I cannot think of anyone who has put forth a scientific hypothesis that mermaids don't exist. You have a link to such a proposal?

The existence of mermaids is not contentious; they are mythical.

I think the confusion is caused by conflating universal statements over an open domain with propositions. Consider the statement

A. "All Creatures discovered in the Atlantic Ocean between 2018-2020 are not mermaids"

This should be regarded as a proposition, precisely because it is falsifiable.

But the open-ended infinite statement

B. "All Creatures are not mermaids" isn't falsifiable, and hence describes nothing , at least, nothing detached from the culture of scientific practice.

Rather, B is an instruction to scientists to exclude mermaids from consideration in their foreseeable scientific endeavours. Moreover, since B cannot be inferred on the basis of finite evidence, B ISN'T an inference, rather, B represents our pragmatically determined science-policy concerning the course of our future investigations on the basis of our finite experience of the past.

It is precisely for this reason that I don't believe in any universal laws of nature in the sense of them describing nature "in itself". Rather, any purported "universal laws of nature" are merely social imperatives that describe how scientists out to frame falsifiable hypotheses that in being falsifiable are necessarily finite and non-universal.

For example, statement B above is a permission-note that allows scientists to create propositions similar to A in the course of their investigations.

Rejecting the existence of mermaids is not the greatest error.

The greatest error is when we assume the truth of the null hypothesis based on that it wasn't rejected. (when doing normality tests for example)

Mermaids have arms. I accept the null hypothesis that I have arms. Therefore I am a mermaid...
This is why I dont believe in statistics.

I cannot think of anyone who has put forth a scientific hypothesis that mermaids don't exist. — noAxioms

Challenge accepted :P

Let's develop a sample set of instances of mermaid sightings and/or findings. As the collection of samples grows we begin to notice a pattern of outcomes.

The outcomes fail to reject the null hypothesis ("mermaids are mythical") and in so doing begin to accumulate a sense of probability weight from quite a few samples taken that fail to demonstrate mermaids are not mythical.

How can we describe the confidence after a string of those test outcomes, and how that confidence-probability estimate changes with additional test results?

There's been rather a lot of what passes for science these days doing the job of just that -- passing as science. — AngleWyrm

Like what?

Rather, B is an instruction to scientists to exclude mermaids from consideration in their foreseeable scientific endeavours. Moreover, since B cannot be inferred on the basis of finite evidence, B ISN'T an inference, rather, B represents our pragmatically determined science-policy concerning the course of our future investigations on the basis of our finite experience of the past. — sime

I was thinking how I would respond to AngleWyrm's post. I like the way you have, so now I don't have to.

It is precisely for this reason that I don't believe in any universal laws of nature in the sense of them describing nature "in itself". Rather, any purported "universal laws of nature" are merely social imperatives that describe how scientists out to frame falsifiable hypotheses that in being falsifiable are necessarily finite and non-universal. — sime

I see what we call universal laws of nature as generalizations of how we have observed the universe behave in the past. The hypothesis to be falsified is that the universe will behave that way in the future.

The outcomes fail to reject the null hypothesis ("mermaids are mythical") and in so doing begin to accumulate a sense of probability weight from quite a few samples taken that fail to demonstrate mermaids are not mythical.

How can we describe the confidence after a string of those test outcomes, and how that confidence-probability estimate changes with additional test results? — AngleWyrm

Let's say we have an opaque bag of marbles. All are the same shape and size. They are of two possible shades - white and black. We reach in without looking and pull out a marble. It's white. We put the marble back in the bag and shake it up. Then we choose another marble. It's white too.

How many marbles do we have to pull out before we can say there are no black marbles in the bag. What if there are three marbles in the bag? What if there are a billion? What if we don't know how many marbles are in the bag?

I cannot think of anyone who has put forth a scientific hypothesis that mermaids don't exist. You have a link to such a proposal? — noAxioms

If the fact that you've never heard of anyone who has put forth a scientific hypothesis that mermaids don't exist is sufficient evidence that no one has in fact put forth a scientific hypothesis that mermaids don't exist, then why wouldn't the fact that you've never heard of anyone who has actually seen a mermaid be sufficient evidence that no one has ever seen a mermaid?

