Yes, I have been thinking. I had a hard time relating. I took the time and read word for word, the lyrics and your right. Maybe I should be sleepin, but I do keep thinkin’ about your smile and I cant get enough. Yea, I’ve never been a real night owl, But these days I’m all turned ’round and I can honestly say I am glad I am. Things are different, Things are fun, things are interesting and you make it that way. But the truth is, when I wake up in the mornings and I see you lying there all wrapped up in the blanket, its just something that cant be explained. It sets the mood for the day and its amazing. So yea Im have been thinking and your right. It is my song, but I am glad it is.

There are a whole bunch of theorems in Riemannian geometry to the effect that “if the Riemannian manifold has property A of the curvature, then it has the topological property B.” Over the rest of MaBloWriMo and in the following weeks, I aim to talk about a few such results. The first one characterizes manifolds of negative curvature.

Negative curvature

Let be a Riemannian manifold with Riemannian metric Say that has negative curvature if for all ,

 (Later I will interpret this in terms of the sectional curvature, which I have not yet defined.)

Statements

Theorem 1 (Cartan-Hadamard) Let be a complete Riemannian manifold of negative curvature. Then for , the map is a covering map. In particular, if is simply connected, then it is diffeomorphic to .

Of course, the diffeomorphism doesn’t have to preserve the Riemannian metric.

The strategy of the proof is as follows. First, we will show that the map is an immersion (though in general not injective), using the discussion yesterday about how Jacobi fields determine the differential of the exponential map. Then we will invoke

Proposition 2 Let be a complete Riemannian manifold. Suppose and the map is an immersion. Then is a covering map.

The condition of the result is often stated to the effect that “ has no conjugate points to .”

To see this, we will appeal to yet another result:

Theorem 3 (Ambrose) Let be a surjective morphisms of Riemannian manifolds with complete. Suppose preserves the metric on the tangent spaces. Then is a covering map.

I will work backwards to prove these three results.

Proof of Ambrose’s theorem

The idea is to use exponential coordinates. Firstly takes geodesics to geodesics, at least locally. Indeed, if is a curve in , geodesics locally minimize length, and is locally an isomorphism of manifolds. By splitting a geodesic in into small pieces, it follows that maps geodesics in to a broken geodesic in , but since is smooth, just maps -geodesics to -geodesics.

So let . We will find a small neighborhood of such that has components diffeomorphic to . Indeed, take an open star-shaped set containing mapped diffeomorphically onto some open set, say . If is taken very small and is chosen as , we can take to be if is the metric on induced by the Riemannian metric.

Let . Because is a local diffeomorphism, is discrete. I claim that

 Indeed, if , then because preserves curve lengths. This implies that the second set is contained in the first.

For the other inclusion, let us choose and draw the commutative diagram

 The image in is , while by Hopf-Rinow II the image in is . From the diagram it is even clear that is a diffeomorphism.

If we can choose a geodesic between and which we can locally, piece-by-piece, lift it to a piecewise-smooth curve starting at and ending at some point of . Now is proportional to so is actually a geodesic (hence smooth) by these arguments. In particular, the length of is , and . This proves the other inclusion.

So we have . Each is diffeomorphic to . All we need to show is that are disjoint for . Otherwise we could choose and choose geodesics from to in , and to in . The images give two different geodesics from to , contradiction. This proves Ambrose’s theorem.

Proof of the proposition

Since the map is surjective (H-R II) and an immersion by assumption, we can consider the pulled back metric on and apply Ambrose’s theorem to it. The only thing we have to check is that with the Riemannian metric on , it is complete. But geodesics through the origin exist of arbitrary length—they are just the straight lines through the origin, since these lines are mapped onto geodesics in . By H-R, this “completeness at a point” implies the completeness of the whole manifold.

I will actually prove the Cartan-Hadamard theorem in the next post.

“The purpose of having a relationship is not to have someone who might complete you, but to have another with whom you might share your completeness.

You have no need for another in order for you to experience – completely – who you are; and yet without another you are nothing.”

Conversations With God Book 1 p.123

Ok, yesterday I covered the basic fact that given a Riemannian manifold , the geodesics on (with respect to the Levi-Civita connection) locally minimize length. Today I will talk about the phenomenon of “geodesic completeness.”

Henceforth, all manifolds are assumed connected.

The first basic remark to make is the following. If is a piecewise -path between and has the smallest length among piecewise paths, then is, up to reparametrization, a geodesic (in particular smooth). The way to see this is to pick very close to each other, so that is contained in a neighborhood of satisfying the conditions of yesterday’s theorem; then must be length-minimizing, so it is a geodesic. We thus see that is locally a geodesic, hence globally.

