User:Physis/Bootstrapping

The word bootstrapping is a highly productive metaphor, grasping the common, related or similar pattern in many diverse phenomena, crosscutting several sciences. These manifestations usually explain the origin of certain (usually complex or nontrivial) phenomena, or even implement them from scratch. Usually, these phenomena are such that their origin is not trivial to understand, as it is hidden behind a sophisticated shift process. A complex phenomenon may turn out to have being built "on top" of the "infrastructure" of another, mostly more basic level phenomen. This underlying "scaffolding" often has become obsolete with the emergence of the new one, it even disappeared, thus the history of the level-sifting process has not been preserved in the "architecture", making its understanding a challenge or even paradoxical (chicken or egg). Thus, the process of this passed takeover, "coup d’état" can usually be traced back only by indirect evidences (simulations, reverse engineering etc).

As mentioned, the metaphor is highly productive: scientists of various fields seem to introduce new manifestations with due certainty, usually keeping correctly the pattern.

Formalization attempts

RELATIONAL CLOSURE: a mathematical concept for distinction-making and complexity analysis. Francis HEYLIGHEN

Relatedness of some of the various manifestations

Does only a superficial analogy connect the various manifestations of "bootstrapping", or are at least some of them related along deeper principles?

Biology and computing

Digital "technologies" of biology

Modern genetic biology often uses deep and correct analogies with digital technologies.^[1]

Thus some analogies, crosscutting the border between such different fields like biology and computing, are not casual things: both nature and technology had to resorted to the digital solutions in order to achieve reliable information transfer and information processing. In the transmission and processing of analog signals, the successive amplifications of the sign results in deterioration of information by cumulative errors into noise (somewhat similarly to Chinese whispers game^[2]). This problem that could be fully solved by digital technology, and nature turned out to find also related solutions.^[3]

Blueprint or recipe?

An egg is surely not a homonculus, this old kind of preformationism is not justified, moreover, it would lead to infinite regression. Or is the differentiation coded directly in the DNA? Is there a direct mapping from the DNA to the shape? Is DNA a blueprint? Althought there are admittedly tecchnological devices which surely can assamble shapes out of one-dimensional "blueprints" by a direct mapping (like television), but in biology, this modern kind of preformationism cannot be verified, either.^[4] As all descendants of the original egg in the developing embryo are genetically identical, there cannot be a direct mapping from genetic information to shape and structure. Instead of being a blueprint, the shape and structure od living beings is rather encoded as a cookbok recipe. Series of commands, there is no one-one mapping from these command series to the possible results. We can study the relationship by selectively modifying the commands, but DNA codes are surely not "scannings" of shapes intto pixel representation.^[5]

Cascading

The development of the embryo ais a result of repeatedly forking (mostly bifurcating) processes, that act locally. Recursive forking is an analogy, implementable easily by recursive programming, and it is easy to viszalize with a "tree-growing" example. The nalogy is very simplified, embryogenesis is a complicated process^[6]

Justified analogy between embryogenesis and punched card booting

According to the above, a deep analogy can be drawn also between the bootstrapping process of computers and the development of the embryo.^[7]

Chicken and egg paradox in embryogenesis

Developmental biology, morphogenesis, embryogenesis.

How does the digital information of the one-dimensional DNA "tape" translate into the spatial pattern of the living being, to those diverse plethora of body forms of the living, the continuous, analog variability? Do living beings have their body plan, and if so, how does it become enforced?

The cells of a complex living beings are not alike, and the different kinds of cells are organized, arranged into sophisticated forms. All these cells share the same genetic information, the differentiation is cased by their selective responses to the same code. In understanding how the whole process is possible, first of all, how embryogenesis takes place, we must understand the two key processes: the interplay between gene expression and its modulation.

These two processes interplay in a way that seems to raise a chicken and egg paradox. How can the pattern of highly differentiated cells develop out of a single cell? Is the pattern of differentiation contained entirely in the chemical content of the egg?

Instead of straightforward, simple mappings (either from the inside of the egg to that of the embryo, or from genotype to phenotype), a sophisticated bootstrapping process takes place, an interplay between

First, let us see the two key processes on their own.

