#alan-turing — Public Fediverse posts on home.social

Alan Turing starb 1954, weitgehend vergessen. Heute ist er überall. Was ist in der Zwischenzeit passiert? Diese Frage hat nicht nur eine historische Antwort – sie hat eine messbare. Die Bibliometrie, die Wissenschaft der Messung wissenschaftlicher Publikationen und ihres Einflusses, macht sichtbar, wie Turings Ideen die Welt durchdrungen haben: zunächst langsam, dann unaufhaltsam. Am 23. Juni 2026 jährt sich Turings Geburtstag zum 114. Mal – ein Anlass, seinen Weg von der Vergessenheit zur Allgegenwart nachzuzeichnen.

Wer war Alan Turing?

Alan Mathison Turing wurde am 23. Juni 1912 in London geboren. Er war Mathematiker, Kryptoanalytiker und Philosoph der Maschine – und einer der unglücklichsten Genies des 20. Jahrhunderts. Im Zweiten Weltkrieg entschlüsselte er mit seinem Team in Bletchley Park die deutsche Enigma-Chiffriermaschine und verkürzte damit den Krieg nach Schätzungen um mehrere Jahre. Dafür erhielt er keinen öffentlichen Dank – die Arbeit blieb Jahrzehnte lang geheim.

1952 wurde Turing wegen Homosexualität verfolgt, chemisch kastriert und seiner Sicherheitsfreigabe beraubt. Am 7. Juni 1954 starb er mit nur 41 Jahren. Die offizielle Version lautete Selbstmord durch Zyanidvergiftung – ob es einer war, ist bis heute nicht abschließend geklärt. 2013, fast 60 Jahre nach seinem Tod, begnadigte die britische Königin Elizabeth II. ihn posthum.

Was blieb, waren seine Texte. Und die veränderten die Welt.

Abbildung: Alan Turing, Plakat der Gesellschaft der Informatik: Pionier der Informatik und Kryptoanalytiker https://gi.de/persoenlichkeiten/alan-turing

Bibliometrie: Einfluss wissenschaftlicher Ideen messen

Bibliometrie fragt: Welche Ideen haben die Wissenschaft verändert – und wie lässt sich das messen? Turings Werk ist dafür ein ideales Anschauungsobjekt. Mehr zu bibliometrischen Methoden und ihrer Anwendung bei der Literaturrecherche erfahren Sie in unserem früheren Blogbeitrag zur Bibliometrie sowie direkt bei unserem Beratungsservice.

Turings Schlüsselwerke – bibliometrisch betrachtet

1. Computing Machinery and Intelligence (1950) – mehrfache Zitationswellen

Turing, A. M. (1950): Computing Machinery and Intelligence. In: Mind, Vol. LIX, No. 236, S. 433–460. DOI: 10.1093/mind/LIX.236.433 | Internet Archive (frei) | PDF (McGill)

Mit der schlichten Frage „Can machines think?“ eröffnete Turing 1950 eine der folgenreichsten wissenschaftlichen Debatten des 20. Jahrhunderts. Das Papier führte den Turing-Test ein und legte den Grundstein der KI-Forschung. Bibliometrisch bemerkenswert: Es erlebt bis heute Zitationswellen – mit jedem neuen Durchbruch in der KI steigen die Zitationen erneut an. (s. Abb. 1 und 2 unten). Laut Google Scholar verzeichnet Turing als Autor über 83.000 Zitationen.

Abbildung 1: Zitationsentwicklung von „Computing Machinery and Intelligence“ in Datenbank Dimesions. Das Paper erlebt mehrere Zitationswellen. Ein erster Anstieg in den 1980ern, als KI zur Wissenschaftsdisziplin reifte. Ein zweiter Sprung nach 2010, mit dem Durchbruch des maschinellen Lernens. Heute, im Zeitalter großer Sprachmodelle und generativer KI, erlebt das Papier seine dritte Welle – jede neue KI-Debatte kommt an Turing nicht vorbei. https://badge.dimensions.ai/details/id/pub.1027055246/citations

Abbildung 2: Publications Metrics in Datenbank Dimension mit Zitationsanzahl, und Altmetric https://app.dimensions.ai/details/publication/pub.1027055246

2. The Chemical Basis of Morphogenesis (1952) – Cross-Domain impact

Turing, A. M. (1952): The Chemical Basis of Morphogenesis. In: Philosophical Transactions of the Royal Society B, Vol. 237, No. 641, S. 37–72. DOI: 10.1098/rstb.1952.0012 | PDF (Caltech) | Semantic Scholar (12.000+ Zitationen)

Turings letztes großes Werk ist das vielleicht unerwartetste: ein mathematisches Modell für biologische Musterbildung – Streifen auf Zebras, Flecken auf Leoparden, Spiralen in Schneckenhäusern. Verfasst von einem Mathematiker, wird es heute in Biologie, Chemie und Physik zitiert. Mit über 12.000 Zitationen auf Semantic Scholar ist es ein Paradebeispiel für fachübergreifenden wissenschaftlichen Einfluss (Cross-Domain Impact).