Say that is geodesically complete if can be defined on all of ; in other words, a geodesic can be continued to . The name is justified by the following theorem:

Theorem 1 (Hopf-Rinow)

The following are equivalent:

• is geodesically complete.
• In the metric on induced by (see here), is a complete metric space

 

Assume the second item: let be complete in the appropriate metric. Then if for an open interval is a geodesic, consider a sequence . Then , since geodesics move at constant speed (cf. the remark after lemma 2 in the link). Thus the form a Cauchy sequence, converging to some . It is easy to check (by splicing two sequences together) that the limit does not depend on the choice of . In local coordinates we can write , when the geodesic property implies

for suitable Christoffel symbols . The first derivatives are bounded (indeed, constant), so the second derivatives are too. Thus extends to the interval with a right-handed derivative at , and moreover the right-hand derivative at exists and is uniformly continuous in a neighborhood of (by the mean value theorem). Now there is locally a geodesic at with . The function

satisfies the geodesic equation everywhere and is defined on . So we can extend these geodesics to the right, and similarly it is done to the left.

To go the other way, we first prove another Hopf-Rinow theorem, interesting in its own right:

Theorem 2 (Hopf-Rinow) Suppose is defined all of . Then for any , there is a geodesic from to that minimizes length.

The proof is really a nice bit of geometry. This is a global result, unlike yesterday’s theorem.

Consider a small sphere around with respect to the metric such that satisfies the conclusion of yesterday’s theorem. Take the point in (which is compact if is not too big at least) with minimized. Then

because of the definition of via lengths of curves.

There is a geodesic travelling at unit speed with , . In particular,

Let be the set of all with . The boxed statement means that , and is evidently closed. If , then we’ll be done—we’ll have a geodesic from to that minimizes length.

Since is closed, pick its largest element , and let . Choose a small neighborhood satisfying the conditions of yesterday’s theorem. Now if we pick the point in closest to , we have evidently

I claim that . First, . The path from to catenated with the geodesic from to forms a path from to of minimizing length , so it is smooth and a geodesic.

In particular, , so we get a contradiction and hence the second theorem.

Since this post has already reached a certain length, I’ll defer the proof of the second implication in the first Hopf-Rinow theorem for tomorrow.  Also, I should add that I’ve followed Milnor’s Morse Theory, chapter 2, in the proof of the second H-R theorem.

Ok, yesterday I covered the basic fact that given a Riemannian manifold , the geodesics on (with respect to the Levi-Civita connection) locally minimize length. Today I will talk about the phenomenon of “geodesic completeness.”

Henceforth, all manifolds are assumed connected.

The first basic remark to make is the following. If is a piecewise -path between and has the smallest length among piecewise paths, then is, up to reparametrization, a geodesic (in particular smooth). The way to see this is to pick very close to each other, so that is contained in a neighborhood of satisfying the conditions of yesterday’s theorem; then must be length-minimizing, so it is a geodesic. We thus see that is locally a geodesic, hence globally.

Say that is geodesically complete if can be defined on all of ; in other words, a geodesic can be continued to . The name is justified by the following theorem:

Theorem 1 (Hopf-Rinow)

The following are equivalent:

• is geodesically complete.
• In the metric on induced by (see here), is a complete metric space

 

Assume the second item: let be complete in the appropriate metric. Then if for an open interval is a geodesic, consider a sequence . Then , since geodesics move at constant speed (cf. the remark after lemma 2 in the link). Thus the form a Cauchy sequence, converging to some . It is easy to check (by splicing two sequences together) that the limit does not depend on the choice of . In local coordinates we can write , when the geodesic property implies

for suitable Christoffel symbols . The first derivatives are bounded (indeed, constant), so the second derivatives are too. Thus extends to the interval with a right-handed derivative at , and moreover the right-hand derivative at exists and is uniformly continuous in a neighborhood of (by the mean value theorem). Now there is locally a geodesic at with . The function

satisfies the geodesic equation everywhere and is defined on . So we can extend these geodesics to the right, and similarly it is done to the left.

To go the other way, we first prove another Hopf-Rinow theorem, interesting in its own right:

Theorem 2 (Hopf-Rinow) Suppose is defined all of . Then for any , there is a geodesic from to that minimizes length.

The proof is really a nice bit of geometry. This is a global result, unlike yesterday’s theorem.

Consider a small sphere around with respect to the metric such that satisfies the conclusion of yesterday’s theorem. Take the point in (which is compact if is not too big at least) with minimized. Then

because of the definition of via lengths of curves.

There is a geodesic travelling at unit speed with , . In particular,

Let be the set of all with . The boxed statement means that , and is evidently closed. If , then we’ll be done—we’ll have a geodesic from to that minimizes length.

Since is closed, pick its largest element , and let . Choose a small neighborhood satisfying the conditions of yesterday’s theorem. Now if we pick the point in closest to , we have evidently

I claim that . First, . The path from to catenated with the geodesic from to forms a path from to of minimizing length , so it is smooth and a geodesic.

In particular, , so we get a contradiction and hence the second theorem.

Since this post has already reached a certain length, I’ll defer the proof of the second implication in the first Hopf-Rinow theorem for tomorrow.  Also, I should add that I’ve followed Milnor’s Morse Theory, chapter 2, in the proof of the second H-R theorem.

