How to be a loser

Adversity is a part of life and sooner or later you will fail trying to accomplish some important goal. In fact I am expecting a major professional set-back in the next couple of months. In anticipation of the pain, anxiety and anguish I have decided that rather than suffer later I should prepare now. My expected downfall is fairly standard and the three-step method that I describe below should apply to most situations when your better judgment did not prevail.

Anger

This is a purifying flame and a source of great satisfaction. Other than fantasizing about the destruction of your enemies and their properties (these exercises you can design yourself), I recommend Jack Reacher novels (any one will do) and Dirty Harry movies. They depict you - supremely confident character who punishes forces of evil with great deal of violence and without a trace of hesitation. You are an outsider and a rebel and weak and stupid constantly stand in your way and slow you down.

After this initial phase you may conclude that life is a bit more complicated and responsibility is not so easy to assign. Perhaps your misfortunes are everybody's fault and the punishment should be more even-handed and spread out. For this phase I recommend movies such as 2012, Deep Impact, Melancholia, and Bambi (particularly these fragments). They will resonate with the need to deliver a punishing blow to entire continents and populations. While you will no longer be in the driving seat of the destruction, the sense of righteousness is likely to be very satisfying.

In the last stage your anger will turn against yourself. You failed and there is no point in blaming anybody else. Instead of fantasizing about pulling a cord on the suicide belt you will wallow in self-pity. Visits to finalexitnetwork.org and reading their guides will become your daily routine and sadness will engulf your soul. Watching Old yeller and reading The Giving Tree  will make you weep for hours. Check this link for additional suggestions of movies that will take you to the bottom of your despair.

Hope

Your anger will eventually burn down and new hope will enter the picture. Yes, you have lost a battle but you may yet win the war. It may take many years but so what. Flicker of hope never glows very brightly but it can last forever. Furthermore, while the nature is patiently working towards rewarding you with the most satisfying solution you do not need to do much but wait.

For this phase I recommend Lassie Come Home, When Harry met Sally together with Sleepless in Seattle. Reading Captain Blood  will warm you up as well. Not only you can live your life as before without introducing much disturbances but in the end you will be paid with interest! Indeed, when the adversities felled you you did not really know what you wanted, and now after many years and endowed with 20/20 vision you have a sense of a fulfillment of your destiny.

Alas, sappy movies and books will leave you longing for more. Rather than waiting for Lassie to come home start planning your next move. Perhaps there is a great deal more randomness in life and for a moment you just drew bad cards? Read Wall Street Journal and watch C-Span - everything you see there is somebody's win and somebody else's loss. Best laid plans are wasted, careers are ruined and this is just the way things are.

At this point reading books and watching movies is no longer enough - you are climbing up from a hole and you need a great deal more. Go shopping! Spend freely and make sure that you are not guided by your household needs. Remember that you are rebuilding your soul, not your kitchen. Depending on your financial stratum this, this or that might provide a lasting lift.

Grand fusion

You are approaching the final stage of your recovery and this step is entirely up to you. Anger and hope coexist next to one another and hang in a perfect balance. You are buoyed by your recent purchases, and your anger slowly transforms into wisdom. You are poised and endowed with a quiet sense of resolve. You work fewer hours and you have developed a sense of another dimension. Colleagues are seeking your opinions and you are back to your usual self without the burden of former responsibilities. It is time to pick up new hobbies and update your wardrobe. Dark clouds have parted and the first day of your new life has just started.

Reading for this period might include Deepak Chopra (particularly this book) or getting familiar with the miracles of modern medicine (as described in  that book).

Diary from the past - a year in turmoil

I have posted translation of my uncle's diary from the 70's year ago (you can
find it here ). Recently I have found a handful of later notes. Evidently they were written sometime after the described events and the chronological order is unclear.

-------------------------

Corn, Beets and Plows

Exactly a year ago I have written that our management has a great deal of concern for the name  of our unit. Evidently plain "Botany Unit" is not inclusive enough and corn people are frustrated and restless. Little I knew... Our new boss  devoted a large part of the year to these issues and still there is no end in sight. The first proposed name was "Corn, Beets and Plows".  It brings most of the things that we care about together with the exception of potatoes. However potato people are too busy doing their work to care about such trivialities. Unfortunately  plows really do not belong. Not only they are not  a part of the world of plants, but also Ministry of Everything has the entire unit to deal with agricultural machinery. Some comrades from other units   were showing irritation and our bosses started backing off.
But this was just the beginning...

Fateful meeting

Two months later an official from the Command Center came for our midday meal. After small talk about the failures of the capitalist pigs in just about any endeavor they embarked upon the conversation turned to the virtues of corn. Evgenij (the leader of the Command Center) very passionately described the newest  from the corn fields - from the obvious and well known (food, animal feed) to newer and important (fuel for various machinery, building materials, and so on). It quickly became obvious that corn  growing married with mechanized farming can change the landscape of our unit. All comrades got quite excited by these ideas and started inquiring about the resources that such a change in our agricultural habits would entail. At this point Evgenij confessed that the resources are much more needed for our comrades in different units, but that the first step in these transformations would be
to change the name of our unit to "Botany and Corn unit". The respect for our leaders kept us applauding  but the logical cracks in these plans did not go unnoticed. Even if corn fuels the ballistic missiles that one day will obliterate our enemies, it is still a plant and "Botany" covers it inasmuch. More discussion followed, some of it in the spirit of whether tomato is a vegetable or a fruit, but ultimately the consensus emerged that our farming community will not benefit from this turmoil.
However, we were already in trouble.


Chaos reigns

Beet people started saying that they can grow better corn, corn people were bringing up long forgotten grievances and life became miserable. Furthermore, farmers got the wind of the changes and started inquiring and complaining. Beet grower union, Corn grower union and various potato grower organizations started asking comrades for their opinions. Suddenly, rather than growing stuff together we had the whole farming community debating whether Beets are from Mars and Corn is from Venus (paraphrasing a trendy capitalist publication).
Sometime I feel that we are at the rough seas, far away from home.


