Insane physicists and mathematicians

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The discussion revolves around the intersection of mental health and genius in the fields of mathematics and physics, with participants sharing anecdotes about notable figures like John Nash and George Ellery Hale. The notion of "crazy" is explored, with some arguing that eccentric behavior can stem from intense intellectual focus rather than true mental illness. The conversation touches on the idea that many brilliant minds, such as Newton and Tesla, exhibited traits that could be classified as unstable or eccentric, yet they contributed significantly to their fields. Participants debate whether it is possible to accelerate mass beyond the speed of light, with a consensus leaning towards the impossibility of this due to the infinite energy required as mass approaches light speed, in line with Einstein's theories. The discussion also highlights the stigma surrounding mental illness, particularly in relation to creativity and intelligence, questioning whether the pressure to conform to societal norms can stifle potential. Overall, the thread reflects on the complexities of genius, mental health, and the societal perceptions of both.
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Anyone heard any stories of great mathematicians and physics going crazy? I always find those stories entertaining.
Physics question: Do you think it is theoretically possible to accelerate mass beyond the speed of light? How certain are we of Einstein's prediction?
 
Physics news on Phys.org
define "crazy" in this particular context.
 
Originally posted by betyoudidntthink
Anyone heard any stories of great mathematicians and physics going crazy? I always find those stories entertaining.
Physics question: Do you think it is theoretically possible to accelerate mass beyond the speed of light? How certain are we of Einstein's prediction?

Well, if you had to deal with abstract Maths, which are virtual descriptions of our Realictic world, then it is enough to test the greatest minds. Of course just contemplating Time within in Nature is enough to make the most craziest? or sane? person undistinguishable!

Of course there is the route wherby one can just label certain theories and their functions as Fantasy, stringtheory and Quantum Mechanics rely on this very notion, wether this is just a vail for the sane outsiders,is open to question.

Yes it is possible to accelerate mass beyond the speed of light, ask any Fantacist!
 
Originally posted by betyoudidntthink
Anyone heard any stories of great mathematicians and physics going crazy? I always find those stories entertaining.
I don't know the entire background to this but there is the story of George Ellery Hale. He was one of the founding fathers of CalTech and was the main fundraiser for Mount Palomar. He had some serious psychological problems. It is said that he had an imaginary elf who acted as his advisor. Whether he went crazy or he was always like that I don't know.

For more on Hale see
http://scienceworld.wolfram.com/biography/Hale.html

Physics question: Do you think it is theoretically possible to accelerate mass beyond the speed of light? How certain are we of Einstein's prediction?
No. The faster the particle moves the larger its mass becomes and approaches infinity as v -> c. Thus it would take an infinite amount of energy to accelerate an elecrtron to the speed of light.
 
Originally posted by NanoTech
define "crazy" in this particular context.

I don't know about the neccesary conditions. How about a sufficient one? Anyone who has an imaginary elf as an advisor is a sufficient reason to refer to them as "crazy."
 
Does John Nash qualify as "crazy"?
Is he just eccentric?
Or maybe, just very imaginative?

I think (as passe and cliche as it sounds) that the line between brilliant and crazy is very thin.
The closer you get to it (from either side) the closer you get to crossing it.
I am not sure, however, who is really qualified to say which side of the line someone may live on.
 
There are a small number of mathematicians, especially who had mental problems. John Nash has been mentioned. Kurt Goedel suffered from clinical paranoia at the end of his life.

But I don't think the rate of mental problems in the "great scientist" category is any higher than in the general population. Einstein was as stable as they come, Feynman too. All the founders of quantum mechanics and quantum field theory and string physics had/have their wits about them.
 
Originally posted by selfAdjoint
Einstein was as stable as they come, Feynman too.
Stable in what sense? It's pretty well known that Einstein had some serious marital problems early in his life. I recall someone once saying I'd love to buy Einstein a beer but I wouldn't introduce him to my sister.

It's also be speculated that he was perhaps dyslexic. Highly intelligent people tend to be.
 
Yea John Nash was crazy, he started seing people, that must be reason enough to be classified as crazy.

I reckons Tesla was Crazy aswell, but not so sure.
 
  • #10
Theodore Kaczynski (aka the Unabomber) .
A Harvard graduate, former math professor at Berkeley, and a murderer - he was as unstable as they come, passing judgement on who should live or die (i.e. the socially elite)

On a minor note he was a plagiarist.
 
