( ) Research question: Why is it important to understand the physical limits of financial trading?
( ) Application: possible training course for supervisors and regulators around the world
I shall be adding to this list of references from time to time and reorganising its entirety when appropriate:
( ) IOSCO'S Recommendation for Standard Regulation on HFTs
Regulatory Issues Raised by the Impact of Technological Changes on Market Integrity and Efficiency - Consultative Report
OISU - ISOCO (July 2011)
http://www.iosco.org/library/pubdocs/pdf/IOSCOPD354.pdf
( ) SEC Report on May 6, 2010 Flash Crash (100930)
http://www.sec.gov/news/studies/2010/marketevents-report.pdf
( ) Zerohedge (100623): http://www.zerohedge.com/article/how-hft-quote-stuffing-caused-market-crash-may-6-and-threatens-destroy-entire-market-any-mom
( ) Nanex Analysis of the Flash Crash (100618): http://www.nanex.net/20100506/FlashCrashAnalysis_CompleteText.html
[ ] pay particular attention to "quote stuffing" which Nanex says should be banned: http://www.nanex.net/20100506/FlashCrashAnalysis_Part4-1.html
( ) Nanex Analysis of the SEC's Flash Crash (May 6, 2010) Report of Sept 30, 2010 (120412):
( ) Email exchange on the definition of LIQUIDITY: http://www.nanex.net/aqck/2977.html
( ) Nanex updated analysis on April 11, 2011--check out the 2nd chart especially when Wadell and Clarke whom the SEC has blamed for the Flash Crash and the W&C has accepted such blame, could NOT PHYSICALLY be the one who was involved in the perpetration of the flash crash! http://www.nanex.net/FlashCrashFinal/FlashCrashAnalysis_WR_Update.html
Background Readings:
[ ] http://www.zerohedge.com/article/guest-post-deconstructing-algos-part-1
[ ] http://www.zerohedge.com/article/guest-post-deconstructing-algos-part-2-leveraging-chaos-high-frequency-arbitrage-opportuniti
[ ] http://www.zerohedge.com/article/guest-post-deconstructing-algos-3-quote-stuffing-means-restoring-arbitrageable-latency-or-cq
[ ] http://www.zerohedge.com/news/guest-post-deconstructing-algos-part-4-phase-space-reconstructions-cnty-busted-trades-suggests-
HFT REVIEW White papers, academic and industry reports
ACADEMIC ARTICLES ON POINT
http://www.hftreview.com/pg/main/academic-studies/
INVESTIGATIONS
[ ] SEC Probes Ties to High Speed Traders
http://online.wsj.com/article/SB10001424052702303816504577321864050711038.html
NY TIMES ARTICLES
135 articles on high frequency trading as of April 4, 2012
http://topics.nytimes.com/topics/reference/timestopics/subjects/h/high_frequency_algorithmic_trading/index.html
EUROPEAN REGULATIONS
[ ] MiFID 2 Barnier
http://hft.thomsonreuters.com/2010/09/23/eus-barnier-throws-spotlight-on-dark-pool-trades/
REUTERS THOMSON HFT NEWS
http://hft.thomsonreuters.com/
WHARTON article
http://knowledge.wharton.upenn.edu/article.cfm?articleid=2345
INSTITUTIONAL INVESTOR
10 articles
http://www.iijournals.com/page/HighFrequencyTrading
ACADEMIC PAPERS
[ ] Conflicting Codes and Codings
How Algorithmic Trading Is Reshaping Financial Regulation
Marc Lenglet
Abstract
Contemporary financial markets have recently witnessed a sea change with the ‘algorithmic revolution’, as trading automats are used to ease the execution sequences and reduce market impact. Being constantly monitored, they take an active part in the shaping of markets, and sometimes generate crises when ‘they mess up’ or when they entail situations where traders cannot go backwards. Algorithms are software codes coding practices in an IT significant ‘textual’ device, designed to replicate trading patterns. To be accepted, however, they need to comply with regulatory texts, which are nothing else but codes of conduct coding accepted practices in the markets. In this article, I draw on ethnographic fieldwork in order to open these black boxes, while trying to describe their existence as devices encapsulating several points of views. I address the question of a possible misalignment between those visions, and more specifically try to draw the consequences raised by such discrepancies as regards the future of financial regulation.