The International

The previous minister was an old and seasoned comrade. He ran our ministry for six years and managed to stay invisible for most of that time. Senior colleagues say that he was injured in the Battle of Kursk and lost some spunk since then, both likely to be true if you ask me. The new minister is of a completely different breed. In a year since his coming we saw a number of new initiatives coming directly from the top. Since repelling capitalist pigs takes most of our resources these initiatives are mostly symbolic yet the powerful propaganda apparatus that we employ on their behalf keeps them very visible. The Botany unit is very much engaged since the fathers of the minister and of our boss served in the same unit during WWII.

So what are these initiatives? One is called MAGELLAN after the discoverer with a dreamy sounding name who was a favorite of Marx and Lenin. The plan, or rather our portion of it, involves virtual
farming. On a practical level it is a pen-pal program where farmers from several countries write to one another and exchange ideas. Unfortunately in order to undercut capitalist enemies in this trying times MAGELLAN is setting very ambitious goals and it is supposed to transform our agriculture. With no real resources allocated I am afraid that these transformations will also be virtual and  no actual farming will occur as a result. However, I hope that it brings us closer to our foreign comrades  and burden on censorship to scrutinize all those letters will not add too much to our administration.

Great leap forward

is another initiative from our management. As it turns out we have many tedious procedures and quality controls. Before we actually plant anything there is a lot of reviewing, testing, consultations and so on. We try to bring best farming experts with detailed knowledge of all sorts of plants and seek their advice.  This takes time, energy and on many occasions what we are told is what we knew all along.  Great leap forward aims at simplifying the process and leveraging our own expertise to make faster and bolder decisions. We already received a handful of one-of-a-kind projects for evaluation and some of our colleagues are quite excited. Some ideas involve using industrial run-off for watering fields in the arid areas, farming salmon in the nuclear reactor cooling towers, and so on. Luckily all are required to be multidisciplinary and this  dilutes the responsibility and somewhat broadens the expertise.

iJob or the end of work alienation

is the last of the new director's gifts. Within the Botany unit it is supposed to work as follows: a farmer is supposed to get together with comrades that process, package, and prepare the food and other things that are made of his agricultural products. This way the whole purpose of  farming is clearly displayed and benefits to the society become apparent. Next a participating farmer and his newly acquired comrades undergo political training and start a cooperative that  is responsible for the totality of the production process from planting the seeds to delivering food items for worker's families. It is not clear to me if afterwards the farmer has any time left for farming but perhaps it is not a big loss. So in the end, our hands were sore from clapping when these plans were unveiled at a yearly gathering of the whole ministry. 



Foreign farmers

In spite of MAGELLAN initiative our treatment of foreign comrades worsened lately quite a bit. Traditionally we were bringing foreign farmers to our farming outposts, most of our working groups involved foreigners and many  comrades escaped oppression to come to our glorious country. 
Since we live in the best system under the sun it is understandable that the foreign comrades are struggling to catch up with us and are a bit starstruck at times. Yet they come here to farm with us and seeing their reduced food rations just because they are from other countries pains me. We have brought up this issue many times but apparently the directives from the Central Committee are making clear that only after a lengthy certification process the treatment could be equal. It is all rather sad and I suppose that in a long run we will not have very many foreign farmers in our working groups.

Continued here.

Science quiz

1. Pair up things that belong together

a. bottle of San Pellegrino water
b. basic science
c. transistor
d. rainfall in the Alps during the Roman times

2. Identify the item that you did not pay for

a. bonuses of the CEO's of top ten US banks
b. national labs
c. nation-building in Iraq, Afghanistan, Libya, etc
d. none of the above, there is no such thing as free lunch

3. Strong science needs strong workforce. It is best if it is left to
(choose one that applies to your country). 

a. free market
b. charitable organizations
c. military
d. other countries

4. Educational system is critical for the scientific develpment of the
country. Your children would benefit most from:

a. public school system
b. religious education (yeshiva, catholic school, madrasa, etc)
c. going abroad
d. tax refund and a home schooling voucher

5. Choose the ending that is not correct.

Calculus is
a. a small stone used for counting
b. an abnormal concretion in the body, usually formed of mineral salts
and found in the gallbladder, kidney, or urinary bladder
c. rapidly developing part  of modern mathematics

6. Which one of the following sentences is true.

Basic science
a. has high priority for support
b. attracts a lot of fanatical supporters
c. has determined the outcome of O.J. Simpson trial
d. drives the politics of climate change legislation

7. Creation of scientific ideas is important because

a. it is  of great interest to the society
b. it often involves people that may not be employable outside academia
c. it is  tied to the prosperity of the country

8. Life is ubiquitus in the universe but nobody seems to be heading in
our direction. Is it because

a. we are not worth talking to?
b. we are not worth listening to?
c. both of the above

9. Name one item that does not belong with the remaining ones

a. science and education
b. neutrinos
c. religion
d. drugs and alcohol

10. The greatest gift a calculus teacher can bestow on humanity is:

a. to teach students a mnemonic rule how to integrate sin^5(x)cos^7(x)
that they will remember twenty years after taking the class

b. to identify future politicians in the class and give them good
grades

c. to go beyond calculus and teach them about stochastic PDEs.

11. Mathematicians and statisticians often do not get along. (Assuming that you err with p-value 0.05) this is because

a. mathematicians are jerks who put everybody down

b. mathematicians are jerks who put everybody down

c. mathematicians are jerks who put everybody down



Answers

1. a-c, d-b 2. d 3. d (for USA)  c (for North Korea) 4. c 5. c 6. b 7. b 8. c 9. b 10. b 11. a through c

For each correct answer you get one point.

If your score is 11 points then you have answered the first question
correctly. Spot on mate - you are ready to talk to the big fish in the
Office of Science and Technology Policy and advocate for basic science research.  Unfortunately, correct answers to the remaining questions indicate cynical and pessimistic outlook on life that is inconsistent with your message. 

