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I think one non-obvious benefit of a good mathematics education is that you have little choice but to develop a tolerance for and understanding of being wrong.

by majos 10y ago

I think one non-obvious benefit of a good mathematics education is that you have little choice but to develop a tolerance for and understanding of being wrong. See Jeremy Kun's blog post [1] for more, but my own experience has been that in e.g. discussing different ways to solve a problem or prove something almost every person eventually has an "oh, no, I see, I'm wrong and you're right" moment. Not that every mathematician is necessarily a font of humility and grace, but I think math offers more regular and irrefutable demonstrations of your own fallibility than many other fields, and this is good. [1] https://medium.com/@jeremyjkun/habits-of-highly-mathematical-people-b719df12d15e#.2ikc1ut7w https://medium.com/@jeremyjkun/habits-of-highly-mathematical...

jdietrich 10y ago
In my experience, a surprising number of people with a humanities education simply don't believe in "wrongness", but merely differences of opinion. They regard truth as peculiar abstraction used by mathematicians and hard scientists, not a phenomenon that actually exists. It's hard for someone to admit to being wrong if they don't even believe in the concept.
- astazangasta 10y ago
  You obviously don't hang out with many statisticians, who also don't tend to believe in truth or being right or wrong; to them, they are just making models that can be tested to reliably approximate some observation. There is no pretense at truth, it's just a model.
  - yummyfajitas 10y ago
    This is a significant misunderstanding of statistics. Statisticians believe in truth, they just accept that it might not be possible to know it.
    - astazangasta 10y ago
      I think we have a disagreement about epistemology. I say, you can't believe in truth if you don't believe it is knowable. In any case, statisticians are not interested in learning the truth, either, and the goal of their enterprise is not access to it.
      - yummyfajitas 10y ago
        The entire goal of statistics is to build approximations which converge to truth in some manner or another. E.g., a Bayesian posterior ideally converges to a delta measure on truth as N -> infty. A frequentist point estimate converges to truth (with P = 1) as N -> infty. The entire purpose of statistics is to quantify the difference between our beliefs and actual truth.
        astazangasta 10y ago
        >A frequentist point estimate converges to truth (with P = 1) as N -> infty. Since we are never at infinity, our observations are always finite, all this is saying is "we always deal with approximations of reality," i.e., statistics is never, in fact, about the "actual truth", it is about testing the set of our limited observations of reality against a model.
        yummyfajitas 10y ago
        This is like saying real analysis is not concerned with irrational numbers since they can only be constructed as limits of sequences of rational ones.
        astazangasta 10y ago
        No, it's not. The fact that observation is a limit on our apprehension of the real world means the "truth" is fundamentally inaccessible, and is a useless concept to the statistician. All you can hope to do is test your model against the observation, you'll never, ever get access to the truth. As a real-world example that I deal with every day, we frequently model the expected distribution of gene expression as a negative binomial. It doesn't matter how closely we observe the actual distribution of gene expression, it is never going to perfectly fit a negative binomial (it won't even get close), even though this is what we test our observation against, because the 'truth' is something different and far too complex for us to apprehend.
- mikebelanger 10y ago
  I had a philosophy professor who believed evolution was 'just a theory', and routinely dismissed it. I don't think she was religious either. Then again, I had another philosophy teacher who taught logic, which is the most pure use of right/wrong that I can think of.
  - PunchTornado 10y ago
    evolution IS 'just a theory'. like relativity and other scientific theories. it is just a coherent framework to explain observations. today it is our best theory, tomorrow it may not be. you cannot say that evolution is Truth. Truth exists only in mathematics, logics etc.
- doozy 10y ago
  Reminds me of something one of my Economics professors said once: An Economist is just a mediocre Engineer, an Engineer is a a real bad Physicist, a Physicist nothing but a bad Mathematician, and a Mathematician the lowest form of Philosopher.
losteverything 10y ago
" develop a tolerance for and understanding of being wrong. " With others. Mathwise I am always right but others can't see it. So I have a deacartes moment with others
- dmfdmf 10y ago
  Descartes?
  - losteverything 10y ago
    If a math guy makes a math statement (in a forest of mom-math-understanders), does it make a sound?
    - dmfdmf 10y ago
      mom-math?
      - losteverything 10y ago
        Non math. My spell check initially game me meth instead of math. Proud methamatician