algorithmic trading codes of conduct codings financial markets practices regulation
Articles citing this article
Codes and Codings in Crisis: Signification, Performativity and Excess
Theory, Culture & Society November 1, 2011 28: 3-23
AbstractFull Text (PDF)
[ ] Investigating Financial Fraud in High Frequency Trading
Afroditi Katika
University of Manchester
Babis Theodoulidis
University of Manchester - Manchester Business School
David Diaz
University of Manchester - Manchester Business School; Universidad de Chile - Escuela de Economia y Negocios
December 20, 2011
Abstract:
Market monitoring is a very important process to the stock market. It is necessary in order to verify that all trades comply with the existing rules, as well as to detect any act of manipulation. Recently, a new kind of trading has emerged, High Frequency Trading, which allows traders to place and execute orders within milliseconds via a program running in a computer. It is doubtful whether existent market systems are capable of detecting inconsistencies in trades at this speed. This project has attempted to propose a design of a detection engine that could be incorporated to a monitoring framework so as to accommodate High Frequency trades. Understanding the field of stock markets and High Frequency Trading was a crucial part of this project. Since it is such a recent phenomenon with no confirmed cases (to the best of our knowledge) of market manipulation, we attempted to answer whether there are certain conditions that could benefit market manipulators. We used business intelligence techniques to analyse historical data and discover what sort of indications our detection engine should look for. Our results show that there have been violations of regulations that were not blocked in real-time which proves the inefficiency of current market monitoring systems. We also prove that an extreme number of orders within seconds can delay an exchange’s processes and systems. In the end we propose a design that takes those results into consideration.
Keywords: high frequency trading, flash crash, quote stuffing, financial markets, market manipulation, fraud detection, market monitoring, market surveillance
Working Paper Series
Date posted: December 20, 2011
Suggested Citation
Katika, Afroditi, Theodoulidis, Babis and Diaz, David, Investigating Financial Fraud in High Frequency Trading (December 20, 2011). Available at SSRN: http://ssrn.com/abstract=1974911
[ ] On the Dark Side of the Market: Identifying and Analyzing Hidden Order Placements
Nikolaus Hautsch
Humboldt-Universität zu Berlin; CASE - Center for Applied Statistics and Economics; CFS
Ruihong Huang
Humboldt University of Berlin
February 8, 2012
Abstract:
Trading under limited pre-trade transparency becomes increasingly popular on financial markets. We provide first evidence on traders' use of (completely) hidden orders which might be placed even inside of the (displayed) bid-ask spread. Employing TotalView-ITCH data on order messages at NASDAQ, we propose a simple method to conduct statistical inference on the location of hidden depth and to test economic hypotheses. Analyzing a wide cross-section of stocks, we show that market conditions reflected by the (visible) bid-ask spread, (visible) depth, recent price movements and trading signals significantly affect the aggressiveness of 'dark' liquidity supply and thus the 'hidden spread'. Our evidence suggests that traders balance hidden order placements to (i) compete for the provision of (hidden) liquidity and (ii) protect themselves against adverse selection, front-running as well as 'hidden order detection strategies' used by high-frequency traders. Accordingly, our results show that hidden liquidity locations are predictable given the observable state of the market.