  • #11
Originally posted by Andy
Yea John Nash was crazy, he started seing people, that must be reason enough to be classified as crazy.

Just as a clarification, I'm pretty sure John Nash didn't see people, he only heard voices. Still qualifies as crazy though.
 
  • #12
Ah well, in the film he was seeing people, damned hollywood if you can't trust them then who can you trust!
 
  • #13
Originally posted by master_coda
Just as a clarification, I'm pretty sure John Nash didn't see people, he only heard voices. Still qualifies as crazy though.

There is always( I think it is correct to state this), some sort of traumatic event?.. that tips people from a balanced footing to one that is deemed 'unstable'by those people around the victim who are not experiencing the Trauma?

I have heard it said also that many top?..students get pushed closer to the 'edge'? as so much is expected from them?

The expression 'Close to the Edge' can relay much about a person, but without actually giving any insights to what this person is experiencing, even machines can go 'Ballistic'

http://physicsweb.org/article/world/17/1/3

Also it is one of my favorite music Albums of all time:http://yescography.tripod.com/closetot.htm



Album-Song-Close to the Edge, Lyric snippit:The time between the notes relates the color to the scenes.
A constant vogue of triumphs dislocate man, it seems.
And space between the focus shape ascend knowledge of love.
As song and chance develop time, lost social temp'rance rules above.
Ah, ah.

Then according to the man who showed his outstretched arm to space,
He turned around and pointed, revealing all the human race.
I shook my head and smiled a whisper, knowing all about the place.
On the hill we viewed the silence of the valley,
Called to witness cycles only of the past.
And we reach all this with movements in between the said remark.

Close to the edge, down by the river.
Down at the end, round by the corner.
Seasons will pass you by,
Now that it's all over and done,
Called to the seed, right to the sun.
Now that you find, now that you're whole.
Seasons will pass you by,
I get up, I get down.
I get up, I get down.
I get up, I get down.
I get up.


And a collarge of colors(my interpretation/doodles for fun?)

http://groups.msn.com/Youcanseehomefromhere/tempusfugititalsodrags.msnw?action=ShowPhoto&PhotoID=8
 
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  • #14
Ranyart, both are beautiful. Too bad that the flash from the camera washed out the bottom of the picture. You did that picture? I am very impressed.
 
  • #15
Originally posted by Evo
Ranyart, both are beautiful. Too bad that the flash from the camera washed out the bottom of the picture. You did that picture? I am very impressed.

Thanks Evo!

Well the truth is that it was intentional(second try-first was to faint), I was reaching for..well a Jungian conscious image! with a Unrugh Radiation, coupled mode of transportation.

Spelling mistakes aside, the picture answers the question?..without actually having a question in the first place, its meant to be viewed, and I assume the veiwer will ask:Whats it all about?

The title gives the answer! a pre-determined perspective?..who knows:wink:
 
  • #16
Originally posted by ranyart
Thanks Evo!

Well the truth is that it was intentional(second try-first was to faint), I was reaching for..well a Jungian conscious image! with a Unrugh Radiation, coupled mode of transportation.

Spelling mistakes aside, the picture answers the question?..without actually having a question in the first place, its meant to be viewed, and I assume the veiwer will ask:Whats it all about?

The title gives the answer! a pre-determined perspective?..who knows:wink:
What's the significance of the Dark Side of the Moon triangle/rainbow at the top of the image?
 
  • #17
Originally posted by Tsunami
What's the significance of the Dark Side of the Moon triangle/rainbow at the top of the image?

If you take a close look from the WhiteHole light source at the right>through the Blackhole Prism(connecting space), the rainbow has a definate border, cutoff point?..follow it through to the left Low energy Gas cloud?

There is a 'Hologram impression' The rest may be up to you, as I'm not saying to much!
 
  • #18
It's interesting how modern medicine has so greatly expounded what consitutes mental illness. If a child wishes to pursue an interest fervently in isolation he must then be anti-social; indeed, he must suffer from social anxiety disorder, so let's get him medicated! I think an Einstein quote best exemplifies this:

Solitude is painful when one is young, but delightful when one is more mature.

