06 Music of Molecules / The Blind Watchmaker

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This is incomparably smaller than winning a lottery (for example, 1 in 10⁷, or one in ten million).
Considering that the estimated number of atoms in the entire universe is about 10⁸⁰ (a number with eighty zeros), the chance is comparable to correctly guessing a single atom out of the universe.

If those four measures are played at a pace of four seconds, then with incredible luck it could happen in as little as four seconds.
But with incredible misfortune, it would take 10⁵³ times the age of the universe (13.8 billion years) to occur by chance.

⸻

In The Blind Watchmaker, Richard Dawkins pointed out that life evolves far more quickly through cumulative selection (chance plus necessity, reinforced by feedback) than by sheer random chance.
Dawkins illustrated this with a computer simulation of monkeys typing at random, eventually producing a line of Shakespeare.
Here, we apply the same idea to music.

Using the cumulative selection (“Weasel”) model, we simulated the evolution of a 64-note melody (12-tone scale) toward a target: a simple “Mozart-like” arpeggio.
In this trial, the simulation reached perfect alignment (64/64 notes correct) in just 76 generations.
Once a “near solution” appears, small mutations plus selection rapidly converge toward the goal.
This intuitive experiment shows that even though the probability of hitting the target by chance alone (1 in 12⁶⁴) is astronomically small, cumulative selection can reach it in a short span.

The repeating sequence:
C – E – G – E – C – E – G – B
resembles a “Mozart-style” arpeggio, alternating between the C major chord and its dominant tones (G and B).

Target (64 notes):
C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B

Gen   0: fitness=6
C# A G F F A# C# G# D C# F# B G# A G# A F# C# A# F F# E D B A G E A F# F F D C# F# A# C A# A D# G C# A G# E C B F A# G# A A D E F F C F# C# G# G# B G# E B

Gen   1: fitness=8
C# A G F F A# C# G# D C# F# B G# A G# A F# C# A# F F# E D B A G E B F# E F D C# F# A# C A# A D# G C# A G# E C B G A# G# A A D E F F C F# C# G# G# B G# E B

Gen   5: fitness=15
C# A G F F A# C# B D C# F# B G# A G# B F# C# G# B F# E D B A G E B C E F D C# F# A# C A# A A# G C# A G# E C B G B G# A B D E F F D# F# E G# E C G# E B

Gen  10: fitness=21
C# A G E F A# C# B D E F# B G# E G# B C E G# B F# E G B A G E B C E F D C# F# A# C A# A A G C# A E E C B G B G# A B D F# F F D# F# E G# E C G# E B

Gen  25: fitness=39
C D G E C E C# B C E G E G# E G# B C E F B F# E G B A G E E C E G B C# F# A# A A# E G B C# D# G E C B G B C F# B D F# E C F# F# E G E C E G B

Gen  50: fitness=59
C E G E C E G B C E G E C E G B C E G B C E G B C E G E C E G B C D A# E C E G B C E G E C E G B C F# G D C E G B C E G E C E G B

Gen  76: fitness=64 (perfect match)
C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B

Through cumulative selection, the simulation reached its target in just 76 generations — about 5 minutes.
By analogy, natural selection, the blind watchmaker, could assemble even something as intricate as LUCA — a nanomachine far surpassing any clock, encoded in 2.5 million DNA base pairs (A, T, G, C) — within tens of millions to a hundred million years.

06分子の音楽／盲目の時計職人

赤ちゃんがランダムに木琴を叩いて、偶然モーツァルトのある曲が出来る確率はどのくらいだろうか？　半音×12音階で、1小節に16音符、4小節でメロディが出来るとしてみれば、10の70乗分の1と言う途方も無い低確率となる。宝くじ（例えば10の7乗分の1=1千万分の1）よりも桁違いに低い。宇宙全体の推定原子数が10の80乗個（つまりゼロが80個付く）だから、宇宙にある原子ひとつを当てることに近い確率である。4小節を4秒の速さで木琴を鳴らすとして、ものすごく運が良ければ最短4秒だが、ものすごく運が悪いと宇宙の年齢138億年の10の53乗倍もかかる計算になる。

「盲目の時計職人」でリチャード・ドーキンス博士は、累積淘汰（偶然＋必然のフィードバック）による生命の進化は偶然の連続によるものよりも遥かに早く成し遂げられると指摘している。ドーキンス博士は猿がランダムに打つタイプライターでシェイクスピアの文章を完成させるシミュレーションを行っているが、ここでは音楽でやってみよう。

「累積淘汰（Weasel）モデル」で12音×64音のメロディがターゲット（簡単な“モーツァルト風”アルペジオ）に進化して一致する様子をシミュレーションしました。今回は 76世代で完全一致（64/64） に到達しています。一度“近い解”を見つけると、小さな突然変異＋選択で急速に目的メロディへ収束する様子が分かります。これは「ランダムに当たる確率（12^64分の1）」が天文学的に小さくても、累積選択だと短期間で辿り着ける、という直感実験です。

