
463 F.Supp. 1295 (1979)
Kevin ARMSTRONG et al., Plaintiffs,
v.
Donald J. O'CONNELL et al., Defendants.
Milwaukee Teachers' Education Association, Undesignated Intervenor.
Civ. A. No. 65-C-173.
United States District Court, E. D. Wisconsin.
February 8, 1979.
*1296 Lloyd A. Barbee, Milwaukee, Wis., for named plaintiffs.
Irvin B. Charne, Milwaukee, Wis., for the absent members of the plaintiff classes.
L. C. Hammond, Jr., Patrick W. Schmidt and Ronald E. Klipsch, Milwaukee, Wis., for defendants.
Curry First, Milwaukee, Wis., for Milwaukee Teachers' Ed. Ass'n, undesignated intervenor.


*1297 FINDINGS OF FACT, CONCLUSIONS OF LAW, AND DECISION AND ORDER
REYNOLDS, District Judge.
On June 28, 1977, in Brennan v. Armstrong, 433 U.S. 672, 97 S.Ct. 2907, 53 L.Ed.2d 1044 (1977), the United States Supreme Court vacated the judgment of the United States Supreme Court of Appeals issued July 23, 1976, in Armstrong v. Brennan, 539 F.2d 625 (7th Cir. 1976), wherein the court of appeals had affirmed the finding of liability made by this court on January 19, 1976, in the above-entitled action. See Amos v. Board of School Directors of the City of Milwaukee, 408 F.Supp. 765 (E.D.Wis.1976). The Supreme Court remanded the case to the court of appeals for reconsideration in light of Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977), and Dayton Board of Education v. Brinkman, 433 U.S. 406, 97 S.Ct. 2766, 53 L.Ed.2d 851 (1977), and the court of appeals thereafter remanded the case to this court for proceedings consistent with the Supreme Court's mandate. Armstrong v. Brennan, 566 F.2d 1175 (7th Cir. 1977).
In Dayton, supra, 433 U.S. at 420, 97 S.Ct. at 2775, the Supreme Court had held:
"The duty of both the District Court and the Court of Appeals in a case such as this, where mandatory segregation by law of the races in the schools has long since ceased, is to first determine whether there was any action in the conduct of the business of the school board which was intended to, and did in fact, discriminate against minority pupils, teachers, or staff. Washington v. Davis, supra [426 U.S. 229, (96 S.Ct. 2040, 48 L.Ed.2d 597) (1976)]. All parties should be free to introduce such additional testimony and other evidence as the District Court may deem appropriate. If such violations are found, the District Court in the first instance, subject to review by the Court of Appeals, must determine how much incremental segregative effect these violations had on the racial distribution of the Dayton school population as presently constituted, when that distribution is compared to what it would have been in the absence of such constitutional violations. The remedy must be designed to redress that difference, and only if there has been a systemwide impact may there be a systemwide remedy. Keyes [v. School District No. 1, Denver, Colorado], 413 U.S. [189 (1973)], at 213, [93 S.Ct. 2686, 37 L.Ed.2d 548]."
Accordingly, after discussion with counsel and over the objection of defendants' counsel, the Court took additional evidence on the issue of past intentional discrimination. On June 1, 1978, the Court found:
"* * * that the defendants discriminated against the plaintiffs with segregative intent * * * and in so doing violated the Equal Protection Clause of the Fourteenth Amendment to the United States Constitution and the Civil Rights Act of 1871, 42 U.S.C. § 1983." Armstrong v. O'Connell, 451 F.Supp. 817, 820 (E.D.Wis.1978).
The Court also found:
"F-89. The objective evidence previously described in detail demonstrates that defendants' decisions, at least since 1950, with respect to teacher assignment and transfers, student bussing, student transfers, school siting, leasing and constructing of school facilities, use of substandard classrooms, and boundary changes were undertaken with an intent to segregate students and teachers by race. In making these decisions, defendants did not believe they were shortchanging black students. Defendants, however, viewed racially-mixed schools as problem schools, likely to be plagued by racial incidents, poor teacher morale, and declining academic standards. Moreover, the prevailing belief of the School Board was that any large influx of blacks into white schools would lower the quality of education available to white students there and would eventually cause the white students to leave those schools. Accordingly, defendants undertook a systematic program designed to prevent *1298 whites from being required to attend classes with large numbers of blacks." Armstrong v. O'Connell, supra, at 866.
Finally, the Court found that defendants
"* * * deliberately separated most of the whites from most of the blacks, and this the Constitution forbids." Armstrong v. O'Connell, supra, at 866.
On July 10, 1978 through July 14, 1978, and on October 23, 1978 through October 25, 1978, the Court took evidence on the issue of the present effects of defendants' past segregative acts. The parties in December 1978 submitted to the court proposed findings of fact and conclusions of law and comments on each other's submissions. The decision which follows draws on those submissions, and it constitutes the Court's findings of fact and conclusions of law on the issue of the present effects on the Milwaukee public school system of the defendants' past intentional segregative acts.
There are two preliminary matters which are determinative of the outcome of this case and which the Court will discuss before making its findings of fact and conclusions of law. First is the impact of the Dayton decision on Keyes and its application to the retrial of this action. Second is the manner in which the Court has viewed the expert testimony which it heard in the second phase of the retrial of this action.
In Keyes v. School District No. 1, Denver, Colorado, 413 U.S. 189, 93 S.Ct. 2686, 37 L.Ed.2d 548 (1973), the Supreme Court examined the principles applicable in a school desegregation case not involving a statutory dual school system. It stated that:
"* * * where plaintiffs prove that the school authorities have carried out a systematic program of segregation affecting a substantial portion of the students, schools, teachers, and facilities within the school system, it is only common sense to conclude that there exists a predicate for a finding of the existence of a dual school system. * * *" 413 U.S. at 201, 93 S.Ct. at 2694.
