
College Notebook by Isaac Newton - r4um
http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/20
======
lambdaphage
I'm always surprised when reading the notes of scientists and mathematicians
working in previous centuries to see just how steeped they were in synthetic
geometry. This was taken to an extreme in the case of the Principia, but one
can't read Gibbs or Maxwell either without realizing that they felt Euclid in
their bones in a way that few people do today, with possible exceptions for
mathematicians trained under the Soviet system.

~~~
atmosx
Why are the mathematicians trained under the Soviet regime an exception?

~~~
lambdaphage
I don't know-- usually the answer to such questions about academic priorities
is "because it was cheaper", but they just seemed to emphasize geometry much
more at the K-12 level. It's a generalization, of course, but a pretty robust
one. One of my professors came from Kazakhstan, and once casually remarked
that a certain problem on a homework set was "impossible unless you were
Russian", since the proof was easy if you knew a certain proposition from
Euclid, but extremely tedious without it.

EDIT: this interview with Izaac Wirzsup comparing the Soviet and US systems
confirms my prejudice:

    
    
      Another extremely harmful feature
      of [the US] school mathematics programs
      is that only about half of our students
      take geometry, and for only one
      year, generally in a concentrated high
      school course. Students cannot be
      expected to master the material taught
      in this way. Moreover, they are not
      being taught solid geometry, and they
      rarely have a workable perception of
      three-dimensional space, which is so
      essential for studying science,
      technical drawing, or engineering.
      Soviet children study geometry
      extensively for ten years, including
      two years of solid geometry.

~~~
netcan
Jut from my own common sense it seems like geometry is important for
understanding the relationship between abstract things and concrete things.
It's easily understandable that shapes are described by geometry and it seems
obviously useful. The square footage of a house. The volume of a bath.

If you try to describe what Calculus is or does, it's abstractions of
abstractions. Rates of change or 'angle of a curve for a certain values. I
think it's hard for students to see this as something useful or even see how
it's a description of the world that opens up ways of understanding it.

~~~
jjoonathan
I don't see calculus as an abstraction of abstractions. The fundamental idea
is completely geometric: "break the domain of a problem into a bunch of pieces
that can be easily described and related (e.g. by physics) then put the pieces
back together." Time is a first-class dimension. Abstractions only enter the
picture when you want to separate the problem of picking a mesh from the
problem of representing mesh elements.

Differential operators perform the task of "breaking into pieces" in a mesh-
invariant way. Differential forms are mesh-invariant pieces. Integration is
the mesh-invariant description of putting the pieces back together.

It's convenient that differential forms can be interpreted physically (by
normalizing, associating with geometric elements, etc) but I'd hesitate to
associate them with any single physical interpretation (e.g. rates of change)
because doing so de-emphasizes the generality of the approach; you can have a
rate with respect to distance, area, or volume just as easily as a rate with
respect to time.

Leibniz notation makes the hop from the geometric approach to the "operator
that maps a function to a function" approach seamless, and since the latter
description isn't nearly so intuitive, I've always suspected that the
geometric approach could profitably be taught first.

------
hawkharris
On a technical note, kudos to Cambridge for developing this beautiful platform
for interacting with documents -- and for doing it without Flash.

On a personal note, everything I wrote during my college career suddenly seems
a little less substantial...

~~~
frik
The page uses SeaDragon (Ajax edition) from Microsoft former "Live Labs". It's
the same infinite zoom technology that powers also Photosynth and DeepZoom
both from Microsoft.

[http://en.wikipedia.org/wiki/Seadragon_Software](http://en.wikipedia.org/wiki/Seadragon_Software)

------
quarterwave
Reminds me of an incident (I forget where I read about it) where Dirac is
giving a lecture in Europe, someone asks a question & Dirac has to start
working it out on the board - and Ehrenfest turns around and yells: Kids, now
we can see how he does these things!, or something like that.

------
3rd3
I wished they would show notebooks like these early in school: "Look, this is
the pinnacle of human thought and it's full of corrected mistakes, scribbles,
attempts and mnemonics".

------
zxexz
Thanks to Cambridge for making this available to the general public, under a
CC 3.0 license! The images are crystal clear, and easy to read. Props to
Newton, as well :)

~~~
dredmorbius
Considering the original works are well outside of copyright, applying CC 3.0
to the images themselves really isn't especially grandiose of them. Though I
appreciate their not trying to assert control.

~~~
leoc
IIRC getting unencumbered high-resolution images of, for example, famous
paintings in public galleries is still far from assured, so (grading on the
curve) it's not to be underestimated.

------
pitchups
This is truly fascinating - a peek into the earliest thinking of arguably one
of the greatest scientific minds who ever lived. It never ceases to amaze me
that Newton, almost single-handedly and working all by himself pretty much
laid the foundations for much of science for the next several hundred years.
And in all likelihood, it all started with the thoughts he formulated while
writing in this little notebook!

