The Learning Curve of Math and Engineering (the advantage of time)

[Helicobacter]

Consider a person (A) who just graduated with a liberal arts masters degree. Now he discovers his passion for math or anyone engineering field. Compared to a graduate student of this field (B) who had a bent for this field since childhood, attending to camps of the subject, undergraduate research etc., what kind of an advantage does B have over A to make a breakthrough contribution in the future (in that field)?

Does the learning curve of math and engineering follow the traditional rules (logarithmic, very low diminishing returns after 10 000 hours...)?

Do people who come up with milestones and seminal contributions to a math or engineering field get their success mostly from talent or time spent on the subject?

 

[Klockan3]

Most critical breakthroughs are done at quite young ages so it would either infer that you need to learn it early to be good but it also means that time isn't a factor since they did most of the important work in a quite short amount of time compared to the lifespan of a human.

 

[Helicobacter]

That's a good point. Crick and Watson made their science breakthroughs at a young age.

 

[Mathnomalous]

It may also mean a young person is more likely to go against established societal norms (i.e. rebelliousness). An ambitious young person trying to make a mark has very little to lose therefore that young person proposes a new theory. If the theory sticks, they are boosted to "genius level", and if the theory does not stick, that person reasoned (s)he had very little to lose anyways. Similarly, a young person is less likely to be "tainted" by reality therefore that young person allows his/her imagination to run wild. If the theory sticks, that person becomes a "wild genius" and if the theory does not stick, the young person is just wild.

In both cases, experienced scientists probably have a reputation to maintain and may be more cautious about proposing something new and wild lest their hard-earned reputation be thrown in the garbage overnight.

In all cases proposed above, we normally track attempts that result in success and seldom track attempts that result in failure. I'm positive there were many intelligent, brilliant people during the late 19th and early 20th century (perhaps more brilliant than Prof. Einstein) that proposed theories that obviously never stuck.

Of course, this is my opinion. Personally, I doubt mathematic, scientific, or engineering knowledge somehow self-selects for age (or genes, ethnicity, country, etc). If these do, why does it not happen in other fields of knowledge?

 

[Noxide]

Consider a person (A) who just graduated with a liberal arts masters degree. Now he discovers his passion for math or anyone engineering field. Compared to a graduate student of this field (B) who had a bent for this field since childhood, attending to camps of the subject, undergraduate research etc., what kind of an advantage does B have over A to make a breakthrough contribution in the future (in that field)?

Does the learning curve of math and engineering follow the traditional rules (logarithmic, very low diminishing returns after 10 000 hours...)?

Do people who come up with milestones and seminal contributions to a math or engineering field get their success mostly from talent or time spent on the subject?

Any contribution made in the sciences is exponentially better than the best contribution in the arts.

 

[snipez90]

Any contribution made in the sciences is exponentially better than the best contribution in the arts.

I disagree, and why is this relevant to the OP's post.

 

[johng23]

I definitely believe that someone could come from a humanities background and become a good scientist. People have overcome bigger challenges than that. I can't imagine doing that though. I'm in my first year of grad school, and I think trying to become a good scientist is hard enough. I feel like I'm coming from behind just because my undergrad was in materials engineering, and there's a lot of physics I don't know. Coming from no scientific background? You'd have to have some latent scientific genius for sure.

It's not the time, but the fact that science has to fit into a career path in some way. If you're in grad school you're expected to accomplish things. You can't take all the time you want to learn background science.

 

[johng23]

Any contribution made in the sciences is exponentially better than the best contribution in the arts.

So your run of the mill researcher who performs some minimally enlightening experiments is more important to humanity than Mozart or Picasso? Please.

Unless your definition of a "contribution" to science is extremely restrictive, there's no way this is remotely true.

 

[rolls]

Any contribution made in the sciences is exponentially better than the best contribution in the arts.

Lol I love saying stuff like this to stir people up, whilst it is true if you restrict your definition of contribution to being a technical contribution that increases our quality of live and ignore entertainment etc (eg music, poetry etc) then yes it most certainly is. I wouldn't say it is that simple however.

there's no way this is remotely true.

Eh I would certainly say it is remotely true, as if you removed all engineering and technical contributions to the world, we would be living in poverty and our quality of life would drastically reduce. However if you only removed art, music and various other arts such as plays etc then we wouldn't have as much entertainment and the world would be particularly ugly, but at least we would have nice warm houses and be free from illness and disease.