Werke von und über Alan Turing

Werke von Turing online frei zugänglich

Turing (1936): On Computable Numbers PDF (ETH Zürich)
Turing (1950): Computing Machinery and Intelligence Internet Archive
Turing (1952): The Chemical Basis of Morphogenesis PDF (Caltech)
Turing Digital Archive (King’s College Cambridge): Manuskripte, Briefe, Typoskripte kings.cam.ac.uk

Bücher über Turing in unserer Bibliothek

Hodges, Andrew: Alan Turing: Enigma (1994) – die maßgebliche Biografie, Grundlage des Films The Imitation Game. ISBN 3211826270
Hochbuth, Rolf: Alan Turing: Erzählung (2018) – 2. Auflage, erweiterte Neuausgabe (Deutsch). ISBN 9783499269974 Abbildung: Cover des Buches von Hochbuth „ Alan Turing: Erzählung
Cooper, Stuart B. (Hg.): Alan Turing: his work and impact (2013) – Published in celebration of the centenary of Alan Turing’s birth in London. Includes a large number of the most significant contributions from the 4-volume set of the Collected Works of A.M. Turing, together with a wide spectrum of accompanying commentaries. ISBN 9780123869807
Turing, Sara: Alan M. Turing (2012) ISBN 9781107020580
Ottaviani, Jim: The imitation game: Alan Turing decoded (2016). ISBN 9781419718939
Andrew W. Appel (Hg.): Alan Turing’s Systems of Logic (2012) – Dieses Buch schildet Turings Arbeit an der Princeton University und enthält ein Faksimile seiner 1936 fertiggestellten Doktorarbeit mit dem Titel „Systems of Logic Based on Orindals“. ISBN 9780691155746
Petzold, Charles: The Annotated Turing (2008) – das 1936er Papier Satz für Satz erklärt. ISBN 9780470229057
Herken, Rolf (Hg.): The Universal Turing Machine – A Half-Century Survey (1988) – wissenschaftliche Wirkungsgeschichte. ISBN 3980105075

Bibliometrie als Werkzeug für Ihre eigene Recherche

Was Turings Werk zeigt, lässt sich auf jedes Fachgebiet übertragen: Zitationsanalysen helfen, Schlüsselwerke schnell zu identifizieren und unerwartete Querverbindungen zu entdecken. Kostenlose Einstiegspunkte sind Open Alex, Google Scholar und Semantic Scholar. Zitationsdatenbanken wie Web of Science oder Scopus stehen Ihnen über unseren Bibliothekszugang zur Verfügung. Bei Fragen berät Sie unser Beratungsservice gerne persönlich.

Turing wurde zu Lebzeiten verkannt – von der Wissenschaft, von der Gesellschaft, von seinem Land. Die Bibliometrie zeigt uns heute in Zahlen, was längst klar ist: Seine Ideen haben die Welt verändert. Entdecken Sie sein Werk – in unserer Bibliothek und kostenlos online.

Quellen & Nachweise

QuelleInhaltLinkWikipedia DE – Alan TuringBiografie, Werk, Rezeptionhttps://de.wikipedia.org/wiki/Alan_TuringGoogle Scholar – Turing-Profil83.000+ Zitationenhttps://scholar.google.com/citations?user=VWCHlwkAAAAJSemantic Scholar – Morphogenesis12.000+ Zitationenhttps://www.semanticscholar.org/paper/The-chemical-basis-of-morphogenesis-Turing/53b85e4066944b1753aae8e3418028a67d9372e1Turing Digital ArchiveOriginalmanuskriptehttps://turingarchive.kings.cam.ac.ukHistory of InformationOn Computable Numbers 1936https://www.historyofinformation.com/detail.php?id=619Internet ArchiveComputing Mach. & Intelligencehttps://archive.org/details/MIND–COMPUTING-MACHINERY-AND-INTELLIGENCERoyal Society PublishingMorphogenesis Originalhttps://doi.org/10.1098/rstb.1952.0012 #LizenzCCBY40INT #Bibliometrie #Zitationsdaten #Informatiker #TuringTest #AlanTuring

