5.3: Kyllo v. United States 533 U.S. 27 (2001)
OCTOBER TERM, 2000
Syllabus
KYLLO v. UNITED STATES
CERTIORARI TO THE UNITED STATES COURT OF APPEALS FOR THE NINTH CIRCUIT
No. 99-8508. Argued February 20, 200l-Decided June 11,2001
Suspicious that marijuana was being grown in petitioner Kyllo’s home in a triplex, agents used a thermal-imaging device to scan the triplex to determine if the amount of heat emanating from it was consistent with the high-intensity lamps typically used for indoor marijuana growth. The scan showed that Kyllo’s garage roof and a side wall were relatively hot compared to the rest of his home and substantially warmer than the neighboring units. Based in part on the thermal imaging, a Federal Magistrate Judge issued a warrant to search Kyllo’s home, where the agents found marijuana growing. After Kyllo was indicted on a federal drug charge, he unsuccessfully moved to suppress the evidence seized from his home and then entered a conditional guilty plea. The Ninth Circuit ultimately affirmed, upholding the thermal imaging on the ground that Kyllo had shown no subjective expectation of privacy because he had made no attempt to conceal the heat escaping from his home. Even if he had, ruled the court, there was no objectively reasonable expectation of privacy because the thermal imager did not expose any intimate details of Kyllo’s life, only amorphous hot spots on his home’s exterior.
Held: Where, as here, the Government uses a device that is not in general public use, to explore details of a private home that would previously have been unknowable without physical intrusion, the surveillance is a Fourth Amendment “search,” and is presumptively unreasonable without a warrant. Pp. 31-41.
(a) The question whether a warrantless search of a home is reasonable and hence constitutional must be answered no in most instances, but the antecedent question whether a Fourth Amendment “search” has occurred is not so simple. This Court has approved warrantless visual surveillance of a home, see California v. Ciraolo, 476 U. S. 207 , 213, ruling that visual observation is no “search” at all, see Dow Chemical Co. v. United States, 476 U. S. 227 , 234-235, 239. In assessing when a search is not a search, the Court has adapted a principle first enunciated in Katz v. United States, 389 U. S. 347 , 361: A “search” does not occur-even when its object is a house explicitly protected by the Fourth Amendment-unless the individual manifested a subjective
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Syllabus
expectation of privacy in the searched object, and society is willing to recognize that expectation as reasonable, see, e. g., California v. Ciraolo, supra, at 211. Pp. 31-33.
(b) While it may be difficult to refine the Katz test in some instances, in the case of the search of a home’s interior-the prototypical and hence most commonly litigated area of protected privacy-there is a ready criterion, with roots deep in the common law, of the minimal expectation of privacy that exists, and that is acknowledged to be reasonable. To withdraw protection of this minimum expectation would be to permit police technology to erode the privacy guaranteed by the Fourth Amendment. Thus, obtaining by sense-enhancing technology any information regarding the home’s interior that could not otherwise have been obtained without physical “intrusion into a constitutionally protected area,” Silverman v. United States, 365 U. S. 505 , 512, constitutes a search-at least where (as here) the technology in question is not in general public use. This assures preservation of that degree of privacy against government that existed when the Fourth Amendment was adopted. Pp. 33-35.
(c) Based on this criterion, the information obtained by the thermal imager in this case was the product of a search. The Court rejects the Government’s argument that the thermal imaging must be upheld because it detected only heat radiating from the home’s external surface. Such a mechanical interpretation of the Fourth Amendment was rejected in Katz, where the eavesdropping device in question picked up only sound waves that reached the exterior of the phone booth to which it was attached. Reversing that approach would leave the homeowner at the mercy of advancing technology-including imaging technology that could discern all human activity in the home. Also rejected is the Government’s contention that the thermal imaging was constitutional because it did not detect “intimate details.” Such an approach would be wrong in principle because, in the sanctity of the home, all details are intimate details. See, e. g., United States v. Karo, 468 U. S. 705; Dow Chemical, supra, at 238, distinguished. It would also be impractical in application, failing to provide a workable accommodation between law enforcement needs and Fourth Amendment interests. See Oliver v. United States, 466 U. S. 170 , 181. Pp. 35-40.
(d) Since the imaging in this case was an unlawful search, it will remain for the District Court to determine whether, without the evidence it provided, the search warrant was supported by probable cause-and if not, whether there is any other basis for supporting admission of that evidence. P. 40.
190 F.3d 1041 , reversed and remanded.
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SCALIA, J., delivered the opinion of the Court, in which SOUTER, THOMAS, GINSBURG, and BREYER, JJ., joined. STEVENS, J., filed a dissenting opinion, in which REHNQUIST, C. J., and O’CONNOR and KENNEDY, JJ., joined, post, p. 41.
Kenneth Lerner, by appointment of the Court, 531 U. S. 955, argued the cause and filed briefs for petitioner.
Deputy Solicitor General Dreeben argued the cause for the United States. With him on the brief were former Solicitor General Waxman, Assistant Attorney General Robinson, Irving L. Gornstein, and Deborah Watson. *
JUSTICE SCALIA delivered the opinion of the Court.
This case presents the question whether the use of a thermal-imaging device aimed at a private home from a public street to detect relative amounts of heat within the home constitutes a “search” within the meaning of the Fourth Amendment.
I
In 1991 Agent William Elliott of the United States Department of the Interior came to suspect that marijuana was being grown in the home belonging to petitioner Danny Kyllo, part of a triplex on Rhododendron Drive in Florence, Oregon. Indoor marijuana growth typically requires highintensity lamps. In order to determine whether an amount of heat was emanating from petitioner’s home consistent with the use of such lamps, at 3:20 a.m. on January 16, 1992, Agent Elliott and Dan Haas used an Agema Thermovision 210 thermal imager to scan the triplex. Thermal imagers detect infrared radiation, which virtually all objects emit but which is not visible to the naked eye. The imager converts radiation into images based on relative warmth-black
*Briefs of amici curiae urging reversal were filed for the Liberty Project by Julie M. Carpenter; and for the National Association of Criminal Defense Lawyers et al. by James J. Tomkovicz, Lisa B. Kemler, and Steven R. Shapiro.
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is cool, white is hot, shades of gray connote relative differences; in that respect, it operates somewhat like a video camera showing heat images. The scan of Kyllo’s home took only a few minutes and was performed from the passenger seat of Agent Elliott’s vehicle across the street from the front of the house and also from the street in back of the house. The scan showed that the roof over the garage and a side wall of petitioner’s home were relatively hot compared to the rest of the home and substantially warmer than neighboring homes in the triplex. Agent Elliott concluded that petitioner was using halide lights to grow marijuana in his house, which indeed he was. Based on tips from informants, utility bills, and the thermal imaging, a Federal Magistrate Judge issued a warrant authorizing a search of petitioner’s home, and the agents found an indoor growing operation involving more than 100 plants. Petitioner was indicted on one count of manufacturing marijuana, in violation of 21 U. s. C. § 841(a)(1). He unsuccessfully moved to suppress the evidence seized from his home and then entered a conditional guilty plea.
The Court of Appeals for the Ninth Circuit remanded the case for an evidentiary hearing regarding the intrusiveness of thermal imaging. On remand the District Court found that the Agema 210 “is a non-intrusive device which emits no rays or beams and shows a crude visual image of the heat being radiated from the outside of the house”; it “did not show any people or activity within the walls of the structure”; “[t]he device used cannot penetrate walls or windows to reveal conversations or human activities”; and “[n]o intimate details of the home were observed.” Supp. App. to Pet. for Cert. 39-40. Based on these findings, the District Court upheld the validity of the warrant that relied in part upon the thermal imaging, and reaffirmed its denial of the motion to suppress. A divided Court of Appeals initially reversed, 140 F.3d 1249 (1998), but that
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opinion was withdrawn and the panel (after a change in composition) affirmed, 190 F.3d 1041 (1999), with Judge Noonan dissenting. The court held that petitioner had shown no subjective expectation of privacy because he had made no attempt to conceal the heat escaping from his home, id., at 1046, and even if he had, there was no objectively reasonable expectation of privacy because the imager “did not expose any intimate details of Kyllo’s life,” only “amorphous ‘hot spots’ on the roof and exterior wall,” id., at 1047. We granted certiorari. 530 U. S. 1305 (2000).
II
The Fourth Amendment provides that “[t]he right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated.” “At the very core” of the Fourth Amendment “stands the right of a man to retreat into his own home and there be free from unreasonable governmental intrusion.” Silverman v. United States, 365 U. S. 505 , 511 (1961). With few exceptions, the question whether a warrantless search of a home is reasonable and hence constitutional must be answered no. See Illinois v. Rodriguez, 497 U. S. 177 , 181 (1990); Payton v. New York, 445 U. S. 573 , 586 (1980).
On the other hand, the antecedent question whether or not a Fourth Amendment “search” has occurred is not so simple under our precedent. The permissibility of ordinary visual surveillance of a home used to be clear because, well into the 20th century, our Fourth Amendment jurisprudence was tied to common-law trespass. See, e. g., Goldman v. United States, 316 U. S. 129 , 134-136 (1942); Olmstead v. United States, 277 U. S. 438 , 464-466 (1928). Cf. Silverman v. United States, supra, at 510-512 (technical trespass not necessary for Fourth Amendment violation; it suffices if there is “actual intrusion into a constitutionally protected area”). Visual surveillance was unquestionably lawful because” ‘the
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eye cannot by the laws of England be guilty of a trespass.'” Boyd v. United States, 116 U. S. 616 , 628 (1886) (quoting Entick v. Carrington, 19 How. St. Tr. 1029, 95 Eng. Rep. 807 (K. B. 1765)). We have since decoupled violation of a person’s Fourth Amendment rights from trespassory violation of his property, see Rakas v. III inois, 439 U. S. 128 , 143 (1978), but the lawfulness of warrantless visual surveillance of a home has still been preserved. As we observed in California v. Ciraolo, 476 U. S. 207 , 213 (1986), “[t]he Fourth Amendment protection of the home has never been extended to require law enforcement officers to shield their eyes when passing by a home on public thoroughfares.”
One might think that the new validating rationale would be that examining the portion of a house that is in plain public view, while it is a “search” 1 despite the absence of trespass, is not an “unreasonable” one under the Fourth Amendment. See Minnesota v. Carter, 525 U. S. 83 , 104 (1998) (BREYER, J., concurring in judgment). But in fact we have held that visual observation is no “search” at allperhaps in order to preserve somewhat more intact our doctrine that warrantless searches are presumptively unconstitutional. See Dow Chemical Co. v. United States, 476 U. S. 227, 234-235, 239 (1986). In assessing when a search is not a search, we have applied somewhat in reverse the principle first enunciated in Katz v. United States, 389 U. S. 347 (1967). Katz involved eavesdropping by means of an electronic listening device placed on the outside of a telephone booth-a location not within the catalog (“persons, houses, papers, and effects”) that the Fourth Amendment protects against unreasonable searches. We held that the
1 When the Fourth Amendment was adopted, as now, to “search” meant “[tJo look over or through for the purpose of finding something; to explore; to examine by inspection; as, to search the house for a book; to search the wood for a thief.” N. Webster, An American Dictionary of the English Language 66 (1828) (reprint 6th ed. 1989).
