Decrypting a Rescue Cat

We adopted a rescue cat. She was trapped, ear-notched, spayed, and vaccinated. It's not normal for a cat that has been ear-notched (indicating sterilization) to end up in a kill-shelter. Normally such cats are released back into their environment to displace fertile feral cats. Nevertheless, she was rescued from the shelter and found her way to Petco where she was available for adoption.  All along the way, her preparation for adoption was subsidized, The adoption fee was just $40. She was estimated to be about 2-1/2 to 3 years old. She was not known to have had a home with humans. She wants to tell her own story but her vocalizations and body language are encrypted in CAT.  It is our job to decrypt her version of events. So we watch and listen to her and build our own picture of her past.

We are pretty sure she had a home at one time. She is too people-oriented to have been born feral but she has wild moments and is obsessed with hunting. So far we've had two half-eaten mice and one dead rat delivered to our bedside from her enclosed catio. She thinks we would enjoy a midnight snack I suppose. If you've ever stepped on half a dead mouse stumbling barefoot to the bathroom in the middle of the night, you will leave a night light on for as long as you own a feral cat. 

She is, not by her choice, an indoor cat; cats don't survive outdoors in our neighborhood. Owls, hawks, bobcats, and coyotes live in the open space adjoining the homes here. Most of her day (when she is not sleeping) is spent looking outside plotting ways to escape. One day we caught her with her paws on the door lever trying to pull it down to escape the house.

Of the more than 20 cats we have owned during our 50+ years of marriage, she stands out in her ability to read us. She looks intensely into our eyes and scans our body language to determine our intentions. She knows by our behavior that we soon will get dressed to go to the theater (she hates that - she expects 100% of our attention on her terms, at home). She anticipates when I'm about to get up and open a door in hopes of escaping into the yard (she succeeded a couple of times - she's lightning-fast). And she is very good at figuring out the perfect hiding place from which to leap in front of us as we walk from room to room.

Her DNA test revealed she was predominantly Norwegian Forest Cat (aka "Wedgie").To let her feel closer to the outdoors, I erected a 6' wire mesh barrier in a 6' 9" door. With no effort, she cleared the barrier from a sitting position. After disappearing for an hour or so she returned home. Clearly, she is an experienced fence jumper likely having honed her jumping skill escaping predators in her feral days. 

She has other escape talents. She instinctively knows the smallest tunnels, picket fence spacing, and openings under fences or fireplace grates that she can enter at full speed.

We are sure she had a litter of kittens, probably lost before she could teach them to hunt. She occasionally yowls a sound that Wedgies use to call kittens back to mom. After yowling, she watches and listens for signs of their return. We teared up when we saw her reaction to a video of kittens searching for their mom. She has never shown an interest in media (TV, computer monitors, etc.) but she leaped onto the laptop circling around it searching for the source of the sound.

She spends the dusk and dawn hours outside in her catio knowing that raccoons and bobcats can't share her quarters and knowing equally well that mice and rats can, rarely successfully. 

Owls hooting put her on high alert. She knows where every owl is at all times. She also is fully aware of other predators, some of which we see and more we don't. If there ever is a cat that could survive our neighborhood, she might be the one but we won't take the chance. She obviously spent a significant portion of her life as a stray or feral successfully spotting and evading danger.

So here's what we think we have decrypted: She did spend time with humans when she was very young; she was lost or abandoned before she was a year old; she weighs in at 8 pounds and probably was
malnourished during her first year of life; she had kittens but lost the litter and still hopes they will return; she learned quickly how to survive attacks by predators and humans with bad intentions; her intelligence and ability to solve problems allowed her to survive in the wild (though she did fall for the feral cat trap, perhaps out of desperation); and she will never give up hunting and searching for her lost litter. 

Like most Wedgies, she is much more like a dog than like other cats we have owned. She waits by the door until we come home, she follows us from room to room, she greets company insisting on being touched but not too much, she comes when her name is called, and she has a much bigger cat vocabulary than other cats. As we get to know her, I hope to decrypt her vocalizations, perhaps by correlating them with her body language which we are beginning to understand pretty well. 

Why Is the Universe Coherent?

