Immortality Part 1

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Immortality

 

The Fountain of Eternal Life in Cleveland, Ohio is described as symbolizing "Man rising above death, reaching upward to God and toward Peace."

 

Immortality is eternal life, being exempt from death; unending existence. Some modern species may possess biological immortality. 

Certain scientists, futurists, and philosophers have theorized about the immortality of the human body, with some suggesting that human immortality may be achievable in the first few decades of the 21st century. Other advocates believe that life extension is a more achievable goal in the short term, with immortality awaiting further research breakthroughs. The absence of aging would provide humans with biological immortality, but not invulnerability to death by disease or physical trauma; although mind uploading could solve that if it proved possible. Whether the process of internal endoimmortality is delivered within the upcoming years depends chiefly on research (and in neuron research in the case of endoimmortality through an immortalized cell line) in the former view and perhaps is an awaited goal in the latter case.

In religious contexts, immortality is often stated to be one of the promises of God (or other deities) to human beings who show goodness or else follow divine law. What form an unending human life would take, or whether an immaterial soul exists and possesses immortality, has been a major point of focus of religion, as well as the subject of speculation and debate. 

Definitions

Scientific

Life extension technologies promise a path to complete rejuvenation. Cryonics holds out the hope that the dead can be revived in the future, following sufficient medical advancements. While, as shown with creatures such as hydra and planarian worms, it is indeed possible for a creature to be biologically immortal, it is not known if it is possible for humans.

Mind uploading is the transference of brain states from a human brain to an alternative medium providing similar functionality. Assuming the process to be possible and repeatable, this would provide immortality to the computation of the original brain, as predicted by futurists such as Ray Kurzweil.

Physical immortality

Physical immortality is a state of life that allows a person to avoid death and maintain conscious thought. It can mean the unending existence of a person from a physical source other than organic life, such as a computer. Active pursuit of physical immortality can either be based on scientific trends, such as cryonics, digital immortality, breakthroughs in rejuvenation or predictions of an impending technological singularity, or because of a spiritual belief, such as those held by Rastafarians or Rebirthers. 

Causes of death

There are three main causes of death: aging, disease and physical trauma. Such issues can be resolved with the solutions provided in research to any end providing such alternate theories at present that require unification. 

Aging

Aubrey de Grey, a leading researcher in the field, defines aging as "a collection of cumulative changes to the molecular and cellular structure of an adult organism, which result in essential metabolic processes, but which also, once they progress far enough, increasingly disrupt metabolism, resulting in pathology and death." The current causes of aging in humans are cell loss (without replacement), DNA damage, oncogenic nuclear mutations and epimutations, cell senescence, mitochondrial mutations, lysosomal aggregates, extracellular aggregates, random extracellular cross-linking, immune system decline, and endocrine changes. Eliminating aging would require finding a solution to each of these causes, a program de Grey calls engineered negligible senescence. There is also a huge body of knowledge indicating that change is characterized by the loss of molecular fidelity.

Disease

Disease is theoretically surmountable via technology. In short, it is an abnormal condition affecting the body of an organism, something the body shouldn't typically have to deal with its natural make up. Human understanding of genetics is leading to cures and treatments for a myriad of previously incurable diseases. The mechanisms by which other diseases do damage are becoming better understood. Sophisticated methods of detecting diseases early are being developed. Preventative medicine is becoming better understood. Neurodegenerative diseases like Parkinson's and Alzheimer's may soon be curable with the use of stem cells. Breakthroughs in cell biology and telomere research are leading to treatments for cancer. Vaccines are being researched for AIDS and tuberculosis. Genes associated with type 1 diabetes and certain types of cancer have been discovered, allowing for new therapies to be developed. Artificial devices attached directly to the nervous system may restore sight to the blind. Drugs are being developed to treat a myriad of other diseases and ailments. 

Trauma

Physical trauma would remain as a threat to perpetual physical life, as an otherwise immortal person would still be subject to unforeseen accidents or catastrophes. The speed and quality of paramedic response remains a determining factor in surviving severe trauma. A body that could automatically repair itself from severe trauma, such as speculated uses for nanotechnology, would mitigate this factor. Being the seat of consciousness, the brain cannot be risked to trauma if a continuous physical life is to be maintained. This aversion to trauma risk to the brain would naturally result in significant behavioral changes that would render physical immortality undesirable for some people. 