It also stated:
"* * * In the absence of such a determination [that the geographical structure of, or the natural boundaries within, a school district have the effect of dividing the district into separate, identifiable and unrelated units], proof of state-imposed segregation in a substantial portion of the district will suffice to support a finding by the trial court of the existence of a dual system. Of course, where that finding is made, as in cases involving statutory dual systems, the school authorities have an affirmative duty `to effectuate a transition to a racially nondiscriminatory school system.' Brown II [Brown v. Board of Education, 349 U.S. 294, (75 S.Ct. 753, 99 L.Ed. 1083) (1955)], supra, at 301." 413 U.S. at 203, 93 S.Ct. at 2695.
The Court held:
"* * * that a finding of intentionally segregative school board actions in a meaningful portion of a school system, as in this case, creates a presumption that other segregated schooling within the system is not adventitious * * * and shifts to those authorities the burden of proving that other segregated schools within the system are not also the result of intentionally segregative actions. * * *" 413 U.S. at 208, 93 S.Ct. at 2697.
With reference to the present effects of systemwide past intentional discrimination by the school board:
"This is not to say, however, that the prima facie case may not be met by evidence supporting a finding that a lesser degree of segregated schooling in the core city area would not have resulted even if the Board had not acted as it did. In Swann [v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, (91 S.Ct. 1267, 28 L.Ed.2d 554) (1971)], we suggested that at some point in time the relationship between past segregative acts and present segregation may become so attenuated as to be incapable of supporting a finding of de jure segregation warranting judicial intervention. 402 U.S., at 31-32, [91 S.Ct. 1267] [Citation omitted.] We made it clear, however, that a connection *1299 between past segregative acts and present segregation may be present even when not apparent and that close examination is required before concluding that the connection does not exist. Intentional school segregation in the past may have been a factor in creating a natural environment for the growth of further segregation. Thus, if respondent School Board cannot disprove segregative intent, it can rebut the prima facie case only by showing that its past segregative acts did not create or contribute to the current segregated condition of the core city schools." 413 U.S. at 211, 93 S.Ct. at 2698.
The defendants suggest that Keyes did not deal with the present effects issue discussed in Dayton and, therefore, that the presumptions created in Keyes are not applicable in this phase of the retrial. In the alternative, they argue that Dayton and other post-Keyes decisions, see, e. g., Austin Independent School District v. United States, 429 U.S. 990, 97 S.Ct. 517, 50 L.Ed.2d 603 (1976) (Powell, J., concurring); Pasadena City Board of Education v. Spangler, 427 U.S. 424, 96 S.Ct. 2697, 49 L.Ed.2d 599 (1976), have modified the analysis required and demand factual proof on a school-by-school basis of the present effects of defendants' past intentional segregative acts.
The plaintiffs and the United States, which has filed a brief as amicus curiae, argue that, as witnessed by the citation to Keyes in Dayton at 433 U.S. 420, 97 S.Ct. 2766, Dayton did not work any fundamental change in the law, and the burden rests on the defendants to show that the segregation in the Milwaukee school system as of the 1975-76 school year did not result from their segregative conduct. In the alternative, plaintiffs submit that they have established by factual proof that defendants' past segregative conduct had a systemwide impact on the Milwaukee school system in the 1975-76 school year.
After reviewing the Keyes and the Dayton decisions, as well as the decisions of the many district courts and courts of appeal which have studied the interrelationship of those decisions since June of 1977,[1] the Court is persuaded that the Keyes decision does have application to the issue of present effects and also that Dayton does not bear the weight which defendants would have it bear as an instrument for overruling Keyes. The Court in Keyes directed its attention specifically to "the relationship between past segregative acts and present segregation," 413 U.S. at 211, 93 S.Ct. at 2699, and it held that after a showing of past intentional segregation having a systemwide effect is made, and the further showing of present systemwide segregation is made, then the defendants must show that their "past segregative acts did not create or contribute to the current segregated condition of the * * * city schools" if they wish to escape the imposition of a systemwide remedy. 413 U.S. at 211, 93 S.Ct. at 2699. The Court in Dayton stated at 433 U.S. 420, 97 S.Ct. at ___ that:
"* * * the District Court * * * must determine how much incremental segregative effect these violations had on the racial distribution of the Dayton school population as presently constituted, when that distribution is compared to what it would have been in the absence of such constitutional violations. * *"
In Dayton, however, the district court found only three isolated instances of intentional segregative conduct. Consequently, none of the predicates for the application of the presumptions discussed in Keyes were present, and plaintiffs retained the burden *1300 of presenting factual proof of the specific effect of each of the defendants' intentionally segregative actions. Whether or not Dayton is a "foreshadowing" of the demise of the Keyes presumptions at least in the area of present effects, see Austin, supra; Pasadena City Board of Education, supra; and "Defendants' Post Trial Memorandum of Law, Memorandum on Proposed Findings of Fact and Conclusions of Law, and Proposed Findings of Fact and Conclusions of Law as to the Issue of Present Effects" filed December 8, 1978, at 5, n. 4, the Supreme Court has not yet arrived at that result. Unless and until it does so, in language more precise than anything contained in the Dayton decision, this Court considers itself bound by the principles set forth in the Keyes decision.
In addition to its significance on the issues of presumptions and burden of proof, Keyes has a second application to this phase of the retrial. In the original decision and order issued in this case on January 19, 1976, Amos v. Board of School Directors of the City of Milwaukee, 408 F.Supp. 765 (E.D.Wis.1976), it was held at 821:
"The Court concludes that the defendants have knowingly carried out a systematic program of segregation affecting all of the city's students, teachers, and school facilities, and have intentionally brought about and maintained a dual school system. * * *"
While the Court did not specifically reiterate its finding of a dual school system in the June 1, 1978, decision, it did make the finding that:
"* * * defendants undertook a systematic program designed to prevent whites from being required to attend classes with large numbers of blacks," Armstrong v. O'Connell, 451 F.Supp. 817, 866 (E.D.Wis.1978),
and in addition that defendants:
"* * * deliberately separated most of the whites from most of the blacks * * *." 451 F.Supp. at 866.