Notes for my marriage counselor

I have always loved science and probably I always will. So it is not surprising that about ten years ago I decided to take my relationship with science to the new level. Alas, romantic affair and marriage are two different things and in my new role there are frustrations that I did not anticipate.  Here are the  topics that I would like to discuss during counseling.

1. She works hard but brings home no money.

She works like a horse indeed but there is no income that I can see. I am not happy that when I buy a new car I pay at least a $100 to a dealer with a gold ring, and another $200 to a guy who  owns a private jet, but not even a penny to the community that came up with the ideas how to build the darn thing. Or take a hedge fund manager - his personal profit  can be comparable to what entire world spends on supporting mathematical sciences. Yet people who developed his toolbox are not shareholders of this wealth.

2. She gives way too much for charity.

If not bringing money home is bad enough, giving everything away is even worse. Take any manufactured item: cd player, car, cell phone. If you take away the skin -metal, plastic, wires and human labor to manufacture it - all that is left inside are scientific ideas of the last 100 years. These gadgets drive economies of entire countries yet science that is inside comes for free. It is the tide that raises all boats. This is great but only for a species endowed with some sense of gratitude.

3. She used to be  the prettiest.

One can marry religion, politics, financial industry or simply a big bag of money, and I see that everybody is after these ugly bitches these days. Am I the only one who thinks that science is the fairest of all?

4.  Is she  too sexy?

I love the fact that my computer costs the same as 30 years ago and it is a million times better. But it has created a revolution that swept me away and changed my life. I threw away my records, will soon follow with cd's and dvd's and I have already tossed away countless cell phones. This is a bit frustrating even if every new product brings new exciting features.  Compare to less sexy science and for example look at an ordinary AA battery. My grandma would know how to use it, it is exactly the same in every country on the planet and the main accomplishment of these  years is that it does not leak anymore. And yes, it is probably ten times better than 50 years ago. This is science that everybody can rely on - steady  and incremental progress on an useful and familiar product.

5. Universal language.

She tells me with pride that scientific ideas are the only abstract form of human thought that can be communicated between any two people. Indeed, as long as math is concerned the entire thought process of one person can be simply encoded and subsequently recreated in a head of another person. This is a bit of a miracle, and the process is so reliable that most people accept the results by proxies. Yet, _any_ two people can participate in this - gimme a break! Twenty-five years of university brainwashing is required to prepare one's mind to receive these missives. You can probably do anything with human brain in such time-frame!

6. She is not there when you need her.

In spite of all the hard work she is missing in action more often than before. We need to know if factoring numbers is hard, and if not then come up with better crypto algorithms. The security of large chunk of economy depends on it and  the time is pressing. I bring it up all the time but she says that it is a matter of the right number of people thinking about it - one of them is bound to get it. Easy to say, but where do we find these people when our society is  on the verge of giving up on research and education.

7. She makes wrong people rich.

She is very proud that scientific ideas drive modern world and are largely responsible for the supply of goods, energy, food, etc.  Yet, the accumulation of wealth has to do with the demand not supply side. Since the "scientific DNA" of any two cameras, cars, planes, etc are virtually the same, people who make fortunes on these things are the ones who predict accurately what will sell better. A guy who can anticipate  the most popular car color in five years is probably more valuable then a person who invented  four-stroke engine!

8. She can be scary.

Love is blind, but sometime I have a feeling that my babe is a bit spooky. I bet that if you dissect a corn kernel, eventually you will find the word Monsanto etched somewhere in its DNA. She often gives what you ask for and she is usually standing by if you get in trouble because of it. Just watch for this nuclear power plant behind your house or a bunch of dudes fracking for natural gas around your summer house.

9. We have lost many friends over the years.

She used to be very popular with children, teenagers, and grown-ups.
Jules Verne and  Star Trek were painting such a bright vision of a world driven by rationality that everybody was in love with science.  Everybody thought of her as a solution to their problems. But today it is different - problems of people lie with other people, not with the surrounding reality.

10. Is she faithful?

Lately she hangs out a lot with Computational Science and Data Science and this smacks of conspiracy. These newly found buddies are quite different. They are hip and immensely successful yet their  discoveries - and there are many -  cannot be followed by a human mind. This is because they are dependent on searching through the mountains of data or performing computations at a blazing speed. Either way, a machine is an integral part of the process.  Sit and watch kind of stuff,  but the pictures and animations are spectacular.

Three postdoc applications from Barcelona

On my trip to Barcelona I accidentally came across some post-doctoral applications from  hundred years ago.

Application 1.

Name of the applicant: Pablo Picasso
Preferred postdoc location: Paris, France

Hola, my name is Pablo Picasso and I am 19 years old. I have been painting for several years now and the thought that one day they might build a museum to exhibit my work from this period gives me creeps. Sadly, all I have done so far is rather crummy. The point is that I get really bored listening to my teachers  and often retreat to painting to avoid socially awkward situations. However, I think that I can paint anything and  in any style. I can be symbolic, geometric, realistic or anything else. I can express any human emotion in visual form in many different ways. To wit,  I have studied Velazquez' Las Meninas and I made over forty paintings that render parts of this great work. These are just sketches, some not really finished,  so I hope that they will not end up in the same museum.

Anyway, the postdoc in Paris is what I need to become a real painter. I need to meet great French artists and a lot of interesting women. This is very hard in Barcelona, particularly with my parents being a suspicious bunch and hovering over me all the time.

The part of the application has to do with presentation of the post-doctoral work plan. I am not really such a great planner, but I expect that when I get to Paris I will work a lot. I have been thinking about simple geometry like cubes to utilize in my work but I am not sure how it will work. If this plan is really important then I propose that I will make all my paintings for next year blue. Blue is a color of depression, solitude and mysticism and all of these might  likely be my companions in Paris if my application is granted.

