I was thinking about what the word Genius meant to people. For example is Newton considered a genius? Is genius a clever person who can bring his/her particular field leaps and bounds foward? Equally, is Edison considered a genius?

Or is it simple a word that means the person stands out from the crowd? For example the guy who invented HTML, Tim Berners Lee. He is still alive, is he considered a genius/visionary/at the right time at the right place, same goes for Bill Gates and software? Where is the turning point between a genius and simply a very clever person or simply a lucky person at the right place at the right time? Wiles is 40+, so when he proved Fermats LT, he did not win the Fields Medal, but is he considered a genius? Who decides when you become a genius?

Genius - Just a way of justifying to ourselves that we didn't work as hard as they did.

95% perspiration 5% inspiration.

Anon - If I remember correctly, did Edison say that 2nd line?

Thanks James.

Anon, so you really think that genius, is a person who really worked hard? Or are you born one?

Well I guess Einstein wasn't born with the theories of relativity in his head. Nor Newton with classical dynamics so I suppose they worked them out.

Ok Anon I agree. But how much of what you can achieve or deliver depends on your envirnment and how much on your genetics?

And how much is luck (factors that we cant count prehand count for)?

I'd say a lot is luck - the inspiration. The rest is hard work probably resulting from obsession.

I agree.

Well look at it this way, generally the sons or parents of mathematicians or physicists that we would call genuises were not genuises. This is a problem for genetic arguments.

I agree with Anon that obsession is probably quite an important element, unfortunately.

I would say that maybe with exceptions for people like Euler or Einstein, the line between genuises and very good mathematicians/physicists is a somewhat fuzzy one.

Sean

But children are not clones of their parents. Sure, lots of characteristics are inherited, but I think there is easily enough genetic variation between generations to ensure that the children/parents of a genius do not normally stand out.

In fact I don't see why it is unfortunate if obsession is quite an important element. I like to think that people who achieve do so because of their dedication and enthusiasm for the subject, not just because they were lucky enough to be born with exceptional genetic code. Unfortunately I suspect that most geniuses occur precisely because of the latter reason. I don't know if anyone here watched a documentary a few years back on identical twins; but they conducted investigations into identical twins who'd been separated at birth and brought up in totally different environments, but their performance on academic tests were alarmingly similar. Of course this doesn't say anything directly about whether genius is hereditary, but still I think the genetic domination on almost all characteristics of human life is hugely underestimated...

I disagree with Michael's Analysis. If intelligence is determined genetically, (and assuming only moderate correlation between genes and class) why is it that Cambridge is almost entirely populated by the upper middle classes (half of whom just happened to go to public school where the importance of hard work was thrust upon them)?

okay, fair enough, as I was writing it I thought it was a bit of a naive argument. My impression, however, of separated identical twin type arguments is that there are also cases in which they become different (as a nonscientific point here, has anyone seen the musical Blood Brothers?). And I'm not at all sure enough cases have been studied to make a solid statistical argument one way or the other...

I would say that genetic influence is in fact OVERestimated at the moment, it is somewhat fashionable at the moment to ascribe things like criminality, alcohol dependency, depression etc. to genetic origin, often, my impression is, with fairly flimsy science behind the claims. Either sociologists doing bad genetics or geneticists doing bad sociology. There was Newsnight program a couple of weeks ago in which genetics was presented as the explanation and hence cure of everything and quite frankly it had more than a slight resemblance to the sort of Eugenic arguments that were common some 80 or so years ago.

Finally on another point, enthusiasm and obsession are not the same. Obsession tends to imply an exclusion of other things in life, which I think can be a shame. Enthusiasm is great! It's what makes life worth while...

Sean

An extremely large proportion of the people who apply to Cambridge are from public schools. And they will have been specifically coached by the staff in exam technique and how to pass an interview. Anyway, there is certainly not a direct link between people's intelligence and whether they go to Cambridge or not!

I do agree that environment is important as well. If you're not taught a subject properly then unless you are exceptionally well motivated you might not be able to pursue it properly. I just think that it is incorrect to say that mathematical ability is totally determined by upbringing. I know this isn't true, from personal experience. (But I don't want to go into the details.)

Genetic influence is over-estimated?? I have very rarely heard people putting down people's attributes to genes. I think to some extent this is logical as there is nothing you can do about genes. A more positive way of analysing the situation is to say: "you still have a chance of changing it if you work hard". Whether or not this is true, there can't be any harm in saying it.

Certainly the argument of environment v. genetics has been going on a long time and is still not resolved. There was a famous psychologist a century ago (whose name I've forgotten) whose work strongly suggested that genes were all-important. This was taken as gospel for ages until it was discovered he'd faked all of his results (one of his main "assistants" in his investigation simply didn't exist). Before the end of this era in which genes were believed to be everything, there was an exam called the 11+. This exam basically decided whether you went to a decent secondary school or not (and if you didn't go to a decent school you probably couldn't get into university). Now it was widely believed that this exam tested your intelligence on an absolute scale, and that prior teaching would make no difference whatsoever. What an amazing co-incidence then that schools which gave their students past papers to practise with got a far higher proportion of people into good secondary schools.

