Persistent vegetative state

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

 

Persistent vegetative state
Specialty	Neurology

A persistent vegetative state (PVS) or post-coma unresponsiveness (PCU) is a disorder of consciousness in which patients with severe brain damage are in a state of partial arousal rather than true awareness. After four weeks in a vegetative state (VS), the patient is classified as being in a persistent vegetative state. This diagnosis is classified as a permanent vegetative state some months (three in the US and six in the UK) after a non-traumatic brain injury or one year after a traumatic injury. The term unresponsive wakefulness syndrome may be alternatively used, as "vegetative state" has some negative connotations among the public.

Definition

There are several definitions that vary by technical versus layman's usage. There are different legal implications in different countries.

Medical definition

Per the British Royal College of Physicians of London, a persistent vegetative state is "a wakeful unconscious state that lasts longer than a few weeks is referred to as a persistent (or 'continuing') vegetative state".

"Vegetative state"

The vegetative state is a chronic or long-term condition. This condition differs from a coma: a coma is a state that lacks both awareness and wakefulness. Patients in a vegetative state may have awoken from a coma, but still have not regained awareness. In the vegetative state patients can open their eyelids occasionally and demonstrate sleep-wake cycles, but completely lack cognitive function. The vegetative state is also called a "coma vigil". The chances of regaining awareness diminish considerably as the time spent in the vegetative state increases.

"Persistent vegetative state"

Persistent vegetative state is the standard usage (except in the UK) for a medical diagnosis, made after numerous neurological and other tests, that due to extensive and irreversible brain damage a patient is highly unlikely ever to achieve higher functions above a vegetative state. This diagnosis does not mean that a doctor has diagnosed improvement as impossible, but does open the possibility, in the US, for a judicial request to end life support. Informal guidelines hold that this diagnosis can be made after four weeks in a vegetative state. US caselaw has shown that successful petitions for termination have been made after a diagnosis of a persistent vegetative state, although in some cases, such as that of Terri Schiavo, such rulings have generated widespread controversy.

In the UK, the term is discouraged in favor of two more precisely defined terms that have been strongly recommended by the Royal College of Physicians (RCP). These guidelines recommend using a continuous vegetative state for patients in a vegetative state for more than four weeks. A medical determination of a permanent vegetative state can be made if, after exhaustive testing and a customary 12 months of observation, a medical diagnosis is made that it is impossible by any informed medical expectations that the mental condition will ever improve. Hence, a "continuous vegetative state" in the UK may remain the diagnosis in cases that would be called "persistent" in the US or elsewhere.

While the actual testing criteria for a diagnosis of "permanent" in the UK are quite similar to the criteria for a diagnosis of "persistent" in the US, the semantic difference imparts in the UK a legal presumption that is commonly used in court applications for ending life support. The UK diagnosis is generally only made after 12 months of observing a static vegetative state. A diagnosis of a persistent vegetative state in the US usually still requires a petitioner to prove in court that recovery is impossible by informed medical opinion, while in the UK the "permanent" diagnosis already gives the petitioner this presumption and may make the legal process less time-consuming.

In common usage, the "permanent" and "persistent" definitions are sometimes conflated and used interchangeably. However, the acronym "PVS" is intended to define a "persistent vegetative state", without necessarily the connotations of permanence, and is used as such throughout this article. Bryan Jennett, who originally coined the term "persistent vegetative state", has now recommended using the UK division between continuous and permanent in his book The Vegetative State, arguing that "the 'persistent' component of this term ... may seem to suggest irreversibility".

The Australian National Health and Medical Research Council has suggested "post coma unresponsiveness" as an alternative term for "vegetative state" in general.

Lack of legal clarity

Unlike brain death, permanent vegetative state (PVS) is recognized by statute law as death in only a very few legal systems. In the US, courts have required petitions before termination of life support that demonstrate that any recovery of cognitive functions above a vegetative state is assessed as impossible by authoritative medical opinion. In England, Wales and Scotland, the legal precedent for withdrawal of clinically assisted nutrition and hydration in cases of patients in a PVS was set in 1993 in the case of Tony Bland, who sustained catastrophic anoxic brain injury in the 1989 Hillsborough disaster. An application to the Court of Protection is no longer required before nutrition and hydration can be withdrawn or withheld from PVS (or 'minimally conscious' – MCS) patients.

