General Cam.ne, 

Dr. Cairns left tlus material for 

you ~o peruse and stated that the other 

appendices are being prepared and he will 

drop them by to you when they are ready. 

He is holding forth in Dr. C ampaigne' s 

Office, Ext. 572. 

eclassified and approved for release "Suzie" 

y NSA on 02-12-2014 pursuant to E.O. 

3526 
1'.l!EF ID:A72044 

See'm"it7 Information 

I I 

J 

Report on SCAMP 

to the 

Director 

of the 

Armed Forces Security Agency 

Submitted by 

Stewart s. Cairns 

8 September 1952 

CONFIBBN!l'Ikb 
Section 

l. 

2. 

3. 

4. 

Appendices 

I. 

II. 

II I. 

IV. 

v. 

VI. 

VII. 

VIII. 

IX. 

x. 

XI. 

REF ID:A72044 

Report on SC.AMP 

T.A:BL~ OF OOBTENTS 

Title 

Introduction, origins of the symposilllll 

The scientific work of the symposium 

Administrative work \ 

Suggestions regarding possible future efforts 

List of participants 

List of seminar meetings 

List of con:f'erences 

List of other reports 

Computatiens attacked 

Reproduced seminar reports 

Reproduced conference reports 

Other reproduced reports 

Budgetary material 

Suggestions from SCAMP members regarding future work 

Miscellaneous selected correspondence 
REF ID:A72044 ~··-~~, .. ________ -_._.~I--~~~.;_:,_~--

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Report on SCAMP 

1. Introduction 

The summer symposium to which ·the name SCAMP was finally attached 

grmv from discussions in SCAG. The initial proposals leading to SC.Ala» 

were made in 1951 by c. B. Tompkins in his role as a member of SCAG. 

Originally, a continuing project was intended. However, after various 

discussions, it was decided to conduct a swmner symposium and, on the 

basis of experie!l-ce therewith. t_o consider the desirability of later 

efforts. This decision was reached in March 1952, with the result that 

only about three months were available for the prelimi-naries to the 

symposium •. .Among· the proposals by Tompkins was the use of the primarily 

mathematical part of SCAG; referred to as SCAM (Special COillillittee 

Advising in Mathematics), in a·n advisory capacity. The code name SCAMP 

was created in AFSA by adding the letter P to SCAM. 

No fixed objectives were off'icia"lly adopted for the symposium. A 

. . set of proposed objectives was contained in a document "Notes on a 

proposed research project and symposium." by Tompkins, 18 March 1952, 

subsequent to an agreement by the writer to serve as leader of the 

symposium.. and these proposed objectives proved usefUl in preparing for 

and conducting the symposium. (The •motes• are in .Appendix XI.) 

Because of the lateness _of the decision to conduct the symposium, 

difficulties were encountered in the recruitment of personnel. .Many 

desirable participants had pre'vious commitments• and the time was too 

F' ;:1 . -.. . 
, . ... -,·:·--~. REF ID:A72044 .: " 

00NPI:BEM'flt£t 

short for the normal clearance procedures. This led to the use largely 

of personnel for whom evidence-of clearability existed and also to'the 

conduct of the symposium largely on a confidential level. though a 

higher ~ecurity level would have bee~ adVa.ntageous. (See Appendix for 

list of participants.) 

Through the cooperation of members of the staff of the Institute 

for Numerical Ailalysis in Los Angeles and of the University of California 

at Los Angeles, adequate office space was provided and provisions made 

' for the-necessary office supplies and equipment •. 

The symposium benefited in a number of ways from b.ei:ci.g located on 

the UCLA campus and associated with the Institute for Numerical Analysis 

of the National Bureau of Standards. A minor, but not inconsiderable, 

advantage was the comparative freedom from excessive summer heat. as a 

result of which more effective ~ork can be accomplished there than in 

most parts of the country. Scientifically, SCAMP benefited by the 

availability of the computing equipment (SWAC and IBM) at the INA and 

by the proximity of mathematicians connected. at least for the summer. 

with UCLA', the INA and the Rand Corporation. This latter advantage extended beyond t~e pleasure and the general st:imulation of associating 

with colleagues. Since one of the principal~problems of the symposium 

was unclassified and of general mathematical interest, SCAMP sponsored 

a seminar on the subject (finite projective planes) and also a shorter 

seminar on mechanical aids to computation. Various mathematicians of 

the groups listed above not only attended the seminar meetings and 

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REF ID:A72044 

participated in discussions, but also took part as invited speaiters. 