Once a finding is made of "state-imposed segregation in a substantial portion of the district," Keyes, 413 U.S. at 203, 93 S.Ct. at 2695, the school board has an affirmative duty "`to effectuate a transition to a racially nondiscriminatory school system.'" Keyes at 203, 93 S.Ct. at 2695; Brown v. Board of Education, 349 U.S. 294, 301, 75 S.Ct. 753, 99 L.Ed. 1083 (1955); Green v. County School Board, 391 U.S. 430, 437-438, 88 S.Ct. 1689, 20 L.Ed.2d 716 (1968).
Defendants have agreed that the Milwaukee school system is "as segregative" "or as integrative"now as it was in 1950. See "Defendants' Post Trial Memorandum of Law, Memorandum on Proposed Findings of Fact and Conclusions of Law, and Proposed Findings of Fact and Conclusions of Law as to the Issue of Present Effects" filed December 8, 1978, at 31-32. Keyes imposes on the defendants the duty to show that the degree of segregation in the Milwaukee school system in 1975-76 would have existed even absent their intentional segregative actions. 413 U.S. at 211, 93 S.Ct. 2686. If the evidence which they present to explain those conditions fails to show that the conditions would have existed even absent their past actions, then the Court believes, following Keyes, that it can make the finding that the degree of present segregation in the Milwaukee school system arises out of the defendants' failure to perform the affirmative duty imposed on them in Keyes to effect a transition to a racially neutral system and is itself a significant present effect of the defendants' past intentional segregative actions.
The defendants also argue that even if the Keyes presumptions survive Dayton, they must be deemed rebutted and have no further application "if * * * a reasonable jury could find the contrary of the presumed fact more probable than not." "Defendants' Post Trial Memorandum of Law, Memorandum on Proposed Findings of Fact and Conclusions of Law, and Proposed Findings of Fact and Conclusions of Law as to the Issue of Present Effects," filed December 8, 1978, at 8. Also they argue that Dayton requires that present segregative effects be measured on a school-by-school basis, that it requires that the present racial distribution of the school *1301 population be compared to what it would have been absent the defendants' violations, and therefore that 
"* * * [t]he untested claims of Drs. Green, Taeuber and Foster [plaintiffs' experts] with respect to psychological attitudinal effects transcend the bounds of the task assigned this Court. The only issue presented is what the racial distribution of the school population would be today, not what psychological harm might have been caused and not what attitudinal concepts might have been developed because of the violations. * *" Defendants' Post Trial Memorandum filed December 8, 1978, at 10.
As stated above, the Court does not read Dayton as requiring a school-by-school analysis. Furthermore, in face of defendants' systematic program of intentional segregative action, a school-by-school analysis which fails to take into account that there may be ramifications of the action felt outside of the individual school or schools involved may fail to measure the "incremental" effect of an individual action or of the individual actions at issue when they are viewed in total. In Keyes, the Court noted at 433 U.S. 203, 93 S.Ct. 2686 that school board actions have an impact beyond their impact on the individual school or schools at which they are directed. Similarly, in Milliken v. Bradley, 433 U.S. 267, 97 S.Ct. 2749, 53 L.Ed.2d 745 (1977), the Court recognized "the broad and flexible equity powers" of the court, 433 U.S. at 288, 97 S.Ct. at 2761, and noted that, depending on the circumstances present in each case, "[p]upil assignment alone does not automatically remedy the impact of previous, unlawful educational isolation * * *." 433 U.S. at 287, 97 S.Ct. at 2761. See also Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971); United States v. Montgomery County Board of Education, 395 U.S. 225, 89 S.Ct. 1670, 23 L.Ed.2d 263 (1969). Even in Dayton, the Court noted that the remedy should be commensurate to the scope of the violations. 433 U.S. at 417, 97 S.Ct. 2766. Thus, if the evidence shows that the present effects of the defendants' past intentional segregative actions include negative psychological attitudinal effects, the Court is unaware of any reason why it should not, to the extent, if any, that it is appropriate, fashion a remedy to cure those effects.
As for defendants' argument with respect to rebutting the Keyes presumptions, that argument presupposes that defendants have presented to the Court sufficient evidence to enable the Court, sitting as the finder of fact, to decide that the present segregated condition of the Milwaukee schools was not caused by the defendants' intentional segregative actions. The defendants limited their presentation of evidence to the schools as to which specific violations were found, and as to those schools, to a comparison of what the present population of each school would have been had the specific violations not occurred to what the population was at the time the violation occurred. For the reasons set forth below, the Court finds that the flaws in the defendants' analysis would preclude it as factfinder from relying on the evidence presented by defendants and therefore would not enable it to make the finding that it was more likely than not that defendants' actions did not contribute to the present segregated conditions in the Milwaukee public schools.
Both matters  the use of evidence relating to psychological attitudinal effects and the analysis and use of evidence of incremental segregative effects as defined by the defendants  raise the issue of the manner in which the Court has viewed the expert testimony presented during the second phase of the retrial of this case. That view is in turn determinative of the outcome of the case and thus will be discussed prior to the making of specific findings of fact and conclusions of law.
Initially, the Court notes that this second phase of the retrial  the so-called "battle of the experts"  has required the Court as factfinder to consider and to evaluate almost entirely contrary sociological and urban geographic theories. In so doing, the Court of necessity has had to rely on the qualifications and the persuasiveness of the expert witnesses in reaching its own conclusions *1302 on the ultimate issue of present effects. Plaintiffs' witnesses were Dr. Robert P. Stuckert, formerly the director of the Milwaukee Fact Book Project; Dr. Robert L. Green, an educational psychologist and presently the dean of one of the colleges at Michigan State University; Dr. Karl Taeuber, a sociologist and urban demographer, presently at the University of Wisconsin-Madison; and Dr. Gordon Foster, presently a professor in the School of Education at the University of Miami. Defendants' witnesses were Dr. William Clark, an urban geographer presently from the University of California at Los Angeles, and Dr. David Armor, a sociologist, formerly from Harvard University and presently with the Rand Corporation.
