Uncle Johannes speaks

[Martin]

Johannes Kepler was the greatest mathematician ever.

 

I found some quotes of his recently.

 

http://www-groups.dcs.st-and.ac.uk/~history/Quotations/Kepler.html

 

From a 1605 letter

 

My aim is to say that the machinery of the heavens is not like a divine animal but like a clock (and anyone who believes a clock has a soul gives the work the honour due to its maker) and that in it almost all the variety of motions is from one very simple magnetic force acting on bodies, as in the clock all motions are from a very simple weight.

Letter to J. G. Herwart von Hohenburg, 16 February 1605, KGW 15, 146.

 

From the introduction, written in 1618, to Book V of The Harmony of the World. Kepler's elation at finding that a planet's orbit period is the three halves power of its average distance

 

Now, eighteen months after the first light, three months after the true day, but a very few days after the pure Sun of that most wonderful revelation began to shine, nothing restrains me; I give myself up to the inspired frenzy, I taunt mankind with the frank acknowledgement that I am stealing the golden vessels of the Egyptians to build with them a tabernacle to my God, far from Egypt's borders. If you forgive me, I shall rejoice; if you are enraged with me, I shall bear it. See, I cast the die, and I write the book. Whether it is to be read by the people of the present or of the future makes no difference: let it await its reader for a hundred years, if God Himself has stood ready for six thousand years for one to study Him.

The Harmony of the World (1619), Book V, Introduction. Trans. E. J. Aiton, A. M. Duncan, and J. V. Field (1997), 391.

 

 

On how he discovered his Third law, the 3/2 power relation, on 8th March, 1618

:

...and if you want the exact moment in time, it was conceived mentally on 8th March in this year one thousand six hundred an eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labor of seventeen years on the observations of Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely certain and exact that the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances ...

Harmonice mundi (Linz, 1619) Book 5, Chapter 3, trans. Aiton, Duncan and Field, p. 411.

 

What is translated here as "the sesquialterate proportion" is how he referred to the THREE HALVES POWER. The Latin root SESQUI- stands for one-and-a-half, like sesquicentennial celebration means 150th anniversary----the one and a half century mark.

 

I wanted to be a theologian; for a long time I was unhappy. Now, behold, God is praised by my work even in astronomy.

Letter to Michael Maestlin, 3 October 1595. KGW 13, 40.

 

 

Geometria una et aeterna est in mente Dei refulgens: cuius consortium hominibus tributum inter causas est, cur homo sit imago Dei.

Geometry is one and eternal shining in the mind of God. That share in it accorded to men is one of the reasons that Man is the image of God.

Conversation with the Sidereal Messenger [an open letter to Galileo Galilei]: Dissertatio cum Nuncio Sidereo (Prague, 1610) KGW 4 308, lines 9 - 10.

 

The cause of the six-sided shape of a snowflake is none other than that of the ordered shapes of plan(e?)ts and of numerical constants; and since in them nothing occurs without supreme reason -- not, to be sure, such as discursive reasoning discovers, but such as existed from the first in the Creator's design and is presented from the origin to the day in the wonderful nature of animal faculties, I do not believe that even in a snowflake this ordered pattern exists at random.

The Six-Cornered Snowflake, (Prague, 1611), edited and translated by Colin Hardie (1966), 33.

 

 

To me "stormed the darkness of my mind" is strong poetry. I think he was a poet as well as a great mathematician.

 

I think that in the history of every planet where mathematics takes root in the living creatures, there is a day when the first truly elegant natural algebraic relation is glimpsed by someone.

 

Not a trivial thing like the area is the SQUARE of something or the volume is the CUBE of something. Those are whole number powers----just multiply the thing by itself a couple or so times, merely some basic polynomial law.

 

Then one day one of the creatures realizes for the first time that the heavenly bodies are following a THREE HALVES POWER LAW. It is a coming of age for that planet, and it sparks the fitting of evermore sophisticated elegant algebra to nature.

 

For us, in the Earth case, it was Johannes Kepler.