#lizenzccby40int #bibliometrie #zitationsdaten #informatiker #turingtest #alanturing

Linna Lu @[email protected] · 2026-06-23 · 08:49 UTC

Wie misst man ein Genie? Alan Turing und der Einfluss seiner Ideen

Ein bibliometrischer Blick auf das meistzitierte Werk der Informatik – zum 114. Geburtstag am 23. Juni

Alan Turing starb 1954, weitgehend vergessen. Heute ist er überall. Was ist in der Zwischenzeit passiert? Diese Frage hat nicht nur eine historische Antwort – sie hat eine messbare. Die Bibliometrie, die Wissenschaft der Messung wissenschaftlicher Publikationen und ihres Einflusses, macht sichtbar, wie Turings Ideen die Welt durchdrungen haben: zunächst langsam, dann unaufhaltsam. Am 23. Juni 2026 jährt sich Turings Geburtstag zum 114. Mal – ein Anlass, seinen Weg von der Vergessenheit zur Allgegenwart nachzuzeichnen.

Wer war Alan Turing?

Alan Mathison Turing wurde am 23. Juni 1912 in London geboren. Er war Mathematiker, Kryptoanalytiker und Philosoph der Maschine – und einer der unglücklichsten Genies des 20. Jahrhunderts. Im Zweiten Weltkrieg entschlüsselte er mit seinem Team in Bletchley Park die deutsche Enigma-Chiffriermaschine und verkürzte damit den Krieg nach Schätzungen um mehrere Jahre. Dafür erhielt er keinen öffentlichen Dank – die Arbeit blieb Jahrzehnte lang geheim.

1952 wurde Turing wegen Homosexualität verfolgt, chemisch kastriert und seiner Sicherheitsfreigabe beraubt. Am 7. Juni 1954 starb er mit nur 41 Jahren. Die offizielle Version lautete Selbstmord durch Zyanidvergiftung – ob es einer war, ist bis heute nicht abschließend geklärt. 2013, fast 60 Jahre nach seinem Tod, begnadigte die britische Königin Elizabeth II. ihn posthum.

Was blieb, waren seine Texte. Und die veränderten die Welt.

Abbildung: Alan Turing, Plakat der Gesellschaft der Informatik: Pionier der Informatik und Kryptoanalytiker https://gi.de/persoenlichkeiten/alan-turing

Bibliometrie: Einfluss wissenschaftlicher Ideen messen

Bibliometrie fragt: Welche Ideen haben die Wissenschaft verändert – und wie lässt sich das messen? Turings Werk ist dafür ein ideales Anschauungsobjekt. Mehr zu bibliometrischen Methoden und ihrer Anwendung bei der Literaturrecherche erfahren Sie in unserem früheren Blogbeitrag zur Bibliometrie sowie direkt bei unserem Beratungsservice.

Turings Schlüsselwerke – bibliometrisch betrachtet

1. Computing Machinery and Intelligence (1950) – mehrfache Zitationswellen

Turing, A. M. (1950): Computing Machinery and Intelligence. In: Mind, Vol. LIX, No. 236, S. 433–460. DOI: 10.1093/mind/LIX.236.433 | Internet Archive (frei) | PDF (McGill)

Mit der schlichten Frage „Can machines think?“ eröffnete Turing 1950 eine der folgenreichsten wissenschaftlichen Debatten des 20. Jahrhunderts. Das Papier führte den Turing-Test ein und legte den Grundstein der KI-Forschung. Bibliometrisch bemerkenswert: Es erlebt bis heute Zitationswellen – mit jedem neuen Durchbruch in der KI steigen die Zitationen erneut an. (s. Abb. 1 und 2 unten). Laut Google Scholar verzeichnet Turing als Autor über 83.000 Zitationen.

