首页 › 探索 › 一张纸对折105次，宇宙就真的放不下了吗？

songxiao530 发表于 2023-8-5 01:15:59

一张纸对折105次，宇宙就真的放不下了吗？

一张纸对折105次，宇宙就真的放不下了吗？

tszqc 发表于 2023-8-5 01:16:29

给你一点小小的数学震撼.
假设一张纸厚度是 https://www.zhihu.com/equation?tex=0.1%5C%2C%5Ctext%7Bmm%7D , 设其对折 https://www.zhihu.com/equation?tex=i 次的厚度是 https://www.zhihu.com/equation?tex=%5Ctext%7BFold%7D_%7B%5C%2Ci%7D , 那么其对折 https://www.zhihu.com/equation?tex=0%5Csim105 次的厚度分别是多少呢?
https://www.zhihu.com/equation?tex=%5Cbegin%7Balign%7D+%5Ctext%7BFold%7D_%7B%5C%2C0%7D%3D%260.1%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C1%7D%3D%260.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C2%7D%3D%260.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C3%7D%3D%260.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C4%7D%3D%261.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C5%7D%3D%263.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C6%7D%3D%266.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C7%7D%3D%2612.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C8%7D%3D%2625.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C9%7D%3D%2651.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C10%7D%3D%26102.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C11%7D%3D%26204.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C12%7D%3D%26409.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C13%7D%3D%26819.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C14%7D%3D%261638.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C15%7D%3D%263276.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C16%7D%3D%266553.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C17%7D%3D%2613107.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C18%7D%3D%2626214.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C19%7D%3D%2652428.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C20%7D%3D%26104857.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C21%7D%3D%26209715.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C22%7D%3D%26419430.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C23%7D%3D%26838860.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C24%7D%3D%261677721.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C25%7D%3D%263355443.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C26%7D%3D%266710886.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C27%7D%3D%2613421772.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C28%7D%3D%2626843545.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C29%7D%3D%2653687091.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C30%7D%3D%26107374182.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C31%7D%3D%26214748364.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C32%7D%3D%26429496729.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C33%7D%3D%26858993459.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C34%7D%3D%261717986918.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C35%7D%3D%263435973836.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C36%7D%3D%266871947673.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C37%7D%3D%2613743895347.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C38%7D%3D%2627487790694.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C39%7D%3D%2654975581388.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C40%7D%3D%26109951162777.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C41%7D%3D%26219902325555.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C42%7D%3D%26439804651110.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C43%7D%3D%26879609302220.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C44%7D%3D%261759218604441.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C45%7D%3D%263518437208883.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C46%7D%3D%267036874417766.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C47%7D%3D%2614073748835532.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C48%7D%3D%2628147497671065.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C49%7D%3D%2656294995342131.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C50%7D%3D%26112589990684262.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C51%7D%3D%26225179981368524.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C52%7D%3D%26450359962737049.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C53%7D%3D%26900719925474099.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C54%7D%3D%261801439850948198.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C55%7D%3D%263602879701896396.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C56%7D%3D%267205759403792793.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C57%7D%3D%2614411518807585587.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C58%7D%3D%2628823037615171174.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C59%7D%3D%2657646075230342348.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C60%7D%3D%26115292150460684697.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C61%7D%3D%26230584300921369395.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C62%7D%3D%26461168601842738790.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C63%7D%3D%26922337203685477580.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C64%7D%3D%261844674407370955161.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C65%7D%3D%263689348814741910323.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C66%7D%3D%267378697629483820646.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C67%7D%3D%2614757395258967641292.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C68%7D%3D%2629514790517935282585.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C69%7D%3D%2659029581035870565171.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C70%7D%3D%26118059162071741130342.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C71%7D%3D%26236118324143482260684.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C72%7D%3D%26472236648286964521369.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C73%7D%3D%26944473296573929042739.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C74%7D%3D%261888946593147858085478.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C75%7D%3D%263777893186295716170956.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C76%7D%3D%267555786372591432341913.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C77%7D%3D%2615111572745182864683827.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C78%7D%3D%2630223145490365729367654.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C79%7D%3D%2660446290980731458735308.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C80%7D%3D%26120892581961462917470617.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C81%7D%3D%26241785163922925834941235.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C82%7D%3D%26483570327845851669882470.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C83%7D%3D%26967140655691703339764940.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C84%7D%3D%261934281311383406679529881.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C85%7D%3D%263868562622766813359059763.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C86%7D%3D%267737125245533626718119526.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C87%7D%3D%2615474250491067253436239052.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C88%7D%3D%2630948500982134506872478105.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C89%7D%3D%2661897001964269013744956211.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C90%7D%3D%26123794003928538027489912422.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C91%7D%3D%26247588007857076054979824844.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C92%7D%3D%26495176015714152109959649689.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C93%7D%3D%26990352031428304219919299379.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C94%7D%3D%261980704062856608439838598758.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C95%7D%3D%263961408125713216879677197516.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C96%7D%3D%267922816251426433759354395033.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C97%7D%3D%2615845632502852867518708790067.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C98%7D%3D%2631691265005705735037417580134.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C99%7D%3D%2663382530011411470074835160268.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C100%7D%3D%26126765060022822940149670320537.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C101%7D%3D%26253530120045645880299340641075.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C102%7D%3D%26507060240091291760598681282150.4%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C103%7D%3D%261014120480182583521197362564300.8%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C104%7D%3D%262028240960365167042394725128601.6%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Ctext%7BFold%7D_%7B%5C%2C105%7D%3D%264056481920730334084789450257203.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Cend%7Balign%7D
不难发现对折次后, 其厚度将达到
https://www.zhihu.com/equation?tex=%5Cbegin%7Balign%7D+%5Ctext%7BFold%7D_%7B%5C%2C105%7D%3D%264056481920730334084789450257203.2%5C%2C%5Ctext%7Bmm%7D%5C%5C+%5Cend%7Balign%7D
也许你对这个厚度没什么概念, 我们将其换为光年