‘It’s a funny way, to make ends meet, when the lights are out on every street. It feels alright, but never complete, without you.’- B.Ditto, ‘Heavy Cross’

‘Painting 2006′, work by Joseph Marioni

As a followup to my previous post, this one covers Public prediction markets.  Up front, I have to admit that my interest in public prediction markets is minimal, mainly because I see very little potential for these types of markets to improve decision-making (public or private).  If they are unable to do this, what good are they?  I started writing this post in May, just after I completed my post on the future of enterprise prediction markets.  Instead of completing this post, I published posts on noteworthy failures of public prediction markets and about market calibration.

Recently, Chris Masse, on his Midas Oracle site, documented the very public failures of prediction markets to forecast the IOC’s eventual decision to hold the 2016 Olympics in Rio and to forecast the winner of the Nobel prize in Economics (or any of the other Nobel prizes, for that matter).  I made several comments on Midas Oracle about these failed markets, and the process has renewed my interest (ever so slightly) in public prediction markets.  Here is the result.

Is there a future for Public Prediction Markets?

Bet on it.  In fact, you may have to.  Exchanges, such as Betfair and InTrade, may be the only sustainable, profitable applications of prediction markets that are available to the public.  Let’s face it, people love to bet on uncertain outcomes.  Even when the odds are against them, people will try to beat the house.  In casinos, the odds are always against the bettor, yet there is no shortage of gamblers and the casinos become glitzier each year.  It’s no mystery where the money is coming from.

Internet-based prediction markets offer the public the convenience of betting at home.  They have the potential to greatly expand the variety and types of things on which wagers may be placed, from political races to trivial events, such as who might win the latest “star search” or who is the best dancer”.   By adding to the variety of betting options, it expands the potential market for bettors.

Take away the real money component, and these prediction markets become nothing more than trivial pursuits.  Hubdub is a good example of a play money marketplace.  While it appears to be well-run, its use for anything other than “entertainment” is questionable.  Eventually, public prediction markets like these will fade away as newer fads invade the consciousness of the play money, esteem-seeking, public bettors.

There is some potential for real (serious) money prediction markets that might provide investors with a hedging mechanism against future events for which there may not be any form of insurance.  For example, a company could hedge against the risk of a particular piece of legislation becoming law (and having adverse effects on the company).

While there is a glimmer of hope that the U.S. anti-gambling laws may be relaxed in the future to allow real money prediction markets, the amounts that may be wagered are likely to be too small to attract any investors who wish to hedge against an uncertain event.  The betting limits will, however, provide a sufficient opening to allow betting exchanges to reach a vast new market in predictions.

Is there any real value in Public Prediction Markets?

Since public prediction markets operate in the same manner as enterprise markets, we can learn more about how these markets work and what makes them work well, by analysing the much more prevalent public prediction markets.  We can learn which types of markets tend to work well and which do not.  This may be useful in identifying appropriate uses for Enterprise Prediction Markets.  We could test public prediction markets to determine their consistency (or lack thereof).  We could make incremental changes to the markets to assess the effects on accuracy, consistency and the potential length of forecasting ability.

We could learn much about the role of information completeness by monitoring the information sets of market participants and comparing markets with similar participants but having differing information sets.  This may lead to insights about using prediction markets to replace some of the costly components of enterprise forecasting processes.  For example, if a public prediction market is able to more accurately (and consistently) forecast key components of an enterprise’s annual budget than the internal corporate methods, it may be possible to improve the efficiency of the planning process.  There may be additional benefits from engaging the enterprise’s customer base in the decision-making process, too. 

Apart from the knowledge gained from operating public prediction markets, one is hard pressed to find any significant benefit of these markets.  Do they help allocate resources to their best uses?  This may be a possible benefit, if the results of certain prediction markets are used to help shape public policy.  But, prediction markets are unproven in their abilities to consistently and accurately forecast or predict future outcomes and events.  Until they overcome these substantial limitations, their use for anything other than trivial pursuits will be rare.

Meditations in James: 28 : Stumbling Christians?

Jas 3:2 We all stumble in many ways. If anyone is never at fault in what he says, he is a perfect man, able to keep his whole body in check.

Have you ever wondered why all the pastoral letters of the New Testament were written?  The simple, short answer is because people aren’t perfect.  Once we can accept that simple truth, the Christian life becomes so much more simple.  If you haven’t realised that, then when you do fail you will feel guilty and the guilt will cling and keep on making you feel bad.  When James says We all stumble in many ways he is saying it to both reassure and to challenge.  When I was a younger Christian I encountered those who preached perfection, and because I knew I was not perfect, I felt really bad about myself. I didn’t realize that when Jesus said, “Be perfect, therefore, as your heavenly Father is perfect” (Mt 5:48) he was giving us a target to aim for, something to work for.

Now theologians sometimes refer to ‘imputed righteousness’ and ‘imparted righteousness’.  Imputed righteousness is the righteousness that God imputes or credits to us when we receive Christ’s salvation.  He declares us righteous in His sight on the basis of the work of Christ.  When we receive Christ we are ‘justified’ or, as some have said, God makes it so it is “just-as-if-I’d” never sinned.  In His sight we are declared righteous.  But any honest Christian knows that from time to time they get it wrong, and there are character imperfections in us that need working on, and this is where ‘imparted righteousness’ comes in.  He has given us His Holy Spirit who is totally righteous, and as we learn to let Him lead us and express Jesus through us, so His righteousness is imparted to us and expressed through us.

