lindsay at niagara falls

historical potpourri

Subject: HISTORICAL POTPOURRI from whence we came

GEORGE WASHINGTON


Guard against the impostures of pretended patriotism.
George Washington

Over grown military establishments are under any form of government inauspicious to liberty, and are to be regarded as particularly hostile to republican liberty.
George Washington

The constitution vests the power of declaring war in Congress; therefore no offensive expedition of importance can be undertaken until after they shall have deliberated upon the subject and authorized such a measure.
George Washington


THOMAS JEFFERSON

I do not find in orthodox Christianity one redeeming feature.
Thomas Jefferson

I have recently been examining all the known superstitions of the world, and do not find in our particular superstition (Christianity) one redeeming feature. They are all alike founded on fables and mythology.
Thomas Jefferson

I hope we shall crush in its birth the aristocracy of our monied corporations which dare already to challenge our government to a trial by strength, and bid defiance to the laws of our country.
Thomas Jefferson

I sincerely believe that banking establishments are more dangerous than standing armies, and that the principle of spending money to be paid by posterity, under the name of funding, is but swindling futurity on a large scale.
Thomas Jefferson

I tremble for my country when I reflect that God is just; that his justice cannot sleep forever.
Thomas Jefferson

In every country and every age, the priest had been hostile to Liberty.
Thomas Jefferson

It does me no injury for my neighbor to say there are twenty gods or no God.
Thomas Jefferson

It is incumbent on every generation to pay its own debts as it goes. A principle which if acted on would save one-half the wars of the world.
Thomas Jefferson

JOHN ADAMS

At some points during the war, Adams feared that the cause would fail because he saw too much greed and commercialism in the colonies. "I have seen all my life such selfishness and littleness even in New England, that I sometimes tremble to think that, although we are engaged in the best cause that ever employed the human heart, yet the prospect of success is doubtful not for want of power or wisdom but of virtue." During the revolution, Adams -- evoking the manner of his Puritan ancestors -- told his friend Benjamin Rush that the colonials would only have a chance of winning, "if we fear God and repent our sins." He even speculated that God might intend for America to be defeated so that its "vicious and luxurious and effeminate appetites, passion and habits" would be cleansed, laying the foundation for a more-deserved victory in the future.

Adams wasn't alone in seeing the events on the ground as a reflection -- positive and negative -- of God's assessment. One minister ascribed the Continental Army's difficulties to the presence of slavery. Noting the brutal winter, the poor crops, the loss of cattle, and the seemingly imminent collapse of the army, a Quaker farmer speculated that it was part of a divinely-ordained set of plagues. When on July 20, 1775 the Continental Congress called for a day of prayer, it was accompanied by a call for fasting, self-reflection and a unified effort to "unfeignedly confess and deplore our many sins."

As the government of the United States is not, in any sense, founded on the Christian religion; as it has in itself no character of enmity against the laws, religion or tranquility of Musselmen … it is declared … that no pretext arising from religious opinion shall ever product an interruption of the harmony existing between the two countries. … The United States is not a Christian nation any more than it is a Jewish or a Mohammedan nation.

Article 11 of the Treaty of Tripoli (1797-01-04, which was carried unanimously by the U.S. Senate and signed into law by John Adams

ABRAHAM LINCOLN


The war has gone on some twenty months; for the expenses of which, together with an inconsiderable old score, the President now claims about one half of the Mexican teritory; and that, by far the better half, so far as concerns our ability to make any thing out of it. It is comparatively uninhabited; so that we could establish land offices in it, and raise some money in that way. But the other half is already inhabited, as I understand it, tolerably densely for the nature of the country; and all it's lands, or all that are valuable, already appropriated as private property. How then are we to make any thing out of these lands with this encumbrance on them? or how, remove the encumbrance? I suppose no one will say we should kill the people, or drive them out, or make slaves of them, or even confiscate their property. How then can we make much out of this part of the teritory? If the prossecution of the war has, in exphe conflict itself should cease. Each looked for an easier triumph, and a result less fundamental and astounding. Both read the same Bible, and pray to the same God; and each invokes His aid against the other. It may seem strange that any men should dare to ask a just God's assistance in wringing their bread from the sweat of other men's faces; but let us judge not that we be not judged. The prayers of both could not be answered; that of neither has been answered fully. The Almighty has his own purposes. "Woe unto the world because of offences! for it must needs be that offences come; but woe to that man by whom the offence cometh!" If we shall suppose that American Slavery is one of those offences which, in the providence of God, must needs come, but which, having continued through His appointed time, He now wills to remove, and that He gives to both North and South, this terrible war, as the woe due to those by whom the offence came, shall we discern therein any departure from those divine attributes which the believers in a Living God always ascribe to Him? Fondly do we hope--fervently do we pray--that this mighty scourge of war may speedily pass away. Yet, if God wills that it continue, until all the wealth piled by the bond-man's two hundred and fifty years of unrequited toil shall be sunk, and until every drop of blood drawn with the lash, shall be paid by another drawn with the sword, as was said three thousand years ago, so still it must be said "the judgments of the Lord, are true and righteous altogether"
Abraham Lincoln 1865

A woman is the only thing I am afraid of that I know will not hurt me.
Abraham Lincoln

I can make more generals, but horses cost money.
Abraham Lincoln

I care not much for a man's religion whose dog and cat are not the better for it.
Abraham Lincoln

It has been my experience that folks who have no vices have very few virtues.
Abraham Lincoln

When you have got an elephant by the hind legs and he is trying to run away, it's best to let him run.
Abraham Lincoln


FRANKLIN ROOSEVELT

A conservative is a man with two perfectly good legs who, however, has never learned how to walk forward.
Franklin D. Roosevelt

Don't forget what I discovered that over ninety percent of all national deficits from 1921 to 1939 were caused by payments for past, present, and future wars.
Franklin D. Roosevelt

Here is my principle: Taxes shall be levied according to ability to pay. That is the only American principle.
Franklin D. Roosevelt

I ask you to judge me by the enemies I have made.
Franklin D. Roosevelt

More than an end to war, we want an end to the beginning of all wars - yes, an end to this brutal, inhuman and thoroughly impractical method of settling the differences between governments.
Franklin D. Roosevelt

DWIGHT D. EISENHOWER

An atheist is a man who watches a Notre Dame - Southern Methodist University game and doesn't care who wins.
Dwight D. Eisenhower

Don't think you are going to conceal thoughts by concealing evidence that they ever existed.
Dwight D. Eisenhower

Every gun that is made, every warship launched, every rocket fired, signifies in the final sense a theft from those who hunger and are not fed, those who are cold and are not clothed.
Dwight D. Eisenhower

Here in America we are descended in blood and in spirit from revolutionists and rebels - men and women who dare to dissent from accepted doctrine. As their heirs, may we never confuse honest dissent with disloyal subversion.
Dwight D. Eisenhower

How far you can go without destroying from within what you are trying to defend from without?
Dwight D. Eisenhower

I hate war as only a soldier who has lived it can, only as one who has seen its brutality, its futility, its stupidity.
Dwight D. Eisenhower

In most communities it is illegal to cry "fire" in a crowded assembly. Should it not be considered serious international misconduct to manufacture a general war scare in an effort to achieve local political aims?
Dwight D. Eisenhower

In the councils of government, we must guard against the acquisition of unwarranted influence, whether sought or unsought, by the military-industrial complex. The potential for the disastrous rise of misplaced power exists and will persist.
Dwight D. Eisenhower

No one should ever sit in this office over 70 years old, and that I know.
Dwight D. Eisenhower

The best morale exist when you never hear the word mentioned. When you hear a lot of talk about it, it's usually lousy.
Dwight D. Eisenhower

The purpose is clear. It is safety with solvency. The country is entitled to both.
Dwight D. Eisenhower

The sergeant is the Army.
Dwight D. Eisenhower

When people speak to you about a preventive war, you tell them to go and fight it. After my experience, I have come to hate war.
Dwight D. Eisenhower

MARTIN LUTHER KING

A nation that continues year after year to spend more money on military defense than on programs of social uplift is approaching spiritual doom.
Martin Luther King, Jr.

Discrimination is a hellhound that gnaws at Negroes in every waking moment of their lives to remind them that the lie of their inferiority is accepted as truth in the society dominating them.
Martin Luther King, Jr.

It is incontestable and deplorable that Negroes have committed crimes; but they are derivative crimes. They are born of the greater crimes of the white society.
Martin Luther King, Jr.

Never forget that everything Hitler did in Germany was legal.
Martin Luther King, Jr.