If your epistemological basis for rejecting empirical claims is that you do so reject those claims when there is a lack of empirical evidence to support it (which seems a fairly reasonable approach), then why all the blather about the null hypothesis?

I have a hunch that comes from hypothesis testing and the practice of rejecting a null hypothesis. That isn't to say the process is wrong, merely that it's poorly expressed to students who then take it as a challenge to present that which cannot be argued against. — AngleWyrm

Wasn't it Garreth Evans who said that we could never find a unicorn's remains? Even if we did find parts of a one-horned horse, the origins of unicorn's existence are entirely within fiction, and therefore, no one could scientifically say that "we have found a unicorn" or that "unicorns existed all along", because that's putting a fictive object in a domain where it doesn't belong.

Let's say we have an opaque bag of marbles. All are the same shape and size. There are of two possible shades - white and black. We reach in without looking and pull out a marble. It's white. We put the marble back in the bag and shake it up. Then we choose another marble. It's white too.

How many marbles do we have to pull out before we can say there are no black marbles in the bag. What if there are three marbles in the bag? What if there are a billion? What if we don't know how many marbles are in the bag? — T Clark

Yes, that captures the basics of the question.

As another example, roll two dice and look for a sum of thirteen. We know beforehand that result isn't possible, but can we demonstrate through a series of trials how the unlikeliness of the outcome increases over the series of tests?

I am reasonably certain that mermaids are mythical, but only because the failed announcements have reached some threshold of certitude.

"There are no mermaids" is falsifiable.

There's been rather a lot of what passes for science these days doing the job of just that -- passing as science. — AngleWyrm

Like what? — darthbarracuda

Test any of the following scenarios:

• If the mass of an entire planet were to suddenly wink out of existence, then ... gravity waves
• If we had some exotic matter, then ... warp drive
• If we travel near the speed of light, then ... relative time distortion
• If we crammed the trillions of tons of material that make up Earth into a marble, then ... black holes

I guess I just don't see the big issue with people believing in things, even if it's ultimately unjustified, if it doesn't hurt anyone. I usually don't really care too much about science (I think most of it is extraordinarily dull) so whether black holes exist or not is not a big concern of mine.

That being said, there is no one single definition of science, and the only method that can be applied to all sciences is "whatever works". Anything goes. And if this includes pie in the sky speculation then so be it. Why do people care so much about being wrong?

If you wish to resort to religion and belief then you're welcome to do so. I do think they have a valid place in both society and our individual lives. And that place is in a temple or church rather than the halls of science, which is mostly about measuring and observing things.

The main difference I see in those two perspectives is merely a level of detail/resolution available to the witness. I understand cell phones work on electromagnetic waves, so it's no longer a magic wand to me. But I don't have enough detail to describe the process by which a stem cell chooses to become any of a variety of available options. So I'm fine with saying it wants to be similar to it's neighbors.

That's effective magical thinking that serves as a handle and a coping mechanism. But if I eventually wish for and have the opportunity to acquire a more detailed understanding, it comes at the price of a loss of mystique.

Notice that at no time have I implied deceit or erroneous behavior. That is the horse of a different odor that I referred to with the garbage-in/garbage-out un-testable scenarios.

As another example, roll two dice and look for a sum of thirteen. We know beforehand that result isn't possible, but can we demonstrate through a series of trials how the unlikeliness of the outcome increases over the series of tests? — AngleWyrm

Now I'm lost. The probability of rolling two dice with a maximum number of pips on any face of six and getting a total greater than 12 is 0, no matter how many times you roll the dice.

That being said, there is no one single definition of science, and the only method that can be applied to all sciences is "whatever works". Anything goes. And if this includes pie in the sky speculation then so be it. Why do people care so much about being wrong? — darthbarracuda

The whole "what is science" discussion has been had many times on this forum and I'm not really interested in picking it up again. I'll just record my position that the term "science" has a specific definition. As for many words, that definition is open to some ambiguity and disagreement. It's not "whatever works," it's "whatever works within the limits of the scientific method."

