数学家兼作家莉莲 R.利伯谈科学、艺术与数学能力之平衡

武夷山

    Lillian R. Lieber（莉莲 R.利伯，1886-1986 ）是出生于俄罗斯一个犹太裔家庭的美国数学家，也是作家。她属于担任过数学领域重要学术岗位的第一代女数学家，在长岛大学做过数学系主任。

    她一辈子写了17本书，其中普及相对论的一本书受到爱因斯坦夸奖。1953年，她发表了一部名著，书名为Infinity: Beyond the Beyond the Beyond （无限：超越之超越之超越）。为此书绘制插图的是她的丈夫、插图家Hugh Gray Lieber，他比莉莲小10岁。该书面向普通读者介绍了“无限”的概念，也探讨了人生哲理：如何成为有限然而完整的、平衡的人。

在该书第二章，她写道：

自然，你晓得

无限

这个主题

总是引起所有人

深深的兴趣

所有人包括

笃信宗教者

诗人

哲学家

数学家

以及T.C. Mits（博主注：书中的一个角色）

（一个著名的普通男人）

还有他的伴侣

Wits

（一个普通的女人）。

你也许亦对无限感兴趣，

否则你不会打开此书。

    该书第一章的标题是“我们的好朋友Sam”。她写道：

对那些没见过SAM的

我想非常简要地

小结一下

他的老相识

也许已经知道的情况，

然后再向你们所有人

讲述他更多的故事。

首先，

SAM这个名字

最初取自
Science（科学）, Art（艺术）, Mathematics（数学）;
但我现在发现

以下解释更加合适：

S表示我们与外部世界的接触；

请注意

我没说

S表示“事实”或“现实”，

因为

我们所能得到的

关于外部世界的

唯一知识

是经由我们的感官

或“延伸的”感官——

如显微镜、望远镜等

它们帮助我们看得更清楚

或是无线电等

它们帮助我们听见一些声音

若没有无线电

我们根本感受不到这些声音的存在，

等等，等等。

但是，当然啦

世上

也许还有

更多的事物

我们尚且感知不到

无论是直接通过我们的感官

或求助于我们的神奇发明。

因此，声称

我们“真的”了解外部世界

其实是很狂妄的。

因此我想对S

给以较谦虚的解释

我强调

S只代表

我们能够接触到的

外部世界的一部分——

因此，即使S

也具有“人性的”内涵。

接着：

SAM中的A表示

我们的直觉，

我们的情感——

爱、恨、恐惧等

因此自然也有

“人性的”内涵。

M表示

我们做出推断的能力

因此包括

数学、逻辑、“常识”

和其他方式

我们利用这些方式

在“结果”发生之前

就在心智上将其导出了。

因此，M也是

充满“人性的”单元。

于是，SAM完全是人性化的

尽管它们不是具体的个人。

进而言之，

科学家利用着自身内部的SAM

因为他必须做出

“观察”（S）

他必须利用自己的“直觉”（A）

以帮助自己形成

一组很好的基本假设，

他的“推理能力”（M）

将帮助他从假说中

引出结论

而这些结论又得

加以“检验”（又是S！）

看看它们是否“正确”。

或许你在想

SAM和科学家

其实是一而二、二而一的，

而我所做的一切

无非就是建议大家都成为

科学家！

但你很快就会发现

完全不是那么回事。

因为，

首先，

太经常发生的是——

呜呼——

当一个科学家

并未实际开展

其科研工作的时候，

他也许“放松”一下

不那么认真地

利用其S、A和M

他会随便张望一下

与我们其余人一样。

    后面，她谈到艺术家也要利用SAM，谈到过度倚重SAM中的一项有什么问题。我不再翻译了，附原文。

Being a SAMite and being a Scientist
are NOT one and the same.

Besides,
a SAMite may not be a Scientist at all,
but an Artist!
For an Artist, too, must use
his “S” in order to “observe” the world,
his “A” (“intuition”) to sense
some basic ways to translate his
“observations”,
and his “M”
to derive his “results” in the form of
drawings, music, and so on.
Thus an Artist, too,
WHEN AT HIS BEST,
is a SAMite.