One such speaker, Assistant Professor Lowell J. Paige of UCLA, later 

became a member of SCAMP for threeweeks. Conversely, a number of 

lectures sponsored by the INA and the Rand Corporation had a direct 

bearing on the interests of SCAMP and were attended with profit by 

various participants. Particularly valuable were (1) a series of talks 

at the INA on programming for computers, and (2) lectures by John 

Ton Neumann and :!jalling Koopmans at Rand on the so-called 11 assigmnent 

problem", whose formulation in terms of matrices is very closely related to one of the mathematical. problems most significant to .Al's.A. 

2. The Scientific Work of the Symposium 

The choice of the problems to which SC.AMP devoted most of its effort 

was determined partly by the need for maintaining a low level of classification and partl7, as t1ae work progressed, by the interests•1of the 

participants. Prior to the opening of the symposium, a number of problems 

were suggested and discussed wi tb. JFSA personnel. In order to avoid a 

scattering of efforts over a variety of special questions ani...·ta erihan.ce 

the likelihood of useful contributions, attention was concentrated on 

introducing and studying 

a. Combinatorial problems with possible numerical. solutions involving permutations, 

b. Computational schemes leading to emaustive attacks on such 

problems, 

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REF ID:A72044 

c. Methods of attack involving the imbedding of such problems in a 

continuous space and the study ot appropriate functions defined 

over the convex hull of the discrete set of potential solutions. 

For a number of reasons, these general subjects were specialized 

to the question of the existence of finite proJective planes of various 

orders. The participants devoted most of their efforts to items a. and 

b., on which definite progress was made. Promising approaches exist to 

the attacks in continuous spaces, and it is to be hoped that later efforts 

' 

will involve their further development. 

The study of finite projective planes leads to general questions invalving permutations. Since every permutation can be realized as a 

cross-wired rotor, and since ever7 cross-wired rotor yields a permutation, 

some fairly direct connections between AFSA1s problems and those encountered in studying finite projective planes may be expected. These 

are outlined. in the paper "Problems related to finite Geometriesa, 

Conference No. 18, .Appendix 'JtIJ:>ut in summary it might be pointed out 

that 

(1) The construction of a hitherto unknown finite projective plane 

_.JI' might ,lead to an example from which new and valuable knoW'l.edge 

of permutations could be gleaned; 

(2) The problem of studying finite proJective planes supports exhaustive attacks on SWAO which are very likely- to carry over to 

.AFSA applications. 

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REF ID:A72044 

In addition, it is true that finite projective planes have long been 

of general mathematical. interest, and research articles are currently 

being published concerning them. Hence it was possible to conduct open 

seminars (see .Appendix for list) in connection with Sc.AMP, thus strengthening our ties with the considerable group of mathematicians in the Los 

.Angeles area during the summer, and stimulating their interest in a pure 

mathematical problem whose solution would be of practical value to Al'SA. • 

.Another short seminar (:four meetings) and several conferences were 

devoted to the capabilities of various computing devices, especially with 

reference to the problems mentioned above. The tsJ.k:s given at these 

meetings were not reproduced, since the existing literature covers their 

eubJect matter. 

Supplementing the open seminars was a series of conference (see 

.Appendix III for list), some of them classified and all of them confined 

to SCAMP participants. 

With few exceptions, the speakers at seminar meetings and at conferences wrote up their material, which was reproduced for later use. 

Copies of the reauliting papers are in the appendices, as are a number of 

other SC.AMP reports written by the participants. The papers resulting 

from the seminar on finite projective planes were reproduced. in su:f'ficient 

quantities to permit some distribution by the Institute for NumericeJ. 

.Analysis, as well as within AFSA and smong members of SCAMP. The remaining papers were not made available to the INA but were entirely reserved 

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REF ID:A72044 

CUEIFI:tm:NfI:Ui 

for .A.FSA and SO.AMP uses. 

The purposes of the conferences were (l) to present introductory 

material indicating, within security limitations, the general area of 

the sponsor's interests (2) to suggest mathematical problems appropriate 

to SCAMP and (3) to discuss results and methods. Conference topics included depths, weights and factors, measures of roughness, information 

theory, and permutation problems. (See Appendix TO) 

Research was pursued on both an individual and a collaborative basis. 