Number of Pages in PDF File: 43
Keywords: limit order market, hidden liquidity, high-frequency trading, non-display order, iceberg orders
JEL Classifications: G14, C24, C25, G17
Working Paper Series
Date posted: February 13, 2012
Suggested Citation
Hautsch, Nikolaus and Huang, Ruihong, On the Dark Side of the Market: Identifying and Analyzing Hidden Order Placements (February 8, 2012). Available at SSRN: http://ssrn.com/abstract=2004231 or http://dx.doi.org/10.2139/ssrn.2004231
CASE STUDIES
[ ] BATS Take-down
http://www.zerohedge.com/news/skynet-wars-how-nasdaq-algo-destroyed-bats
[ ] http://www.zerohedge.com/news/presenting-todays-21-least-mini-flash-crashes
[ ] http://www.zerohedge.com/article/fractal-limit-order-buster-latest-market-manipulation-algo-gimmick
[ ] Man Vs Machine: How Each Sees The Stock Market
Submitted by Tyler Durden on 04/03/2012
available at: http://www.zerohedge.com/news/man-vs-machine-how-each-sees-stock-market
[ ] http://www.zerohedge.com/news/fractal-algo-strikes-again-time-impacts-popular-bond-bear-etf-tbt
[ ] http://www.zerohedge.com/news/stop-loss-terminator-algo-reemerges-picks-national-bank-greece-todays-victim
[ ] http://www.zerohedge.com/news/dear-hft-please-explain
[ ] http://www.zerohedge.com/news/step-right-its-hft-whack-mole-time
[ ] http://www.zerohedge.com/news/whack-mole-algo-back
[ ] http://www.zerohedge.com/article/are-hft-algos-taking-aim-dominating-and-manipulating-wonderful-world-etfs-next
[ ] http://www.zerohedge.com/article/visualizing-market-topology-video-real-time-exchange-routing
[ ] http://www.zerohedge.com/news/does-high-frequency-trading-adds-market-liquidity-vote-here
[ ] http://www.zerohedge.com/article/hft-now-business-frontrunning-each-others-regulatory-capture
[ ] http://www.zerohedge.com/article/caught-act-hft-option-algos-observed-frontrunning-todays-pmi-release
[ ] http://www.zerohedge.com/article/some-observations-spy-vwap-and-block-manipulation-fsa-launches-probe-front-running-block-tra
[ ] http://www.zerohedge.com/article/no-its-not-nat-gas-fractal-algo-nanex-discloses-very-ominous-implications-todays-berserk-cru
[ ] http://www.zerohedge.com/article/another-algo-gone-wild
RANDOM QUOTES:
[ ] Guest Post: Deconstructing Algos, Part 4 -Phase Space Reconstructions Of CNTY Busted Trades Suggests High Speed Gang-Bangs In The Market
Submitted by The World Complex Deconstructing Algos, Part 4: Phase Space ... Volatility Submitted by The World ComplexDeconstructing Algos, Part 4: Phase Space Reconstructions ... the algos picked up by Nanex on June 21, 2011 in CNTY using the data appended here . ...
Story - Tyler Durden - 07/31/2011 - 17:43 - 39 comments - 0 attachments
[ ] Guest Post: Deconstructing Algos, Part 2: Leveraging Chaos Into High-Frequency Arbitrage Opportunities
Submitted by The World Complex Deconstructing Algos, Part 2: Leveraging Chaos Into High-Frequency Arbitrage Opportunities The recent elegant explanation for the activities of the HFT algos ... Natural Gas Submitted by The World ComplexDeconstructing Algos, Part 2: Leveraging Chaos ...
[ ] Story - Tyler Durden - 07/01/2011 - 00:21 - 32 comments - 0 attachments
Guest Post: Deconstructing Algos 3: Quote Stuffing As A Means Of Restoring Arbitrageable Latency; Or Is The CQS TRYING To Crash The Market?
Submitted by The World Complex Deconstructing Algos 3: Quote Stuffing As A Means ... ComplexDeconstructing Algos 3: Quote Stuffing As A Means Of Restoring Arbitrageable LatencyIn a recent article Nanex has ... at least 33% too low. 3. An algo is testing how much more quote noise it needs to generate to cause ...
