I wouldn't be so quick to pull generalizations about what disciplines have better scientists.
Most computer engineers are programming and can get away with not being up to speed with calculus/stats. As can most practicing psychologists (to a much greater degree).
Phd computer scientists doing research are typically not 'weak' at maths.
Among other things, there's a lot of confusion about statistical significance, and how and when it's calculated. There are people out there, especially in the cognitive and social sciences, who think it's OK to run an experiment to gather some data, and then look for statistically significant trends in the data and draw whatever conclusions they can. They're p-hacking and they don't even know they're doing it; they think it's science. And the people judging their papers sometimes think the same thing. How do you fix a field like this?
This issue lies at the root of the reproducibility problem. The example someone gave about an undergrad cheering (that she didn't have to do any more math) points at one of the causes.
This seems like a pretty wild claim to me- what is your basis for it?
* I know that's pretty subjective.
PS: "most successful" is ambiguous. Success is not really comparable. You can have many small successes, revolutions in fields that today feel like common knowledge and not scientific at all, and many nameless contributors. Medicin, chemistry, and many interdisciplinary fields.
Fixating on a single field only to argue in the end that all other fields are basically just subfields of ... metamatics, is funny, but missing the point. There is a large perceived disconnect between the natural sciences and "others". That's the real problem OP was pointing out, I guess.
Someone to compare with Einstein? Freud. This guy is no less known to public, and influenced society maybe even more, by breaking taboos around sexual desires. Moreover, he shaped all the modern psychology.
Another measure of the success of a scientist is how well their theories stand the test of time, and by that standard, mathematical rigor probably contributes a lot.
What was Freud wrong about? His theory is a model of human mind, which has its application even today and suits it well. It is like Newtonian mechanics and gravity: did Newton was wrong? No, he developed a model of reality that works even today.
There are a lot of other theories which replicate psychoanalysis in many aspects. Even humanistic psychology highly influenced by psychoanalysis despite of (or in spite of) negativism of Carl Rogers who didn't liked idea of explaining all of the mind work by primitive impulses. Rogers just made new model of mind by changing words and turning psychoanalysis upside down: mind is driven not by primitive impulses but by the need of self-actualization. The same eggs in a side view.
> how well their theories stand the test of time
What it means to stand the test of time? It is social sciences, not the math or physics, the landscape here is constantly shifting, nothing is true and nothing is false. The only way I see to measure the success of scientist is to measure its influence on others. If so, then Freud is the total winner among psychologists. No one even come close to him.
There are others -- Skinner, for example. But even Skinner's behavioral approach moves towards Freud ideas: now it is cognitive-behavioral approach, with hidden cognitive processes and conflicts between them. What the difference between coping strategies and defence mechanisms?
I'm not trying to say, that psychoanalysis is the best, I do not like it really. As for me it oversimplifies things. But I acknowledge influence of psychoanalysis on modern views.
> What was Freud wrong about?
To cite just a few examples: women (penis envy, hysteria, female orgasms); psychosexual stages, including the idea that homosexuality is anal fixation; the id, ego, and superego; the oedipus complex; schizophrenia.
> nothing is true and nothing is false
Then it's not science.
Few people in Asia have ever heard of it. It's not as influential or popular on a global scale as one might think.
I don't know how to answer this. For example, he proposed two structures of mind topographical and dynamic (I'm not sure how they named in English, and I'm too lazy to search), and proposed how that layers interacts. His ideas of psychological defences, inner conflicts... Is it counts for "Freud was right", or it is too obvious now and does not look as important ideas? All the views on a mind working are highly influenced by Freud, sometimes it is hard to find his ideas in our views, because we are too accustomed for them and therefore we are unable to see them.
> To cite just a few examples: women (penis envy, hysteria, female orgasms);
Yes, and no. Histeria and similar conditions even for now are treated with regard to psychoanalitic views -- unconscious conflicts based on repression or some other psychological defence. Psychosomatic -- I attended for classes in psychosomatics and sow patients with psychosomatic conditions. The behavioral approach does not do well, because it ignores the roots of conflit which lead to strange behaviour, and one cannot cure anorexia or hysteria relying on drugs or behavioural training. Behavioural approach can change sympthoms, for example, to make a bulimia from anorexia. Or help patient to regain control of paralized hand, but then patient would start having seizures. If conflict had not resolved, than it manifest itself somehow. Patient needs to go through the breaking of psychological defenses to understanding of conflict and to resolving that conflict. The only signigicant difference from psychoanalysis is that conflict does not nessessarily comes from psychological trauma experienced at age of 6 month.
