7 ms·

> 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. H

by 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

by Pyret 12y ago

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