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Fourth Amendment nonetheless protected Katz from the warrantless eavesdropping because he “justifiably relied” upon the privacy of the telephone booth. Id., at 353. As Justice Harlan’s oft-quoted concurrence described it, a Fourth Amendment search occurs when the government violates a subjective expectation of privacy that society recognizes as reasonable. See id., at 361. We have subsequently applied this principle to hold that a Fourth Amendment search does not occur-even when the explicitly protected location of a house is concerned-unless “the individual manifested a subjective expectation of privacy in the object of the challenged search,” and “society [is] willing to recognize that expectation as reasonable.” Ciraolo, supra, at 211. We have applied this test in holding that it is not a search for the police to use a pen register at the phone company to determine what numbers were dialed in a private home, Smith v. Maryland, 442 U. S. 735 , 743744 (1979), and we have applied the test on two different occasions in holding that aerial surveillance of private homes and surrounding areas does not constitute a search, Ciraolo, supra; Florida v. Riley, 488 U. S. 445 (1989).
The present case involves officers on a public street engaged in more than naked-eye surveillance of a home. We have previously reserved judgment as to how much technological enhancement of ordinary perception from such a vantage point, if any, is too much. While we upheld enhanced aerial photography of an industrial complex in Dow Chemical, we noted that we found “it important that this is not an area immediately adjacent to a private home, where privacy expectations are most heightened,” 476 U. S., at 237, n. 4 (emphasis in original).
III
It would be foolish to contend that the degree of privacy secured to citizens by the Fourth Amendment has been
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entirely unaffected by the advance of technology. For example, as the cases discussed above make clear, the technology enabling human flight has exposed to public view (and hence, we have said, to official observation) uncovered portions of the house and its curtilage that once were private. See Ciraolo, supra, at 215. The question we confront today is what limits there are upon this power of technology to shrink the realm of guaranteed privacy.
The Katz test-whether the individual has an expectation of privacy that society is prepared to recognize as reasonable-has often been criticized as circular, and hence subjective and unpredictable. See 1 W. LaFave, Search and Seizure § 2.1(d), pp. 393-394 (3d ed. 1996); Posner, The Uncertain Protection of Privacy by the Supreme Court, 1979 S. Ct. Rev. 173, 188; Carter, supra, at 97 (SCALIA, J., concurring). But see Rakas, supra, at 143-144, n.12. While it may be difficult to refine Katz when the search of areas such as telephone booths, automobiles, or even the curtilage and uncovered portions of residences is at issue, in the case of the search of the interior of homes-the prototypical and hence most commonly litigated area of protected privacythere is a ready criterion, with roots deep in the common law, of the minimal expectation of privacy that exists, and that is acknowledged to be reasonable. To withdraw protection of this minimum expectation would be to permit police technology to erode the privacy guaranteed by the Fourth Amendment. We think that obtaining by senseenhancing technology any information regarding the interior of the home that could not otherwise have been obtained without physical “intrusion into a constitutionally protected area,” Silverman, 365 U. S., at 512, constitutes a searchat least where (as here) the technology in question is not in general public use. This assures preservation of that degree of privacy against government that existed when the Fourth Amendment was adopted. On the basis of this criterion, the
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information obtained by the thermal imager in this case was the product of a search.2
The Government maintains, however, that the thermal imaging must be upheld because it detected “only heat radiating from the external surface of the house,” Brief for United States 26. The dissent makes this its leading point, see post, at 41, contending that there is a fundamental difference between what it calls “off-the-wall” observations and “through-the-wall surveillance.” But just as a thermal imager captures only heat emanating from a house, so also a powerful directional microphone picks up only sound emanating from a house-and a satellite capable of scanning from many miles away would pick up only visible light emanating from a house. We rejected such a mechanical interpretation of the Fourth Amendment in Katz, where the eavesdropping device picked up only sound waves that reached the exterior of the phone booth. Reversing that approach would leave the homeowner at the mercy of advancing technologyincluding imaging technology that could discern all human
2 The dissent’s repeated assertion that the thermal imaging did not obtain information regarding the interior of the home, post, at 43, 44 (opinion of STEVENS, J.), is simply inaccurate. A thermal imager reveals the relative heat of various rooms in the home. The dissent may not find that information particularly private or important, see post, at 43-44, 45, 4950, but there is no basis for saying it is not information regarding the interior of the home. The dissent’s comparison of the thermal imaging to various circumstances in which outside observers might be able to perceive, without technology, the heat of the home-for example, by observing snowmelt on the roof, post, at 43-is quite irrelevant. The fact that equivalent information could sometimes be obtained by other means does not make lawful the use of means that violate the Fourth Amendment. The police might, for example, learn how many people are in a particular house by setting up year-round surveillance; but that does not make breaking and entering to find out the same information lawful. In any event, on the night of January 16, 1992, no outside observer could have discerned the relative heat of Kyllo’s home without thermal imaging.
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activity in the home. While the technology used in the present case was relatively crude, the rule we adopt must take account of more sophisticated systems that are already in use or in development.3 The dissent’s reliance on the distinction between “off-the-wall” and “through-the-wall” observation is entirely incompatible with the dissent’s belief, which we discuss below, that thermal-imaging observations of the intimate details of a home are impermissible. The most sophisticated thermal-imaging devices continue to measure heat “off-the-wall” rather than “through-the-wall”; the dissent’s disapproval of those more sophisticated thermalimaging devices, see post, at 49, is an acknowledgment that there is no substance to this distinction. As for the dissent’s extraordinary assertion that anything learned through “an inference” cannot be a search, see post, at 44, that would validate even the “through-the-wall” technologies that the dissent purports to disapprove. Surely the dissent does not believe that the through-the-wall radar or ultrasound technology produces an 8-by-10 Kodak glossy that needs no analysis (i. e., the making of inferences). And, of course, the novel proposition that inference insulates a search is blatantly contrary to United States v. Karo, 468 U. S. 705 (1984), where the police “inferred” from the activation of a beeper that a certain can of ether was in the home. The police ac-
3 The ability to “see” through walls and other opaque barriers is a clear, and scientifically feasible, goal of law enforcement research and development. The National Law Enforcement and Corrections Technology Center, a program within the United States Department of Justice, features on its Internet Website projects that include a “RadarBased Through-the-Wall Surveillance System,” “Handheld Ultrasound Through the Wall Surveillance,” and a “Radar Flashlight” that “will enable law enforcement officers to detect individuals through interior building walls.” www.nlectc.org/techproj/ (visited May 3, 2001). Some devices may emit low levels of radiation that travel “through-the-wall,” but others, such as more sophisticated thermal-imaging devices, are entirely passive, or “off-the-wall” as the dissent puts it.
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tivity was held to be a search, and the search was held unlawfu1.4
The Government also contends that the thermal imaging was constitutional because it did not “detect private activities occurring in private areas,” Brief for United States 22. It points out that in Dow Chemical we observed that the enhanced aerial photography did not reveal any “intimate details.” 476 U. S., at 238. Dow Chemical, however, involved enhanced aerial photography of an industrial complex, which does not share the Fourth Amendment sanctity of the home. The Fourth Amendment’s protection of the home has never been tied to measurement of the quality or quantity of information obtained. In Silverman, for example, we made clear that any physical invasion of the structure of the home, “by even a fraction of an inch,” was too much, 365 U. S., at 512, and there is certainly no exception to the warrant requirement for the officer who barely cracks open the front door and sees nothing but the nonintimate rug on the vestibule floor. In the home, our cases show, all details are intimate details, because the entire area is held safe from prying government eyes. Thus, in Karo, supra, the only thing detected was a can of ether in the
4 The dissent asserts, post, at 44-45, n. 3, that we have misunderstood its point, which is not that inference insulates a search, but that inference alone is not a search. If we misunderstood the point, it was only in a good-faith effort to render the point germane to the case at hand. The issue in this case is not the police’s allegedly unlawful inferencing, but their allegedly unlawful thermal-imaging measurement of the emanations from a house. We say such measurement is a search; the dissent says it is not, because an inference is not a search. We took that to mean that, since the technologically enhanced emanations had to be the basis of inferences before anything inside the house could be known, the use of the emanations could not be a search. But the dissent certainly knows better than we what it intends. And if it means only that an inference is not a search, we certainly agree. That has no bearing, however, upon whether hi-tech measurement of emanations from a house is a search.
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home; and in Arizona v. Hicks, 480 U. S. 321 (1987), the only thing detected by a physical search that went beyond what officers lawfully present could observe in “plain view” was the registration number of a phonograph turntable. These were intimate details because they were details of the home, just as was the detail of how warm-or even how relatively warm-Kyllo was heating his residence.5
Limiting the prohibition of thermal imaging to “intimate details” would not only be wrong in principle; it would be impractical in application, failing to provide “a workable accommodation between the needs of law enforcement and the interests protected by the Fourth Amendment,” Oliver v. United States, 466 U. S. 170 , 181 (1984). To begin with, there is no necessary connection between the sophistication of the surveillance equipment and the “intimacy” of the details that it observes-which means that one cannot say (and the police cannot be assured) that use of the relatively crude equipment at issue here will always be lawful. The Agema Thermovision 210 might disclose, for example, at what hour each night the lady of the house takes her daily sauna and bath-a detail that many would consider “intimate”; and a much more sophisticated system might detect nothing more intimate than the fact that someone left a closet light on. We could not, in other words, develop a rule approving only that through-the-wall surveillance which identifies objects no smaller than 36 by 36 inches, but would have to develop a jurisprudence specifying which
5The Government cites our statement in California v. Ciraolo, 476 U. S. 207 (1986), noting apparent agreement with the State of California that aerial surveillance of a house’s curtilage could become “‘invasive'” if “‘modern technology'” revealed “‘those intimate associations, objects or activities otherwise imperceptible to police or fellow citizens.'” Id., at 215, n. 3 (quoting Brief for State of California 14-15). We think the Court’s focus in this secondhand dictum was not upon intimacy but upon otherwise-imperceptibility, which is precisely the principle we vindicate today.
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home activities are “intimate” and which are not. And even when (if ever) that jurisprudence were fully developed, no police officer would be able to know in advance whether his through-the-wall surveillance picks up “intimate” detailsand thus would be unable to know in advance whether it is constitutional.
