Collingwood <1>
March 25/41. <2>
My dear Sir
If you are not quite ennuyé <3> of the finite & the infinite I will beg leave to rise in explanation of my last.
Dialogue 2. On Space time & Infinity
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A. We got puzzled I think in our last. Let us get back to first principles, revenons a nos moutons. <4> Whatever is not infinite is finite!
B. A fair field & no quarter.– Well. Agreed.
A. If a really existing quantity of a given kind be finite, a quantity of the same kind may be imagined greater than it
B. Do you take me for a Turk or an Anthropophagite, <5> to put that to me as a postulate. Try me with stronger meat.
A. If two really existing quantities of a given kind be finite a quantity of the same kind may be imagined greater than either of them
B. How stately is the March of Great truths! Agreed.
A. If any number of really existing quantities of a given kind be finite, a quantity of the same kind may be imagined greater than any of them
B. You will drive me mad.– Pray get on
A. If all really existing quantities of a given kind be finite a quantity of the same kind may be imagined greater than each and every of them.
B. No doubt at all about it. But do come to particulars.
A. Can you imagine yourself in the Center of the Universe?
B. I could crowd myself in a nutshell and fancy myself a king of infinite space but that I have bad dreams.
A. Then every really existing body in the universe is at a finite distance from you – You agreed to that.
B. I did! I wish I had not. I never liked it. I always had a misgiving about it. But after all it seemed proved.
A. I will prove it again if you like.
B. No! no!! no!!! anything rather than that over again
A. Then you can conceive in your imagination (or if you cannot, it can be conceived) a distance greater than any really existing distance of a corporeal body of any really existing corporeal body from you, & of all such
B. Why if I must I must.
A. Well then conceive such a distance and with center yourself and radius that distance describe a sphere.
B. A monstrous bubble! But if it burst?
A. It shall not burst. Let it contract gradatim <6> preserving its spherical form and its center. Then since all really existing corporeal bodies of necessity exist within it – you admit that?
B. O I admit anything – “Magna est veritas et prevalebit” <7> only be cautious.
A. Then in its gradual contraction it will first encounter some one or other of them.
B. Aye! There he goes – the Crystalline orb will shrink to a nutshell and we shall all be cracked.
A. That one will be the most distant. You see I am adopting your own Idea.
B. When the sky falls, the highest soaring bird will be the first-caught. Does not the proverb say so?
A. And then all the rest in their turns. So we have got in the first place an imaginary sphere of greater dimension than the assemblage of all created corporeal beings – and in the next place we have proved your assertion that there must be a most distant one.
B. My assertion! A happy blunder. If it is proved the greater is my luck. My dear A do let us have a cigar and a glass of the comfortable creature and forget all this.
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Dialogue iii April 6.
A.– The punch was rather strong and left me a little misty last night. I should like to get clear about it. Can you listen
B.– You have a winning way! Only be brief
A. Whatever distance has a distinct beginning and end is not infinite.–
B. Agreed.
A. There are no two bodies really existing, whose mutual distance has not a distinct beginning (at one of them) and a distinct end (at the other)
B. Agreed again
A. Therefore there are no two bodies, than whose distance a greater, but yet finite, distance may not be taken
B. I suppose you omit elegantić gratia <8> the intermediate step, viz: that “Whatever distance is not infinite, a greater finite distance may be taken.”
A. Just so.– Now then Postulatum – With any finite distance as a radius a sphere may be concieved and described.–
B. I admit it – Oh dear (Yawns sepulchrally)
A. Then there are no two bodies in the universe which may are not be comprehended within a finite concievable sphere of which one of them is the center.– I see you are asleep but I shall go on with my argument now I have begun it.–
Then if you concieve yourself to be one of the bodies there is no other body which may is not be comprehended within a finite concievable sphere of which you occupy the center Then, there is a finite concievable sphere such that no other body is not comprehended within it
Concieve such a sphere – then concieve yourself your station shifted to the outside of it and you have got the universe fairly enclosed in a nutshell, for no other body is on the outside ex hypothesi. <9>
JFWH
And after all, there is a subtilty about this which evades all verbal forms of expression. This, by negatives, come nearest the mark.H. F. Talbot Esqr
Lacock Abbey
Chippenham Wilts
[a draft of the same dialogue, kept by JFWH, is in the hand of Margaret Brodie Herschel, with her corrections:]
Collingwood
March 25th/41
My dear Sir –
If you are not quite ennuyé of the finite & the infinite I will beg leave to rise in explanation of my last.