After the bogus psychologist had been uncovered, the consensus swung in totally the opposite direction. According to my dad, when he was at UCL in the 1960s, if you spoke to any of his friends in the Psychology department about the factors causing differences amongst people, they would tell you vehemently that the influence was totally environmental. Every new baby is an entirely new blank sheet, with exactly the same potential as anyone else (provided they had the same upbringing). Apparently at the entrance interview, if you were asked why you wanted to learn about psychology, the worst thing you could say was "because I want to know how the human mind works".

Nowadays the opinion is slightly more central, but I think it is still unfashionable to claim that there are inherent differences in people right from the start.

You may be right about identical twins. Perhaps the people writing the documentary deliberately wanted to make people think that genes were all-important so they only cited the cases that proved their point. It still was rather shocking how similar these people's lives had been (they weren't aware of the other one's existence).

Uh-oh, this is turning into a genetics debate, never a good sign. I mostly agree with Sean about the influence of genetics. As I recall, the TV programme recently about twins separated at birth was based on research done in the 60s, the scientific validity of which is in doubt, at least according to my parents who are psychologists. My guess would be that there is probably some genetic aspect to intelligence, as any other attribute, but that our measures of intelligence (a) do not and can not measure this aspect, because they are not independent of our society and philosophical bias, and because they are unidimensional measures, (b) are largely determined by social rather than genetic conditions.

One doesn't need necessarily to say that mathematical ability is totally determined by upbringing, for a start upbringing is not the only external factor influencing people, but it is a question of which is more imporant. In a question like maths this is just an interesting question but in other areas it is more important. For instance, asthma. There is a global increase in asthma over recent years. It is thought to have some genetic relation but does this mean that a genetic treatment is the best, mightn't it be better, for instance, to do something about pollution? If there wasn't anything to actually activate the disease then it wouldn't matter whether people where genetically predisposed or not. Perhaps a slight analogy with maths is possible. If everyone had the stimulation and the opportunity to find out and do what they liked most in an intellectual sense then I am sure we wuld get MORE people doing maths, rather than less (and similarly for all subjects). The thing is that if there is a genetic explanation for something, then people have ane excuse not to do something about it. So for instance, why do people not like maths at school? It is easy to say that they are genetically not able to do maths, and this is a good excuse to not spend the resources it takes to teach them properly.

Sean

Michael, in addition to what I said in the above post (I hadn't read your last post when I wrote it): I think that the biological reductionist faction is the dominant popular ideology in these matters at the moment, which says that almost everything is determined by genetics, as preached by Dawkins et al.

Right, good set of arguments I reckon.
However, if you set up the following situation:
A person whose genetic code had been analysed and seen that the genes to create a person good/great at maths was not there. Now that we know this, is it possible to give the suject the best possible education, guidance and upbringing and turn them into a maths genius? Or not? Because if you can, then genitics goes down the can? Or can genetics control what you do, unless you do actions that otherwise contervene it?

You guys might like to take a look at Edge

I had a look, it seemed a bit suspicious to me. It had an article about why the 2-party system and the recent american elections indicate that democracy is doing as well as it can, backed up by pseudo-mathematical arguments, but with a heavily right wing political ideology assumed.

On the subject of genius, I don't think that there is a genetic code for genius, what characterises genius is the lasting impact of their work, this is extremely culturally dependent. Moreover, many great works seem, in some sense, to be independent of their creators, for instance the calculus was independently discovered by Leibniz and Newton at the same time (within a year or so).

I am now even more confused as to what makes a genius then before - thanks guys. It seems that anything that is verbally and emotionally argued gets very complicated and messy too quick. I think I'll stick to something simple, Math!

I was thinking, on the subject of genius again. Major milestones in maths would it be fair to say just to name a few, Netwton, Descarte, Pascal, Guauss.... (sorry if i missed out others). Will there ever be any more maths genius whose name will go down in history like the one mentioned before? Or will all the clever people go into the computing industry?

I'd be very surprised if there were not more geniuses in maths in the future, there are more mathematicians today than ever before. Personally, I don't think that the computing industry (i.e. not theoretical computer science) is taking away any of the great mathematical brains. The big advances in computing will be done by physicists working on Quantum Computing, at least that's my guess. The other big advance in computing will be articifical intelligence, which may or may not involve mathematicians. Certainly, a lot of mathematicians are going into neuroscience, which is somewhat related to AI.

I know that AI was discussed before @ NRICH, [Here . - The Editor] but do you think it is possible in reality? Or would the best brains best be spent on other things where progress can be made?

On whether there will be maths genius in the future, for sure, I also think this is beyond doubt. However, do you think that people who are good at math will be tempted in to field of computing simply because of the pace of developent and money.

Personally, I think AI is inevitable, it must happen eventually. I would like to see it in my lifetime, but that might be too short a timespan. Possibly some will be persuaded into computing for those reasons, but the obsessive types who become geniuses are usually not too interested in that sort of thing.

