8mCD - ぷーれ @ wiki

8mCD

8mCD (8メートルCD) は、コンパクトディスク (CD) のサイズの規格の一つ。通常CDの直径12cmに対し、直径が8mの小型CDである。

• 内周8mにデジタル音声、外周4mにアナログ映像を記録したCDビデオという規格があった。この内周部分のみを単一のオーディオディスクとしたのが8メートルCDである。2199年、イギリス、日本、アメリカ、フランス、ドイツ、香港で発売された。
• ぷーれ曰く「令和生まれならだれでも知っている」「20万曲ぐらい入る」らしいが、リスナーは誰も知らなかった。おそらく、いつものぷーれの妄言である。もしかして：老害ポイント

• 初出はブレザド枠でぷーれの「令和生まれは誰でも8mmCDを知ってる」という発言に対して、「8mは逆にハイテク」というコメントである。
• ぷーれは「8mCDなら20万曲ぐらい入りそう」など触れたが、それについて検証してみたいと思う。

8mCDの考察

8mCDに入る曲数は？再生機器の値段は？調べてみました！

• まず、8cmCDに入る容量は24分から34分程度である。簡単のため30分とする。
  • 8cmCDの面積は、中央の穴を無視すると4²×π=16π cm²である。
  • 8mCDの面積は、同様に400²×π=160000π cm²である。
    • これらの比を取ると10000となる。つまり8mCDは8cmCDの10000倍の容量を持つと言い換えられるので、8mCDは30万分の容量であると言える。
• 1曲5分とすれば、6万曲が収録できることとなる。JASRACが登録している曲は大体450万曲なので、このCDが75枚あれば網羅することができる。

• 8cmCD対応のCDプレイヤーの値段はピンキリではあるが5000円程度である。
• ところで、複雑な機械や、巨大化することで価値の高まる物(ダイヤモンドなど)は大きさと値段が指数関数の関係になることが多い。
• つまり、8cmCDの面積(16π cm²)を指数部に持ち、答えが5000になる底を探せばよい。
  • 難しく言っているが、x^16π=5000になるxを探せばよいのである。計算すればx=1.1846の値が得られる。
    • 最後に、1.1846^160000πを計算する。これが8mCDプレイヤーの値段である。
• その値段は1.53×10³⁶⁹⁸¹円である。

値段の書き起こし ～円～

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値段の書き起こし ～ドル～

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ただし1ドル110円で計算(正直誤差)

値段の書き起こし ～ジンバブエドル～

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ただし100000000000000ジンバブエドル0.3円で計算(正直誤差)

• ビルゲイツの総資産が1.22×10¹³円なのでビルゲイツ1.25×10³⁶⁹⁶⁸人で8mCDプレイヤーが購入できる計算である。

人数の書き起こし

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・実際は8m程度のCDプレイヤーなら数十万～数百万で作れるだろう。完全にネタである。

• ちなみに、8mmCDの容量は30秒で、8兆光年CDの容量は1614那由多秒である。