Environmental change

Organisms otherwise unaffected by these causes of death would still face the problem of obtaining sustenance (whether from currently available agricultural processes or from hypothetical future technological processes) in the face of changing availability of suitable resources as environmental conditions change. After avoiding aging, disease, and trauma, you could still starve to death. 

If there is no limitation on the degree of gradual mitigation of risk then it is possible that the cumulative probability of death over an infinite horizon is less than certainty, even when the risk of fatal trauma in any finite period is greater than zero. Mathematically, this is an aspect of achieving "actuarial escape velocity" 

Biological immortality

Human chromosomes (grey) capped by telomeres (white)

 

Biological immortality is an absence of aging. Specifically it is the absence of a sustained increase in rate of mortality as a function of chronological age. A cell or organism that does not experience aging, or ceases to age at some point, is biologically immortal.

Biologists have chosen the word "immortal" to designate cells that are not limited by the Hayflick limit, where cells no longer divide because of DNA damage or shortened telomeres. The first and still most widely used immortal cell line is HeLa, developed from cells taken from the malignant cervical tumor of Henrietta Lacks without her consent in 1951. Prior to the 1961 work of Leonard Hayflick, there was the erroneous belief fostered by Alexis Carrel that all normal somatic cells are immortal. By preventing cells from reaching senescence one can achieve biological immortality; telomeres, a "cap" at the end of DNA, are thought to be the cause of cell aging. Every time a cell divides the telomere becomes a bit shorter; when it is finally worn down, the cell is unable to split and dies. Telomerase is an enzyme which rebuilds the telomeres in stem cells and cancer cells, allowing them to replicate an infinite number of times. No definitive work has yet demonstrated that telomerase can be used in human somatic cells to prevent healthy tissues from aging. On the other hand, scientists hope to be able to grow organs with the help of stem cells, allowing organ transplants without the risk of rejection, another step in extending human life expectancy. These technologies are the subject of ongoing research, and are not yet realized.

Biologically immortal species

Life defined as biologically immortal is still susceptible to causes of death besides aging, including disease and trauma, as defined above. Notable immortal species include:

• Bacteria – Bacteria reproduce through binary fission. A parent bacterium splits itself into two identical daughter cells which eventually then split themselves in half. This process repeats, thus making the bacterium essentially immortal. A 2005 PLoS Biology paper suggests that after each division the daughter cells can be identified as the older and the younger, and the older is slightly smaller, weaker, and more likely to die than the younger.
• Turritopsis dohrnii, a jellyfish (phylum Cnidaria, class Hydrozoa, order Anthoathecata), after becoming a sexually mature adult, can transform itself back into a polyp using the cell conversion process of transdifferentiation. Turritopsis dohrnii repeats this cycle, meaning that it may have an indefinite lifespan. Its immortal adaptation has allowed it to spread from its original habitat in the Caribbean to "all over the world".
• Hydra is a genus belonging to the phylum Cnidaria, the class Hydrozoa and the order Anthomedusae. They are simple fresh-water predatory animals possessing radial symmetry.
• Bristlecone pines are speculated to be potentially immortal; the oldest known living specimen is over 5,000 years old.
  

Evolution of aging

As the existence of biologically immortal species demonstrates, there is no thermodynamic necessity for senescence: a defining feature of life is that it takes in free energy from the environment and unloads its entropy as waste. Living systems can even build themselves up from seed, and routinely repair themselves. Aging is therefore presumed to be a byproduct of evolution, but why mortality should be selected for remains a subject of research and debate. Programmed cell death and the telomere "end replication problem" are found even in the earliest and simplest of organisms. This may be a tradeoff between selecting for cancer and selecting for aging.

Modern theories on the evolution of aging include the following:

• Mutation accumulation is a theory formulated by Peter Medawar in 1952 to explain how evolution would select for aging. Essentially, aging is never selected against, as organisms have offspring before the mortal mutations surface in an individual.
• Antagonistic pleiotropy is a theory proposed as an alternative by George C. Williams, a critic of Medawar, in 1957. In antagonistic pleiotropy, genes carry effects that are both beneficial and detrimental. In essence this refers to genes that offer benefits early in life, but exact a cost later on, i.e. decline and death.
• The disposable soma theory was proposed in 1977 by Thomas Kirkwood, which states that an individual body must allocate energy for metabolism, reproduction, and maintenance, and must compromise when there is food scarcity. Compromise in allocating energy to the repair function is what causes the body gradually to deteriorate with age, according to Kirkwood.
  