Feb. 4, 1968: "God didn't call America to engage in a senseless, unjust war. . . . And we are criminals in that war. We've committed more war crimes almost than any nation in the world, and I'm going to continue to say it. And we won't stop it because of our pride and our arrogance as a nation. But God has a way of even putting nations in their place." King then predicted this response from the Almighty: "And if you don't stop your reckless course, I'll rise up and break the backbone of your power."

commentarimathhelv

hello again:

to paraphrase arnold swartzenegger, i am back. or rather, i have ceased being back and i am on the road again.

today, i journeyed from rochester, new york, to lausanne, switzerland, by way of continental airlines, newark, new jersey, air india, paris, paris france, and the tgv. actually, it took two days and i was exhausted.

the trip began in the rochester airport where michelle ravenel had dropped me off. a rather mild rain was causing water to leak into their computer system. nonetheless, they were able to get it together and send me on my way.

in Newark, homeland security was in full force. the taking off of shoes, the policy of no liquids, absolutely no pocket knives, not even the dullest swiss army knife, is accepted by the american people. i had to mail mine back to my house at a cost of $9.99. i detect marketing here.

in the restrictions as to what you are allowed to carry, there is no thought, no discrimination. people accept the bush line that they must endure inconvenience, long lines and delays. they are totally cowed. they do not think to ask themselves if all this is necessary. if what is being checked is what should be checked. they do not ask if the dick cheneys of the world have to go through this too. the answer, of course, is no and there is already the beginnings of a security system based on class. yet the american people do not seem ready to rebel, not ready to even get a little nasty and sarcastic in order to insure equality of treatment. fear.

anyway, i left the american security paranoia behind and walked approximately 100 feet to the domain of air india. it was a trip back to the old indian culture. they felt the need to repeat the security check in their own very old fashioned indian way. this meant going through the motions for the sake of appearances, the only purpose being to create a long line to stand in. people wandered back and forth from the supposedly secure area to the supposedly insecure area. there was absolutely no way of distinguishing between those who had been checked and those who had not. it was not chaos. it was pointless obedience by the bureaucracy and uncomplaining resignation by the customers. fortunately, i had lots of time to kill.

the flight on air india was a revelation. it was as if i was in a different time, in a new culture which had more to do with the modern present than the colonial past. most of the people were native indians who were going on to mumbai. inside the plane, the crew and passengers seemed totally normal, that is to say, they seemed western, as if they came from the suburbs of rochester. 30 years ago, i knew some indians of a different sort. for example, i knew harsh pittie (his real name!), who was a totally sophisticated citizen coming from an upper-class indian family. harsh knew and was confident of his place in the world. he was certainly not typical. you could not find enough harsh pitties to fill up an enormous plane. i thought at the time that a more typical case was an indian mathematician at the institute for advanced study who was very insecure. he seemed to live in fear of being sent back to poverty the streets of calcutta. not so the people on the plane. they were just plain folks who seemed to have no hang-ups about their place in the world. perhaps this was because there was such a high percentage of indians on the plane. or perhaps it reflects the transformation of at least part of india to a modern society. if so, it seems to affect both the young and the old.

on the plane, i had a nice lamb curry and the chance to make almost final preparations on my number 5 and number 6 lectures. that leaves only numbers 7 and 8 to prepare. they are fairly well thought out and don’t have to be given for two weeks. so all that is well in hand.

i arrived in paris and was pleased to discover an air france bus which would take me directly to the gare de lyon and my tgv train to lausanne. no problems at all!

arriving in the train station, i paid 50 cents to use a toilet and to wash up. this was an excellent decision.

having time to kill and being hungry, i paid a culinary tribute to richard kane. i had the french version of a bacon, lettuce and tomato sandwich, literally, a bacon, salade, et tomate on a baguette, a BST! tres excellent! especially when combined with a lipton’s ice tea with peach flavoring. it was less sweet that the american version. perhaps because of this, it seemed to have more of the essence of peach in it. ah yes, when it comes to ingestibles, the french seem to understand even the small things.

finally, off i went on the tgv, glad to just sit and nap for 4 hours. it was rather warm in paris but there was snow in the passes as we crossed into switzerland. then it was warm again in lausanne, even at 8 o’clock at night. i took the short steep walk up the hill to the hotel, pulling my luggage behind me. kathryn had told me that a young fellow named Jonathan scott had biked up the hill on his last day here. i couldn’t do that now. but i was reminded of a hill in the finger lakes of new york state which i had once biked twenty years ago. a workman saw me struggling up the hill and remarked that i must be hard as nails to do it. it was of course long before my aortic dissection and i must have been forty pounds lighter. but in my memory, it was a comparable hill, only longer. so i must get rid of those unwanted forty pounds!

i lecture tomorrow. tonight i sleep.

tomorrow has come and gone. the students and i seem to have survived the first two hour lecture. i have an audience of approximately 20. that is a lot of students for a class at this level. i had to leave a few things out but it all seemed to remain coherent. today i give the second two hour lecture and then we have time off for, believe it or not, approximately two weeks before another four hour bunch of talks.

i am still settling in. i need to figure out how to do laundry without paying the hotel the small fortune of 8 swiss franks per shirt. there must be a laundromat somewhere and i will find it. otherwise, i will start doing laundry in the bathtub.

up in the town square, there is a wonderful cafe where i plan to eat breakfast. the pastries looked great and i will sample them together with some cappucino. america has not caught up with europe when it comes to quality of pastry.

i have been paid. it is just like portugal. i have been handed over 4000 swiss franks in cold hard cash and must now worry about where to keep it. for the moment i carry it with me everywhere i go. i plan to learn to use the combination safe which is in the room and relieve myself of this burden.

today or tomorrow i must establish an internet connection. it is the usual situation. i can receive but i cannot send.

time flies! i have now finished 4 hours of lectures. it is hard to believe that, after 3 days here, i am half finished with all i have to present. i still have some preparation to do for the final 4 hours but not so much that i am worried that i cannot do it all in 2 weeks. the localization lectures are over and the chain models lectures are yet to begin. the latter is what they really know well around here and i must prepare it well if i am to survive. my only strength is that i have a different point of view then they have, less explicit, more conceptual, more princetonesque.

for lunch today, i had beef tartare and frites. it was much different than i expected. there was a lot of tomato sauce mixed in with the raw beef. that makes the raw meat much less exotic. kathryn assures me that this is a common way of doing it and it is a good way. her husband is fond of it. so i guess i have passed the beef tartare test. it is as easy as the sushi test. the dish is tasty and good in a quite normal way. it needs no courage or aclimatization to enjoy it. i expected more of a challenge.

i need something different to eat, something which is a true test of swissness. what could it be? like the tibetans, do the swiss have a version of rancid butter that they are fond of? mountain cheeses, while wonderful, tend to be tamer than the smelly lowland stuff the french love. so what is true mountain food? how about cows that die over the winter? or are those only eaten by wolves? there must be some food which will keep an entire winter, probably hard and dry. some food which modern swiss hate but which is still savoured by traditionalists.

they have very good yogurt here, mixed with good things like muesli. that is very swiss. and they have good bread, substantial and tasty stuff. since this is french switzerland, i have not yet encountered a good version of a bratwurst. however, there are hot dog stands and shops to get sandwiches. the turks sell kebobs and falafel which should be tasty.






hello again from the alpha-palmiers hotel in downdown lausanne, right up the hill from the train station: 

i see from the BBC that the weather in the northeastern USA involves a massive return to winter.  even at the masters golf tournament in augusta, it does not seem to be warm.  oh well, it is warm here and that is all that counts for me.

sometimes i cannot see what is right in front of my eyes.  how can one wonder what to eat in switzerland without recalling dairy products?  all those cows up in the mountains are the foundation of a wonderful dairy tradition.  it starts with wonderful yogurt, complete with the ultraswiss addition of birchermuesli, those little bits of fruit, nuts, and grain which are the foundation of good swiss breakfasts.  and here is something which seems to be completely unknown in the USA, buttermilk flavored with fruit, strawberry, cherry, or my favorite, mango.  this is a wonderful thing to do with buttermilk.

and of course, there is chocolate.  but one cannot live by chocolate alone!  you can however almost live on a diet of chocolate milk alone.

the swiss are also famous for melting cheese.  in the winter, they do fondue.  now begins the season for raclette, melted cheese with potatoes. kathryn tells me that one must distinguish between the two forms of melted cheese. i think it is similar to the fact that the inuit have hundreds of names for varieties of snow and we have so few because we don't really understand snow.   this weekend, i am looking forward to having raclette at kathryn's home outside of lausanne.  it is also nice that i have an invitation to do laundry.

today, i am headed off to a large park in the city.  the map shows pictures of mountain goats there.  maybe it is like a zoo.  it is hard to believe that mountain goats could grow wild in the city.  i plan to end the day at a bavarian brasserie with a plate of fois gras. great stuff!

yesterday, i spent the day contemplating an old paper of john moore on universal hopf algebras.  it is amazing that the existence of bipolynomial hopf algebras boils down to the classical fact that all symmetric functions can be expressed in terms of the elementary symmetric functions.  this stuff relates to my current theme. how do certain things stay hidden in algebraic topology but are there nonetheless.  the most striking example is so-called neisendorfer localization but with a large assist from haynes miller, alex zabrodsky, and emmanuel dror-farjoun.   the attempt to cut off the bottom homotopy groups of a finite complex does not in fact get rid of the memory of them.  theory says that you can get them back by a functor.  but, if you don't know beforehand what you are supposed to get back, know one knows what is going on. you only know that the machine makes sausage when you know that you put sausage scraps into it or that you are getting sausage out.   at least one very competent person, aka clarence, has tried and failed to understand this.   

a more elementary example is in the bott-samelson theorem. the loops on a suspension retains the memory of the coalgebra structure of the space which is suspended.   the suspension remembers the something about the space that it is the suspension of.  this is expressed more generally by observing that the eilenberg-moore models have the coalgebra structure in them.  but it comes from the geometry of the eilenberg-zilber map, it is not just algebra. it can be hard to get your hands on.  maybe i can make some contribution to the theory of the eilenberg-moore approximations by coming up with an effective way to get at this. the key word is effective, ineffective theory is not enough.  but the book comes first.

as i typed the above two paragraphs, i realized that i was not addressing my whole audience.  oh well, live with it.  the truth is that i don't write these things primarily for you but to amuse myself in the hotel room.  if you think about it, you realize that there are only a few things to do in a hotel room and, even in switzerland, some of these are illegal.  so, in the absence of nicole kidman, i feel free to type some mathematical thoughts.

