# Does Testing Theories Against Data (Evolution and Blood Circulation) Require Math?

[Moderator's Note: Thread spun off from previous thread in General Discussion since it is more specifically about particular scientific theories and how to test them against data.]

I disagree. Even a "simple observation" can usually be made quantitative, e.g. X>0. I don't know what sort of valid scientific evidence would not be mathematical/quantitative.
So in your opinion, everything in the list below is quantitative, not qualitative?

https://en.wikipedia.org/wiki/Evidence_of_common_descent

atyy, DrClaude and BillTre

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Dale
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So in your opinion, everything in the list below is quantitative, not qualitative?

https://en.wikipedia.org/wiki/Evidence_of_common_descent
Let's see:

"More closely related species have a greater fraction of identical sequence and shared substitutions compared to more distantly related species."

"neutral human DNA sequences are approximately 1.2% divergent (based on substitutions) from those of their nearest genetic relative"

"it can be calculated how long ago the two species diverged by ..."

I suspect that some of the observations in the list are not quantitative and cannot be made quantitative, but those observations would probably not count as scientific evidence since their non-observation would not falsify the theory. These are generally what @russ_watters was referring to as "an observed phenomena in nature".

With evolution this issue is particularly confusing because the same name is used to talk about the theory and the observed phenomena. The theory is the part of evolution that deals with models of the mechanisms whereby the observed phenomena are produced (e.g. natural selection, sexual selection, mutation, gene transmission, etc.). To determine whether an observation is adequately explained, e.g. by mutation, it is necessary to model the mutation process and come up with a number that can be compared to the evidence. That is the theory part of evolution. Until you have that model that can be compared against the experimental evidence you have a collection of observed phenomena, not a scientific theory.

russ_watters and PeterDonis
BillTre
Gold Member
Rather than argue about the poorly defined need for math to make something scientific, I will give counter-examples that show the these rules don't apply.

In order to have a scientific theory it must be falsifiable. That means that you must be able to make specific predictions about the outcome of experimental measurements whose result will either validate or falsify a theory. This is central to the scientific method. I see no way to do that without math.

Evolution was not a scientific theory in that sense for quite some time after it was developed. When experimental evolution was developed it most certainly used math to make quantitative experimental predictions that were then compared to the measured outcome of actual experiments. It took time for the theory of evolution to reach that point and it is perfectly reasonable to say it wasn't a "real" theory (meaning a scientific theory) until that point.
I see no problem with that. Evolution is like "gravity" - it is primarily a name for an observed phenomena in nature. Darwin noticed the phenomena exists and came up with a partial explanation for how it worked. Which is great, but still limited.
Darwin had two different major points in his book.
For those who doubt science can be done without science, The Origin of Species is a good read, (or Darwin for wikipedians).
One point was that change in biological forms occurs over time (Evolution occurs and is real).
The other was that an important mechanism driving the changes was natural (or artificial selection (as opposed to drift or other mechanism of evolutionary change in populations)). Providing a mechanism made the existence of the change more plausible.

Although experiments in long term historical sciences are not always immediately rewarded, they did exist, and observations on selection existed, even back then.

In trait transmission to offspring and the ability to modify those traits: Darwin sought out animal breeders whose history and records support both evolution (change of traits in a population) occurring as well as the ability of selection to change the frequency of those traits in a population.
Genetics was not at that time a mature science. Ideas of genes and how they were transmitted from parent to offspring were not clear.
There was no biochemistry.
Cell theory was in the process of being established.
Evolution was based on observations of traits (many which were not well defined either) and analyzing how they changed over time.

Darwin's hypothesis of natural selection was a reasonable mechanism based on what was known to provide a mechanism for evolutionary change.
The most obvious expression of this at his time was the artificial selection "experiments" of breeders.
There were not you modern breeder's records with detailed records of frequencies of traits of each generation so that the quantitative rate of change in a population could be determined.
They were probably more like: this line begot this line and that line by the year 1835 and in turn that line begot this other one after a new variant arose in 1845.
Much can be done with qualitative differences alone.

Darwin drew the first phylogenetic tree and using his awareness of this way of thinking's obvious predictions of common ancestors and their "intermediate" characteristics, predicted the existence of these ancestral species with "intermediate" traits.
This is similar to Mendeleev's predicting new elements in the holes is his table.
A good and seemingly unlikely prediction that takes a while to be fulfilled, but provides strong support if found.
If you are able to generate a seemingly "out of the blue" prediction, even though it may not be formally falsifiable, if found, it demonstrates a great ability for the idea to make valid predictions.