Seth Lloyd, a professor at MIT, proposed the first feasible design for a quantum computer. There are now many quantum computers operating around the world. Lloyd specializes in quantum communication, quantum computation, and quantum biology. A few years ago I read Lloyd's book, "Programming the Universe". I was researching the topic of universal consciousness. Lloyd concluded that the universe is a quantum computer that operates using the information inherent in all elementary particles in the universe. What does it compute? It computes itself. It occurred to me that this might be what makes the universe coherent. 

The universe obviously is not a ragtag collection of uncoordinated particles randomly bouncing around; it operates as if it were somehow centrally organized following a rule book that requires every component of the universe to behave according to a grand program containing the laws of physics.

Whether you believe the coherence of the universe is the result of an omnipotent creator or is inherent in the natural laws of physics, there is underlying coordination and communications between all parts of the universe that make it operate in a comprehensible and harmonious manner. How do the components of the universe communicate and coordinate?

Computers manage information by managing bits. Abstract bits are represented by the numbers 0 and 1 but the physical medium for bits can be anything that has two states. A state may be magnetized or not, light present or not, electricity flowing or not, and so forth. Morse code uses dashes and dots as bits. A flash drive uses electrons contained in a "trap" and an empty trap each representing bits. The important point is that organized bits are the building blocks for information storage, transmission, and processing in your smartphone, computer, or other digital devices.

Computers use logic gates to "flip" bits (change 0 into 1 or vice versa) to organize and reorganize bits to perform calculations, create images on a monitor, and produce written characters in a document.

You might guess by now that I am going to conclude elementary particles in the universe organize themselves by carrying and processing bits of information. That's looking in the right direction but the whole story is much more interesting than that. Stay with me; I will try to keep the story simple but coherent.

Elementary particles in the universe carry bits of information; the particle exists in a state that either has yet to express its bit-state, or it has a state that is one or another bit ready to be flipped under the right conditions. At the Big Bang, elementary particles flew in all directions, each carrying its own bit or potential bits. The early universe was nearly uniform revealing no tendency to become interestingly complex. Almost everything everywhere was essentially the same.

Then gravity, a relatively weak force in the universe, began to exploit small variations in the distribution of particles to collect small clumps of stuff. The nature of gravity is to multiply its power as clumps grow; more massive clumps have greater gravitational field and therefore make even bigger clumps. Solid matter and clouds of gasses gathered to form features that would become stars, galaxies, and planets.

As gravity gathers nearby particles, the particles collide. The average atom contains about 20 bits of information. When atoms collide, the result is equivalent to information processing that is performed by a computer. Thus when atoms formed and interacted in the universe, the universe revealed itself to function as a computer.

Physicists and philosophers distinguish between goal-oriented information processing and chaotic information processing. Not all information processing results in something coherent. The universe is computing by flipping bits, there is no doubt about that. So what does it compute? Most material objects simply compute themselves. The chair I am sitting in has coherence because its bits flip in a manner that makes it a reliable place to sit.

Information needs to be preserved (stored, however briefly) to be useful in information processing. A single atom of iron behaves according to quantum mechanics which isn't very useful to store or process data. Put twelve iron atoms together and the quantum behavior aggregates into more classical behavior. The small clumps of iron behave more like the iron that we magnetize to store data. Matter begins to be more coherent. The states of these tiny pieces are now influenced by outside magnetic influences; the 12-atom iron structures begin to communicate with each other. They begin to behave according to rules that allow for ever-increasing complexity. But how does increasing complexity spontaneously spawn more complexity?

Bits can be data or instructions. A few bits of data, combined with very simple instructions that combine data, can result in surprisingly complex patterns. For example, consider Conway's Game of Life. It starts with a simple rule that specifies how a single shaded grid on graph paper affects the shading of one or more of its 8 neighbors (adjoining and diagonal). Repeating the rule over and over generates unexpectedly complex patterns. In other words, complexity can arise from small components and a simple program. The resulting complexity is not evident in the early implementation of the rule.

The coherence of the universe depends on the natural emergence of information-processing rules like clumps of iron "talking" to each other through magnetic influences.

Knowing the rules doesn't give us the ability to predict the future of the universe, they just stimulate complexity that will play out as it will. Mathematics and logic (Gödel's incompleteness theorem and the Halting Problem) have been used to prove that the future course of the universe is inherently unpredictable however structured are the rules. Five billion years ago, the evolution of humans could not have been predicted as inevitable by any amount of information processing in any conceivable computer anywhere in the universe. Quantum behavior continually messes with complex behaviors because of its inherent randomness.