Prospects for human biological immortality

Life-extending substances

Some scientists believe that boosting the amount or proportion of telomerase in the body, a naturally forming enzyme that helps maintain the protective caps at the ends of chromosomes, could prevent cells from dying and so may ultimately lead to extended, healthier lifespans. A team of researchers at the Spanish National Cancer Centre (Madrid) tested the hypothesis on mice. It was found that those mice which were genetically engineered to produce 10 times the normal levels of telomerase lived 50% longer than normal mice.

In normal circumstances, without the presence of telomerase, if a cell divides repeatedly, at some point all the progeny will reach their Hayflick limit. With the presence of telomerase, each dividing cell can replace the lost bit of DNA, and any single cell can then divide unbounded. While this unbounded growth property has excited many researchers, caution is warranted in exploiting this property, as exactly this same unbounded growth is a crucial step in enabling cancerous growth. If an organism can replicate its body cells faster, then it would theoretically stop aging.

Embryonic stem cells express telomerase, which allows them to divide repeatedly and form the individual. In adults, telomerase is highly expressed in cells that need to divide regularly (e.g., in the immune system), whereas most somatic cells express it only at very low levels in a cell-cycle dependent manner. 

Technological immortality, biological machines, and "swallowing the doctor"

Technological immortality is the prospect for much longer life spans made possible by scientific advances in a variety of fields: nanotechnology, emergency room procedures, genetics, biological engineering, regenerative medicine, microbiology, and others. Contemporary life spans in the advanced industrial societies are already markedly longer than those of the past because of better nutrition, availability of health care, standard of living and bio-medical scientific advances. Technological immortality predicts further progress for the same reasons over the near term. An important aspect of current scientific thinking about immortality is that some combination of human cloning, cryonics or nanotechnology will play an essential role in extreme life extension. Robert Freitas, a nanorobotics theorist, suggests tiny medical nanorobots could be created to go through human bloodstreams, find dangerous things like cancer cells and bacteria, and destroy them. Freitas anticipates that gene-therapies and nanotechnology will eventually make the human body effectively self-sustainable and capable of living indefinitely in empty space, short of severe brain trauma. This supports the theory that we will be able to continually create biological or synthetic replacement parts to replace damaged or dying ones. Future advances in nanomedicine could give rise to life extension through the repair of many processes thought to be responsible for aging. K. Eric Drexler, one of the founders of nanotechnology, postulated cell repair devices, including ones operating within cells and utilizing as yet hypothetical biological machines, in his 1986 book Engines of Creation. Raymond Kurzweil, a futurist and transhumanist, stated in his book The Singularity Is Near that he believes that advanced medical nanorobotics could completely remedy the effects of aging by 2030. According to Richard Feynman, it was his former graduate student and collaborator Albert Hibbs who originally suggested to him (circa 1959) the idea of a medical use for Feynman's theoretical micromachines. Hibbs suggested that certain repair machines might one day be reduced in size to the point that it would, in theory, be possible to (as Feynman put it) "swallow the doctor". The idea was incorporated into Feynman's 1959 essay There's Plenty of Room at the Bottom. 

Cryonics

Cryonics, the practice of preserving organisms (either intact specimens or only their brains) for possible future revival by storing them at cryogenic temperatures where metabolism and decay are almost completely stopped, can be used to 'pause' for those who believe that life extension technologies will not develop sufficiently within their lifetime. Ideally, cryonics would allow clinically dead people to be brought back in the future after cures to the patients' diseases have been discovered and aging is reversible. Modern cryonics procedures use a process called vitrification which creates a glass-like state rather than freezing as the body is brought to low temperatures. This process reduces the risk of ice crystals damaging the cell-structure, which would be especially detrimental to cell structures in the brain, as their minute adjustment evokes the individual's mind. 

