(Two to the 100th Power)
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A Way to Visualize the Powers of Two
Just a simple table, but it clearly shows the progression of geometrically-increasing numbers.
Just a simple table, but it clearly shows the progression of geometrically-increasing numbers.
Cuts Pieces Thickness (most values rounded)
0 1 0.1 mm
1 2 0.2 mm
2 4 0.4 mm
3 8 0.8 mm
4 16 1.6 mm
5 32 3.2 mm
6 64 6.4 mm
7 128 1.28 cm
8 256 2.56 cm 1 inch
9 512 5.12 cm 2 inches
10 1,024 10 cm 4 inches
11 2,048 20 cm 8 inches
12 4,096 41 cm 16 inches
13 8,192 82 cm 32 inches
14 16,384 1.6 m 64 inches
15 32,768 3.3 m 10 feet
16 65,536 6.6 m 20 feet
17 131,072 13 m 40 feet
18 262,144 26 m 80 feet
19 524,288 52 m 160 feet
20 1,048,576 105 m 320 feet
21 2,097,152 210 m 1 city block
22 4,194,304 420 m 2 city blocks
23 8,388,608 840 m 4 city blocks
24 16,777,216 1.7 km 1 mile
25 33,554,432 3.4 km 2 miles
26 67,108,864 6.7 km 4 miles
27 134,217,728 13 km 8 miles
28 268,435,456 27 km 16 miles
29 536,870,912 54 km 32 miles
30 1,073,741,824 107 km 64 miles
31 2,147,483,648 215 km 128 miles
32 4,294,967,296 430 km 256 miles
33 8,589,934,592 860 km 512 miles
34 17,179,869,184
35 34,359,738,368 Almost across the USA
36 68,719,476,736
37 137,438,953,472
38 274,877,906,944
39 549,755,813,888
40 1,099,511,627,776
41 2,199,023,255,552
42 4,398,046,511,104 Past the Moon
43 8,796,093,022,208
44 17,592,186,044,416
45 35,184,372,088,832
46 70,368,744,177,664
47 140,737,488,355,328
48 281,474,976,710,656
49 562,949,953,421,312
50 1,125,899,906,842,624
51 2,251,799,813,685,248 Past the Sun
52 4,503,599,627,370,496
53 9,007,199,254,740,992
54 18,014,398,509,481,984
55 36,028,797,018,963,968
56 72,057,594,037,927,936 Beyond Pluto
57 144,115,188,075,855,872
58 288,230,376,151,711,744
59 576,460,752,303,423,488
60 1,152,921,504,606,846,976
61 2,305,843,009,213,693,952
62 4,611,686,018,427,387,904
63 9,223,372,036,854,775,808
64 18,446,744,073,709,551,616
65 36,893,488,147,419,103,232
66 73,786,976,294,838,206,464
67 147,573,952,589,676,412,928 More than 1 light-year
68 295,147,905,179,352,825,856
69 590,295,810,358,705,651,712 Beyond Proxima Centauri
70 1,180,591,620,717,411,303,424
71 2,361,183,241,434,822,606,848
72 4,722,366,482,869,645,213,696
73 9,444,732,965,739,290,427,392
74 18,889,465,931,478,580,854,784
75 37,778,931,862,957,161,709,568
76 75,557,863,725,914,323,419,136
77 151,115,727,451,828,646,838,272 To the bright star Deneb
78 302,231,454,903,657,293,676,544
79 604,462,909,807,314,587,353,088
80 1,208,925,819,614,629,174,706,176
81 2,417,851,639,229,258,349,412,352
82 4,835,703,278,458,516,698,824,704
83 9,671,406,556,917,033,397,649,408
84 19,342,813,113,834,066,795,298,816 Across the Milky Way
85 38,685,626,227,668,133,590,597,632
86 77,371,252,455,336,267,181,195,264
87 154,742,504,910,672,534,362,390,528
88 309,485,009,821,345,068,724,781,056 To the Andromeda galaxy
89 618,970,019,642,690,137,449,562,112
90 1,237,940,039,285,380,274,899,124,224
91 2,475,880,078,570,760,549,798,248,448
92 4,951,760,157,141,521,099,596,496,896
93 9,903,520,314,283,042,199,192,993,792
94 19,807,040,628,566,084,398,385,987,584
95 39,614,081,257,132,168,796,771,975,168
96 79,228,162,514,264,337,593,543,950,336
97 158,456,325,028,528,675,187,087,900,672
98 316,912,650,057,057,350,374,175,801,344
99 633,825,300,114,114,700,748,351,602,688
100 1,267,650,600,228,229,401,496,703,205,376 Past the farthest galaxy
The making of layered steel depends on this same mathematical progression. A large number of very thin layers of two kinds of metal can be sandwiched together in a few minutes. A block of hard steel, which can hold a very sharp edge, and a block of iron or soft steel, which resists cracking, are heated and hammered together, to give two layers. They are hammered thin enough to fold the resulting sheet over, giving three layers. (The two inside layers are the same metal, so fuse into one.) If the sheet is folded ten times, 1,025 layers will result.
French pastries are made similarly. The dough is rolled into a square, buttered, and folded in thirds so as to make three layers. These steps are repeated, usually a total of six times, giving 729 layers. A seventh rolling and folding will give 2,187 layers. In French, the pastry is called mille feuille, or "thousand layers".
In order to have the stack of paper end up with pieces one centimeter square (the size of a fingernail), the original sheet would have to be the size of Pluto's orbit. Its mass would be about the same as Earth's mass.
Sizes of city blocks vary, but a common length in the USA is 660 feet in the long direction, including the street width. That is 8 blocks per mile. Such blocks are typically 440 feet in the short direction, or 12 per mile.
The speed of light in vacuum is very nearly 300,000,000 meters per second.
A light-year is 9,460,536,000,000,000 meters, or about 6 trillion miles.
Observations by the Wilkinson Microwave Anisotropy Probe, reported in February 2003, indicate that the Universe is 13.7 billion years old, plus or minus 1%, and that the cosmic background radiation was emitted about 380,000 years after the Big Bang. They also indicate that the first stars began to shine just 200 million years after the Big Bang.
The image representing the Milky Way is actually a Hubble Space Telescope image of galaxy NGC 4414.
Most of the Space images in this essay can be found in NASA's Astronomy Picture of the Day archive.
The image of the Andromeda Galaxy is copyrighted by Jason Ware, who
took the photo through his
I'd like to thank Charles and Ray Eames, Isaac Asimov, Rich Brown, and Ben Huset, without whose insight and support the existence of these pages would have been highly improbable.
To my Space and Science home page
Jeff Root
August 31, 2003