i have just returned from my explorations.  i first went to the cathedral, a very impressive place with nice stained glass windows and a wondrous organ which was restored by, among others, the husband of our friend, kathryn lesh. she is a mathematician who finished at MIT at the same time as our kathryn here. the organ is spectacular.

i kept walking until the i reached the large bois de sauvabelin, a park with many hills and a small lake with boats and a restaurant.  it is a very pleasant place which reminds me of the small lake in seneca park in rochester.  our lake is actually nicer, but it is often under threat from our country administration who want to curtail it for various forms of corporate use and development.  on the other hand, the lake here seems to a treasured and lively place with a cafe where you can get coffee, ice cream, and even fondue.  altogether it was a pleasant day. 

during the walk, i thought about what i shall say in my new lectures.  mainly, the first question is:  what is the appropriate chain model for a fibration?  rather than choose the newer quillenesque notion, i choose the older cartan inspired notion of construction.  the difference is that you are doing abelian homological algebra rather than the nonabelian version due to quillen.  i have nothing against the quillen ideas and have even used them in my now ancient rational past.  but the abelian version is sometimes much easier to compute.  so that is what i will use.  i have some convincing arguments that this is not a bad idea. the main theorem of eilenberg-moore is that they give chain models of homotopy pullbacks via cotensor products.   and they have some of the formal properties of fibrations in the sense that cotensor products with these creatures is homologically invariant.  oops!  we are getting a little too technical.

since this is also the land of knives, as in the swiss army versions, i have begun to evaluate the selection of knives with the intent of purchasing an interesting swiss army knife.  in the meantime, i have purchased an opinel, the primitive but very useful french knife which is great for cutting things to eat.  you can never have too many of them and they are cheap.

by the way, i manage the basic tasks of life rather well with my primitive french.  i can not discuss the finer points of philosophy in french but what i have is adequate for expressing what food i want to order, to thank them for it when i get it, and even to express my disgust with george bush if i so wish.  le government de usa, c'est horrible, c'est fou,  no? c'est vrai, oui?  oui, oui!

kathryn tells me that my month's work entitles me to become part of the swiss retirement program. in fact, i am required to fill out the form and assured that i will receive a monthly payment if i bother to inform them when i officially retire.  i suspect that it will not be a massive sum, perhaps enough to purchase one small bar of chocolate per year.  one nice thing about the swiss is that they have rules which they follow.  i suspect that it derives from all those cold winters in the mountains where you had to get along or go outside and die.  but that does not mean that they are as cowed and repressed as the typical american.  far from it!  only in america does puritanism thrive in its peculiar southern mutation. 

last night i returned from my visit to the home of kathryn and her husband felipe in the town of aigle. it is a half hour on the train from lausanne and very pleasantly located in the valley on the way to sion.  there are mountains all around.  local trains will take  you up to the mountain resorts.  it is a very nice place to live and to raise their 4 boys, who are, by the way, quite well behaved. it is a warm place with good skiing a few minutes away up the mountains.  the dinner of raclette (melted cheese with potatoes, mushrooms, and pickles) was excellent and was accompanied by a nice dry white wine of the region. i think i like the pure cheese of raclette better than the mixture of wine and cheese which is fondue.  the town of aigle has a castle and it has the high school which was attended by the great mathematician georges de rham.

today is the monday after easter and, except for places to eat, everything is closed.  tomorrow, i will buy an economical and attractive sweater so that i can impersonate a dressed up person.  today is a good day to prepare some lectures. 

after putting in a good start on the lecture preparation, i decided to meet up with a rhubarb tart i had noticed at the manora, the pleasant lausanne version of a cafeteria.  it was very good with a renverse (= coffee with cream).  afterwards, i walked up to the park in front of the hall of justice.   the blue of the lake and the grey mountains topped with white snow were stunningly beautiful.    it is quite a contrast to the continuing weather reports about the snow in  eastern north america.  the fact that there is enough snow to close the toronto airport makes me think that the situation in rochester is probably not much better.  the big difference between here and there is that the snow here is all high up in the mountains and it is beautiful warm spring-like weather down here.

by the way, i have internet access from the university but not from the hotel. so that is the reason for the gap in messages over the long easter weekend. 




is fonda fond of fondue?


just a little tongue twister in the title, no sense to it, although i am of a generation where many were fond of fonda.  and you must admit that it is musical.

hello once again from warm and sunny switzerland:

just to let you folks know, i sleep with the window open.  it is that warm.

i noticed today that john milnor is giving a lecture in zurich on april 12. the occasion is to honor beno eckmann (it must be his ninetieth birthday). the subject of the lecture is “topology in the 50s and 60s.”  it will probably be a great lecture and very interesting to me who was born as a topologist in the later part of this period. this was, after all, the golden age of topology.  but i soon realized that, small as switzerland is, it would be a five to six hour train ride to get to zurich.  this would not be easy. even though milnor is one of the great math lecturers of my lifetime, i am doomed not to hear him this time.  

i consoled myself by having dinner at a swiss brewery with good beer and a nice strassbourg version of a pizza, a so-called flaming tart with onions, cream, smoked meat, and little cut up wieners on a thin crust.  not bad but it will not replace traditional pizza.

kathryn gave me a delayed easter present, a chocolate egg filled with individual chocolates, sort of a chocolate box of chocolates.  it is made in aigle, her home town.  these are some very good tasting chocolates. 

in contradiction to the above paragraph, i have returned from zurich where they were having a conference in honor of the 90th birthday of beno eckmann.  it was good to see old friends like henry glover, guido mislin, peter hilton, and john milnor.  at least i know them well enough to say hello to.  lunch was at the eigennosishen technishe hochscule in the very pleasant rooftop cafeteria with a lovely view of the city and of lake zurich.  at lunch, jean-pierre serre, perhaps the greatest mathematician of his time if it isn't milnor, happened to pass by, tripped over my knapsack on the floor and almost took a tumble.  as someone said, "that could have been a career ender right there." not that i have to worry about that now. i did not even get a chance to reintroduce myself.  after all, chuck and i proved a conjecture of his and he should be able to recall that.

beno eckmann, 90 though he may be, seems to be in excellent physical condition.  unfortunately, the same cannot be said for peter hilton who is 86 and, while bright and alert, has trouble with his balance. as always, he was very gracious.  i also stopped to say hello to albrecht dold.  he  is very hard of hearing and seems to have some of the symptoms of altzimer's disease.  sad. i don't know what he would do without his wife.  she remembered me much better than he did. when octavian cornea was my student 15 years ago, his work overlapped with some work of albrecht.  in fact, octavian had better results then but there was no doubt that dold still possessed an agile and sharp mind.

the trip from lausanne to zurich and back was a very pleasant exercise in the swiss train system.  zooming back along the lake by neuchatel is very attractive.  at first, i thought the trip would take 5 hours each way but it turned out to be a pleasant 2 hours each way.  the trains zoom through the swiss countryside with a rocking suspension system which the swiss call pendular. the view was not deep mountain scenery but it was quite nice, a mixture of cows and vineyards in different parts.  in switzerland at least, the german swiss seem to have more cows and the french swiss more wine. but my limited survey could be wrong about that. in france, they certainly have a lot of cows.

i learn that the swiss have slightly different electrical outlet plugs than the rest of europe.  the swiss plugs are 3 pronged and thus better grounded but otherwise they seem the same.  my experience is that you can use a european plug in a swiss outlet but not the other way around.  so i will wait until i get to france before buying some plugs.

i gave kathryn a quick outline of my last 4 lectures and she seemed pleased with the minor insights i am adding to the field.  i think that one of the pleasures of mathematical old age is that you have the time to reflect on the best way of doing things.  you do not have to restrict yourself to the quickest way of just getting the job done.  it is a lot like sex in that respect. except that you get better at exposition as you get older.

the weather here is delightful.  we just had coffee outside in the bright sunshine with the mountains and lake in the background, as pretty and idyllic as a postcard. 

kathryn is really enthusiastic about one of my ideas.  i had hesitated to tell her about these particular ideas because i thought she might find them too trivial and obvious.  there is a simple way to express multiplication of loops in terms of maps of homotopy pullback diagrams.  she is thinking about the ideas and has already come up with cute new things to say about them.  she thinks more abstractly than i do and is going to incorporate the ideas into things i would never have thought of.  more power to her.  she is going to bring some life to the subject. i will just sit back and watch.

kathryn thinks that my questions about "change of rings" (whatever that is) are the right ones to ask and is confident that she can answer them in the affirmative.  i hope so.  i can use the machinery if it works. in the writing of my book, i have to do some handsprings to avoid this more natural way of doing things. 

here is a friendly jab at bill singer.  when i emailed him about this issue, he rightly pointed out that i didn't really need to do all this and that i could do what i wanted with constructions that were in an old cartan seminar.  this is true but it is not esthetic.  it only works since you can compute the algebra structure and you know that you have a hopf algebra structure.  if you work over the integers, it turns out that this coalgebra structure is uniquely determined.   so you get the coalgebra structure in a round about way.  it is more esthetic if you can go directly at the coalgebra structure and that is what i want to do.  i repeat, bill is right, but kathryn understands me.  if you start with an algebra, then the homology of the bar construction should give you a coalgebra.  getting an algebra and forcing the coalgebra structure is a form of rape and someday, if not now, you will pay for it. 

i have missed my chance to have duck with olives at my favorite  cafeteria. by the time i got around to it, they had sold out.  instead, i had some nice trout filet with blanched cabbage.  the cabbage was excellent.  don't knock it until you try it.  the blanching makes the cabbage mild enough so that it doesn't overpower the fish.  it goes well.