[ ] Story - Tyler Durden - 07/08/2011 - 22:08 - 63 comments - 0 attachments
Guest Post: Deconstructing Algos, Part 1
Submitted by The World Complex Deconstructing algos, part 1 The third part ... Natural Gas Submitted by The World ComplexDeconstructing algos, part 1 The third part of the series ... are critical to the decision-making module of the algo. The reconstructed phase space The difficulties ...
[ ] Story - Tyler Durden - 06/24/2011 - 21:16 - 82 comments - 0 attachments
Gold Tumbles More Than $100 As $1700 Stops Triggered
to algo driven liquidations following the earlier described shift in sentiment, or has some assistance ... whispers? Felt Any MFG style whispers? Felt like a bit more than algos. More like a company iquidation ...
Friday, 13 April 2012
Thursday, 12 April 2012
Default Invariance: Product & Sum Modules - Sans Esquisses
Default Invariance:
Product and Sum Category Theory Models of Financial Contracts
Product Model: Pay or Not-Pay
Sum Model: Financial Legal Remedies
1. Recall the Arrow-Debreu-Sharpe model of t0 to t1 corresponding to the state of initial financial contract in a world of infinite contingent states and the state of pay, respectively.
2. We improved the ADS Model to a Default Invariance Model where the t1 state is now bi-valued to include (a) Pay and (b) Not-Pay, i.e. P and -P.
3. If t1 results in -P then the infinite contingent states continues at t1. This is equivalent (or isomorphic) to the infinite-contingent-states being multiplied by 1.
4. If t1 results in P then the infinite contingent states is annihilated and the certainty of payment makes the financial contract certain and therefore, immediately disengages from the infinitely contingent states of world. This is equivalent (or isomorphic) to the inifinite-contingent-states being multiplied by 0.
5. The 2-state at t1 default invariance model can be further specified in terms of Product and Sum. [This is going to get a bit technical, I warn you.]
Definition of Product
An object P together with a pair of maps P1:P->B1, and P2:P->B2 is called a product of B1 and B2 if for each object X and each pair of maps f1:X->B1, f2:X->B2, there is exactly one map f:X->P for which both f1=P1f and f2=P2f. [See Lawvere & Schanuel, 2009, p. 217.]
[I'll insert a diagram later. Hint: it looks like a chevron with X on the left and an arrow from X to P which is, another arrow from X to B1 labelled f1, an arrow P1 from P to B1, an arrow from X to B2 labelled f2, and an arrow P2 from P to B2.]
6. Given this definition of Product, we can now apply what we stated in an earlier blog that payment of a financial contract makes it certain and therefore, takes it out of the realm of uncertainty and is no longer part of ("resides in") a world of infinite contingent states. Thus, an occurrence of payment is equivalent to the value of 0 in the infinite contingent world. In our Product Diagram B1 = (Infinite-Contigency) x (0). Another way of saying this is B1 = Uncertainty x 0, which means, no more uncertainty. This valuation is not what Sharpe and others had supposed, and had in fact given payment the value of 1, which leads to inconsistent and contradictory results.
7. Also, we can see that non-payment or not-paying at t1 means that the infinite-contingent-states of the world continues at t1. This is equivalent to: (infinite-contingent-states) x (1). So, non-payment is actually an identity morphism. In our Default Invariance Product Diagram, B2 = 1. Strangely, f2 will have to be equivalent to infinite contingency divided by infinite contingency.
8. As a sum, we have the following definition:
A pair j1: B1->S, j2; B2->S, of maps in a category makes S a sum of B1 and B2 if for ach object Y and each pair g1:B1-Y, g2:B2-Y, there is exactly one map g:S->Y for which both g1 = gj1 and g2 = gj2. [See Lawvere & Schanuel (2009) Conceptual Mathematics, p. 222]
It is my contention that a legal remedy to a financial contract has the form of a sum as above, where Y is a legal remedy and B1 and B2 to breach and not-breach situations of the contract. This is of course a first approximation of a legal risk theory.
