7 ms·

>The result is that biology loses out due to the minimal real contact with math– the special opportunity of benefiting from the extra sense is lost, and convers

>The result is that biology loses out due to the minimal real contact with math– the special opportunity of benefiting from the extra sense is lost, and conversely math loses the opportunity to engage biology When I was a biology grad student, I was the only person in the department that tried to do active collaboration with the math department. I took more math classes during my graduate program than biology classes. On the biology side, I got ridiculed for all the 'hand waving' that seems to happen with the math. Biologists want to see concrete experiments and results. On the math side I found people to be much more open and fascinated by the biology, but they had a tough time explaining what they were doing to a lay audience. No easy answers, but I think more programs should graduate people with dual skills in both subjects(and of course have job opportunities for those grads, instead of having them jump into industry like I did).

Pyret 12y ago
> On the biology side, I got ridiculed for all the 'hand waving' that seems to happen with the math. Biologists want to see concrete experiments and results. How interesting. Usually, it's the math folk who ridicule everyone else for being sloppy with their reasoning. For example, physics = hand-wavery :D
- wwweston 12y ago
  Mathematicians tend to be very particular about reasoning (and by comparison even other scientists can be sloppy). However, they can also be pretty free with their assumptions (which can be wild, though if reasoned from carefully usually turn out to be useful even if nobody anticipated that they would). People working with mathematicians probably spend a lot of time wondering why they're so persnickety about some things most people would consider obvious ("but how do you really know 2+2=4?") but sometimes not so much about whether the constructions they're working with actually reflect a particular concrete reality.
- Fomite 12y ago
  It's a different kind of hand waving. When presented with a system of ODEs describing a system, a mathematician may be content with some assumptions that make the analytical solution more straightforward, or not be terribly worried about particular values for parameters because they're looking at the more general behavior of the system. Biologists (or in my case epidemiologists) may, on the other hand, be very concerned about why the value you chose for a particular parameter is 6 instead of 7, and whether or not it's really exponentially distributed.
  - wolfgke 12y ago
    In my experience mathematicians are definitely concerned whether, say, the assumption of exponential distribution is really justified. But what they are interested in is typically a quite general class of (in this case) distributions, where they typically begin with the "simple" cases (which are often normal or exponential distributions).
    - Fomite 12y ago
      nod That example was more to illustrate one of several choices a mathematician might make in order to make a problem analytically tractable that might bother a biologist. Another way of putting it is "A mathematician might be interested in the general properties of dynamical systems, and a biologists entire research agenda at the moment may very well be this set of equations with a very specific parameter set."
      - wolfgke 12y ago
        > Another way of putting it is "A mathematician might be interested in the general properties of dynamical systems, and a biologists entire research agenda at the moment may very well be this set of equations with a very specific parameter set." I surely won't disagree, but I want to add the point that when the model turns out to be wrong (and most will), also the biologist will have an interest to know, whether just some parameters (say values of constants, wrong probablility assumption) are wrong or the fundamental model has to be reconsidered.
- j2kun 12y ago
  The issue with physics isn't that they're hand-wavy, it's that they teach their students demonstrably false things. Such as, an infinite point-impulse is a function with integral 1, and the sum of all positive integers is -1/12, and other such nonsense about "convergent" sequences. They balk at the nuance of mathematics when it actually matters to us.
  - nilkn 12y ago
    The nuances of mathematics are really extremely important in modern theoretical physics, too, given that most problems in quantum field theory have historically involved divergent integrals that physicists need to converge. (This is also what's preventing a quantum theory of gravity.) Physics today does have some remarkably talented mathematical thinkers, like Edward Witten, but most of them are involved in very fanciful theories like string theory.
  - tjradcliffe 12y ago
    I've never heard a physicist claim the sum of all positive integers is -1/12. Such people may exist, but they are extremely rare. And the Dirac delta is the limit of a function with integral 1, not a function. Maybe you need to hang out with a better class of physicists? There are certainly plenty of mathematicians who believe odds things, but I'd be leery of tarring the whole lot with the same brush.