John in his first letter also alluded to this: “I write this to you so that you will not sin. But if anybody does sin, we have one who speaks to the Father in our defence–Jesus Christ, the Righteous One.” (1 Jn 2:1). In other words sin, or getting it wrong, should not be a common thing in our lives now, but the reality is that we will stumble, we will trip over our feet and get it wrong sometimes.  John gives two answers to that.  Answer number one: “If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness” (1 Jn 1:9). That is our side of it. Answer number two: if anybody does sin, we have one who speaks to the Father in our defence–Jesus Christ.” (1 Jn 2:1). That is God’s side of it, Jesus speaking up in our defence, reminding the Father that he has died for all our sins.  The challenge that comes with all this, is can we aim to keep sin out of our lives as much as possible?

But then James says something that seems both an impossibility but at the same time a challenge: If anyone is never at fault in what he says, he is a perfect man, able to keep his whole body in check. The person who is careful in what they say and is never at fault in speaking, is a perfect person and that ability to speak righteously reveals the heart that is within and that heart enables us to control our whole life.  Now is it possible to be perfect?  Well, we’ve already covered that above in the first paragraph.  Maturity is certainly something that the Bible suggests we can achieve.  The writer to the Hebrews commented, “solid food is for the mature, who by constant use have trained themselves to distinguish good from evil.” (Heb 5:14).  There are therefore mature people.  Paul also said, “We do, however, speak a message of wisdom among the mature.” (1 Cor 2:6) implying the same thing.  James said earlier, “Perseverance must finish its work so that you may be mature and complete, not lacking anything.” (Jas 1:4).  There he linked it with being complete or whole. Jesus’ call to perfection in Matthew 5 is actually a call to wholeness or completeness. So, rather than worrying about being ‘perfect’, and constantly feeling bad when we spot things that are less than perfect, can we instead aim for maturity, for wholeness and completion? This then becomes a goal to work for rather than a means of condemnation. Recognize that you have some way to go, but actually set yourself the goal of letting God change you, like his word says (2 Cor 3:18), to become more and more like Jesus.

There are two things we can do to facilitate this process of change. The first thing is to let the Holy Spirit search you and help you face up to how you fall short. This is similar to the assessing that Paul says should go on in us when we come to take Communion: “A man ought to examine himself before he eats of the bread and drinks of the cup.” (1 Cor 11:28). There are some things that will be obvious and we need to confess them and deal with them.  Some things we may feel we need the Lord’s help to overcome.  Ask Him.  The second thing is simply to develop your relationship with the Lord.  As we do that, His presence will change us.  Now there are basic disciplines that Christians through the ages have found build and change us – reading the Bible, praying, worshipping, fellowshipping with other Christians, being a witness to others – all these things work in the process of changing us.

So, to summarise, recognize that sometimes you will get it wrong but there are two things to help us there (see above).  Don’t be content with those imperfections: confess them, seek God’s help to overcome them, and at the same time work positively to develop your relationship with Him.  Be changed!

Do I love you because you’re beautiful,
Or are you beautiful because I love you? -Richard Rodgers and Oscar Hammerstein II, Cinderella

King, you can take back your horses.

I don’t need your men.

I am now whole – I’ve been put together again.

It’s all thanks to one – who showed me that he cared.

And now he is with me – even in heart, everywhere.

I am complete; no help is due.

King take back your men, I’m like brand new.

The force that fills the world  text ©2009,  Raj Arumugam; pictures: burningwell

life offers me the best  text ©2009,  Raj Arumugam; pictures: burningwell

Life offers me the best.

Always. Life offers me blessings, hope and energy to accomplish the things I want.

Life offers me vitality and happiness.

I know what I want in life.

I have my vision and my goals.

I have examined my wants and my vision thoroughly

and I know this is what I want.

I have a clear plan for achieving what I want.

Everyday I take several definite steps towards achieving my goals.

Life offers me the best.

Always. Life offers me blessings, hope and energy to accomplish the things I want.

Life offers me vitality and happiness.

Each day I step closer to my goals as I take several specific and purposeful action towards achieving my goals.

I am positive; I am energetic.

I am powerful and purposeful, and each day I move towards my goals and desires.

this new and great day text © 2009, Raj Arumugam; pictures: burningwell

It is a new day.

I wake up to its glory. I wake up to this new moment in life.

It is a new day.

There is hope, there is freshness, and there is new vigor.

I feel the strength this day.  I awake eagerly to the potential of this day.

I wake with eagerness to the opportunities and gifts life brings me this day.

It is a new day.

I wake up to its glory. I wake up to this new moment in life.

I feel the strength of the day.

I feel the energy of this day.

And like the day, I too am strong, I too am energetic.

I wake up to the tremendous potential of this day.

I wake up to the promise and hope each moment brings.

I wake up to energy, opportunity and I wake up to life.

the depth of my mind  text © 2009, Raj Arumugam, pictures: burningwell

My mind is like the sky. It stretches as far as one’s eyes can see.