Indeed, it can be, and it is my opinion that many Einstein'esque minds were lost due to parental ambitions to prevent such solitude. The solitude that the likes of Newton and Einstein enjoyed in the creation of their magnum opus' would most certainly be considered a fit of mental illness by today's standards. I've even read reports by psychologists who indicated that Newton suffered from manic-depressive disorder.

If they had the menagerie of medication available for such ostensible mental dysfunction as we do today, would we still have the Principia? Would Isaac Newton on Prozac be the Isaac Newton? Why is there such a need to render such scintillating intellects quiescent? I understand there are legitimate illnesses that require attention, but it seems we are all too quick to medicate our children at the slightest abberation from the socio-norm.
 
  • #19
Originally posted by Descartes
Indeed, it can be, and it is my opinion that many Einstein'esque minds were lost due to parental ambitions to prevent such solitude.

And how many Einstein'esque minds were lost due to parents ignoring their solitude?

Arguments involving peoples children becoming the next Einstein generally don't have much merit. They're generally based on speculation, not really solid facts.


Of course, I'm not saying that children aren't overmedicated. I think too much emphasis is put on being "normal", whatever that's supposed to mean. But this just isn't a very good argument.
 
  • #20
Later in life, Faraday suffered from debilitating depression.

Tesla suffered his whole life from severe obsessive-compulsive disorder. He was compelled to perform lengthy, pointless tasks before allowing himself to do something he needed or wanted to do, fearing that if he didn't there would be dire consequences. He could not eat, for instance, unless he first calculated the volume of the bowl or dish holding his food.
 
  • #21
Originally posted by zoobyshoe
Later in life, Faraday suffered from debilitating depression.

Tesla suffered his whole life from severe obsessive-compulsive disorder. He was compelled to perform lengthy, pointless tasks before allowing himself to do something he needed or wanted to do, fearing that if he didn't there would be dire consequences. He could not eat, for instance, unless he first calculated the volume of the bowl or dish holding his food.
There you are! I wondered where you went! Hotel California, huh? Must have been FUN!

So...I'm assuming Tesla did not also suffer from obesity...?:wink:

Maybe all of the additional 'hard-wiring' needed for brainiacs to do what they do causes a lot more short-circuiting problems than in the non-brainiac population. I wonder what the percentages would be?
 
  • #22
Originally posted by Tsunami
Maybe all of the additional 'hard-wiring' needed for brainiacs to do what they do causes a lot more short-circuiting problems than in the non-brainiac population.

Or, maybe the brilliant ones understand better what reality is and how we should/shouldn't act.
Perhaps they know that the rest of us are really the crazy ones.
Maybe the maniacal laughter of the psychotics is really jubilation because they realized that the rest of us are all nuts and all the rules we follow are just absurd.
Maybe it is the laughter of relief.
 
  • #23
Originally posted by Tsunami
There you are! I wondered where you went! Hotel California, huh? Must have been FUN!
It's weird. I'm all checked out but for some reason haven't left yet.
So...I'm assuming Tesla did not also suffer from obesity...?:wink:
He was always on the lean and underfed side.
Maybe all of the additional 'hard-wiring' needed for brainiacs to do what they do causes a lot more short-circuiting problems than in the non-brainiac population. I wonder what the percentages would be?
It seems to me there is less craziness among the major scientists of western civilization than there is among its major artists and composers. A scientist can't succeed without retaining a large capacity for logical thinking, whatever side problems interfere.
 
  • #24
Originally posted by zoobyshoe
It's weird. I'm all checked out but for some reason haven't left yet.
I've missed you!

It seems to me there is less craziness among the major scientists of western civilization than there is among its major artists and composers. A scientist can't succeed without retaining a large capacity for logical thinking, whatever side problems interfere.
Good point, Mr. Zooby. Idiot savants can 'excel' in a number of arenas. Writing, painting, mathematics... Correct? (Have you ever seen any research of PET scans done on an idiot savant? Thay might be very interesting.) And I haven't found that they have changed that term, yet! Isn't that term considered somewhat politically incorrect?
 
  • #25
Originally posted by master_coda
And how many Einstein'esque minds were lost due to parents ignoring their solitude?

That isn't what I said. You pulled a single sentence out of context and rephrased it.

Arguments involving peoples children becoming the next Einstein generally don't have much merit. They're generally based on speculation, not really solid facts.