Gene expression

A plethora of different chemical reactions are taking place inside a cell. How are the different reactions organized, how are they separated from each other? Physical separation is not the only solution. The enzymes, functioning as catalysts, are able to control several different reactions in ts shared environment. The enzymes are produced according to the information stored in DNA.^[8]

Regulation of gene expression

It is the chemical materials inside a cell that determines the way the cell interprets the genetic "message": parts of the message are selectively "switched on" or "switched off".^[9]

Their interplay

In understanding the interrelatedness of processes like gene expression, the role of enzymes and the epigenetic development, the cellular differentiation, we can reveal a chicken or egg paradox.

Genetic information determines the produced enzymes, and the presence of enzymes determine the mode of interpretation of the genetic information.

On the other hand, the functioning of the cell is exactly the production of enzymes and other chemical materials according to its genetic code. The differentiation is orchestrated by the chemical materials of the inside of the cell, which itself is result of enzyme-producing cells arranged by a former stage of the same differentiation process.

How can this chicken or egg paradox be resolved?

Computer analogy

For explaining the solution chosen by nature — a bootstrapping process — we can use the analogous problem and solution on the example of old, punched tape fed computers. How is the machine instructed to be able to interpret its own input punched tape? This is told by the booting program — but how is the booting program itself read in? (In old machines the booting program was not hardwired.) Again, this seems to raise a chicken or egg question.

The problem can be solved by a bootstrapping process: reading stepwise the information to set the rules of processing further. The most elementary things are input on keys, manually. They suffice to instruct the machine how to read the first few parts of the punched tape of the booting program. This small part of the tape contains further instructions how to read the next few parts of the punched tape. Stepwise, iterating these bootstrapping steps, the whole booting program is read in on the punched tape. As soon as the booting pragram is read in, the machine is able to read any punched tape.

As promised above, this bootstrapping solution can illustrate the similar solution of nature in solving embryogenesis: the pieces of "further information for processing" is "read-in" stepwise.^[7]

Details

Homeotic gene, homeobox,^[10]
concentration gradient, French flag model,^[11] morphogen, body plan.
gene cascade,^[12] gene regulatory network

Manifestations

The pattern above has been manifested in such diverse fields like theories trying to explain abiogenesis,^[13] complex communication schemes, building a complex infrastructure from scratch,^[14] explaining the emergence of such complex phenomena like mind or culture.^[15]

Abiogenesis

Bootstrapping from one kind replicator to another one (prebiotic self-reproduction → genetic,^[13] genetic → extrasomatic^[15]) [1]

Autopoietic bootstrap

[2]

Hermeneutic circle and AI

In the notion of hermeneutic circle, the circularity of the whole and its part resembles to the notion of bootstrapping, and it yields fruitful insights in artificial intelligence research.^[16]

Search for "hermeneutic bootstrapping" [3] [4] [5]

Compilers

Computing

Related phenomena

There are a lot of commonly-known phenomana that are related to the above schemen, but the authors describing them did not use the term "bootstrapping".

Evolution

Cascading cranes, as contrasted to skyhook.^[17]

Communication

We send a primitive message first, in a straightforward code,the only aim is only to attract attention, to communicate that it has some meaning, it can be regarded as a message at all. Later we specify a coding method, a "machinery" (e.g. a table, matrix orfunction) in this simple, primitive code. Finally, we can use the above specified "coding machinery" for coding further messages: we shift from the original, primitive method to the new one. The new coding can be much comfortable or swift than the former one, but because of its sophisticatedness it could have never been "taught" to the partner without using the former, "bootstrapping" method.

Knocking alphabet

The prisonars in Tzarist Russian prisons developed a means of communication: they "knocked" messages to each other on the wall. This Russian knocking alphabet raised an interesting chicken or egg problem in practice: although the "habitue" prisoners were able to send news and messages to each other, how could they teach the knocking alphabet itself to a novice fellow prisoner? They had to explain somehow what the coding system was, how the patterns of knocks could be assigned to the letters of the Russian alphabet. But the knocking code could be explained only by the knocking on the wall, because the captives had no chance to meet personally or exchange letters! How could they resolve this circulus vitiosus, this chicken or egg problem?