i was at the main post office and i read a plaque which identified it as the site where, between 1783 and 1793, Edward Gibbon wrote large parts of his "decline and fall of the roman empire."  john harper should pay a pilgrimage to the site even though it is now totally subsumed in a large post office building.  if the building were out of the way, the view would be terrific, as good as the view from the park by the casino.

compared to the dark passions of portugal, the swiss seem to lead a more ordered life.  kathryn tells me that this can be deceptive.  some female  olympic athlete was murdered by her husband in the mountains above where kathryn lives.  it took a long time before they could find him.  this is the dark side of mountain life, probably caused by being cooped up all winter with no way to get away from each other.  like rats in a cage.  somehow it is different from the wild passions of the south.  and different from the loneliness of the fado singer in portugal waiting for her fisherman husband to return from the cod fishery. in fact, the husband has probably drowned.  there is no need to murder him or to be murdered by him and he is fondly remembered. 

i had some fois gras at the bavarian brasserie near the hotel.  it was very good but with a slight taste of liver that was totally absent from the fois gras in provence.  but it was a good sweet fois gras nonetheless.  the only problem was that the waiter mistranslated my french into a half bottle of white wine when i really wanted just a glass.  fortunately, there was no problem taking the unfinished bottle back to the hotel room.

this weekend, i will try to finish the preparation of my last 2 lectures.  this should not be too hard.  i have to do 2 things.  one, i need to compute the mod p homology of the double loop space of an odd dimensional sphere.  this is a straightforward application of the theory i have already prepared.  two, i need to develop hopf invariants so that i can compute the bockstein spectral sequence and achieve the crowning glory of the fact that the integral homology has exponent p.  my last lectures occur next tuesday and wednesday.  in the words of woody woodpecker, 'that's all, folks!"

then i am thinking of running away for a weekend at the hotel mont-collon in arolla. i would spend the weekend at the foot of the glacier.  this place i know well and  i am known there.  i should even get some kind of special welcome.  if possible, it would be pleasant to  hike up to the cabine des rouges aigles (= the cabin of the red eagles).  but snow in the mountains may make that impossible.  if so, i can be a vegetable too.  arolla is the place where chuck mcgibbon discovered the joys of climbing.  i am wondering how he is doing on everest right now. when he reads this, let him know that our solution to the serre conjecture was well received here just as it was in portugal last october.  even though this stuff is old, it is attractive, understandable and it still sells.




once more into the breech:

the more i read about the albigensian crusade and the subsequent inquisition, the more i am convinced that bush and cheney are the pope and simon de monfort of our time. back then, a crusade was said to be needed to suppress heresy but in fact it was motivated by economic reasons. a very wealthy region of france did not believe in worshipping the relics of saints and in enriching the established church. so for economic reasons and for the sheer greed of confiscation a crusade was declared. hundreds of thousands were killed, poor and rich alike. properties were confiscated by the crusaders and became hereditary fiefs. the survivors were made public examples of, were forced to recant, and to make expensive and long pilgrimages. if it had not already been stolen, they often had to abandon their property. Once they reached the pilgrimage site, they had documents to be signed by the local church authorities to prove they had reached the appointed goal. This practice continues today in santiago de compostella but the documents are now signed by more lowly clerics. it is just like the republicans reaping the spoils of washington and of government contracts while preaching a morality they do not live up to. or you can pretend to drive out corruption from the world bank while using the funds to enrich your mistress. in short, we live in a time of hypocrisy, reminiscent of the albigensian crusade but with mass killings not yet in full swing.

i spent saturday in the deserted math building preparing some lectures and looking out the window at the sheep mowing the lawn with the mountains in the background. it was a nice way to finish up the preparation of lecture 7 of 8.

before that, i decided to sample the characteristic swiss potato dish called rosti. it is much like hash browns but served with, for example, mushrooms and veal in a cream sauce. too rich for me. i can do without it. maybe i will try it with fried eggs and ketchup. i think the swiss do a version of that too.

i just took a nice walk down to the lake. i discovered restaurants there which deserve return visits. for example, one place was advertising some mussels and frites. but my dinner plans were already made. all i had room for in my stomach were an expresso, and 3 boules of ice cream. i had this at the universal swiss ice cream restaurant chain, movenpick. the pistachio was astoundingly good. i returned to my hotel room where i had my planned dinner of salad, cheese, and fois gras. even though it was supermarket fois gras it was still rather good.

then i got down to work and finished the preparation of my last lecture. i develop hopf invariants and use them to compute the bockstein spectral sequence of the double loop space of a sphere. old stuff but with some new twists.

now i have no more compulsory work to do and can think in a scattered way. if i get a chance to give more lectures, i will trust that i can lecture on familiar stuff without further preparation. i can always leave out details i don’t remember. i think i remember these details well enough to know that i must leave them out. for example, i know how to get the generators of a kernel inside a free lie algebra but i probably would have trouble proving it works on the spot. instead i would justify it by analogy with the generators for the kernel of a free group. no proofs.

anyway, i have been virtuous enough and have done everything so far pretty much from first principles. if i lecture beyond this week, it is time for me and my audience, if i still have any then, to take a break. we can still talk but we will fly.

brayton has asked me a question about eilenberg-moore spectral sequences. at the moment, my passion is to avoid them by the use of small coalgebra models. then the homological algebra is computing what you want without any nonsense. in this style, you use spectral sequences only for comparison theorems to prove that two things are equal. then you use one of them to get the answer exactly. when it works, it is a joy. but you need to know the space you are looking at, or some of its properties, like maybe that it is the total space of a principal bundle. in this way, you might get a small model for it.

the alpha-palmiers is a fine hotel but i have one criticism of it. i think that i charges too much for an internet connection. it was wonderful to always have an internet connection in my room in portugal. it made it easy to send email, to phone with skype, and also to look up stuff on the web. it is not too bad to have to wait to go to the office and i will survive. but i miss the entertainment.

the office email has one other drawback. i had to change my sender to send. this means that no record is kept of the messages i send out unless i send a copy to myself. i have been forgetting to do this and so i have no record of what i have written except for my longer messages.

once again, cnn is issuing weather warnings against travel in the northeastern united states. i am glad i am not there. it is so warm and sunny here.

cnn does not seem to think that the weather on the top of everest is worth reporting. the closest news is that there is flooding in thailand. if the weather is bad in thailand, it probably is worse in the Himalayan. for chuck’s sake, i hope the weather is good in the mountains.

i am beginning to get worried that there is not enough about food and culture in my messages. this means that i am leading a narrow life with most of my interest being focused on mathematics. that is not a bad thing. i have learned things in preparing the lectures. it will help the book. and it is interesting to me. but somehow i feel i am not living up to the standards set by my hero, anthony bourdain. i don’t feel that i have eaten anything really weird or interesting. the beef tartare was fairly tame. maybe i should go get some more. i read that they can make it hotter. the food is very good but it is not adventurous. after all, how adventurous can yogurt with cereal be? and i actually am not very fond of having my meat prepared in a cream sauce. that is too much dairy. and, if i cared, i don’t think it is kosher.

i had a good pasta with salmon and mussels. but once again it had a sort of curry cream sauce! i will try the thai restaurant in the hotel. i want no dairy mixed with meat. i want some heat, some spice! i need a change.

what would anthony do? even he did not like warthog anus. but he ate it and it had no cream sauce. he also ate ostrich eggs scrambled in an ash fire. eggs are not dairy. chicken are not cows. i need to get something eggy, but without the ashes. do the swiss eat any insects?

what would be the swiss of equivalent of a canadian maple latte? would the swiss sink that low? no, a caramel machiato is their extreme in that direction.

i thought of something. the swiss have some kind of gluey nut cake with whole hazelnuts in it, it seems to be some sort of gargantuan swiss baklava. i will try it. i am desperate. i would even welcome a club sandwich, disgraceful as that would be in anthony’s eyes. seriously, they do have good sandwiches. the bread is wonderful. ok, here is the plan. get a sandwich for lunch and have a thai dinner. maybe shrimp.

another thing that is missing from my messages is a sense of sin. in portugal and spain, the sense of the middle ages was so present, so powerful, that your thoughts were filled with sin and lust. and there was fado. and there was crawling to santiago de compostella on your knees, and there was sophia loren tieing the body of el cid to his horse. all these things to remind you of the dark and forbidden passions. the swiss do not seem to have this. as orson wells said, “the italians have a history filled with murder and lust and they created the renaissance. the swiss have had an orderly life for centuries and the best they could come up with was the cuckoo clock.” maybe it would have been different if william tell had slipped and aimed a little bit lower. putting an arrow through your son’s brain should give a culture a sense of guilt.

but where is the passion? where is the abundance? where is the sophia? heidi just doesn’t cut it. maybe i am underestimating heidi. i don’t know her that well. could yodeling ever match fado? i don’t think so. it is hard to express yearning with a yodel. or any thought at all. and the zither is far too upbeat an instrument.

still i love this country. life here is more the way life should be than most other lives are. it is certainly more beautiful.

wait a minute! i am not that far from geneva! that is where that religious fanatic john calvin reigned. even though the passions are buried deep in calvinism and are not at all attractive, still they were strong, even twisted. i think you can distinguish them from the current southern bush version because they are less hypocritical. predestination is a harder road than republicanism. it is even harder than mormanism. by the way, has there ever been a morman democrat?

so let me see if i can fantasize about calvinism. let us see? first, sex has to be without taking your clothes off. well, that doesn’t help. but you could walk up to the most beautiful girl in geneva and claim that your union was god’s plan.