~~~
stiff
This is simply completely untrue. Newton synthesized a lot of earlier results
in physics and mathematics into a unified framework, and he deserves a lot of
credit for that obviously, but nevertheless it was a synthesis and not
something done "single-handedly and all by himself", in fact you are
contradicting Newtons famous own words that he was "standing at the shoulders
of giants".

Isaac Barrow, Newtons teacher, had already discovered the rudiments of
calculus:

[http://en.wikipedia.org/wiki/Isaac_Barrow](http://en.wikipedia.org/wiki/Isaac_Barrow)

Hooke played a significant role in establishing the law of universal
gravitation:

[http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gra...](http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation#History)

Newtons first law comes from Galileo's principle of inertia:

[http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newto...](http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton.27s_1st_Law)

And so on and so forth, lookup Kepler, Galileo, Huygens, Hooke, Barrow,
Descartes, Fermat and so on in the Wikipedia, or better read any serious
scholarly history of physics about this period, this is only scratching the
surface of people whose work Newton very directly built upon. There is no
synthesis to be done without a period of establishing a great many of
particular results.

~~~
JoeAltmaier
Easy to dismiss genius as 'obvious', don't err too far on that side! Newton
was certainly the greatest Scientist in a couple of centuries, instrumental in
advancing three areas of Science. Not single-handedly certainly but nothing we
ever do works that way.

Hooke, btw, was an enemy of Newton. Hooke would publish books of drivel about
'what if' physics worked by a certain equation; Newton derived why physics
Must work a certain way. 'Hookes Law' of springs should be another of Newton's
laws, but Hooke had actually written down that spring law with no proof and no
motivation, but nevertheless published first. Newton argued (correctly) why
springs worked that way. So a basic rule of physics has the name of someone
who did no physics.

Or so the story goes.

~~~
stiff
I do not deny his genius, but popular accounts of scientific work certainly
tend to overemphasize individual contributions and downplay the overall
incremental progress a generation of scientists of various statue can make. It
has the practical effect of discouraging young people from doing actual
scientific work on small, particular results, instead they feel they should
immediately have an idea for a grand theory of everything.

~~~
Myrmornis
Practical consequences are irrelevant to questions of historical veracity.

------
Oculus
This reminds me of a blog I read by Stephen Wolfram discussing his viewing of
Leibniz's notes.

[http://blog.stephenwolfram.com/2013/05/dropping-in-on-
gottfr...](http://blog.stephenwolfram.com/2013/05/dropping-in-on-gottfried-
leibniz/)

~~~
factorizer
I like this Wolfram guy. Blogging about Leibniz and the first sentence is
obiously about stuff "he made" that now makes the world a better place.

Yeah yeah, Leibniz, Newton, Einstein and Wolfram. What a team!

~~~
atmosx
I recently read a quote on "Quicksilver" (Stephenson's novel) about his
imaginary character "Daniel Waterhouse":

"Daniel was angry with God. God had implanted on him a passion for natural
philosophy. He wanted to be one of the greats. But God brought him on earth
the same era with individuals like Hooke, Leibniz and Newton. What where the
chances?"

At this point in the novel, only Daniel has a clear view on Newton's genius,
Hooke was renowned and Leibniz was not into mathematics (he studied to lawyer
first, then turned into mathematics according to the novel, but knowing
Stephenson I think it's true).

~~~
jayvanguard
His interactions with Newton are what got me hooked on the book. Brilliantly
done.

------
misiti3780
This is one of the most interesting posts I have seen on HN in a while. kudos

~~~
camus2
I agree, this is huge.