> psychosexual stages, including the idea that homosexuality is anal fixation
There are a lot of authors who developed that ideas and the stages of developmet remained the same in general, explanations was changed.
> the id, ego, and superego;
Whats wrong with them?
> the oedipus complex;
Yes, I also do not like it. But a developing sexuality of a child and a sexuality of a parent do interact somehow. The oedipus complex seems not the best way to describe this interaction, but Freud was the first researcher in the field. If we can call him a researcher -- his empirical methods was controversial indeed.
> schizophrenia
And even now no one knows what shizipheria is. Seems that diagnosis "schizophrenia" is a way to say "we don't know whats wrong with him". I agree, Freud was wrong about schizophrenia, just trying to point that modern authors also do not know.
> Then it's not science.
I think I understand your point, because I moved from tech and math into psychology, and years ago I also could say something like this -- "it is not a science". But now I think that this phrase means "is not the physics and it is not the math". Yes, social sciences are different. They are continuously failing to make formal models, written with pretty greek letters in the math language. Lack of formalization leads to a lot of problems, but I see no way to formalize the field. And I know that there are a lot of people who are much stronger than me with math and they do not see the way to create a formal models either. There are formal models for local phenomena, but very limited ones.
The lack of formalization comes from complexity of the object of research. Should we claim that science that failed to be a formal and strict because of complexity is not a science? If so, than what we should do next? To stop any attempts to make a science in this area?
Human mind is much more complex object to deal with in research than quarks. At least there are only six flavours of quarks, while all humans are different. All the social models are models which works only conditionally. In many situations no one even know what that conditions are. For any given model we can find conditions when that model would give us correct predictions. And for any given model we can find conditions under which model would fail. It is means that everything is true and everything is false. Boolean logic fails and the law of excluded middle does not works.
Social sciences are dealing with problems for which science has no ready-made tools. The reproducibility crisis is a social sciences invention, it is impossible in physics and is inevitable in social science. Now social sciences are searching for tools to fight it. Physics does not need such a complex tools, because it digs deeper, not forward. Physicists laugh at philosophy now, because they need no philosophy any more. Philosophy now all about social science problems.
So, maybe social sciences are not sciences. But at least they are meta-sciences, they are trying to build science which would be able to deal with social problems in scientific ways. And we have nothing to replace social sciences in their area.
It seems that economics and sociology do play a role there. Both are heavy with statistics and game-theory. While Psychology is only looking at individual. Humans are more complex than fundamental particles and molecules. It's not chemistry or biology either. But Neuro-Science is most promising in this regard. "Nerven-Arzt" is a dated German term for Psychotherapist, after all.
On the other hand, what would a psychologist say to the urge to formalize everything? :)
that's very stiff.
There is a thing to say about the beauty of maths as a universal language. In that spirit, I see Freud closer to philosophy, in the sense that philosophy is highly divided and regional.
Was freud really that influential? The "freudian slip" is certainly a very useful tool for analysis. But his "psycho analysis" is outdated, or at least overcome. And sexual freedom is progressing far slower.
Sexuality is a baseline of human development. You made a very good point.
Most social scientists are not that good at maths. It used to be mostly harmless before they started dabbling in experimental science involving statistics.
A bigger problem is Economists; many of whom are also bad at maths, but litter their articles with formulas anyway, to add some pseudo-intellectual rigour.
https://books.google.com/books?id=kdm9nmAkKvIC&pg=PA1103&lpg...
It's worse: IME in grad school, the field is politicized beyond reason. It was a very depressing realization.
- The main focus of my advisor was a life-or-death struggle with a researcher at distant university over the number of angels that dance on the head of a pin - utterly inconsequential, self-justifying research and counter-research that ultimately served nothing more than to keep the 'publish-or-perish' wolf from the door. Just enough math was involved to keep it from being sociology.