 

And the day was March 8, 1618

 

Everything we think of as science that is at all mathematically subtle came after.

[Martin]

Just came across a German version of the passage at the end of the introduction to Harmony Book V

 

I don't have Kepler's Latin, but the German version gives a bit more perspective on it----and he may have been thinking it out in German as he wrote it down in Latin, originally.

 

My copy is partly blurred and illegible so I have to guess at some words

 

 

Jetzt, nachdem vor achtzehn Monaten das erste Morgenlicht,

vor drei Monaten der helle Tag,

vor ganz wenigen Tagen aber die volle Sonne

einer höchts wunderbaren Schau aufgegangen ist,

hält mich nichts züruck.

 

Jawohl, ich überlasse mich heiliger Raserei.

 

[this has to be one of the great lines of all time, given the situation. "Jawohl, I give myself up to holy madness". Raserei means, I believe, frenzied raving madness. Kepler had discovered something about the heavenly motions the likes of which had not even remotely been conceived before. It must have been quite an experience. and he said Jawohl, and went with it.]

 

Ich trotze höhnend den Sterblichen mit dem offenen Bekenntnis:

Ich habe die goldenen Gefässe der Ägypter geraubt, um meinem Gott daraus

eine heilge Hütte einzurichten weitab den Grenzen Ägyptens.

 

I believe that "trotze höhnend den Sterblichen" would nowadays be best rendered as

"I give the finger to everybody" but literally I guess it means

"I spite defiantly and mockingly the mortals, i.e. the mankind."

In other words SCREW EVERYBODY I'M WRITING MY BOOK.

 

Verzeiht ihr mir, so freue ich mich. Zürnt ihr mir, so ertrage ich es.

 

(remember you could easily get burned for the wrong opinion in those days. indeed

Kepler's mother did time in jail for being a witch and came within an inch of being burned----she was confronted with instruments of torture but refused to confess. all sorts of things could happen if you antagonized the wrong people. but he simply says

 

IF YOU FORGIVE ME, SO I'M HAPPY ABOUT IT. IF YOU ARE ANGRY, I'LL BEAR IT.

 

Wohlan ich werfe den Würfel und schreibe ein Buch für die Gegenwart oder die Nachwelt. Mir ist es gleich. Es mag hundert Jahre seines Lesers harren, hat doch auch Gott sechstausend Jahre auf den Beschauer gewartet.

 

In any case I'm throwing the dice right now and I'll write this book whether it is for today's audience or for the future. I DON'T CARE WHICH. It can wait around for a hundred years until it gets a reader----after all God has waited for 6000 years until someone discovered what he did (until I discovered his pattern of planet motions)

 

very spunky guy. feisty little sucker.

[matt grime]

Not sure I condone the assertion that Kepler was a mathematician.

[Martin]

Not sure I condone the assertion that Kepler was a mathematician.

 

his title at the HRE court was "mathematicus"

 

science did not exist as a set of institutions and professions

there werent any people called "physicists"----that came later

 

I didnt check but I think the HRE Emperor was called Rudolf

and I think he had his court in the city of Prague

and I think he appointed Kepler to be his "mathematicus" around 1600

 

as a practical matter, the main job of the Imperial Mathematician was to compute horoscopes

 

 

whatever modern-day category you choose to apply to the 1600s Kepler, I think the emergence of the concept of empirical science, and of the various professions that implement it, is interesting history

 

IIRC Kepler's first real university job was in the Mathematics Faculty

(he did a stint initially teaching Latin Poetry, because there was no opening for him as mathematician, but soon moved over into the regular Math faculty-----this was when he was younger, before the Imperial appointment.)

[matt grime]

Well, I'm also not sure that I would label what was called mathematics pre1800 as mathematics as we now know it either.

[Martin]

Well, I'm also not sure that I would label what was called mathematics pre1800 as mathematics either.