C – E – G – E – C – E – G – B　　ド-ミ-ソ-ミ-ド-ミ-ソ-シ

これを繰り返すと、「Cメジャー和音」と「属音＋導音（GとB）」が交互に出てくる、いわゆるモーツァルト風のアルペジオに似せたパターンになっています。

Target (64 notes):
C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B

Gen   0: fitness=6
C# A G F F A# C# G# D C# F# B G# A G# A F# C# A# F F# E D B A G E A F# F F D C# F# A# C A# A D# G C# A G# E C B F A# G# A A D E F F C F# C# G# G# B G# E B

Gen   1: fitness=8
C# A G F F A# C# G# D C# F# B G# A G# A F# C# A# F F# E D B A G E B F# E F D C# F# A# C A# A D# G C# A G# E C B G A# G# A A D E F F C F# C# G# G# B G# E B

Gen   5: fitness=15
C# A G F F A# C# B D C# F# B G# A G# B F# C# G# B F# E D B A G E B C E F D C# F# A# C A# A A# G C# A G# E C B G B G# A B D E F F D# F# E G# E C G# E B

Gen  10: fitness=21
C# A G E F A# C# B D E F# B G# E G# B C E G# B F# E G B A G E B C E F D C# F# A# C A# A A G C# A E E C B G B G# A B D F# F F D# F# E G# E C G# E B

Gen  25: fitness=39
C D G E C E C# B C E G E G# E G# B C E F B F# E G B A G E E C E G B C# F# A# A A# E G B C# D# G E C B G B C F# B D F# E C F# F# E G E C E G B

Gen  50: fitness=59
C E G E C E G B C E G E C E G B C E G B C E G B C E G E C E G B C D A# E C E G B C E G E C E G B C F# G D C E G B C E G E C E G B

Gen  76: fitness=64
C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B

累積淘汰なら76世代、わずか5分で到達する！！
同様の計算で、自然という盲目の時計職人の手によりA.T.G.Cからなる250万文字のDNAを持つLUCA（時計を遥かに凌ぐ超精巧なナノマシン）でも、数千万～1億年以上で作られていくという結果になった。