Application 2

Name of the applicant: Joan Miro
Preferred postdoc location: Paris, France

Hola,
my name is Joan Miro and I want to be a painter.  I have been painting since I was 13 but most of the time I have been doing what others told me to and this is not very good. What I really like to do is to doodle, and I wonder if there is a future in such activity. So far my work has not been well received, and I do not even mention doodles.  Friends tell me that I can make living as a tattoo designer but no respectable person would get one so what kind of living is that. Perhaps in a hundred years...

A postdoc in Paris would be a way to get my doodling career started. By meeting more open-minded and more sophisticated colleagues I can get my doodles to be appreciated. I feel that these ideas are simple but quite expressive.  In fact, I often see that the doodles that I make on napkins - and I doodle incessantly - are being put aside between book pages rather than tossed in the dustbin.  Once I get sure-footed I anticipate doodling for the rest of my life. Quite frankly I may change my style a bit every few years but at this point my doodling skills are superior to anyone else's.
In Paris I plan to interact with surrealists, but the main goal is to get my career off the ground. One day I might have a museum with 14,000 of my doodles but it will not happen if I do not go to Paris soon.

Application 3

Name of the applicant: Antoni Gaudi
Preferred postdoc location: Paris, France

Hola,
my name is Antoni Gaudi. I want to be an architect and my parents want me to go to Paris to study. I suspect that they are worried that I will become a religious freak and atmosphere of Paris might be an antidote. I disagree completely, I want to live in Barcelona all my life and I do not like to travel. As far as studying I do not see the point. I think about buildings all the time and I know what there is to know. I design my buildings in my head to the finest detail. I want special bricks, moldings, door handles, furniture and I have neat ideas how to use  them. People complain that I do not care for indoor plumbing, building codes, or fire hazards but these things are not very interesting anyway.  Here is my postdoc plan - a sketch only but I can elaborate on request. I know precisely what I want to build. I expect that all this work will require help of thousands of people and many, many years. This is ok, in fact I suspect that completely different building materials would allow my designs to be executed better. I have something concrete in mind, a plaster like material that can be molded and sets to rock hardness. These might be invented before some of my projects are finished. Another thing that I am really lacking is better computational and modelling tools. I make models in large scale and compute in my head but there ought to be a way to do it symbolically. My math teacher told me about a guy named Babbage who made a computing machine but I never found out more.
I believe that complexity arises by compounding simplicity and in my designs I use the next best thing after a straight line  - a degree two curve.  This is as much as I can handle in my mind, but too much for most of the workers. This may sound arrogant but both better materials and better computational tools ought to exist because my designs require them. I view my ideas as coming straight from nature, everything that I make can be resolved all the way to water and clay and a bit of math that ties it together. Some people tell me that my buildings look like an American amusement park but I do not believe it, even though I have never been to America. Just come closer and look at the details, my works are part of nature just like other God's creatures.

I hope that this application will be denied. I have no need to go anywhere, and I want to get a cathedral started here in Barcelona. I am not sure about financing, but who knows  - maybe one day Chinese will be paying the construction costs.

Third hand

I am a strong supporter of the evolution theory and I am certain that this theory correctly explains the emergence of complex life forms on Earth. Yet, there is one aspect that I find puzzling and hard to explain, and it is not what we can see but rather what is conspicuously missing. Here is a small example and it concerns a third hand - an organ which should be abundantly present. For simplicity let us concentrate on vertebrates - close to 60,000 species including mammals, birds, fishes, reptiles and  amphibians. All have symmetric bodies and the organs that appear on the symmetry plane are relatively small such as nose, penis, beak, tongue, tail, etc. Under the hood so to speak, symmetry is gone with single organs like liver, heart, pancreas, etc thrown randomly into the body cavity.

Third hand would have been a great gift from nature for just any vertebrate, yet none has it!  For some silly reason  nature nixes  a development of a flexible appendage staring somewhere on the breastplate and ending with six or eight cute little fingers. The advantages for humans are completely clear - texting, eating popcorn while playing video games, scratching - third hand would have been a great help. For countless everyday tasks third hand would provide support and efficiency. I am not sure whether it would be helpful in sports other than boxing, car racing (for changing gears), climbing
and hand to hand combat. Certainly humans with a third hand would live longer and have tremendous evolutionary advantage. This is how a small bump on a chest of a Neanderthal man should have grown bigger and over several hundred generations evolved into this much needed organ.  Quite frankly the lack of it can only be attributed to un-intelligent design, particularly when so much of the evolutionary energy was devoted to perfecting often useless tails.

The benefits for hand-less animals would have been far greater. Consider birds with their sloppy and un-hygienic eating habits throwing away most of what they try to eat. Equipped with a third hand they would elegantly feed themselves with their head raised and on a lookout for predators. Fish would not have to use their mouth to dig in the mud, and cleaning their gills would have been a triviality. Furthermore, a third hand would have allowed them to groom each other, hopefully leading to the development of a more intelligent
biological community.

Are there any drawbacks of having a third hand? It is hard to think of any but for humans there might have been a small problem of what to do with it when it is not used. Should it hang like a weird tie or should one nonchalantly wrap it around the neck? Perhaps it should roll into a ball, or wrap around the waist? No matter what, I am certain that  we would have figured it out.

The lack of a third hand was bothering me for quite a while. I mentioned it to my wife and she immediately came up with a theory which sadly made me realize that greater forces might be at work. The main evolutionary disadvantage of the third hand is that it provides ability for endless and biologically useless sexual gratification. In other words, it is conceivable that Nature kept providing us with the third hand but the owners foolishly did not produce enough offspring and this part of the Tree of Life kept on drying up.

Diversity

These days our institution is quite concerned with diversity and
broadening participation. Recently we had a presentation devoted to a
single question: Why are there so few women at the
top US mathematics departments?

Popular culture identifies three factors that contribute to individual's success: perseverance, will power and hard work;  talent and natural abilities; and supportive environment.