These are predictions that although not (in the short term) of the falsifiable type, but they provide strong support for the source of the prediction.
This is also similar to predictions of new particles by physicists.
They predict some particle with properties in some range of values, build a mega-colilder, and look for positive results.
Keep looking until you find it or perhaps later when you get enough negative evidence that people give up looking, or a different contrary result invalidates the search.
It uses math, but its not invalidation activity.
However, most people would call it science.

An associated science from that time (which was important to Darwin's thinking), geology did not require much math (except prehaps for mapping purposes).
At that time, the ideas of gradualism were in conflict with the biblically inspired castrastrophism.
Demonstrating the the significance of sedimentary layers, the great age of geological features, and finding features indicative of (as of then unknown) great prolonged forces that change the features of the land were important issues for geologists like Lyell at the time.
The geological stratgraphic record was being compiled at this time. This would result in a series of hypotheses like, what layers should be between A and C on the other side of that hill, compared to what was found there.

Motore, atyy and weirdoguy
Dale
Mentor
I will give counter-examples that show the these rules don't apply.
Sorry, but your counter examples are not very convincing.

an important mechanism driving the changes was natural (or artificial selection (as opposed to drift or other mechanism of evolutionary change in populations)) ... this line begot this line and that line by the year 1835 and in turn that line begot this other one after a new variant arose in 1845.
I am not sure that this observation can be considered evidence for the theory. First, its non observation would not falsify the theory. Second, its observation does not distinguish between the proposed natural/artificial selection mechanism and other alternative mechanisms. So I don’t think it is actually evidence.

Now, your characterization of these records could be incorrect, and the records could contain information about trait frequency and selection procedures. Then you could observe that the frequency of a selected trait increases while frequencies of other traits do not. That would be evidence, but it would also be quantitative. If the frequency did not change that would falsify the theory, if the frequency decreased of a selected-for trait then that would also falsify it. Etc.

For some observation, ##O##, to be evidence for a hypothesis, ##H##, then $$\frac{P(O|H)}{P(O|\lnot H)}>1$$ and I don’t think that can be claimed with this. That calculation may not be performed explicitly, but it is the core of what constitutes scientific evidence.

Darwin sought out animal breeders whose history and records support both evolution (change of traits in a population) occurring as well as the ability of selection to change the frequency of those traits in a population
This seems more reasonable evidence, but this is quantitative. Frequencies can increase or decrease or vary randomly or stay constant. That is all math.

Darwin drew the first phylogenetic tree and using his awareness of this way of thinking's obvious predictions of common ancestors and their "intermediate" characteristics, predicted the existence of these ancestral species with "intermediate" traits.
The phylogenetic trees are not observations. Fossil records are observations, but again, these can be quantitatively expressed in terms of frequencies of traits.

These are predictions that although not (in the short term) of the falsifiable type
Hmm, I think you are confusing feasibility with falsifiability. For example, even before the technology to detect gravitational waves was developed, the existence of gravitational waves was a falsifiable prediction.

They predict some particle with properties in some range of values, build a mega-colilder, and look for positive results.
Keep looking until you find it
You appear to not recognize that different models make different specific predictions about the energy range of a given particle. If they do not see it in a particular range then yes they will continue looking elsewhere, but that non-observation already eliminates some of the theories.

In any case, I am unsure why you brought that up since it really doesn’t seem to support your claim at all.

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Motore, russ_watters, BillTre and 2 others
BillTre
Gold Member
an important mechanism driving the changes was natural (or artificial selection (as opposed to drift or other mechanism of evolutionary change in populations)) ... this line begot this line and that line by the year 1835 and in turn that line begot this other one after a new variant arose in 1845.
I am not sure that this observation can be considered evidence for the theory. First, its non observation would not falsify the theory. Second, its observation does not distinguish between the proposed natural/artificial selection mechanism and other alternative mechanisms. So I don’t think it is actually evidence.
At the time, those other evolutionary mechanisms were not available. The alternatives were no change or change from Lamarkian mechanisms (for which problematic issues were arising).
If the mechanism identified can subsequently be used to further breeding efforts, then it works as a confirmation.