Mind-to-computer uploading

One idea that has been advanced involves uploading an individual's habits and memories via direct mind-computer interface. The individual's memory may be loaded to a computer or to a new organic body. Extropian futurists like Moravec and Kurzweil have proposed that, thanks to exponentially growing computing power, it will someday be possible to upload human consciousness onto a computer system, and exist indefinitely in a virtual environment. This could be accomplished via advanced cybernetics, where computer hardware would initially be installed in the brain to help sort memory or accelerate thought processes. Components would be added gradually until the person's entire brain functions were handled by artificial devices, avoiding sharp transitions that would lead to issues of identity, thus running the risk of the person to be declared dead and thus not be a legitimate owner of his or her property. After this point, the human body could be treated as an optional accessory and the program implementing the person could be transferred to any sufficiently powerful computer. Another possible mechanism for mind upload is to perform a detailed scan of an individual's original, organic brain and simulate the entire structure in a computer. What level of detail such scans and simulations would need to achieve to emulate awareness, and whether the scanning process would destroy the brain, is still to be determined. It is suggested that achieving immortality through this mechanism would require specific consideration to be given to the role of consciousness in the functions of the mind. An uploaded mind would only be a copy of the original mind, and not the conscious mind of the living entity associated in such a transfer. Without a simultaneous upload of consciousness, the original living entity remains mortal, thus not achieving true immortality. Research on neural correlates of consciousness is yet inconclusive on this issue. Whatever the route to mind upload, persons in this state could then be considered essentially immortal, short of loss or traumatic destruction of the machines that maintained them.

Cybernetics

Transforming a human into a cyborg can include brain implants or extracting a human processing unit and placing it in a robotic life-support system. Even replacing biological organs with robotic ones could increase life span (e.g. pace makers) and depending on the definition, many technological upgrades to the body, like genetic modifications or the addition of nanobots would qualify an individual as a cyborg. Some people believe that such modifications would make one impervious to aging and disease and theoretically immortal unless killed or destroyed.

Immortal DNA strand hypothesis

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Immortal_DNA_strand_hypothesis

 

The immortal DNA strand hypothesis was proposed in 1975 by John Cairns as a mechanism for adult stem cells to minimize mutations in their genomes. This hypothesis proposes that instead of segregating their DNA during mitosis in a random manner, adult stem cells divide their DNA asymmetrically, and retain a distinct template set of DNA strands (parental strands) in each division. By retaining the same set of template DNA strands, adult stem cells would pass mutations arising from errors in DNA replication on to non-stem cell daughters that soon terminally differentiate (end mitotic divisions and become a functional cell). Passing on these replication errors would allow adult stem cells to reduce their rate of accumulation of mutations that could lead to serious genetic disorders such as cancer.

Although evidence for this mechanism exists, whether it is a mechanism acting in adult stem cells in vivo is still controversial.

Methods

Two main assays are used to detect immortal DNA strand segregation: label-retention and label-release pulse/chase assays. 

In the label-retention assay, the goal is to mark 'immortal' or parental DNA strands with a DNA label such as tritiated thymidine or bromodeoxyuridine (BrdU). These types of DNA labels will incorporate into the newly synthesized DNA of dividing cells during S phase. A pulse of DNA label is given to adult stem cells under conditions where they have not yet delineated an immortal DNA strand. During these conditions, the adult stem cells are either dividing symmetrically (thus with each division a new 'immortal' strand is determined and in at least one of the stem cells the immortal DNA strand will be marked with DNA label), or the adult stem cells have not yet been determined (thus their precursors are dividing symmetrically, and once they differentiate into adult stem cells and choose an 'immortal' strand, the 'immortal strand' will already have been marked). Experimentally, adult stem cells are undergoing symmetric divisions during growth and after wound healing, and are not yet determined at neonatal stages. Once the immortal DNA strand is labelled and the adult stem cell has begun or resumed asymmetric divisions, the DNA label is chased out. In symmetric divisions (most mitotic cells), DNA is segregating randomly and the DNA label will be diluted out to levels below detection after five divisions. If, however, cells are using an immortal DNA strand mechanism, then all the labeled DNA will continue to co-segregate with the adult stem cell, and after five (or more) divisions will still be detected within the adult stem cell. These cells are sometimes called label-retaining cells (LRCs). 