查询到一光年约为 https://www.zhihu.com/equation?tex=9.46073047258%5Ctimes10%5E%7B18%7D%5C%2C%5Ctext%7Bmm%7D
因此, 有
https://www.zhihu.com/equation?tex=%5Cbegin%7Balign%7D+%5Ctext%7BFold%7D_%7B%5C%2C105%7D%3D%264056481920730334084789450257203.2%5C%2C%5Ctext%7Bmm%7D%5C%5C%5C%5C+%3D%26%5Cfrac%7B4056481920730334084789450257203.2%7D%7B9.46073047258%5Ctimes10%5E%7B18%7D%7D%5C%2C%5Ctext%7BLightyear%7D%5C%5C%5C%5C+%3D%26%5Cfrac%7B40564819207303340847894502572032%7D%7B946073047258%5Ctimes10%5E%7B8%7D%7D%5C%2C%5Ctext%7BLightyear%7D%5C%5C%5C%5C+%3D%26428770477341.8099768830620%5C%2C%5Ctext%7BLightyear%7D%5C%5C%5C%5C+%3D%264.287704%5Ctimes%7B10%7D%5E%7B11%7D%5C%2C%5Ctext%7BLightyear%7D+%5Cend%7Balign%7D
这什么概念, 可观测宇宙才 https://www.zhihu.com/equation?tex=9.3%5Ctimes10%5E%7B10%7D 光年而已,


所以一张纸折叠次, 可观测宇宙是肯定放不下的.
实际上, 不仅如此, 如果一张纸能够复制, 那么他的质量也远超宇宙的质量.
给你一点小小的数学震撼.

xzshengli 发表于 2023-8-5 01:17:21

如果真有一张能够对折105次的纸，即使不对折，宇宙也放不下它。

ligb 发表于 2023-8-5 01:18:06

折叠105次。
https://www.zhihu.com/equation?tex=2%5E%7B105%7D%5Capprox4.0568192073+%5Ctimes10%5E%7B31%7D


一张a4纸，0.1毫米

https://www.zhihu.com/equation?tex=4.05%2A10%5E%7B31%7D%2A0.1%3D4.05%2A10%5E%7B30%7D