American mythology puts premium on hard work and natural abilities, while modern thinking (as in Gladwell's book "Outliers") points to the environmental factors.

Clearly a tenure at Math Department at Harvard requires plenty of talent, hard work and as much support as one can get. Yet I will argue that environmental factors alone can account for the observable disparity between men and women at the top academic tier of mathematical sciences, and one does not need to look further.

In this context environment relates to a myriad of stimuli, some positive and some negative, that one receives while pursuing professional  goals. Each of these stimuli is not significant, and they do not raise to the level of being a behaviour changing factors, yet collectively they shape one's direction, particularly over a long period of time.

The main point is that the overall effect of the environment seems to be exponential. For example, in   a large group of students learning a difficult subject one will generally observe that certain percentage of them will drop out after one semester, similar percentage after another semester and so on. In other words, the rate of change is proportional to the quantity that is measured which means that  the attrition rate follows an exponential curve. In such situation, even tiny difference in the way one interacts with the environment leads to a dramatic difference twenty years later - a time it takes to climb near the top of the ladder in mathematical sciences.  Another simple example illustrating this phenomenon is as follows - suppose that getting  tenure is akin to getting certain number of heads in a long sequence of coin tosses (with asymmetric coin). If the probability of getting a head in a single toss is larger than some threshold value then the probability of success is very high and it goes exponentially to one as the length of the trial increases. On the other hand, if the probability of success is lower than the threshold value then the odds of success go exponentially to zero at a rate that depends on the difference between the threshold value and the number of trials.

How would one test the effect of the environment?
We need to find an activity that is somewhat similar to doing mathematics, but where it takes much less time to reach super-star status and (ideally) where the environmental factors are more gender blind.  Mathematicians may be upset with this choice but I think that spelling is the right comparison and it proves the point.

Spelling is a curious activity which has a well organized support system. No US kid can escape being pushed to the maximum level that  their ability and patience will allow. Spelling talent is easily recognizable, training is straightforward and the very ability to do super-human spelling is not
intimidating. Year after year the group of top 100 US spellers has the numbers of boys and girls, minorities, poor and rich kids, etc., that conform to the anticipated frequency. Statistics that deviate from the expected values are mostly genetic - having super-spellers in the family, etc.
Inescapable conclusion is that both ability and will power to be a super-speller is distributed in the population quite evenly and even-handed system aimed at identifying top performers and eliciting from them several years of hard work to reach the finals of the  National Spelling-Bee works well.

Back to mathematics - the path to the comparable status in mathematics takes about twenty years. Mathematics is far more intimidating than spelling and performing at the higher level will not automatically get you in touch with likewise gifted people. Quite the opposite, mathematically gifted kids endure years of boredom at school and often question their own sanity. Assessing mathematical talent and nurturing it is not easy and in this respect the system works moderately well only at the graduate school level. Overall the path is long,  steep and arduous.

The educational system favors men when mathematics and other sciences
are concerned. It is not a strong bias but rather a persistent push
which gives a sense of swimming against the current. Women are
constantly discouraged from pursuing mathematics - by teachers,
families, friends and media. Because of the gender imbalance there are far
fewer role models and support networks. On the path to mathematical
pantheon, one has to go through graduate school and one or two
postdoctoral positions. While men can move their families with relative
ease, women often face the phenomenon of an immovable spouse. Dream job requires tremendous level of accomplishment and related commitment of time and energy. It is safe to say that at a time these efforts are needed women have more on their plate than men.  To get a job one needs a number of publications in top journals. These days a lot of work is collaborative and it is fairly common that in cases of joint work involving  male and female mathematicians, the men's work is often viewed as more substantial.   Professional success of female mathematicians that happen to be  good looking and attractive often brings another type of speculations - yet another small insult that is painful and difficult to confront.

There is much more to say here but the point is perhaps clear - climbing to the top of mathematical profession is just a tad harder for women than for men. Those who succeeded devoted approximately half of their life to it. Just having a few extra hoops to jump through makes a lot of difference in this endurance race.

If one accepts this argument then there is a natural follow up supported by Bayesian statistics. If one succeeds against the odds then with high likelihood there is  a compensating factor.  Consequently, women at top math departments were more driven to succeed or they were simply better mathematicians than their male counterparts - both possibilities easily supported by anecdotal evidence.

Literature and Mathematics

Just recently I had an opportunity to witness a Ph.D. defence in comparative literature. The location was a well known university famous for trend-setting in the humanities and sciences alike. Its ascent to ivy-league status was arrested only by the location, where the acute problems of modern society are clearly visible within a half mile of the campus.
The Ph.D. candidate was was well prepared, professionally dressed and only odd looking shoes with heels looking like tree stumps may have betrayed a wilder side of her character.
The defense was a small gathering, four committe members, a handful of fellow students and friends and an older couple, who were most certainly the candidate's parents,  cowering in the corner.  The first question concerned the basic idea behind the thesis, its structure, origins and the thought process that led from the beginning to the final product. Given the open format of the proceedings I was assuming that the procedure is sort of like professional wrestling - lots of body slams, impressive chokes and eye gouging but in the end nobody gets hurt. Perhaps it is so, but nevertheless it felt like a real cliff-hanger.
The subject of the thesis was a comparison between two national literatures and the basis for it was several specific examples spanning several centuries. The candidate made an opening gambit by attempting to put in question the basic premises of her work, She indicated that the work was perhaps inconclusive, main claims were not supported by research as strongly as she would have liked it, key similarities between both societies may have been superficial, and so on. At this point, the father of the candidate sitting in the corner started viciously chewing on his fingernails providing much unneeded soundtrack. However, the committee took all this in stride. They put down their prepared questions and embarked on a forceful defense of the project, which at least in part must have been based on their input. Afterwards, the clouds parted and what followed was an interesting 90 minute discussion illuminating scientific methods of the field. For a complete outsider like myself, I was very impressed with the methodological issues - careful definitions of the terms, establishing the mechanism for the selection of sources, building support for conclusions based on findings, and ultimately explaining the link between two subject areas. The discussion moved slowly through establishing intellectual foundations for the work and surveying the landscape that came to view. All four committee members represented different countries and different national literatures so there was some tendency to make comparisons that were beyond the scope of this Ph.D. but in the end the work stood on its own and offered several interesting directions for continuation. At the conclusion, and after a short recess, the new Doctor of Philosophy was announced.

