### Spencer Heath's

## Series

Spencer Heath Archive

Item 10

Penned letter from Heath to Laura Jean McAdams, Durham NC, written on Washington Duke Hotel—Durham NC letterhead.

March 6, 1943

Dearest L.J.

How shall I ever keep up with you? Two more letters today — written Wednesday and Thursday.

First of all, the cold is __some__ better. I’d have left here this morning, 7:30 A.M. for Maryland via Warrenton VA and Washington DC but the weather was very bad, so I didn’t venture. But it cleared this afternoon and I’m all set to go in the morning. Address me henceforth – Roadsend Gardens, Elkridge, Md. I’m swabbing my throat with Scott’s Solution – surgical mercurochrome – and have some elixir terpinhydrate to take in case I cough much. No signs of getting any worse now.

Yes, no doubt the foreign study was better than staying at Duke – and it’s not too late now for the Ph.D.

Yes, I only thought of perhaps giving some lectures or having some classes at the College. My helping the Henry George School of Social Science was not significant except that it was the __first__. Anyhow, if I had no end of money to give I don’t think I’d give much to any institution except I be working right with it.

How strange I should have written you from Chapel Hill yesterday such a lot about space and Euclid and dimensions and geometry and all that while your letter of Wednesday full of the same matter was on its way to me. I didn’t read what I had written but it seems to me I covered (from my point of view) just about everything you have written to me. The fact that men can invent a dozen kinds of geometry has little more significance to me* *than that they can invent a dozen different kinds of chess games. They all start with arbitrary assumptions and artificial rules. But Euclid’s assumption of straight lines, and all equal, is closest to experience. It is unreal in that it deals with the space (completed motion) element of the trinitarian unity as if it could exist without the other two — viz, mass and duration, or as if __they__ did not exist. A triangle whose sides are not straight lines is simply no triangle. If __anything__ can be called a triangle, then a “triangle” can have __any__ kind of angles and they can add up to __anything__. The straight line of Euclid is fundamental to all curved lines or surfaces; it is the only reference by which they are established as __being__ curved. If Euclid had developed none but plane geometry and solid geometry had waited for Lobachevski et al, then we may suppose they would have called their solid geometry “Non-Euclidean.” Lines drawn on a curved surface cannot have the same relationships to each other as straight lines on a plane surface because they __cannot be straight lines.__ There are no lines on a curved surface that constitute any such triangle as are formed by __straight__ lines. There is no such thing (in any meaningful sense) as an angle between two curved lines, anyhow. Just what is an angle between two intersecting areas? Mind, I didn^{’}t say, between their tangents that intersect at the same point. An angle presupposes two __straight__ lines — if the word, “angle,” is going to mean anything. An angle between two curves is a contradiction in terms — if the terms __mean__ anything.

Quest of the __Absolute__ long dogged infantile philosophy. (To an infant mind there are no gradations.) We do not experience or cognize Reality otherwise than in the relationships of the three aspects that constitute its unity into an experience or cognition. For all we know, __existence__ is relationship and __process__ is changing relationship and existence is process, for process includes not only mass and motion (space — potential) but also time; hence process is __reality__.

Until we can have absolute or perfect measurement we cannot measure of a perfect unit of measure. But for our purposes __in__ __experience__ a measure is as good as perfect when it approximates within the limit of our imperfect perceptions. A perfect meter would (at present) be of no greater service to us than the one we have.

To be sure, “science has a purely relative value.” Its descriptions — analyses — are purely quantitative — __relative__ as to magnitudes. Meta-physics is that physics that lies beyond the frontiers of science — that is known to us only by feeling, emotion, consciousness, and has not been reduced to measurement or quantitative description — rationalized in terms of its quantitative ratios. And who shall say that subjective experience cannot be (ever) described in terms of object measurement? All physics was once Meta-physics. Meta-physics is the subjective, emotional, intuitive universe — the world of religion and the creative arts — out of which all the sciences are born.

Who says (and proves) that “curvature is inherent in space?” And does this mean that straightness is __not__? Curvature would seem to __depend__ on straightness, for __any__ departure from straightness is curvature, but any departure from curvature is not straightness — the possibilities are almost infinity to one.

I wrote you what I think about fourth dimensions etc. As soon as we know that dimensions are but measured directions we can see that we have plenty of them — and still nothing new or strange.

Your affirmation of the infinity of space is excellent. I gave the grounds for it in my last letter.

Your speculation on what a fourth dimension may be — ______________ — depends upon it being __different__ (otherwise than in direction) from the other dimensions.

No, I’m not asleep, but I should be, and that cough is just starting a little again. I did want to tell you something about the conversation with Dr. Gilvant that involved Bergson and vitalism etc. — but too much expatiation on the spatial for that now — or for much happy ending for this. So, here goes for all of mine too.

S

Have to be up at 6:00 in the morning. And must __swab__ and take the terpinhydrate.

Love,

### Metadata

Title |
Correspondence - 10 - Non-Euclidean Geometry |

Collection Name |
Spencer Heath Archive |

Series |
Correspondence |

Box number |
1:1-116 |

Document number |
10 |

Date / Year |
1943-03-06 |

Authors / Creators / Correspondents |
Laura Jean McAdams |

Description |
Penned letter from Heath, written on Washington Duke Hotel—Durham NC letterhead |

Keywords |
Geometry |