Science and math.

[Jolly Joker]

Math, however, has nothing to do with science and its findings or observations. It has nothing to do with any bias either.

I'm pretty sure Descartes would disagree.

It would be Descartes' one more error for him, then. Interestingly enough his "scientifical" work was rather flawed, while his philosophical and mathematical work is rather neat.

[Corribus]

Bias' effect on science is that until a method (and there is none yet) is created to eliminate all bias all findings are limited to human perceptions.

That's very vague. Be specific. Define: "eliminate all bias", "all findings" and "human perceptions" and the connection between them.

Be it instrument bias (the instruments can only pick up what we tell it to, which perhaps means it misses variables because we do not know of them).

An instrument is designed to test for something. You can't say that an instrument which is designed to test for photons is flawed because it doesn't test for sound waves. Define "misses variables". You are throwing these terms around haphazardly and they don't mean anything. And You still haven't defined what you feel constitutes bias.

For instance, your example of photons. Lets say we only know of one kind of photon, but there are 103. We can not create a instrument to pick up the other 102 kinds, because we do not know they exsist.

There's a hundred and three kinds of photons? And playing along as if there are (for whatever reason), is there any difference between only testing for one kind because we are not aware of another 102, and only testing for one kind because that's all we want to test for? And furthermore, I *still* don't see how that constitutes bias.

So therefore a instrument set to record the number of photons that hit it would only be 1/103 parts correct.

No, it doesn't work like that. It's 100% correct for the type of phenomenon for which we are looking. And being incorrect is not the same as bias.

I am just saying there IS bias, and that we have no idea if we are on the right track or billions of miles away from it.

Being incorrect or inaccurate is not the same as bias. Protecyon was kind enough to copy a dictionary definition. I suggest you read it carefully.

Imagine a play. The auditorium is huge, one might say infinite in size. Now, we only see one or two parts of this, have no handbook that tells us what the play is about, and we are in the far back of the auditorium. We might see what the one or two parts (of billions of parts) and think we know what the play is about. Until we realise we were watching stage hands, who had nothing to do with the actual play.

What does this have to do with bias? Nobody is arguing that we know everything there is not know.

Yet, often I have heard people stating such things as "Well if we did encounter other intelligent species, they would see things this way, cause it is the only way."

Who said this?

This is vanity. They may have a much better seat and see a lot more then us in this play we call the universe.

More likely they've been sitting there a lot longer, to carry on your analogy. Mmmm... but how is this bias again?

actually an instrument will pick up what it is capable of picking up, which is not necessarily limited to what we tell it to ....

Possible, yes.

I think that you're referring to definition 2 in bias, and definition 1 and 2 in prejudice, correct me if I'm wrong. Now if those are the definitions you're referring to then I fail to see how an instrument can have "any preconceived opinion or feeling, either favorable or unfavorable." I would agree that a human being has preconceived opinions, however this is not bias, or prejudice because contrary to definition 1 a scientist will have formed an opinion out of reason. Nonetheless, even if we say a scientist is biased, science itself is unbiased as the bias is weeded out through an iterative process of peer review.

Thank you for copying the definition for Mytical's benefit. I will recopy that part of the definition here:

Bias: 2. a particular tendency or inclination, esp. one that prevents unprejudiced consideration of a question; prejudice.

Prejudice: any preconceived opinion or feeling, either favorable or unfavorable.

Protecyon is right, of course. An electronic instrument can NOT have a preconceived opinion or feeling. It measures what it measures and provides the data. That is it.

Bias *is* a serious problem for the experimentalist. Here is a REAL example of bias. The technique I am currently learning/doing involves looking at fluorescence from single molecules (or single clusters of molecules) using a confocal microscope. One hypothesis that one might have is that, starting with a certain bunch of molecules that have some baseline fluorescent capability, if I do something specific to the molecules (whatever it might be) that I can increase the fluorescent capability of the molecules 10 fold. I would most likely have some reason to hypothesize this. Bias comes into play here in that, having a certain expectation in mind, I - consciously or unconsciously - collect data in such a way that I try to make the data agree with the hypothesis. I have a preconceived notion that my hypothesis is right, and so I bias the experiment to have this outcome. There are a few ways this can happen.

For instance, in the experimental design I have two microscope slides, one that has my unaltered molecules (my control, for comparison) and then my new ones that should be brighter. These slides are labelled (original and new) and I know which one is which. I put the slides on the microscope one after the other and begin acquiring fluorescence intensities of many single molecules so that I generate a volume of data (from which I will make a histogram). If my hypothesis is right, then the body of data from the "new" sample will contain a greater number of large values than the other sample. The instrument (a detector which detects photons) has no bias. The detector doesn't care what sample is what. It sees photons and it records the data. The potential bias comes from me. On each microscope slide, particles are not necessarily distributed evenly. There may be patches of bright molecules and patches of dark particles on each slide. If I know which slide is which, I can bias the experiment by tending to look at brighter patches on the "new" slide and darker patches on the "old" slide. This may not be a conscious decision. Yet since I have a preconceived notion of what I might want the outcome to be, I can help bring that outcome out - even if it's not the truth - just by manipulating the data as a collect it. Note that the instrument shares no role in this bias.