In the label-release assay, the goal is to mark the newly synthesized DNA that is normally passed on to the daughter (non-stem) cell. A pulse of DNA label is given to adult stem cells under conditions where they are dividing asymmetrically. Under conditions of homeostasis, adult stem cells should be dividing asymmetrically so that the same number of adult stem cells is maintained in the tissue compartment. After pulsing for long enough to label all the newly replicated DNA, the DNA label is chased out (each DNA replication now incorporates unlabeled nucleotides) and the adult stem cells are assayed for loss of the DNA label after two cell divisions. If cells are using a random segregation mechanism, then enough DNA label should remain in the cell to be detected. If, however, the adult stem cells are using an immortal DNA strand mechanism, they are obligated to retain the unlabeled 'immortal' DNA, and will release all the newly synthesized labeled DNA to their differentiating daughter cells in two divisions. 

Some scientists have combined the two approaches, by first using one DNA label to label the immortal strands, allowing to adult stem cells to begin dividing asymmetrically, and then using a different DNA label to label the newly synthesized DNA. Thus, the adult stem cells will retain one DNA label and release the other within two divisions. 

Evidence

Evidence for the immortal DNA strand hypothesis has been found in various systems. One of the earliest studies by Karl Lark et al. demonstrated co-segregation of DNA in the cells of plant root tips. Plant root tips labeled with tritiated thymidine tended to segregate their labeled DNA to the same daughter cell. Though not all the labeled DNA segregated to the same daughter, the amount of thymidine-labeled DNA seen in the daughter with less label corresponded to the amount that would have arisen from sister-chromatid exchange. Later studies by Christopher Potten et al. (2002), using pulse/chase experiments with tritiated thymidine, found long-term label-retaining cells in the small intestinal crypts of neonatal mice. These researchers hypothesized that long-term incorporation of tritiated thymidine occurred because neonatal mice have undeveloped small intestines, and that pulsing tritiated thymidine soon after the birth of the mice allowed the 'immortal' DNA of adult stem cells to be labeled during their formation. These long-term cells were demonstrated to be actively cycling, as demonstrated by incorporation and release of BrdU.

Since these cells were cycling but continued to contain the BrdU label in their DNA, the researchers reasoned that they must be segregating their DNA using an immortal DNA strand mechanism. Joshua Merok et al. from the lab of James Sherley engineered mammalian cells with an inducible p53 gene that controls asymmetric divisions. BrdU pulse/chase experiments with these cells demonstrated that chromosomes segregated non-randomly only when the cells were induced to divide asymmetrically like adult stem cells. These asymmetrically dividing cells provide an in vitro model for demonstration and investigation of immortal strand mechanisms.

Scientists have strived to demonstrate that this immortal DNA strand mechanism exists in vivo in other types of adult stem cells. In 1996 Nik Zeps published the first paper demonstrating label retaining cells were present in the mouse mammary gland and this was confirmed in 2005 by Gilbert Smith who also published evidence that a subset of mouse mammary epithelial cells could retain DNA label and release DNA label in a manner consistent with the immortal DNA strand mechanism. Soon after, scientists from the laboratory of Derek van der Kooy showed that mice have neural stem cells that are BrdU-retaining and continue to be mitotically active. Asymmetric segregation of DNA was shown using real-time imaging of cells in culture. In 2006, scientists in the lab of Shahragim Tajbakhsh presented evidence that muscle satellite cells, which are proposed to be adult stem cells of the skeletal muscle compartment, exhibited asymmetric segregation of BrdU-labelled DNA when put into culture. They also had evidence that demonstrated BrdU release kinetics consistent with an immortal DNA strand mechanism were operating in vivo, using juvenile mice and mice with muscle regeneration induced by freezing.

These experiments supporting the immortal strand hypothesis, however, are not conclusive. While the Lark experiments demonstrated co-segregation, the co-segregation may have been an artifact of radiation from the tritium. Although Potten identified the cycling, label-retaining cells as adult stem cells, these cells are difficult to identify unequivocally as adult stem cells. While the engineered cells provide an elegant model for co-segregation of chromosomes, studies with these cells were done in vitro with engineered cells. Some features may not be present in vivo or may be absent in vitro. In May 2007 evidence in support of the Immortal DNA Strand theory was discovered by Michael Conboy et al., using the muscle stem/satellite cell model during tissue regeneration, where there is tremendous cell division during a relatively brief period of time. Using two BrdU analogs to label template and newly synthesized DNA strands, they saw that about half of the dividing cells in regenerating muscle sort the older "Immortal" DNA to one daughter cell and the younger DNA to the other. In keeping with the stem cell hypothesis, the more undifferentiated daughter typically inherited the chromatids with the older DNA, while the more differentiated daughter inherited the younger DNA.