The dissent’s proposed standard-whether the technology offers the “functional equivalent of actual presence in the area being searched,” post, at 47-would seem quite similar to our own at first blush. The dissent concludes that Katz was such a case, but then inexplicably asserts that if the same listening device only revealed the volume of the conversation, the surveillance would be permissible, post, at 49-50. Yet if, without technology, the police could not discern volume without being actually present in the phone booth, JUSTICE STEVENS should conclude a search has occurred. Cf. Karo, 468 U. S., at 735 (STEVENS, J., concurring in part and dissenting in part) (“I find little comfort in the Court’s notion that no invasion of privacy occurs until a listener obtains some significant information by use of the device …. A bathtub is a less private area when the plumber is present even if his back is turned”). The same should hold for the interior heat of the home if only a person present in the home could discern the heat. Thus the driving force of the dissent, despite its recitation of the above standard, appears to be a distinction among different types of information-whether the “homeowner would even care if anybody noticed,” post, at 50. The dissent offers no practical guidance for the application of this standard, and for reasons already discussed, we believe there can be none. The people in their houses, as well as the police, deserve more precision.6
6 The dissent argues that we have injected potential uncertainty into the constitutional analysis by noting that whether or not the technology is in general public use may be a factor. See post, at 47. That quarrel,
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We have said that the Fourth Amendment draws “a firm line at the entrance to the house,” Payton, 445 U. S., at 590. That line, we think, must be not only firm but also brightwhich requires clear specification of those methods of surveillance that require a warrant. While it is certainly possible to conclude from the videotape of the thermal imaging that occurred in this case that no “significant” compromise of the homeowner’s privacy has occurred, we must take the long view, from the original meaning of the Fourth Amendment forward.
“The Fourth Amendment is to be construed in the light of what was deemed an unreasonable search and seizure when it was adopted, and in a manner which will conserve public interests as well as the interests and rights of individual citizens.” Carroll v. United States, 267 U. S. 132, 149 (1925).
Where, as here, the Government uses a device that is not in general public use, to explore details of the home that would previously have been unknowable without physical intrusion, the surveillance is a “search” and is presumptively unreasonable without a warrant.
Since we hold the Thermovision imaging to have been an unlawful search, it will remain for the District Court to determine whether, without the evidence it provided, the search warrant issued in this case was supported by probable cause-and if not, whether there is any other basis for supporting admission of the evidence that the search pursuant to the warrant produced.
however, is not with us but with this Court’s precedent. See Ciraolo, supra, at 215 (“In an age where private and commercial flight in the public airways is routine, it is unreasonable for respondent to expect that his marijuana plants were constitutionally protected from being observed with the naked eye from an altitude of 1,000 feet”). Given that we can quite confidently say that thermal imaging is not “routine,” we decline in this case to reexamine that factor.
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***
The judgment of the Court of Appeals is reversed; the case is remanded for further proceedings consistent with this opinion.
It is so ordered.
JUSTICE STEVENS, with whom THE CHIEF JUSTICE, JusTICE O’CONNOR, and JUSTICE KENNEDY join, dissenting.
There is, in my judgment, a distinction of constitutional magnitude between “through-the-wall surveillance” that gives the observer or listener direct access to information in a private area, on the one hand, and the thought processes used to draw inferences from information in the public domain, on the other hand. The Court has crafted a rule that purports to deal with direct observations of the inside of the home, but the case before us merely involves indirect deductions from “off-the-wall” surveillance, that is, observations of the exterior of the home. Those observations were made with a fairly primitive thermal imager that gathered data exposed on the outside of petitioner’s home but did not invade any constitutionally protected interest in privacy.l Moreover, I believe that the supposedly “bright-line” rule the Court has created in response to its concerns about future technological developments is unnecessary, unwise, and inconsistent with the Fourth Amendment.
I
There is no need for the Court to craft a new rule to decide this case, as it is controlled by established principles from
1 After an evidentiary hearing, the District Court found:
“[T]he use of the thermal imaging device here was not an intrusion into Kyllo’s home. No intimate details of the home were observed, and there was no intrusion upon the privacy of the individuals within the home. The device used cannot penetrate walls or windows to reveal conversations or human activities. The device recorded only the heat being emitted from the home.” Supp. App. to Pet. for Cert. 40.
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our Fourth Amendment jurisprudence. One of those core principles, of course, is that “searches and seizures inside a home without a warrant are presumptively unreasonable.” Payton v. New York, 445 U. S. 573 , 586 (1980) (emphasis added). But it is equally well settled that searches and seizures of property in plain view are presumptively reasonable. See id., at 586-587.2 Whether that property is residential or commercial, the basic principle is the same: “‘What a person knowingly exposes to the public, even in his own home or office, is not a subject of Fourth Amendment protection.'” California v. Ciraolo, 476 U. S. 207 , 213 (1986) (quoting Katz v. United States, 389 U. S. 347 , 351 (1967)); see Florida v. Riley, 488 U. S. 445 , 449-450 (1989); California v. Greenwood, 486 U. S. 35 , 40-41 (1988); Dow Chemical Co. v. United States, 476 U. S. 227 , 235-236 (1986); Air Pollution Variance Bd. of Colo. v. Western Alfalfa Corp., 416 U. S. 861 , 865 (1974). That is the principle implicated here.
While the Court “take[s] the long view” and decides this case based largely on the potential of yet-to-be-developed technology that might allow “through-the-wall surveillance,” ante, at 38-40; see ante, at 36, n. 3, this case involves nothing more than off-the-wall surveillance by law enforcement officers to gather information exposed to the general public from the outside of petitioner’s home. All that the infrared camera did in this case was passively measure heat emitted
2 Thus, for example, we have found consistent with the Fourth Amendment, even absent a warrant, the search and seizure of garbage left for collection outside the curtilage of a home, California v. Greenwood, 486 U. S. 35 (1988); the aerial surveillance of a fenced-in backyard from an altitude of 1,000 feet, California v. Ciraolo, 476 U. S. 207 (1986); the aerial observation of a partially exposed interior of a residential greenhouse from 400 feet above, Florida v. Riley, 488 U. S. 445 (1989); the aerial photography of an industrial complex from several thousand feet above, Dow Chemical Co. v. United States, 476 U. S. 227 (1986); and the observation of smoke emanating from chimney stacks, Air Pollution Variance Bd. of Colo. v. Western Alfalfa Corp., 416 U. S. 861 (1974).
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from the exterior surfaces of petitioner’s home; all that those measurements showed were relative differences in emission levels, vaguely indicating that some areas of the roof and outside walls were warmer than others. As still images from the infrared scans show, see Appendix, infra, no details regarding the interior of petitioner’s home were revealed. Unlike an x-ray scan, or other possible “throughthe-wall” techniques, the detection of infrared radiation emanating from the home did not accomplish “an unauthorized physical penetration into the premises,” Silverman v. United States, 365 U. S. 505 , 509 (1961), nor did it “obtain information that it could not have obtained by observation from outside the curtilage of the house,” United States v. Karo, 468 U. S. 705 , 715 (1984).
Indeed, the ordinary use of the senses might enable a neighbor or passerby to notice the heat emanating from a building, particularly if it is vented, as was the case here. Additionally, any member of the public might notice that one part of a house is warmer than another part or a nearby building if, for example, rainwater evaporates or snow melts at different rates across its surfaces. Such use of the senses would not convert into an unreasonable search if, instead, an adjoining neighbor allowed an officer onto her property to verify her perceptions with a sensitive thermometer. Nor, in my view, does such observation become an unreasonable search if made from a distance with the aid of a device that merely discloses that the exterior of one house, or one area of the house, is much warmer than another. Nothing more occurred in this case.
Thus, the notion that heat emissions from the outside of a dwelling are a private matter implicating the protections of the Fourth Amendment (the text of which guarantees the right of people “to be secure in their … houses” against unreasonable searches and seizures (emphasis added)) is not only unprecedented but also quite difficult to take seriously. Heat waves, like aromas that are generated in a kitchen, or
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in a laboratory or opium den, enter the public domain if and when they leave a building. A subjective expectation that they would remain private is not only implausible but also surely not “one that society is prepared to recognize as ‘reasonable.'” Katz, 389 U. S., at 361 (Harlan, J., concurring).
To be sure, the homeowner has a reasonable expectation of privacy concerning what takes place within the home, and the Fourth Amendment’s protection against physical invasions of the home should apply to their functional equivalent. But the equipment in this case did not penetrate the walls of petitioner’s home, and while it did pick up “details of the home” that were exposed to the public, ante, at 38, it did not obtain “any information regarding the interior of the home,” ante, at 34 (emphasis added). In the Court’s own words, based on what the thermal imager “showed” regarding the outside of petitioner’s home, the officers “concluded” that petitioner was engaging in illegal activity inside the home. Ante, at 30. It would be quite absurd to characterize their thought processes as “searches,” regardless of whether they inferred (rightly) that petitioner was growing marijuana in his house, or (wrongly) that “the lady of the house [was taking] her daily sauna and bath.” Ante, at 38. In either case, the only conclusions the officers reached concerning the interior of the home were at least as indirect as those that might have been inferred from the contents of discarded garbage, see California v. Greenwood, 486 U. S. 35 (1988), or pen register data, see Smith v. Maryland, 442 U. S. 735 (1979), or, as in this case, subpoenaed utility records, see 190 F.3d 1041 , 1043 (CA9 1999). For the first time in its history, the Court assumes that an inference can amount to a Fourth Amendment violation. See ante, at 36-37.3
3 Although the Court credits us with the “novel proposition that inference insulates a search,” ante, at 36, our point simply is that an inference cannot be a search, contrary to the Court’s reasoning. See supra this page. Thus, the Court’s use of United States v. Karo, 468 U. S. 705
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Notwithstanding the implications of today’s decision, there is a strong public interest in avoiding constitutional litigation over the monitoring of emissions from homes, and over the inferences drawn from such monitoring. Just as “the police cannot reasonably be expected to avert their eyes from evidence of criminal activity that could have been observed by any member of the public,” Greenwood, 486 U. S., at 41, so too public officials should not have to avert their senses or their equipment from detecting emissions in the public domain such as excessive heat, traces of smoke, suspicious odors, odorless gases, airborne particulates, or radioactive emissions, any of which could identify hazards to the community. In my judgment, monitoring such emissions with “sense-enhancing technology,” ante, at 34, and drawing useful conclusions from such monitoring, is an entirely reasonable public service.
On the other hand, the countervailing privacy interest is at best trivial. After all, homes generally are insulated to keep heat in, rather than to prevent the detection of heat going out, and it does not seem to me that society will suffer from a rule requiring the rare homeowner who both intends to engage in uncommon activities that produce extraordinary amounts of heat, and wishes to conceal that production from outsiders, to make sure that the surrounding area is well insulated. Cf. United States v. Jacobsen, 466 U. S. 109 , 122 (1984) (“The concept of an interest in privacy that society is prepared to recognize as reasonable is, by its very nature, critically different from the mere expectation, however well
(1984), to refute a point we do not make underscores the fact that the Court has no real answer (either in logic or in law) to the point we do make. Of course, Karo itself does not provide any support for the Court’s view that inferences can amount to unconstitutional searches. The illegality in that case was “the monitoring of a beeper in a private residence” to obtain information that “could not have [been] obtained by observation from outside,” id., at 714-715, rather than any thought processes that flowed from such monitoring.