9. The virtue of a Product and a Sum Model for the fundamental and universal unit of law and finance is that by putting them together THROUGH TIME (that is, from t0, t1, t2,...tn) we begin to have a view of how law and finance may be seen under one perspective that allows for both (1) simplification and anticipation of direct results -- i.e., "rough and ready" calculations that border on immediate insight through very complex legal and financial phenomena; and (2) a very detailed and rigorous, bookkeeping or tracking methodology to ensure that our predictions make sense and are grounded on facts.
Product and Sum Category Theory Models of Financial Contracts
Product Model: Pay or Not-Pay
Sum Model: Financial Legal Remedies
1. Recall the Arrow-Debreu-Sharpe model of t0 to t1 corresponding to the state of initial financial contract in a world of infinite contingent states and the state of pay, respectively.
2. We improved the ADS Model to a Default Invariance Model where the t1 state is now bi-valued to include (a) Pay and (b) Not-Pay, i.e. P and -P.
3. If t1 results in -P then the infinite contingent states continues at t1. This is equivalent (or isomorphic) to the infinite-contingent-states being multiplied by 1.
4. If t1 results in P then the infinite contingent states is annihilated and the certainty of payment makes the financial contract certain and therefore, immediately disengages from the infinitely contingent states of world. This is equivalent (or isomorphic) to the inifinite-contingent-states being multiplied by 0.
5. The 2-state at t1 default invariance model can be further specified in terms of Product and Sum. [This is going to get a bit technical, I warn you.]
Definition of Product
An object P together with a pair of maps P1:P->B1, and P2:P->B2 is called a product of B1 and B2 if for each object X and each pair of maps f1:X->B1, f2:X->B2, there is exactly one map f:X->P for which both f1=P1f and f2=P2f. [See Lawvere & Schanuel, 2009, p. 217.]
[I'll insert a diagram later. Hint: it looks like a chevron with X on the left and an arrow from X to P which is
6. Given this definition of Product, we can now apply what we stated in an earlier blog that payment of a financial contract makes it certain and therefore, takes it out of the realm of uncertainty and is no longer part of ("resides in") a world of infinite contingent states. Thus, an occurrence of payment is equivalent to the value of 0 in the infinite contingent world. In our Product Diagram B1 = (Infinite-Contigency) x (0). Another way of saying this is B1 = Uncertainty x 0, which means, no more uncertainty. This valuation is not what Sharpe and others had supposed, and had in fact given payment the value of 1, which leads to inconsistent and contradictory results.
7. Also, we can see that non-payment or not-paying at t1 means that the infinite-contingent-states of the world continues at t1. This is equivalent to: (infinite-contingent-states) x (1). So, non-payment is actually an identity morphism. In our Default Invariance Product Diagram, B2 = 1. Strangely, f2 will have to be equivalent to infinite contingency divided by infinite contingency.
8. As a sum, we have the following definition:
A pair j1: B1->S, j2; B2->S, of maps in a category makes S a sum of B1 and B2 if for ach object Y and each pair g1:B1-Y, g2:B2-Y, there is exactly one map g:S->Y for which both g1 = gj1 and g2 = gj2. [See Lawvere & Schanuel (2009) Conceptual Mathematics, p. 222]
It is my contention that a legal remedy to a financial contract has the form of a sum as above, where Y is a legal remedy and B1 and B2 to breach and not-breach situations of the contract. This is of course a first approximation of a legal risk theory.
9. The virtue of a Product and a Sum Model for the fundamental and universal unit of law and finance is that by putting them together THROUGH TIME (that is, from t0, t1, t2,...tn) we begin to have a view of how law and finance may be seen under one perspective that allows for both (1) simplification and anticipation of direct results -- i.e., "rough and ready" calculations that border on immediate insight through very complex legal and financial phenomena; and (2) a very detailed and rigorous, bookkeeping or tracking methodology to ensure that our predictions make sense and are grounded on facts.