Experimental evidence against the immortal strand hypothesis is sparse. In one study, researchers incorporated tritiated thymidine into dividing murine epidermal basal cells. They followed the release of tritiated thymidine after various chase periods, but the pattern of release was not consistent with the immortal strand hypothesis. Although they found label-retaining cells, they were not within the putative stem cell compartment. With increasing lengths of time for the chase periods, these label-retaining cells were located farther from the putative stem cell compartment, suggesting that the label-retaining cells had moved. However, finding conclusive evidence against the immortal strand hypothesis has proven difficult. 

Further models

After Cairns first proposed the immortal DNA strand mechanism, the theory has undergone several refinements. 

In 2002, he proposed that in addition to using immortal DNA strand mechanisms to segregate DNA, when the immortal DNA strands of adult stem cells undergo damage, they will choose to die (apoptose) rather than use DNA repair mechanisms that are normally used in non-stem cells.

Emmanuel David Tannenbaum and James Sherley developed a quantitative model describing how repair of point mutations might differ in adult stem cells. They found that in adult stem cells, repair was most efficient if they used an immortal DNA strand mechanism for segregating DNA, rather than a random segregation mechanism. This method would be beneficial because it avoids wrongly fixing DNA mutations in both DNA strands and propagating the mutation. 

Mechanisms

The complete proof of a concept generally requires a plausible mechanism that could mediate the effect. Although controversial, there is a suggestion that this could be provided by the Dynein Motor. This paper is accompanied by a comment summarizing the findings and background.

However, this work has highly respected biologists among its detractors as exemplified by a further comment on a paper by the same authors from 2006. The authors have rebutted the criticism.

Wien's displacement law

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Wien's_displacement_law

 

Black-body radiation as a function of wavelength for various temperatures. Each temperature curve peaks at a different wavelength and Wien's law describes the shift of that peak.

Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness of black-body radiation as a function of wavelength at any given temperature. However, it had been discovered by Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black-body radiation toward shorter wavelengths as temperature increases. 

Formally, Wien's displacement law states that the spectral radiance of black-body radiation per unit wavelength, peaks at the wavelength λ_max given by:

${\displaystyle \lambda _{\text{max}}={\frac {b}{T}}}$

where T is the absolute temperature in kelvins. b is a constant of proportionality called Wien's displacement constant, equal to 2.897771955...×10⁻³ m⋅K, or to obtain wavelength in micrometers, b ≈ 2898 μm⋅K. If one is considering the peak of black body emission per unit frequency or per proportional bandwidth, one must use a different proportionality constant. However, the form of the law remains the same: the peak wavelength is inversely proportional to temperature, and the peak frequency is directly proportional to temperature. 

Wien's displacement law may be referred to as "Wien's law", a term which is also used for the Wien approximation. 

Examples

Wien's displacement law is relevant to some everyday experiences:

• A piece of metal heated by a blow torch first becomes "red hot" as the very longest visible wavelengths appear red, then becomes more orange-red as the temperature is increased, and at very high temperatures would be described as "white hot" as shorter and shorter wavelengths come to predominate the black body emission spectrum. Before it had even reached the red hot temperature, the thermal emission was mainly at longer infrared wavelengths, which are not visible; nevertheless, that radiation could be felt as it warms one's nearby skin.
• One easily observes changes in the color of an incandescent light bulb (which produces light through thermal radiation) as the temperature of its filament is varied by a light dimmer. As the light is dimmed and the filament temperature decreases, the distribution of color shifts toward longer wavelengths and the light appears redder, as well as dimmer.
• A wood fire at 1500 K puts out peak radiation at about 2000 nm. 98% of its radiation is at wavelengths longer than 1000 nm, and only a tiny proportion at visible wavelengths (390–700 nm). Consequently, a campfire can keep one warm but is a poor source of visible light.
• The effective temperature of the Sun is 5778 K. Using Wien's law, one finds a peak emission per nanometer (of wavelength) at a wavelength of about 500 nm, in the green portion of the spectrum near the peak sensitivity of the human eye. On the other hand, in terms of power per unit optical frequency, the Sun's peak emission is at 343 THz or a wavelength of 883 nm in the near infrared. In terms of power per percentage bandwidth, the peak is at about 635 nm, a red wavelength. Regardless of how one wants to plot the spectrum, about half of the sun's radiation is at wavelengths shorter than 710 nm, about the limit of the human vision. Of that, about 12% is at wavelengths shorter than 400 nm, ultraviolet wavelengths, which is invisible to an unaided human eye. It can be appreciated that a rather large amount of the Sun's radiation falls in the fairly small visible spectrum.