For more than half of the history of the universe, complexity naturally grew without life on earth. Galaxies and solar systems formed from gravitational forces and the bit flipping collision of elementary particles. Then information processing took a small but critical step. Information processing produced the most primitive form of life on earth. There was no magic spark, just a random combination of flipped bits that combined chemicals in a unique manner that allowed self-reproduction.

Were it not for the random influence of quantum physics (more on this in a later blog) life may have ended there. A tedious replicating of identical primitive organisms would likely not have survived long. But quantum behavior is inherently random. Elementary particles exist in an ambiguous state having two binary states at once. When an elementary particle interacts with another particle, quantum behavior demands that one or another state be expressed; the particle can no longer hide behind its quantum veil. In the presence of another particle, the bit has a 50% chance of having one state or the other. This randomness is inherent in all things. Life on earth could not result in identical organisms reproducing without random changes for better or for worse. Lloyd describes one of his favorite steps in complexity as the information revolution called sex which triggered billions of experimental forms of life and subsequent evolution.

Thus evolution happened because quantum mechanics randomly disturbed life generation after generation. In humans, DNA is an elaborate set of instructions and a huge amount of data. Every base pair of DNA has two bits that can be preserved or flipped by information processing instructions inherent in our biology. We are programming ourselves and our offspring with lots of random variation (See a prior blog post "I almost didn't exist").

Messing with reproduction has both good and bad consequences. Surviving organisms reproduce to have a better chance of improving the survival of their species. Weaker organisms become fewer in number on average and, without a turn of luck, will die out. Complexity marches on, building more complexity upon the more successful complexity. Seth Lloyd is fond of likening this process to successive information revolutions that each depend of previous revolutions. Human language preceded written language which in turn preceded printing, and so forth. Each information processing revolution could not have occurred were it not for the previous revolutions.

Seth Lloyd makes a compelling case that quantum mechanics introduces random "experiments" into the emergence of complexity and produces more even complexity. I view this as a sort of "survival of the fittest information processing" that is inherent in the laws of nature. It is fitting that today's information revolution is building on a deeper knowledge of quantum mechanics which is at the very core of a coherent universe.

Check out the many videos and interviews Seth Lloyd has produced for more depth on this subject. And if this subject interests you, I recommend reading "Programming the Universe".

Five Little Known Facts

Which are true?

1. The easternmost, westernmost, northernmost, and southernmost states are respectively, Maine, Alaska, Alaska, and Hawaii. False. Alaska is the most eastern thus holding three of the four positions. Because Alaska reaches into the eastern hemisphere, it is, according to geographers, farther east than Maine.

2. If you and your friend Google the same query, you will get the same list of websites. False. Google builds personalized profiles that deliver different suggested sites to people with different interests. There is a downside to this. Your beliefs, both right and wrong, can be reinforced rather than balanced with objectivity, thus Google can encourage confirmation bias. If you prefer cats to dogs or vice versa, for example, start with your own preference then Google the question that fits your preference first followed by the other question: "are cats better than dogs?" Or Google "are dogs better than cats?"  

3. Only humans deliberately lie. False. Koko, a gorilla who learned sign language, blamed a kitten for tearing a sink from a wall.

4. There is a Nobel Prize in economics. True, but with an explanation. The prize in economics is technically the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. In 1968 Riksbank, Sweden's central bank, donated money to the Nobel Foundation in memory of Alfred Nobel to be awarded to economists for outstanding contributions to the field. It is referred to as the "Nobel Memorial Prize" to distinguish it from the "Nobel Prize" referenced in Alfred Nobel's will. The Nobel Prize is limited to the sciences listed in Nobel's will.

5. Four Corners National Monument plaque marks where Utah, Arizona, Colorado, and New Mexico meet. Mostly true. However, in 1925 a Supreme Court decision overrode an 1860's act of congress to make that true. The original plaque was not placed at the congressionally-designated designated parallel and meridian lines due to primitive survey equipment. In 1925 the Supreme Court ruled that the congressionally designated description of the state boundaries is superseded by the placement of the original survey markers even though the markers were incorrectly placed. 

