Why are there girls in the world?

[Resha Caner]

There have been plenty of mathematically savvy biologists who have applied mathematics to aspects of biology ...

Sure. I never said otherwise.

... but the field does not lend itself to the kind of mathematical generalizations that physics does.

I would tweak your choice of words. I would say the paradigms to which biologists have become accustomed (due to the historical development of the field) do not lend themselves to mathematical generalizations as physics does. But that's my point. Newton discarded similar tendencies in physics, and was successful in doing so - though it didn't happen without a few battles.

 

[The Barbarian]

Yes, that was a joke. It's the usual misunderstandings about evolution and math. Sorry.

The actual mathematics that describe evolutionary processes are found in fields like population genetics. There are mathematical models for selection, mutation, gene flow, and genetic drift that accurately describe observed Darwinian evolution.

A simple example is the Hardy-Weinberg equation, which is a way to measure the amount of selection in a population in a specific environment.

If there are just two alleles for a specific gene, then the proportions for each possible genome will be:

AA = p X p aa = q x q and Aa = 2pq, where p= frequency of A and q=frequency of a in the previous generation.

If the certain conditions exist, and the proportion of genomes is not as predicted, that demonstrates selection is acting on the population.

The seven assumptions underlying Hardy–Weinberg equilibrium are as follows:[3]

• organisms are diploid
• only sexual reproduction occurs
• generations are nonoverlapping
• mating is random
• population size is infinitely large
• allele frequencies are equal in the sexes
• there is no migration, mutation or selection

Hardy–Weinberg principle - Wikipedia

 

[Resha Caner]

A simple example is the Hardy-Weinberg equation ...

* there is no migration, mutation or selection

I think this demonstrates what I'm talking about. So, biology has a concept called "migration". The mathematics of the Hardy-Weinberg equation are not constructed to include migration.

Paradigm first, math second (PM).

The alternative approach is to define a fundamental principle that is described mathematically. The equations are then worked to their logical conclusion, and names are given to the resulting phenomena.

Math first, paradigm second (MP).

I'm not saying biology is fully PM and physics is fully MP, but it seems biology leans toward PM and physics leans toward MP.

 

[sfs]

I would tweak your choice of words. I would say the paradigms to which biologists have become accustomed (due to the historical development of the field) do not lend themselves to mathematical generalizations as physics does.

That's not tweaking my words -- it's the position I am flat-out disagreeing with.

 

[Resha Caner]

That's not tweaking my words -- it's the position I am flat-out disagreeing with.

OK. So why does the field of biology "not lend itself to the kind of mathematical generalizations that physics does"?

 

[sfs]

I think this demonstrates what I'm talking about. So, biology has a concept called "migration". The mathematics of the Hardy-Weinberg equation are not constructed to include migration.

Paradigm first, math second (PM).

The alternative approach is to define a fundamental principle that is described mathematically. The equations are then worked to their logical conclusion, and names are given to the resulting phenomena.

Math first, paradigm second (MP).

No, I don't think that's an accurate description of how either biology or physics works. Neither field starts with fundamental principles. Both start with observations of phenomena and then attempt to figure out general principles that can be used to describe them. Both attempt to model them mathematically -- and yes, in biology, that very much includes modeling migration. The difference is that in physics you can write down equations that apply generally to a wide range of phenomena in a useful and that are simple enough to be tractable. By and large you can't do that in biology; a mathematical model that captures the relevant behavior of a biological system is typically quite complicated and generalizes poorly. That includes the many biological models that have been constructed by physicists, mathematicians and even electrical engineers who've moved into biology.

 

[Resha Caner]

No, I don't think that's an accurate description of how either biology or physics works. Neither field starts with fundamental principles. Both start with observations of phenomena and then attempt to figure out general principles that can be used to describe them. Both attempt to model them mathematically -- and yes, in biology, that very much includes modeling migration. The difference is that in physics you can write down equations that apply generally to a wide range of phenomena in a useful and that are simple enough to be tractable. By and large you can't do that in biology; a mathematical model that captures the relevant behavior of a biological system is typically quite complicated and generalizes poorly. That includes the many biological models that have been constructed by physicists, mathematicians and even electrical engineers who've moved into biology.

I disagree. It's not as if physicists have accepted impetus as a concept for describing motion caused by gravity and force as a concept describing motion caused by magnetism. Rather, force is a unifying, fundamental principle for all motion. Further, the definitions of motion are difference based when they don't have to be (they could be geometric, proportional, etc.) and they are defined orthogonally so as to guarantee independence. From there, all subsequent principles obey Buckingham Pi to prevent confounding.