Of course, I'm not saying that children aren't overmedicated. I think too much emphasis is put on being "normal", whatever that's supposed to mean. But this just isn't a very good argument.

My point was simply this: Children considered overly nuanced today are often medicated, and as a result whatever creative/intellectual ferver they experienced in their previous states are greatly diminished. It's this attempt to normalize the behaviors of everyone that I disagree with.
 
  • #26
Originally posted by Tsunami
I've missed you!
Everything's been breaking here. I had to pause to learn about stuff like water heaters.
Idiot savants can 'excel' in a number of arenas. Writing, painting, mathematics... Correct?
Not writing. They mainly excel in things that are based on their prodigious memorization abilities.
(Have you ever seen any research of PET scans done on an idiot savant?
No, I haven't run across anything along these lines.
And I haven't found that they have changed that term, yet! Isn't that term considered somewhat politically incorrect?
Autistic/savant is the term universally used now.
 
  • #27
Originally posted by zoobyshoe
Autistic/savant is the term universally used now.
I had come across that term at this site
http://www.directessays.com/viewpaper/84021.html

before I posted to you, but at a glance I didn't think they were the same thing. Thanks for the info. And you're right about the writing, of course. Don't know what I was thinking. Must be the sleep deprivation... If I get a chance, I'll do some research and/or quiz some docs tonight about the PET scan.
 
  • #28
I seem to recall reading somewhere on PF that the guy who discovered PCR was fairly nutzo. Of course, the idea for PCR came to him while he was on acid! LSD of course being a psychomimetic inducing mental conditions somewhat similar to schizophrenia.

Tesla may not have been the craziest, but he was definitely the most prototypical Mad Scientist ever. I mean, he seriously entertained the idea of building a death ray. Poor guy didn't realize he could've just bought one from Acme.
 
  • #29
I seem to recall reading somewhere on PF that the guy who discovered PCR was fairly nutzo. Of course, the idea for PCR came to him while he was on acid!

Absolutely true. I read an interview with him in the Berkeley Journal.

https://www.physicsforums.com/showthread.php?s=&threadid=7933&perpage=12&highlight=lsd&pagenumber=1
 
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  • #30
Also, for many years Feynman was a drunk.
 
  • #31
Originally posted by hypnagogue Tesla may not have been the craziest, but he was definitely the most prototypical Mad Scientist ever. I mean, he seriously entertained the idea of building a death ray. Poor guy didn't realize he could've just bought one from Acme.
Close examination of the fine print reveals that Acme sell the Tesla death ray.
 
  • #32
Originally posted by Tsunami
If I get a chance, I'll do some research and/or quiz some docs tonight about the PET scan.
Yes, I'm betting it would be interesting to find out what parts of their brains they favor.

The freakiest pet scan I ever saw was one of a bipolar person in a manic state: both hemispheres fully lit up and glowing everywhere.
 
  • #33
Originally posted by zoobyshoe
Close examination of the fine print reveals that Acme sell the Tesla death ray.

Good detective work, Zoob. Now this begs the question: if Lou Gehrig can miraculously contract Lou Gehrig's disease, how is it that Tesla could live his whole life without stumbling across the Tesla death ray? I guess the death ray market was too big back in those days.
 
  • #34
Originally posted by zoobyshoe
The freakiest pet scan I ever saw was one of a bipolar person in a manic state: both hemispheres fully lit up and glowing everywhere.

I wish I could get my brain to do that.

Wonder how they managed to catch that. "Are you in? OK, good. Now, be manic on the count of 3."
 
  • #35
Originally posted by zoobyshoe
Yes, I'm betting it would be interesting to find out what parts of their brains they favor.

The freakiest pet scan I ever saw was one of a bipolar person in a manic state: both hemispheres fully lit up and glowing everywhere.
Did they indicate that this was a unique phenomenon or is this how all bipolar manic brains look with PET?
I've been searching for images, but no luck yet. There are lots of articles available (I googled PET scans + austic savants) - one of which indicates a left anterior temporal lobe dysfunction (which is also present in schizophrenics) dx'd from a PET scan, but I don't know yet if this is typical of all savants.
Interesting...
 
  • #36
Originally posted by hypnagogue
I wish I could get my brain to do that.