This bias is easily eliminated, however. One thing that I can do is to have someone else prepare my samples and label them with a code, and then give them to me to measure. Or I can design the experiment, prepare the samples, and give them to someone else. Either way, since I (or the anonymous measurer) have no knowledge of which sample is which, of which sample is supposed to ultimately be the brighter one, there's no way I can bias the measurement. Bias towards picking bright patches in one slide and dark patches in the other is much less probable. Such a "blind" study would be completely unbiased, at least as far the experiment goes. I of course can then bias the results by my interpretation of the data, but this is much harder to do AND there is a peer review process which ensures that nonpartial people will check the data as well. There can also be bias in the review process (reviewer reviews the paper negatively because they have a similar study) but there doesn't have to be. The point is that good experimental design effectively eliminates the possibility of biased data.

Now according to you, the fact that my instrument didn't look for 102 other kinds of photons which may or may not be there constitutes bias in my experiment, but it's not. That's a lack of knowledge. That's not bias. It's not biased because I'm not trying to skew the results towards a preconceived end. You can certainly argue that all scientific experiments can possibly be affected by what we don't know, and so no results may be completley 100% trustworthy. I'd say that's a rather pessimistic, unproductive, unhelpful and useless way to look at the scientific method, and though philosophically maybe correct, it has no practical utility. But ignorance does not in itself equate to bias.

Like I've posted in one of my earlier posts (apparently nobody payed attention to it), that the human psychological biases usually work against the accepting of science, especially in people who cannot understand it (like you), and who do not find the answers it gives satisfying enough.

Bingo. Someone rejecting a scientific finding because, for instance, it goes against their preconceived religious beliefs - or worse, interpreting scientific data in an ad-hoc manner as support of some ridiculous notion of, e.g., a young earth - is among the worst practioners of bias.

Really? Coz imo it works both ways.

You're right, it does. If some experiment was designed to test for God (or against God) and a scientist performed the experiment in such a way to lead to one result or the other, OR rejected the experimental results out of hand because they didn't agree with his preconceived notion that God did not exist, that would be bias. Insofar as no such experiment has been devised, you cannot say yet that I am necessarily biased against the idea. Beliefs DO lead to bias, but only if you let them. Beliefs also impact what you test for. But once the experiment has been designed, and designed well, if you are willing to put your beliefs aside and impartially let the data say what they say and then accept the results for what they are, you are being unbiased.

[okrane]

Oh no... another logical black hole... I've been gone for like 2 weeks and you kids started another one without me...

I'm gonna say just one thing:

Science is about making stuff that WORK and Math is a tool. Who cares if it's biased, of course it's biased... models are biased. Take Newton's gravity laws, they introduce Forces as a model. Forces do not exist in facto, they are just a representation of reality, that WORKS in an approximate scale.
There are other models to gravity, like Einstein's space time curvature or the exchange of gravitons between bodies.

All these are just biases... models perceived by some scientists. Important is that THEY WORK, thus allowing us to DO useful things.

anyway... I agree and support Corribus in all he said...

[Caradoc]

A few tidbits:

The Spirtualists used to claim that the reason the spirits would not appear in scientific experiments was that they were offended that the scientists doubted their existence. Experimental bias in reverse.

There was a recent report in Nature that found major statistical errors in a large percentage of articles they had published.

Another odd factoid that may have some relevance here is that a statistician has established that a coin toss is not a 50-50 proposition. It turns out to be 51-49 in favor of the side that was originally up.

[Banedon]

The Spirtualists used to claim that the reason the spirits would not appear in scientific experiments was that they were offended that the scientists doubted their existence. Experimental bias in reverse.

That's not a good scientific theory because, as I wrote above, it is not falsifiable. If scientists believed in spirits and still cannot find them, spiritualists will say spirits don't want to be found (or some other explanation). These explanations cannot be proved wrong and so cannot be called scientific.

Another odd factoid that may have some relevance here is that a statistician has established that a coin toss is not a 50-50 proposition. It turns out to be 51-49 in favor of the side that was originally up.

Odd? I remember it's 'heads' as slightly more favoured because the face of 'heads' is slightly heavier.