My mind is like the ocean. There is great depth.

My mind is powerful. My mind is limitless.

It has infinite potential.

I love my mind. I use my mind.

I use my mind to achieve the things I want.

With positive thinking and will, I am strong. I am creative.

I achieve the things I decide  I want to have.

My mind is powerful. My mind is limitless.

It has infinite potential.

I use my mind. I love my mind.

thinking about positive thinking…

text ©2009,  Raj Arumugam;pictures:burningwell

Positive thinking as a natural flow

Positive thinking is our natural state.

Consider, for example, the children amongst us and the young.

They are always full of positive feeling and energy until the adult world changes them through its insidious and prevalent cynicism…and through a long series of tests and evaluations that derive a negative power…and through a constant threat of what the mature world deems to be failure.

Still, people bounce back and many reclaim their natural positivism.

Positive thinking is powerful. It is your birthright. Look carefully in your mind and your environment; look clearly and you will see your resilient nature, waiting and ready.

Seize it. It’s yours.

Purposeful action

Thinking alone will not bring you what you want.

One must have a clear and definite purpose – and one must have a plan to achieve one’s goals.

And one’s plans must be backed up by action and persistence – sustained effort and action which are purposeful, and which draws one closer to one’s dreams and aspirations. Positive thinking, so inextricably linked with our wholesome desires, is that force that gives the initial impetus and which provides the strength and energy throughout the journey, and on in new journeys.

In this context, one should remind oneself of Napoleon Hill’s rather terse statement about one of the main requirements for personal success:

A definite plan, expressed in continuous action.

Napoleon Hill, though his most famous work is entitled Think and Grow Rich, did not certainly suggest that thinking alone was enough.

Central to his teachings is the need for action.

When does it become naivety?

One of the secrets of using this power of positive thinking is to see when mere wishful thinking or plain naivety disguises itself as positive thinking.

The truly positive person will see this disguise and cannot be deceived by this negative force or its representatives. Nor can those in their natural state of positivism be discouraged for long from marching on towards their goals with precise and purposeful action.

For, such people, as Napoleon Hill tells us, have a mind that is closed tightly against all negative and discouraging influences, including negative suggestions of relatives, friends and acquaintances.

Some relevant words from George S. Calson’s ‘The Richest Man in Babylon‘:

Here are a few relevant quotes from the chapter Meet the Goddess of Good Luck.

I have modified the language slightly in order to render the language a bit more contemporary.

Arkad:

During my long life I have watched generation following generation, marching forward along those avenues of trade, science and learning that lead to success in life. Opportunities came to all these people. Some grasped theirs and moved steadily to the gratification of their deepest desires, but the majority hesitated, faltered and fell behind.

The cloth weaver:

From our discussion have I learned that to attract good luck to oneself, it is necessary to take advantage of opportunities.

Arkad:

The truth is this: Good luck can be enticed by accepting opportunity.

Action will lead you forward to the successes you desire.

The person of action is favoured by the goddess of good luck.

This is an essential item. Without hope, I am lost every day. In fact, every minute of every day.

And so, when I am filled with Him and the power of His HOLY Spirit, I hope unswervingly. I don’t deviate from hope at all. This leads me to maturity. This leads me to completeness.

But for right now, until that completeness, we have three things to do to lead us toward that consummation: Trust steadily in God, hope unswervingly, love extravagantly. And the best of the three is love. 1 Corinthians 13:13

begin with love text ©2009, Raj Arumugam; pictures: burningwell

Is there a way in which we can ensure that positive thinking is abiding, strong and easily renewed?
There is a way -  just begin with love.
Love yourself, and love the world – and positive thinking is always yours.

Let’s look at it this way.
If you love your siblings, if you love your parents, your wife or husband you wouldn’t want anything but the best for them, would you?
So love motivates - love brings positive thinking that is ever renewed.

Do everything you do because of this love you have for others – and positive thinking will be yours always. You’ll always be charged and motivated – all you have to do is to think about your loved ones.

When things look difficult and tough, you know you are doing it for those you love, and that will keep you going. When things are right, you’ll be even happier because what you have done is not just for yourself but for people you love.

Expand this love to include  people beyond your family and relatives – expand your love to include your town, your city, your state, your country and even the world – and do everything you do with love. You’ll feel that same power that you feel as when you do things for your loved ones – except now, if you can learn to love the world, your satisfaction is even greater. You have made an even larger group of people happier.

Love yourself too. Just as you love your relatives and the world, you can love yourself. And just as you do things for others, you should also do things for yourself. Love yourself.

Love yourself and love the world.

That love that includes the self, the family, the group and the world will charge you with an awesome power and it will keep you energetic and positive always.
Do everything you do with love and you’ll get there to your aspirations and objectives sooner.
Begin with love. That way you’ll find your positive energy always abiding and constantly self-renewing.

begin with love text ©2009, Raj Arumugam; pictures: burningwell

Gallery – work-study job – reading the preface to the Phenomenology in Kaufmann’s Hegel – after one half hour inspired the thought,

“George Clinton is really cool.” Funk-intelechy

I know that if I try to organize my universe in a way that seems fitting to me I will be in conflict with what I perceive the organization of the world at large to be.