The spirit of teamwork was strong, and the participants from .A.FSA furnished 

valuable assistance in directing the other members along useful lines • 

.Among the results obtained, the following may be mentioned as samples. 

They are mere samples, and their listing here should not be taken to imply 

that they a.re considered. more significant than otlaer results which might 

have been listed. 

(1) In a paper by Paige and Wexler (.Appendix VI, No. 2) new light 

was thrown on methods for passing 'back and forth between an 

incidence matrix of a finite projective plane and a corresponding 

set of mutuall;y orthogonal latin squares. 

(2) Certain rational matrices associated with finite proJective 

planes were developed and presented in a seminar talk by Albert, 

who plans, it' approval. is granted, to publish the results in a 

research journal. 

(3) Dr. Ward concentrated his efforts on computationaJ. procedures. 

Ee developed and successfully tried out a SWM program of a 

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REF ID :A72044 e 

search for so-called "magic sets" or 11 transversals" in a 

latin square. of order 10, also for a test to see 'Whether 

such a square contains magic sets so related as to assure 

the existence of an orthogonal mate. This latter is a 

necessary, but not sufficient, condition for tae existence of 

a finite projective plane of order 10. The methods can be 

used thro~ order 12 on SWAC. (Report to be added to 

.Appendix VI). 

(4) Dr. Tompkins, besides stimulating and advising other members 

on a variety of problems, obtained on SWAC a difference set 

of 513 numbers connected with a finite proJective plane o! 

order 512. In connection therewith, he programmed a search 

for a certain class of irreducible polynomials. (.Appendix 

VI, Nos. 14, 15). 

(5) A brief method was presented by :Botts tor demonstrating the 

non-existence of five mutually orthogonal 6 x 6 latin 

squares, hence the non-existence of a projective geometry of 

order 6. While the result was known, the method is new azid 

may lead to successful attacks on unknown cases. (Report to 

be added to .Appendix VI). 

(6) A theorem was proved by Hanson on the :number of permutations 

associated with a given difference set. (Report to be added 

to .Appendix VI). 

Various promising attacks on problems were initiated but left 

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REF ID :A72044 e 

incomplete at the end of the symposium. Among these may be mentioned 

a collaborative approach by D. W. Hall end G. A. Hedlund to the problem 

of the existence of a finite projective plane of order 10. Furthermore, 

the results listed above are mere stages on the way toward larger problems and thus also represent incomplete attacks. In addition, members 

of SC.AMP proposed, for possible future consideration, several problems 

related to those on which actu.aJ. work was performed. 

The valuable work of the participants from .AFSA is not individually 

recorded in this report, since it would be difficult to do so vi thout 

seeming to make comparisons among them. Much of their contributions took 

the form of oral dil'QUsaions and of direct assistance to the other 

members of SCAMP, who are relatively un:f'amiliar with the problems of .A.FSA. 

3. .Administrative work. 

As indicated in Section 1 above, SC.AMP was brought into being with 

little time for advance planning. The writer, as chairman, assumed 

responsibility for almost all phases of the arrangements: (1) administration of funds (2) recruitment of personnel (3) scheduling of conferences and seminars (4) general supervision of research activities, 

and of the reproduction of reports. 'lhese duties might well have been 

divided among a number of people. The important matter of arranging for 

office space and equipment was handled with the aid of c. :e. Tompkins, 

who was in the Los Angeles area in advance of the s;vmposiwn, and with 

the cooperation of staff members of INA and UCLA. 

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REF ID :A72044 e 

I 

~e space occupied by SCAMP coneisted of Rooms 323 and 325-329 inclusiTe in the old Chemistry :Building at UCLA. Room 323 has a capacity 

of six persons without crovding, as does 325, which is divided into two 

rooms holding three each. !.oom 327 is likewise thus divided, with three 

desks in one part and appropriate space in the other for the sa.f e file , 

the librarian and the chairman. Rooms 326 and 329 are offices for three 

each, and :Boom 328 was used as a conference room. Such space is 

adequate for a eymposiwn of the size of SCAMP. 