This analytic approach is equivalent to a cladistic analysis (looking at the distribution of traits in a phylogenetic tree (a hypothesis) to see if the structure of the tree can explain the distribution of the traits on that particular tree.

For some observation, , to be evidence for a hypothesis, , then and I don’t think that can be claimed with this. That calculation may not be performed explicitly, but it is the core of what constitutes scientific evidence.
Please explain where this comes from and what equation is supposed to mean. I don't understand your jargon.
It's a general forum.

This seems more reasonable evidence, but this is quantitative. Frequencies can increase or decrease or vary randomly or stay constant. That is all math.
If analyzed cladistically (which is evolutionary thinking formalized) then its does not require any frequencies other than something is present (0 or 1; if you really need a number) or it isn't. Its not about the frequencies, its about traits being found in one part of the tree but not in others.
The frequency stuff is a refinement that lead to many great findings, but not required for all such decisions.

The phylogenetic trees are not observations. Fossil records are observations, but again, these can be quantitatively expressed in terms of frequencies of traits.
I think you miss the point.
The phylogenetic tree is the hypothesis.
It predicts ancestors with particular traits.
These can be found in fossils, fulfilling a prediction.
The frequencies at which they are found are irrelevant if one solid case is found.

Hmm, I think you are confusing feasibility with falsifiability. For example, even before the technology to detect gravitational waves was developed, the existence of gravitational waves was a falsifiable prediction.
By that logic, the theory of evolution was falsifiable (if you looked at all rocks on earth and did not find intermediate forms).

You appear to not recognize that different models make different specific predictions about the energy range of a given particle. If they do not see it in a particular range then yes they will continue looking elsewhere, but that non-observation already eliminates some of the theories.
Those that are eliminated are hypotheses (falsifiable) then of where some particle might be found.
This would be similar to a hypothesis saying "I think I'll be finding a fossil intermediate between birds and dinosaurs under this rock here. Opps, didn't find it there. Lets look over here. now".

Consider how blood flow was initially described. Harvey use un-quantified observations (as well as quantified ones in some cases) to successfully make his argument that the blood circulated in one direction, powered by the heart.

Ophiolite and atyy
PeterDonis
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The frequencies at which they are found are irrelevant if one solid case is found.
No, the frequencies of traits are not irrelevant, because the hypothesis to be tested is that traits evolve due to natural selection. That is a claim about the frequencies of traits and their relationship to selective pressures. It is not a claim about the simple presence or absence of traits.

Your view of what "evolutionary theory" consists of appears to me to be much too simplistic.

BillTre
Gold Member
With math, yes, as @Dale has already pointed out.
With math not required, as I have already pointed out:
I think you miss the point.
The phylogenetic tree is the hypothesis.
It predicts ancestors with particular traits.
These can be found in fossils, fulfilling a prediction.
The frequencies at which they are found are irrelevant if one solid case is found.
So far you have failed to give any case which can be done math free; every example you have proposed has been refuted.
Only if you want to not read, understand, or consider what I am writing, maybe so.

The only way you can make that argument with the cladistics example, is if you require to frequencies to replace any determination of whether something is present or not.
On its face, an absurd interpretation.

Similarly for the example of the discovery of blood circulating.
Blocking a blood vessel, resulting in build up of blood volume or lose of peripheral pulse.
These are not quantitative results. They are something that happens or it doesn't.
Or, I guess it had to be converted to a frequency of 1 or 0 before it could be compared in a scientific manner.
???

Your view of what "evolutionary theory" consists of appears to me to be much too simplistic.
You should read some of my posts on evolution.
You should also read some history of science (perhaps beyond physics).
You should also read The Origin of Species (1859).
It might give you a better idea of what evolutionary theory is about.

Ophiolite and atyy
PeterDonis
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With math not required, as I have already pointed out:
I've already responded to this. I think you are greatly oversimplifying what the actual theoretical predictions are and how they have to be tested.

You should read some of my posts on evolution.
I'll take a look.

You should also read some history of science (perhaps beyond physics).

You should also read The Origin of Species (1859).
I have. I've also read Descent of Man, not to mention a lot of books on evolutionary theory published in the intervening years.

It might give you a better idea of what evolutionary theory is about.
I think you need to consider the possibility that your own understanding needs some work. Quite possibly mine does too, but telling me to read things I've already read won't help with that.

weirdoguy and russ_watters
PeterDonis
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You should read some of my posts on evolution.
Btw, quick question since you gave these references: how many of the specific theoretical predictions discussed in the threads you linked to do not, in your opinion, require math to test them against data?