First, they used a simpler variant. They coded each letter of the alphabet by that many knockings as the number of the letter in the Russian alphabet was: one knock, A, two knocks, B etc. This simple system could easily be taught by simple examples "Who are you?" etc. Later they taught to the novice a more sophisticated coding system "on top of" this simple one. Indeed, they explained a "machine", a coding table, and the way it way it worked. After having explained the machinery of the coding, they shifted from the simple (but slow and uncomfortable) method to the sophisticated one.^[18]

Fictions and proposals

Also some fictions and proposals contain the pattern above. For example, the novel Contact (written by Carl Sagan) mentions the idea of sending first a series of prime numbers (because we do not know abundant natural phenomena emitting prime-number-related patterns). Later the message contains a technical description of a machine, and the more interesting things will be transferred by the machine itself. A similar motif can be read in A for Andromeda (written by Fred Hoyle).

Also the artificial language called Lincos (proposed for sending messages to extraterrestral intelligent beings by mathematician Dr Hans Freudenthal) is based on sequence of levels.

Foundations of mathematics

if we build a system of logic, we often use set theory for "holding" collections, we often use natural numbers for indexing etc. That seems to be a circulus vitiosus: set theory and arithmetic is based on logic, logic is based on set theory and arithmetic? In fact, the problem can be resolved by a kind of bootstrapping: we build first a "dummy" version of arithmetic and set theory, integrated deeply in the very syntax of our system of logic, then we build our system of logic, afterwards we can use our system of logic to build the "unabridged" arithmetic and set theory.

The problem is discussed in details in a monograph, but without calling it "bootstrapping", instead, it is called "taming circulus vitiosus into spiral".^[19] Another book of the same author shows waya making numeral-related statements without numerals in logical calculus.^[20]

A similar problem is given also as an exercise in the book about surreal numbers by Donald Knuth,^[21] but also other introductory books mention the similar problem without details.^[22]

Mathematical logic is also capable of inspecting its own methods, but only after a certain part has already built.^[23]

A resolution attempt to the unexpected hanging paradox resorts to a series of leveled argumentation, resembling to bootstrapping.

A king promises to a captive, that he will be hanged on the next week, but during the whole week each day will pass so that he will not know the previous day whether he is hanged that day. The captive infers by induction that he cannot be hanged on Sunday. Then he iterated the induction and he infers that he cannot be hanged on Saturday, either. Soon, he infers that he cannot be hanged at all. The king simply throws a "seven-sided dice" and hangs the captive on Wednesday dawn. How can be the paradox solved? The solution can be layered in "levels" and is related also to Gödel's theorem.

Etymology

Origin of the word "bootstrap"

Tall boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers or a tool to provide better leverage in pulling the boots on. The saying "to pull yourself up by your bootstraps." ^[24] was already in use during the 1800s as an example of an impossible task. Bootstrap as a metaphor, meaning to better oneself by one's own unaided efforts, was in use in 1922.^[25] This metaphor spawned additional metaphors for a series of self-sustaining processes that proceed without external help. ^[26]

The computer word bootstrap began as a 1950s metaphor derived from using a strap to pull on leather boots without outside help. In computers, pressing a bootstrap button caused a hardwired program to read a bootstrap program from a punched card and then execute the bootstrap program which became a self-sustaining process that proceeded without external help. As a computing term, bootstrap has been used since at least 1958^[27].

The term bootstrap was used in Robert A. Heinlein's 1941 short story By His Bootstraps about recursive time travel.

Other languages

The Hungarian name for bootstrapping — "behúzás" — means "pulling-in", mostly used in computing.

The metaphor fits well to the early practice of computers, where first part of the punched tape the literally "pulled in" (by the encoded the booting code, holding the information for processing further) the remaining part of the punched tape.^[28]

My All whatworks is wonderful (series: World - University, publisher: Vince) describes bootstrapping (for early computers).

behúzás (kezdeti betöltés) boot behúzófeszültség locking voltage [6], locking voltage [7]

Notes

^ Dawkins 1996: 23–25
^ Dawkins 1996: 26
^ Dawkins 1996: 23–24
^ Dawkins 19994b: 264–265
^ Dawkins 19994b: 266–267
^ Dawkins 19994b: 51–53
^ ^a ^b Dawkins 1996: 29–32
^ Dawkins 1996: 28
^ Maynard Smith & Eörs 2000: 123–125
^ Maynard & Eörs 2000: 133–135
^ Maynard & Eörs 2000: 131–132
^ Maynard & Eörs 2000: 133
^ ^a ^b Ludwig 1993: 277–260 (see online)
^ Traugott & Huddleston 1998 (see online)
^ ^a ^b Agapow 1995 (see online)
^ Mallery & Hurwitz & Duffy 1986: 2 (see online)
^ Dennett 1998, p. 80–81
^ Kennan 1888: 403–404 (scanned online pp 403 and 404, or search in the textual version)
^ Ruzsa 1988
^ Ruzsa 2000, p. 99
^ Knuth 1987: 131 (= Problem 4, proposed after chpt 6)
^ Csirmaz 1994: 7–8 (see online in Hungarian)
^ Csirmaz 1994: 8 (see online in Hungarian)
^ Bootstrap citations from 1800s
^ Ulysses cited in the Oxford English Dictionary
^ Phrase Finder
^ Oxford English Dictionary. Oxford University.
^ Dawkins 1996: 29