As another example, roll two dice and look for a sum of thirteen. We know beforehand that result isn't possible, but can we demonstrate through a series of trials how the unlikeliness of the outcome increases over the series of tests? — AngleWyrm

Yes, we can *demonstrate* provided we carefully understand that our "demonstration through a series of trials of the unlikeliness of an outcome" refers to our behavioural disposition in response to the trial outcomes we are getting, as opposed to understanding this demonstration in the usual way as being solely reducible to the dice roll outcomes in themselves.

For we cannot *represent* solely in terms of a collection of repeated trials the unlikeliness of rolling 13.

In my opinion the cause of Hume's problem of induction is the result of failing to recognise that induction and inference refer to the behavioural adaptation of an organism in response to the environment. When recognised as such, it makes no more sense to seek logical justification for our empirical inferences than it does for our digestion.

...roll two dice and look for a sum of thirteen. We know beforehand that result isn't possible, but can we demonstrate through a series of trials how the unlikeliness of the outcome increases over the series of tests? — AngleWyrm

Now I'm lost. The probability of rolling two dice with a maximum number of pips on any face of six and getting a total greater than 12 is 0, no matter how many times you roll the dice. — T Clark

That is not a test of the researcher's present knowledge, it is a test of a system wherein there is unknown state that we happen to know beforehand so we can validate the results. The experiment run to test for the outcome thirteen will always fail, and we understand why that is so. The question is that if we didn't have that information, how does each toss (and the resultant failure to get a thirteen) affect our prediction of future tosses?

If done without knowing ahead of time that the result is impossible, there is some accumulation of failures and failure to accumulate successes that eventually reaches a threshold of decision-making wherein we say "it has always failed, and I predict it will continue to fail" based entirely on test results.

It is this shift from a starting position of "let's see what happens" to "I'm reasonably certain of the outcome of this test," that represents a variable we can call confidence. We see it happen, we make those judgements, so we should be able to measure it.

It is this shift from a starting position of "let's see what happens" to "I'm reasonably certain of the outcome of this test," that represents a variable we can call confidence. We see it happen, we make those judgements, so we should be able to measure it. — AngleWyrm

I'm not sure that works. Let's go back to the marbles. I know there are 1,000 marbles in the bag. In reality there are 999 white marbles and one black one, but I don't know that. I start pulling out marbles. I pull out 1,000, all white. Am I now "reasonably certain of the outcome of this test?" I'm not that good with probability, but if my calculations are correct, the chance that I will pull out 1,000 white marbles without pulling out a black marble is about 37%. Somebody please check that.

I believe that we can model the process of arriving at a confidence threshold with a very simple formula:

This chart was generated by rolling two virtual dice and testing for the outcome of a sum of seven, which has a probability of 6 chances out of 36 outcomes, 6/36 = 1/6 chance/outcome.

As the history accumulates both successes and number of tries, the resulting proportion approximates the ideal prediction.

I know there are 1,000 marbles in the bag. In reality there are 999 white marbles and one black one, but I don't know that. I start pulling out marbles. I pull out 1,000, all white. — T Clark

The last sentence indicates that the marbles are being placed back in the bag after each pull; the technical name for that is sampling with replacement, which is identical to rolling a die or spinning a roulette wheel. The alternative is sampling without replacement which is what happens when drawing cards from a deck, lottery balls, and names from a hat.

For the D&D nerds like me, a similar chart can be done with 3d6.The number of chances of a given sum coming up can be directly read off the polynomial expansion of Sum(x^i)^numDice as the coefficients, where Sum goes from 1 to sidesPerDie.

( x^1 + x^2 + x^3 + x^4 + x^5 + x^6 )^3 =
1x^3 + 3x^4 + 6x^5 + 10x^6 + 15x^7 + 21x^8 + 25x^9 + 27x^10 + 27x^11 + 25x^12 + 21x^13 + 15x^14 + 10x^15 + 6x^16 + 3x^17 + 1x^18

So here's the result of rolling 3d6 a bunch and testing for the outcome 12, which appears 25 times in the 216 possible outcomes, and so the approximation should approach 25/216.


In the above image, a green-tinted region shows an approach from the right side of the graph. At some point the approach reaches an unacceptable level of noise in the data, a variance beyond a desired error level. How can we determine how close to zero (how few tests) we can get without exceeding a desired error level?