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justified, that certain facts will not come to the attention of the authorities”). The interest in concealing the heat escaping from one’s house pales in significance to “the chief evil against which the wording of the Fourth Amendment is directed,” the “physical entry of the home,” United States v. United States Dist. Court for Eastern Dist. of Mich., 407 U. S. 297, 313 (1972), and it is hard to believe that it is an interest the Framers sought to protect in our Constitution.
Since what was involved in this case was nothing more than drawing inferences from off-the-wall surveillance, rather than any “through-the-wall” surveillance, the officers’ conduct did not amount to a search and was perfectly reasonable.4
II
Instead of trying to answer the question whether the use of the thermal imager in this case was even arguably unreasonable, the Court has fashioned a rule that is intended to provide essential guidance for the day when “more sophisticated systems” gain the “ability to ‘see’ through walls and other opaque barriers.” Ante, at 36, and n. 3. The newly minted rule encompasses “obtaining [1] by senseenhancing technology [2] any information regarding the interior of the home [3] that could not otherwise have been obtained without physical intrusion into a constitutionally protected area … [4] at least where (as here) the technology in question is not in general public use.” Ante, at 34 (internal quotation marks omitted). In my judgment, the
4 This view comports with that of all the Courts of Appeals that have resolved the issue. See 190 F.3d 1041 (CA9 1999); United States v. Robinson, 62 F.3d 1325 (CAll 1995) (upholding warrantless use of thermal imager); United States v. Myers, 46 F.3d 668 (CA7 1995) (same); United States v. Ishmael, 48 F.3d 850 (CA5 1995) (same); United States v. Pinson, 24 F.3d 1056 (CA8 1994) (same). But see United States v. Cusumano, 67 F.3d 1497 (CAW 1995) (warrantless use of thermal imager violated Fourth Amendment), vacated and decided on other grounds, 83 F.3d 1247 (CAW 1996) (en bane).
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Court’s new rule is at once too broad and too narrow, and is not justified by the Court’s explanation for its adoption. As I have suggested, I would not erect a constitutional impediment to the use of sense-enhancing technology unless it provides its user with the functional equivalent of actual presence in the area being searched.
Despite the Court’s attempt to draw a line that is “not only firm but also bright,” ante, at 40, the contours of its new rule are uncertain because its protection apparently dissipates as soon as the relevant technology is “in general public use,” ante, at 34. Yet how much use is general public use is not even hinted at by the Court’s opinion, which makes the somewhat doubtful assumption that the thermal imager used in this case does not satisfy that criterion.5 In any event, putting aside its lack of clarity, this criterion is somewhat perverse because it seems likely that the threat to privacy will grow, rather than recede, as the use of intrusive equipment becomes more readily available.
It is clear, however, that the category of “sense-enhancing technology” covered by the new rule, ibid., is far too broad. It would, for example, embrace potential mechanical substitutes for dogs trained to react when they sniff narcotics. But in United States v. Place, 462 U. S. 696 , 707 (1983), we held that a dog sniff that “discloses only the presence or absence of narcotics” does “not constitute a ‘search’ within the meaning of the Fourth Amendment,” and it must follow that sense-enhancing equipment that identifies nothing but illegal
5 The record describes a device that numbers close to a thousand manufactured units; that has a predecessor numbering in the neighborhood of 4,000 to 5,000 units; that competes with a similar product numbering from 5,000 to 6,000 units; and that is “readily available to the public” for commercial, personal, or law enforcement purposes, and is just an 800number away from being rented from “half a dozen national companies” by anyone who wants one. App. 18. Since, by virtue of the Court’s new rule, the issue is one of first impression, perhaps it should order an evidentiary hearing to determine whether these facts suffice to establish “general public use.”
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activity is not a search either. Nevertheless, the use of such a device would be unconstitutional under the Court’s rule, as would the use of other new devices that might detect the odor of deadly bacteria or chemicals for making a new type of high explosive, even if the devices (like the dog sniffs) are “so limited both in the manner in which” they obtain information and “in the content of the information” they reveal. Ibid. If nothing more than that sort of information could be obtained by using the devices in a public place to monitor emissions from a house, then their use would be no more objectionable than the use of the thermal imager in this case.
The application of the Court’s new rule to “any information regarding the interior of the home,” ante, at 34, is also unnecessarily broad. If it takes sensitive equipment to detect an odor that identifies criminal conduct and nothing else, the fact that the odor emanates from the interior of a home should not provide it with constitutional protection. See supra, at 47 and this page. The criterion, moreover, is too sweeping in that information “regarding” the interior of a home apparently is not just information obtained through its walls, but also information concerning the outside of the building that could lead to (however many) inferences “regarding” what might be inside. Under that expansive view, I suppose, an officer using an infrared camera to observe a man silently entering the side door of a house at night carrying a pizza might conclude that its interior is now occupied by someone who likes pizza, and by doing so the officer would be guilty of conducting an unconstitutional “search” of the home.
Because the new rule applies to information regarding the “interior” of the home, it is too narrow as well as too broad. Clearly, a rule that is designed to protect individuals from the overly intrusive use of sense-enhancing equipment should not be limited to a home. If such equipment
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did provide its user with the functional equivalent of access to a private place-such as, for example, the telephone booth involved in Katz, or an office building-then the rule should apply to such an area as well as to a home. See Katz, 389 U. S., at 351 (“[T]he Fourth Amendment protects people, not places”).
The final requirement of the Court’s new rule, that the information “could not otherwise have been obtained without physical intrusion into a constitutionally protected area,” ante, at 34 (internal quotation marks omitted), also extends too far as the Court applies it. As noted, the Court effectively treats the mental process of analyzing data obtained from external sources as the equivalent of a physical intrusion into the home. See supra, at 44. As I have explained, however, the process of drawing inferences from data in the public domain should not be characterized as a search.
The two reasons advanced by the Court as justifications for the adoption of its new rule are both unpersuasive. First, the Court suggests that its rule is compelled by our holding in Katz, because in that case, as in this, the surveillance consisted of nothing more than the monitoring of waves emanating from a private area into the public domain. See ante, at 35. Yet there are critical differences between the cases. In Katz, the electronic listening device attached to the outside of the phone booth allowed the officers to pick up the content of the conversation inside the booth, making them the functional equivalent of intruders because they gathered information that was otherwise available only to someone inside the private area; it would be as if, in this case, the thermal imager presented a view of the heat-generating activity inside petitioner’s home. By contrast, the thermal imager here disclosed only the relative amounts of heat radiating from the house; it would be as if, in Katz, the listening device disclosed only the rela-
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tive volume of sound leaving the booth, which presumably was discernible in the public domain.6 Surely, there is a significant difference between the general and well-settled expectation that strangers will not have direct access to the contents of private communications, on the one hand, and the rather theoretical expectation that an occasional homeowner would even care if anybody noticed the relative amounts of heat emanating from the walls of his house, on the other. It is pure hyperbole for the Court to suggest that refusing to extend the holding of Katz to this case would leave the homeowner at the mercy of “technology that could discern all human activity in the home.” Ante, at 35-36.
Second, the Court argues that the permissibility of “through-the-wall surveillance” cannot depend on a distinction between observing “intimate details” such as “the lady of the house [taking] her daily sauna and bath,” and noticing only “the nonintimate rug on the vestibule floor” or “objects no smaller than 36 by 36 inches.” Ante, at 37, 3839. This entire argument assumes, of course, that the thermal imager in this case could or did perform “through-thewall surveillance” that could identify any detail “that would previously have been unknowable without physical intrusion.” Ante, at 39-40. In fact, the device could not, see n. 1, supra, and did not, see Appendix, infra, enable its user to identify either the lady of the house, the rug on the vestibule floor, or anything else inside the house, whether smaller or larger than 36 by 36 inches. Indeed, the vague thermal images of petitioner’s home that are reproduced in the Appendix were submitted by him to the District Court as part of an expert report raising the question whether the device could even take “accurate, consistent infrared images” of the
6 The use of the latter device would be constitutional given Smith v.
Maryland, 442 U. S. 735 , 741 (1979), which upheld the use of pen registers to record numbers dialed on a phone because, unlike “the listening device employed in Katz … pen registers do not acquire the contents of communications.”
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outside of his house. Defendant’s Exh. 107, p. 4. But even if the device could reliably show extraordinary differences in the amounts of heat leaving his home, drawing the inference that there was something suspicious occurring inside the residence-a conclusion that officers far less gifted than Sherlock Holmes would readily draw-does not qualify as “through-the-wall surveillance,” much less a Fourth Amendment violation.
III
Although the Court is properly and commendably concerned about the threats to privacy that may flow from advances in the technology available to the law enforcement profession, it has unfortunately failed to heed the tried and true counsel of judicial restraint. Instead of concentrating on the rather mundane issue that is actually presented by the case before it, the Court has endeavored to craft an all-encompassing rule for the future. It would be far wiser to give legislators an unimpeded opportunity to grapple with these emerging issues rather than to shackle them with prematurely devised constitutional constraints.
I respectfully dissent.
[Appendix to opinion of STEVENS, J., follows this page.]
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Appendix to opinion of STEVENS, J.
APPENDIX TO OPINION OF STEVENS, J. (Images and text reproduced from defendant’s exhibit 107) Top left: Infrared image of a video frame from the videotape submitted as evidence in this case. The thermogram indicates the suspect house as it appeared with the Gain and contrast in its default setting. Only the outline of the house is visible. The camera used was the Thermovision 210. Top Right: Infrared image of a subsequent videoframe taken from the videotape. The gain and contrast settings have been increased in order to make the walls and roof of the structure appear hotter than what it actually is.
Bottom Left: Infrared image of the opposite side of the suspects house. The thermogram is also taken from the same videotape. The camera settings are in the default mode and the outline of the house is barely visible. Only the hot electrical transformer and the street light are identifiable.
Bottom Right: The same image, but with the gain and contrast increased. This change in camera settings cause any object to appear hotter than what it actually is. The arrow indicates the overloading of an area immediately around a hot object in this case the electrical transformer and the streetlight. This overloading of the image is an inherent design flaw in the camera itself.
Contributors and Attributions
- Authored by : US Government. Located at : https://supreme.justia.com/cases/federal/us/533/27/case.html . License : Public Domain: No Known Copyright


6.8: The Matrix of a Linear Transformation II
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Outcomes
- Find the matrix of a linear transformation with respect to general bases.
We begin this section with an important lemma.
Lemma \(\PageIndex{1}\): Mapping of a Basis
Let \(T: \mathbb{R}^n \mapsto \mathbb{R}^n\) be an isomorphism. Then \(T\) maps any basis of \(\mathbb{R}^n\) to another basis for \(\mathbb{R}^n\).
Conversely, if \(T: \mathbb{R}^n \mapsto \mathbb{R}^n\) is a linear transformation which maps a basis of \(\mathbb{R}^n\) to another basis of \(\mathbb{R}^n\), then it is an isomorphism.
