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in Chat

Hello, this is a really exciting site and project, and I am grateful for and happy about the opportunity to participate.

I am oriented towards math, the sciences, and music. My undergrad degree was from U. Penn. in Math. My most memorable learning experiences there were in linear algebra, in the shocking precipice of abstract algebra, and taking differential geometry in senior year with E. Calabi. He walked around the room with his arms horizontally outstretched, pivoting in an airplane like way, to illustrate what torsion was. I came to him with some ideas about integrating functions on manifolds, which were all quite wrong, because I hadn't grasped differential forms. He gave me the deepest lecture I can ever remember. I was frustrated at not being able to connect the abstract symbolism of the tensors with a geometric vision, and I asked him if he could see them pictorially. He said something like Always, and he transmitted that this field of forms was like a swirling painting in his mind. Then he told me not to worry about the difficulty translating from algebra to geometry, that it was like learning French and Italian -- first you have to learn each language before being able to translate between them. That lecture stuck with me for decades.

In my younger days I built all kinds contraptions with electronic circuits, and landed a job working in a wood-working shop, redesigning the logic for a relay-controlled 20 foot by 20 foot automatic power saw.

Since then I've worked as a software developer, including work as a lab programmer in the psychology department and the Center for Neural Science at NYU. I did a Ph.D. in computer science at Courant. My dissertation was on a query-processing problem for a restricted type of expert system. Suppose, for example, you have a medical expert system, that asks a doctor for a series of observations about a patient, and then makes various diagnostic assertions. Consider, then the following type of meta-question that we can pose about the system: If the doctor inputs a very low value for blood sugar, which is below a specified threshold, then can the given set of inference rules machine still reach the conclusion of Diabetes? In a dual sense, if the input value for blood sugar is very high, then do the rules inevitably reach the conclusion of Diabetes? For a special class of rule systems, I came up with an algorithm that would solve these reachability queries. There was some really interesting logic there, but, alas, we never came up with a meaty enough application of this type of rule system (they are hard to scale up from toy examples) to justify the work, and only one publication resulted. I didn't succeed in the Journal race. So be it.

Now I'm settled into a career as a professional software developer in the NYC area. We live in Brooklyn -- my wife, myself and two daughters 9 and 11. We're very much into Balkan music. I have been taking Jazz guitar lessons for about 15 years. It's all about Signal Processing. One day I may apply the DFT to some Afro-Cuban rhythms, in search of a formula for Swing. Blasphemous? Impossible? Perhaps. Although I am of Eastern European descent, I have some environmental Latin heritage, having lived the first five years of life in Spanish Harlem, the land of Tito Puente.

Here are some broad research problems that I ponder. How can we represent the structure of scientific theory -- embedded within its social context -- on a machine? For example, general relativity, or evolution. I'm picturing a Wiki that has a formal, structured core, containing axioms, definitions, theorems, algorithms, programs and data observations. How would you represent, on a machine, debates and contradictions between contending theories? Take, for example, Classical, Marxian, and Neo-Classical economic theories. Each theory is a very complex graph of nodes (each containing a definition, theorem, example, etc.), and the ensemble of the theories is a larger graph -- but the larger graph has relationships of contradiction and inconsistency between the nodes of the the conflicting theories. For that matter, there may be relationships of inconsistency among the nodes of each of the theories alone. We need tools and methodologies to help us sift through the morass of theories in social science. All the more so, because of the highly politicized nature of the social domain. (This deserves its own discussion thread, I will repost this paragraph elsewhere.)

In any case, I'm glad to be Here. This is the most meaningful and productive context that I have found for dealing with the challenging -- and daunting -- problems of life on Earth today.

Best Regards

I am oriented towards math, the sciences, and music. My undergrad degree was from U. Penn. in Math. My most memorable learning experiences there were in linear algebra, in the shocking precipice of abstract algebra, and taking differential geometry in senior year with E. Calabi. He walked around the room with his arms horizontally outstretched, pivoting in an airplane like way, to illustrate what torsion was. I came to him with some ideas about integrating functions on manifolds, which were all quite wrong, because I hadn't grasped differential forms. He gave me the deepest lecture I can ever remember. I was frustrated at not being able to connect the abstract symbolism of the tensors with a geometric vision, and I asked him if he could see them pictorially. He said something like Always, and he transmitted that this field of forms was like a swirling painting in his mind. Then he told me not to worry about the difficulty translating from algebra to geometry, that it was like learning French and Italian -- first you have to learn each language before being able to translate between them. That lecture stuck with me for decades.

In my younger days I built all kinds contraptions with electronic circuits, and landed a job working in a wood-working shop, redesigning the logic for a relay-controlled 20 foot by 20 foot automatic power saw.