 

[Ryker]

Eh I would certainly say it is remotely true, as if you removed all engineering and technical contributions to the world, we would be living in poverty and our quality of life would drastically reduce. However if you only removed art, music and various other arts such as plays etc then we wouldn't have as much entertainment and the world would be particularly ugly, but at least we would have nice warm houses and be free from illness and disease.

How would be free of ilness and disease if we wouldn't have an organized health care system, which is a product of an "arts contribution"?

 

[rolls]

How would be free of ilness and disease if we wouldn't have an organized health care system, which is a product of an "arts contribution"?

Is that a joke? How is that part of an arts contribution, medicine is the place a lot of technological advancements are seen each year. The amount of engineering that has gone into the human genome and researching disease and illness is amazing, not to mention the science and engineering that goes into the medical equipment we use.

 

[Ryker]

Why would I joke about democracy, the state, the organization of public administration etc. not being advances made by life/natural sciences?

 

[rolls]

Why would I joke about democracy, the state, the organization of public administration etc. not being advances made by life/natural sciences?

Sure they are very useful and make everything work much better but without the medicine in the first place it would be useless. If you removed them and only had medicine you would still be able to use it just not as effectively.

 

[Klockan3]

Why would I joke about democracy, the state, the organization of public administration etc. not being advances made by life/natural sciences?

Social science is still a science and not an art. He didn't say that natural sciences > all, he said that science>art.

 

[Ryker]

Yeah, that's true, I guess I thought the distinction as it pertains to the topic at hand was made akin to the distinction between B.Sc. and B.A.

 

[Heisenberg.]

Eh I would certainly say it is remotely true, as if you removed all engineering and technical contributions to the world, we would be living in poverty and our quality of life would drastically reduce. However if you only removed art, music and various other arts such as plays etc then we wouldn't have as much entertainment and the world would be particularly ugly, but at least we would have nice warm houses and be free from illness and disease.

hm I believe the debate is being thought of a little two linearly. My opinion: The basis of fantastic art work (now most of you have been using this word a little flimsily for art in general can encompass theater, dancing, music, photography, sketching, forms of writing etc - in my definition of art I will include all these) is creativity. The basis of fantastic theories - in most cases, is undoubtedly creativity. Of course an artist who drudges through a program in a conservatory, or arts program can simply be creating their interpretation as of what's been already done, as well as a professor who may be very intelligent and an excellent problem solver but mainly deals with equations that have already been established. Now I mean no disrespect to the aforementioned artist and professor: their work is key to understanding on a deeper level that of which has already been created. The important thing to remember that being an artist does not necessarily include that every artist is wonderfully creative. The word creativity is key - and this is both present in the arts and sciences. How in the world did Riemann, who has attributed the first to more or less formally propose dimensions higher than three or four, even think of that in the first place? How can anyone be the first to think of something that has never been thought of before? Creativity. Now my claim is we are not Riemannss, or Einsteins whose work for the most part was new and different. They were creative on a fundamental level we can only dream of. But for those of us who would like to open our minds outside the realms of numbers, and start dangerously thinking outside of the box, even if it be in the confines of our own minds - the arts is a great inlet and if not necessary.
Einstein himself was one of the foremost endorsers of using our imagination - he himself attributes some of his greatest insights when improvising on his violin. Now do you have to be affiliated in some with arts (even if means listening to Vivaldi's winter while you study)to be a scientist? Of course not. The evidence is clearly stated in the above posts. But we, including everyone here and the professor's diligently working on this problem, does not know why creativity is seemingly more present in some individuals than others. So I believe it is not fair to make bold statements about art being less important than science - for they both share a key foundation. Perhaps more scientists need to take a gander into some of the arts - not only for inspiration, but to unlock the creativity that must be inherent in all of us.

Edit: As for the OP - even with my rant on creativity being important, I feel the best option is to be a hard science major WHILE taking some arts classes or on your own finding an inlet for art CONCURRENTLY. It just seems easier. But when there is a will, there is a way - and it indeed is possible. But perhaps not very probable. It will take a few years of catch up I can imagine - before one's mind is even ready to start thinking about ideas that would be "possible milestones". But again anything is possible, I believe Bohr was 28 when he finally finished some of his papers that won him the nobel prize in 1922.