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Lila Gleitman wrote:

I now happen to be reading "Team of Rivals," basically a history of Lincoln's cabinet. Anyhow, there is constant mention (and pix of venues) showing Lincoln talking to very large indoor and outdoor audiences (at least once 2000 is the number of listeners mentioned). They say he had a slightly high clear voice that carried very well, but still I can hardly conceive that he, and others of those times who are mentioned as speaking outdoors to multitudes too, notably Douglas of course., could be heard without amplification. You must know all about this. Can you tell me? or tell me how to look this up? It flummoxes me every time I read of these seemingly prodigious feats of speaking-listening, the authors don't even seem to remark on how astounding it seems (or seems to seem, to me).



I responded that Lila was treading in the conceptual footsteps of Benjamin Franklin, who wrote in his autobiography:

In 1739 arrived among us from Ireland the Reverend Mr. Whitefield, who had made himself remarkable there as an itinerant preacher. He was at first permitted to preach in some of our churches; but the clergy, taking a dislike to him, soon refus'd him their pulpits, and he was oblig'd to preach in the fields. The multitudes of all sects and denominations that attended his sermons were enormous, and it was matter of speculation to me, who was one of the number, to observe the extraordinary influence of his oratory on his hearers, and bow much they admir'd and respected him, notwithstanding his common abuse of them, by assuring them that they were naturally half beasts and half devils. […]

He had a loud and clear voice, and articulated his words and sentences so perfectly, that he might be heard and understood at a great distance, especially as his auditories, however numerous, observ'd the most exact silence. He preach'd one evening from the top of the Court-house steps, which are in the middle of Market-street, and on the west side of Second-street, which crosses it at right angles.

Both streets were fill'd with his hearers to a considerable distance. Being among the hindmost in Market-street, I had the curiosity to learn how far he could be heard, by retiring backwards down the street towards the river; and I found his voice distinct till I came near Front-street, when some noise in that street obscur'd it. Imagining then a semi-circle, of which my distance should be the radius, and that it were fill'd with auditors, to each of whom I allow'd two square feet, I computed that he might well be heard by more than thirty thousand. This reconcil'd me to the newspaper accounts of his having preach'd to twenty-five thousand people in the fields, and to the antient histories of generals haranguing whole armies, of which I had sometimes doubted.

I observed that

If you allow two square feet per person, as Ben did, then the semi-circle radius in question would only be

(pi*r^2)/2 = 2*25000

r = sqrt(4*25000/pi) = 178 feet

That's 59 yards. It's not a superhuman feat to stand on the goal line and speak so as to be heard by somebody on the opponents' 40 yard line — in a quiet stadium, anyhow.

On that allowance, the radius required for 2,000 people in a semi-circle would be

sqrt(4*2000/pi)

which is a bit more than 50 feet, or almost 17 yards — which seems easy.

But two square feet per person is rather squashed, at least by modern standards. According to the Jacobs Method

A loose crowd, one where each person is an arm's length from the body of his or her nearest neighbors, needs 10 square feet per person. A more tightly packed crowd fills 4.5 square feet per person. A truly scary mob of mosh-pit density would get about 2.5 square feet per person.

If we go to 4 square feet per person, we get a semicircle of radius

sqrt(2*4*2000/pi) = 71.4 feet

for an audience of 2,000; or at 6 square feet per person, it's still just 87.4 feet, or about 29 yards.

According to Google Maps, the distance from the west side of 2nd Street to Front Street along Market St. is 144.3 meters, which is about 473 feet. A semicircle of that size has an area of 702,865 square feet, which at 2 square feet per person would be more than 350,000 people; even at 10 square feet per person, it's more than 70,000 people.

So Ben might have been honest, but he wasn't all that good at either measurement or SAT-level calculation…

Lila wrote back:

fabulous — proves (a) they (especially, I guess, those professional speakers with careful training and ruly audiences) could have spoken to multitudes without amplification, (b) it's cosy to have the data from our local neighborhood where it can be checked centuries later, and (c) honesty isn't enough.

And later added:

… chatting with people after your analysis of crowds, amplification or lack thereof, and Franklin's and your calculated estimate of the distance X crowd limits, all thought this deserves a post on llog and I agree. Doubtless this issue has crossed many people's minds and having Franklin laying out the space (albeit with imperfect calculations) from 2nd St to Front St, which still exists) would make such a piece particularly tasty.

Meanwhile I have continued reading "Team of Rivals" (Doris Kearns Goodwin) and found more information. Concerning the Gettysburg address. The crowd was estimated: "Roughly nine thousand stretched away from the platform in a half circle." And here's an interesting tidbit: "George Gitt, a fifteen-year-old who had stationed himself beneath the speaker's stand, later remembered that the 'flutter and motion of the crowd ceased the moment the President was on his feet. Such was the quiet that his footfalls, I remember very distinctly, woke echoes, and with the creaking of a the boards, it was as if some one were walking through the hallways of an empty house'."

I was particularly interested to read this because it had occured to me that even if you and Franklin are right about the possibility of projecting to so large a crowd (and though I might doubt Franklin a little, I am always sure of YOU), a further condition would have to be rather absolute crowd silence, and a lack of wind besides. (the estimate and passage about Gitt are p. 585 of Goodwin's book, paperback edition). Why don't you write a little post on this, including your and Franklin's calculations (and the quote from him) and perhaps some of this Gettysburg info.

Which I have done.

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