This legal grey area has led to vocal advocates that those in PVS should be allowed to die. Others are equally determined that, if recovery is at all possible, care should continue. The existence of a small number of diagnosed PVS cases that have eventually resulted in improvement makes defining recovery as "impossible" particularly difficult in a legal sense. This legal and ethical issue raises questions about autonomy, quality of life, appropriate use of resources, the wishes of family members, and professional responsibilities.

Signs and symptoms

Most PVS patients are unresponsive to external stimuli and their conditions are associated with different levels of consciousness. Some level of consciousness means a person can still respond, in varying degrees, to stimulation. A person in a coma, however, cannot. In addition, PVS patients often open their eyes in response to feeding, which has to be done by others; they are capable of swallowing, whereas patients in a coma subsist with their eyes closed.

Cerebral cortical function (e.g. communication, thinking, purposeful movement, etc.) is lost while brainstem functions (e.g. breathing, maintaining circulation and hemodynamic stability, etc.) are preserved.  Non-cognitive upper brainstem functions such as eye-opening, occasional vocalizations (e.g. crying, laughing), maintaining normal sleep patterns, and spontaneous non-purposeful movements often remain intact.

PVS patients' eyes might be in a relatively fixed position, or track moving objects, or move in a disconjugate (i.e., completely unsynchronized) manner. They may experience sleep-wake cycles, or be in a state of chronic wakefulness. They may exhibit some behaviors that can be construed as arising from partial consciousness, such as grinding their teeth, swallowing, smiling, shedding tears, grunting, moaning, or screaming without any apparent external stimulus.

Individuals in PVS are seldom on any life-sustaining equipment other than a feeding tube because the brainstem, the center of vegetative functions (such as heart rate and rhythm, respiration, and gastrointestinal activity) is relatively intact.

Recovery

Many people emerge spontaneously from a vegetative state within a few weeks. The chances of recovery depend on the extent of injury to the brain and the patient's age – younger patients having a better chance of recovery than older patients. A 1994 report found that of those who were in a vegetative state a month after a trauma, 54% had regained consciousness by a year after the trauma, whereas 28% had died and 18% were still in the vegetative state. For non-traumatic injuries such as strokes, only 14% had recovered consciousness at one year, 47% had died, and 39% were still vegetative. Patients who were vegetative six months after the initial event were much less likely to have recovered consciousness a year after the event than in the case of those who were simply reported vegetative at one month. A New Scientist article from 2000 gives a pair of graphs showing changes of patient status during the first 12 months after head injury and after incidents depriving the brain of oxygen. After a year, the chances that a PVS patient will regain consciousness are very low and most patients who do recover consciousness experience significant disability. The longer a patient is in a PVS, the more severe the resulting disabilities are likely to be. Rehabilitation can contribute to recovery, but many patients never progress to the point of being able to take care of themselves.

The medical literature also includes case reports of the recovery of a small number of patients following the removal of assisted respiration with cold oxygen. The researchers found that in many nursing homes and hospitals unheated oxygen is given to non-responsive patients via tracheal intubation. This bypasses the warming of the upper respiratory tract and causes a chilling of aortic blood and chilling of the brain which the authors believe may contribute to the person's nonresponsive state. The researchers describe a small number of cases in which removal of the chilled oxygen was followed by recovery from the PVS and recommend either warming of oxygen with a heated nebulizer or removal of the assisted oxygen if it is no longer needed. The authors further recommend additional research to determine if this chilling effect may either delay recovery or even may contribute to brain damage.

There are two dimensions of recovery from a persistent vegetative state: recovery of consciousness and recovery of function. Recovery of consciousness can be verified by reliable evidence of awareness of self and the environment, consistent voluntary behavioral responses to visual and auditory stimuli, and interaction with others. Recovery of function is characterized by communication, the ability to learn and to perform adaptive tasks, mobility, self-care, and participation in recreational or vocational activities. Recovery of consciousness may occur without functional recovery, but functional recovery cannot occur without recovery of consciousness.