I Almost Didn't Exist

What are the chances of you or me existing at all? I'm not going to conclude by stating probabilities; it is an impossible calculation as you will see. I am more interested in how people approach this question. I will address two approaches in this post

Whether you believe in a creator or not, the discussion is pertinent. Whether you evolved from a single-celled animal or were created by an omnipotent entity, an exact copy of you would require the same level of complexity.  In other words, however, you came to be it is equally unlikely that you would be among the chosen creatures to walk on this earth.

Regardless of how you approach the question, you will come to a point where you need to calculate the number of combinations of unique genetic material that are possible and ask how likely it is that your exact combination exists. Let's start with the DNA of identical twins. They are not the same person although they have the same combination of genes at birth. Obviously, combinations of genes can't be the entire answer to the question. In addition, an unknown number of possible genetic combinations are not viable human beings. And there are a large number of factors outside genetic codes that matter. 

Nevertheless, conservative assumptions produce numbers. A postdoc in computational biology reports the probability of randomly selecting two identical viable human genes to be: 1/x where x is 1 followed by 10 million zeros. The largest number I know is googol = 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 That's only 100 zeros (Google picked its name as a variation of this to indicate it intended to access a nearly infinite amount of information). Imagine replacing the 100 zeros with 10 million zeros! By the way, there is not even a googol of atoms in the universe by current estimates. And combinations of genes are just one step in the calculation of the chances of you being here at all.

Let's look at the question from a different angle. The average man produces over 30 trillion unique sperms in his lifetime none of which are exactly alike. Neither are two eggs exactly produced by a female alike. You are the unique result of one particular sperm and one particular egg. The probability of your parents coming up with the one and only combination to produce you is incomprehensibly small (less than 1 in 10 trillion).

Then we need to consider the same calculation for your grandparents, and their parents and so forth back through the 40,000 generations or so in human history. We get a nearly infinitesimal number: 1/x where x is 2 with nearly a million zeros following. This is a larger probability than the first approach calculating probabilities of genetic combinations but still pretty small.

But, you are here. Call it a miracle, argue that the probability of your existence equals one, or claim that your creator bypassed all the evolutionary steps and designed you in all that detail from scratch. However you look at it, you won the ultimate lottery; you're here reading this blog post sharing my bizarre musing.

I stated at the beginning of this blog post that such calculations literally are impossible. If you live your life mostly out of harm's way, you are incalculably lucky. There is no greater lottery to win. Enjoy your winnings as best you are able.

Abstraction

I cannot summarize here the thousands of pages written about the concept of abstraction. Instead, I will focus on abstraction in mathematics and discuss some generalizations that naturally arise in the dialogue. Before you set aside this blog post thinking it will get technical, rest assured I will be exploring concepts, not mathematics per se. 

The primary question in this blog post is why mathematics is so tightly connected to concrete phenomena. When I was a young teenager I simply assumed that mathematics was like a language that describes reality. Of course, any description of reality would have a counterpart in the physical world.

But in high school, I became fascinated with Einstein's general theory of relativity. I learned that he used mathematics to predict phenomena that had never been observed. In 1915 he predicted that light would not travel in a straight line but would be bent and twisted by gravity even though it had no mass. Later, in 1919 the phenomenon was actually observed to be true.

This shocked me at the time. If mathematics were just a language that describes reality, how could it describe things that had never been observed in reality? How could it predict future observations?

In my first year of college, I took my first course in philosophy and encountered the concept of abstraction. The answer to my dilemma was there all the time, I had focused too much on physics and too little on philosophy (probably because I spent too many teenage years reading science fiction).

Mathematics is indeed a language that can describe the laws of nature. But, it is not a description of reality, It is a description of reality that strips away irrelevant specifics. For example, the mass of an object does not affect the rate at which it falls in a vacuum (you can drop two bricks and they will fall at the same rate when you glue the two bricks together and drop twice the mass as a single object). Thus, mathematics is an abstraction of related events.

Mathematics "predicts" the same will be true of falling rocks, falling rain, etc. We don't need to observe these events to describe them, mathematics conveniently extrapolates to unobserved events.