I sit on the floor eating breakfast. How could I possibly be? I am instead writing. I sit on a folded metal chair. Passive voice. The chair is a structured support. The chair holds my ass more than twelve feet from the floor, no more, certainly less. I think … do you? what is needed here is a lifeguard chair… a life guard’s chair would bring a completeness, a peace to this job, to this life, I feel has been lacking since they took my television away.

Some online commercial advert shows two young girls looking at Michelangelo’s David on a computer monitor. One girl says something like “He’s kind of cute, I’d go out with him…”

The largest consumer group is of course everyone. Therefor I am attempting to create a product that everyone will buy – only once in ten years. No, this is not a pyramid scheme. It will work, I tell you. I’ve just got to figure out what that one thing is.

Can’t buy me love, oh
can’t buy me love oh

I hope to appal to other people by acting in a manner I myself find appealing. I need to get a really good objective look at myself – perhaps I’ll hire a private detective to film me while I am unaware, with a hidden camera – Yes! another film – Hidden Camera – in which a person hires a private detective to*

I see those eyelashes like ailerons clicking across the hallway.

*to film his or her person, unbeknownst to his or herself. How could this be made into a film – of low budget? Quite easily – and if an actual hidden camera was being used…

Goddamnit! We were on to something there – back in High School – AP English class if only… well – what can I write, besides: Tomato Sauce gives me stinky gas – make that ass gas. As opposed to automobile gasoline.

A majority of people walk right by the first exhibit – Eamon DeValera – which is a good piece – even though the author’s flailed badly (as do most aging white intellectuals who spent the 1960s in college) on their characterization of the event, of Native Americans in general. Yep, I myself have read A Yellow Raft on Blue Water and Desert Solitaire but I don’t go around getting all bent out of shape about the god damned injuns. If you want to know, I’m just as much a native american as I am French – maybe more so – though roughly one sixteenth, which isn’t very much of anything. If you look at a ruler with  the inches divided into sixteenths you will see that one sixteenth is small.

where are the monads?
there should be monads

If anyone ever got it no one would believe them anyway.

I wonder if it would be a good idea to call 1 800 US SEARCH (as seen on tv) and have them find A. I could probably find her myself and save fifty dollars, but I would need a computer link-up – to the information – information versus reality. Information claims certain people are dead who are in fact living, and sends social security checks to dead people.

You, yes you – bastard! Bad penisboy.

When do all objects become symbolic of death?

…

Still October 21st or tomorrow – after twelve midnight. I let the entire evening slip away. Writing class was cancelled again tonight – as on last Monday – but this time I went u to the classroom to make sure – saw an 8 x 8 or so sketch pad on the piano – which turned out to be someone’s diary/ journal – usually about how nothing good happened over the weekend and a girlfriend. I glanced through it briefly – on the way down in the elevator then gave it to the security guard – nothing about me within, that I could see. Back at the apartment I fell into a state of torpor, stifling ennui, perusing porno mags and fantasizing about faceless, nameless prostitutes. Ended up masturbating for the rest of the evening – from nearly eight o’clock until twelve o’clock. Today I purchased an erotic adult comic – for eight dollars – but it wasn’t any good – mainly the story was boring – how this frigid rich bitch turned into an insatiable slut on a rampage with the click of a button.

Yes, I know that sex is destroying me, and my attempt to integrate sex has not been a complete success, having cost money and been physically dangerous. Mentally I’ve lost days, even weeks but have not lost complete months as has happened previously. I don’t want to keep the magazines now. They are an enticement but the act of merely negating those words and images is not substantial – is really just an act – a staged gesture, I’m so sick of the cycle.

Strange though how girls I find attractive sell their flesh for money – most of the American porn stars get the thumbs down, but some of the European sex workers… Of course I’ve never seen any of those girls in person that I know of, and though the physical can’t be separated out from any person’s general appeal  – physical beauty  seems now like a hoax. Everything seems like a hoax – and I am my own victim. How is it that I can be so careless? What kind of mental barely conscious game of chicken am I playing with myself? See my shirt rumpled, thrown haphazardly on the floor. The dirty dishes in the sink, the incomplete homework. Dirty socks, empty bags, piles of notebooks, papers, books and I know not what, unfinished work left until the last moment, this heavy, soft and lazy mindlessness, I could stay awake for hours more simply staring, all this points toward a hectic morning, no breakfast and a last-ditch attempt to finish my 2D design homework when I should be eating lunch and shopping for something to finish off the base of my 3D project – I should have completed my 3D revision already – but have not begun. What happened to my motivation, when in the face of a simple change in schedule do I decide to cease functioning entirely? Was it this confusion I’m suffering about a girl in writing class? Partly yes. And also the deadly if then game, the unrelenting cause and effect forced to mate, an outcome no one wants. Only halfway formulated, something like this “If I read the adult comic I bought today before going to writing class then nothing will happen between me and girl X.” Then in spite of my having forbidden myself to look at the comic – on pain of losing the girl, I of course look at the comic anyway. At what moment am I saying “I dare you?” How did this entire scheme of relating to the world (Which I have so often renounced and still fear) come to be? I seem to be searching for some sort of oracle – and at the same time it’s Orpheus all over again – Lot’s wife all over again, the needless child all over again. The forbidden is thereby exponentially more tempting. Maybe I need to stop thinking of myself as some sort of super hero. Do I think of myself as a super hero? A fictional movie/ literary character, the complex hero, a cast-off bastard stepchild of Romanticism. A real Howard Doark. A cry baby son of a bitch no talent motherfucker. A prime candidate fo successful and worthwhile suicide. A dictionary owning dick slapper. A monkey spanking layabout.