by majos 10y ago

jdietrich 10y ago

In my experience, a surprising number of people with a humanities education simply don't believe in "wrongness", but merely differences of opinion. They regard truth as peculiar abstraction used by mathematicians and hard scientists, not a phenomenon that actually exists. It's hard for someone to admit to being wrong if they don't even believe in the concept.

astazangasta 10y ago
You obviously don't hang out with many statisticians, who also don't tend to believe in truth or being right or wrong; to them, they are just making models that can be tested to reliably approximate some observation. There is no pretense at truth, it's just a model.
- yummyfajitas 10y ago
  This is a significant misunderstanding of statistics. Statisticians believe in truth, they just accept that it might not be possible to know it.
  - astazangasta 10y ago
    I think we have a disagreement about epistemology. I say, you can't believe in truth if you don't believe it is knowable. In any case, statisticians are not interested in learning the truth, either, and the goal of their enterprise is not access to it.
    - yummyfajitas 10y ago
      The entire goal of statistics is to build approximations which converge to truth in some manner or another. E.g., a Bayesian posterior ideally converges to a delta measure on truth as N -> infty. A frequentist point estimate converges to truth (with P = 1) as N -> infty. The entire purpose of statistics is to quantify the difference between our beliefs and actual truth.
      - astazangasta 10y ago
        >A frequentist point estimate converges to truth (with P = 1) as N -> infty. Since we are never at infinity, our observations are always finite, all this is saying is "we always deal with approximations of reality," i.e., statistics is never, in fact, about the "actual truth", it is about testing the set of our limited observations of reality against a model.
        yummyfajitas 10y ago
        This is like saying real analysis is not concerned with irrational numbers since they can only be constructed as limits of sequences of rational ones.
        astazangasta 10y ago
        No, it's not. The fact that observation is a limit on our apprehension of the real world means the "truth" is fundamentally inaccessible, and is a useless concept to the statistician. All you can hope to do is test your model against the observation, you'll never, ever get access to the truth. As a real-world example that I deal with every day, we frequently model the expected distribution of gene expression as a negative binomial. It doesn't matter how closely we observe the actual distribution of gene expression, it is never going to perfectly fit a negative binomial (it won't even get close), even though this is what we test our observation against, because the 'truth' is something different and far too complex for us to apprehend.
mikebelanger 10y ago
I had a philosophy professor who believed evolution was 'just a theory', and routinely dismissed it. I don't think she was religious either. Then again, I had another philosophy teacher who taught logic, which is the most pure use of right/wrong that I can think of.
- PunchTornado 10y ago
  evolution IS 'just a theory'. like relativity and other scientific theories. it is just a coherent framework to explain observations. today it is our best theory, tomorrow it may not be. you cannot say that evolution is Truth. Truth exists only in mathematics, logics etc.
doozy 10y ago
Reminds me of something one of my Economics professors said once: An Economist is just a mediocre Engineer, an Engineer is a a real bad Physicist, a Physicist nothing but a bad Mathematician, and a Mathematician the lowest form of Philosopher.

losteverything 10y ago

" develop a tolerance for and understanding of being wrong. " With others. Mathwise I am always right but others can't see it. So I have a deacartes moment with others

dmfdmf 10y ago
Descartes?
- losteverything 10y ago
  If a math guy makes a math statement (in a forest of mom-math-understanders), does it make a sound?
  - dmfdmf 10y ago
    mom-math?
    - losteverything 10y ago
      Non math. My spell check initially game me meth instead of math. Proud methamatician