Fingers at 483 Feet
On 3 October 1951 Bobby Thomson's home run won the New York Giants the pennant. Fifty years later, Giants players told the Wall Street Journal that from 20 July that season the team had watched opposing catchers' finger signs through a telescope in the clubhouse behind center field. The base of that clubhouse stood 483 feet from home plate. Could anyone read fingers from there without the telescope?
The model has a catcher's fingers about 2 cm wide with 1 cm gaps, seen from 147 m, the distance to the clubhouse's base; the window was further back. It assumes an eye with 20/20 vision, which picks out detail about one arcminute across: a Snellen letter is five arcminutes tall and its strokes are one. The picture is blurred by that limit divided by the magnification. Haze, heat shimmer and the catcher's own hand movements would make it harder still.
The arithmetic
A 2 cm finger at 147 m covers 0.02 ÷ 147 of a radian, about 28 arcseconds, or half an arcminute. That is half what a sharp eye can resolve, so to the naked eye the fingers run together into one pale blob. Magnify twice and they are just at the limit; ten times and each finger is five arcminutes wide, the height of a letter on the eye chart's 20/20 line. Schenz and later coach Herman Franks only had to tell one finger from two, and send one buzz or two.
One buzz for a fastball
The relay ran on a buzzer wire from the clubhouse to phones in the Giants' dugout and bullpen: one buzz for a fastball, two for an off-speed pitch.
What stands on what
| Item | Source |
|---|---|
| Telescope from 20 July 1951, Hank Schenz then Herman Franks, buzzer wire, one buzz or two | Wikipedia, Shot Heard 'Round the World (baseball), citing Joshua Prager, Wall Street Journal, 31 January 2001 |
| Backup catcher Sal Yvars said he relayed the fastball sign to Thomson for that pitch. Thomson always said he did not take it. | Same article, citing the New York Times (2008) |
| MLB banned stealing signs with optical or mechanical aids in 1961 | Same article |
| Clubhouse base 483 ft from home plate; left-field line 279 ft | Wikipedia, Polo Grounds |
| 20/20: letters 5 arcminutes tall, detail 1 arcminute | Wikipedia, Visual acuity |
| Finger width 2 cm, the blur model | My assumptions |