Causes

There are three main causes of PVS (persistent vegetative state):

1. Acute traumatic brain injury
2. Non-traumatic: neurodegenerative disorder or metabolic disorder of the brain
3. Severe congenital abnormality of the central nervous system

Potential causes of PVS are:

• Bacterial, viral, or fungal infection, including meningitis
• Increased intracranial pressure, such as a tumor or abscess
• Vascular pressure which causes intracranial hemorrhaging or stroke
• Hypoxic ischemic injury (hypotension, cardiac arrest, arrhythmia, near-drowning)
• Toxins such as uremia, ethanol, atropine, opiates, lead, dimethylmercury, endrin, parathion, and colloidal silver
• Physical trauma: Concussion, contusion, etc.
• Seizure, both nonconvulsive status epilepticus and postconvulsive state (postictal state)
• Electrolyte imbalance, which involves hyponatremia, hypernatremia, hypomagnesemia, hypoglycemia, hyperglycemia, hypercalcemia, and hypocalcemia
• Postinfectious: Acute disseminated encephalomyelitis (ADEM)
• Endocrine disorders such as adrenal insufficiency and thyroid disorders
• Degenerative and metabolic diseases including urea cycle disorders, Reye syndrome, and mitochondrial disease
• Systemic infection and sepsis
• Hepatic encephalopathy

In addition, these authors claim that doctors sometimes use the mnemonic device AEIOU-TIPS to recall portions of the differential diagnosis: Alcohol ingestion and acidosis, Epilepsy and encephalopathy, Infection, Opiates, Uremia, Trauma, Insulin overdose or inflammatory disorders, Poisoning and psychogenic causes, and Shock.

Diagnosis

Despite converging agreement about the definition of persistent vegetative state, recent reports have raised concerns about the accuracy of diagnosis in some patients, and the extent to which, in a selection of cases, residual cognitive functions may remain undetected and patients are diagnosed as being in a persistent vegetative state. Objective assessment of residual cognitive function can be extremely difficult as motor responses may be minimal, inconsistent, and difficult to document in many patients, or may be undetectable in others because no cognitive output is possible. In recent years, a number of studies have demonstrated an important role for functional neuroimaging in the identification of residual cognitive function in persistent vegetative state; this technology is providing new insights into cerebral activity in patients with severe brain damage. Such studies, when successful, may be particularly useful where there is concern about the accuracy of the diagnosis and the possibility that residual cognitive function has remained undetected.

Diagnostic experiments

Researchers have begun to use functional neuroimaging studies to study implicit cognitive processing in patients with a clinical diagnosis of persistent vegetative state. Activations in response to sensory stimuli with positron emission tomography (PET), functional magnetic resonance imaging (fMRI), and electrophysiological methods can provide information on the presence, degree, and location of any residual brain function. However, use of these techniques in people with severe brain damage is methodologically, clinically, and theoretically complex and needs careful quantitative analysis and interpretation.

For example, PET studies have shown the identification of residual cognitive function in persistent vegetative state. That is, an external stimulation, such as a painful stimulus, still activates "primary" sensory cortices in these patients but these areas are functionally disconnected from "higher order" associative areas needed for awareness. These results show that parts of the cortex are indeed still functioning in "vegetative" patients.

In addition, other PET studies have revealed preserved and consistent responses in predicted regions of auditory cortex in response to intelligible speech stimuli. Moreover, a preliminary fMRI examination revealed partially intact responses to semantically ambiguous stimuli, which are known to tap higher aspects of speech comprehension.

Furthermore, several studies have used PET to assess the central processing of noxious somatosensory stimuli in patients in PVS. Noxious somatosensory stimulation activated midbrain, contralateral thalamus, and primary somatosensory cortex in each and every PVS patient, even in the absence of detectable cortical evoked potentials. In conclusion, somatosensory stimulation of PVS patients, at intensities that elicited pain in controls, resulted in increased neuronal activity in primary somatosensory cortex, even if resting brain metabolism was severely impaired. However, this activation of primary cortex seems to be isolated and dissociated from higher-order associative cortices.