Tuesday, 3 April 2012
Platonic Signage: From Discrete Algebraic Individual Complaints to Continuous Geometric Social Solutions
Or, Infinite Smoothness: From The Discrete Complaints of Individuality to The Ironic Continuum of Small Rules
1. I think it's in book 2 or 3 of The Republic that Plato makes a rhetorical analogy that is engrained in the way we argue and complain about ourselves and our relations to society. He asks to transfer the argument about whether a person's happiness depends on power and money rather than virtue (that is, knowledge of the good) to a much larger body that can be dissected objectively, namely, the body of society. The move from examining the personal body and its object of happiness (what we might now call psychology) to the social body and its aim of good government, may seem quite weak, for how can we trust in an answer to a problem which is at a level different from the problem itself. The problem is more particular and local than the solution which is general and indeed, allegedly universal.
2. This move has bothered me for 42 years. Now, I think I have an answer to the quandary both at the substantive and procedural levels. And both technically can be viewed from what we call a category theory. We can also immediately understand Plato's overall strategy as a movement from a local composition in algebra to a general conception of geometry. (There is an apocryphal saying that the signage above Plato's Academy said something to the effect, "Let no one without Geometry enter [this space]."
3. I would also temper this interpretation with a couple caveats. First, Plato though genius of the first degree did not have the devices necessary to found category theory. Second, when I call out the term of art, category theory, I mean in the first and foremost instance, the conceptualisation of certain data about objects, arrows (morphisms), the associativity axiom [(a*b)*c = a*(b*c)], and the identity axiom [a*I = a = 1*a]. In its most austere form and substance, namely, in diagrams or sketches ("esquisses") very very complex structures that would not be very comprehensible in a grammatical English are very evidently laid out like Dr. Seuss drawings. One can for example re-wire quantum mechanical expressions rather naturally in category theory and understand how so-complex financial contracts work in an infinitely contingent world.
4. Coming back to the Platonic move from small (individual) to big (society), we recall Socrates' reason for this move was because he was trapped. The two nephews of Plato, x and y, [i can't remember their names but will look them up later--maybe Glaucon and Adimentaus?] had argued so eloquently and convincingly that at the PERSONAL level only power and money counted for anything in a real person's real happiness. This was an argument based on personal observation ("what is evidently and evidentially true"). So, Platonic philosophy based whole heartedly on one's personal knowledge and education could hardly win against someone whose argument was based on personally observed facts.
5. Socrates had to go a level up. Plato through Socrates was making an argument about the SPACE around the individual, the interconnections, the networks, the various specialised objects ("specialists are better for the good of the whole society than the inefficient workings of generalists"), and how ultimately, this led to an analysis of governance, from benevolent dictator to timocracy, oligarchy, democracy and tyrant. All of this was rounded by the question asked of Socrates, "And what if none of what you have imagined comes about?" Socrates' answer again is of a SPACE, "Well then, we have not wasted time, because forever and a day, people will now know where they should be heading." In other words, Socrates had literally given future generations a map to travel, with signposts and monuments. Now, just as no one on the tube in London can say that the tube maps are what the tubes and tube lines are, we can't say that Plato's Republic describes exactly what is front of us. Much depends on our understanding of how to make the correspondences between the map and our own presence or location. We use the map as a guide to help make sure we steer ourselves to a particular destination.
6. The more general meaning and thus, philosophical import of the move from individual psyche to the social space is in the form of generalisation. Note that the rules defining the linkages in the local space, i.e., the relations between individuals, which in a strict sense might be defined as "rules" establish a structure which is the definition of the entire space in which any and all individuals exist. This movement from particular individual mind to the structures which link us together may appear to be a type of algebraic expression of composition, that is, combinations of bilateral transactions. But the point is that these groups defined by rules when applied generally literally create a geometry of social space. It is a space that is topologically continuous.