My own expertise, acquired late in life, is in evaluating and assessing projects in mathematical sciences and I was quite surprised at the intellectual rigor of this work in literature. There is a stark contrast with the quite fuzzy and vague ways in which modern mathematics is assessed. The projects that I am looking at are forward looking, exciting, beautiful, compelling, or alternatively they are narrow in scope, solid, incremental or unrealistic. When the fundamentals of what is being proposed are very precise and well rooted in the overall mathematical landscape, the  uncertain and speculative assessment of the outcomes invites soft and imprecise language which offers hedging against error in judgment. Apparently quite the opposite in literature - the subjectivity in which art is received  and the multitude of ways in which literary works can be interpreted asks for a precise methodology and analysis that takes things down to their fundamentals and dissects the literary works into bits and pieces of comparable nature.
It appears as if in terms of presence of precision and analytical thinking both literature and mathematics yield  a zero-sum game when the product and its evaluation are considered jointly. If it was indeed the case, rather than a superficial observation, it would support a post-modernist view that in the end truth is a cultural construct and regardless of the field of study the overall level of the scientific discourse is tied up to our cultural baggage rather than the intrinsic demands of the field.

Three functions

One, two, three, four - by certain age counting to
hundred, thousand or some other number is a well established
skill. Next, in the first grade, comes addition, and year later -
multiplication. By the end of elementary school we conquer
exponentiation. There is a reason why these operations appear in this
order, and to see it lets make a short mathematical detour. Consider
operation of composition (or stacking up) and look back at addition,
multiplication and exponentiation. In these terms, counting, that is
repeatedly adding one, is the simplest one. In order to compute x+y
one needs to take x as an input and repeat (compose) adding one y
times. To get xy we start with x and repeat addition y times, and
finally for x^y we begin with x and repeat multiplication y
times. This of course can be continued forever leading to even more
complicated operations, but we may not need to go any further. Note
that in this approach the role of x and y are quite different. While x
is an ordinary integer which is an input, y tells us how many times
some operation has to be repeated. A computer scientist would say that
these are different data types. Consequently the obvious fact that x+y
is the same as y+x is not that clear in this setting and the fact that
x and y can be interchanged is no longer true for exponentiation and
beyond. This approach points to a mathematical hierarchy and this in
turn indicates increasing complexity level.

I will try to picture the universe as seen by these three functions. The underlying mathematical hierarchy will imply that these pictures have also increasing complexity and the next one subsumes the previous ones. Each next one will offer a bigger picture and it will provide understanding of the
one below which cannot be accomplished there. This can be viewed as a
mathematical analogy similar to being in dimension one, two, three and so on.

To avoid confusion we will adopt anti-platonistic or phenomenological view of reality which seems to be quite well rooted in the current physical theories. Rather than seeing the reality as a
collection of instantiations of some primordial ideas (ala Plato), we will assume that reality is well defined and quite concrete. However, only small fragment of it is accessible to us and furthermore,
abstract ideas are tokens that we use to communicate our thoughts about it. Consequently, as individuals we can live in quite different worlds, and see the reality quite differently.

Additive World


Additive World is rather flat. It is populated by various quantities and it does not give us significant tools to compare them. Most numbers have units attached to them and it is not easy to sort it
out. We have trillions of dollars of national debt, 10% unemployment, hundreds of microsiverts of radiation from broken Japanese nuclear reactor, and so on. Each number has a song to sing but it all adds up to a lot of noise. In the end, we have only that much capacity for retention of this information, and not much use for it.

Additive World is also static, or at least it does not change in a predictable and quantifiable way. Like everything it evolves and changes slowly. But it carries us through these changes without meaningful control or understanding of these transformations. We can sense the difference and long for "good old days" but the basic fabric of everyday life is more or less constant. It is very possible that Additive World is what was meant for us because it makes us part of nature and guarantees stability.

The main survival tool in the Additive World is memory, and in the evolutionary scale the ability to produce offspring which pays attention to their parent's lessons. With very limited ability to control, predict and craft the future, most energy is used to draw from the catalog of past experiences, individual or group-wise. Having a large repertoire of standard behaviors gives an obvious advantage.

Media and advertising cater to our additive side and throw information at us without requiring or wanting us to process it. Internet, which is heralded as the expansion of human mind, creates a overpowering torrent of data. Citizens of the Additive World are not well equipped to handle it.

Living in the Additive World does not obscure the complexities of the reality. However, complex phenomena cannot be dissected and analyzed at this level. The fact that birds can fly is no different from the fact that Superman can fly - both were gifted to their recipients
without their participation or consent. These and similar things can be acknowledged and taken advantage of but they cannot be fully understood.

On the other hand, the lack of ability to explain things in the Additive World is matched by the lack of ability to ask good questions. In fact in the Additive World which is populated by most
living things there is no cognitive gap at all - they ask no questions and seek no answers. It appears that at the moment humans are the only creatures that can move on to the next level.

Multiplicative World

This is Arcadia of scientific revolution, and the picture of the universe which is responsible for the current state of affairs. Even though Babylonians and Greeks knew quite a bit about multiplication,
the understanding at the level that I have in mind is due to Newton. Calculus embodies the essence of the Multiplicative World. Its logo is a zigzagging function with maxima and minima
clearly mapped out. That is right - a function represents some physical process, placement of maxima and minima carry out nearly complete description of it, and calculus is the technology to find all
this information.