The color of a star is determined by its temperature, according to Wien's law. In the constellation of Orion, one can compare Betelgeuse (T ≈ 3300 K, upper left), Rigel (T = 12100 K, bottom right), Bellatrix (T = 22000 K, upper right), and Mintaka (T = 31800 K, rightmost of the 3 "belt stars" in the middle).

• The preponderance of emission in the visible range, however, is not the case in most stars. The hot supergiant Rigel emits 60% of its light in the ultraviolet, while the cool supergiant Betelgeuse emits 85% of its light at infrared wavelengths. With both stars prominent in the constellation of Orion, one can easily appreciate the color difference between the blue-white Rigel (T = 12100 K) and the red Betelgeuse (T ≈ 3300 K). While few stars are as hot as Rigel, stars cooler than the sun or even as cool as Betelgeuse are very commonplace.
• Mammals with a skin temperature of about 300 K emit peak radiation at around 10 μm in the far infrared. This is therefore the range of infrared wavelengths that pit viper snakes and passive IR cameras must sense.
• When comparing the apparent color of lighting sources (including fluorescent lights, LED lighting, computer monitors, and photoflash), it is customary to cite the color temperature. Although the spectra of such lights are not accurately described by the black-body radiation curve, a color temperature is quoted for which black-body radiation would most closely match the subjective color of that source. For instance, the blue-white fluorescent light sometimes used in an office may have a color temperature of 6500 K, whereas the reddish tint of a dimmed incandescent light may have a color temperature (and an actual filament temperature) of 2000 K. Note that the informal description of the former (bluish) color as "cool" and the latter (reddish) as "warm" is exactly opposite the actual temperature change involved in black-body radiation.
  

Discovery

The law is named for Wilhelm Wien, who derived it in 1893 based on a thermodynamic argument. Wien considered adiabatic expansion of a cavity containing waves of light in thermal equilibrium. He showed that, under slow expansion or contraction, the energy of light reflecting off the walls changes in exactly the same way as the frequency. A general principle of thermodynamics is that a thermal equilibrium state, when expanded very slowly, stays in thermal equilibrium. The adiabatic principle allowed Wien to conclude that for each mode, the adiabatic invariant energy/frequency is only a function of the other adiabatic invariant, the frequency/temperature. A modern variant of Wien's derivation can be found in the textbook by Wannier.

The consequence is that the shape of the black-body radiation function (which was not yet understood) would shift proportionally in frequency (or inversely proportionally in wavelength) with temperature. When Max Planck later formulated the correct black-body radiation function it did not explicitly include Wien's constant b. Rather, Planck's constant h was created and introduced into his new formula. From Planck's constant h and the Boltzmann constant k, Wien's constant b can be obtained. 

Frequency-dependent formulation

For spectral flux considered per unit frequency ${\displaystyle d\nu }$ (in hertz), Wien's displacement law describes a peak emission at the optical frequency ${\displaystyle \nu _{\max }}$ given by:

${\displaystyle \nu _{\max }={\alpha \over h}kT\approx (5.879\times 10^{10}\ \mathrm {Hz/K} )\cdot T}$

or equivalently

${\displaystyle h\nu _{\max }=\alpha kT\approx (2.431\times 10^{-4}\ \mathrm {eV/K} )\cdot T}$

where α ≈ 2.8214391... is a constant resulting from the numerical solution of the maximization equation, k is the Boltzmann constant, h is the Planck constant, and T is the temperature (in kelvins). With the emission now considered per unit frequency, this peak now corresponds to a wavelength 70% longer than the peak considered per unit wavelength. The relevant math is detailed in the next section. 