PeterDonis
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The only way you can make that argument with the cladistics example, is if you require to frequencies to replace any determination of whether something is present or not.
Go back and read my post #6.

BillTre
Gold Member
I've already responded to this. You are greatly oversimplifying what the actual theoretical predictions are and how they have to be tested.
Your response seems to lack any understanding of what it is to consider trait distributions on a phylogenetic tree.

The only way you can make that argument with the cladistics example, is if you require to frequencies to replace any determination of whether something is present or not.
Go back and read my post #59.
which would be this I guess:
No, the frequencies of traits are not irrelevant, because the hypothesis to be tested is that traits evolve due to natural selection. That is a claim about the frequencies of traits and their relationship to selective pressures. It is not a claim about the simple presence or absence of traits.
You seem to be thinking of studies on changes in populations frequencies in short term studies. Yes numbers used there.

However, that is not my counter-example which you are claiming to have refuted (I get t choose my counter-example, not you).
Stick to the subject your own self! Don't try to turn my example into yours.
I am talking about in what branch of a phylogenetic tree is a trait found in the phylogenetic record.
It is a yes or no answer. These are completely different things.
Talk about distributions on phylogenetic trees, not fractions of a population (which is only poorly know at best for most kinds of fossils. That is what my example is about and you seem to be ignoring it.

You are also not explaining how math was required to determine blood circulation.

atyy and BWV
PeterDonis
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Apparently I haven't made it clear enough what the issue is. See below.

I am talking about in what branch of a phylogenetic tree is a trait found in the phylogenetic record.
What theoretical prediction is this supposed to be confirming? The theoretical prediction you are discussing in this particular example, as I understand it, is based on the hypothesis of common descent, which is part of the overall hypothesis of evolution by natural selection. That hypothesis does not predict simple yes/no answers for which traits we should find where in organisms; more precisely, just yes/no answers are not sufficient to confirm the hypothesis. The hypothesis predicts, roughly speaking, that the number of shared traits between two organisms should vary based on how long ago their last common ancestor lived and how much selection pressure each lineage was subjected to since diverging from the last common ancestors. That is the sort of comparison with data that needs to be done to confirm the hypothesis, and it cannot be done without math.

weirdoguy
PeterDonis
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You are also not explaining how math was required to determine blood circulation.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2776239/

Quoting from the article (emphasis mine):

In Chapter 13, Harvey summarized the substance of his findings: "It has been shown by reason and experiment that blood by the beat of the ventricles flows through the lungs and heart and is pumped to the whole body. There it passes through pores in the flesh into the veins through which it returns from the periphery everywhere to the centre, from the smaller veins into the larger ones, finally coming to the vena cava and right atrium. This occurs in such an amount, with such an outflow through the arteries and such a reflux through the veins, that it cannot be supplied by the food consumed. It is also much more than is needed for nutrition. It must therefore be concluded that the blood in the animal body moves around in a circle continuously and that the action or function of the heart is to accomplish this by pumping. This is only reason for the motion and beat of the heart."
Looks like Harvey was making a quantitative claim based on math to me.

Motore, weirdoguy and Dale
BillTre
Gold Member
The theoretical prediction you are discussing in this particular example, as I understand it, is based on the hypothesis of common descent, which is part of the overall hypothesis of evolution by natural selection.
This is wrong.
It is about a the existence of a hypothesized ancestor.
I don't know why you have such difficulty believing this is what I am talking about.
The existence of a hypothetical ancestor does not depend upon the mechanisms that underlies evolutionary changes.
You keep arguing that I am talking about something else, despite my frequent protests.

Not all evolutionary questions are answered through population dynamics.

Looks like Harvey was making a quantitative claim based on math to me.
He was in that small part.
The point is that he used a lot of other pieces of evidence for this.
Sorry to disappoint you, but I am not claiming no math is ever involved, but I am claiming that math was not required for every conclusion. I have tried to make that clear several times.
The conclusions about the blood flow are the point here. Direction of flow, effects of blocking flow, etc. Math not required.

atyy
Dale
Mentor
If analyzed cladistically (which is evolutionary thinking formalized) then its does not require any frequencies other than something is present (0 or 1; if you really need a number) or it isn't. Its not about the frequencies, its about traits being found in one part of the tree but not in others.
A cladistical analysis is highly mathematical. You are sorting objects into heirercial categories based on closeness measured in terms of numbers of shared traits. I mean that is math on several levels. Sorry, this one may have just sunk your claim altogether.