7. As we say in the old lingo, "from the many to the one." We can now understand this as a movement from the particular algebraic rules that appear discrete in form but are actually, when taken together, define the infinite smoothness of the skin of reality. The slogan here is, "small rules define big space."
8. As a meditation one might take the slogan to its limit in breath, balance and humour.
1. I think it's in book 2 or 3 of The Republic that Plato makes a rhetorical analogy that is engrained in the way we argue and complain about ourselves and our relations to society. He asks to transfer the argument about whether a person's happiness depends on power and money rather than virtue (that is, knowledge of the good) to a much larger body that can be dissected objectively, namely, the body of society. The move from examining the personal body and its object of happiness (what we might now call psychology) to the social body and its aim of good government, may seem quite weak, for how can we trust in an answer to a problem which is at a level different from the problem itself. The problem is more particular and local than the solution which is general and indeed, allegedly universal.
2. This move has bothered me for 42 years. Now, I think I have an answer to the quandary both at the substantive and procedural levels. And both technically can be viewed from what we call a category theory. We can also immediately understand Plato's overall strategy as a movement from a local composition in algebra to a general conception of geometry. (There is an apocryphal saying that the signage above Plato's Academy said something to the effect, "Let no one without Geometry enter [this space]."
3. I would also temper this interpretation with a couple caveats. First, Plato though genius of the first degree did not have the devices necessary to found category theory. Second, when I call out the term of art, category theory, I mean in the first and foremost instance, the conceptualisation of certain data about objects, arrows (morphisms), the associativity axiom [(a*b)*c = a*(b*c)], and the identity axiom [a*I = a = 1*a]. In its most austere form and substance, namely, in diagrams or sketches ("esquisses") very very complex structures that would not be very comprehensible in a grammatical English are very evidently laid out like Dr. Seuss drawings. One can for example re-wire quantum mechanical expressions rather naturally in category theory and understand how so-complex financial contracts work in an infinitely contingent world.
4. Coming back to the Platonic move from small (individual) to big (society), we recall Socrates' reason for this move was because he was trapped. The two nephews of Plato, x and y, [i can't remember their names but will look them up later--maybe Glaucon and Adimentaus?] had argued so eloquently and convincingly that at the PERSONAL level only power and money counted for anything in a real person's real happiness. This was an argument based on personal observation ("what is evidently and evidentially true"). So, Platonic philosophy based whole heartedly on one's personal knowledge and education could hardly win against someone whose argument was based on personally observed facts.
5. Socrates had to go a level up. Plato through Socrates was making an argument about the SPACE around the individual, the interconnections, the networks, the various specialised objects ("specialists are better for the good of the whole society than the inefficient workings of generalists"), and how ultimately, this led to an analysis of governance, from benevolent dictator to timocracy, oligarchy, democracy and tyrant. All of this was rounded by the question asked of Socrates, "And what if none of what you have imagined comes about?" Socrates' answer again is of a SPACE, "Well then, we have not wasted time, because forever and a day, people will now know where they should be heading." In other words, Socrates had literally given future generations a map to travel, with signposts and monuments. Now, just as no one on the tube in London can say that the tube maps are what the tubes and tube lines are, we can't say that Plato's Republic describes exactly what is front of us. Much depends on our understanding of how to make the correspondences between the map and our own presence or location. We use the map as a guide to help make sure we steer ourselves to a particular destination.
6. The more general meaning and thus, philosophical import of the move from individual psyche to the social space is in the form of generalisation. Note that the rules defining the linkages in the local space, i.e., the relations between individuals, which in a strict sense might be defined as "rules" establish a structure which is the definition of the entire space in which any and all individuals exist. This movement from particular individual mind to the structures which link us together may appear to be a type of algebraic expression of composition, that is, combinations of bilateral transactions. But the point is that these groups defined by rules when applied generally literally create a geometry of social space. It is a space that is topologically continuous.
7. As we say in the old lingo, "from the many to the one." We can now understand this as a movement from the particular algebraic rules that appear discrete in form but are actually, when taken together, define the infinite smoothness of the skin of reality. The slogan here is, "small rules define big space."