Abstraction is, for present purposes, simplification. It works in situations that go beyond mathematical predictions. It allows the categorization of things in general and in specifics. We can parse the universe into that which lies outside the earth's atmosphere and that that lies inside. The inside stuff can be divided into living and non-living things and further distinguish cats from dogs. Things get more specific when I identify our cat, Tikvah among living things; more so yet when I say Tikvah sleeping on my lap as I write this, and so forth.

By forming layers of abstraction, we come to understand reality. We know we shouldn't: try to walk through brick walls, tease mama bears, or leap onto a street from a third-story balcony. We need not treat one brick wall differently from another and we don't need the address of the balcony to determine if we can fly from it. In the blog post, "A Conversation" we can thank abstraction for knowing a brick is a brick.

Evolution has tuned our senses, and those of other animals, to maximize our respective chances of survival and reproduction. Useful abstractions form around these senses. Humans see details in daylight that Tikvah does not see and Tikvah sees details at night we cannot see; she has better peripheral vision and is nearsighted so a mouse has little chance of survival close to her. Below is a comparison between human and cat vision in daylight and at night.

Tikvah's senses categorize her nighttime world into mouse/no mouse and movement/no-movement. Humans see more detail in daylight to spot edible berries on a bush or a hungry predator in the woods. All animals pay special attention to abstract categories that matter most to their survival and the survival of their species. Evolution has embedded in our respective physical bodies the ability to sense what we need to survive and filters out unnecessary information. If we depended on chasing mice at night, we would have better night vision, and our abstract art would be, well, less interesting in my human eyes. It makes sense to me that abstraction is defined by the eyes and mind of the beholder.

The top panels simulate what a human sees,
the bottom panels simulate what a cat sees.

Tangled Musings

I started this blog simply to have a record of my random thoughts. I had no particular goal except to organize and sort my musings, fact-check my preconceived beliefs, and hopefully become more enlightened. The learning is happening as each blog entangles others. 

Like strings in a box that become knotted with small agitations (we've all been there), the random nature of my musings becomes more tangled the more I write. Looking back at the post that precedes this one (What makes it ... IT), there are tentacles reaching into earlier posts that reach into other posts forming an increasingly complex knot. My discussion of essence is deliberately tied to "A Conversation". It happened to tie to "A Lifelong Attitude Adjustment". Eventually, I expect the entire blog will, without deliberation, become a tangled tapestry that weaves every musing into an abstract mural that has yet to take form. Why?

At the University of California, San Diego, Dorian Reymer and Douglas Smith showed that agitated strings in a box had a probability of knotting that increased sharply with long agitation time, long length and higher flexibility. They approached the problem scientifically and mathematically. They agitated strings of various lengths and flexibility by tumbling them in boxes of different sizes. The project explained why "strings" (necklaces, electrical cords, ropes, etc.) seemed to spontaneously tangle. Indeed, it took very little agitation to knot the strings. Interestingly, a knot always began at one end and became more complicated with more agitation. Once a knot began to form at one end, it was rare that a knot would form at the other end.

I expect that the longer is my blog and the more flexible are my topics, the more entangled the posts will become, like knots in a string. It makes me wonder if all the stuff I have in my memory is a string, if my head is a box, and mental agitation is me messing with the string. I just hope as I age my individual musings add up to an accurate portrait of who I hope to be.

It was the post about Deidre drawing my attention to the essence of things that was the end of the string that relates directly to the knot in my blog. If I were more clever, I probably could find a level of abstraction that mathematically relates agitated strings to all my future blog posts. 

I intend to devote a future post to the concept of abstraction. And, of course, that will further agitate the string. In a few years, I will look back and see the evolving whole that will say a lot about me --I hope I like it.

What makes it ... IT?

In an earlier blog post titled "A Conversation With My Son," I promised a later blog would answer the questions: What makes a brick a brick, what makes our car our car, what makes Ali, Ali? The conversation was with our son, Branden.

As an economist, I naturally thought about property rights. There are no preordained lists of natural resources waiting to be claimed. Yes, early humans laid claim to a cave or captured territory rich with food, but it was human declaration backed by social power or brute force that enforced such claims. 

Today our laws and institutions, together with land surveyors, pound stakes in the ground, and make my property mine. The car is ours because it is registered to us in a database secured by government authority. Cars have embedded identifiers in whole (a VIN) and in part (part numbers). The property right to the car, even when the parts are changed, is established by databases that house these numbers. A brick looks like a brick, feels like a brick, and is used in ways bricks are used. Ownership of the brick is established by trade and it becomes mine when I purchase it to build a wall on my property. Change out a brick and the wall remains mine. Change out all bricks and it is still my wall.