Earlier today while walking around downtown I was in such good spirits I could hardly keep from smiling outloud, laughing to myself inside. But now I’m sucking shit from a straw shoved up my own ass. I’m feeding lifelessly on my own excreta. I’m wasting time I never had to begin with, still sitting on this fence. Must like that fence post up the ass. The only way out to turn all the violence my pornographic vision perpetrates onto myself. To will myself to sit the fence for no damn good reason. Stinking fingers. Ass. I, I really just need someone to talk to besides myself. A friend, maybe two, but people equal only so much trauma, taking Santa Fe as case in point – how many wrong decisions are possible? All of them, basically. I can’t really worry about anyone else right now, I need to worry about myself. Yet I can’t possibly avoid the unwritten conflict isolation draws me into – with myself as both protagonist and antagonist – and also consider my complete failure to adjust to society (at times, though not always) when exiting a period of isolation. At other times the re-entry has been best – that season of change – a season lacking in any but anemic guttering weather-wise in this East Coast metropolis of an erstwhile forgotten ideal. Brotherly Love. The season does not change. I find no feeling the air that proclaims this October to be Autumn – yet October powerfully reminds me of a time once, long ago, I exchanged my leeched and stringy soul for England, and we all know what happened there, the days are well documented in the pages of this journal.

I once knew a girl up in Gunny
who on long distance calls spent no money
her run ins with men
sometimes ended in sin
but in the end it was all sort of funny

There once was an artist in Philly
who had no place for his poor willy
Through this lack of use
grew a taste for abuse
while dressed up in stockings so frilly

She drew men in like flies
to fat, fresh cow pies

So when E called at eight
this made her quite late
cause the things that he said were so funny

Recently, there have been several very glaring public prediction market failures, including the IOC site selection and the Economics Nobel Prize markets.  Some followers of prediction markets are a bit shocked and concerned, but most, like Chris Masse (Midas Oracle), me, and others are not.  These particular types of prediction markets never had a chance to be accurate.  Had any of these markets actually managed to “pick” the right outcome, it would have been nothing more than a fluke.  Why we continue to waste our time on these types of markets, I’ll never understand.

Jed Christiansen (Mercury’s Blog) is an occasional commenter on Midas Oracle.  I may not always agree with him, but I respect his positions in a number of areas.  However, in response to these very public failures of prediction markets, Jed provided a number of factors that influence the accuracy of prediction markets.  It appears that his comments apply only to outcomes that are determined by a group.  Essentially, he means outcomes that are determined through some form of voting or polling, including elections, IOC site selection, Academy Awards, Nobel Prizes, etc…  While I applaud his efforts to identify the factors affecting prediction market accuracy, I find some of his comments confusing.

For example, Jed mentions that “more members/voters will be better than fewer” (in terms of improving the accuracy of prediction markets).  In these types of markets, the members/voters are determining the actual outcome.  This is entirely independent of a prediction market attempting to predict that same outcome.  Consequently, having more members involved in determining the actual outcome will have no effect, whatsoever, on the accuracy of any related prediction market.  Jed’s comment makes no sense.

Jed is absolutely correct to say that “more objective criteria will be better than less.”  However, all this means is that the more objective the determinants of the outcome, the more likely the market participants will be able to figure them out and predict the outcome.  The fewer the factors and the less uncertainty surrounding their roles in determining the outcome, the easier it will be to predict the actual outcome.  In the extreme, if a condition arises that determines (or causes) the future outcome with a high degree of certainty, the market will be able to predict with uncanny precision.  However,  if the outcome is this easily predicted, perhaps a simple decision model (If… Then…) would have provided the same “prediction”, without the bother of setting up a prediction market.

Generally, I would agree with Jed that “constrained choices will be better than unconstrained choices.”  In keeping with this statement, the fewer the choices, the more likely it is that the outcome will be predictable (only because there are fewer incorrect options)!  However, the IOC markets showed that, even with only four choices, the markets failed.  The real problem is that these markets did not have the necessary information to choose among even a very small number of alternatives.

Again, I agree with Jed that “voters signalling choices before a vote is better than if they don’t.”  Where the outcome is determined by a vote, any prior information about how some or all of the group intends to vote will be important information to be assessed by the market participants.  This merely supports the information completeness principle.  We see many examples of this type of information being accessed by participants (in the IOWA political prediction markets) where political polling influences the market prices.