The SCAMP budget was set at a lump sum of $25,000, transferred from 

.AFSA through the ONR to the INA, with assurances of further funds if 

essential to the success of the undertaking. Roughly speaking, about 

$18,000 was allocated to salaries, travel e~enses mid associated overhead, about $6, 000 to computing ( SWAC and IBM) , and about $1 , 000 to 

office equipment, supplies, telephone charges, and so on. Some computing 

on SWAC is still in progress, and some other additional e:x;penses are yet 

to be incurred before the work of SC.AMP 1s completed. In a stq>plement 

to this report, a breakdown of actual e:x;pendi tures as of 15 September 

will be given, It appears likely that some unexpended funds will remain 

after that date and might well be used for further computation growing 

directly out of the work of SO.AMP. Appendix IX contains correspondence 

relating to budgetary matters. 

4. Proposals for the future 

Suggestions for the immediate future were made to the Director of 

the Armed Forces Security Agency when he visited SO.AMP on 14 .An.go.st and 

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REF ID :A72044 e 

conferred with the available SCAG members. s. s. Cairns, B. P. Robertson 

and C. B. Tompkins. It was recommended (1) that .AFSA sponsor a second 

summer symposium similar to SCAMP at the same location in 1953 (2) that 

there be some work at UCLA on a reduced scale during the academic year 

1952-3, to avoid a diseontinui ty between the two s;ymposi1lllls and (3) that 

decisions concerning later efforts be reserved until the work of SCAMP 

has been suitably evaluated. 

The following suggestions, some of them abvious and some resulting 

from the e:xperience of this year's symposium, may prove helpful in future 

planning. 

(1) It is of the greatest importance to start as early as practicable 

on the task: of recruiting and clearing personnel, since clearance procedures are notoriously time-consuming and since the 

most desirable mathematicians are likely to make other commitments for the summer, if not approached early. 

(2) .Al though the research program will be partly dictated by the 

talents and mterests of the participants, there should be an 

early decision as to general objectives. Reference is made to 

the following items in .Appendix XI: 

(a) "Notes on a proposed research project and s;ymposiu.m0 , 

18 March 1952 by c. B. Tompkins. 

(b) Letter of 24 June 1952 from Tompkins to D. c. 

Spencer. 

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REF ID:A72044 

COl!ITI5lf!Uf1 

(c) Memorandum on nTb.e Objectives of SCAMP" from 

s. s. Cairns to the members of SCAMP, 16 Jul1' 1952. 

Prospective participants should be informed of the 

general obJectives in advance and also, insofar as 

possible, of particular problems proposed for attack. 

(3) It might be well to have both an administrative and a technical 

chairman. The technical chairman, who might be chosen from 

the INA or from UCLA, would assume respons1bili ty for financial 

negotiations with prospective participants and for the provision 

of suitable working space, office equipment and so on. Some 

secretarial assistance might be provided by the INA, al though 

an AFSA librarian is also needed to take care of the classified 

files, to prepare classified reports and to supervise their 

reproduction. The technical chairman could concentrate on the 

research program, including the planning of expositor1 background lectures, presentation of new results and conference 

discussions devoted to work in progress. He should also have 

the duty of preparing a final report. If' thus freed from the 

non-research administrative burden, he might have time to do 

\ 

some mathematics himself. This division of duties, or some 

modification thereof, should make it easier to secure a good 

technical chair.man. 

(4) From the first planning stage on, there might well be an ad-

¥isory committee of fully cleared mathematicians, who would 

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CODIJZlftta:ci 
REF ID:A72044 

COD:Uliili!Um 

nominate the chairman or chairmen, establish a calendar of 

deadlines, nominate ke;y personnel, and who would be kept informed of significant developments both before and during 

the symposium, so as to be in a position to render the most 

useful advice. The advisory committee should, in cooperation 

vith the chairman, ensure that the problems attacked during 

the symposium are relevant and important to applications on a 

high security level. 

(5) A few carefully selected .AFSA personnel should be assigned to 

the symposium for its entire duration and others, as this swmner, 

for shorter periods of time. Those assigned for the whole 

period should include persons thoroughly familiar both w1 th the 

mathematical problems of AFSA and with their prospective applications. 'Ol.estions of security (classification of problems, 

reports and so on) should be decided by AFSA representatives • 

.Appendix X contains suggestions from SC.AMP participants relatiJJg to 

various aspects of possible future projects analogo~ to SCAMP. 

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