Bias' effect on science is that until a method (and there is none yet) is created to eliminate all bias all findings are limited to human perceptions. Be it instrument bias (the instruments can only pick up what we tell it to, which perhaps means it misses variables because we do not know of them). For instance, your example of photons. Lets say we only know of one kind of photon, but there are 103. We can not create a instrument to pick up the other 102 kinds, because we do not know they exsist. So therefore a instrument set to record the number of photons that hit it would only be 1/103 parts correct. Now I am not saying that this is useless as you seem to think I am. I am just saying there IS bias, and that we have no idea if we are on the right track or billions of miles away from it.

I don't think this constitutes instrument bias. It just means there're another 102 kinds of photons we did not dream existed and do not know exist. It means that science is not complete because we have not explained the remaining 102 kinds of photons, but it doesn't mean science is biased. We simply don't know that those photons are there. If and when we discover them, we'll explain them and put them into a theoretical framework, just like when Marie Curie discovered radiation, mankind explained - and learned a lot - about atomic structure. If there were 103 kinds of photons in total, I would believe the same process will take place. The current models of particle physics would have to be modified, but the new one that replaces it will be more complete - that's how science works.

[Chai26]

My mind cant even understand half of this thread, you guys really are good

[Corribus]

@Caradoc:

There was a recent report in Nature that found major statistical errors in a large percentage of articles they had published.

There have also been papers that have been shown to have data that was totally made up. By the way, what was the statistical error in the report that you refer to?

[ThunderTitan]

Oh, and about math: base 10 anyone?

[asandir]

I prefer base 2 .... for confusing people anyway

[Banedon]

This is something I'm puzzling over, wonder if anyone has any thoughts on the matter...

Godel's Incompleteness theorem essentially states that there exists certain statements in mathematics that cannot be proved from the other axioms we already know. In other words, there're some statements like Goldbach's Conjecture that cannot be proved, but have to be accepted as axioms.

Now the problem is, to the best of my knowledge, a proof that a proof cannot exist does not exist - that is, it is impossible to prove that it is impossible to prove a statement (it's a tough sentence I know). If it were possible then some conjectures will already have been labelled as axioms. So we're stuck with conjectures that cannot be proved...yet, if at all.

Now from Godel's Incompleteness theorems, we will eventually run into conjectures that simply cannot be proved, no matter how hard we look for a proof. However, neither can we know it is impossible to prove. We're stuck with a statement which remains ambivalent for eternity, because we can't prove it nor disprove it. Obviously this is no way forward; mathematicians have even worked assuming a certain conjecture is true, then deriving some new result.

So what happens next? To progress we will eventually have to establish some of these statements as new axioms. However, we simply don't know if these axioms are actually axioms. What if they are actually wrong, what if a counterexample exists? They don't exist, but we don't know they don't exist. If a counterexample were ever found, it would destroy a lot of work.

This rather resembles the situation in the pure sciences. None of the theories of science are true, because scientific theories are unprovable. We just know with very high confidence they are correct, we know under what conditions they hold. But this doesn't work for mathematics. Mathematical statements must hold for a certain set (eg. all natural numbers, all differentiable functions, etc), or with very special exceptions (all eigenvalues except 0, etc). If someone actually disproved a conjecture we'd listed as an axiom, lots of work simply vanishes. We can have a lot of reassurance that a given conjecture is right, just like we assembled mountains of evidence for Newton's Laws. But just having mountains of evidence does not make things right, and...

I don't know, the future of mathematics seems a bit murky to me. Any thoughts?

[Pol]

Maybe this is where will come to help other science disciplines.
(and that maybe is only figure of speech this time)
..for me was currently enough to repairing your url, by assigning correct ascii hex entities. Dunno if I know why the system is not doing itself. I may create one axiome on that immediately.

[Kristo]

Mathematics and science are supposed to be an endless quest for the truth, right? It seems to me that one would rejoice over finally finding a counterexample to one of these so-called unprovable axioms. At least then you've learned something. Until then, you have no recourse but to assume they're right and press on. Are there no interesting problems left to solve in mathematics?

[Gaidal Cain]

Now the problem is, to the best of my knowledge, a proof that a proof cannot exist does not exist - that is, it is impossible to prove that it is impossible to prove a statement (it's a tough sentence I know). If it were possible then some conjectures will already have been labelled as axioms. So we're stuck with conjectures that cannot be proved...yet, if at all.

Well, you have to be more specific: it's quite easy to prove that there is no proof for the square root of two being a rational number, by just proving that it's irrational.

[winterfate]

I don't know, the future of mathematics seems a bit murky to me. Any thoughts?

That's the reason I hate Math!

Seriously though...that all sounds really confusing!

I have to agree with what Kristo says though:

Mathematics and science are supposed to be an endless quest for the truth, right?

We may never find everything out. Discovery is half the fun!