The defendants have criticized plaintiffs' witnesses for failing to make detailed analyses of the Milwaukee urban area and residential living patterns and of the Milwaukee public school system. Also, defendants have criticized them for testifying as to the "psychological attitudinal effects" of defendants' past segregative actions rather than trying to quantify except by use of terms like "substantial" or "not minimal," the incremental effects of the defendants' constitutional violations. (Defendants' Memorandum filed December 8, 1978, at 10, 12-13.)
The Court has already determined that evidence of psychological attitudinal effects is relevant to its present inquiry and that a remedy can be predicated on a finding that such effects exist. With respect to the failure of plaintiffs' witnesses to quantify present effects mathematically, this Court is in agreement with the statement of the Court in Booker v. Special School District No. 1, Minneapolis, Minnesota, 451 F.Supp. 659, 662 (D.Minn.1978), that the use of an "`alternative universe theory,'" i. e., a comparison of a universe where no violations occurred to what in fact exists, is fraught with difficulties and moreover is probably not what the Supreme Court intended in Dayton. As stated by the Court in Booker in note 5 at 663:
"* * * [T]he many problems of the statistical approach defendants have used reinforces this Court's view that Dayton cannot be interpreted so `mathematically.' As another court has remarked, no court in any school case will ever be able to say with any assurance `where people would have lived, where schools would have been located [or] how much integration would have obtained' absent officially imposed discrimination. U. S. v. Columbus Municipal Separate School Dist., 558 F.2d 228, 231 n. 11 (5th Cir. 1977), cert. denied 434 U.S. 1013, 98 S.Ct. 728, 54 L.Ed.2d 757 (1978)."
See also Teamsters v. United States, 431 U.S. 324, 372, 97 S.Ct. 1843, 52 L.Ed.2d 396 (1977). Any "alternative universe" created, whether by plaintiffs' or defendants' experts, will necessarily be an approximation of what in fact would have existed absent the defendants' constitutional violations. Consequently, use of a term like "substantial" to quantify the present effect of past actions by a person whose expertise qualifies him to make a judgment on present effects is all that is reasonably possible and all, in the opinion of this Court, that the law presently requires.
Finally, the defendants take too narrow a view of what their constitutional violations were as found by the Court in its June 1, 1978, decision. They have examined and used in this second phase of the trial the individual violations which the Court found but have ignored the Court's conclusion that:
"* * * the defendants acted with a discriminatory intent in their decisions and actions respecting boundary changes, site selection, and school construction." Armstrong v. O'Connell, 451 F.Supp. 817, 866 (E.D.Wis.1978).
They have also ignored the Court's conclusion that:
"[t]he objective evidence previously described in detail demonstrates that defendants' decisions, at least since 1950, with respect to teacher assignment and transfers, student bussing, student transfers, school siting, leasing and constructing *1303 of school facilities, use of substandard classrooms, and boundary changes were undertaken with an intent to segregate students and teachers by race. * * * Accordingly, defendants undertook a systematic program designed to prevent whites from being required to attend classes with large numbers of blacks." Ibid., at 866. (Emphasis added.)
The Court concluded in the just-quoted findings that the defendants' violations occurred on a systemwide basis and not merely in the individual instances set forth earlier in the June 1, 1978, decision. By choosing to ignore the Court's conclusions, the defendants have also taken too narrow a view of the evidence on which the opinions of plaintiffs' witnesses were based. The criticism leveled at plaintiffs' witnesses of failing to make the proper analysis of the Milwaukee public school system could therefore better by leveled at defendants' witnesses who failed to take into account the most significant of the findings made by the Court on the issue of defendants' past intentional segregative acts.
Defendants' witness, Dr. William Clark, testified about the reciprocal effects of segregated schooling on residential patterns. In reliance on his testimony, the defendants have suggested that the Court adopt the following finding of fact:
"40. The primary forces which influence residential patterns are economics, spatial forces, geographic barriers, choice and discrimination (Tr. II-37, Clark). All of these forces contribute to the way in which people behave with respect to residential selection, one aspect of which is that people tend to move shorter distances rather than longer ones (Tr. II-18-21, Clark). One way to measure this observed behavior is through the use of a scientific device called a `distance decay curve,' which itself represents the forces that go into the selection of new residences (Tr. II-21, Clark). By taking the distance decay curve and doing a scientific simulation based upon the probabilities of individuals moving particular distances, one can simulate where people would be expected to live if the forces which comprise the distance decay curve are valid (Tr. II-25-26, 27-29, Clark). If the simulated pattern one obtains from running the study is close to the actual pattern (based upon census information), then the simulation establishes that the forces which are at work in contributing to the distance decay curve are causing the actual pattern to develop (Tr. II-40, Clark).
"Dr. Clark conducted a simulation study of the movements of black families for the City of Milwaukee for the period of 1960 to 1970 using a distance decay curve of the white population (Tr. II-44, Clark). By using this curve rather than the distance decay curve for blacks, the portion of observed behavior which is due to discrimination is eliminated and therefore whatever correlation this simulation has to the actual will reflect those factors which are part of the distance decay curve except for discrimination (Tr. II-44-5, Clark). The simulations which Dr. Clark ran produced a mathematical correlation of .81 and .83 which establishes that the distance decay curve was a good representation of the movements of black households (Tr. II-39, Clark). The difference between the correlation number received and the number one represents the factors which are left over that are not included in the distance decay formula, which factors include discrimination (Tr. II-102, Clark). Dr. Clark has always tended to think that each of the factors, economics, barriers, spatial factors, choice and discrimination have about 20% of the explanation for residential living patterns (Tr. II-121, Clark). The discrimination element, which is in the range of 15-20%, includes both individual and governmental discrimination (Tr. II-123, Clark). Since individual acts of discrimination and other governmental discrimination besides the School Board are part of the residual of 20% which explain the black living patterns, the Court-found violations are far outweighed as having any influence on residential patterns (Tr. II-42, Clark). Dr. Clark testified that he did *1304 not think that the School Board had an impact on the residential patterns and that there was no evidence in the literature that school boards have been a force in influencing the residential mosaic, and this Court agrees with that testimony and so finds (Tr. II-43, Clark)." (Defendants' memorandum filed December 8, 1978, at 35-36.)