- Proof
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First, suppose \(T:\mathbb{R}^n \mapsto \mathbb{R}^n\) is a linear transformation which is one to one and onto. Let \(\left\{ \vec{v}_{1},\cdots ,\vec{v}_{n}\right\}\) be a basis for \(\mathbb{R}^n\). We wish to show that \(\left\{ T(\vec{v}_{1}),\cdots , T(\vec{v}_{n})\right\}\) is also a basis for \(\mathbb{R}^n\).
First consider why it is linearly independent. Suppose \(\sum_{k=1}^{n}a_{k}T(\vec{v}_{k})=\vec{0}\). Then by linearity we have \(T\left( \sum_{k=1}^{n}a_{k}\vec{v}_{k}\right) =\vec{0}\) and since \(T\) is one to one, it follows that \(\sum_{k=1}^{n}a_{k}\vec{v}_{k}=\vec{0}\). This requires that each \(a_{k}=0\) because \(\left\{ \vec{v}_{1},\cdots, \vec{v}_{n}\right\}\) is independent, and it follows that \(\left\{ T(\vec{v}_{1}),\cdots , T(\vec{v}_{n})\right\}\) is linearly independent.
Next take \(\vec{w}\in \mathbb{R}^n.\) Since \(T\) is onto, there exists \(\vec{v}\in \mathbb{R}^n\) such that \(T(\vec{v})=\vec{w}\). Since \(\left\{ \vec{v}_{1},\cdots ,\vec{v}_{n}\right\}\) is a basis, in particular it is a spanning set and there are scalars \(b_{k}\) such that \(T\left( \sum_{k=1}^{n}b_{k}\vec{v} _{k}\right) =T\left( \vec{v}\right) =\vec{w}\). Therefore \(\vec{w} =\sum_{k=1}^{n}b_{k}T(\vec{v}_{k})\) which is in the \(\mathrm{span}\left\{ T(\vec{v}_{1}),\cdots , T(\vec{v}_{n})\right\} .\) Therefore, \(\left\{ T(\vec{v}_{1}),\cdots ,T(\vec{v}_{n}) \right\}\) is a basis as claimed.
Suppose now that \(T: \mathbb{R}^n \mapsto \mathbb{R}^n\) is a linear transformation such that \(T(\vec{v}_{i})=\vec{w}_{i}\) where \(\left\{\vec{v} _{1},\cdots ,\vec{v}_{n}\right\}\) and \(\left\{ \vec{w}_{1},\cdots , \vec{w}_{n}\right\}\) are two bases for \(\mathbb{R}^n\).
To show that \(T\) is one to one, let \(T\left( \sum_{k=1}^{n}c_{k}\vec{v}_{k}\right) =\vec{0}\). Then \(\sum_{k=1}^{n}c_{k}T(\vec{v}_{k})=\sum_{k=1}^{n}c_{k}\vec{w}_{k}=\vec{ 0}\). It follows that each \(c_{k} = 0\) because it is given that \(\left\{ \vec{w} _{1},\cdots ,\vec{w}_{n}\right\}\) is linearly independent. Hence \(T\left( \sum_{k=1}^{n}c_{k}\vec{v}_{k}\right) =\vec{0}\) implies that \(\sum_{k=1}^{n}c_{k}\vec{v}_{k}=\vec{0}\) and so \(T\) is one to one.
To show that \(T\) is onto, let \(\vec{w}\) be an arbitrary vector in \(\mathbb{R}^n\). This vector can be written as \(\vec{w} = \sum_{k=1}^{n}d_k\vec{w}_k = \sum_{k=1}^{n}d_{k}T(\vec{v}_{k})=T\left( \sum_{k=1}^{n}d_{k} \vec{v}_{k}\right) .\) Therefore, \(T\) is also onto.
Consider now an important definition.
Definition \(\PageIndex{1}\) : Coordinate Vector
Let \(B = \left\{ \vec{v}_1, \vec{v}_2, \cdots, \vec{v}_n \right\}\) be a basis for \(\mathbb{R}^n\) and let \(\vec{x}\) be an arbitrary vector in \(\mathbb{R}^n\). Then \(\vec{x}\) is uniquely represented as \(\vec{x} = a_1\vec{v}_1 + a_2\vec{v}_2 + \cdots + a_n\vec{v}_n\) for scalars \(a_1, \cdots, a_n\).
The coordinate vector of \(\vec{x}\) with respect to the basis \(B\), written \(C_B(\vec{x})\) or \([\vec{x}]_B\), is given by \[C_B(\vec{x}) = C_B \left( a_1\vec{v}_1 + a_2\vec{v}_2 + \cdots + a_n\vec{v}_n \right) = \left [ \begin{array}{c} a_1 \\ a_2 \\ \vdots \\ a_n \end{array} \right ]\nonumber \]
Consider the following example.
Example \(\PageIndex{1}\): Coordinate Vector
Let \(B = \left\{ \left [ \begin{array}{r} 1 \\ 0 \end{array} \right ], \left [ \begin{array}{r} -1 \\ 1 \end{array} \right ] \right\}\) be a basis of \(\mathbb{R}^2\) and let \(\vec{x} = \left [ \begin{array}{r} 3 \\ -1 \end{array} \right ]\) be a vector in \(\mathbb{R}^2\). Find \(C_B(\vec{x})\).
Solution
First, note the order of the basis is important so label the vectors in the basis \(B\) as \[B = \left\{ \left [ \begin{array}{r} 1 \\ 0 \end{array} \right ], \left [ \begin{array}{r} -1 \\ 1 \end{array} \right ] \right\} = \left\{ \vec{v}_1, \vec{v}_2 \right\}\nonumber \] Now we need to find \(a_1, a_2\) such that \(\vec{x} = a_1 \vec{v}_1 + a_2 \vec{v}_2\), that is: \[\left [ \begin{array}{r} 3 \\ -1 \end{array} \right ] = a_1 \left [ \begin{array}{r} 1 \\ 0 \end{array} \right ] + a_2 \left [ \begin{array}{r} -1 \\ 1 \end{array} \right ]\nonumber \] Solving this system gives \(a_1 = 2, a_2 = -1\). Therefore the coordinate vector of \(\vec{x}\) with respect to the basis \(B\) is \[C_B(\vec{x}) = \left [ \begin{array}{r} a_1 \\ a_2 \end{array}\right ] = \left [ \begin{array}{r} 2 \\ -1 \end{array} \right ]\nonumber \]
Given any basis \(B\), one can easily verify that the coordinate function is actually an isomorphism.
We now discuss the main result of this section, that is how to represent a linear transformation with respect to different bases.
Theorem \(\PageIndex{2}\): The Matrix of a Linear
Let \(T: \mathbb{R}^n \mapsto \mathbb{R}^m\) be a linear transformation, and let \(B_1\) and \(B_2\) be bases of \(\mathbb{R}^{n}\) and \(\mathbb{R}^{m}\) respectively.
Then the following holds \[C_{B_2} T = M_{B_{2} B_{1}} C_{B_1} \label{matrixequation}\] where \(M_{B_{2} B_{1}}\) is a unique \(m \times n\) matrix.
If the basis \(B_1\) is given by \(B_1=\{ \vec{v}_1, \cdots, \vec{v}_n \}\) in this order, then \[M_{B_{2} B_{1}} = \left [ C_{B_2}(T(\vec{v}_1)) \; C_{B_2}(T(\vec{v}_2)) \; \cdots C_{B_2}(T(\vec{v}_n)) \right ]\nonumber \]
- Proof
-
The above equation \(\eqref{matrixequation}\) can be represented by the following diagram. \[\begin{array}{rrcll} & & T & & \\ & \mathbb{R}^n & \rightarrow & \mathbb{R}^m & \\ & C_{B_{1} }\downarrow & \circ & \downarrow C_{B_{2} } & \\ & \mathbb{R}^{n} & \rightarrow & \mathbb{R}^{m} & \\ & & M_{B_{2} B_{1} } & & \end{array}\nonumber \]
Since \(C_{B_1}\) is an isomorphism, then the matrix we are looking for is the matrix of the linear transformation \[C_{B_2} T C^{-1}_{B_1} : \mathbb{R}^n \mapsto \mathbb{R}^m.\nonumber \] By Theorem 5.2.2 , the columns are given by the image of the standard basis \(\left\{ \vec{e}_1, \vec{e}_2, \cdots, \vec{e}_n \right\}\). But since \(C^{-1}_{B_1}( \vec{e}_i) = \vec{v}_i\), we readily obtain that \[\begin{array}{ll} M_{B_{2} B_{1}} & = \left [ C_{B_2}T C^{-1}_{B_1} (\vec{e}_1) \;\; C_{B_2}T C^{-1}_{B_1} (\vec{2}_2) \;\; \cdots \;\; C_{B_2}T C^{-1}_{B_1} (\vec{e}_n) \right ] \\ & = \left [ C_{B_2}(T(\vec{v}_1)) \;\; C_{B_2}(T(\vec{v}_2)) \;\; \cdots \;\; C_{B_2}(T(\vec{v}_n)) \right ] \end{array}\nonumber \] and this completes the proof.
Consider the following example.
Example \(\PageIndex{2}\): Matrix of a Linear
Let \(T: \mathbb{R}^2 \mapsto \mathbb{R}^2\) be a linear transformation defined by \(T \left( \left [ \begin{array}{r} a \\ b \end{array} \right ] \right) = \left [ \begin{array}{r} b \\ a \end{array} \right ]\).
Consider the two bases \[B_1 = \left\{ \vec{v}_{1}, \vec{v}_{2} \right\} = \left\{ \left [ \begin{array}{r} 1 \\ 0 \end{array}\right ], \left [ \begin{array}{r} -1 \\ 1 \end{array} \right ] \right\}\nonumber \] and \[B_2 = \left\{ \left [ \begin{array}{r} 1 \\ 1 \end{array} \right ], \left [ \begin{array}{r} 1 \\ -1 \end{array} \right ] \right\}\nonumber \]
Find the matrix \(M_{B_2,B_1}\) of \(T\) with respect to the bases \(B_1\) and \(B_2\).
Solution
By Theorem \(\PageIndex{2}\) , the columns of \(M_{B_{2} B_{1}}\) are the coordinate vectors of \(T(\vec{v}_{1}), T(\vec{v}_{2})\) with respect to \(B_2\).
Since \[T \left( \left [ \begin{array}{r} 1 \\ 0 \end{array}\right ] \right) = \left [ \begin{array}{r} 0 \\ 1 \end{array}\right ] ,\nonumber \] a standard calculation yields \[\left [ \begin{array}{r} 0 \\ 1 \end{array}\right ] = \left(\frac{1}{2} \right)\left [ \begin{array}{r} 1 \\ 1 \end{array} \right ] + \left(-\frac{1}{2} \right) \left [ \begin{array}{r} 1 \\ -1 \end{array} \right ],\nonumber \] the first column of \(M_{B_{2} B_{1}}\) is \(\left [ \begin{array}{r} \frac{1}{2}\\ -\frac{1}{2} \end{array}\right ]\).