~~~
purpleturtle
These are the types of comments that will soon disappear thanks to the magic
of Pending Comments™.

~~~
hayksaakian
In all seriousness, does this comment tree contribute to the discussion of the
OP?

------
pbhjpbhj
Page 31, [http://cudl.lib.cam.ac.uk/view/MS-
ADD-04000/31](http://cudl.lib.cam.ac.uk/view/MS-ADD-04000/31), has errors in
just about every numeric value it seems.

The page reads (from the manuscript image, interpreting the abbreviations)
"[...] an arithmetic progression increasing from an unite by 1 composeth
triangles by 2, composes squares by 3, composes pentangles by 4, hexangles &c.
as 1.2.3.4.5.6. composes the triangles [...]".

In the "Transcription (normalised)" this is

"[...] an arithmet: progres: increasing from an unite by b=2 formula composeth
triangles. by a=5/3, composes squares. by y=22/61, composes pentangles. by
x=33/61, hexang: &c as 1 compose the triangles 2 &c likewise 3 compose 4 &c So
1.2.3.4.5.6. compose the quintangles [...].

It appears nearly all the 'MathML formulas' are wrong? There is also a textual
transcription error "quintangles" which should read "triangles".

This is the only page I looked at. The "Transcription (diplomatic)" appears to
bear the same errors. If this page is typical I hate to think how the hard to
read or complex mathematical pages have been rendered in transcription.

Edit: I've just noticed that the erroneous MathML formulas are correct
renderings of other expressions on the same page, this is probably a
coding/markup error?

~~~
CamDigLib
Thank you for spotting this. The transcriptions for the Newton papers are
supplied by a third party (The Newton Project,
[http://www.newtonproject.sussex.ac.uk](http://www.newtonproject.sussex.ac.uk))
so we will pass this onto them. At a quick glance at a few pages it seems
browsers are rendering various sections differently which may account for some
errors. Thanks again, Cambridge Digital Library

~~~
pbhjpbhj
FYI then I'm using FF 28.0 on Kubuntu 13.10.

I see the same in Google Chrome browser version 33.0.1750.152 and in Opera
12.16.

------
chronolitus
I see no straightforward way to download the entire notebook, only one image
at a time.

It would be pleasant to be able to read the thing offline, it's frankly
fascinating. Great post!

~~~
pbhjpbhj
I was on page 31, the download was
[http://cudl.lib.cam.ac.uk/download/image%252Fjpg/document-
im...](http://cudl.lib.cam.ac.uk/download/image%252Fjpg/document-
image31.jpg?path=/content/images/MS-ADD-04000-000-00031.jpg) ... I think a
simple curl or wget with a range from [0]1 to 340 should work?

wget example.com/{1..30}.html

gets docs 1.html, 2.html ... 30.html FWIW.

You may not be authorised to do that of course.

~~~
escherplex
Initially tried using WinHTTrack on the document folder but DL rate was only
25kB/s. So if mentally you resort to sublimated-OCD mode the whole notebook
can be downloaded, one page at a time, then combined and cropped in Acrobat
for offline reading in about 1/2 - 3/4 hour. Final size = 80MB (and a very
nice .pdf it is to have in your archives!)

Curious to see the use of Y^e and Y^t for the words 'the' and 'that' in the
mid 1600s. Figured they would have reverted to the 'thorn' letter rather than
the earlier French printer's substitute.

~~~
pbhjpbhj
It is interesting - also his curly e and the use of pentangles, and such.

Looking around briefly I found this
[http://ocp.hul.harvard.edu/reading/commonplace.html](http://ocp.hul.harvard.edu/reading/commonplace.html)
listing of manuscript books by date. In particular this,
[http://pds.lib.harvard.edu/pds/view/14003562?n=5&imagesize=1...](http://pds.lib.harvard.edu/pds/view/14003562?n=5&imagesize=1200&jp2Res=.25&printThumbnails=no),
from early 1600s uses the same y^e form.

I tried to find Wren or Boyle's manuscripts but a 2 minute search didn't yield
them.

~~~
escherplex
Found BBC has the Royal Society - Boyle manuscripts archive online at:

[http://www.bbk.ac.uk/boyle/boyle_papers/boylepapers_index.ht...](http://www.bbk.ac.uk/boyle/boyle_papers/boylepapers_index.htm#bp02)

A casual but chronological search of the material suggests Y^e was colloquial
but in the process of fizzling out. Boyle, unlike the young Isaac, also made
extensive use of the descending 's' (looked like an 'f' without the horizontal
bar). As a kid, after seeing all these 'f-s' in ancient books you probably
wondered whether people back then collectively spoke with a lisp. [fun
diversion]

------
tsenkov
Now, whoever finds an error in Newton's exercises would feel like a god. :)

------
donniezazen
I take extensive amounts of notes to keep myself awake and focused. I rarely
go back and refer to them.

------
fogleman
Nice. I'm kind of surprised how readable his english is (i.e. it hasn't
changed too much)

------
theef
love this. slight nitpick, might be helpful for an intern or somebody to help
clear up some of the {illeg} pieces that can't be read artificially.

edit: switched browsers, hover over {illeg} is understandable.

------
jayvanguard
I'm just glad to see he can't draw circles well either.

------
Dale1
Super Magical and ever so geometric comment here <<