I never said biologists don't model migration. My point was that migration models are not derived from the same fundamental principles as a model used for mate selection. It's not as if biologists started with F=ma and then derived that both migration and mate choice are consequences of that principle. There is no guarantee that migration and mate choice are independent principles or that the model for one doesn't violate a key assumption of the other. Maybe migration and mate choice are human intellectual constructs, and maybe Brownian motion or some field principle would describe them both while at the same time securing proper independence, etc.

 

[sfs]

I disagree. It's not as if physicists have accepted impetus as a concept for describing motion caused by gravity and force as a concept describing motion caused by magnetism.Rather, force is a unifying, fundamental principle for all motion.

Except when they don't. They do not use force in describing the motion of an electron through a double slit, for example.

I never said biologists don't model migration. My point was that migration models are not derived from the same fundamental principles as a model used for mate selection.

No, they're not derived from the same fundamental principles, because there are no fundamental principles at work here, apart from the fundamental principles of chemistry and physics. You seem to be assuming that there are. What's your assumption based on? Surely you're aware that biologists look for such things.

There is no guarantee that migration and mate choice are independent principles or that the model for one doesn't violate a key assumption of the other. Maybe migration and mate choice are human intellectual constructs, and maybe Brownian motion or some field principle would describe them both while at the same time securing proper independence, etc.

Of course migration and mate choice are human intellectual constructs -- as is force. They're all intellectual constructs to describe different aspects of the natural world. Brownian motion isn't a fundamental principle -- it's a model of a particular physical process. Sure, the mathematical framework for describing Brownian motion might be useful for describing some biological phenomena, and biologists are perfectly happy to apply such frameworks wherever they're useful. That's why they use diffusion theory in genetics, for example, and network theory in lots of applications.

 

[BNR32FAN]

It’s all part of God’s plan to save us. He had to create women because Adam was such a standup guy and obeyed God. That is until Eve came along.

 

[Resha Caner]

Except when they don't. They do not use force in describing the motion of an electron through a double slit, for example.

Sigh. I was giving an example from classical mechanics of two conflicting concepts of motion. So, yes, when you get to the wavicle level, you use something like Schrodinger's equation to generalize concepts like force. But that is a generalization of classical ideas (which incorporated both waves and particles but didn't synthesize them). As I emphasized early on, I understand physics isn't fully one thing and biology another. Rather physics leans one direction and biology the other.

You seemed to agree physics and biology tend in different directions, but "not lending itself to mathematical generalization" is a pretty vague response. I asked you to expand on that comment. Please, if you would be so kind, I am still asking that question.

You seem to be assuming that there are.

I'm not.

Surely you're aware that biologists look for such things.

I am. You seem to have forgotten that I asked that very question here at CF, and that you participated in the conversation.

Of course migration and mate choice are human intellectual constructs -- as is force.

Yes, yes. Of course 'force' is a human construct. I wasn't trying to say otherwise. My point is that 'force' was given a mathematical description by Newton, and that motion was derived from the basic definitions. My impression of biology is that the opposite happens. Biologists try to fit mathematical expressions to a variety of pre-existing concepts with no underlying unifying structure that drives mathematical consistency.

If I'm wrong, I'd like to know that. But you'll need to explain that underlying structure to me rather than just disagreeing with my posts.

 

[The Barbarian]

I think this demonstrates what I'm talking about. So, biology has a concept called "migration". The mathematics of the Hardy-Weinberg equation are not constructed to include migration.

Pretty much like the mathematics of kinetic theory are not constructed to include antimatter.

Paradigm first, math second (PM).

Nevertheless, chemistry works very well, as does population genetics. Bottom line, predictions made on the basis of these theories, turn out to be correct most of the time, and when they don't, it's because somone missed a factor that should have been accounted for.

The alternative approach is to define a fundamental principle that is described mathematically.

The binomial expansion is a pretty fundamental math concept, I would think. Incidentally, Wilhelm Weinbert, a pure mathematician, shared the credit (with geneticist G.H. Hardy) for showing mathematically, why recessives are not driven out of a population over time.

The equations were then worked to their logical conclusion, and hence the Hardy-Weinberg principle.

In science, there's always the "what was that?" moment, when an observation seems to make no sense. Following that, there's always hypotheses, and testing. That's where the math comes in.

Pretty much the way that the first useful application of information theory as formulated by Claude Shannon, turned out to be in population genetics.

 

[Resha Caner]

Nevertheless, chemistry works very well, as does population genetics.

Sure.

Bottom line, predictions made on the basis of these theories, turn out to be correct most of the time, and when they don't, it's because somone missed a factor that should have been accounted for.

This is the interesting aspect of science first noted by Ernst Mach - that when results don't correlate, scientists assume it's because of an error in one of the factors rather than an error in the first principles. 99% of the time (or maybe more) that's the right conclusion, yet revolutions in science happen when someone assumes differently.