The second column is found in a similar way. We have \[T \left( \left [ \begin{array}{r} -1 \\ 1 \end{array} \right ] \right) = \left [ \begin{array}{r} 1 \\ -1 \end{array}\right ] ,\nonumber \] and with respect to \(B_2\) calculate: \[\left [ \begin{array}{r} 1 \\ -1 \end{array}\right ] = 0 \left [ \begin{array}{r} 1 \\ 1 \end{array} \right ] + 1 \left [ \begin{array}{r} 1 \\ -1 \end{array} \right ]\nonumber \] Hence the second column of \(M_{B_{2} B_{1}}\) is given by \(\left [ \begin{array}{r} 0 \\ 1 \end{array} \right ]\). We thus obtain \[M_{B_{2} B_{1}} = \left [ \begin{array}{rr} \frac{1}{2} & 0 \\ -\frac{1}{2} & 1 \end{array} \right ]\nonumber \]
We can verify that this is the correct matrix \(M_{B_{2} B_{1}}\) on the specific example \[\vec{v} = \left [ \begin{array}{r} 3 \\ -1 \end{array} \right ]\nonumber \] First applying \(T\) gives \[T( \vec{v} ) = T \left( \left [ \begin{array}{r} 3 \\ -1 \end{array} \right ] \right) = \left [ \begin{array}{r} -1\\ 3 \end{array} \right ]\nonumber \] and one can compute that \[C_{B_2} \left( \left [ \begin{array}{r} -1 \\ 3 \end{array} \right ] \right) = \left [ \begin{array}{r} 1\\ -2 \end{array} \right ] .\nonumber \]
On the other hand, one compute \(C_{B_1}( \vec{v})\) as \[C_{B_1} \left( \left [ \begin{array}{r} 3 \\ -1 \end{array} \right ] \right) = \left [ \begin{array}{r} 2\\ -1 \end{array} \right ] ,\nonumber \] and finally applying \(M_{B_1 B_2}\) gives \[\left [ \begin{array}{rr} \frac{1}{2} & 0 \\ -\frac{1}{2} & 1 \end{array} \right ] \left [ \begin{array}{r} 2 \\ -1 \end{array}\right ] = \left [ \begin{array}{r} 1 \\ -2 \end{array} \right ]\nonumber \] as above.
We see that the same vector results from either method, as suggested by Theorem \(\PageIndex{2}\) .
If the bases \(B_1\) and \(B_2\) are equal, say \(B\), then we write \(M_{B}\) instead of \(M_{B B}\). The following example illustrates how to compute such a matrix. Note that this is what we did earlier when we considered only \(B_1=B_2\) to be the standard basis.
Example \(\PageIndex{3}\): Matrix of a Linear Transformation with respect to an Arbitrary
Consider the basis \(B\) of \(\mathbb{R}^3\) given by \[B = \{\vec{v}_1 , \vec{v}_2, \vec{v}_3 \} = \left\{ \left [ \begin{array}{r} 1 \\ 0 \\ 1 \end{array} \right ] ,\left [ \begin{array}{r} 1 \\ 1 \\ 1 \end{array} \right ] ,\left [ \begin{array}{r} -1 \\ 1 \\ 0 \end{array} \right ] \right\}\nonumber \] And let \(T :\mathbb{R}^{3}\mapsto \mathbb{R}^{3}\) be the linear transformation defined on \(B\) as: \[T\left [ \begin{array}{r} 1 \\ 0 \\ 1 \end{array} \right ] =\left [ \begin{array}{r} 1 \\ -1 \\ 1 \end{array} \right ] ,T \left [ \begin{array}{c} 1 \\ 1 \\ 1 \end{array} \right ] =\left [ \begin{array}{r} 1 \\ 2 \\ -1 \end{array} \right ] ,T\left [ \begin{array}{r} -1 \\ 1 \\ 0 \end{array} \right ] =\left [ \begin{array}{r} 0 \\ 1 \\ 1 \end{array} \right ]\nonumber \]
- Find the matrix \(M_{B}\) of \(T\) relative to the basis \(B\).
- Then find the usual matrix of \(T\) with respect to the standard basis of \(\mathbb{R}^{3}\).
Solution
Equation \(\eqref{matrixequation}\) gives \(C_BT=M_{B}C_B\), and thus \(M_{B} = C_BTC^{-1}_B\).
Now \(C_B(\vec{v}_i) = \vec{e}_i\), so the matrix of \(C_B^{-1}\) (with respect to the standard basis) is given by \[\left [ C_B^{-1}(\vec{e}_1) \;\; C_B^{-1}(\vec{e}_2) \;\; C_B^{-1}(\vec{e}_2) \right ] = \left [ \begin{array}{rrr} 1 & 1 & -1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{array} \right ]\nonumber \] Moreover the matrix of \(T C_B^{-1}\) is given by \[\left [ TC_B^{-1}(\vec{e}_1) \;\; TC_B^{-1}(\vec{e}_2) \;\; TC_B^{-1}(\vec{e}_2) \right ] = \left [ \begin{array}{rrr} 1 & 1 & 0 \\ -1 & 2 & 1 \\ 1 & -1 & 1 \end{array} \right ]\nonumber \] Thus \[\begin{array}{ll} M_{B} & = C_BTC^{-1}_B = [C^{-1}_B]^{-1} [TC^{-1}_B] \\ & = \left [ \begin{array}{rrr} 1 & 1 & -1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{array} \right ] ^{-1}\left [ \begin{array}{rrr} 1 & 1 & 0 \\ -1 & 2 & 1 \\ 1 & -1 & 1 \end{array} \right ] \\ &=\left [ \begin{array}{rrr} 2 & -5 & 1 \\ -1 & 4 & 0 \\ 0 & -2 & 1 \end{array} \right ] \end{array}\nonumber \]
Consider how this works. Let \(\vec{b} = \left [ \begin{array}{r} b_1 \\ b_2 \\ b_3 \end{array} \right ]\) be an arbitrary vector in \(\mathbb{R}^3\).
Apply \(C^{-1}_{B}\) to \(\vec{b}\) to get \[b_1\left [ \begin{array}{r} 1 \\ 0 \\ 1 \end{array} \right ] + b_2\left [ \begin{array}{r} 1 \\ 1 \\ 1 \end{array} \right ] + b_3\left [ \begin{array}{r} -1 \\ 1 \\ 0 \end{array} \right ]\nonumber \] Apply \(T\) to this linear combination to obtain \[b_1\left [ \begin{array}{r} 1 \\ -1 \\ 1 \end{array} \right ] + b_2\left [ \begin{array}{r} 1 \\ 2 \\ -1 \end{array} \right ] + b_3\left [ \begin{array}{r} 0 \\ 1 \\ 1 \end{array} \right ] =\left [ \begin{array}{c} b_1+b_2 \\ -b_1 + 2b_2+ b_3 \\ b_1-b_2+b_3 \end{array} \right ]\nonumber \] Now take the matrix \(M_{B}\) of the transformation (as found above) and multiply it by \(\vec{b}\). \[\left [ \begin{array}{rrr} 2 & -5 & 1 \\ -1 & 4 & 0 \\ 0 & -2 & 1 \end{array} \right ] \left [ \begin{array}{c} b_1 \\ b_2 \\ b_3 \end{array} \right ] =\left [ \begin{array}{c} 2b_1-5b_2+b_3 \\ -b_1 + 4b_2 \\ -2b_2 + b_3 \end{array} \right ]\nonumber \] Is this the coordinate vector of the above relative to the given basis? We check as follows. \[\left( 2b_1-5b_2+b_3\right) \left [ \begin{array}{c} 1 \\ 0 \\ 1 \end{array} \right ] +\left( -b_1 + 4b_2\right) \left [ \begin{array}{c} 1 \\ 1 \\ 1 \end{array} \right ] +\left( -2b_2+b_3\right) \left [ \begin{array}{c} -1 \\ 1 \\ 0 \end{array} \right ]\nonumber \] \[= \left [ \begin{array}{c} b_1+b_2 \\ -b_1 + 2b_2+b_3 \\ b_1-b_2+b_3 \end{array} \right ]\nonumber \] You see it is the same thing.
Now lets find the matrix of \(T\) with respect to the standard basis. Let \(A\) be this matrix. That is, multiplication by \(A\) is the same as doing \(T\). Thus \[A\left [ \begin{array}{rrr} 1 & 1 & -1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{array} \right ] =\left [ \begin{array}{rrr} 1 & 1 & 0 \\ -1 & 2 & 1 \\ 1 & -1 & 1 \end{array} \right ]\nonumber \] Hence \[A=\left [ \begin{array}{rrr} 1 & 1 & 0 \\ -1 & 2 & 1 \\ 1 & -1 & 1 \end{array} \right ] \left [ \begin{array}{rrr} 1 & 1 & -1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{array} \right ] ^{-1}=\left [ \begin{array}{rrr} 0 & 0 & 1 \\ 2 & 3 & -3 \\ -3 & -2 & 4 \end{array} \right ]\nonumber \] Of course this is a very different matrix than the matrix of the linear transformation with respect to the non standard basis.


3.2: Properties of Alkanes
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Objectives
After completing this section, you should be able to
- arrange a number of given straight-chain alkanes in order of increasing or decreasing boiling point or melting point.
- arrange a series of isomeric alkanes in order of increasing or decreasing boiling point.
- explain the difference in boiling points between a given number of alkanes.
Key Terms
Make certain that you can define, and use in context, the key term below.
- van der Waals force (also known as London Dispersion force)
Alkanes are not very reactive and have little biological activity; all alkanes are colorless and odorless non-polar compounds. The relative weak London dispersion forces of alkanes result in gaseous substances for short carbon chains, volatile liquids with densities around 0.7 g/mL for moderate carbon chains, and solids for long carbon chains. For molecules with the same functional groups, there is a direct relationship between the size and shape of molecules and the strength of the intermolecular forces (IMFs) causing the differences in the physical states.
Boiling Points
Table \(\PageIndex{1}\) describes some of the properties of some straight-chain alkanes. There is not a significant electronegativity difference between carbon and hydrogen, thus, there is not any significant bond polarity. The molecules themselves also have very little polarity. A totally symmetrical molecule like methane is completely non-polar, meaning that the only attractions between one molecule and its neighbors will be Van der Waals dispersion forces. These forces will be very small for a molecule like methane but will increase as the molecules get bigger. Therefore, the boiling points of the alkanes increase with molecular size.
For isomers, the more branched the chain, the lower the boiling point tends to be. Van der Waals dispersion forces are smaller for shorter molecules and only operate over very short distances between one molecule and its neighbors. It is more difficult for short, fat molecules (with lots of branching) to lie as close together as long, thin molecules.