The Court declines to adopt the finding. As stated within it, the finding assumes that "[i]f the simulated pattern one obtains from running the study is close to the actual pattern * * *, then the simulation establishes that the forces which are at work in contributing to the distance decay curve are causing the actual pattern to develop * * *." What the forces are, however, is determined by the person conducting the study. No attempt was made by Dr. Clark to determine whether or not a set of other factors taken in conjunction, or several such sets, might have created the same pattern. Consequently, of course, no effort was made by him, and his study does not show, that the set of forces on which he chose to base the study was the only set which could have created the actual pattern.
Dr. Armor undertook to evaluate each individual discriminatory act which the Court found in its June 1, 1978, decision, and to predict, assuming an otherwise static situation, what the present population of the school or district involved would have been absent the single act of discrimination, or what the rate of contact between black and white students would be today absent the act of discrimination. The Court finds several fundamental flaws in his analysis. First, it fails to take into account that the individual violations set forth in the June 1, 1978, decision were not the only violations which the Court found to have occurred, but rather that the Court found, based on those individual acts, that systemwide violations had occurred. Second, the analysis assumes that had the individual intentionally discriminatory acts not occurred, no other neutral and nondiscriminatory actions would have been taken. Third, the analysis ignores the possible psychological and attitudinal effects of the acts, i. e., it measures integration on the basis of contact alone without regard for the nature of the contact. Finally, the analysis fails to take into account that a single act of discrimination may have an effect beyond that felt by the persons, or in the schools or districts of immediate impact. For other criticisms of Dr. Armor's work, see United States v. Board of School Commissioners of the City of Indianapolis, Indiana, 503 F.2d 68, 85 and n. 21 at 85 (7th Cir. 1974); Northcross v. Board of Education of Memphis, 466 F.2d 890, 894 (6th Cir. 1972).
The Court recognizes, as all courts which have looked at the problem have done, the difficulties of proof of cause and effect in the context of school segregation. Relying on the Keyes decision, the Court is of the opinion that its finding of systemwide intentional discrimination, in conjunction with defendants' failure to present satisfactory evidence that the present segregated condition of the Milwaukee public school system would have been the same even absent the acts of intentional discrimination, necessitates imposition of a systemwide remedy. As stated by the Court in Booker v. Special School District No. 1, Minneapolis, Minnesota, 451 F.Supp. 659, 663-664 (D.Minn.1978):
"Indeed, at bottom, there is an inherent contradiction in attempting to apply either of defendants' views of Dayton to a systemic school segregation case. This Court's findings of a systemwide pattern of discrimination in the Minneapolis schools cannot now be challenged or relitigated and Dayton itself reemphasized that once systemwide impact is found, a systemwide remedy must be imposed. Dayton did not overrule the cases which have guided the district courts in formulating systemwide remedies  the goal is to desegregate the entire system `root and branch,' Keyes v. School District No. 1, 413 U.S. 189, 213, 93 S.Ct. 2686, 37 L.Ed.2d 548 (1973), quoting Green v. County School Board, 391 U.S. 430, 438, 88 S.Ct. 1689, 20 L.Ed.2d 716 (1968), and to achieve the `greatest possible degree of *1305 actual desegregation, taking into account the practicalities of the situation,' Davis v. Board of School Commissioners, 402 U.S. 33, 37, [91 S.Ct. 1289, 28 L.Ed.2d 577] (1971). See U. S. v. Columbus Municipal Separate School Dist., 558 F.2d 228, 230-31 (5th Cir. 1977), cert. denied, 434 U.S. 1013, 98 S.Ct. 728, 54 L.Ed.2d 757 (1978). The concept of `incremental segregative effect,' however it may be interpreted or applied when a district court is faced in the first instance with isolated unconstitutional acts, has little application where the segregative effect has already been determined to have been pervasive and to require a systemwide remedy. * * *"
Nevertheless, even assuming that the Keyes presumptions should not be applied to the present effects analysis, the Court is persuaded that plaintiffs have presented sufficient evidence during the second phase of the retrial to justify imposition of a systemwide remedy.
The Court makes the following findings of fact and conclusions of law on the issue of the proper scope of the remedy to be imposed in this case.[2] These findings and conclusions are supplemental to, and generally in harmony with, those findings and conclusions on the same issue contained in the Court's original decision in this case, Amos v. Board of School Directors of the City of Milwaukee, 408 F.Supp. 765 (E.D. Wis.1976). In case of a conflict, however, between the findings and conclusions of the original decision and the findings and conclusions of this decision, the later ones are intended as controlling. The findings of fact are numbered consecutively below, with each number being preceded by the designation "F," while the conclusions of law are numbered consecutively in a separate sequence, with each number being preceded by the designation "L."

FINDINGS OF FACT AND CONCLUSIONS OF LAW
L-1. Where, as in this case, the trial court has made a finding of segregative intent, the Court is then required to make a determination of what are the present effects of the defendants' past intentional segregative actions. Dayton Board of Education v. Brinkman, 433 U.S. 406, 97 S.Ct. 2766, 53 L.Ed.2d 851 (1977); Brennan v. Armstrong, 433 U.S. 672, 97 S.Ct. 2907, 53 L.Ed.2d 1044 (1977).
F-1. For the purposes of this case, "present effects" should be judged as of the 1975-76 school year, which was the last year prior to the phasing in of a court-ordered remedy in this case.
