing with my husband’s Interactive Brokers Trading Workstation, I care much more about randomness. His trading pals say that randomness is an important part of markets. (See: http://www.dailyspeculations.com/wordpress/?p=6210 )  Yet I’ve found that when I click the mouse lots of times on some numbers on the IB Workstation that are flashing, other numbers at the top of the screen ALWAYS change colors from green to red. It happens everytime. And then my husband yells at me. This seems to happen everytime. So I don’t think it’s random. […]

  9. Andrew Berman on April 14, 2011 6:22 pm

    Here’s an interesting information-theoretic way to think of randomness.

    If you think about knowledge as ‘bits you can compute,’ then a random bit is one that you cannot compute before you receive it. In that sense, a random bit is precisely the same as new information. Indeed, the “Omega number,” (see http://en.wikipedia.org/wiki/Chaitin’s_constant) is simultaneously random by any statistical test and contains all the answers to any mathematical question you could devise.

    BTW, I was drawn to this site by a recommendation from Victor’s brother Roy, who let me know that my father–Meyer–was mentioned on it.

  10. E. Harokopos on April 15, 2011 12:19 pm

    The issue is not known unknowns versus unknown unknowns (as per Ramsfeld’s poetry) but whether these unknown unknowns are unknowable. According to Fitch’s paradox “if all truths are knowable in principle then all truths are in fact known”. Defining randomness in terms of unknowable truths basically, by contraposition, argues that there are truths that can never been known.

    As far as markets go, this cannot be true since all truths about the markets are created by market agents and participants, therefore, all market truths are knowable, and as a conclusion, there is no randomness in the markets in this sense.
    Even if some truths are created by random causes, like natural disasters, to be reflected in the market, participant interaction is required. Thus, any randomness in the markets, if it exists, cannot be linked to any “unknown unknowns”, because there are none. The cause of the randomness should be found elsewhere and it is possibly an epiphenomenal randomness, created by some human participants so that it provides the necessary volatility for them to profit from weak hands.

    http://www.digitalcosmology.com/Articles/markets/markets.html

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