The boiling points shown are for the "straight chain" isomers of which there is more than one. The first four alkanes are gases at room temperature, and solids do not begin to appear until about \(C_{17}H_{36}\), but this is imprecise because different isomers typically have different melting and boiling points. 3.2. 1
| Molecular Name | Formula | Melting Point (°C) | Boiling Point (°C) | Density (20°C)* | Physical State (at 20°C) |
|---|---|---|---|---|---|
| methane | CH 4 | –182 | –164 | 0.668 g/L | gas |
| ethane | C 2 H 6 | –183 | –89 | 1.265 g/L | gas |
| propane | C 3 H 8 | –190 | –42 | 1.867 g/L | gas |
| butane | C 4 H 10 | –138 | –1 | 2.493 g/L | gas |
| pentane | C 5 H 12 | –130 | 36 | 0.626 g/mL | liquid |
| hexane | C 6 H 14 | –95 | 69 | 0.659 g/mL | liquid |
| octane | C 8 H 18 | –57 | 125 | 0.703 g/mL | liquid |
| decane | C 10 H 22 | –30 | 174 | 0.730 g mL | liquid |
| *Note the change in units going from gases (grams per liter) to liquids (grams per milliliter). Gas densities are at 1 atm pressure. |
The boiling points for the "straight chain" isomers and isoalkanes isomers are shown to demonstrate that branching decreases the surfaces area, weakens the IMFs, and lowers the boiling point.
Example \(\PageIndex{1}\): Boiling Points of Alkanes
For example, the boiling points of the three isomers of \(C_5H_{12}\) are:
- pentane: 309.2 K
- 2-methylbutane: 301.0 K
- 2,2-dimethylpropane: 282.6 K
The slightly higher boiling points for the cycloalkanes are presumably because the molecules can get closer together because the ring structure makes them better able!
Exercise \(\PageIndex{1}\)
For each of the following pairs of compounds, select the substance which you expect to have the higher boiling point:
- octane and nonane.
- octane and 2,2,3,3-tetramethylbutane.
Solution
- nonane, since it has more atoms it will have greater IMF
- octane, since it is not branched, the molecules can pack closer together increasing IMF
Solubility
Alkanes are virtually insoluble in water, but dissolve in organic solvents. However, liquid alkanes are good solvents for many other non-ionic organic compounds.
Solubility in Water
When a molecular substance dissolves in water, the following must occur:
- break the intermolecular forces within the substance. In the case of the alkanes, these are the Van der Waals dispersion forces.
- break the intermolecular forces in the water so that the substance can fit between the water molecules. In water, the primary intermolecular attractions are hydrogen bonds.
Breaking either of these attractions requires energy, although the amount of energy to break the Van der Waals dispersion forces in something like methane is relatively negligible; this is not true of the hydrogen bonds in water.
As something of a simplification, a substance will dissolve if there is enough energy released when new bonds are made between the substance and the water to compensate for what is used in breaking the original attractions. The only new attractions between the alkane and the water molecules are Van der Waals forces. These forces do not release a sufficient amount of energy to compensate for the energy required to break the hydrogen bonds in water. The alkane does not dissolve.
This is a simplification because entropic effects are important when things dissolve.
Solubility in organic solvents
In most organic solvents, the primary forces of attraction between the solvent molecules are Van der Waals . Therefore, when an alkane dissolves in an organic solvent, the Van der Waals forces are broken and are replaced by new Van der Waals forces. The two processes more or less cancel each other out energetically; thus, there is no barrier to solubility.
Exercise \(\PageIndex{1}\)
For each of the following pairs of compounds, select the substance you expect to have the higher boiling point.
- octane and nonane.
- octane and 2,2,3,3‑tetramethylbutane.
- Answer
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Nonane will have a higher boiling point than octane, because it has a longer carbon chain than octane. Octane will have a higher boiling point than 2,2,3,3‑tetramethylbutane, because it branches less than 2,2,3,3‑tetramethylbutane, and therefore has a larger “surface area” and more van der Waals forces.
Note: The actual boiling points are:
- nonane, 150.8°C
- octane, 125.7°C
- 2,2,3,3‑tetramethylbutane, 106.5°C
Reactions of Alkanes
Alkanes undergo very few reactions. There are two important reactions that are still possible, combustion and halogenation. The halogenation reaction is very important in organic chemistry because it opens a gateway to further chemical reactions.
Combustion
Complete combustion (given sufficient oxygen) of any hydrocarbon produces carbon dioxide, water, and a significant amount of heat. Due to the exothermic nature of these combustion reactions, alkanes are commonly used as a fuel source (for example: propane for outdoor grills, butane for lighters). The hydrocarbons become harder to ignite as the molecules get bigger. This is because the larger molecules don't vaporize as easily. If the liquid is not very volatile, only those molecules on the surface can react with the oxygen. Larger molecules have greater Van der Waals attractions which makes it more difficult for them to break away from their neighbors and become a gas. An example combustion reaction is shown for propane:
\[ \ce{ C_3H_8 + O_2 -> 3CO_2 + 4H_2O + 2044 kJ/mol} \nonumber \]
Halogenation
Halogenation is the replacement of one or more hydrogen atoms in an organic compound by a halogen (fluorine, chlorine, bromine or iodine). Unlike the complex transformations of combustion, the halogenation of an alkane appears to be a simple substitution reaction in which a C-H bond is broken and a new C-X bond is formed.
Since only two covalent bonds are broken (C-H & Cl-Cl) and two covalent bonds are formed (C-Cl & H-Cl), this reaction seems to be an ideal case for mechanistic investigation and speculation. However, one complication is that all the hydrogen atoms of an alkane may undergo substitution, resulting in a mixture of products, as shown in the following unbalanced equation . The relative amounts of the various products depend on the proportion of the two reactants used. In the case of methane, a large excess of the hydrocarbon favors formation of methyl chloride as the chief product; whereas, an excess of chlorine favors formation of chloroform and carbon tetrachloride.
\[\ce{CH_4 + Cl_2 \rightarrow CH_3Cl + CH_2Cl + CHCl_3 + CCl_4 + HCl} \nonumber \]
Looking Closer: An Alkane Basis for Properties of Other Compounds
An understanding of the physical properties of alkanes is important since petroleum and natural gas and the many products derived from them—gasoline, bottled gas, solvents, plastics, and more—are composed primarily of alkanes. This understanding is also vital because it is the basis for describing the properties of other organic and biological compound families. For example, large portions of the structures of lipids consist of nonpolar alkyl groups. Lipids include the dietary fats and fat like compounds called phospholipids and sphingolipids that serve as structural components of living tissues. These compounds have both polar and nonpolar groups, enabling them to bridge the gap between water-soluble and water-insoluble phases. This characteristic is essential for the selective permeability of cell membranes.


2.1: Agents of Socialization
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- Rebecca Laff and Wendy Ruiz
- College of the Canyons
Socialization is the manner used to internalize the norms and ideas of a society, and helps maintain social and cultural continuity. It is the way children learn about and begin to understand the world they live in. This develops as children interact with various “agencies” in their lives. Some of the strongest agents of socialization are discussed below.
Family
Family is the first and most important agent of socialization. Mothers and fathers, siblings and grandparents, plus members of an extended family, all teach a child what he or she needs to know. For example, they show the child how to use objects (such as clothes, computers, eating utensils, books, bikes); how to relate to others (some as “family,” others as “friends,” still others as “strangers” or “teachers” or “neighbors”); and how the world works (what is “real” and what is “imagined”). As you are aware, either from your own experience as a child or from your role in helping to raise one, socialization includes teaching and learning about an unending array of objects and ideas.
Part of the reason we turn out much like our parents, for better or worse, is that our families are such an important part of our socialization process. When we are born, our primary caregivers are almost always one or both of our parents. For several years, we have more contact with them than with any other adults. Because this contact occurs in our most formative years, our parents’ interaction with us and the messages they teach us can have a profound impact throughout our lives.
Keep in mind, however, that families do not socialize children in a vacuum. Many social factors affect the way a family raises its children. For example, we can use our imagination to recognize that individual behaviors are affected by the historical period in which they take place. Sixty years ago, it would not have been considered especially strict for a father to hit his son with a wooden spoon or a belt if he misbehaved, but today that same action in some places might be considered child abuse.
Sociologists recognize that race, social class, religion, and other societal factors play an important role in family socialization. Families may socialize for obedience and conformity, judgment, creativity, and problem-solving, depending on the values they hold. Children may also be socialized to abide by gender norms, perceptions of race, and class-related behaviors.
In Sweden, for instance, stay-at-home fathers are an accepted part of the social landscape. A government policy provides subsidized time off work—480 days for families with newborns—with the option of the paid leave being shared between mothers and fathers. As one stay-at-home dad says, being home to take care of his baby son “is a real fatherly thing to do. I think that’s very masculine” (Associated Press 2011). Close to 90 percent of Swedish fathers use their paternity leave (about 340,000 dads); on average they take seven weeks per birth (The Economist, 2014). How do U.S. policies—and our society’s expected gender roles—compare? How will Swedish children raised this way be socialized to parental gender norms? How might that be different from parental gender norms in the United States?
Check-in Time!
What are your thoughts…. Should parents get the credit when their children turn out to be “good” kids and even go on to accomplish great things in life? Should they get the blame if their children turn out to be “bad”?
Understanding Racial Socialization
In a society that is still racially prejudiced, African American parents continue to find it necessary to teach their children about African American culture and to prepare them for the bias and discrimination they can expect to encounter. Scholars in sociology and other disciplines have studied this process of racial socialization. One of their most interesting findings is that African American parents differ in the degree of racial socialization they practice: some parents emphasize African American identity and racial prejudice to a considerable degree, while other parents mention these topics to their children only minimally. The reasons for these differences have remained unclear.
Sociologist Jason E. Shelton (2008) analyzed data from a national random sample of African Americans to determine these reasons, in what he called “one of the most comprehensive analyses to date of racial socialization strategies among African Americans” (p. 237). Among other questions, respondents were asked whether “in raising your children, have you done or told them things to help them know what it means to be Black.” They were also asked whether “there are any other things you’ve done or told your children to help them know how to get along with White people.”
In his major results, Shelton found that respondents were more likely to practice racial socialization if they were older, female, and living outside the South; if they perceived that racial discrimination was a growing problem and were members of civil rights or other organizations aimed at helping African Americans; and if they had higher incomes.
These results led Shelton to conclude that “African Americans are not a culturally monolithic group,” as they differ in “the parental lessons they impart to their children about race relations” (2008, p. 253). Further, the parents who do practice racial socialization “do so in order to demystify and empower their offspring to seize opportunities in the larger society” (p. 253).
Shelton’s study helps us to understand the factors accounting for differences in racial socialization by African American parents, and it also helps us understand that the parents who do attempt to make their children aware of U.S. race relations are merely trying, as most parents do, to help their children get ahead in life. By increasing our understanding of these matters, Shelton’s research has helped make a difference.