References

Agapow, Paul-Michael. "Bootstrapping Evolution with Extra-Somatic Information". Complexity International. 02. ISSN 1320-0682.
Csirmaz, László (1994). "Bevezetés". Matematikai logika (in Hungarian). Budapest: Eötvös Loránd University. {{cite book}}: |format= requires |url= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help) The chapter means "Introduction", the title means Mathematical logic. Each chapter is downloadable seriatim on author's page.
Dawkins, Richard (1995). "The digital river". River Out of Eden. A Darwinian View of Life. Basic Books. ISBN 0-465-01606-5.
Dawkins, Richard (1996). "A digitális folyam". Folyam az Édenkertből. Darwinista elmélkedések az életről. Világ — Egyetem (in Hungarian). Budapest: Kulturtrade Kiadó. pp. 11–33. ISBN 963-7826-89-0. Translation of Dawkins 1995.
Dennett, Daniel Clement (1995), Darwin's dangerous idea, Simon & Schuster, ISBN 0-670-03186-0
Dennett, Daniel Clement (1998), Darwin veszélyes ideája, Test és Lélek, Budapest: Typotex, ISBN 963-9132-15-2. Hungarian publication of Dennett 1995
Kennan, George (January 1888). "Russian Provincial Prisons". The Century. 35 (3).{{cite journal}}: CS1 maint: date and year (link) The journal was a popular quarterly. See the cited pages 403 and 404 scanned online.
Knuth, Donald Ervin (1974). "Postscript". Surreal numbers. How Two Ex-Students Turned on to Pure mathematics and Found Total Happiness. Reading • Massachusetts: Addison-Wesley Publishing Company. pp. 113–. ISBN 0-201-03812-9.
Knuth, Donald Ervin (1987). "Utószó". Számok valóson innen és túl (in Hungarian). Budapest: Gondolat. pp. 129–136. ISBN 963-281-864-4. Translation of Knuth 1974.
Ludwig, Mark A. (1993). "The Real World: Beginnings". Computer Viruses, Artificial Life and Evolution. Tucson (Arizona): American Eagle Publications. ISBN 0-929408-07-1.
Mallery, John C. & Hurwitz, Roger & Duffy, Gavan (May 1986). "Hermeneutics: From Textual Explication to Computer Understanding?" (Document). Massachusetts Institute of Technology Artificial Intelligence Laboratory. {{cite document}}: Unknown parameter |url= ignored (help); Unknown parameter |version= ignored (help)CS1 maint: multiple names: authors list (link)
Maynard Smith, John (1999). "The evolution of many-celled organisms". The Origins of Life. From the birth of life to the origin of language. New York: Oxford University Press. pp. 109–124. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
Maynard Smith, John (2000). "A többsejtű szervezetek evolúciója". A földi élet regénye. Az élet születésétől a nyelv kialakulásáig. Tudomány — Egyetem (in Hungarian). Budapest: Vince Kiadó. pp. 121–137. ISBN 963-9192-69-4. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help) The translation is based on Maynard Smith & Eörs 1999.
Ruzsa, Imre (1988). Logikai szintaxis és szemantika I (in Hungarian). Budapest: Akadémiai Kiadó. ISBN 963-05-4720-1.
Ruzsa, Imre (1997). Bevezetés a modern logikába. Osiris tankönyvek (in Hungarian). Budapest: Osiris Kiadó. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
Ruzsa, Imre (2000), Bevezetés a modern logikába, Osiris tankönyvek, Budapest: Osiris, ISBN 963-379-978-3
Traugott, Steve (1998). Bootstrapping an Infrastructure. 12^th Systems Administration Conference (LISA '98). {{cite conference}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)