 

it's your call what you call it---and it's possible you are joking but I will reply as if completely serious for sake of discussion

 

it was a different culture and worldview back then and one option is to try to see them at least partially ON THEIR OWN TERMS

 

 

the medieval/renaissance college curriculum (before you got into specialties like Law, Theology, Architecture, Medicine to prepare you for some kind of work) consisted IIRC of SEVEN SUBJECTS of which the first three were related to verbal (Latin grammar, rhetoric, logical argument called dialectic that combined logic and debate)

they were called the TRIVIA because there were three subjects

 

and the other four, the QUADRIVIA, were Arithmetic, Geometry, Music, Astronomy

and strangely enough that was what a mathematician was the expert in.

 

not in actual practical music, like singing, but knowing about proportions---the theory of music as then understood.

 

so, whether it seems right or wrong to us now, a mathematician was someone who they thought could understand and teach quadrivia subjects like Arith, Geom, Astro, and Music (theory I guess one would say)

 

 

I think it is interesting that when Kepler wrote his great 1618 book Harmonice Mundi (The Harmony of the World) he tried to UNIFY several parts of the quadrivium.

He tried to come up with a model of the solar system that he related to MUSICAL INTERVALS and also to the PLATONIC SOLIDS-----he wanted to relate the distances to planets to these geometric figures one inside the other, and to Pythagorean freqency ratios

 

In a sense Kepler was PRE-SCIENCE and one of the big reasons we have a math-based science at all is because he found deep mathematical relations in the solar system-----in effect triggering Newtonian mechanics and several centuries of mechanistic explanation.

 

I think it is reasonable to wonder what universe-models might look like in 2400 AD

 

and ask if what you or other mathematicians do circa 2000 will look as recognizable or unrecognizable to them in 400 years

as what Kepler was doing in 1600.

 

If you don't recognize Kepler 1600 work as mathematics that would suggest that maybe in 2400 the research that our Math faculties do today will also be hardly recognizable as mathematics.

 

Id say that, to me, stuff accomplished by Pythagoras, Euclid, Archimedes, Hipparchus, Kepler is sort of the essence of mathematics and typifies what it can do for us-----its ability at times to transform culture and inspire revolutionary change. Like the moment that Einstein first read Euclid's elements, as a kid, and was changed by that, was a moment that defines something for me. An essence that is millennia-class--- effectively for always (or what passes for always).

 

 

Anyway, it will be 8 March in a few days, Matt.

How would you like to observe Kepler Day?

Would you like to observe it at all? and if so what notice shall it be given?

[fua]

Just a little question.

I have read that you had accessed the original books.

Can you tell me (or put the latin extract) of the meaning of mean distance?

As you probably know there is a little correction to the semplified notation mean distance = major semiaxis.

I comes out that the correct (proven) approach is that the mean distance should be the time averaged mean distance.

What was the Kepler original notation for mean distance?

Spatial based or time based?

Thanks to everybody

 

Fua

[fua]

OK,

after a quick search it seems that the data at that time were related to the major axis (starting from Copernicus data).

So the original law was related to the relation between the major axis of the ellipse and the period.

As a matter of fact, having a time-averaged distance sounds difficult!

Andrea

[Martin]

OK,

after a quick search it seems that the data at that time were related to the major axis (starting from Copernicus data).

So the original law was related to the relation between the major axis of the ellipse and the period.

As a matter of fact, having a time-averaged distance sounds difficult!

Andrea

 

Indeed some years ago I did look at the Latin text of Harmonice Mundi but my xerox copy and notes have gotten buried. I might not be able to locate them.

 

I think you are right---the distance he was talking about was the major axis of the ellipse, or half the major axis.

 

Half the major axis is also the "mean" of the nearest and farthest. So in a simple way one can think of the semimajor axis as the planet's mean distance from sun.

 

You may be better with Latin than I (who am no great scholar!) and I would be interested to hear about any more looking into this that you do.

 

IIRC it is the introduction to the 4th book of the Harmonice that is so interesting (but my memory is unreliable about this)

 

that is where he says that on 15 May 1618 the realization about the "sesquipotentia" (one and a half power) returned to him and "stormed the darkness of my mind"

 

his description of the experience of discovery and his triumphant feeling about it come across very vividly in English and so I was curious to know how it sounds in the original.