Finally, Jed made a curious statement about “secretive and less secretive” committees that make decisions and that “neither will likely be as accurate as traditional open prediction markets.”  I have no idea what he means, here!  The committees (secretive or not) are the ones determining (creating) the actual outcome.  The committee has nothing to do with being “accurate” or predicting the outcome.  Traditional markets are expected to predict actual outcomes.  Jed is simply wrong to try and compare these two concepts!

Panos Ipeirotis asked if there is a more principled method of capturing the determinants of prediction market accuracy.  In response, I would suggest that we look to the first principles of prediction markets.  Perhaps the most important of which is that the market possess a sufficient degree of information completeness.  In the examples noted, the prediction market participants did not have an adequate level of information completeness to be able to arrive at accurate predictions, because the method of determining the outcome was far too complex and subjective, even when the choices were limited to four.

The only way, to provide the necessary information to the prediction market, in order for it to accurately determine the otucome, would have been to make all (or many) of the outcome voters (committee members) participants in the prediction market.  Of course, this would be a needless redundancy.  Note that in most of the enterprise prediction markets, many of the participants also take part in the internal forecasting process, effectively including the body of corporate information in the prediction markets.  If internal forecasting processes were to be replaced by prediction markets, it is highly doubtful that the markets would be able to provide accurate predictions.  The required information to make those accurate predictions would be missing.

These types of markets suffer from a fatal flaw, as well.  They are trying to predict a discrete (non-continuous variable) outcome.  “Coming close” means being completely wrong.  These types of markets are only suitable for betting purposes, and even then, only if they are proven to be “well-calibrated”.  It is questionable whether these particular markets were well-calibrated.

I have written fairly extensively on the determinants of prediction market usefulness.  I am especially concerned with their accuracy and consistency, for without these, their use in decision-making is not warranted.  I draw your attention to the following posts:

The Forgotten Principle Behind Prediction Markets

Calibration = Prediction Market Accuracy?

To answer Panos, we do have a general, principled model for assessing prediction market accuracy.  Now, we need to fill in the details.

look up at the sky…text©2009, Raj Arumugam; pictures: burningwell

…look up at the sky – Oh, do look up at the sky…look up at the sky that stretches in all directions and wherever one may turn…look up at the sky all above and that falls beyond the end of the visible earth…look up at the sky that stretches beyond one’s vision and look beyond the sky into limitless space…

…see, time and care and the narrowness of one’s conditioning confine one and bends one’s mind – as one’s back is bent, and one’s neck is loaded down; and one’s eyes are fixed to the spotlight-defined meters as one stands one’s ground…Oh , but just look up at the sky…

…look up at the sky in the day and see its deep blue…look up at the sky and see the clouds and the sun, and the brilliance and the lack of limits and confines…look up at the sky in the morning and see the sun rise, and behold its wonder and its colors…look up at the sky at twilight and look at it at night with the moon and the stars and the infinite space that stretches beyond…

…look up at the sky and behold its wonders and splendor and its power… look up at the sky and the space beyond and behold its brilliance and limitlessness…

Oh, look up at the sky and the space beyond – and behold the limitlessness of the mind…behold there the infinite stretch of your mind, of the mind…behold the skies and space, and behold the power and glory and the unconfined, unconditioned freedom and brilliance of your mind and your being, of the unconfined mind and of unconditioned being…

look up at the sky…text©2009, Raj Arumugam; pictures: burningwell

walk into peace  © 2009; Raj Arumugam, painting by Liang Kai

…a walk brings peace; a walk brings quiet and bliss…a walk brings energy and silence and hope, brightness and balance….

…walk in silence amongst the trees and the woods…there are no objectives in this walk…let it be a walk of love…of that love between oneself and life…of that love in oneself, in nature – of  love in the world…

…if you walk alone, it is good to walk without all that chatter in one’s mind; if you walk with a friend or partner, it is good to walk in silence…… let there be silence as one walks – silence within one, and between oneself and one’s companions…rather, see for  yourself how one is but part of the world as you walk…be part of the nature that surrounds you as you walk…

…observe the trees and the plants and the very path one walks on…observe the very flowers that greet one in one’s walk….there is no need to remark on the beauty or quiet or the special-ness of the place one walks in…one just walks, being part of the world one is in…

…just observe, and meet the trees and the woods and the flowers and the fields that greet one in one’s walk…

…a walk brings peace; a walk brings quiet and bliss…a walk brings energy and silence and hope, brightness and balance….

walk into peace  © 2009; Raj Arumugam, painting by Liang Kai

a quiet walk text © 2009; Raj Arumugam, painting by Tang Yin

a quiet walk

did no one harm;

away from the clamor and the ambitions

and leaving the clutter and vanities

a walk in the silence

and amongst the trees

and just being with the colors

and the feel and the texture of the trunks;

and being with the  tender touch of the branches

that reach out to one

when solitude is crisp silence;

all these being simply  part of oneself

and one’s calm and peace;

walk then, now,

in this and in these ample grounds

amongst the trees and observing the gentle leaves;

let us enter the wholeness that is ours

a quiet walk text © 2009; Raj Arumugam, painting by Tang Yin