Da Gulliver a Googol e oltre. Viaggio agli estremi dimensionali Maurizio Zani Matematica alfabeto dell'universo, Fondazione Culturale Ambrosianeum, Milano 20/04/2022 Fond. Cult. Ambrosianeum “Queste son di quelle difficoltà che derivano dal discorrer che noi facciamo col nostro intelletto finito intorno a gl’infiniti, dandogli quelli attributi che noi diamo alle cose finite e terminate; il che penso che sia inconveniente…” Galileo Galilei https://www.treccani.it/vocabolario/grande Jonathan Swift (1726) Lilliput Brobdingna g Gulliver 6 in 180 cm 60 ft ÷12 *12 Jack Black (2010) Richard Harris (1977) Ted Danson (1996) 20 ÷ 20 000 Hz 300 ÷ 700 nm 0.1 mm ÷ 100 mm 0.1 s 1 °C Sensibilità Intervallo Edward Kasner, James Newman (1938) googol 10100 googolplex 10googol 1 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 n° di Graham ??? https://astrogear.blog/2019/07/17/grandi-numeri-il-googol Larry Page, Sergey Brin (1996) 1 googol = 10100 = 1 0000000000 0000000000 ... 0000000000 0000000000 100 zeri massa del neutrino: massa del Sole: massa della Via Lattea: massa dell'universo osservabile: universo fatto di granelli di senape: • diametro del granello: 1/2 mm • raggio dell'universo: 4ꞏ1010 anni luce 8.91ꞏ10-38 kg 1.99ꞏ1030 kg 6.82ꞏ1011 MS = 1.36ꞏ1042 kg 3.00ꞏ1053 kg 1090 1 googolplex = 10googol = 1 0000000000 0000000000 ... 0000000000 0000000000 google zeri addizione: incremento iterato 2+3 = 2+(1+1+1) = 5 moltiplicazione: addizione iterata 2x3 = 2+2+2 = 6 3 volte 3 volte elevamento a potenza: moltiplicazione iterata 23 = 2^3 = 2↑3 = 2x2x2 = 8 3 volte tetrazione: elevamento a potenza iterato 2↑↑3 = 2↑2↑2 = 2↑4 = 2^4 = 16 3 volte 2↑↑↑3 = 2↑↑2↑↑2 = 2↑↑4 = 65 536 3 volte freccia di Knuth n° di Graham? Micro1 Å 1 nm 10 nm 100 nm 10 m 100 m 10 mm = 1 cm 10-2 m 10-3 m 10-4 m 10-5 m 10-6 m 10-7 m 10-8 m 10-9 m 10-10 m Nano1 mm 1 m Macroviti ~ 10 mm anello di atomi ~ 14 nm transistor ~ 50 nm MEMS ~ 10 m Cose artificiali globuli rossi 10 m capello umano ~ 100 m formica ~ 5 mm atomi ~ 0.1 nm DNA ~ 2 nm Cose naturali P(M) = M -1.6 10-5 10-4 10-3 10-2 M- M+ P(M) (arb. units)M/Mtot https://aip.scitation.org/doi/10.1063/1.1616994 metodo induttivometodo magneto-ottico https://pubs.acs.org/doi/10.1021/acs.langmuir.6b01117 https://www.sciencedirect.com/science/article/pii/S0304399117304904 https://www.esrf.fr 350 m ID13 distance ≈ 100 m beam size = 100 nm E ≈ 15 keV (X-ray)  ≈ 0.1 nm T = 90 K https://iopscience.iop.org/article/10.1088/0957- 4484/23/15/155702 r = 23.1ꞏ109 km (= 155.7 UA = 21.4 light hour) p = 2πr = ... π = 3.1415926535 89 π = 3.14 Δp = 462ꞏ106 km Δp = 46 m 12 decimali https://voyager.jpl.nasa.gov Missione spaziale Voyager 1 (1977) William Shatner James Kirk 08/09/1966 13/10/2021 "Là dove nessun uomo è mai giunto prima" "Everybody in the world needs to do this. Everybody in the world needs to see ... it was unbelievable. I mean, the little things, the weightlessness, and to see the blue color whip by and now you’re staring into blackness. That’s the thing. This covering of blue is this sheet, this blanket, this comforter of blue around that we have around us. We think ‘oh, that’s blue sky’ and suddenly you shoot through it all of a sudden, like you whip a sheet off you when you’re asleep, and you’re looking into blackness, into black ugliness. And you look down, there’s the blue down there, and the black up there, and there is Mother Earth and comfort and there is... is there death? " https://www.youtube.com/watch?v=OTfQVMH5SuI "If the universe had a diameter of 80 million light years, using 35 decimal places for pi the perimeter would be wrong of about 10 nm" Isaac Asimov