who could be the sex kitten of this culture? maybe bette davis? or, yuck, joan crawford? this is going nowhere! i hear that jane fonda has gotten religion. so maybe we could combine her past with her now. she would be ok.

what came so easy when you have the image of the smoking censor swinging toward the sky in santiago is so difficult here. and it is easy when you find the bones of an apostle just when you need them 1000 years after he died. this is good stuff! your history is loaded!

what happened to history in switzerland? hasn’t anything deep and disturbing, calvin excepted, happened here since hannibal crossed the alps? i read that julius caesar slaughtered a lot of helvetians but they were not on their home turf at the time. i think they were in provence.

provence and especially langedoc has a dark history, what with the albigensian crusades and all. greed, death, violent men, and poisonous women fill the history of france. and of spain and of portugal. and we don’t even have to talk about italy, the popes, and the medici! even the french thought that catherine de medici was a dangerous piece of work.
and the less said about the greeks, the better. the germans have had different sorts of problems. but they all have history, even the austrians. in terms of big events in history, switzerland is like gertrude stein’s description of oakland, “there is no there there.” people find refuge here, people like vladimir lenin. they run away to here.

don’t think i don’t like it here. i like it very much. right now, i am running away to here.

p.s. you should look up this spelling of the word “breech.” i did and i was surprised. what the hell did henry the second mean when he urged on the english, “once more into the breech!” maybe everything the french say about the english is true?






modeling of chains:

tomorrow i start my lectures on chain models. but first here is some history from wikipedia about how to forge your own chains:

“In 59 BC, Julius Caesar declared he was so shocked by the incursions of the dangerous Helvetii tribe into Gaul, and the suffering of the Gaulish peoples, that he had himself appointed 'protector of the Gauls'. By the time he'd finished protecting them, a million Gauls were dead and Julius Caesar owned most of Gaul.”

sound familiar?

today i took kathryn’s advice and ate at the thai restaurant at the hotel. i ordered a shrimp dish served with a green chili sauce. it was mixed with coconut milk and flavored with lemon grass. superb! this was what i needed. for a change, a meal with no dairy in it. i think that this is definitely a better thai restaurant than we have in rochester. and we do have at least one good one.

the haze had burnt off and the mountains were sharp and clear in the distance. there can be no prettier city than this. poor zurich! it has a nice lake but not lausanne’s nearby mountains.

i finished ina caro’s “road to the past,” an historical guide to a road trip through france. i enjoyed the first half but i am glad to be done with it. instead of the serious and deadly history of the albigensian crusade in the south and of the hundred years war in the middle, we end up in the north of france with the petty concerns related to pretty chateaux, elegant gardens, stylish furniture, and the frivolous intrigues and corruption of the french court in the time of absolute monarchy. such subjects are not worthy of the companion to the biographer of robert moses and lyndon johnson. those are two guys who would fit right into the middle ages.

ina caro seems fascinated by petty privilege and should be writing about the current crop of republicans. in contradiction to their name, our republicans want imperial rome or imperial france. the divine right of kings is their ideal. but bush and cheney are really an ineffectual medieval pope and an ineffectual simon de monfort. vive la revolution! things may have gotten out of hand, but robespierre had a point.

the first two hours of my second set of lectures went ok but this stuff requires more definitions and that takes longer. so i am behind schedule. i will probably have to make it up by assuming that hopf invariants are known and then just using them or by just skipping the use of them altogether. that would be a shame since they tie in so nicely to the computation of the mod p homology of the double loop space of a 2n+1 sphere. oh well, the students are going to soon get the perfection of the xerox of my lecture notes, the lecture notes do it all as it should be done.

i had some sushi for dinner tonight. not very swiss but good basic japanese stuff, just like you can get at the tokyo house in rochester. this is part of my current theme to remain kosher in the sense that i am not mixing meat and dairy. however, my form of kosher encourages the eating of most crustaceans! but not with cream sauce even though melted butter is acceptable.

the lectures are over. i had to rush through hopf invariants and gave only the quickest connection to the computation of bockstein spectral sequences. it could be argued that it was better this way. it was the shortest path to the application may have created the most clarity and interest.

now all i have to worry about are two things: what food to eat and how to get completely over this fluish bug that is wiping out most of my energy.

on the question of food, i plan to revert to more salads and also more sausages. i just want to minimize sauces. the sauces tend to taste too rich for me. some sausage and kraut would be a nice change. no sauce there so even sausage will be lighter. or a nice salad. for some reason, i can’t seem to find tuna sandwiches. in france, they were everywhere. maybe this unhappiness with diet has something to do with this flu. could it be that you need health and energy to properly enjoy food?

i think i am getting better. my energy level seems to be higher. and the phlegm that has been clogging my throat and nasal passages seems to be diminishing. until i get better, i will postpone by quick trip into the brisk mountain air of mont-collon. the presciption calls for hot drinks with honey and for my old reliable cure of submersion in hot bath water. i recall that i survived the pain of the night before the diagnonis of the aortic dissection by spending the night in hot bath water. hence, i have a lot of faith in this cure.

From: jnei@math.rochester.edu
Subject: deskyped
Date: April 21, 2007 11:47:53 AM EDT (CA)
To: michelle@ravenel.net
Cc: lewinjacques@bellsouth.net, norman.stein@wanadoo.fr, rkane@uwo.ca, Jan_Pearce@berea.edu, mbenders@math.hunter.cuny.edu, chuck.mcgibbon@gmail.com, tr@teammedia.net, dancefairy@cox.net, jrobin@math.rochester.edu, dharper1@frontiernet.net, harper@math.rochester.edu, and 11 more…

hello all: i was marveling at the fact that i seemed to be able to make an infinite number of skype calls without having my available credit decrease when,
all of a sudden, my skype ran out and now i am having trouble paying them for more time. bummer! i must wait for a reply from their support service.

i am only now being cured of my horrible chest cold by a product of the swiss pharmaceutical industry. it is called "antigrippine" which, i think, means that
it fights things that have a grip on you. i think that the stuff works. it must be powerful since you are allowed to take only 3 a day. anyway, i am less clogged up and more able to drag my tired body up and down the hills of lausanne.

i have been complaining to kathryn about the overuse of cream in the swiss preparation of meat. she claims that it is all the fault of the german swiss and that
she can make some of the very same dishes more palatable by substituting turkey for beef and by substituting coconut milk with lime juice for cream. in a weak moment, i accepted an invitation to dinner at her house in order to test this hypothesis. actually, i still feel under the weather and probably would have been wiser to just be a vegetable in the hotel.

but i have acquired a bottle of the wine, a white one, which is local to her town and will bring it with me on the train. kathryn makes this trip every day and the beauty of the town and its setting makes it worth it but she does live halfway to sion, 40 minutes on a fast train from lausanne. in my current condition, i regard it as a major journey.

now i have returned from a pleasant dinner at kathryn's. i have learned why kathryn splurges for the first class train ticket. on weekends, this train on frida, is standing room only. fortunately, i arrived early and got one of the few remaining seats. but when it is not so crowded, then you can enjoy yourself and even get some work done. no so on this particular train. it was crowded with college kids going home for the weekend and with italians going home to milan, 5 hours way. there even was an out of place old indian couple. they are much to late to get to aishwarya rai's wedding on time. (in case you haven't heard, this is a enormous event in bollywood!)

as kathryn indicated she would, she did a nice fusion dish of turkey in coconut milk with lime juice. except for fact that this dish was prepared in switzerland, there seemed to be very little that was swiss about it. it was quite good but i was not able to do it justice. i think that you need a certain health level in order to consume and enjoy food. but i could appreciate it abstractly. and the closing dessert of movenpick pistachio ice cream would be irresistable even at death's door. and it combines well with a little bit of movenpick chocolate ice cream. this is swiss dairy as it should be! with no meat in it!

as i write this, i am eating a beet salad. it is wonderful. all my life i have eaten overcooked beets and i have loved them nonetheless. i love these more! as far as i can taste, these have no marinade and certainly no thick harvard beet sauce. it is just pure beet goodness!

one more technical point conquered for the book! it is a simple and old thing but i really have worked out well how george whitehead's suspension operator works in the eilenberg moore game. very nice, very simple, and it proves things that are a mess to do otherwise. actually, i knew before several versions of how this goes. but not i know then in a consistent and integrated way. hooray! even though i am stuck in a time warp in the 1950s.!

and i am pleased also that i am going to add to the book a proof of bott periodicity. it is an illustration of the power of the eilenberg-moore game and also as an illustration of some of its hidden complications, namely the fact that the coalgebra structure, while there, is hard to predict by purely algebraic means. Maybe someday it will be possible. kathryn is inching towards it and it is part of moore's dream but it is a long way off. but it is nice to see that in many cases you can handle it by what harper calls generating complexes.

the bott stuff is old and pretty and historically important and it is nice to be able to do it fast.

i will close now. this is one of those days when the air has no haze and the mountains are sharp and clear. it is a shame i am not ready to walk in them.

best wishes,

joe n


happy birthday to me:

i celebrated my birthday by taking a walk in the park by the palace of justice. it has a wonderful view of the lake and the mountains. the best thing is that i felt healthier and stronger. it was nice just to sit on a bench in the warm sun and to think about how very simple the cartan seminar proof of the bott periodicity theorem really is.