Of course there is much more - Multiplicative World is a world of quantifiable change. In this world plain numbers have meaning. If you divide the anticipated outcome of plan A and plan B
then this number is telling us something and allows to make choices. In the Multiplicative World we can compute all sorts of cool things, build theories and verify them, and visualize the future
before we make it a reality. When our predictive power fails, as it sometimes happen, we can still postmortem the failures to see what we missed.

Concept of probability and randomness makes its debut at this level, together with all sorts of statistical tools. We can quantify uncertainty and deal with situations where too many things get in a way to be precise.

Complicated phenomena are very well explained in this world. Celestial mechanics, theory of electro-magnetic interactions are cases where three laws or four equations yield almost complete understandig of physical reality.

The Multiplicative World is a world of action, it gives a mindset of a conqueror. It is a reality where you shoot first and ask questions later. It is almost certain that it represents an evolutionary blind alley as its main product is extremely efficient yet compartmentalized thinking
subjugated to interest of an individual.

It is not only the technological revolution that has roots in the Multiplicative World. Experimentation with social systems of last 400 years are direct results of it. Marx said "The philosophers have only interpreted the world, in various ways; the point, however, is to change it." This is perhaps the Multiplicative World at its extreme - intellectual arrogance and sense of invincibility that easily leads to mayhem and destruction.

Exponential world

This world is dark, gloomy and not well understood. Very few people live there and I can only get a glimpse of it. The logo of exponential world is a point with three curves coming out of it - a depiction of state of water as a function of pressure and temperature. The curves represent phase transitions between different states e.g. gas vs liquid. This is a much more complicated and general picture than a function with maxima and minima, although it includes it as a very special one-dimensional
case. A phase transition is a more complex change than passing through a maximum or minimum and we do not have good science to describe it. There is a great deal of mathematics that needs to be
developed to deal with these questions and only some of it exists at the moment.

I would say that Darwin was the first citizen of the Exponential World. Theory of evolution unravels phenomena that do not belong to the Multiplicative World and cannot be adequately explained
there. Cosmic inflation proposed by Guth is another such phenomenon. Both explain phenomenally well lots of very fundamental questions yet most people do not understand neither theory. Perhaps macroscopic manifestations of quantum mechanics belong to this level as well. Of these two perhaps only Darwin's theory has a flavor of a law of nature while Guth's theory is just a very plausible way to explain the observable.

We are more or less lost in Exponential World and our power of mapping the future is nearly gone. Not only that, even our ability to reconstruct present from the past - when all the information is given - is not that easy either. The Exponential World is circumscribed by Now and past and future seem rather irrelevant and disconnected. If in the Multiplicative World wisdom is measured by the ability to change things, in Exponential World wise are the ones who make as little change as possible.

The Exponential World is very complex, with many non-linear interactions. There are perhaps many phenomena related to non-commutativity, existence of time probably most important of them. While multiplicative view opened the wealth of possibilities, the exponential world in contrast is much more
negative - most real life processes cannot be predicted accurately andthis is a feature of complexity that appears at this level. The Additive World from the perspective of the Multiplicative World is
easy to understand with all of its inner workings in plain view, and consequently Exponential World ought to be simple from the viewpoint of the next one up. Yet, as I will argue below, our chances of gaining this higher vantage point are practically non-existent.

Phenomena belonging to the Exponential World are present in everyday life, many as artifacts of out of bounds multiplicative thinking. Market crashes, global warming, emergence of new diseases are the well known negatives, but many biological processes such as growth of a cell, phenomena in population dynamics, and so on, are at this level of complexity as well. Finally, human beings as biological cognitive machines may perhaps be completely describable at this level of complexity. The Multiplicative World handles reality extremely well within domains encompassed by various phase transitions, and it only fails when those boundaries are crossed and entirely new phenomena emerge.

The Additive World is a perception that we share with every other species, and it is based on sensing rather than controlling. The Multiplicative world is perhaps uniquely human and it gave us tools to control many aspects of life on Earth. As this seems to be a result of just few mutations - ability to develop language being perhaps the most important one - it is not
clear that our existence is an evolutionary necessity or a fluke that spells doom for us and the rest of life forms cohabiting the planet.

In any case, the Multiplicative World is perhaps the Golden Age of
Humanity where creation of abstract ideas leads to shaping of reality on a global scale. Finally, the Exponential World is the natural final step in the self-discovery as it points out to the inherent limitations.

More worlds


From purely mathematical standpoint it
would be disappointing if there was no higher way of thinking than the
Exponential world, and the hierarchy should go on forever in a
meaningful way. Perhaps it does, yet I am very dubious if human mind
can go beyond the Exponential World, and in fact whether even the
Exponential World can be fully internalized. I am quite convinced that
Super-exponential world would yield god-like understanding of human
affairs and life on Earth, and if so this is probably off limits to
us. This is because humans as species or individuals are specific life
forms that in all likelihood can be fully understood and explained
within the framework of the Exponential World. The sliver of reality
that we carve for ourselves is as complex as we are and thus it puts a
natural boundary on our cognition.

The panel

Depletion of the ozone layer, deforestation, climate change, pollution, species extinction - the list can go on forever. Changes to the biosphere became a dominant factor in shaping the life of humans, and consequently other species as well. At the same time, from the advances in modeling it became clear that humans might not represent the evolutionary high point. Consequently, in search for how to fix the planet we had to widen the net and reach out for help in unusual places. After the discovery of life on Mars and alien life forms in Lake Mono, decisions have been made to accept proposal submissions from non-human species. Our funding agency was selected to receive and evaluate these projects. Few were expecting anything dramatic, other than the complaints from those who are nearly extinct. Overall, the program is brand new and few know about it. The rules are the same as for humans, with an allowance for supplementary documents in species-specific communication form. Non-humans have to submit through US based institutions and the overhead is several billion percent of the budget. This covers the cost of translation from the native mode of communication to a form that is acceptable to grants.gov. There is a discount if one comes through an EPSCoR state but the costs of explaining what EPSCoR is to notoriously suspicious clients are prohibitively high. Consequently most non-human proposals come through one of our math institutes, which is eager to broaden its base. Proposals from other species usually demand non-human reviews but this is lagging behind. According to lawyers familiar with the issues the conflict of interest rules require detailed analysis of the entire Tree of Life in addition to "who eats who" on a case by case analysis. This is an unexpected boon for our fast growing mathematical biology program. Translation to human readable form is another area where a lot more research is needed. I include below my review of one of the proposals just to indicate the typical product that we have to deal with.