Since then I've worked as a software developer, including work as a lab programmer in the psychology department and the Center for Neural Science at NYU. I did a Ph.D. in computer science at Courant. My dissertation was on a query-processing problem for a restricted type of expert system. Suppose, for example, you have a medical expert system, that asks a doctor for a series of observations about a patient, and then makes various diagnostic assertions. Consider, then the following type of meta-question that we can pose about the system: If the doctor inputs a very low value for blood sugar, which is below a specified threshold, then can the given set of inference rules machine still reach the conclusion of Diabetes? In a dual sense, if the input value for blood sugar is very high, then do the rules inevitably reach the conclusion of Diabetes? For a special class of rule systems, I came up with an algorithm that would solve these reachability queries. There was some really interesting logic there, but, alas, we never came up with a meaty enough application of this type of rule system (they are hard to scale up from toy examples) to justify the work, and only one publication resulted. I didn't succeed in the Journal race. So be it.

Now I'm settled into a career as a professional software developer in the NYC area. We live in Brooklyn -- my wife, myself and two daughters 9 and 11. We're very much into Balkan music. I have been taking Jazz guitar lessons for about 15 years. It's all about Signal Processing. One day I may apply the DFT to some Afro-Cuban rhythms, in search of a formula for Swing. Blasphemous? Impossible? Perhaps. Although I am of Eastern European descent, I have some environmental Latin heritage, having lived the first five years of life in Spanish Harlem, the land of Tito Puente.

Here are some broad research problems that I ponder. How can we represent the structure of scientific theory -- embedded within its social context -- on a machine? For example, general relativity, or evolution. I'm picturing a Wiki that has a formal, structured core, containing axioms, definitions, theorems, algorithms, programs and data observations. How would you represent, on a machine, debates and contradictions between contending theories? Take, for example, Classical, Marxian, and Neo-Classical economic theories. Each theory is a very complex graph of nodes (each containing a definition, theorem, example, etc.), and the ensemble of the theories is a larger graph -- but the larger graph has relationships of contradiction and inconsistency between the nodes of the the conflicting theories. For that matter, there may be relationships of inconsistency among the nodes of each of the theories alone. We need tools and methodologies to help us sift through the morass of theories in social science. All the more so, because of the highly politicized nature of the social domain. (This deserves its own discussion thread, I will repost this paragraph elsewhere.)

In any case, I'm glad to be Here. This is the most meaningful and productive context that I have found for dealing with the challenging -- and daunting -- problems of life on Earth today.

Best Regards

## Comments

Welcome!

In that case you may be interested in the work of mathematician Jason Brown who analyzed Beatles songs using FFT, you can find an intro to his findings here: “Hard Day’s Night” Mystery chord solved using math.

`Welcome! <blockquote> <p> I have been taking Jazz guitar lessons for about 15 years. It's all about Signal Processing. One day I may apply the DFT to some Afro-Cuban rhythms, in search of a formula for Swing. Blasphemous? Impossible? Perhaps. </p> </blockquote> In that case you may be interested in the work of mathematician Jason Brown who analyzed Beatles songs using [[FFT]], you can find an intro to his findings here: <a href="http://www.noiseaddicts.com/2008/11/beatles-hard-days-night-mystery-chord-solved/">“Hard Day’s Night” Mystery chord solved using math</a>.`

Hi David, You might like http://www.cs.uu.nl/wiki/GenericProgramming/HarmTrace.

"(Harmony Analysis and Retrieval of Music with Type-level Representations of Abstract Chords Entities) is a system for automatic harmony analysis of music. It takes a sequence of chords as input and produces a harmony analysis, which can be visualised as a tree."

It's fun.

`Hi David, You might like <http://www.cs.uu.nl/wiki/GenericProgramming/HarmTrace>. "(Harmony Analysis and Retrieval of Music with Type-level Representations of Abstract Chords Entities) is a system for automatic harmony analysis of music. It takes a sequence of chords as input and produces a harmony analysis, which can be visualised as a tree." It's fun.`

Welcome to the Azimuth team, David Tanzer! It's great to hear about your diverse interests. A number of us do music things here, including me. Maybe we should form a band someday.

But even better is that you're bringing your diverse skills to the Azimuth Project.

You wrote:

This is a very big problem. I'm glad to see you're interested in related but smaller and more manageable 'toy problems' like the ones that can be handled with stochastic Petri nets. That's how I'm trying to tackle 'network theory': starting small, understanding simple formalisms fairly thoroughly, then gradually working up.