Abbildung 1: Zitationsentwicklung von „Computing Machinery and Intelligence“ in Datenbank Dimesions. Das Paper erlebt mehrere Zitationswellen. Ein erster Anstieg in den 1980ern, als KI zur Wissenschaftsdisziplin reifte. Ein zweiter Sprung nach 2010, mit dem Durchbruch des maschinellen Lernens. Heute, im Zeitalter großer Sprachmodelle und generativer KI, erlebt das Papier seine dritte Welle – jede neue KI-Debatte kommt an Turing nicht vorbei. https://badge.dimensions.ai/details/id/pub.1027055246/citations

Abbildung 2: Publications Metrics in Datenbank Dimension mit Zitationsanzahl, und Altmetric https://app.dimensions.ai/details/publication/pub.1027055246

2. The Chemical Basis of Morphogenesis (1952) – Cross-Domain impact

Turing, A. M. (1952): The Chemical Basis of Morphogenesis. In: Philosophical Transactions of the Royal Society B, Vol. 237, No. 641, S. 37–72. DOI: 10.1098/rstb.1952.0012 | PDF (Caltech) | Semantic Scholar (12.000+ Zitationen)

Turings letztes großes Werk ist das vielleicht unerwartetste: ein mathematisches Modell für biologische Musterbildung – Streifen auf Zebras, Flecken auf Leoparden, Spiralen in Schneckenhäusern. Verfasst von einem Mathematiker, wird es heute in Biologie, Chemie und Physik zitiert. Mit über 12.000 Zitationen auf Semantic Scholar ist es ein Paradebeispiel für fachübergreifenden wissenschaftlichen Einfluss (Cross-Domain Impact).

Werke von und über Alan Turing

Werke von Turing online frei zugänglich

Turing (1936): On Computable Numbers PDF (ETH Zürich)
Turing (1950): Computing Machinery and Intelligence Internet Archive
Turing (1952): The Chemical Basis of Morphogenesis PDF (Caltech)
Turing Digital Archive (King’s College Cambridge): Manuskripte, Briefe, Typoskripte kings.cam.ac.uk

Bücher über Turing in unserer Bibliothek

Hodges, Andrew: Alan Turing: Enigma (1994) – die maßgebliche Biografie, Grundlage des Films The Imitation Game. ISBN 3211826270
Hochbuth, Rolf: Alan Turing: Erzählung (2018) – 2. Auflage, erweiterte Neuausgabe (Deutsch). ISBN 9783499269974 Abbildung: Cover des Buches von Hochbuth „ Alan Turing: Erzählung
Cooper, Stuart B. (Hg.): Alan Turing: his work and impact (2013) – Published in celebration of the centenary of Alan Turing’s birth in London. Includes a large number of the most significant contributions from the 4-volume set of the Collected Works of A.M. Turing, together with a wide spectrum of accompanying commentaries. ISBN 9780123869807
Turing, Sara: Alan M. Turing (2012) ISBN 9781107020580
Ottaviani, Jim: The imitation game: Alan Turing decoded (2016). ISBN 9781419718939
Andrew W. Appel (Hg.): Alan Turing’s Systems of Logic (2012) – Dieses Buch schildet Turings Arbeit an der Princeton University und enthält ein Faksimile seiner 1936 fertiggestellten Doktorarbeit mit dem Titel „Systems of Logic Based on Orindals“. ISBN 9780691155746
Petzold, Charles: The Annotated Turing (2008) – das 1936er Papier Satz für Satz erklärt. ISBN 9780470229057
Herken, Rolf (Hg.): The Universal Turing Machine – A Half-Century Survey (1988) – wissenschaftliche Wirkungsgeschichte. ISBN 3980105075

Bibliometrie als Werkzeug für Ihre eigene Recherche

Was Turings Werk zeigt, lässt sich auf jedes Fachgebiet übertragen: Zitationsanalysen helfen, Schlüsselwerke schnell zu identifizieren und unerwartete Querverbindungen zu entdecken. Kostenlose Einstiegspunkte sind Open Alex, Google Scholar und Semantic Scholar. Zitationsdatenbanken wie Web of Science oder Scopus stehen Ihnen über unseren Bibliothekszugang zur Verfügung. Bei Fragen berät Sie unser Beratungsservice gerne persönlich.

Turing wurde zu Lebzeiten verkannt – von der Wissenschaft, von der Gesellschaft, von seinem Land. Die Bibliometrie zeigt uns heute in Zahlen, was längst klar ist: Seine Ideen haben die Welt verändert. Entdecken Sie sein Werk – in unserer Bibliothek und kostenlos online.