    - jdpage 12y ago
      The sum of all positive integers can actually be considered to be -1/12 in a self-consistent fashion. It isn't equal in the same sense that 2+2=4, and it's still true that the limit at infinity of the partial sum of the positive integers doesn't exist. On the other hand, it really is a useful result. The negative part is, for example, why the Casimir force is attractive. Here's an article about the whole thing, with links to the various Numberphile videos and Phil Plait articles that have been done about it: http://physicsbuzz.physicscentral.com/2014/01/does-1234-112.html http://physicsbuzz.physicscentral.com/2014/01/does-1234-112....
      - 12y ago
jamesli 12y ago
Biology is enormous, as the author pointed out. Our understanding in biology at present might be less than 1% than the whole knowledge. For most biological research, it doesn't require any advanced knowledge in math beyond basic statistics. For example, many labs have been studying an important gene and how other genes are functionally related to it for more than 10 years. The research involved are simply tedious, but indispensable, biological experiments. It is a waste of time to study math for this work, because it doesn't apply, except some basic statistics on data analysis. Disclaimer: I have advanced degrees in both biology and computer science, and has multiple years of biomedical research experience. I have met exceptionally smart people working in both biology, CS, math, and physics. Yes, these smart biologists don't understand advanced topics in math and physics. I believe, however, if they had studied math or physics, they would have been excellent mathematicians or physicists.
- eli_gottlieb 12y ago
  Wouldn't it be entirely useful for biologists to know more advanced statistical methods?
  - bjelkeman-again 12y ago
    I agree that more advanced statistical methods would be useful. A surprising number of scientists have poor knowledge about statistics whilst being dependent on it to prove their research.
    - Fomite 12y ago
      If anyone is depending on statistics to "prove" anything, they're in trouble.
      - marktangotango 12y ago
        Touche, 95% of people who prove things on the internet use statistics.
      - 12y ago
epistasis 12y ago
I think there's definitely a trend in institutions to integrating these fields. Princeton has an Integrated Science program [1] which includes highly quantitative study of biology. And genomics in general has forced the combination of biology, stats, and math. Classical genetics and evolution departments are often seeded with lots of appreciation for mathematics, as well. However, pure molecular biology doesn't often have that much to say to non-applied math, and vice versa. http://www.princeton.edu/integratedscience/ http://www.princeton.edu/integratedscience/
tjradcliffe 12y ago
I'm a physicist who has worked in genomics and found biologist's attitudes toward math to be fairly weird. Some get it, most don't. But the way physicists think about math is for the most part antithetical to the way mathematicians think about it. To a physicist, math is a language for talking about things with in-built protections against contradictions. Math looks more like a very special natural language to us, which attitude drives mathematicians nuts. The odd thing is that this difference in attitudes between physicists and biologists seems to me to be at least as much historically contingent as really dependent on the subject matter. Physics is hugely sprawling too, and a great deal of it is only passingly-mathematical. If Darwin had been more mathematically minded he could have easily come at the problem of the origin of species from a viewpoint as strongly idealized and mathematically compact as Newton did with regard to physics. Newton was admittedly blessed with a very-nearly ideal system to study (the solar system) but was able to apply his ideas to other systems using a wide variety of increasingly sketchy approximations. But I'm still pretty sure a mathematical mind on the order of Newton's could find a way to state evolution by variation and natural selection as a theorem rather than a theory, that follows necessarily from the laws of probability and the facts of chemistry (many of which Darwin didn't know, but still). It is at the very least a fun idea to speculate about: http://www.amazon.com/Darwins-Theorem-TJ-Radcliffe-ebook/dp/B00KBH5O8K/ref=sr_1_1?ie=UTF8&qid=1420059619&sr=8-1&keywords=darwin%27s+theorem http://www.amazon.com/Darwins-Theorem-TJ-Radcliffe-ebook/dp/...
- dnautics 12y ago
  The biggest gulf between physics and biology is the general principle that ockham's razor is a poor heuristic for biology. A second source is that biological phenomena exhibit strong path-dependence, and physicists are typically trained to think from a path-independent (state function) point of view.
  - danieltillett 12y ago
    This is so true. Trying to use the mental tools that work well in physics with biology will lead you astray most of the time.
- 12y ago