L-2. Once the defendants are found to have engaged in intentionally segregative conduct in a meaningful portion of the school system, see Armstrong v. O'Connell, 451 F.Supp. 817, 866 (E.D.Wis.1978), the burden shifts to the defendants to show that the present segregated condition of the school system would have occurred even absent the defendants' intentionally segregative conduct, Keyes v. School District No. 1, Denver, Colorado, 413 U.S. 189, 211, 93 S.Ct. 2686, 37 L.Ed.2d 548 (1973). In this case, however, even without the use of the Keyes presumption, the plaintiffs have established that the defendants' unconstitutional conduct had a substantial systemwide impact on the racial distribution of students and teachers in the Milwaukee public school system.
F-2. The Court previously found that defendants themselves fallaciously assumed that "educationally undesirable characteristics are common to all black children" and that "the influx of a large number of black students into a white school would lower the quality of education in that school." Armstrong v. O'Connell, 451 F.Supp. 817, 866 (E.D.Wis.1978). As a result of defendants' unconstitutional decisionmaking, similar false assumptions were taught to Milwaukee school children and the Milwaukee community in general. Specifically, defendants' discriminatory conduct has taught school children and adults in Milwaukee *1306 that racial separation is legitimate and desirable behavior. It has taught white children that this is a white-dominant society and that white children need not have more than token contact with black children or black professionals. It has taught whites that blacks are in some ways inferior and that interracial contact is detrimental and to be avoided. Defendants' conduct provided the same lessons to black children and black adults. Moreover, defendants' conduct was a message that a major government agency in Milwaukee formally and openly sanctioned racial discrimination and segregation. Defendants' deliberate separation of white and black children in a variety of ways, and their separation of white children from black teachers, thus had the effect of fostering general attitudes of prejudice and racial hostility throughout the Milwaukee area.
F-3. Intact busing conveyed the message to whites that their children were being protected from blacks because even if it was necessary to bus largely black classes to predominantly white schools, there was nothing to fear because the busing would be temporary and the bused children would be kept reasonably separate at the white schools. Intact busing taught blacks that black children were not welcome in white schools, that black parents were not welcome at the white schools' P.T.A.'s, and that blacks were not likely to make friends in the white areas of Milwaukee. Milwaukee public school busing practices also taught both black and white students that blacks were inferior. Accordingly, the great efforts made by the school system through its busing practices to minimize contact between students from black and white schools reinforced defendants' general educational message that white contact with too many blacks is unfortunate and to be avoided.
F-4. The impact of intact busing is uncertain; however, a substantial number of parents and children had first-hand knowledge of intact busing. Moreover, in light of the community conflict over intact busing and the media coverage of the conflict, Milwaukeeans in general were aware of intact busing practices and the racial lessons they taught.
F-5. The deliberate concentration of black teachers in schools outside of the predominantly white areas of the city conveyed the message that an important government agency, the school board, did not want blacks in the white areas of the city. It also was a message to school children that whites are dominant and that blacks are to be kept apart in Milwaukee's public schools and in the city generally.
F-6. Defendants' free and open transfer policies let whites know that their children would be permitted to escape from schools becoming increasingly black, and facilitated defendants' policy of "deliberately separat[ing] most of the whites from most of the blacks," Armstrong v. O'Connell, 451 F.Supp. 817, 866 (E.D.Wis.1978). These policies had the further effect of identifying certain neighborhoods in Milwaukee as being no longer suitable for whites.
F-7. The attitudinal effects resulting from defendants' intentionally segregative conduct have broad social consequences. These attitudinal effects influence the behavior of teachers and school administrators throughout the school system in carrying out their duties, and they affect other government officials in discharging their public responsibilities. They also influence the behavior of private citizens as members of the community and as actors in the housing market. In addition to being broad in scope, unless there is an extensive program of remediation, these attitudinal effects will last a lifetime. Brown v. Board of Education, 347 U.S. 483, 494, 74 S.Ct. 686, 98 L.Ed. 873 (1954).
F-8. In 1950, approximately 3½% of Milwaukee's citizens were black. In that year, no census tracts were more than 90% black, and only five tracts were majority black. Although in 1950 some blocks in Milwaukee were predominantly black, no black person lived more than four blocks from a majority white residential area. Thus, unlike in other large northern cities in 1950, as a result of the small percentage of black citizens, *1307 Milwaukee blacks lived in relatively close geographic proximity to whites; on the other hand, the residential living pattern was extremely concentrated and there was a high degree of residential segregation.
F-9. From 1950 through 1970, Milwaukee's black population nearly quintupled, and by 1970 blacks constituted approximately 14½% of the city's population. Milwaukee's ghetto, defined herein as a concentrated area of predominantly black residents, grew up since 1950, and principally in the 1960's. In 1970, seventeen census tracts were more than 90% black and an additional twenty tracts were majority black.
F-10. Defendants' segregative decisionmaking thus occurred simultaneously with the growth of Milwaukee's black ghetto. An expert witness called by plaintiffs, Dr. Karl Taeuber, whom one of the defendants' experts described as a very well-known, renowned demographer best known for his work on race-related issues and on cities, testified that in Milwaukee "there was a continuing reciprocal interplay between schooling and housing, such that the highly concentrated black ghetto and the highly concentrated portions of the school system grew up together, and the reciprocal influence on the white areas produced solidly white resident and school areas." (Transcript of July 11, 1978, at 255) The Court, in its January 19, 1976, opinion, indicated that it did not doubt that schools had a reciprocal effect on housing, but that the evidence then in the record did not support such a finding. Amos v. Board of School Directors of the City of Milwaukee, 408 F.Supp. 765, 821-822 (E.D.Wis.1976). Based on the evidence presented at the second phase of the retrial on present effects, a reciprocal effect finding, as stated in the above-quoted excerpt from Dr. Taeuber's testimony, is now justified. See also Swann v. Charlotte-Mecklenburg Board of Education, 402 U.S. 1, 20-21, 91 S.Ct. 1267, 28 L.Ed.2d 554 (1971); Keyes v. School District No. 1, Denver, Colorado, 413 U.S. 189, 202, 93 S.Ct. 2686, 37 L.Ed.2d 548 (1973).