Quellen & Nachweise

QuelleInhaltLinkWikipedia DE – Alan TuringBiografie, Werk, Rezeptionhttps://de.wikipedia.org/wiki/Alan_TuringGoogle Scholar – Turing-Profil83.000+ Zitationenhttps://scholar.google.com/citations?user=VWCHlwkAAAAJSemantic Scholar – Morphogenesis12.000+ Zitationenhttps://www.semanticscholar.org/paper/The-chemical-basis-of-morphogenesis-Turing/53b85e4066944b1753aae8e3418028a67d9372e1Turing Digital ArchiveOriginalmanuskriptehttps://turingarchive.kings.cam.ac.ukHistory of InformationOn Computable Numbers 1936https://www.historyofinformation.com/detail.php?id=619Internet ArchiveComputing Mach. & Intelligencehttps://archive.org/details/MIND–COMPUTING-MACHINERY-AND-INTELLIGENCERoyal Society PublishingMorphogenesis Originalhttps://doi.org/10.1098/rstb.1952.0012 #Zitationsdaten #Informatiker #TuringTest #AlanTuring #LizenzCCBY40INT #Bibliometrie

#zitationsdaten #informatiker #turingtest #alanturing #lizenzccby40int #bibliometrie

X-tof @[email protected] · 2026-06-16 · 21:01 UTC

@carofi hui, von all den Zitaten dort habe ich auch dieses fotografiert. 😯
#Strommuseum #AlanTuring #Turing

#strommuseum #alanturing #turing

Richard Carlsson @[email protected] · 2026-06-12 · 12:18 UTC

Turing memorial #manchester #AlanTuring

#manchester #alanturing

Richard Carlsson @[email protected] · 2026-06-12 · 12:18 UTC

Turing memorial #manchester #AlanTuring

#manchester #alanturing

Asakiyume @[email protected] · 2026-06-07 · 22:01 UTC

Sonya Taaffe on AI on the occasion of the anniversary of Alan Turing's death:

"The flaw in the imitation game is not the mimicry of the machine, but the mirror test of humanity which has such difficulty recognizing itself to begin with. How much more readily the present of this future ascribes personhood to an app than acknowledges it in a rainbow."

--Amen.

#Pridemonth #AlanTuring

#pridemonth #alanturing

Asakiyume @[email protected] · 2026-06-07 · 22:01 UTC

Sonya Taaffe on AI on the occasion of the anniversary of Alan Turing's death:

"The flaw in the imitation game is not the mimicry of the machine, but the mirror test of humanity which has such difficulty recognizing itself to begin with. How much more readily the present of this future ascribes personhood to an app than acknowledges it in a rainbow."

--Amen.

#Pridemonth #AlanTuring

#pridemonth #alanturing

Church of Jeff @[email protected] · 2026-06-07 · 18:48 UTC

https://en.wikipedia.org/wiki/Alan_Turing

#AlanTuring #LGBTQHistory #PrideMonth #History #ComputerScience #Pride #LGBTQ #LGBTQIA #Antifa

#alanturing #lgbtqhistory #pridemonth #history #computerscience #pride

Church of Jeff @[email protected] · 2026-06-07 · 18:48 UTC

https://en.wikipedia.org/wiki/Alan_Turing

#AlanTuring #LGBTQHistory #PrideMonth #History #ComputerScience #Pride #LGBTQ #LGBTQIA #Antifa

#alanturing #lgbtqhistory #pridemonth #history #computerscience #pride

(Roughly) Daily @[email protected] · 2026-06-07 · 08:00 UTC

“Things that are so far removed from our daily experience… are inherently hard to understand”*…

That’s certainly true of numbers. And as the numbers grow, the cognitive challenges grow with them. (Indeed, by way of example: 1 million seconds, is roughly 11.5 days; 1 billion seconds is almost 32 years.)

We’ve looked before at the mysterious extremes of math: zero and infinity [and here]. But as Dan Falk reminds us, the numbers in between can seem pretty strange as well– especially the extremely large ones. In a review of Richard Elwes‘ Huge Numbers: A Story of Counting Ambitiously, From 4½ to Fish 7, Falk spotlights some of the largest numbers humans have ever contemplated…