- A grad student with an engineering background was dismissed for discretely pointing out that the measurement tools for one professor's lab's flagship experiment series were an order of magnitude too inaccurate for the measurements they were being used to perform. This was commonplace - another was warned for pointing out (privately, not in public) that requiring us to pass all our submitted papers through TurnitIn was also signing over our legal rights to anything we submitted as part of our coursework (which could potentially cause publication problems)
Math is hard. Pretty much period. Often, you can trick yourself into forgetting how hard it is. More, you can assume that mastery of something that takes high math to describe, somehow indicates mastery of the high math. Consider juggling as an easy example, can be very complicated to explain what is happening, yet I don't think it would be wise to assume that all jugglers are good at higher math. Even if the ones you find are.
The principle is that you must not fool yourself, and you are the easiest person to fool.Regardless of that, the point of the example was precisely the point you seem to be using against me. Most practices in many fields, including much of physics and engineering, don't actually need advanced math. They are helped considerably by it, though.
I don't think being good at juggling makes you any better at describing the dynamics of juggling, nor the physiological characteristics that enable it.
Regarding Feynman (comment below), yes it is very important not to fool yourself, but knowing mathematics well makes it easier not to fool yourself.
The juggling example was supposed to be an obvious example of people doing something that takes complicated math to analyze. I'm asserting it is not much different to many engineering jobs. Nor do I think that most physicists have a terribly strong intuition for math.
I confess to not having numbers to back this. :(
Proof?
A completely anecdotal experience: During my undergraduate (MPhys) I lived in halls with about 20 psychologists. I remember one night during the second year (of 4) they all had a huge celebration. The reason for the celebration was that they had had their last ever maths exam of the undergraduate. I remember one girl proclaimed "Thank god, I've never have to do any maths ever again!". She was met with a roar of support... I couldn't help but cringe thinking about the necessity of statistics in their future research.
I'd say maybe 10% of students who take psychology actually go on to do anything with research. Most of my friends in psychology are now counsellors, social workers, occupational therapists etc., and are good at their jobs, and this would not change if they had to take multivariate calculus.
At the same time, I do think psychological research would benefit if the people performing that research were better trained in math (actually when I say math, I specifically mean statistics and linear algebra).
I think the problem is that psychology is so broad that it can't possibly do a good job at catering to all these different concerns. Even at the graduate level, in order to become a clinical psychologist, you have to do a lot of research. The scientist-clinician model sounds good, but in practice I found that a lot of people who just didn't care about research were doing research. I found the same thing with medical students who were doing research to pad their resumes.
I also think that you can't just take a physicist or mathematician and plop them in psychology and start fixing everything. The problems often require a ton of theory, are really expensive to test, and the data quality is often terrible (because of human error, measurement error etc). Relevant XKCD: https://xkcd.com/1831/
Because the math is easier, and all you need is statistics. As the article states, the problem is, it seems even that lower bar isn't being met.
I am sorry if I give the impression of nitpicking but I live in a Celsius world and zero c is special because it means water freezes. (and snow instead of rain)
Whereas 0K is the absolute minimum temperature, so that's a really special value!
I agree that Fredrickson is grasping for relevance. However, 0 °C is special to water-based lifeforms.
0 °C is defined as 273.15 K, or the temperature at which the three phases of water are in a thermodynamic equilibrium — at a pressure of 1 atm, or 1 standard atmosphere.
The degree Celsius is defined as equal to the kelvin, so the Celsius scale is a shifted version of the Kelvin scale.
https://www.bipm.org/en/publications/si-brochure/kelvin.html
https://www.bipm.org/jsp/en/ViewCGPMResolution.jsp?CGPM=10&R...
The triple point is a better standard and is used now, but it's not exactly 0 °C because that was defined by calling the melting point of water 0 °C.
> "Not many psychologists are very good at maths," says Brown. "Not many psychologists are even good at the maths and statistics you have to do as a psychologist."
It's amazing -- well not at all amazing really! -- that the most successful people in any scientific field come from an engineering and physics background.
One of my favourite quotes is from Kelvin:
> I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be."
And ... mentioning Kelvin is a nice segue to this quote from the article:
> "Just as zero degrees celsius is a special number in thermodynamics," wrote Fredrickson in Positivity, "the 3-to-1 positivity ratio may well be a magic number in human psychology."
Almost Sokal-ish in its attempt to borrow some relevance. Zero C is not very special. Zero Kelvin is!