F-11. It is an impossible task  at least for this court and this judge  to determine with any degree of specificity how substantial the reciprocal effect of schooling on housing in Milwaukee has been. There is credible evidence in the record to support the finding, which the Court now makes, that the factors of economics, choice, spatial factors, and discrimination also have a substantial role in creating residential segregation. Nevertheless, based on Dr. Taeuber's testimony, the Court is persuaded that the school board's actions also were one of the substantial causes of residential segregation in Milwaukee.
F-12. The Court, in its June 1, 1978, decision, found that defendants' decisions to deal with overcrowding in inner city schools, including the building and siting of new schools, building additions to existing schools, leasing or purchasing unused buildings for school purposes, utilizing substandard classrooms, changing district boundaries, and intact busing, "individually and in conjunction with each other had the effect of increasing racial imbalance." Armstrong v. O'Connell, 451 F.Supp. 817 (E.D.Wis. 1978). Together these actions formed a "pattern of boundary compression and facility expansion" which resulted in many instances in schools in contiguous districts being of one race or another. Armstrong, at 859. Thus, defendants' unlawful conduct increased the racial identifiability of schools. Moreover, the intentional concentration of black teachers in those schools attended by large numbers of black children perpetuated the racial identifiability of schools. Similarly, defendants' transfer policies facilitated a much more rapid transition in school racial identifiability than would come about simply through neighborhood residential change.
F-13. A school, as a principal and visible neighborhood entity, often acts as the central identifying institution for a neighborhood. Within an otherwise undifferentiated residential area, school boundaries tend to be the most meaningful boundaries in defining a neighborhood. Thus, the racial identifiability of a school helps to racially identify the neighborhood. This racial identifiability, in conjunction with the message *1308 conveyed by defendants' unlawful conduct that contact between blacks and whites is to be avoided, had a substantial impact on the housing patterns in Milwaukee. It contributed to the drying up of the demand by whites for housing in areas which, in part as a result of defendants' wrongful acts, were racially earmarked as being for blacks. Similarly, defendants' conduct contributed to the black housing demand being channeled into the black residential areas of Milwaukee rather than being dispersed throughout the city.
F-14. Dayton Board of Education v. Brinkman, 433 U.S. 406, 420, 97 S.Ct. 2766, 2775, 53 L.Ed.2d 851 (1977), requires the Court to consider, as part of its "present effects" determination, what the "school population as presently constituted * * would have been in the absence of such [defendants'] constitutional violations." The record in this case demonstrates that the Milwaukee public school system would have been substantially less segregated in 1975-76 had defendants not engaged in the intentionally segregative conduct found by the Court in its June 1, 1978, decision. Milwaukee would have had substantially less housing segregation in 1975 and, as a result, substantially less school segregation had defendants administered the school system in a racially neutral manner.
F-15. Had defendants assigned teachers in a racially neutral manner and administered the rest of the system in such a manner, many more white students throughout the system would have had first-hand experiences with both black and white teachers. The school system, by example, would have taught these white students and white Milwaukeeans generally that blacks and whites were equally capable of educational attainment, of handling major responsibilities, and of working together harmoniously; black students and black Milwaukeeans generally would have been taught the same lesson and would have had the example of the school system practicing equal rights and ignoring racial prejudices. Schools would not have been racially identifiable on the basis of the racial composition of their staffs. There is a substantial probability that fewer Milwaukeeans would have engaged in discriminatory housing practices and that more would have sought out and resided in racially mixed residential areas.
F-16. Had defendants assigned teachers in a racially neutral manner, more black teachers would have been dispersed throughout the system. There is a substantial probability that some of the black teachers who would have been assigned to white schools outside the inner city would have chosen to live closer to their assigned school and to enroll their children in that school; that they would have demonstrated that blacks could be good neighbors; and that, as a result of this interracial contact, which defendants by their conduct discouraged, whites would have accepted other black families as their neighbors. Black demand for housing, therefore, would have been dispersed throughout the city rather than concentrated in one area.
F-17. Had defendants mixed bused students rather than intact bused students from majority black schools to majority white schools, thousands of black and white students would have had meaningful interracial contact. Social psychological evidence in the record indicates that persons who have had meaningful interracial experiences in school as children are more likely to seek out and live in integrated residential areas as adults. Moreover, had mixed busing been employed, Milwaukee public school busing practices would not have been perceived by the community as a device to protect white students from attending school with black students on an equal basis. Had defendants engaged in a racially neutral busing practice and administered the rest of the system in a neutral manner, students and citizens of Milwaukee would have been given a lesson in racial tolerance rather than racial intolerance. There is a substantial probability that more citizens would have sought racially mixed housing. Furthermore, many of the white and black students are now young adults. They are renting or buying homes and deciding where to send their own children to school. Had these students had meaningful interracial *1309 contact, facilitated by mixed busing, there is a substantial probability that many more of them would seek out racially mixed rather than racially isolated residential areas.
F-18. Had defendants operated a racially neutral student transfer program and administered the rest of the system in a racially neutral manner, there is a substantial probability that housing in Milwaukee would have been less segregated; that there would have been fewer white transfers out of schools with increasing black student populations; that neighborhoods would not have been as identifiable and considered as no longer suitable for whites; and that the white demand for housing in those areas would not have dried up. Had there been a majority to minority transfer plan or some type of neutral transfer program, black parents seeking interracial education for their children would have been better able to secure it. These parents would have acquired a whole different set of attitudes that affect housing choices and, therefore, they would have made different housing choices.
F-19. Had defendants engaged in neutral policies relating to school siting, construction and boundary changes, and operated the rest of the system neutrally, schools would have been less racially identifiable. More students and parents would have been exposed to interracial education. There is a substantial probability that a greater number of Milwaukeeans would have chosen to live in interracial neighborhoods, and the development of the solid black ghetto would have been diminished.