Wonder how they managed to catch that. "Are you in? OK, good. Now, be manic on the count of 3."
Sometimes, a trigger is all that's needed. For me, it's the musical intro to original Star Trek. They just put me in the scanner and start playing it, and I immediately go into an intensly manic state. :wink: They have to strap me down so I don't go ballistic and try to destroy the sound system thinking I'm trying to kill Captain Kirk.
 
  • #37
Originally posted by Tsunami
Did they indicate that this was a unique phenomenon or is this how all bipolar manic brains look with PET?
As I recall this was presented as a typical manic PET. It was juxtaposed with a schizophrenic PET which showed strange darkness in the frontal lobes.
I've been searching for images, but no luck yet. There are lots of articles available (I googled PET scans + austic savants) - one of which indicates a left anterior temporal lobe dysfunction (which is also present in schizophrenics) dx'd from a PET scan, but I don't know yet if this is typical of all savants.
The trouble is there are too many different things that "schizophrenia" can be. It's really a grab bag diagnosis they've never been able to link to a definite cause.
 
  • #38
Originally posted by hypnagogue
Wonder how they managed to catch that. "Are you in? OK, good. Now, be manic on the count of 3."
I wasn't sure if you were joking or not, but in case not, the way they "catch" this is easy: a manic episode can last weeks. Normally they're shorter; a few days, but there would almost always be time to do a PET scan.
 
  • #39
Originally posted by zoobyshoe
The trouble is there are too many different things that "schizophrenia" can be. It's really a grab bag diagnosis they've never been able to link to a definite cause.

This is a little OT, but this isn't entirely accurate. At the very least, schizophrenia is no more "grab bag" than bipolar disorder. It isn't just some disease assigned to people when they have a mental illness we can't diagnose.
 
  • #40
Originally posted by master_coda
It isn't just some disease assigned to people when they have a mental illness we can't diagnose.
Yes, I wasn't clear. What I mean is that the list of possible causes is a grab bag: enlarged ventricles, brain infections, too much dopamine production, too many dopamine receptors, improper metabolism of sugars, and others.
"Schizophrenia" describes a range of symptoms without providing a clue to the actual cause in a given individual. My sense about bipolar from what I've read so far, is that the bag of speculative possible causes contains a lot fewer items.
 
  • #41
Master-coda is right, the diagnosis of schizophrenia, bipolar etc is much more of an exact science than personality disorders, subtle variation of autism such as Asperger's etc. The latter can require 8 hours of neuropsycological testing before it can be made. Zooby shoe is right in that we really don't know what causes it. For that matter, we don't know what causes ADHD, bipolar disease, major clinical depression, OCDs etc.

I think associating untreated mental illness with "freeing" a brilliant mind is erroneous. The majority of homeless wanderers who are unable to contribute to our society are untreated schizophrenics etc. Remember, most schizophrenics and bipolars are normal until they reach a certain age and a "psychotic break" occurs...so bringing up medication of children does not apply to them. This was the case with John Nash. This was the case with my brother, a physicist at Princeton. Luckily, he was a bipolar which is much easily treated. He went from wandering around homeless and undergoing repeated instituionalization in Los Angeles until I got him to stay on his lithium. He is now a full time, brilliant consultant and is productive, creative and happy. As for medicating kids, let's not forget that teenagers have the highest rates of successful suicides...brilliant or not, that pretty much puts them out of the picture if we are to ignore real clinical depression in teenagers. I think some of the bad taste associated with medicating children involves those with ADHD. Tha'ts because some were misdiagnosed (either just chronically sleep deprived, over caffeninated and sugarized etc.) The latest Lancet continues with further proof that this is a physical disease, (less frontal temporal brain size and greater amount of grey matter by MRIs.) PET scans show a almost silent brain...even a alzheimer's patient has more activity on a PET scan and the PET scan changes when an activator such as strattera or ritalin is added. This was at a neuro conference at Wake Forest Medical School in North Caroline two years ago.

Anyway, that's my two cents worth.
 
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  • #42
Originally posted by adrenaline I think associating untreated mental illness with "freeing" a brilliant mind is erroneous.
I agree with this 100%. The percentage of mentally ill who might do something brilliant is exceptionally small compared to the overwhelming majority who are just suffering.
 
  • #43
Originally posted by adrenaline
I think associating untreated mental illness with "freeing" a brilliant mind is erroneous.