经过105次折叠后，一张a4纸的厚度为4.05*10^30mm，即4.05*10^24km，一光年等于9460730472580 千米，经过105次折叠的a4纸直径约为4.28万亿光年，太阳系直径不到2光年，可观测宇宙约930亿光年，这张纸在105次折叠后，几个可观测宇宙都放不下它。
每次折叠会让a4纸长度减半，起始长度约为300mm，在经过105次折叠后，a4纸的长度变为0.739*10^-29mm，原子大小约为3×10^-14mm，夸克大小大约是0.43 x 10^-22mm，夸克的直径比折叠后的a4纸大约100万倍，也就是说想要折叠105次纸张，需要在把a4纸拆成夸克之后，再暴力破解夸克禁闭，把夸克重复递归撕碎20次。
组成a4纸的粒子是费米子，参与强相互作用力，当我们暴力折叠a4纸的时候，需要克服强相互作用力，由于强核力大小是由交换虚子所决定的，需要计算机模拟来描述和预测，这里使用通常情况下的观测值来代为计算，约是电磁相互作用力的一百万倍，

https://www.zhihu.com/equation?tex=F%3DKq_%7B1%7Dq_%7B2%7D%2Fr%5E2

强相互作用力作用范围在10-15m以内，计算可得，从折叠到夸克尺度开始，每次折叠都需要超10^22N的力，目前人类能制造的顶端力之一的火箭发动机的动力大小约为10^7N。
目前没有发现比夸克更小的基本粒子，从折叠到夸克尺度开始，需要折叠者具有破坏现有物理规则的能力，才能继续拆开夸克。
德国电子-质子加速器HERA的质子束流能量单个粒子高达920GeV未能成功击穿夸克禁闭，有理论认为夸克就是组成物质的最小单位，此时暂时忽略物理规则的限制，一张纸的质量约为5g，当第105次折叠时纸的两端需要跨越2.14万亿光年，因为原回答者表示可以随随便便折叠到，这里认为他能突破光速，在1秒内跨越2.14万亿光年，此时根据公式：

https://www.zhihu.com/equation?tex=E%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E%7B2%7D

他在一秒内做的功约为2.025*10^58J。
宇宙的总能量约为1.4*10^70J.

综上，能把一张纸折叠105次的男人的量级大约在宇宙结构到单体宇宙之间，如果说把长度计入量级，该男子的量级大约是超单体级。

bands 发表于 2023-8-5 01:18:14

我确信我找到了完美的证明办法，但是纸太小了，不够折

ewf8336 发表于 2023-8-5 01:18:37

宇宙确实放不下！这就是指数级增长的惊人力量。
这种问题最初给人的感觉都是挺“可笑”的，人们往往也草率地认为是不可能的。
类似的问题其实还有很多，比如：
一次性给你1亿元，或者是第一天给以1块钱，然后以后每天给你前一天的2倍金额，连续给你一个月。
大部分人都会选择一次性接受1亿元。因为后边的支付方式感觉不会太高，怎么样也不可能高过1亿元的金额，因为在我们常人的眼里，1块钱与1亿元钱之间有着巨大的鸿沟。但实际情况却是，第二种支付方式，其实累计可以获得10.7亿元，要远远高于1亿元。


下面我们就来算一算，一张纸对折105次到底有多大。
从上面的例子我们已经可以意识到，这个数据可能是非常庞大的。
首先我们需要给出一张纸的厚度数据，这里我们就拿标准A4纸0.1毫米的厚度进行计算。假设这张A4纸无限的大，可以持续地进行折叠，毕竟按照常识来讲，一张纸是不可能折叠105次的，一般折叠7次都很难了。
具体计算过程如下图所示：


由上图可见，
一张纸折叠105次以后尺寸是：
4056481920730330000000000000米
而宇宙的尺寸是：
879847933950014000000000000米
折叠105次的尺寸大概是宇宙尺寸的4.6倍，也就是说要5个可观测宇宙才能放得下一张折叠了105次的A4纸。
任何事物一旦涉及到指数级增长，那么前途都是不可估量的。任何事物也不要只看最初的基础数据，很多时候我们都会被一些“习惯性认知”所误导，最终的选择也就可能产生偏差。

查看完整版本: 一张纸对折105次，宇宙就真的放不下了吗？