I think you might be interested in a formalism that's more flexible and complex than Petri nets but still perhaps mathematically beautiful: the formalism of bigraphical reaction rules. I've begun trying to learn about this, nudged along by Ken Webb and Cameron Martin here. You might try these, though I suspect something much clearer could be written:

A brief introduction to bigraphs, Programming, Logic, and Semantics group (PLS) at IT University of Copenhagen.

Robin Milner, Bigraphical reactive systems: basic theory.

I'm really glad both you and Ken are interested in explaining Petri nets from a more practical, computer-based perspective than my own. Maybe someday we can build some interesting and useful models of biosystems, ecosystems or climate systems. That would be the big payoff of all this theoretical work. I'm trying to come up with some ideas about that... more later.

`Welcome to the Azimuth team, David Tanzer! It's great to hear about your diverse interests. A number of us do music things here, including [me](http://math.ucr.edu/home/baez/music/). Maybe we should form a band someday. <img src = "http://math.ucr.edu/home/baez/emoticons/tongue2.gif" alt = ""/> But even better is that you're bringing your diverse skills to the Azimuth Project. You wrote: > Here are some broad research problems that I ponder. How can we represent the structure of scientific theory -- embedded within its social context -- on a machine? For example, general relativity, or evolution. I'm picturing a Wiki that has a formal, structured core, containing axioms, definitions, theorems, algorithms, programs and data observations. How would you represent, on a machine, debates and contradictions between contending theories? This is a very big problem. I'm glad to see you're interested in related but smaller and more manageable 'toy problems' like the ones that can be handled with stochastic Petri nets. That's how I'm trying to tackle 'network theory': starting small, understanding simple formalisms fairly thoroughly, then gradually working up. I think you might be interested in a formalism that's more flexible and complex than Petri nets but still perhaps mathematically beautiful: the formalism of bigraphical reaction rules. I've begun trying to learn about this, nudged along by Ken Webb and Cameron Martin here. You might try these, though I suspect something much clearer could be written: * [A brief introduction to bigraphs](http://www.itu.dk/research/pls/wiki/index.php/A_Brief_Introduction_To_Bigraphs), Programming, Logic, and Semantics group (PLS) at IT University of Copenhagen. * Robin Milner, [Bigraphical reactive systems: basic theory](http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-523.pdf). I'm really glad both you and Ken are interested in explaining Petri nets from a more practical, computer-based perspective than my own. Maybe someday we can build some interesting and useful models of biosystems, ecosystems or climate systems. That would be the big payoff of all this theoretical work. I'm trying to come up with some ideas about that... more later.`

Hi John, Tim and Jim, Thanks for the warm welcome, and the reading references.

John, it would be great to eventually build the types of models you mention. Something to help people understand more about what is going on. I like the idea that clear software can work as a bridge between abstract theory and its effective interpretation. It's one text with two interpretations.

Well I have a lot to catch up on here. I will be following up on other threads. I may have some questions about bigraphs that you, Ken or Cameron could help with.

Regards, Dave

`Hi John, Tim and Jim, Thanks for the warm welcome, and the reading references. John, it would be great to eventually build the types of models you mention. Something to help people understand more about what is going on. I like the idea that clear software can work as a bridge between abstract theory and its effective interpretation. It's one text with two interpretations. Well I have a lot to catch up on here. I will be following up on other threads. I may have some questions about bigraphs that you, Ken or Cameron could help with. Regards, Dave`

I am just beginning to learn about bigraphs, but if you ask questions I can learn a lot by pretending to be an expert and answering them.

`I am just beginning to learn about bigraphs, but if you ask questions I can learn a lot by pretending to be an expert and answering them. <img src = "http://math.ucr.edu/home/baez/emoticons/tongue2.gif" alt = ""/>`

Hi David -- it's nice to see you here. I'm also a software developer living in Brooklyn. Music ain't so bad either. And as for Petri nets...

Looking forwards to talking with you further!

`Hi David -- it's nice to see you here. I'm also a software developer living in Brooklyn. Music ain't so bad either. And as for Petri nets... Looking forwards to talking with you further!`

Allan, Great, we have a lot in common. Also I'm employed in the financial sector. I live in Park Slope. My daughters are 9 and 11. I can play rhythm guitar -- swing. Are there any other members in the NYC area? We should have a coffee. You can ring me on gmail, I go by the name of dave.tanzer.

Cheers

p.s. Maybe you could give me a lesson on Haskell.

`Allan, Great, we have a lot in common. Also I'm employed in the financial sector. I live in Park Slope. My daughters are 9 and 11. I can play rhythm guitar -- swing. Are there any other members in the NYC area? We should have a coffee. You can ring me on gmail, I go by the name of dave.tanzer. Cheers p.s. Maybe you could give me a lesson on Haskell.`