Also, there is evidence of partially functional cerebral regions in catastrophically injured brains. To study five patients in PVS with different behavioral features, researchers employed PET, MRI and magnetoencephalographic (MEG) responses to sensory stimulation. In three of the five patients, co-registered PET/MRI correlate areas of relatively preserved brain metabolism with isolated fragments of behavior. Two patients had had anoxic injuries and demonstrated marked decreases in overall cerebral metabolism to 30–40% of normal. Two other patients with non-anoxic, multifocal brain injuries demonstrated several isolated brain regions with higher metabolic rates, that ranged up to 50–80% of normal. Nevertheless, their global metabolic rates remained <50% of normal. MEG recordings from three PVS patients provide clear evidence for the absence, abnormality or reduction of evoked responses. Despite major abnormalities, however, these data also provide evidence for localized residual activity at the cortical level. Each patient partially preserved restricted sensory representations, as evidenced by slow evoked magnetic fields and gamma band activity. In two patients, these activations correlate with isolated behavioral patterns and metabolic activity. Remaining active regions identified in the three PVS patients with behavioral fragments appear to consist of segregated corticothalamic networks that retain connectivity and partial functional integrity. A single patient who sustained severe injury to the tegmental mesencephalon and paramedian thalamus showed widely preserved cortical metabolism, and a global average metabolic rate of 65% of normal. The relatively high preservation of cortical metabolism in this patient defines the first functional correlate of clinical–pathological reports associating permanent unconsciousness with structural damage to these regions. The specific patterns of preserved metabolic activity identified in these patients reflect novel evidence of the modular nature of individual functional networks that underlie conscious brain function. The variations in cerebral metabolism in chronic PVS patients indicate that some cerebral regions can retain partial function in catastrophically injured brains.

Misdiagnoses

Statistical PVS misdiagnosis is common. An example study with 40 patients in the United Kingdom reported 43% of their patients classified as PVS were believed so and another 33% had recovered whilst the study was underway. Some PVS cases may actually be a misdiagnosis of patients being in an undiagnosed minimally conscious state. Since the exact diagnostic criteria of the minimally conscious state were only formulated in 2002, there may be chronic patients diagnosed as PVS before the secondary notion of the minimally conscious state became known.

Whether or not there is any conscious awareness with a patient's vegetative state is a prominent issue. Three completely different aspects of this should be distinguished. First, some patients can be conscious simply because they are misdiagnosed (see above). In fact, they are not in vegetative states. Second, sometimes a patient was correctly diagnosed but is then examined during the early stages of recovery. Third, perhaps some day the notion itself of vegetative states will change so to include elements of conscious awareness. Inability to disentangle these three example cases causes confusion. An example of such confusion is the response to an experiment using functional magnetic resonance imaging which revealed that a woman diagnosed with PVS was able to activate predictable portions of her brain in response to the tester's requests that she imagine herself playing tennis or moving from room to room in her house. The brain activity in response to these instructions was indistinguishable from those of healthy patients.

In 2010, Martin Monti and fellow researchers, working at the MRC Cognition and Brain Sciences Unit at the University of Cambridge, reported in an article in the New England Journal of Medicine that some patients in persistent vegetative states responded to verbal instructions by displaying different patterns of brain activity on fMRI scans. Five out of a total of 54 diagnosed patients were apparently able to respond when instructed to think about one of two different physical activities. One of these five was also able to "answer" yes or no questions, again by imagining one of these two activities. It is unclear, however, whether the fact that portions of the patients' brains light up on fMRI could help these patients assume their own medical decision making.

In November 2011, a publication in The Lancet presented bedside EEG apparatus and indicated that its signal could be used to detect awareness in three of 16 patients diagnosed in the vegetative state.

Treatment

Currently no treatment for vegetative state exists that would satisfy the efficacy criteria of evidence-based medicine. Several methods have been proposed which can roughly be subdivided into four categories: pharmacological methods, surgery, physical therapy, and various stimulation techniques. Pharmacological therapy mainly uses activating substances such as tricyclic antidepressants or methylphenidate. Mixed results have been reported using dopaminergic drugs such as amantadine and bromocriptine and stimulants such as dextroamphetamine. Surgical methods such as deep brain stimulation are used less frequently due to the invasiveness of the procedures. Stimulation techniques include sensory stimulation, sensory regulation, music and musicokinetic therapy, social-tactile interaction, and cortical stimulation.

Zolpidem

There is limited evidence that the hypnotic drug zolpidem has an effect. The results of the few scientific studies that have been published so far on the effectiveness of zolpidem have been contradictory.

Epidemiology

In the United States, it is estimated that there may be between 15,000 and 40,000 patients who are in a persistent vegetative state, but due to poor nursing home records exact figures are hard to determine.