The ways in which our parents socialize us depend on many factors, two of the most important of which are our parents’ social class and our own biological sex. Melvin Kohn (1965, 1977) found that working-class and middle-class parents tend to socialize their children very differently. Kohn reasoned that working-class parents tend to hold factory and other jobs in which they have little autonomy and instead are told what to do and how to do it. In such jobs, obedience is an important value, lest the workers be punished for not doing their jobs correctly. Working-class parents, Kohn thought, should thus emphasize obedience and respect for authority as they raise their children, and they should favor spanking as a primary way of disciplining their kids when they disobey. In contrast, middle-class parents tend to hold white-collar jobs where autonomy and independent judgment are valued and workers get ahead by being creative. These parents should emphasize independence as they raise their children and should be less likely than working-class parents to spank their kids when they disobey.
If parents’ social class influences how they raise their children, it is also true that the sex of their children affects how they are socialized by their parents. Many studies find that parents raise their daughters and sons quite differently as they interact with them from birth. Parents help their girls learn how to act and think “like girls,” and they help their boys learn how to act and think “like boys.” That is, they help their daughters and sons learn their gender (Wood, 2009). For example, they are gentler with their daughters and rougher with their sons.  Girls may be made of “sugar and spice and everything nice” and boys something quite different, but their parents help them greatly, for better or worse, turn out that way. To the extent this is true, our gender stems much more from socialization than from biological differences between the sexes, or so many sociologists assume. If theorist Carol Gilligan is right that boys and girls reach moral judgments differently, perhaps socialization matters more than biology for how they reach these judgments.
Peers
When you were a 16-year-old, how many times did you complain to your parent(s), “All of my friends are [doing so and so]. Why can’t I? It isn’t fair!” As this all-too-common example indicates, our friends play a very important role in our lives. This is especially true during adolescence, when peers influence our tastes in music, clothes, and so many other aspects of our lives, as the now-common image of the teenager always on a cell phone reminds us. But friends are important during other parts of the life course as well. We rely on them for fun, for emotional comfort and support, and for companionship. That is the upside of friendships.
The downside of friendships is called peer pressure , with which you are undoubtedly familiar. Suppose it is Friday night, and you are studying for a big exam on Monday. Your friends come by and ask you to go with them to get a pizza and a drink. You would probably agree to go with them, partly because you really dislike studying on a Friday night, but also because there is at least some subtle pressure on you to do so. As this example indicates, our friends can influence us in many ways. During adolescence, their interests can affect our own interests in film, music, and other aspects of popular culture. More ominously, adolescent peer influences have been implicated in underage drinking, drug use, delinquency, and hate crimes (Agnew, 2007).
After we reach our 20s and 30s, our peers become less important in our lives, especially if we get married. Yet even then our peers do not lose all their importance, as parents with young children still manage to get out with friends now and then. Scholars have also begun to emphasize the importance of friendships with coworkers for emotional and practical support and for our continuing socialization (Elsesser & Peplau, 2006; Marks, 1994).
and would make for a safer society. Certainly the concern and debate over mass media violence will continue for years to come.
Check-in Time!
How did peers play an important role in your life? How did “peer pressure” impact decisions that you made as a teenager?
School
Most U.S. children spend about seven hours a day, 180 days a year, in school, which makes it hard to deny the importance school has on their socialization (U.S. Department of Education 2004). Students are not in school only to study math, reading, science, and other subjects—the manifest function of this system. Schools also serve a latent function in society by socializing children into behaviors like practicing teamwork, following a schedule, and using textbooks.
School and classroom rituals, led by teachers serving as role models and leaders, regularly reinforce what society expects from children. Sociologists describe this aspect of schools as the hidden curriculum, the informal teaching done by schools.
For example, in the United States, schools have built a sense of competition into the way grades are awarded and the way teachers evaluate students (Bowles and Gintis 1976). When children participate in a relay race or a math contest, they learn there are winners and losers in society. When children are required to work together on a project, they practice teamwork with other people in cooperative situations. The hidden curriculum prepares children for the adult world. Children learn how to deal with bureaucracy, rules, expectations, waiting their turn, and sitting still for hours during the day. The latent functions of teamwork and dealing with bureaucracy are features of U.S. culture. Schools in different cultures socialize children differently in order to prepare them to function well in those cultures.
Schools also socialize children by teaching them about citizenship and national pride. In the United States, children are taught to say the Pledge of Allegiance. Most school districts require classes about U.S. history and geography. As academic understanding of history evolves, textbooks in the United States have been scrutinized and revised to update attitudes toward other cultures as well as perspectives on historical events; thus, children are socialized to a different national or world history than earlier textbooks may have done. For example, information about the mistreatment of African Americans and Native American Indians more accurately reflects those events than in textbooks of the past.
Check-in Time!
What are some examples of “hidden curriculum” that you experienced? How did it impact you then and now? Share any books that you read (either assigned or personal choice) that might have influenced any thoughts or ideas that you had as a child or teenager. How did they impact you now and then?
Controversial Textbooks
On August 13, 2001, twenty South Korean men gathered in Seoul.  These men took drastic measures to protest eight middle school textbooks approved by Tokyo for use in Japanese middle schools. According to the Korean government (and other East Asian nations), the textbooks glossed over negative events in Japan’s history at the expense of other Asian countries.
In the early 1900s, Japan was one of Asia’s more aggressive nations. For instance, it held Korea as a colony between 1910 and 1945. Today, Koreans argue that the Japanese are whitewashing that colonial history through these textbooks. One major criticism is that they do not mention that, during World War II, the Japanese forced Korean women into sexual slavery. The textbooks describe the women as having been “drafted” to work, a euphemism that downplays the brutality of what actually occurred. Some Japanese textbooks dismiss an important Korean independence demonstration in 1919 as a “riot.” In reality, Japanese soldiers attacked peaceful demonstrators, leaving roughly 6,000 dead and 15,000 wounded (Crampton 2002).
Although it may seem extreme that people are so enraged about how events are described in a textbook that they would resort to dismemberment, the protest affirms that textbooks are a significant tool of socialization in state-run education systems.
The Workplace
Just as children spend much of their day at school, many U.S. adults at some point invest a significant amount of time at a place of employment. Although socialized into their culture since birth, workers require new socialization into a workplace, in terms of both material culture (such as how to operate the copy machine) and nonmaterial culture (such as whether it’s okay to speak directly to the boss or how to share the refrigerator).
Different Workplaces
|
A factory |
An office |
Emergency workers |
Figure \(\PageIndex{4}\): There are a variety of work environments that people must become socialized to and are socialized by.[4]
Different jobs require different types of socialization. In the past, many people worked a single job until retirement. Today, the trend is to switch jobs at least once a decade. Between the ages of eighteen and forty-six, the average baby boomer of the younger set held 11.3 different jobs (U.S. Bureau of Labor Statistics, 2014). This means that people must become socialized to, and socialized by, a variety of work environments.
Government
Although we do not think about it, many of the rites of passage people go through today are based on age norms established by the government. In mainstream America, to be defined as an “adult” usually means being eighteen years old, the age at which a person becomes legally responsible for him- or herself. And sixty-five years old is the start of “old age” since most people become eligible for senior benefits at that point.
Each time we embark on one of these new categories—senior, adult, taxpayer—we must be socialized into our new role. Seniors must learn the ropes of Medicare, Social Security benefits, and senior shopping discounts. When U.S. males turn eighteen, they must register with the Selective Service System within thirty days to be entered into a database for possible military service. These government dictates mark the points at which we require socialization into a new category.
Mass Media
Mass media distribute impersonal information to a wide audience, via television, newspapers, radio, and the Internet. With the average person spending over four hours a day in front of the television (and children averaging even more screen time), media greatly influences social norms (Roberts, Foehr, and Rideout 2005). People learn about objects of material culture (like new technology and transportation options), as well as nonmaterial culture—what is true (beliefs), what is important (values), and what is expected (norms). [5]
[6]
Pixar is one of the largest producers of children’s movies in the world and has released large box office draws, such as Toy Story, Cars, The Incredibles, and Up. What Pixar has never before produced is a movie with a female lead role. This changed with Pixar’s movie Brave, which was released in 2012. Before Brave, women in Pixar served as supporting characters and love interests. In Up, for example, the only human female character dies within the first ten minutes of the film. For the millions of girls watching Pixar films, there are few strong characters or roles for them to relate to. If they do not see possible versions of themselves, they may come to view women as secondary to the lives of men.
The animated films of Pixar’s parent company, Disney, have many female lead roles. Disney is well known for films with female leads, such as Snow White, Cinderella, The Little Mermaid, and Mulan. Many of Disney’s movies star a female, and she is nearly always a princess figure. If she is not a princess to begin with, she typically ends the movie by marrying a prince or, in the case of Mulan, a military general. Although not all “princesses” in Disney movies play a passive role in their lives, they typically find themselves needing to be rescued by a man, and the happy ending they all search for includes marriage.
Alongside this prevalence of princesses, many parents are expressing concern about the culture of princesses that Disney has created. Peggy Orenstein addresses this problem in her popular book, Cinderella Ate My Daughter.  Another mother wondered what she did wrong when her three-year-old daughter refused to do “nonprincessy” things, including running and jumping. The effects of this princess culture can have negative consequences for girls throughout life. An early emphasis on beauty and sexiness can lead to eating disorders, low self-esteem, and risky sexual behavior among older girls.
Check-in Time!
What movies or tv shows impacted you as a child? How did they influence your social norms and values?
[1] Image by Randen Pederson is licensed under CC BY 2.0
[2] Image by Nate Grigg is licensed under CC BY 2.0
[3] Image by USAG- Humphreys is licensed under CC BY 2.0
[4] Factory: Image on pxhere
Office: Image by Lyncconf Games is licensed under CC BY 2.0
Emergency workers: Image by Spapa003 is licensed under CC BY-SA 4.0
[5] Sociology - Module 3: Socialization and Interaction by Lumen Learning is licensed under CC BY 4.0
[6] Sociology - Module 3: Socialization and Interaction by Lumen Learning is licensed under CC BY 4.0


3.11: Chair
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Chair
Norwegian-American Maker unknown; decoration attributed to Per Lysne, c.1930 Wood, paint Little Norway Collection, Gift of Scott & Jennifer Winner MHAHS 2014.050.0049 |
The revival of rosemaling in the United States is credited to the painter of this small chair, Per Lysne. Born in Norway in 1880, Lysne was trained in Norwegian decoration by his father. After immigrating with his wife to Stoughton, Wisconsin in 1907, he was initially employed as a wagon painter. In search of work during the Great Depression, he returned to traditional Norwegian decoration. Having faded from popularity, rosemaling reached astounding new heights in Lysne’s skilled hands. In addition to non-traditional items such as plates, Lysne also decorated traditional Norwegian objects including trunks, wooden boxes and three-legged chairs. The original owner of this chair was Agnes (Dahle) Green of Mount Horeb. It was later donated to Little Norway and exhibited for many years.