Please explain where this comes from and what equation is supposed to mean. I don't understand your jargon.
It's a general forum.
This is derived from Bayes theorem which is a cornerstone of all inductive reasoning with uncertain information. In words it says that an observation only considered to be evidence for a hypothesis if the probability of the observation given the hypothesis is greater than the probability of the observation given not the hypothesis. That quantity is also known as the likelihood ratio or the Bayes factor.

This is the very basis of inductive reasoning which is, in turn, the core of science.

Motore, Klystron and weirdoguy
BillTre
Gold Member
A cladistical analysis is highly mathematical. You are sorting objects into heirercial categories based on closeness measured in terms of numbers of shared traits. I mean that is math on several levels. Sorry, this one may have just sunk your claim altogether.
Today cladistic analyses are highly mathematical.
At earlier times not so. The most primitive formal cladistic analyses were done by see where traits fell on proposed trees, and only with stable (non-homeoplastic traits-those that don't change much and better reflec tree structure.
Prior to the formalization of cladistics, is was similar but much less rigorous.

Ophiolite and atyy
PeterDonis
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It is about a the existence of a hypothesized ancestor.
Ok, so how does finding a single shared trait prove that that organism is a common ancestor?

Answer: it doesn't. You have to look at how many shared traits there are and how that matches up with your expectations based on how long ago the supposed ancestor lived and what selective pressures each lineage was subjected to in between.

PeterDonis
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He was in that small part.
The summary I quoted, as noted, was Harvey's own summary of the substance of his findings, and the math on the amount of blood wasn't just a "small part". It was the essence of his argument for his conclusion, and what enabled him to refute the competing hypothesis he refuted. See below.

The conclusions about the blood flow are the point here. Direction of flow, effects of blocking flow, etc.
Those weren't conclusions, those were observations. They were part of the evidence he was using, not conclusions he was drawing.

The conclusion was that the amount of blood that was observed to be flowing in all those ways could not have been supplied continuously in such quantity from outside the body, by digestion of food--which was the hypothesis his contemporaries held, as noted in the article. He also, as the article notes near the end, used mathematical data to show that that amount of blood could not be consumed continuously by the tissues, as his contemporaries believed. Therefore, the blood must be circulating within the body. Confirming that conclusion, and falsifying the competing hypothesis, required math. And that is exactly the kind of thing I was talking about in the article.

BillTre
Gold Member
You really want to discount any conclusion that doesn't not involve math.
If it doesn't involve math, it doesn't count. Logic as a joke.

And, your'e still missing out on the cladistic argument.

Motore, atyy and weirdoguy
PeterDonis
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You really want to discount any conclusion that doesn't not involve math.
This is not a substantive response. I have been making specific arguments, and so have others. Vague complaints are not a valid response to specific arguments.

your'e still missing out on the cladistic argument.
See post #17.

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weirdoguy
Fervent Freyja
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Your view of what "evolutionary theory" consists of appears to me to be much too simplistic.
Try to explain evolutionary theory.

It’s a mere conceptual summary.

I offer a criticism to counter yours against the OP: I’ve observed that you are one of the most intelligent and quality contributors to PF, with likely the same to value to your chosen field: why didn’t you chose biology instead? You could have solved long standing problems in biology that directly reduces world suffering. Why didn’t you do that instead? I’m curious.

PeterDonis
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I’ve observed that you are one of the most intelligent and quality contributors to PF
Thank you!

You could have solved long standing problems in biology that directly reduces world suffering.
I think you are drastically underestimating what it takes to actually solve problems in a scientific field. It takes a lot more than it takes simply to have an informed opinion about some particular questions in a scientific field, which is all that my article was discussing and all that I have exhibited in this thread, or in any of my posts on PF for that matter. If you want me to discuss what it actually takes to make advances in a scientific field, I guess I need to write a second article.

PeterDonis
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Why didn’t you do that instead?
Because I only have one life and I can't possibly become enough of an expert to actually make advances in every field in which I'm interested. And those fields aren't even limited to science. My actual day job is not even a scientific job, and never has been.

PeterDonis
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Try to explain evolutionary theory.

It’s a mere conceptual summary.
I don't understand your point here.

atyy