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Comment by IndianAstronaut | Hacker News Reader

>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).

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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.

Wouldn't it be entirely useful for biologists to know more advanced statistical methods?

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.

If anyone is depending on statistics to "prove" anything, they're in trouble.

Touche, 95% of people who prove things on the internet use statistics.

With statistics I can definitely prove that something holds with a confidence, of, say 0,95, under the model assumptions [...].

If you mistake the p-value on a frequentist hypothesis test for a Bayesian posterior probability, you've already messed up.

How do you prove that a medicine is safe and effective if not through large scale studies, which you then use statistics to show whether your hypotesus was correct or not?

It depends on what research they're doing. It's also quite easy to be led astray and produce poor work by trying to throw the newest, shiniest thing at something when a much more basic technique will do.

For example, for much of the work I do, you could get away with never using anything more sophisticated than ANOVA.

It is, for sure.

There are some other points to consider. First, the dataset sizes for most biomedical research are very small. Most advanced statistical methods don't apply. Due to curiosity, I took some advanced stat courses and tried to apply the methods to our lab's data. It didn't provide any significant improvement compared to basic ones, like linear regression, logistic regression, etc.

Second, biomedical research is highly collaborative these days. For some research that generate a large amount of data, either the researchers themselves understand statistics very well, or they collaborate with statisticians very closely. There is a field called biostatistics. Most biostatistics professors are either math or stat major, and many of them are adjoint professors in biomedical departments.

Biomedical research is really tedious and time-consuming. The professors I knew when I was doing biomedical research worked more than 60 hours a day, and they wish they had more time. One young woman professor came to the lab at 8am, left at 6pm, spent some time with her 4 children, and came back to lab at 9pm again, and worked until midnight, on every weekday. She brought her children to the lab on Saturday, and worked the whole day. IMHO, it is better for her to focus all her energy on the biomedical part, which she is best at, and collaborate with statisticians.

This is a very important point I think - only in very rare cases have I found my research actively improved by having a more sophisticated method available, and most projects have a statistician as a collaborator already. If not, they're readily available. It benefits a biologist to know what the statistician is talking about, and not just treating the analysis as a black box, but there's a reason we have subject matter experts. Sometimes, someone saying "Make sure to use robust variance" is enough information.

I take the opposite stance - if biologists knew about advanced statistical methods they might be tempted to use them.

The general rule in biology is if you need to use statistics you did the wrong experiment. The reason for this rule is it is all too easy to use clever statistical methods to solve a flawed experimental design.

It should be noted that "Biology" also encompasses fields where you are limited to uncontrolled observational experiments, which often necessitate more advanced methods.

True, but in this case you should have chosen another field :)

Well said.

The study of biology is further complicated by the large number of confounding factors that muddle experimental results. Because of this, it is hard to know exactly when it is appropriate to bring in mathematics. Without a proper understanding of all the variables, math can only get you so far.

Well,

Another way to consider this is that biologists have not pushed back hard enough to mathematicians in the sense of asking for some tools which would allow for just slurping up a vast amount of unstructured, unprocessed data and getting something out of it.

It is certainly true that mathematical modeling as it is done now currently will indeed only get you so far.

But spirit of math in conjunction with physics has been to create tools that allow leaps and bounds. If we want to follow that spirit, it seems appropriate to ask for tools to help with messy things that now can't easily be dealt with. It may not be possible but it seems worthwhile to go all the way to the brick wall and pound on it.

Unfortunately biologist have been taken for a ride many times by people selling mathematical snake-oil. For example, the whole field of DNA microarrays [1] turned out to be an illusion woven out of applying complex statistical tools to "vast amount of unstructured, unprocessed data". There really is no way you can gain real understanding from poorly designed and unrepeatable experiments by apply obscure mathematical tools.

1. http://en.wikipedia.org/wiki/DNA_microarray

Luckily, complex numbers and polynomials are not snake oil.

IANAB. From what I understand, DNA research seems to have lots of still low hanging fruits for simple mathematical models to achieve big breakthroughs. Yamanaka won a nobel price for cell reprogramming that simply came from neglecting the previous brute force method to find the correct molecule combination that lead to many years of Biologists trying out combination after combination. Instead he basically deduced it through simple modelling and applying the scientific method. A quick google has brought the following thesis, which bases some more modelling on Yamanaka in order to refine stem cell reprogramming [1]. From my point of view, the really outstanding work in biology currently rather comes from outsiders that break out of the usual methods of biologists, such as the applied mathematician Erez Lieberman Aiden who showed how genome folding works and actually has an important function (activating / deactivating regions in order to program cell functions), purely through mathematical modelling of the signals we can get out of current instruments and throwing HPC at it. I'm pretty sure the field would benefit greatly from more cross pollination from other fields.

[1] https://www2.hu-berlin.de/biologie/theorybp/docs/dipl_scharp...

[2] http://www.sciencemag.org/content/326/5950/289.short

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/...

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.

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.

>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

Apart from the chemistry part (where I don't understand what you mean), biology has had this for 85 years, with numerous extensions and generalizations [1].

[1] http://www.ias.ac.in/jgenet/Vol74Nos1&2/19.pdf

Worth mentioning that the "Fundamental Theorem of Natural Selection" was proposed by R.A. Fisher who was responsible for developing the following techniques and theorems (among many other things):

    - Analysis of variance (ANOVA)
    - Maximum likelihood estimation (MLE)
    - Fisher's exact test
    - The Fisher-Yeats shuffle algorithm

In many ways Fisher exemplifies the author's point about what can happen when someone is both fluent in biology and mathematics!

> 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

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.

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.

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).

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."

> 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.

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.

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.

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.

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....

Forgetting for a moment that the entire post is an appeal to authority (in other words, ignoring all logic) here's the culprit quote from the post:

> In the Wikipedia article, they have an equation that looks like this \zeta(-3)=1/120, but the stuff on the left hand side is just another way of writing 1^3+2^3+3^3 +4^3+...

If you can't explain why the above claim is screwy, then every time you claim, "the sum of all positive integers is -1/12," you need to qualify it with "I have no idea why, but I know there's some complicated mathematics that removes the word 'sum' and 'positive integers' and replaces them with more complicated concepts I'm don't have the time to learn about, and we physicists abuse it to say what I just said."

He also says things like

> If QED is correct ... then I would argue that the things that go into QED calculations must be just as correct.

Also not how logic works.

the sum of all positive integers is -1/12, and other such nonsense

Sure sure, but do know that a lot of all that hacky regularization stuff can be made mathematically sound after all --see for instance [1,2].

[1] http://www.maths.qmul.ac.uk/~tp/talks/casimir.pdf#page55

[2] http://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin...

Of course I know (I'm a mathematician, I'm the one who cringes at all that). The abuse doesn't stop there though... :(

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/

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