… Aficionados of huge numbers are called “googologists,” a reference to the number 10100, known as a googol. Such numbers have a peculiar sort of existence. For the vast majority of us, they’re of limited everyday value. Calculations at the supermarket checkout, or at tax time in April, typically involve far more modest figures. Perhaps we’ve read that the U.S. national debt is in excess of $38 trillion — a mind-numbing figure, to be sure, but it’s not as though any one individual needs to count it up in stacks of $20 bills.
And yet, much larger numbers await those who seek them out. Consider the kinds of numbers that crop up in problems involving combinations and permutations. For example, in how many distinct ways can one shuffle a deck of cards? Elwes takes us through the calculation, and we end up with a figure of about 8×1067. Compared to that number, the odds of getting a royal flush when dealt a five-card poker hand seem pretty decent, sitting at a mere 1 in 649,740 (still rare enough that many poker players have never held such a hand). Or consider that famous 1980s cultural touchstone, the Rubik’s cube. In how many ways can one scramble the cube? It turns out that the figure is about 43 quintillion, or 4.3×1019 — but in spite of that ridiculously large figure, people do routinely solve the puzzle, and champions can do it in mere seconds. In fact, as Elwes explains, no Rubik’s cube arrangement is more than 20 moves away from any other arrangement.
Or consider the age of the universe, estimated to be about 13.8 billion years. This may seem like a lengthy span of time, but our cosmic future is where the really big numbers come up. Elwes examines the so-called heat death of the universe, in which all matter has broken down into subatomic particles. We may reach this point in [10 raised to the 10th power, raised again to the 120th power] years — this dizzying figure is 10 raised to the power of 10120 — at which point, Elwes says, the universe will have ballooned up to a diameter of 10 to the power of 10 to the power of 10120 light years. (Yes, that’s [10 raised to the 10th power, again to the 10th power, then to the 120th power] light years.) Elwes adds a footnote: “At this point, the choice of units hardly matters; the distance is so immense that whether we choose to measure it in Planck lengths or giga-light years makes little difference.” Let that sink in!
As mind numbing as such figures are, the highest numbers contemplated by humans come not from physics but from pure mathematics and computer science. Like “Graham’s number” — an immense figure put forward as the upper-bound for solutions to a problem in a branch of mathematics known as Ramsey theory. Some readers may find the ensuing discussion of multi-dimensional hypercubes a bit challenging, but one can enjoy the payoff regardless: We end up with a number that can’t even be expressed in conventional notation, and which earned a mention in the 1980 edition of the “Guinness Book of World Records” as “the highest number ever used in a mathematical proof.”
Reading this book is a little bit like sitting in the back row of an auction house where a rare Picasso (let’s say) is up for grabs: How high is this thing going to go? And indeed, Elwes keeps going. We eventually meet the so-called busy beaver numbers, a set of numbers that crop up in theoretical computer science, when one tries to deduce whether a particular computer program will eventually stop, or keep going forever — a conundrum known as the “halting problem.” As Elwes explains, it’s not at all straightforward to distinguish the two types of programs (and if it was, it would help mathematicians tackle some of the most vexing problems in their field).
The fifth busy beaver number, known as BB(5) — associated with a computer program that can access five internal states — works out to 47,176,870. And that’s as far as we’ve gotten, Elwes explains. No one has worked out the value of BB(6), but he assures us that it’s beyond the range of any physical computer; and BB(16) leaves even Graham’s number in the dust.
But wait, there’s more! “Rayo’s number,” concocted by Agustín Rayo — a dean and professor at MIT — using set theory, is bigger still (here’s a fun video about it); and “Fish 7,” mentioned in the book’s subtitle, named for a Japanese googologist who goes by the pseudonym “Fish,” builds on Rayo’s number, and … well, the details are not easily digested, but the mind-melting nature of these numbers comes across as a feature, not a bug, of Elwes’s story… the narrative is enlivened by explorations of the peculiarities of math history…
… Archimedes tried to estimate how many grains of sand would be needed to fill up the known universe, back in the third century B.C. Did he simply have too much time on his hands? Not at all, insists Elwes: The Greek thinker was articulating an important idea — that no matter how unfathomably large a quantity may be, we can describe it with precision, thanks to mathematics. “Archimedes,” he writes, “was penning a manifesto for the expressive power of large numbers.”…
… [Elwes focuses] on numbers that are ridiculously large and yet finite. In the end, perhaps this is the most mind-boggling fact of all: that these enormous numbers, from Graham’s number to Fish 7 and beyond, fall as far short of infinity as does the humble number 1…

The mysteries of the massive: “The Mind-Boggling Science of Enormous Numbers,” @danfalk.bsky.social on @richardelwes.bsky.social in @undark.org.

* Steven Strogatz

###

As we enumerate enormity, we might spare a thought for a seminal mathematician, Alan Turing; he died on this date in 1954. He was a foundational computer science pioneer (inventor of the Turing Machine (an influential model for the general-purpose computer), creator of the “Turing Test” (only too relevant in these AI-infected times), inspiration for “The Turing Award” (the “Nobel Prize of computing“), and cryptographer (leading member of the team that cracked the Enigma code during WWII).

source

#AlanTuring #computing #cryptography #culture #enigmaCode #googologist #googologists #history #infinity #largeNumbers #Math #Mathematics #Numbers #RichardElwes #Science #TuringMachine #TuringPrize #TuringTest #zero

#alanturing #computing #cryptography #culture #enigmacode #googologist

(Roughly) Daily @[email protected] · 2026-06-07 · 08:00 UTC

“Things that are so far removed from our daily experience… are inherently hard to understand”*…

That’s certainly true of numbers. And as the numbers grow, the cognitive challenges grow with them. (Indeed, by way of example: 1 million seconds, is roughly 11.5 days; 1 billion seconds is almost 32 years.)