Proposal Title: Bees -- request help CCD

Review: This is a proposal from Bees and it concerns CCD (colony
collapse disorder). The project is only two pages long and the quality
of writing is very low. Even the title is barely comprehensible. Close
to 9,000 hours of video depicting bee dances explaining the proposal is
of little help. From what I understand, CCD is a species-threatening
syndrome which manifests itself in the disappearance of entire bee
colonies. Humans do not know what causes it and apparently bees are in
the dark as well. A lot of finger pointing ensues and bees come across
as real whiners. Without presenting real scientific evidence they have
the chutzpah to blame human pollution and excessive honey extraction
for their troubles. They request reviewing from turnips and passion
fruit, both plants exclusively pollinated by bees. Leaving aside the
fact that this is a clear conflict of interest, getting a review from
a plant species is in initial stages and requires several more years of research and development. Typically one gets half a page, most of which is complaining about climate change and dirty water, because plants are not really all that compassionate and caring. Anyway, bees are threatening to cut down on honey production and pollination efforts if stricter environmental laws are not introduced by bee populated countries. They mention flowers, sky, sun and other things that are not really relevant. They brag about honey being the only food item with infinite shelf life. Apparently, they were told that they should not worry since their species is already preserved on a DNA microarray. However, this does not seem to alleviate their concerns. Overall, a disappointing submission from a species that has a strong record of being useful.

Recommendation: Ignore
%end of review


This year we had several similar projects. One from chickens was really silly (although we are strongly discouraged to use derogatory language when discussing animal projects). They demanded clear cut definitions of free roaming, at least one hour outdoors for each chicken per day, non egg-laying days and so on. With market forces already pushing in this direction they were persuaded that this is not worth 50 years of egg production and withdrew the proposal.

Yet another unfortunate attempt came from yeast. The submitting institution is a small college in Napa Valley and the project is quite well put together. Although it is very clear that the proposal originates from wine makers, there is no mention of wine yeast at all. Instead the project focuses on their lesser comrades - the bread making variety. What follows is the usual litany of complaints. Apparently yeast hates to be in dried form - they find the drying process unpleasant and disrespectful. They like to be in "cubby" soft form, and enjoy being in the refrigerator with the other food rather than in the freezer in total darkness. They do not like Costco and are generally fearful of big containers. In exchange for abandoning the dried form, they propose to clean the Gulf of Mexico from the oil spill. This speaks of their excellent orientation in current affairs but panelists questioned their oil processing ability.

A truly fascinating project (which I did not review) came from
cockroaches. It started a long discussion and went well beyond what
our agency calls "potentially transformative". The proposal from roaches came through grants.gov. It was written in perfect English and submitted by a well-known university renowned for fiercely loyal and luxuriously paid faculty. Its microbiology department is rated as first in the country. The roaches established their track record quickly, although the very details were not easy to check. Their claimed to own controlling packets of stocks of many companies, including Terminix, SC Johnson  (the manufacturer of Raid) and many others. They claim to own tankers and subs that allow them to move around with ease. This all sounded like science fiction and several reviewers started ridiculing the project and claiming that it was a rogue submission originating from humans. Maybe so, but during this discussion someone noticed that facade of the building across the street suddenly started peeling off in an unusual way and we no longer were certain who is in charge.

As for the demands - roaches ask for the sub-planet, that is total control of everything that is more than 300ft below the ground level. They are willing to make exceptions for mines, caves etc, but it is clear that they do not like us snooping around. In return they offer extraction of raw materials - gold, uranium, copper etc. The process is purely biological and the stuff accumulates in the agreed upon location. The extraction occurs simultaneously in a huge volume in a process that is completely unlike human mining. Roaches also offer sequestering of CO_2 (they seem to like the stuff and need it to grow bigger) which on face value represents a potential solution to the global warming problem. Water purification and desalinization is yet another thing that they nonchalantly throw in. Even if this is an exaggeration perpetrated by fairly disgusting insects it is clear that we should consider it seriously. The project concludes with an offer to cure several diseases and then provides a little detail that indicates profound understanding of human affairs. Apparently roaches own a patent for Viagra, having invented the stuff themselves (via human proxies). They offer to put it in public domain and distribute Viagra in our tap water just like fluoride. There are few technical details - this whole section is a one paragraph really - but basically they propose to use viruses as carriers and arrange activation based on the length of telomeres in target cells (so that people below a certain age would not be affected.) This component of the proposal resonated very strongly with our panel, which consisted mostly of middle aged men. Suddenly there was a lot of support for what one female panelist later described as a fire sale of the entire planet. While our panel recommendation is not significant, and the governing bodies of most of the countries will have to approve the deal, the very composition of these bodies leaves little doubt about the final outcome. A reviewer from former East Germany who traded in 1989 his Trabant for a BMW urged some caution. Others warned about bio-terrorism and noted that roaches can equally well distribute sex inhibitors that will wipe most of the human race; after all they need us only to turn on the tap. Alas, this was all for nothing, these warnings were drowned in the collective affirmation of oncoming sexual bliss.

The final submission was massively non-compliant and in fact incomprehensible. Our friends in the Department of Defense assured us that this is indeed a proposal but that it was submitted to grants.gov by mistake. In the end, the leading theory was that this was a submission to a non-human funding agency, run by roaches by the look of it. Apparently, promises made by roaches require the collaboration of many other species and roaches have lined up their ducks up before making their offer. It is clear that there is a new sheriff in town.