i went to the palace hotel brasserie for a lunch which anthony bourdain would have enjoyed. it consisted of braised beef shoulder and bone marrow and root vegetables. i know now why anthony likes bone marrow. he likes fatty things. and this is a very fatty thing. the beef shoulder reminded me of the traditional irish meal of corned beef except that the cabbage was replaced by root vegetables. not that that is a bad thing. in truth, i enjoyed it and finished it off with an expresso and chocolate mouse. quite satisfactory.

i should add that i was entertained at lunch by a long carnival parade. it was a combination of mummers, astecs, and incas. the south american flute music was very nice as the imitation incas danced by. i was not able to tell whether this parade was the opening of a carnival or some lausanne festival which happens every year. either way, it was a good thing.

the french are holding a presidential election today. a main issue seems to be job security. some people think that there is too much of it, and since it is so hard to fire someone, businesses are very reluctant to hire young people. the result is that the young people are emigrating to, for example, england where they can get jobs.

my generation of mathematicians is aware of the downsides of too much job security. excellent people suffered from the fact that tenured slots were full. on the other hand, the people who are in charge cannot be trusted to make fair decisions. balance is required and, unfortunately, that balance is only maintained in a time of labor shortage.

the pub across the street from my hotel was offering a dinner of horse meat and frites. why not? i have never eaten horse before. it does not taste like chicken but rather like very lean beef. i think cows are better to eat but there is nothing wrong with horse and i do not see why it ever got such a bad reputation.

but the lunch of perch meuniere at university’s copernic restaurant was much better. the perch are from lac leman and are served with potatoes and a nice salad. simple and good.

i made my reservation at the hotel mont-collon in arolla. but i should have checked earlier since they are closing for a spring break and i will have to transfer to another hotel. actually, it couldn’t have been avoided since i really did not want to leave lausanne before friday. at least i get two days at the mont-collon before the transfer.

i will move to another nearby hotel before making the transition to france. all the train schedules are checked and worked. there is no reason not to go and buy tickets and make train reservations. i am ready for a new phase, especially since i have totally soured on getting skype to accept payment for more calls.

best wishes,

joe n



arollaing around the mountains and eating through provence:



hello from the hotel mont-collon, at least we start there:

let me begin with a message to two people that i feel somewhat guilty about
not communicating with.  i speak of michelle ravenel and of kathryn hess but for different reasons.  first of all, realize that i have been in an email dessert in the mountains and now in provence.  so let me announce right here and now that i am well and happy and looking forward to my eventual return to rochester.  let me take this belated opportunity to thank kathryn who was a wonderful host to me in lausanne.  it was swell.  and i found it to be a very productive pace to think about mathematics.  kathryn; thank you again.  and to michelle, i am truly sorry to be such a sorry correspondent.  and, since i am typing this on a french keyboard, let me end now.

by the way, this is what typing on a french keyboard would look like if no care were  taken:  the auick brozn fox ju,ped over the lqwy dog.

i think that the french think that q is a more common letter than a and hence it needs to be more convenient to the fingers.

this message is being sent to you courtesy of norman stein's computer and you should not repy to this address.  not that most of you guys reply much anyway!

the main text begins now!
   
i am now at my favorite hotel in the whole world, right at the foot of the glacier coming off mont collon.  i have been suitably welcomed by madame. and she has informed me that this hotel too now has internet acdess.  so this is still the perfect hotel even though it is going to close in two days until june. madame has promised to drive me up the hill to my new hotel, the hotel du glacier, where they have promised to prepare trout mauniere  so everything has worked out.

i think i will take some short walks and begin to write more of the book.  i need to finish chapter 10.  that is the immediate project.

 i start by turning into book form some classical computations of homology of loop spaces which were the subject of my lectures in lausanne.

 i am perhaps inspired to add something to the book which may seem out of place in a book on algebraic methods in unstable homotopy theory.  but one should always remember that the division into unstable and stable is artificial.

the paper of rene thom on unoriented cobordism is surely a landmark among the papers in homotopy theory in the 1950s.  among other things it is a major illustration of serre’s localization theory and of the usefulness of the computation of the cohomology of eilenberg-maclane spaces and of classifying spaces.

i hope i am not being overconfident but  i am estimating that a nice coverage of the heart of the thom paper can be done in approximately 20 pages. for example, one can compute the additive structure of the oriented cobordism ring very quickly.  with modern methods to determine which modules over the steenrod algebra are free, that is just a question of ranks.  surely, the inclusion of this into the book would be a contribution.

i had hoped that milnor’s work on the complex cobordism ring would provide a clear way to determine the ring structure of a cobordism ring.  alas, milnor only wrote part one and never got around to writing part two which would have included the ring structure.  so there is no version written by the master of exposition.  it is possible that this question of the ring structure is so intrinsically hard that no one can write a beautiful treatment. 

one should always remember that the two most important classical groups are the orthogonal and unitary. ok, maybe the special orthogonal and special unitary are contenders, but after all they have a special relationship to the first two.

 anyway,  it is worthwhile focusing on their properties and those of their classifying spaces.  it is rather easy to get hold of the cohomologies of these groups and of their classifying spaces. 

what seems to be a little difficult in both cases is to identify the cohomologies of the classifying spaces with the symmetric functions in the cohomologies of maximal tori..  from this identification can come the product formulas of Whitney and Chern.  so it needs to be gotten. and at the moment i am having some difficulty recalling this part.  i see a way to do it but it is convoluted, uses a bit of algebra and  some might not like it.  probably, this will be remedied instantly in the presence of milnor’s characteristic classes but for now it is frustrating.

thom’s work is a paper in stable homotopy theory which was born before the creation of stable homotopy theory as a separate subject.    thom’s results are certainly geometric.  for that reason, this paper has its unstable aspects. nonetheless, this paper has a claim to being the paper that established that stable homotopy theory has a connection to reality. 

thom’s results were created early in the 1950s and it took years for homotopy theory to catch up.  only in the 1960s do we see a major return to the subject of cobordism from a homotopy point of view.   thom’s paper had already had strong geometric influence way before that in the geometric work of milnor and others.  ironically, milnor was one of the people who restarted the homotopy aspects of this work.

i just had a realization that any treatment of the eilenberg-moore materail is incomplete and downright flabby if it does not contain a clear and concise treatment of the suspension.
so that is what i have thought out today.  i will write some text tomorrow.

i took a short walk up to the glacier today.  i saw skiers who had just come off the glacier.  that is one mean glacier and you do not traverse it lightly.  the glacier spills off the mountain.  it is quite steep and very broken up.  you could die there.  easy!  crampons and belays are required lest you disappear into a crevasse never to be seen again. and, after you get off the snow, you have to walk an awful long way on a narrow downward path carrying skis until you reach a road. 

the weather here is beautiful mountain weather, warm and sunny in the afternoon and cool in the evenings.  perfect.

i walked down to the village of les hauderes.  it was approximately a 2 and a half hour walk, mainly downhill so not tiring at all.  then i took the postal bus back.  very civilized.

i have to add that one can see the effects of the imminent shutdown of the hotel in the quality of the food.  the kitchen staff is cut way back and the menu is just not up to what i am accustomed to here.  but it is not terrible. just uninspired.  or perhaps it just was  bad luck on the lamb.  this lamb was done in some gravy, seemd a little tough, and really could have used some kick, perhaps some garlic and thyme or even some mint jelly.  the english are not total food idiots. and they do understand lamb.

perception of the quality of food also suffers from the comparison between lausanne and the mountains.  in lausanne, the quality was usually high, even if it was not often exciting.

one of the dangers of having all the time you need is that you will use it in reflection and speculation.  i am contemplating what is the purpose of this book.  in a way, a book at this stage of my career is a sort of biography.  you write about the mathematical life you have lived.  so you write about the way things were but you also get  a chance to correct some things to the way things should have been.  those corners you cut in life can now be fully filled and rounded.  there is no reason to write such a book unless you are going to do it right. but most of all you get a chance to write about those things which you have loved and respected.  one leaves a legacy in the sense that, whether or not these things are popular now, there is now a level of knowledge about them which should be recorded lest it be lost.

by the way, i am now in a situation which is common with internet in european hotels.  i can access the web and i can receive email but i cannot send.  oy vey!  tomorrow i move to the hotel du glacier and perhaps i will have better luck there.  not bloody likely!  i suspect that it all has something to do with hoss’ overwhelming desire that no outside person be allowed to use the u of r internet. it is difficult to believe that everyone has this same problem.

sorry there is not more about the food and culture.  frankly, both have not been that exciting lately.

the internet situation has improved.  i am not sure what has been wrong but things are definitely better.  i will try to send this message out by bringing my computer near to the internet transmitter for the hotel.  we shall see.

this may seem trivial but i have discovered that the restaurant at lac bleu makes a great mixed salad. it has lots of chopped celery root, tomatos, and shredded carrots.  and the dressing is great. this makes up for a disappointing trout mauniere.

now we have seen the internet situation and the culprit seems to be, at least in large part, the server at the university of rochester math department.  the evidence for this is that the math department website and my own related website is unreachable, totally shut off.  this is coupled with a shut down of the email server since yesterday.

oh well, i am resigned to no internet.  after a while, it gets frustrating to worry about it too much.  it is a waste of time, time which is better spent taking walks and thinking about mathematics.  it is a good feeling to be doing precisely the mathematics that one wants to do and to know that, whatever the result, the credit or the blame all belong to you.  coauthors have always been a mixed bag.  i have had some great ones who contributed a great deal to the joint projects and some not so great who did not pull their share of the load.   on the whole, in the absence of the mathematical equivalent of nicole kidman, it is nice to be working alone, especially on a book where the main point is to do things in a way that one finds intellectually honest and attractive.