The binomial expansion is a pretty fundamental math concept, I would think.

It is. It was crucial to Newton's development of Calculus. However, many people seem to miss the subtleties involved. As I mentioned earlier, it led to Newton developing a differential calculus, and that influenced what we consider to be a "linear" system, and that influenced what we consider to be "real" about the systems we're studying.

But differential calculus is not the only calculus. Using a different calculus leads to different definitions of time & motion etcetera, etcetera.

 

[The Barbarian]

It is. It was crucial to Newton's development of Calculus.

Leibniz, who seems to have independently discovered calculus, went at it in an entirely different way.

 

[Resha Caner]

Leibniz, who seems to have independently discovered calculus, went at it in an entirely different way.

I'm aware of that. Are you trying to say there is only one correct form for Calculus?

 

[The Barbarian]

I'm aware of that. Are you trying to say there is only one correct form for Calculus?

No. I'm just noting that for each of them, the paradigm came first and the math second.

 

[Resha Caner]

No. I'm just noting that for each of them, the paradigm came first and the math second.

Maybe, but I don't think so ... at least not the differential paradigm. I say that because DesCartes, Newton, Leibniz, and Hook argued over which paradigm was correct (more or less - DesCartes died before the latter 3 achieved recognition), indicating they were well aware that math sets a paradigm. Newton famously tried to distance himself from the "force at a distance" paradigm (which contradicted DesCartes' view), indicating he just went where the math took him, regardless of the consequences.

Curiosity prompts me to do the same. One of the examples that really got me going was the Parallel Postulate, which seems an obvious case of PM where the paradigm seems very likely to have been wrong. There are other fascinating stories about how people have viewed "number" over the millennia, and why that led them to label certain numerical concepts as improper, irrational, imaginary, and transcendental ... even though, in the end, those concepts turned out to be very useful.

The consequence is that I have an instrumentalist view of science. So, while I understand the utility of evolutionary theory for localized cases, I don't ever think of it as "reality", and I think it outruns its headlights when it begins to wax philosophic with grand claims as an explanation for the diversity of all life.

With that said, this is a fair question, and in one instance in the past, I said, "Yeah, OK, let's dig in and see." However, in order to do that, I wanted a quantitative structure - not just a lot of chest thumping on the Internet. I didn't see any unifying theme to biology (as far as math goes), but rather this concept here and that concept there. So I proposed a few things.

 

[The Barbarian]

Maybe, but I don't think so ... at least not the differential paradigm. I say that because DesCartes, Newton, Leibniz, and Hook argued over which paradigm was correct (more or less - DesCartes died before the latter 3 achieved recognition), indicating they were well aware that math sets a paradigm. Newton famously tried to distance himself from the "force at a distance" paradigm (which contradicted DesCartes' view), indicating he just went where the math took him, regardless of the consequences.

People who imagine they don't have a paradigm beforehand, seem to be unaware of their own predispositions.

The consequence is that I have an instrumentalist view of science. So, while I understand the utility of evolutionary theory for localized cases, I don't ever think of it as "reality", and I think it outruns its headlights when it begins to wax philosophic with grand claims as an explanation for the diversity of all life.

It comes down to evidence. And there, we see all of it consistent with common descent and none of it consistent with special creation. That being so, there's no point in denial.

Math is just a tool for biology. So is physics. Biology is just a higher level discipline, drawing from more fundamental sciences like physics and chemistry. This is why biology is at the cutting edge of science for now.

 

[Resha Caner]

People who imagine they don't have a paradigm beforehand, seem to be unaware of their own predispositions.

You don't know what you don't know. But part of my post regarded the awareness of Newton, et. al.

Math is just a tool for biology.

I see. So mathematical assumptions have no bearing on the outcome. What was that you were saying earlier about people unaware of their own predispositions?

It comes down to evidence.

I assume you don't mean just any evidence, but trustworthy evidence.

 

[The Barbarian]

You don't know what you don't know. But part of my post regarded the awareness of Newton, et. al.

Just noting that in each case, the paradigm came first, math second.

Math is just a tool for science.

I see. So mathematical assumptions have no bearing on the outcome.

What assumptions? You're suggesting that , for example, a different result would occur if I expected something else from a mathematical operation?

What was that you were saying earlier about people unaware of their own predispositions?

I was suggesting that Newton and Leibniz proceeded, each according to his own paradigm, which came first.

Barbarian, regarding common descent:
Comes down to the evidence.

I assume you don't mean just any evidence, but trustworthy evidence.

Reproducible results, yes. If we run the DNA analyses, for example, they better be reproduced when someone else does it.

 

[Resha Caner]

You're suggesting that , for example, a different result would occur if I expected something else from a mathematical operation?

Given a line and a point, how many lines parallel to the first should I draw through the point?