Pyret 12y ago

> On the biology side, I got ridiculed for all the 'hand waving' that seems to happen with the math. Biologists want to see concrete experiments and results. How interesting. Usually, it's the math folk who ridicule everyone else for being sloppy with their reasoning. For example, physics = hand-wavery :D

wwweston 12y ago
Mathematicians tend to be very particular about reasoning (and by comparison even other scientists can be sloppy). However, they can also be pretty free with their assumptions (which can be wild, though if reasoned from carefully usually turn out to be useful even if nobody anticipated that they would). People working with mathematicians probably spend a lot of time wondering why they're so persnickety about some things most people would consider obvious ("but how do you really know 2+2=4?") but sometimes not so much about whether the constructions they're working with actually reflect a particular concrete reality.
Fomite 12y ago
It's a different kind of hand waving. When presented with a system of ODEs describing a system, a mathematician may be content with some assumptions that make the analytical solution more straightforward, or not be terribly worried about particular values for parameters because they're looking at the more general behavior of the system. Biologists (or in my case epidemiologists) may, on the other hand, be very concerned about why the value you chose for a particular parameter is 6 instead of 7, and whether or not it's really exponentially distributed.
- wolfgke 12y ago
  In my experience mathematicians are definitely concerned whether, say, the assumption of exponential distribution is really justified. But what they are interested in is typically a quite general class of (in this case) distributions, where they typically begin with the "simple" cases (which are often normal or exponential distributions).
  - Fomite 12y ago
    nod That example was more to illustrate one of several choices a mathematician might make in order to make a problem analytically tractable that might bother a biologist. Another way of putting it is "A mathematician might be interested in the general properties of dynamical systems, and a biologists entire research agenda at the moment may very well be this set of equations with a very specific parameter set."
    - wolfgke 12y ago
      > Another way of putting it is "A mathematician might be interested in the general properties of dynamical systems, and a biologists entire research agenda at the moment may very well be this set of equations with a very specific parameter set." I surely won't disagree, but I want to add the point that when the model turns out to be wrong (and most will), also the biologist will have an interest to know, whether just some parameters (say values of constants, wrong probablility assumption) are wrong or the fundamental model has to be reconsidered.
j2kun 12y ago
The issue with physics isn't that they're hand-wavy, it's that they teach their students demonstrably false things. Such as, an infinite point-impulse is a function with integral 1, and the sum of all positive integers is -1/12, and other such nonsense about "convergent" sequences. They balk at the nuance of mathematics when it actually matters to us.
- nilkn 12y ago
  The nuances of mathematics are really extremely important in modern theoretical physics, too, given that most problems in quantum field theory have historically involved divergent integrals that physicists need to converge. (This is also what's preventing a quantum theory of gravity.) Physics today does have some remarkably talented mathematical thinkers, like Edward Witten, but most of them are involved in very fanciful theories like string theory.
- tjradcliffe 12y ago
  I've never heard a physicist claim the sum of all positive integers is -1/12. Such people may exist, but they are extremely rare. And the Dirac delta is the limit of a function with integral 1, not a function. Maybe you need to hang out with a better class of physicists? There are certainly plenty of mathematicians who believe odds things, but I'd be leery of tarring the whole lot with the same brush.
  - jdpage 12y ago
    The sum of all positive integers can actually be considered to be -1/12 in a self-consistent fashion. It isn't equal in the same sense that 2+2=4, and it's still true that the limit at infinity of the partial sum of the positive integers doesn't exist. On the other hand, it really is a useful result. The negative part is, for example, why the Casimir force is attractive. Here's an article about the whole thing, with links to the various Numberphile videos and Phil Plait articles that have been done about it: http://physicsbuzz.physicscentral.com/2014/01/does-1234-112.html http://physicsbuzz.physicscentral.com/2014/01/does-1234-112....
    - 12y ago