5794/7500

How likely is it that a baby, striking a xylophone at random, would accidentally produce a piece by Mozart? If we assume twelve semitones, sixteen notes per measure, and four measures to form a melody, the probability comes out to an astronomical 1 in 10⁷⁰. This is incomparably smaller than winning a lottery (for example, 1 in 10⁷, or one in ten million). Considering that the estimated number of atoms in the entire universe is about 10⁸⁰ (a number with eighty zeros), the chance is comparable to correctly guessing a single atom out of the universe. If those four measures are played at a pace of four seconds, then with incredible luck it could happen in as little as four seconds. But with incredible misfortune, it would take 10⁵³ times the age of the universe (13.8 billion years) to occur by chance. ⸻ In The Blind Watchmaker, Richard Dawkins pointed out that life evolves far more quickly through cumulative selection (chance plus necessity, reinforced by feedback) than by sheer random chance. Dawkins illustrated this with a computer simulation of monkeys typing at random, eventually producing a line of Shakespeare. Here, we apply the same idea to music. Using the cumulative selection (“Weasel”) model, we simulated the evolution of a 64-note melody (12-tone scale) toward a target: a simple “Mozart-like” arpeggio. In this trial, the simulation reached perfect alignment (64/64 notes correct) in just 76 generations. Once a “near solution” appears, small mutations plus selection rapidly converge toward the goal. This intuitive experiment shows that even though the probability of hitting the target by chance alone (1 in 12⁶⁴) is astronomically small, cumulative selection can reach it in a short span. The repeating sequence: C – E – G – E – C – E – G – B resembles a “Mozart-style” arpeggio, alternating between the C major chord and its dominant tones (G and B). Target (64 notes): C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B Gen 0: fitness=6 C# A G F F A# C# G# D C# F# B G# A G# A F# C# A# F F# E D B A G E A F# F F D C# F# A# C A# A D# G C# A G# E C B F A# G# A A D E F F C F# C# G# G# B G# E B Gen 1: fitness=8 C# A G F F A# C# G# D C# F# B G# A G# A F# C# A# F F# E D B A G E B F# E F D C# F# A# C A# A D# G C# A G# E C B G A# G# A A D E F F C F# C# G# G# B G# E B Gen 5: fitness=15 C# A G F F A# C# B D C# F# B G# A G# B F# C# G# B F# E D B A G E B C E F D C# F# A# C A# A A# G C# A G# E C B G B G# A B D E F F D# F# E G# E C G# E B Gen 10: fitness=21 C# A G E F A# C# B D E F# B G# E G# B C E G# B F# E G B A G E B C E F D C# F# A# C A# A A G C# A E E C B G B G# A B D F# F F D# F# E G# E C G# E B Gen 25: fitness=39 C D G E C E C# B C E G E G# E G# B C E F B F# E G B A G E E C E G B C# F# A# A A# E G B C# D# G E C B G B C F# B D F# E C F# F# E G E C E G B Gen 50: fitness=59 C E G E C E G B C E G E C E G B C E G B C E G B C E G E C E G B C D A# E C E G B C E G E C E G B C F# G D C E G B C E G E C E G B Gen 76: fitness=64 (perfect match) C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B Through cumulative selection, the simulation reached its target in just 76 generations — about 5 minutes. By analogy, natural selection, the blind watchmaker, could assemble even something as intricate as LUCA — a nanomachine far surpassing any clock, encoded in 2.5 million DNA base pairs (A, T, G, C) — within tens of millions to a hundred million years. 06分子の音楽／盲目の時計職人赤ちゃんがランダムに木琴を叩いて、偶然モーツァルトのある曲が出来る確率はどのくらいだろうか？　半音×12音階で、1小節に16音符、4小節でメロディが出来るとしてみれば、10の70乗分の1と言う途方も無い低確率となる。宝くじ（例えば10の7乗分の1=1千万分の1）よりも桁違いに低い。宇宙全体の推定原子数が10の80乗個（つまりゼロが80個付く）だから、宇宙にある原子ひとつを当てることに近い確率である。4小節を4秒の速さで木琴を鳴らすとして、ものすごく運が良ければ最短4秒だが、ものすごく運が悪いと宇宙の年齢138億年の10の53乗倍もかかる計算になる。「盲目の時計職人」でリチャード・ドーキンス博士は、累積淘汰（偶然＋必然のフィードバック）による生命の進化は偶然の連続によるものよりも遥かに早く成し遂げられると指摘している。ドーキンス博士は猿がランダムに打つタイプライターでシェイクスピアの文章を完成させるシミュレーションを行っているが、ここでは音楽でやってみよう。「累積淘汰（Weasel）モデル」で12音×64音のメロディがターゲット（簡単な“モーツァルト風”アルペジオ）に進化して一致する様子をシミュレーションしました。今回は 76世代で完全一致（64/64）に到達しています。一度“近い解”を見つけると、小さな突然変異＋選択で急速に目的メロディへ収束する様子が分かります。これは「ランダムに当たる確率（12^64分の1）」が天文学的に小さくても、累積選択だと短期間で辿り着ける、という直感実験です。 C – E – G – E – C – E – G – B　　ド-ミ-ソ-ミ-ド-ミ-ソ-シこれを繰り返すと、「Cメジャー和音」と「属音＋導音（GとB）」が交互に出てくる、いわゆるモーツァルト風のアルペジオに似せたパターンになっています。 Target (64 notes): C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B Gen 0: fitness=6 C# A G F F A# C# G# D C# F# B G# A G# A F# C# A# F F# E D B A G E A F# F F D C# F# A# C A# A D# G C# A G# E C B F A# G# A A D E F F C F# C# G# G# B G# E B Gen 1: fitness=8 C# A G F F A# C# G# D C# F# B G# A G# A F# C# A# F F# E D B A G E B F# E F D C# F# A# C A# A D# G C# A G# E C B G A# G# A A D E F F C F# C# G# G# B G# E B Gen 5: fitness=15 C# A G F F A# C# B D C# F# B G# A G# B F# C# G# B F# E D B A G E B C E F D C# F# A# C A# A A# G C# A G# E C B G B G# A B D E F F D# F# E G# E C G# E B Gen 10: fitness=21 C# A G E F A# C# B D E F# B G# E G# B C E G# B F# E G B A G E B C E F D C# F# A# C A# A A G C# A E E C B G B G# A B D F# F F D# F# E G# E C G# E B Gen 25: fitness=39 C D G E C E C# B C E G E G# E G# B C E F B F# E G B A G E E C E G B C# F# A# A A# E G B C# D# G E C B G B C F# B D F# E C F# F# E G E C E G B Gen 50: fitness=59 C E G E C E G B C E G E C E G B C E G B C E G B C E G E C E G B C D A# E C E G B C E G E C E G B C F# G D C E G B C E G E C E G B Gen 76: fitness=64 C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B C E G E C E G B 累積淘汰なら76世代、わずか5分で到達する！！同様の計算で、自然という盲目の時計職人の手によりA.T.G.Cからなる250万文字のDNAを持つLUCA（時計を遥かに凌ぐ超精巧なナノマシン）でも、数千万～1億年以上で作られていくという結果になった。

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