We’ve looked before at the mysterious extremes of math: zero and infinity [and here]. But as Dan Falk reminds us, the numbers in between can seem pretty strange as well– especially the extremely large ones. In a review of Richard Elwes‘ Huge Numbers: A Story of Counting Ambitiously, From 4½ to Fish 7, Falk spotlights some of the largest numbers humans have ever contemplated…

… Aficionados of huge numbers are called “googologists,” a reference to the number 10100, known as a googol. Such numbers have a peculiar sort of existence. For the vast majority of us, they’re of limited everyday value. Calculations at the supermarket checkout, or at tax time in April, typically involve far more modest figures. Perhaps we’ve read that the U.S. national debt is in excess of $38 trillion — a mind-numbing figure, to be sure, but it’s not as though any one individual needs to count it up in stacks of $20 bills.
And yet, much larger numbers await those who seek them out. Consider the kinds of numbers that crop up in problems involving combinations and permutations. For example, in how many distinct ways can one shuffle a deck of cards? Elwes takes us through the calculation, and we end up with a figure of about 8×1067. Compared to that number, the odds of getting a royal flush when dealt a five-card poker hand seem pretty decent, sitting at a mere 1 in 649,740 (still rare enough that many poker players have never held such a hand). Or consider that famous 1980s cultural touchstone, the Rubik’s cube. In how many ways can one scramble the cube? It turns out that the figure is about 43 quintillion, or 4.3×1019 — but in spite of that ridiculously large figure, people do routinely solve the puzzle, and champions can do it in mere seconds. In fact, as Elwes explains, no Rubik’s cube arrangement is more than 20 moves away from any other arrangement.
Or consider the age of the universe, estimated to be about 13.8 billion years. This may seem like a lengthy span of time, but our cosmic future is where the really big numbers come up. Elwes examines the so-called heat death of the universe, in which all matter has broken down into subatomic particles. We may reach this point in [10 raised to the 10th power, raised again to the 120th power] years — this dizzying figure is 10 raised to the power of 10120 — at which point, Elwes says, the universe will have ballooned up to a diameter of 10 to the power of 10 to the power of 10120 light years. (Yes, that’s [10 raised to the 10th power, again to the 10th power, then to the 120th power] light years.) Elwes adds a footnote: “At this point, the choice of units hardly matters; the distance is so immense that whether we choose to measure it in Planck lengths or giga-light years makes little difference.” Let that sink in!
As mind numbing as such figures are, the highest numbers contemplated by humans come not from physics but from pure mathematics and computer science. Like “Graham’s number” — an immense figure put forward as the upper-bound for solutions to a problem in a branch of mathematics known as Ramsey theory. Some readers may find the ensuing discussion of multi-dimensional hypercubes a bit challenging, but one can enjoy the payoff regardless: We end up with a number that can’t even be expressed in conventional notation, and which earned a mention in the 1980 edition of the “Guinness Book of World Records” as “the highest number ever used in a mathematical proof.”
Reading this book is a little bit like sitting in the back row of an auction house where a rare Picasso (let’s say) is up for grabs: How high is this thing going to go? And indeed, Elwes keeps going. We eventually meet the so-called busy beaver numbers, a set of numbers that crop up in theoretical computer science, when one tries to deduce whether a particular computer program will eventually stop, or keep going forever — a conundrum known as the “halting problem.” As Elwes explains, it’s not at all straightforward to distinguish the two types of programs (and if it was, it would help mathematicians tackle some of the most vexing problems in their field).
The fifth busy beaver number, known as BB(5) — associated with a computer program that can access five internal states — works out to 47,176,870. And that’s as far as we’ve gotten, Elwes explains. No one has worked out the value of BB(6), but he assures us that it’s beyond the range of any physical computer; and BB(16) leaves even Graham’s number in the dust.
But wait, there’s more! “Rayo’s number,” concocted by Agustín Rayo — a dean and professor at MIT — using set theory, is bigger still (here’s a fun video about it); and “Fish 7,” mentioned in the book’s subtitle, named for a Japanese googologist who goes by the pseudonym “Fish,” builds on Rayo’s number, and … well, the details are not easily digested, but the mind-melting nature of these numbers comes across as a feature, not a bug, of Elwes’s story… the narrative is enlivened by explorations of the peculiarities of math history…
… Archimedes tried to estimate how many grains of sand would be needed to fill up the known universe, back in the third century B.C. Did he simply have too much time on his hands? Not at all, insists Elwes: The Greek thinker was articulating an important idea — that no matter how unfathomably large a quantity may be, we can describe it with precision, thanks to mathematics. “Archimedes,” he writes, “was penning a manifesto for the expressive power of large numbers.”…
… [Elwes focuses] on numbers that are ridiculously large and yet finite. In the end, perhaps this is the most mind-boggling fact of all: that these enormous numbers, from Graham’s number to Fish 7 and beyond, fall as far short of infinity as does the humble number 1…