Derivation from Planck's law

Planck's law for the spectrum of black body radiation predicts the Wien displacement law and may be used to numerically evaluate the constant relating temperature and the peak parameter value for any particular parameterization. Commonly a wavelength parameterization is used and in that case the black body spectral radiance (power per emitting area per solid angle) is:

${\displaystyle u_{\lambda }(\lambda ,T)={2hc^{2} \over \lambda ^{5}}{1 \over e^{hc/\lambda kT}-1}.}$

Differentiating u(λ,T) with respect to λ and setting the derivative equal to zero gives:

${\displaystyle {\partial u \over \partial \lambda }=2hc^{2}\left({hc \over kT\lambda ^{7}}{e^{hc/\lambda kT} \over \left(e^{hc/\lambda kT}-1\right)^{2}}-{1 \over \lambda ^{6}}{5 \over e^{hc/\lambda kT}-1}\right)=0,}$

which can be simplified to give:

${\displaystyle {hc \over \lambda kT}{e^{hc/\lambda kT} \over e^{hc/\lambda kT}-1}-5=0.}$

By defining:

${\displaystyle x\equiv {hc \over \lambda kT},}$

the equation becomes one in the single variable x:

${\displaystyle {xe^{x} \over e^{x}-1}-5=0.}$

which is equivalent to:

${\displaystyle (x-5)e^{x}+5=0.}$

This equation is easily numerically solved using Newton's method yielding  x = 4.965114231744276 to double precision floating point accuracy. Solving for the wavelength λ in units of nanometers, and using kelvins for the temperature yields:

${\displaystyle \lambda _{\text{max}}={\frac {hc}{x}}{\frac {1}{kT}}={\frac {2.897771955185172\times 10^{6}~{\text{nm}}{\cdot }{\text{K}}}{T}}.}$

Parameterization by frequency

Another common parameterization is by frequency. The derivation yielding peak parameter value is similar, but starts with the form of Planck's law as a function of frequency ν:

${\displaystyle u_{\nu }(\nu ,T)={2h\nu ^{3} \over c^{2}}{1 \over e^{h\nu /kT}-1}.}$

The preceding process using this equation yields:

${\displaystyle -{h\nu \over kT}{e^{h\nu /kT} \over e^{h\nu /kT}-1}+3=0.}$

The net result is:

${\displaystyle (x-3)e^{x}+3=0.}$

This is similarly solved with Newton's method yielding x = 2.8214393721220787 to double precision floating point accuracy. Solving for ν produces:

${\displaystyle \nu _{\text{max}}={\frac {xk}{h}}T=({0.05878923811360855~{\text{THz}}{\cdot }{\text{K}}^{-1}})\cdot {T}.}$

Maxima differ according to parameterization

Notice that for a given temperature, parameterization by frequency implies a different maximal wavelength than parameterization by wavelength.

For example, using T = 6000 K and parameterization by wavelength, the wavelength for maximal spectral radiance is λ = 482.962 nm with corresponding frequency ν = 620.737 THz. For the same temperature, but parameterizing by frequency, the frequency for maximal spectral radiance is ν = 352.735 THz with corresponding wavelength λ = 849.907 nm. 

These functions are radiance density functions, which are probability density functions scaled to give units of radiance. The density function has different shapes for different parameterizations, depending on relative stretching or compression of the abscissa, which measures the change in probability density relative to a linear change in a given parameter. Since wavelength and frequency have a reciprocal relation, they represent significantly non-linear shifts in probability density relative to one another. 

The total radiance is the integral of the distribution over all positive values, and that is invariant for a given temperature under any parameterization. Additionally, for a given temperature the radiance consisting of all photons between two wavelengths must be the same regardless of which distribution you use. That is to say, integrating the wavelength distribution from λ₁ to λ₂ will result in the same value as integrating the frequency distribution between the two frequencies that correspond to λ₁ and λ₂, namely from c/λ₂ to c/λ₁. However, the distribution shape depends on the parameterization, and for a different parameterization the distribution will typically have a different peak density, as these calculations demonstrate. 

Using the value 4 to solve the implicit equation yields the peak in the spectral radiance density function expressed in the parameter radiance per proportional bandwidth. This is perhaps a more intuitive way of presenting "wavelength of peak emission". That yields x = 3.9206903948728864 to double precision floating point accuracy. 

The important point of Wien's law, however, is that any such wavelength marker, including the median wavelength (or, alternatively, the wavelength below which any specified percentage of the emission occurs) is proportional to the reciprocal of temperature. That is, the shape of the distribution for a given parameterization, scales with and translates according to temperature, and can be calculated once for a canonical temperature, then appropriately shifted and scaled to obtain the distribution for another temperature. This is a consequence of the strong statement of Wien's law.