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