8. As a meditation one might take the slogan to its limit in breath, balance and humour.
Sunday, 1 April 2012
The Baby Blue Eyes of the Universe: Philosophical Calculations of Governance and Infinity
Philosophical Calculations
1. The great Greek philosophers Plato and Aristotle identified the problem of (1) how to distinguish between a benevolent dictator and a tyrant, and (2) how to determine the continuous from the discrete, respectively. Plato's insight into the problem of governance comes in books VIII to IX of the Republic, and Aristotle's conundrums of the infinity of points in space and time come from his recollection of the paradoxes of Zeno of Elea in the first books of the Metaphysics.
2. Both problems cut through what might be called epistemology, or the limits of our knowledge. For example, how can we possibly distinguish between two persons who say, "believe me for I know the good." Answer: we can't unless we ourselves (read here, each and every one of us) have educated ourselves enough to make this discrimination. No one can give us this knowledge. We have to come upon it ourselves. We have to be ruthlessly Descartian. In terms of the pure metaphysical problem of infinity of points, this becomes a matter of discriminating between the continuous and the discrete, between the one and the many. Modernly, we can resolve this tension to an awfully abstract sense of proportions if we move diligently from nominal, interval, ordinal and rational scales, and have some notation to help us with the precise bookkeeping (a type of Thesesusian string in the minotaur's cave) so we can accurately account for how apparently different forms are essentially together in a weakened form of equivalence. A few algebraic expressions define the local key to the global code of a geometry, and the geometry gives us an insight to the totality of global meanings of finite algebraic expressions. The Buddha says this by carrying a flower, the mathematicus writes a few squiggles, a few angels sing, and the infant's eyes reflect the absolute depth of the pure blue sky.
3. Belief in a stranger tells us something about us. We can never know the other except through abstractions. But these abstractions are obviously not the other. Don't be greedy. Let the composition come. What comes naturally is already embedded and as some say, the one. To wait for the one is to let the universe do the calculation. To ride the winds, to move in every direction, is the way nature calculates answers directly through us.
1. The great Greek philosophers Plato and Aristotle identified the problem of (1) how to distinguish between a benevolent dictator and a tyrant, and (2) how to determine the continuous from the discrete, respectively. Plato's insight into the problem of governance comes in books VIII to IX of the Republic, and Aristotle's conundrums of the infinity of points in space and time come from his recollection of the paradoxes of Zeno of Elea in the first books of the Metaphysics.
2. Both problems cut through what might be called epistemology, or the limits of our knowledge. For example, how can we possibly distinguish between two persons who say, "believe me for I know the good." Answer: we can't unless we ourselves (read here, each and every one of us) have educated ourselves enough to make this discrimination. No one can give us this knowledge. We have to come upon it ourselves. We have to be ruthlessly Descartian. In terms of the pure metaphysical problem of infinity of points, this becomes a matter of discriminating between the continuous and the discrete, between the one and the many. Modernly, we can resolve this tension to an awfully abstract sense of proportions if we move diligently from nominal, interval, ordinal and rational scales, and have some notation to help us with the precise bookkeeping (a type of Thesesusian string in the minotaur's cave) so we can accurately account for how apparently different forms are essentially together in a weakened form of equivalence. A few algebraic expressions define the local key to the global code of a geometry, and the geometry gives us an insight to the totality of global meanings of finite algebraic expressions. The Buddha says this by carrying a flower, the mathematicus writes a few squiggles, a few angels sing, and the infant's eyes reflect the absolute depth of the pure blue sky.
3. Belief in a stranger tells us something about us. We can never know the other except through abstractions. But these abstractions are obviously not the other. Don't be greedy. Let the composition come. What comes naturally is already embedded and as some say, the one. To wait for the one is to let the universe do the calculation. To ride the winds, to move in every direction, is the way nature calculates answers directly through us.
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