    接着，她谈到健康的自由和病态的自由：

Now consider a person
who is SOMETIMES or OFTEN like this:
SaM.
He is evidently relying very heavily on
his “intuition”, his “hunches”, his “emotions”,
hardly checking to see whether
the “observations” of the outside world (“S”)
and his own reasoning powers (“M”)
show his “hunch” to be correct or not!
And so,
precious as our “intuition” may be,
it can go terribly “haywire”
if not checked and double-checked
by “S” and “M”.
Thus, a person who
habitually behaves like this
is allowing his “S” and “M” to
become practically atrophied,
and is the wild, “over-emotional” type,
who is not only a nuisance to have around,
but is hurting himself and
not allowing himself to become
adjusted to the world he lives in.
Such a person,
with an exaggerated “A”,
and atrophied “S” and “M”,
has a feeling of “freedom”,
of not being held down by “S” and “M”
(“facts” and “reason”) ;
but, as you can easily see
this makes for Anarchy,
for a lack of “self-control” —
and can lead
to fatty degeneration from
feeling “free” to eat all he wants;
to the D.T.’s from
feeling “free” to drink all he wants;
to accidents because
he feels “free” to drive as fast as he wants
and to “hog” the road;
to a sadistic lack of
consideration for others
by feeling “free” to
kick them in the teeth for “nuttin'”;
to antisocial “black market” practices
from a similar feeling of “freedom”,
giving “free” reign to the “A”
without the necessary consideration of “facts” (“S”) and “reason” (“M”).
Needless to say this is a
PATHOLOGICAL FREEDOM
as against
a NORMAL, HEALTHY FREEDOM of
the well-balanced SAM
which is so necessary in society
in which EACH individual
must be guided by the SAM within himself
in order to avoid conflict with
the SAM in someone else.
This is something that
a bully does not understand —
that if he acts like a pathological sAm,
he induces sAmite-ism in others,
as in mob violence;
this is indeed a horrible “ism”
that can destroy a society as well as
individuals in it.

    她又讨论了另一种不平衡：只看到分离的事实，看不到完整的大图景。

Similarly,
there is the Sam type:
he may be called the “tourist” type —
running around seeing this and that
but without the “imagination” (“A”)
or the reasoning power (“M”)
to put his observations together
with either heart (“A”) or mind (“M”),
but is concerned only with
ISOLATED BITS OF INFORMATION:
he is like the man who,
seeing a crowd had gathered,
wanted to know what happened.
and, when someone told him
“Ein Mann hat sich dem Kopf zerbrochen”
(It happened to be in Germany),
corrected the speaker’s grammar
and said “DEN Kopf!”
He knew his bit of grammar,
but what an inadequate reaction
under the circumstances.
don’t you think?

    接着她描述了一些过分理性的人。

And there is also the saM type —
one who can reason (“M”)
but starts with perhaps
some postulate (“A”) favoring murder.
Such a man would make
a wonderfully “rational”
homicidal maniac or crook
who could plan you a murder
calmly and rationally enough
to surprise any who are not familiar with
this sAM type of pathological case.

    总之，她这本书的宗旨就是要通过SAM来考察自身和他人的行为。

Thus SAM gives us a way of
examining our own behavior
and that of others,
taking into account the “facts” (“S”),
and using imagination and sympathy (“A”)
in a rational way (“M”).

Are you perhaps thinking,
“Well, this may be interesting,
but
why all this talk about SAM,
when you are writing a book about
Infinity?”
To which the answer is:
The yearning for Infinity,
for Immortality,
is an “intuitive” yearning (“A”):
we look for support for it
in the physical world (“S”),
we try to reason about it (“M”), —
but only when we turn
the full light of SAM upon it
are we able to make
genuine progress in considering
Infinity.

    她最后强调，即使一个很平衡、不走极端的SAM人，也只满足了必要条件，而不是充分条件。

There is only one more point
I must make here:
Namely, that
even being a well-balanced
SAMite —
and not a pathological anti-SAMite
like SAM, etc. etc. —
is NECESSARY but NOT SUFFICIENT.
You will probably agree that
it is further necessary
to have our SAM up-to-date.
For he is a GROWING boy,
and what was good enough for him in 1800
is utterly inadequate in 1953;
and unless the “S” is up-to-date
and the postulates (“A”)
and reasoning (“M”)
are appropriately MODERN,
we cannot make proper

s definitely NOT the
ANARCHICAL freedom of SAM,
but is a sort of
CONTROLLED FREEDOM —
controlled by facts and reason
and is therefore SELF-controlled
(by the SAM within us)
and hence implies
VOLUNTARY COOPERATION rather than FORCE.
Thus anyone who demands
“freedom unlimited” as his right,
is a pathological SAM,
a destructive creature;
whereas,
in mathematics
you will find the
CONTROLLED FREEDOM of SAM
and you will feel refreshed to see
how genuine progress can be made
with this kind of freedom.