The mysteries of the massive: “The Mind-Boggling Science of Enormous Numbers,” @danfalk.bsky.social on @richardelwes.bsky.social in @undark.org.

* Steven Strogatz

###

As we enumerate enormity, we might spare a thought for a seminal mathematician, Alan Turing; he died on this date in 1954. He was a foundational computer science pioneer (inventor of the Turing Machine (an influential model for the general-purpose computer), creator of the “Turing Test” (only too relevant in these AI-infected times), inspiration for “The Turing Award” (the “Nobel Prize of computing“), and cryptographer (leading member of the team that cracked the Enigma code during WWII).

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#AlanTuring #computing #cryptography #culture #enigmaCode #googologist #googologists #history #infinity #largeNumbers #Math #Mathematics #Numbers #RichardElwes #Science #TuringMachine #TuringPrize #TuringTest #zero

#alanturing #computing #cryptography #culture #enigmacode #googologist

Elektra @[email protected] · 2026-06-02 · 00:39 UTC

@Priyajsridhar
Which queer historical figure who contributed to science catches your eye? What is one nice thing you would say to them?

I'm a computer scientist with a lifetime fascination with cryphtography and one of my heroes is on this list.

Alan Turing, I see you, you gifted, brilliant man. Love is love. Nothing you've ever done is wrong--hold on to that.

Now--I wish the world had been more understanding to Turing.

#Writephant #AlanTuring #turingtest

#writephant #alanturing #turingtest

Fucina Fibonacci @[email protected] · 2026-05-29 · 19:35 UTC

#AlanTuring, la dignità e il codice https://www.avvenire.it/rubriche/interferenze/alan-turing-la-dignita-e-il-codice_108888

@cultura

#GabriellaGreison #AI

#alanturing #gabriellagreison #ai

Fucina Fibonacci @[email protected] · 2026-05-29 · 19:35 UTC

#AlanTuring, la dignità e il codice https://www.avvenire.it/rubriche/interferenze/alan-turing-la-dignita-e-il-codice_108888

@cultura

#GabriellaGreison #AI

#alanturing #gabriellagreison #ai

fsolt @[email protected] · 2026-05-24 · 16:16 UTC

Criptonomicón – Neal Stephenson (1999)

Me resulta difícil escribir una reseña sobre Criptonomicón sin que esta sea tan larga como la obra (en castellano sólo he podido encontrar una edición de Penguin Random House que divide la historia en tres volúmenes, con un total de unas ~1500 páginas), ya que la cantidad de temas que trata es tan grande que una mera enumeración puede llegar a abrumar: el desarrollo de la computación; el proceso de romper la máquina Enigma; distintas campañas militares durante la segunda guerra […]

https://fsolt.es/2026/05/criptonomicon-neal-stephenson-1999/

#alanturing #bitcoin #criptografia #criptonomicon #enigma #libros

fsolt @[email protected] · 2026-05-24 · 16:16 UTC

Criptonomicón – Neal Stephenson (1999)

Me resulta difícil escribir una reseña sobre Criptonomicón sin que esta sea tan larga como la obra (en castellano sólo he podido encontrar una edición de Penguin Random House que divide la historia en tres volúmenes, con un total de unas ~1500 páginas), ya que la cantidad de temas que trata es tan grande que una mera enumeración puede llegar a abrumar: el desarrollo de la computación; el proceso de romper la máquina Enigma; distintas campañas militares durante la segunda guerra […]

https://fsolt.es/2026/05/criptonomicon-neal-stephenson-1999/

#alanturing #bitcoin #criptografia #criptonomicon #enigma #libros