jamesli 12y ago

Biology is enormous, as the author pointed out. Our understanding in biology at present might be less than 1% than the whole knowledge. For most biological research, it doesn't require any advanced knowledge in math beyond basic statistics. For example, many labs have been studying an important gene and how other genes are functionally related to it for more than 10 years. The research involved are simply tedious, but indispensable, biological experiments. It is a waste of time to study math for this work, because it doesn't apply, except some basic statistics on data analysis. Disclaimer: I have advanced degrees in both biology and computer science, and has multiple years of biomedical research experience. I have met exceptionally smart people working in both biology, CS, math, and physics. Yes, these smart biologists don't understand advanced topics in math and physics. I believe, however, if they had studied math or physics, they would have been excellent mathematicians or physicists.

eli_gottlieb 12y ago
Wouldn't it be entirely useful for biologists to know more advanced statistical methods?
- bjelkeman-again 12y ago
  I agree that more advanced statistical methods would be useful. A surprising number of scientists have poor knowledge about statistics whilst being dependent on it to prove their research.
  - Fomite 12y ago
    If anyone is depending on statistics to "prove" anything, they're in trouble.
    - marktangotango 12y ago
      Touche, 95% of people who prove things on the internet use statistics.
    - 12y ago

epistasis 12y ago

I think there's definitely a trend in institutions to integrating these fields. Princeton has an Integrated Science program [1] which includes highly quantitative study of biology. And genomics in general has forced the combination of biology, stats, and math. Classical genetics and evolution departments are often seeded with lots of appreciation for mathematics, as well. However, pure molecular biology doesn't often have that much to say to non-applied math, and vice versa. http://www.princeton.edu/integratedscience/ http://www.princeton.edu/integratedscience/

tjradcliffe 12y ago

I'm a physicist who has worked in genomics and found biologist's attitudes toward math to be fairly weird. Some get it, most don't. But the way physicists think about math is for the most part antithetical to the way mathematicians think about it. To a physicist, math is a language for talking about things with in-built protections against contradictions. Math looks more like a very special natural language to us, which attitude drives mathematicians nuts. The odd thing is that this difference in attitudes between physicists and biologists seems to me to be at least as much historically contingent as really dependent on the subject matter. Physics is hugely sprawling too, and a great deal of it is only passingly-mathematical. If Darwin had been more mathematically minded he could have easily come at the problem of the origin of species from a viewpoint as strongly idealized and mathematically compact as Newton did with regard to physics. Newton was admittedly blessed with a very-nearly ideal system to study (the solar system) but was able to apply his ideas to other systems using a wide variety of increasingly sketchy approximations. But I'm still pretty sure a mathematical mind on the order of Newton's could find a way to state evolution by variation and natural selection as a theorem rather than a theory, that follows necessarily from the laws of probability and the facts of chemistry (many of which Darwin didn't know, but still). It is at the very least a fun idea to speculate about: http://www.amazon.com/Darwins-Theorem-TJ-Radcliffe-ebook/dp/B00KBH5O8K/ref=sr_1_1?ie=UTF8&qid=1420059619&sr=8-1&keywords=darwin%27s+theorem http://www.amazon.com/Darwins-Theorem-TJ-Radcliffe-ebook/dp/...

dnautics 12y ago
The biggest gulf between physics and biology is the general principle that ockham's razor is a poor heuristic for biology. A second source is that biological phenomena exhibit strong path-dependence, and physicists are typically trained to think from a path-independent (state function) point of view.
- danieltillett 12y ago
  This is so true. Trying to use the mental tools that work well in physics with biology will lead you astray most of the time.
12y ago