But the question about Ali stumped me. He sheds millions of cells every day and they become the "property" of mites, plants, and whatever in nature recycles them. Clearly, there is a deeper question here. Ali remains himself and he is more than a walking talking collection of cells to which he has property rights. Like the car, codes are embedded in the cells that can identify him (DNA, e.g.). But that answer isn't satisfying; it misses the deeper point of the question. Ali is who he is, not just because of his DNA, but because he has a history, feelings, a community of family and friends, and aspirations that are not entirely dependent upon the particular cells that constitute his body at any one time.

Branden rarely accepted as fact things that weren't logically anchored in his mind. He once challenged his junior high teacher who claimed that the number represented by .999 (ad infinitum) was equal to the number 1.0. The teacher later described asymptotic convergence as an infinitely long curve forever approaching, but never actually touching a horizontal line. Branden argued that you can't have it both ways.

His conversation about bricks, our car, and his friend Ali was typical of his unusual queries. I became determined to understand, to the best of my ability, the answer to his question "what makes anything itself"? Property rights and (biological or digital) data don't really lead to a satisfying answer to the question.

It was our daughter, Deidre, who (unknowingly) led me to the answer that satisfied me. Deidre constantly surprised me with her natural ability to see the essence of things. Conversations with her are filled with insights that hit one with the impact of a punch line to a joke. You don't see it coming, but when it is there, you recognize she has cut right to the heart of an issue.

This talent has its downsides. She has a hard time telling long jokes. I told her a joke attributed to Ronald Reagan. He had addressed a group of lawyers explaining that FDA researchers in Washington DC began substituting lawyers for rats in their experiments. Why? There are more of them, you don't get attached to them in the laboratory, and there are some things rats just won't do.

Deidre retold the joke: "So, there are these white rats with red eyes and, ... uh ... they won't do what they are supposed to do but lawyers will." The joke had evoked a vivid image of the red-eyed white rats and a lab full of lawyers doing whatever they were told to do. The punch line was an incidental detail appended to the essence of what Deidre experienced listening to the joke. And that steered me towards the answer I was seeking.

A brick is a brick not just because it looks like a brick and feels like a brick. A brick is what made up the house the big bad wolf couldn't blowdown. It is what angry protesters throw at things they hate. It has a unique history in one's mind and a physical place in one's yard. The essence of a brick is everything a brick has been in one's experience.

Each of us is familiar with bricks because we are biologically similar enough to be able to identify and name objects that have familiar characteristics. But when we encounter bricks, our brain accesses, consciously or unconsciously, uniquely personal memories of our experiences with bricks. The essence of bricks is made up of these experiences. The essence of something is not the "picture" our senses transmit to our brains but is a by-product of model-dependent realism; according to Steven Hawking and Leonard Mlodinow we cannot know what is really "out there", we can only "know" the model our brain assembles from its sensory input. Our mental model of a brick is the sum total of all the information we have acquired about bricks.

Ali is Ali, not only because the momentary collection of his cells look like Ali. He is Ali because of his history, his relationships with others, his personality that evolves over the years. The cells, both dead and alive, are just the vehicle that allowed older versions of Ali to become newer versions of Ali. Yes, information is retained in Ali's cells by virtue of his DNA and other biological elements, but that the essence of Ali. Ali's friends have a model of Ali embedded in their brains that is independent of his present form. The essence of Ali is uniquely personal to each person (or animal) that knows Ali.

I envy Deidre but I cannot aspire to match her ability to effortlessly see the essence beneath the form. It is a source of great creativity, humor, and, at times I am sure, her discomforts. It makes her a great writer, an excellent photographer, and a very creative problem solver. I love the insights that I get from her unique perspectives. Without her, I would (sadly) still be pondering Branden's question thinking about property rights, quantum physics, entanglement, and the nature of material things.

Thank you, Branden. You taught me to listen to children more deeply and thoughtfully. Thank you, Deidre. You taught me that the words and pictures we wrap around our experiences often cloak the essence of what's really there. My life has been greatly enriched by both of you.