Dialogue 2 On Space & [illegible deletion] Time & Infinity
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A. I think we got puzzled in our last – Let us go back to first principles, revenons ŕ nos moutons – Whatever is not infinite is finite! –
B. A fair field & no quarter– Well – agreed –
A. If a really existing quantity of a given kind be finite, a quantity of the same kind may be imagined greater than it –
B. Do you take me for a Turk or an Anthropophagite, to put that to me as a postulate – Try me with stronger meat –
A. If two really existing quantities of a given kind be finite a quantity of the same kind may be imagined greater than either of them –
B. How stately is the march of great truths! Proceed
A. If any number of really existing quantities of a given kind be finite, a quantity of the same kind may be imagined greater than any of them –
B. You will drive me mad with your Fee Fa Fum. <10>– Pray, get on –
A. If all really existing quantities of a given kind be finite a quantity of the same kind may be imagined greater than each & every of them –
B. I thought the blood of the Englishman would not be long in coming. Well no doubt at all about it. But do come to particulars.
A. Can you imagine yourself in the Centre of the Universe
B. I could crowd myself into a nutshell & fancy myself a king of infinite space, but that I have bad dreams –
A. Then every really existing body in the universe is at a finite distance from you – You agreed to that –
B. I did! I wish I had not! – I never liked it, I always had a misgiving about it – but after all, it seemed proved –
A. I will prove it again if you like –
B. No! No!! No!!! – Anything rather than that over again –
A. The you can conceive in your imagination (or if you cannot, it can be concieved) a distance greater than any really existing distance of any really existing corporeal body from you, & of all such –
B. Why if I must – I must –
A. Well then conceive such a distance & with centre yourself & radius that distance describe a sphere
B. A monstrous bubble! But if it burst? –
A. It shall not burst – Let it contract gradatim, preserving its spherical form & its centre – Then since all really existing corporeal bodies of necessity exist within it – You admit that? –
B. Oh I admit anything “Magna est veritas et prevalebit,” only be cautious –
A. Then in its gradual contraction it will first encounter some one or other of them –
B. Aye, there he goes – the Crystalline orb will shrink to a nutshell & we shall all be cracked –
A. That one will be the most distant – You see I’m adopting your own Idea.
B. When the sky falls, the highest soaring bird will be the first caught – Does not the proverb say so? –
A. And then all the rest in their turns. So we have got in the first place an imaginary sphere of greater dimensions than the assemblage of all created corporeal beings – and in the next place we have proved your assertion that there is must be a most distant one –
B. My assertion! – A happy blunder – If it is proved the greater is my luck – My dear A. do let us have a cigar & a glass of the comfortable creature and forget all this –
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Dialogue iii, April 6 –
A. The punch was rather strong & left me a little misty last night – I shd like to get clear about it – Can you listen? –
B.– You have a winning way! – Only be brief –
A. Whatever distance has a distinct beginning & end is not infinite–
B. Agreed –
A. There are no two bodies really existing, whose mutual distance has not a distinct beginning (at one of them) & a distinct end (at the other) –
B. Agreed again –
A. Therefore there are no two bodies, that whose distance a greater, but yet finite, distance may not be taken
B. I suppose you omit elegantić gratia the intermediate step – viz. “Whatever distance is not infinite, a greater finite distance may be taken” –
A. Just so – Now then Postulatum – With any finite distance as a radius a sphere may be conceived and described –
B. I admit it – Oh dear! (Yawns sepulchrally) –
A. Then there are no two bodies in the universe which are not comprehended within a finite conceivable sphere of which one of them is the centre – I see you are asleep, but I shall go on with my argument now I have begun it – Then if you conceive yourself to be one of the bodies, there is no other body which is not comprehended within a finite conceivable sphere of which you occupy the centre – Then there is a finite concievable sphere [of which your are the centre] NB such that no other body is not comprehended within it Conceive such a sphere – then conceive your station shifted to the outside of it, and you have got the universe fairly enclosed in a nutshell, for no other body is on the outside ex hypothesi.
J.F.W.H.
And after all, there is a subtilty about this which evades all verbal forms of expression. This by negatives comes nearest the mark.Notes:
1. Hawkhurst, Kent.
2. Sent to WHFT 6 April, with Doc. No: 04236.
3. Bored.
4. Let us get back to our sheep, that is, return to the main point.
5. Cannibal.
6. Gradually.
7. Truth is great and will prevail.
8. For the sake of simplicity.
9. By definition of the hypothesis.
10. This additional doggeral and metaphor from ‘Jack the Giant Killer’ is continued in the next reply from ‘B’. Both additions differ from the version in Herschel’s own hand.