The Dream Café

Steven Brust: “A masterful storyteller of contagious glee and self-deprecating badassery” —Skyler White

Brust's Law of Mathematical Formulations

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The probability of someone making a mathematical formulation on a non-mathematical subject is inversely proportional to its usefulness.

corwin

Author: corwin

Site administrative account, so probably Corwin, Felix or DD-B.

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  1. 82% of all statistics are made up on the spot.

    (Yeah, it’s old).

    ed

  2. Grrr

    Ed @2 beat me to it.

  3. If we need to solve for the Chance (C) of mathematical calculations being applied to non-mathematical situations, then we must first find the quotient of Assholes (A) divided into the overall subset of People (P).

    This is then multiplied by the degree of Reliability (R) of the mathematical capacity of the speaker.

    So we see, the result of this is:

    C=R*(A/P)

  4. I was sure you were going to propose something like this, but I don’t really see that it has any real applications.

  5. I’m trying to consider this idea to see if I agree with it, but I’m having trouble because I can’t think of any non-mathematical subjects.

    Do you mean that in the sense of subjects which have no intersection with any aspect of mathematics including probability and logic?

  6. corwin

    Majikjon @ 4: You win.

    Rathgar @ 6: Serious question? I was thinking of things like, “The amount of religious freedom in a given society is inversely proportional to the strength of the strongest religion.”

  7. Eh, it’s just a question of whether they make up the right formula.

    For THE mathematical formulation of Science (and thus, everything inferred from Evidence), track down the two papers “Minimum Message Length and Kolmogorov Complexity” by C. S. Wallace and D. L. Dowe, and “Minimum Description Length Induction, Bayesianism and Kolmogorov Complexity” by Paul M. B. Vitányi and Ming Li.

    Be warned, they’re written at a very technical level of math.

  8. Now, the question is…is this law itself a mathematical subject? And if not, given that the probability of an event which has already occurred is, well, unity, does that automatically render its utility nonexistent? 🙂

  9. corwin

    Touchstone @ 9: No, it just makes it autological. 🙂

  10. You’re more of an optimist that I am. I’ve always felt that that it was inversely proportional to the square of it’s usefulness.

  11. Generally, I agree with the statement starting the thread. There is one exception I use when traveling.

    The bar/church ration is directly proportional to how much fun one can have in a town. Having grown up in small-town Pennsylvania, a bar/church ration of >1 by at least .2 was highly indicative of how much those seeking fun were not likely to be constrained by a puritanical set of social mores.

    The corollary, by the way, is that a bar/church ration of lower than .75 means you have to look harder for the fun stuff, but it tends to be a bit wilder because of the repressive envrionment.

    (To make it even less useful, by the way, my experience suggests that this rule goes out the window when dealing with permanent populations of greater than 50,000.)

    Cheers.

  12. There is no such thing as a non-mathematical subject. One way or another everything boils
    down to chemistry or physics each of which
    have mathematics at their foundation.

  13. There are certainly subjects that are non-mathematical. Or, more correctly, where mathematics is not useful.

    Mathematics studies subjects that are based on empirical evidence, or have real world foundations. While math can be applied to metaphysical or religious discussions, the usefulness of math in these cases is generally overshadowed by the blatant intangibility of the subjects.

    How many people was Christ? 1 or 3? Yes, these are numbers, and hence, mathematical, but how useful is mathematics really in the debate over the Nicene Creed?

    How do you use a tool for logic in studying a subject that is not itself logical? The logical answer to this question is generally “very poorly”.

  14. How many people was Christ? 1 or 3?

    I’m going with “zero,” but that’s just me.

  15. Well, perhaps. But there’s another discussion that doesn’t really involve mathematics. 😉

  16. LH @ 14,

    Majikon @ 15 answers well. I’ll add just a few more. There’s a question children are prone to ask which goes something like “How do you know when you’re in love?” And the answer, as everyone knows is, “You just know.” Kinda the opposite where numbers and/or chemistry are particularly useful (the claims of Match.com and others notwithstanding).

    Generally, questions about systems in which act are notoriously troublesome.

    Douglas Adams has a great take on this in an observation made by Dirk Gently (in _The Long Dark, Tea Time of the Soul_). Sherlock Holmes believed that you eliminate the impossible and whatever is left, no matter how improbable, must be the truth. Douglas’ detective differs strongly: To call something impossible just means that there is something we don’t know enough about — and there are plenty of those — while the merely improbable requires us to ignore everything we know about a person or situation. But, as Christina Ricci says in “The Adams Family,” axe murders look just like everybody else.

    By the time you do the equation to catch the split -finger fastball, it’s already several seconds since smacked you in the privates.

  17. There’s a question children are prone to ask which goes something like “How do you know when you’re in love?” And the answer, as everyone knows is, “You just know.”

    Well, that just seems an instance of metaphorical schmaltz getting mixed up in a literal-dependent situation. If there’s a puddle of love and I am lying in it, then I know I’m in love. If there’s a room with “Love” on the nameplate, and I have entered it, I know I’m in love.

    But love isn’t a location, so I can’t be in it, literally.

    And, Majikjon, you’re right. But I rarely let pertinence get in the way of my goofery. :D~

  18. corwin

    Lewis @ 14: To say that other disciplines have mathematics “at their foundation” is to utterly miss the point. Chemistry and physics are both studies of the laws of motion of matter under certain conditions; but the laws of motion of each must be learned and understood independently. To apply the laws of motion of simple mechanics to sub-atomic particles is to get nonsense. In the same way, simply “applying” mathematics to, for example, literary criticism is get nonsense.

    2.

  19. Abstraction and logical reasoning are also part of mathematics and, hopefully, part of a well written work of literary criticism.

