Gene Expression

Evolgen says:

Let’s focus on two things: the hypothetical deductive method and essential information that you must know to be able to read the science section of a newspaper.

Hm. Amen. Sort of. Scientists in many fields needed to be straight-jacketed into the “hypothetico-deductive” model for a reason. I remember a phylogeneticist telling a group of us why the hypothetico-deductive method was crucial in his own work, before his time taxonomists would get into arguments where they would justify their opinion about systematic relationships with an operational “Cuz I said so!” Testing hypotheses is essential for science. That being said, scientists do more than test truths derived from their models.

Scientists obviously engage in abduction, which is roughly the reverse of deduction. Instead of starting from truths, you work back to truths (hypotheses) based on the data. People don’t have a problem with abduction, ad hoc “theories” of the world based on scant data seems to be the norm in all manner of discourse.

But, my issue is with induction. People know what they should believe, whether it be from their political leaders, their preachers or their parents, they have their doctrine from on high. On the other hand how many times have I heard “but that’s a generalization” over the past 10 years? The reality is that we generalize constantly in our day to day lives, but people have a problem with cognitive biases like the law of small numbers. Too often “you can’t generalize” is just a flip way to dismiss trends you don’t find congenial, as I’ve noted the same people who exhibit great skepticism about generalization engage in that practice habitually when it comes to topics or opinions commonly held within group.1

Of course, this relates to Evolgen’s earlier point: “What is probability?” From a practical viewpoint it might do our educational system wonders if we replaced calculus with probability, as it seems to me that the latter is far more practical in day to day life than the former.

Related: Janet has more.

1 – For example, in many circles I travel in it is not acceptable to generalize about the boorish behavior of Muslims in the aggregate, but it is not forbidden to make jokes and slurs toward crank-addled “crackers,” or more politely, “white trash.” Similarly, the same social conservatives who complain about unfair depictions in the media will turn around and paint unpleasant pictures of “pagans, witches and atheists,” as if evil is one satanic amorphous mass.

Comments

  1. #1 Matt McIntosh
    April 26, 2006

    “What is probability?”

    Mathematicians and philosophers have been squabbling over that one for ages, so I think expecting high school kids to answer it is a bit much! (Unless he just means knowing the formalisms…)

  2. #2 boojieboy
    April 26, 2006

    OK, color me confused. I couldn’t resist this topic as the subject given by the title is near and dear to my heart.

    THe three processes (induction, deduction, and abduction) are all things that working scientists do. Here is my basic understanding of them. Tell me where I am wrong:

    induction is reasoning from evidence alone to create theories to explain that evidence, where there is no pre-existing theory in place, only assumptions to guide the form that the theory can take

    deduction is using a prexisting theory to make predictions about what one might observe given that certain conditions (specified by the theory) are met.

    abduction is akin to diagnostic reasoning, which is to take observations as “symptoms” and to try to find a preexisting model or theory that explains those symptoms. So doctors and car mechanics are commonly engaged in abductive, and not inductive, reasoning. Abductive reasoning rarely is meant to create a theory. When they’ve got a theory that they think accounts for the symptoms, they then might test that theory by deducing additional (as yet unobserved) symptoms and looking for them.

    The confusion stems from misapplications of the terms in the public discourse: for example, when Sherlock Holmes declares “What can we deduce, Watson, from that fleck of gray hair in the deceased’s apartment?” He really means “what can we abduce etc?” We can abduce, since age causes gray hair, that the person who owned that hair was old.

  3. #3 pconroy
    April 26, 2006

    Razib,

    I agree wholeheartedly with your modest proposal to replace Calculus with Probability. I always did well in Math, but never really liked it, until I met Statistics and Probability – it was only later in college studying Physics that I began to love Calculus – as they are wonderfully applicable to everyday life. I think the more applied math is taught in general the more accessible and fun it becomes. I have know quite a few people who could never understand Calculus, and never could wrap their minds around what it was or why it worked…

  4. #4 pconroy
    April 26, 2006

    BTW, Graph Theory is another really fun area of Math, that probably could be taught earlier, especially to the spatially inclined, and is something that most of us use unwittingly everyday – like what the quickest way to cross town and avoid traffic…

  5. #5 Boknekht
    April 26, 2006

    I’m a dummy here at GNXP. I’ve never studied calculus, statistics or graph-theory, & i’m pretty sure that i couldn’t master any of them, since they involve the manipulation of complexity. My problem lies in my working memory; that is, i have trouble(alot of it)seeing complex relationships between many variables, or manipulating those variables. In short, i have an almost impossible time manipulating complexity or sorting it out. I can’t seem to deal with the manipulation of many variables & sorting out complex interrelationships between them. This problem leads me to *trust* in the theories & opinions of smart people more than analyse them – makes me feel like a victim. Subjects like high-level finance or economics really tax my working memory, sometimes to the point where my whole mind goes blank & i completely lose everything, repeatedly. I think that this is only made worse by my psychological conditions, like my involuntary sleep deprivation & such. I feel like i could die any week. I wonder how many point this is shaving of my IQ?

  6. #6 razib
    April 27, 2006

    The confusion stems from misapplications of the terms in the public discourse: for example, when Sherlock Holmes declares “What can we deduce, Watson, from that fleck of gray hair in the deceased’s apartment?” He really means “what can we abduce etc?” We can abduce, since age causes gray hair, that the person who owned that hair was old.

    yes.

  7. #7 matoko_ifriitah
    April 27, 2006

    razib, which calculus should be replaced with probability? Lambda calculus? Situational calculus? multivariate? differential?
    ;)

  8. #8 Dan Dare
    April 27, 2006

    I don’t understand this thread.

    I was taught probability and statistics in my country at senior high school level i.e. yrs 11 & 12, as far as normal, binomial, Poisson and hypergeometric distributions.

    We were also taught differential and integral calculus as far as trigonometric and exponential functions. Also differential equations as far as second order linear. A typical problem (I am looking at my old textbook) involves setting up and solving the equation governing a simple series or parallel LCR electronic circuit. Also simple harmonic motion of a mass on a spring.

    My biggest problem is remembering half of this stuff.

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