i just finished writing up the treatment of the homology suspension.  it is nice but more difficult than i had at first imagined.  but now the path is clear to the end of chapter 10.  in chapter 10, there is only one section left and it is devoted to giving some classical examples of the theory so far developed, the homology of the double loops on spheres and the homology of the loops on some classical groups. 

after that, there will remain to be done two short computational chapters.  all the background is done to finish off the exposition of the exponent theory, which has been the guiding principle of the book. 

the last chapter on classifying spaces should not have great difficulties and will finish off with the fireworks of a quick treatment of bott periodicity for the unitary group (a cinch!) and a quick computation of the unoriented cobordism ring, at least additively.  then there should be a trumpet fanfare! the book will be done.

i think that chapter 10 was the last big obstacle.  a lot of theory had to be organized and presented.  i am especially proud of the fact that i have given an honest and original treatment of products in the eilenberg-moore models. even such an expert as kathryn thinks i had something new and useful to say on this subject.

i just read milnor’s introduction to his collected papers on differential topology.  in it, he makes the remarkable statement that his simple purpose throughout much of the 1950s was to understand manifolds which were connected up to the middle dimension.  and out of that simple purpose came a revolution! he was and is a smart fellow.

well, i am not making a revolution with this book.  but i will present:

homotopy groups with coefficients, the most general theory of localization which includes completion and so called neisendorfer localization, a basic theory of particular homotopy limits, hilton-james-toda hopf invariants and their application to exponent results, samelson products and homotopy bockstein spectral sequences, lie algebras and universal enveloping algebras with applications to higher order torsion in the homotopy of moore spaces, the theory of chain models for loop spaces and the eilenberg-moore spectral sequence, the application to the odd primary exponents of the homotopy groups of spheres, chain models for classifying spaces with applications to bott periodicity and unoriented cobordism.

that is not a bad list.

today, may 2 in arolla, we have a snow storm, heavy wet stuff coming down hard.  if you look out the window, the landscape is becoming all white,  it is a good day to stay inside and work more on the book.  tomorrow, i will get up early and travel most of the day to end up in ste-cecile in provence. i hope it is warm and the sun is shining there.

I am in rochegude, one town away from the steins at ste-cecille, settled at my gite.  last night, the steins treated me to a nice roast veal.  today, it is raining on and off.  it is rather chilly.  But the food is much improved. 

I have at last found a form of rabbit that i really like.  rabbit pate made by the local butcher is really good.  and he makes an excellent head cheese.  he makes a lot of excellent things, such as a mousse made with zuchini, a calamari salad, artichokes in olive oil, and some sort of meat loaf with a green chopped vegetable in it. 

tomorrow judy will take me to the market in ste-cecille.  more good food is there,  maybe some cheese or another nice pate.  i have to remember to get some fresh vegetables.  with vegetables and eggs and a little something extra like a provencal stew, i will eat well.  it is good to have something to say about food again.

the washing machine here was made in italy.  washing machines, like military hardware, should be made by germans.  even the swiss and the steins agree with this.  my italian machine seems to have a mind of its own. it decides on its own that i really want to leave my clothes soaking in water.  i would really prefer the spin cycle to get most of the water out.  so i am reduced to hand wringing the wet clothes and hanging them out to dry.  it is a little better than doing laundry in a hotel room.

the gite is very nice and so is the scnery.  it is all very provencale, yellows and blues, like the flowers and sky.  in this, it is chromatically similar to bavaria but has a certain  style which is all its own, harmonius and distinctive.

 a nice feature of the gite, which is run by judy’s friend sarah from england, is that the television here has access to the bbc and other british television. this is not fantastic but it is a great improvement over cnn.

the heat is on in the gite and it is making my life much  more comfortable. maybe it will even dry out the wet laundry if i bring it inside?

jacques and margaret have arrived at the avignon tgv station.  it is the beginning of a food festival, our very own festival as jacques cooks and eats his way through provence. 

food starts with a trip to an enormous market in the town of vaison a romaine.

 i bought a belt which i needed. my pants will stop falling down.

 the weekly market had all sorts of stuff but the food is the center point.  i got some excellent cheese of gruyere type. of course, the girl selling the cheese included a gift of some excellent goat cheese.  it is a sort of goodwill gesture to induce return purchases.   it is my experience that cheese is always acquired in pairs., one piece you buy and one piece that is given to you.

we also bought a chicken which roasted up quite nicely, a very succulent and tasty bird which went nicely with asparagus and potato salad.

we cooked a duck for dinner and inivited our landlady, sarah, and the steins over for dinner.  the food was simple and successful, sauteed duck, leeks, potato salad (with just onions, olive oil and vinegar added), and a some nice ice creams or sherberts to finish, pistachio, coffee, vanilla, and raspberry. we had wine but that does not interest me as much as solid food.  after all, wine is just grape juice with alcohol. well, there you are, it was our best meal until the next one when we went out to the local one star restaurant.

at the local one star, i started with some foie gras and a very nice ris (= pancreas or kidney) de goat cooked in a wonderful brown sauce and served on a bed of green lentils.  at a restaurant of that quality, they are always throwing in little extras, like some hordeaurves including caramelized olives and an extra dessert with a tiny creme brulee.  my main dessert was a grand marnier souffle.  but the surprise of the meal was the added extra of a sort of tuna ceviche (raw marinated in vinegar) topped with whipped cream infused with asparagus.  weird, unusual. but rather good.

today, we go to norman and judy’s for another meal.  but before that we bought some salade de museau, which is a sort of liquid head cheese, cheap cuts of pork in a light vinegar.  it looks frightening but it turned out to be tamer than i expected.  i like it.

meanwhile, i am suffering from a lack of mathematical information.  there is no internet and no math library.  norman stein shocked me by not having a copy of steenrod’s book on cohomology operations. he says that he used to know all that stuff and never felt the need to buy one!  i could really use a copy right now.  or a copy of a certain cartan seminar would be nice.  but i am in the middle of a mathematical desert right here.  even brayton gray in uzes lacks an adequate supply of mathematical references.  how does he get any work done?  he evidently does.

today jacques cooked some andouille.  this is a sausage made of tripe. i am glad that i tried it but i am not a fan of the stuff.  the smell of stomachs and intentines gives me a very slight gag reflex.  so i am barred from enjoyment of this speciality.

here is an overall comment on french food.  some of it is truly wonderful.  in particular, the fruits and vegetables are great, fresh and with lots of flavour. some of the cooked meats are wonderful.  a nice cog au vin is a very nice thing to do with an old and tough rooster to make him tender and tasty.  and some of the stews are fantastic.  it goes without saying that the high end of french food is incomparably good, things like braised veal cheeks and ris de veau are gifts from god.  and a roast veal, which is not uniquely french, is of course wonderful.

but i am not a fan of all of french food.  for example, on the whole the germans do sausage better.  i do not think that internal organs always make good sausage. sometimes they do but not always.

and i prefer green asparagus to the white stuff that the french bury in the ground to keep it from developing chlorophyl. 

and now comes the really controversial statement.  wine is overrated. sometimes it is very good, but not always.  it is like beer but without the mistique.  i suspect that the reverence in which it is held has something to do with the worship of alcohol.  remember that plants influence us by pandering to our weaknesses and that alcohol is one of them. sometimes a nice clear apple juice is just the thing.  and this they serve in intensive care!

today i drove jacques and margaret to the avignon train station to pick up their rental car.  the muslim attendent at their cut rate rental place seemed to have little interest in giving them a car, even thought they had arranged the rental in the states.  his boss had a similar attitude.  jacques even investigated the possibility of upgrading to avis but decided the cost was too high.  eventually, the cut rate peope gave them a car which they had had all along.   jacques and margaret departed hastily, leaving me to back out of the very tight quarters that jacques had put my car into.  i have to give credit to the muslim attendent.  he helped direct me to back out without any damage to my car or to the cars in his charge.

with the departure of jacques and margaret, i purchased some boudin and cooked it on the grill.  boudin is a sausage pudding made from pig’s blood and pork, flavored with onions.  it is a warm pudding with a wholesome taste. i remember that my mother was fond of a german version but that she boiled it.  it is good stuff, in taste reminiscent of haggis.  i like it a lot, enough that i will search for a version that is available in the united states.  by the way, my hero anthony bourdain loves boudin.  but anthony is also fond of tripe and intestines.  i cannot follow him there.  anthony has even eaten warthog anus as a courtesy to the bushmen in the kalihari desert but you could tell that he was not fond of that.  he said something about there being too much dirt and shit in that meal and he speculated on the possible need for some antibiotics.  afterwards, he was overjoyed to get some roasted beetles.  you sprinkle salt  on them and suck the insides out.. 

the french make a yogurt flavored with bits of grapefruit.  it is amazingly good.

i visited brayton and sophie in their wonderful house in uzes.  there was a very nice leek soup.  leeks are underestimated in america. 

brayton has restored my faith in universal models for relative samelson products.  brayton pointed out to me that i even referred to this faith in an introduction of one of my papers.  but i had a crisis of confidence.  in fact, i can no longer remember why i lost this faith.  since i am now going to include a section in the book on these universal models, i hope that my current belief is the right one.  if correct, it does make one part of the exponent splittings cleaner. it is just what john moore wanted me to do so long ago, but at the time, i found an ad hoc way around it. 
 




last day in paris:

after a pleasant farewell pizza dinner with the steins and my landlady sarah at the local pizzeria, i departed the next day on the tgv for paris. as usual the tgv ride was smooth and trouble free.