L-2. Defendants' discriminatory conduct conveyed a clear message to the entire Milwaukee community that a governmental institution was intentionally protecting white students from attending schools with large numbers of black students and from being taught by black teachers. Milwaukeeans were taught lessons of racial prejudice and hostility which molded and reinforced prejudicial attitudes. These attitudes influenced the housing decisions of black and white Milwaukeeans. Had the defendants operated the school system in a racially neutral manner, Milwaukeeans would have received a different message  that a governmental institution was approving treatment of blacks and whites on an equal basis. Defendants, by direct example, would have taught Milwaukeeans lessons of racial tolerance and acceptance which would have formed and reinforced positive racial attitudes. There is a substantial probability that more Milwaukeeans would have made housing choices which would have resulted in much greater housing desegregation and, in turn, much greater school desegregation. Thus, defendants' constitutional violations had an incremental segregative effect throughout the school system.
L-3. In order to redress the pervasive, systemwide impact of defendants' constitutional violations, a systemwide remedy encompassing both student population and teacher assignment is required.
L-4. Defendants contend that since plaintiffs were unable to prove with precision what the racial make-up of each school in the system would be in 1975-76 had defendants' constitutional violations not occurred, plaintiffs are not entitled to this remedy. Unfortunately, it is true that the overriding effect which defendants' unlawful conduct had on housing patterns makes it impossible to determine with precision how each school in the system would have looked had defendants not violated plaintiffs' constitutional rights. No court in any school case will ever be able to determine with statistical precision "where people would have lived, where schools would have been located [or] how much integration would have been obtained" in the absence of officially imposed discrimination. United States v. Columbus Separate School District, 558 F.2d 228, 231 n. 11 (5th Cir. 1977), cert. denied 434 U.S. 1013, 98 S.Ct. 728, 54 L.Ed.2d 757 (1978), and Booker v. Special School District No. 1, Minneapolis, Minnesota, 451 F.Supp. 659, 663 n. 5 (D.Minn.1978).
In this case the special master previously reported:

*1310 "* * * It may be that we have no way of knowing what the Milwaukee Public School system would look like today had the defendants not violated the plaintiffs' constitutional rights. I would submit, however, that the defendants should not be permitted to profit from their wrongdoing by using such uncertainty as the basis for resisting imposition of an appropriate remedy." (Special Master's Progress Report and Recommendations, February 17, 1977, at 10.)
This view is jurisprudentially sound. Indeed, it is an accepted principle of law that a wrongdoer cannot invoke the complexity of his wrong to avoid answering for it. For example, in antitrust law the very success of a violation may make it impossible to compute damages as, for instance, when a monopolist drives a competitor out of business. The violator's success, however, is not a reason for allowing him to retain the fruits of his misdeeds. Zenith Radio Corp. v. Hazeltine Research, Inc., 395 U.S. 100, 123-125, 89 S.Ct. 1562, 23 L.Ed.2d 129 (1969). The violator must accept, as part of the cost of his violation, the fact that the remedy may be less precise than would be necessary in a world of perfect information. In any event, Dayton cannot be read to require the mathematical precision requested by defendants. Booker, supra, 451 F.Supp. at 663 n. 5. Moreover, since defendants have not themselves proven that the present segregated condition of the Milwaukee public school system would not have been the same even absent their constitutional violations, see Keyes v. School District No. 1, Denver, Colorado, 413 U.S. 189, 211, 93 S.Ct. 2686, 37 L.Ed.2d 548 (1973), this court, sitting as a court of equity, cannot be "so callous as to accept the contention that although vestiges of de jure discrimination pervade to this day, it is helpless to fashion a remedy to root them out." Evans v. Buchanan, 582 F.2d 750, 766 (3d Cir. 1978) (en banc).
The Court will require the plaintiffs to prepare a proposed remedial plan designed to cure the present effects of the defendants' past constitutional violations. The defendants will have an opportunity to comment on the plan or to submit their own plan, and a hearing on the plan(s) will be held at the end of March 1979, as hereafter set forth:

ORDER
For the foregoing reasons,
IT IS ORDERED that this decision shall constitute the findings of fact and conclusions of law made pursuant to the remand of this action from the United States Court of Appeals for the Seventh Circuit on the issue of the present effects of the defendants' past constitutional violations.
IT IS FURTHER ORDERED that the parties shall observe the following scheduling dates:
1. On or before February 23, 1979, the plaintiffs shall serve and file a proposed remedial plan designed to cure the present effects, as found in this decision and order, of the defendants' past constitutional violations.
2. On or before March 9, 1979, the defendants shall serve and file their comments, if any, on the plaintiffs' proposed remedial plan or, if they choose, an alternative plan.
3. On or before March 16, 1979, the plaintiffs shall serve and file their response, if any, to the defendants' comments, or their comments on the defendants' plan.
4. A hearing on the proposed remedial plan(s) is scheduled for 9:30 A.M. on Friday, March 23, 1979, in Courtroom 425 of the Federal Building, 517 East Wisconsin Avenue, Milwaukee.
NOTES
[1]  See, e. g., Brinkman v. Gilligan, 583 F.2d 243 (6th Cir. 1978), cert. granted ___ U.S. ___, 99 S.Ct. 831, 59 L.Ed.2d 31 (1979); Penick v. Columbus Board of Education, 583 F.2d 787 (6th Cir. 1978), cert. granted ___ U.S. ___, 99 S.Ct. 831, 59 L.Ed.2d 31, (1979); Evans v. Buchanan, 582 F.2d 750 (3d Cir. 1978); United States v. Texas Education Agency, 579 F.2d 910 (5th Cir. 1978) (en banc); Arthur v. Nyquist, 573 F.2d 134 (2d Cir. 1978); United States v. School District of Omaha, 565 F.2d 127 (8th Cir. 1977) (en banc); Booker v. Special School District No. 1, Minneapolis, Minnesota, 451 F.Supp. 659 (D.Minn.1978); Berry v. School District of Benton Harbor, 442 F.Supp. 1280 (W.D.Mich.1977).
[2]  The Court has adapted its findings of fact and conclusions of law from the plaintiffs' proposed findings of fact and conclusions of law filed December 8, 1978, with such minor additions and deletions as the Court has considered proper.