I also definitely agree with this. Most people with a mental illness are like most people without one...they are not geniuses. Avoiding treating them because we don't want to "level out" a brilliant mind seems irresponsible to me.
 
  • #44
As good as it is, and [Helen and Henry] Wright's is one of the best scientific biographies available [of George Ellery Hale], she does stand guilty of starting a terrible misconception about Hale's mental state. It is generally well known that Hale suffered from nervous breakdowns that were at times completely incapacitating. Wright gets the credit for starting the story about Hale's supposed little "elf" that visited and talked to him, and who has come to represent his illness. Historians William Sheehan and Donald Osterbrock trace it to a misunderstanding of one of Hale's letters to a friend and note that the "'demon' (the word he actually used) was a metaphor, referring either to his conscience or to his depressed mood (like Winston Churchill's 'black dog'), and certainly not an apparition." ...

Book Review of Explorer of the Universe: A Biography of George Ellery Hale (History of Modern Physics and Astronomy, Vol 14) at booksunderreview.com

***

I was rather hoping it was true myself...

P
 
  • #45
I'm not sure I understand. Hale used the term "demon" as a metaphor and they changed demon to "elf"? If so, why did they do that?
 
  • #46
The first paragraph of my post was from a book review by John Rummel in Capital Skies. You may find the text at:

http://www.madisonastro.org/capskies/2002/2002_10/Cap_Skies_2002_October.pdf

I was unable to find the Sheehan and Osterbrock source that he cites for the 'elf' story being spurious. I did find one book by Osterbrock, on the history of the Yerkes Observatory, that confirmed that Hale suffered from mental illness as an adult, but there was no mention of either metaphorical demons or actual elves.

Perhaps someone has a copy of the Sheehan and Osterbrock text? Or a source that can give the text of the letters upon which the story is allegedly based?

P
 
  • #47
The Sheehan and Osterbrock quote comes from a letter published in the New York Times in response to a statement in a book review by Carolyn Hughes. I contacted John Rummel, and he forwarded me a link to the letter to the editor:

To the Editor:

Concerning Carolyn T. Hughes's review of Richard Panek's ''Seeing and Believing'' (Books in Brief, Feb. 14), it is certainly true that George Ellery Hale was the greatest telescope builder of all time. He was also a manic-depressive who had several nervous breakdowns. But it is a complete myth that he thought he was visited by an elf who spoke to him. This statement first appeared in an otherwise excellent biography of Hale, ''Explorer of the Universe'' (1966), by Helen Wright, who misinterpreted one letter Hale wrote to Hugh F. Newall, an astronomer friend in England. In reality, Hale's ''demon'' (the word he actually used) was a metaphor, referring either to his conscience or to his depressed mood (like Winston Churchill's ''black dog''), and certainly not an apparition. Nevertheless, the ''elf'' has taken on a life of its own in the history of astronomy, referred to not only by Panek but in several other books and on television programs from PBS shows to ''The X-Files.''
Donald Osterbrock
Santa Cruz, Calif.

This appears at http://www.nytimes.com/books/99/03/14/letters/letters.html
(You must register with nytimes.com to read it, but that's free and painless.)

P
 
  • #48
Thanks for your trouble, rocketcity. It is a situation not unlike that of Maxwell, who never used the word "demon" in proposing his molecule monitoring fellow, but who rather simply called it an "entity".

I wonder if Hale's original letter is written such that it is easy to misinterpret, or if the biographer authentically lacked enough of a poetic bent to realize he was expressing himself metaphorically?

-Zooby
 
  • #49
One of the greatest intellectuals to walk this Earth would be defined as "mentally unstable" by the psychological definitions. Newton was known to be very anti-social and short-tempered to an extreme. e.g never leave his house,never socialize. Would you consider him to be "crazy" after all of the work of genious he developed? I believe there is a fine line between personality disorders and intellectually proficient behavior. What some people perceive as being antisocial, others perceive it as very concentrated on a subject of matter.
 
  • #50
Originally posted by NanoTech
Would you consider him to be "crazy" after all of the work of genious he developed?
Yes, more or less. His accomplishments were in spite of whatever psychological problems he had, not because of.

Perfectly emotionally stable people are capable of very great things. Mental problems are not a sign of genius. Go back and read the post by Adrenaline in this thread: mental illness 99.99999 % ot the time simply incapacitates people.
 
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