i arrived at the ibis hotel next to the airport to discover that someone had stolen their computer and they now had no internet for customers at all. when i was here last november they at least had an overpriced version, 15 euros for something like an hour. i resigned myself to having no internet until i return to rochester in 2 days.

in the meantime, i have scheduled a day in paris.

it has been a long, long time since i last saw paris. the first time i saw it i had just finished my thesis. john moore was in those days always in paris in the summer and he was my port for breakfast in the morning. his hotel was too expensive for me to stay at but he pointed me to a more reasonably priced one. it was pleasant to splurge on the hot chocolate and croissants to have a better breakfast and talk to moore about paris and mathematics. i also ate most dinners at some simple bistro with moore. foodwise, it was heaven. and moore added to it by arranging one of his famous dinner parties at a two star restaurant. i was included on the guest list along with the last minute addition of claudine serre. claudine was so last minute that she was dressed in blue jeans and we all crowded around her so that the restaurant staff would not see her state of dress and eject her and/or us all. the particulars of that meal have faded from my memory but i remember that it was terrifically good. i do remember a whiskey sorbet.

at that long ago time, i visited some of the classic parisian sites, including notre dame, the louvre (saw the mona lisa and lots of rembrandt), the gallerie where they had the water lily murals of monet, etc. i went out to chartres and have always remembered the emotion i felt there. anyway, i can’t really explain why i never went back to spend more time in paris. foreign vacations tended to get planned around mathematics conferences. and there just were no suitable mathematical occasions for my specialty, algebraic topology. so i didn’t go back. i went other places, oxford, cambridge, aarhus, kyoto, durham, the list goes on and they were certainly good places. but they were not paris.


even when i went to france, it was my custom to go directly to and from where i was going, luminy near marseiles being one example. well, i am here to admit that this was a mistake not to see more of paris. paris is a wonderful town. the views, the history, the food are all terrific. i will never again plan to just skip this big city. it is always worth visiting.

I began by taking the train from the airport hotel into the city. in honor of the fabled yale full immersion language course, i got off at the luxembourg gardens, site of the fictional flrtation between mareille and robert and the site where her younger sister mari-laure was always having trouble with her sailboat at the most inopportune times. for those who do not know this course, it is still availabe on the internet by the courtesy of the annenberg media foundation. it has attained a cult status. a new generation has a running blog on this course and wonders about the fate of the now old and grey actors. of particular interest is the actress valerie allain who played mareille. many of these cultists are in love with her and with good reason. there was a distressing rumour that valerie had become a french porn star. it is a confusion. there is a french porn star by that name but it is not our valerie. the most that valerie has ever done is take her clothes off on camera. and that is practically mandatory for a french actress and in no way makes valerie into a porn star. you see, i am one of valerie’s fans. by the way, the actor who played robert has actually communicated to the blog. but the actress who played her younger sister has completely disappeared.

the luxembourg gardens have much to offer, including statues of all the french queens and a statue of saint genevieve. saint genevieve was not a queen but she did the nontrivial thing of successfully praying to god to direct attila the hun away from paris and towards orleans. evidently god didn’t mind if attila sacked orleans. anyway, according to the sculptor, saint genevieve was a very physically attractive young lady. this is more than you can say about some of the french queens. on the whole, the further back in time the queen, the prettier the sculptors made her look.

after leaving the gardens, i immediately encountered a macdonalds where i noticed people using laptop computers. hurrying inside and taking a seat, i took my laptop out of my backpack and i discovered that macdonalds was providing reliable and free internet! it was a lure to attract customers from the nearby sorbonne university. i could receve email and i think i succeeded in sending out some replies.

but since my battery supply was low, my computer shut itself off before i could completely research the mod 2 cohomology rings of the special orthogonal groups. oh well, you can’t have everything and i was truly happy to have found this brief internet connection. and it was free!

and i am amused to find that even people who hate macdonalds must admit that they have excellent toilets and internet.

i continued on my walk, passed the ruins of the old abbey of cluny, reached the seine with a lovely view of the cathedral of notre dame. unfortunately, notre dame had an enormously long line of tourists waiting to get in. i contented myself with taking some pictures of the exterior and with visiting a festival tent in honor of the making of bread. bread was actually being made and sold there. since i had already made plans to go back to a brasserie for some mussels and frites (= french fries), i passed up the opportunity to sample the bread.

my main plan was to walk along the seine and to see paris. wow! the louvre and the tuileries garden were just stunning displays of civilization and grandeur. paris is culture on a scale which makes it have no match anywhere else. and i am talking about just the outside of these things. what is inside takes longer to see. i did not have time to do that. i had to pass up the great art that is there. but the outside was enough for me.

i had formed a strange desire to see the palace of discovery. it is a science museum and my michellin guide to paris assured me that the math exhibit was high toned, not dumbed down, an exhibit for professionals. alas, this michellin guide was not written by a mathematician. the museum seemed most proud of the fact that you could find recorded there the current record for the number of digits in the computation of pi. i was devastated and decided to head back.

the museum was located at the intersection of the avenue franklin delano roosevelt and the rue de general eisenhower. ( i bet there will never be an avenue george bush except in various portions of brain dead america.)

by the way, there are monuments for charles de gaulle and winston churchill. the french are truly grateful for having their collective butts saved in world war two. but, in all fairness, there should be some monument to joseph stalin or at least to the russian people. the russians did more than anyone to win world war two. i won’t make the argument here but you could just look up the numbers of dead on both sides and look at where the bulk of the german army was.


the french love their holidays, even ones that mean nothing more to them than a day off. for example, while i was here, two holidays occurred. all the stores were closed. the first occasion was the aforementioned world war two victory. the french had nothing to do with accomplishing this.

the second holiday was the feast of the ascension. the french, having become for the most part secular, are celebrating the ascension into heaven of somebocy they really don’t worship much. but, as i indicated, it is the days off that is the true religion of the french. one sees this more in the small towns of provence than in the lively atmosphere of paris. the french should quake in their boots now that they have elected someone like zarkosy who believes in the mass of people working hard without excessive benefits.


as i walked along the seine, i discovered a new brand of homeless people. some young people had pitched some good quality mountain tents along secluced portions of the banks of the seine. they were living in them. i do not know where the nearest toilet facilities were. perhaps it was the seine.

I returned to the vicinity of notre dame and went in to visit the conciergerie on the ile de la cite (= isle of the city). this is the historic castle of louis the first. after the kings of france moved up in the world to fancier palaces, prisoners were kept here. and trials were held here during the french revolution. from small cells with beds of stone covered straw, people were carted off to the guillotine. i guess that was better than being burned alive at the stake the way the grand master of the knights of the templars was. king philip the fair noticed that the templars were very rich, a definite threat to the power of the king. he decided to suppress them. this means that he decided to kill all the templars he could find. he also decided to
confiscate their estates and all the templar gold he could find. there is a legend that the main part of the templar treasure survived along with many templars. the legend says that the templars disappeared into the heart of the swiss alps where they founded banks and became the gnomes of zurich. other evidence for this is that the swiss fighting ability suddenly became much more effective at this time. after all, the templars were warrior knights.

the conciergerie is a lovely medieval hall. it has big fireplaces where lots of meat could be roasted. off to the side, it has little jail cells where people, the high and the low, were kept before being guillotined. robespierre and marie antoinette were among the temporary residents.

to the side of the conciergerie is the chapel of sainte chapelle. this is a lovely chapel dating from the 12th century. it was built by the king siant louis to house the crown of thorns, the real crown of thorns, the one supposedly worn by the founder of a major religion. this was found on a crusade by a french nobleman who pawned it to the venetians and then appealed to louis to redeem his pawn. this louis did, being a saint or about to become one, and then he had to build a suitable housing for it.

it is a big chapel, with towering and beautiful stained glass windows. in a time when cathedrals took a hundred years or more to bulid, this place took 33 months to build in the 12th century. granted that a chapel is not as big as a cathedral, that is fast construction. i doubt if kellog, brown, and root or bechtel or any of the firms which our current administration likes to employ could do as well. but architecture in the middle ages, especially religious architecture, reached a peak that it has never climbed to again. so perhaps the friends of bush can be forgiven for not living up to these standards. and i think that they had such a thing as huge cost overruns in those days too.

seriously, there are two big differences between those guys in the past and our current crowd. one, in the past they were more competant. two, in the past they were sincerely ruthless. they did not feel any need to hide it with a smirk. similar to the romans in these respects. whatever else you might say about them, these guys understood the concept of “bottom line.”

i ended up at the brasserie where i had planned to have mussels and frites. although the waiter was young and slow, he came through with some wonderful mussels. the frites were good enough to add to the pleasure of the meal which i ate with a nice kronenbourg draft beer. it was excellent! the mussels were cooked in a liquid with onions, parsley, and carrots. i finished by eating the liquid as if it were a soup. it was a classic brasserie meal.

but the frites were disappointing. on the frite quality scale, i rank frites as follows. up at the top are my mother’s frites, browned and a little crisp on the outside with a soft tender inside, the best frites.

the frites you can find in stands on french or also canadian highways (even in ontario!) are almost the equal of my mother’s frites.

close behind them are the frites called new york fries which you can only buy in canadian malls.

in the days when macdonalds made their frites with true and unhealthy grease their frites were very good. even such a discriminating gourmet as frank peterson acknowledged that macdonalds’ frites were not bad. alas, macdonalds has given in to health concerns and their frites are just not as good as they used to be.

after all these frites come the frties i had with my mussels at the brasserie. but they are still better than most frites and they went well with the mussels.

so after a closing expresso, i said a fond farewell to paris and hopped on the train back to the airport hotel.

over and out,

joe n