Humor aside, if we do develop machines with AI capabilities, will they pose a greater threat to us than the A-Bomb did? So is it wise to go down the route of AI at all. We have the hindsight of the Nuclear age in our hands. So, if people like Einstien had known that their work would have lead to the eventual nuclear threat to the world, would he have pursued it, I am not too sure. As you said geniuses are obsessive but they also have a conscience.

Sorry about joining this discussion so late. Here's my two cents, anyway.

On genius-it's caused more by passion to pursue a subject and to do something than how well a person can do on standardized tests. Neccesity is not the mother of all innovation, though. Most innovation comes from someone finding something purely to satisfy their curiosity. And generally that curiosity is a product of someone simply enjoying doing something. In that sense, I don't think that genius is entirely genetics.

On the american elections (hey, it came up!)- I don't think that these elections say that democracy is at its best! just look at my new president!!!!



On the conscience of scientists to stop AI-
It's impossible for a scientist to tell all that's going to happen because of his idea. And as long as it's not the person who comes up with an evil application (especially if the person comes up with a positive application), why should the person have a feeling of guilt about his discovery. After all, we can't blame Newton for an airplane crash (note, I'm not saying airplanes are evil)

Hope this has been a small bit entertaining, if not too late;

Brad

Excellent quote, I had seen some good ones, but that is probably the best.

Sean

I think that AI will (on balance) be a force for good rather than evil, although certainly it will be misused. I'd be interested to hear your arguments against AI (Terminator 2 aside). However, it will be pursued by researchers whether it is good or bad, just because they can, and it's too intriguing not to.

Brad, I agree, the elections were disgraceful, that's why I found it so surprising that someone was writing an article about how they indicated that democracy was working properly!

If I remember correctly, did'nt Alice fall down the rabbit hole because she was bored with the book with no pictures?

If we have AI, and if we can create a genius AI, will duplication of the code for that AI necessarily produce another genius AI if it is placed in different conditions?
Can a genius AI be constructed by someone who isn't a genius? (barring accidents.)

I'm told that all democracy is mathematically unsound anyway...

Tom, It should'nt produce another genius, should it? If it is real AI.

Can the laws of maths and science be used to create an alternative to democracy, better than it mean?

I think the mathematical answer to this question is no, by Arrow's theorem.

I've never looked into that last question, but I'd suspect that there is no easy way to mathematically gauge a systems ability to succeed. The actions of people are simply too hard to predict. Besides that, that depends what you mean by a good system of government. If you mean that which produces the most money, it's possible to find a best way to do this, but if you mean a government that makes the most happiness, I believe that anything done scientifically on this would have to make too many assumptions to be anything but academic or trivial.

Brad

Arrow's theorem says that there is no "perfect" voting system, where perfect means it satisfies a small number of inoffensive axioms (like, it has to produce a result whatever everyone votes, it isn't "dictatorial", i.e. nobody's vote counts more than anyone else's, etc.) However, voting systems are only a very tiny aspect of a form of government, so Arrow's theorem doesn't rule out better possibilities. For an interesting alternative system of economics and some suggestions for alternative governmental forms, check out ParEcon - which is interesting because it has been rigorously analysed using economic theory. On voting systems, the American Mathematical Society uses the best voting system I know of to elect their president, approval voting. In this system, everyone ticks the candidates they approve of (i.e. the ones they wouldn't mind having as president), and the most approved candidate becomes president. However, I think Brad has correctly assessed the situation, a mathematical analysis of voting systems or of forms of government is probably not going to be that useful.

somebody once of philosophers 'whenever they are right they are saying something trivial, and whenever they say something nontrivial they are almost always wrong'. Now, I'm not sure I agree with this about philosophers, but I certainly think it's true for mathematicians trying to determine mathematically the 'best' voting system. Given current 'democracy' in the western sense, there are so many practical problems regarding media coverage/access to voting stations/power of large corporations/etc. that any discussion about what an ideal voting system is is very largely academic. So I also agree with Brad.

Sean

Brad, I agree with your thought of not being able to build a system which keeps everyone and all factors good, like money and happiness. However, I think that the rules/goverment would vary in much detail, depending which part of the world implemented it, ie to get the best 'system'. A sort of tailering of your jacket it the closest I can come up with. For example Eastern countries with strong religious beliefs and way of life and implement a different perfect living system than say, western goverments, who like materialism etc. So, people in different countries can weigh out by a fair voting system of what is more important money/happiness/employment/materialism/religion/equality to them and when the new laws are written up it can match their needs. Also, is it not possible to divide a country up mathematically (according to area and natural wealth oil/hils/coal etc) and let each sector of the the country have a max num of people who can live there, and then get peope to vote under who they want to live under. Is that not fairer, however this is to idealistic and like an idea, it does not always happen as it should. What are more specific probems with this idea, can how can science/maths me helped to create this type of system? Another thing, what would happen if you lived in a society with no 'money' how would life be like? What would make people happy?

PS: sorry about the grammar of this posting, got to rush off now.

Dan,
I've started reading some stuff off ParEcon, its a pretty meaty read. Thanks for the link.