    Anyway, chew on this for a while:

    For any formal recursively enumerable (i.e., effectively generated) theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

  20. Brust’s Law does not account for the huge amount of pure mathematical work done by mathematicians which not only lacks utility but which even defies understanding by all except a small subculture of specialists in its area. Most of this stuff is more fully outside of public view and public consciousness than the raunchiest pornography.

    Mathematics at heart is a study of patterns — whether one is studying quantum particles, social relationships, or written texts, mathematical formualtions can be useful to the extent that relevant properties can be generalized as patterned relationships.

    Of course, SOME phenomena are more susceptible to mathematical formulation than others because (a) the relevant properties are more recognizable; or (b) the relevant properties are not easily formalized using existing mathematical tools. Both problems are common in anthropology and are frequently used as excuses for resisting the use of mathematical formulation.

    My response to such excuses is to point out that mathematics is a kind of “field language” for studying the patterned relationships which organize human activities and thought. It provides researchers with a set of tools for perceiving and communicating relationships which cannot be articulated well in verbal language. Thus it functions as an important complement to other ways of thinking about anthropological phenomena.

    Many anthropologists ignore mathematical formalism; many still can do excellent research without this dimension to their work. But one problem which emerges within the field is that anthropologists who avoid mathematics — through dislike, lack of training, or various other reasons — congregate in subfields where it seems less useful and thus less essential to research. Then when theses subfields encounter a new, useful mathematical formalism, often it is not viewed as “useful” because, strictly speaking, it is not useful to most of the practitioners in the field. Consequently, a lot of this work has been diverted into interdisciplinary programs outside of mainstream anthropology. For some examples of these programs, see:

    http://hcs.ucla.edu/home.htm
    http://eclectic.ss.uci.edu/~drwhite/center/cac.html

    These and a growing number of other, similar interdisciplinary programs are magnets for social scientists whose mathematical work lay outside the norm for their home disciplines.

    Ultimately, the value given to mathematical formulation depends as much on the cost and benefits to specific individuals as on the subject matter. My niece, an Asian Studies major, recognizes many more subtleties watching Rashomon than I do; I benefit much more from a mathematical description of population growth or social network growth than from the comparable verbal description which my niece would prefer. Both reflect our background, training, and interests. Because the “value” of mathematical formulation is so specific to individuals, its assessment needs to proceed cautiously.

  21. Majikjon:

    Mathematics studies subjects that are based on empirical evidence, or have real world foundations.

    Wow, do I disagree. 100%, even. Mathematics studies subjects that are completely in the mind — it is the least empirical of disciplines.

    In The Mathematical Experience Davis & Hersh argue — persuasively, to my mind — that mathematics is not a science, it is actually the simplest of the humanities. Mathematics is human mental experience so radically stripped down and simplified that it can *accurately* convey mental states, so two mathematicians can follow each other’s trains of thought farther and through much more complex terrain than thinkers in other fields.

    Math isn’t just one of the humanities, it’s the closest things we have to *telepathy*. The catch is, your thoughts have to be stripped away from almost everything that makes them personal or relevant.

    What is fascinating is that something so entirely mental can often be so useful for empirical work — possibly because the habit of radical simplification makes other problems easier to deal with, too.

  22. Doctor Science @ 23:

    You’re talking about how mathematics WORKS, not what it studies.

    Yes, Math is a tool for abstracting the concrete. However, the subject has to be concrete, or at least quantifiable, or else math cannot study it by definition.

  23. Whoa – to everything.

    Am back to step I, in my little one celled brain – which is: is there evidence of the absolute nonexistance (ever) of …well….. any’ol’thing? If so – then….. what would that be?

    Speaking of math, what “…ions” (ect)
    follow “a trillion,” and at what point do i have to begin using the “to the power of” symbols? (just tryin’ to work out my budget & debts for the next 40 years).

  24. While I find the original statement humorous, it is also made me think about what studies are on non-mathmathical subjects. Honestly, wracking my poor sleep deprived brain I can’t come up with one.

    What does come to mind are studies which use data incorrectly, or have poor data to begin with and extrapolated it out to reach conclusions which were preposterous (I’m looking at you literal-KingJames-no-dinosaur people). You can (and people often do) torture data until it tells you what you want it to (Phillip Morris…), but who writes mathmatical formulations on religion? There’s no data.

    Music can be studied mathmatically, emotions can be studied mathmatically. About the only thing I can come up with is philosophy, which I admit can be due to my lack of in-depth study on the subject.

    There are many mathmatical formulations which are useless. But they are usually on a subject that could be studied mathmatically given better data.

    for example: my thesis (a long time ago) was trying to determine the likelihood of restaurants buying locally grown fresh-water shrimp. What I determined was the questions that should be asked on a following study – my mathmatical formulas produced no useful data because I had shitty data from research. If I had perfect knowledge to start with the study would have been designed to bring back data which could have been analysed to produce useful statistics.

    Lies, damn lies and statistics…

  25. Now that I’ve had over 16 hours to think on “Brust’s Law…” i think the probability of the forementioned formulation, mathematicaly speaking, would be a coin toss – if both sides of the coin were heads and one head was inverted/a mirror image of the other. But – but…but, it also might depend on who’s tossing the coin – since anything & everything & all is possible (and probable, too), some of us might have the ability to manipulate the tosses in favor of any desired direction.

    Still – in the end i trust it would all come out a 50/50 thingydeal.

  26. I dunno — I sorted out the question “What is the meaning of Life” with math. Still no clues as to the meaning of my life — but Life was a breeze.

    Gotta carry the one.

  27. corwin

    I’m not strong enough. Last time I tried, I got a hernia.

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