History

The syndrome was first described in 1940 by Ernst Kretschmer who called it apallic syndrome. The term persistent vegetative state was coined in 1972 by Scottish spinal surgeon Bryan Jennett and American neurologist Fred Plum to describe a syndrome that seemed to have been made possible by medicine's increased capacities to keep patients' bodies alive.

Society and culture

Ethics and policy

An ongoing debate exists as to how much care, if any, patients in a persistent vegetative state should receive in health systems plagued by limited resources. In a case before the New Jersey Superior Court, Betancourt v. Trinitas Hospital, a community hospital sought a ruling that dialysis and CPR for such a patient constitutes futile care. An American bioethicist, Jacob M. Appel, argued that any money spent treating PVS patients would be better spent on other patients with a higher likelihood of recovery. The patient died naturally prior to a decision in the case, resulting in the court finding the issue moot.

In 2010, British and Belgian researchers reported in an article in the New England Journal of Medicine that some patients in persistent vegetative states actually had enough consciousness to "answer" yes or no questions on fMRI scans. However, it is unclear whether the fact that portions of the patients' brains light up on fMRI will help these patient assume their own medical decision making. Professor Geraint Rees, Director of the Institute of Cognitive Neuroscience at University College London, responded to the study by observing that, "As a clinician, it would be important to satisfy oneself that the individual that you are communicating with is competent to make those decisions. At the moment it is premature to conclude that the individual able to answer 5 out of 6 yes/no questions is fully conscious like you or I." In contrast, Jacob M. Appel of the Mount Sinai Hospital told the Telegraph that this development could be a welcome step toward clarifying the wishes of such patients. Appel stated: "I see no reason why, if we are truly convinced such patients are communicating, society should not honour their wishes. In fact, as a physician, I think a compelling case can be made that doctors have an ethical obligation to assist such patients by removing treatment. I suspect that, if such individuals are indeed trapped in their bodies, they may be living in great torment and will request to have their care terminated or even active euthanasia."

Notable cases

• Tony Bland – first patient in English legal history to be allowed to die
• Paul Brophy – first American to die after court-authorization
• Sunny von Bülow – lived almost 28 years in a persistent vegetative state until her death
• Gustavo Cerati – Argentine singer-songwriter, composer and producer who died after four years in a coma
• Prichard Colón – Puerto Rican former professional boxer and gold medal winner who spent years in a vegetative state after a bout
• Nancy Cruzan – American woman involved in a landmark United States Supreme Court case
• Gary Dockery – American police officer who entered, emerged and later reentered a persistent vegetative state
• Eluana Englaro – Italian woman from Lecco whose life was ended after a legal case after spending 17 years in a vegetative state
• Elaine Esposito – American woman who was a previous record holder for having spent 37 years in a coma
• Lia Lee – Hmong person who spent 26 years in a vegetative state and was the subject of a 1997 book by Anne Fadiman
• Martin Pistorius South African man who is a rare example of a survivor as his state progressed to minimally conscious after 3 years, locked in syndrome after another 4 more years, and fully came out of a coma after another 5 years. He is now a web designer, developer, and author. In 2011, he wrote a book called Ghost Boy, in which he describes his many years of being comatose.
• Annie Shapiro Canadian woman who is also another rare example of a survivor as it is known she couldn't think for her first 2 years of her 29 years total of being comatose. In 1992 she awakened fully recovered and lived her last 10 years peacefully. She is the longest a person has been in a coma and woken up apart from the catatonic stupor patients in Awakenings.
• Haleigh Poutre
• Karen Ann Quinlan
• Terri Schiavo
• Rita Greene
• Aruna Shanbaug – Indian woman in persistent vegetative state for 42 years until her death. Owing to her case, the Supreme Court of India allowed passive euthanasia in the country.
• Ariel Sharon
• Chayito Valdez
• Vice Vukov
• Helga Wanglie
• Otto Warmbier

Mathematics of paper folding

From Wikipedia, the free encyclopedia

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

 

Map folding for a 2×2 grid of squares

The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability (whether the model can be flattened without damaging it), and the use of paper folds to solve up-to cubic mathematical equations.

Computational origami is a recent branch of computer science that is concerned with studying algorithms that solve paper-folding problems. The field of computational origami has also grown significantly since its inception in the 1990s with Robert Lang's TreeMaker algorithm to assist in the precise folding of bases. Computational origami results either address origami design or origami foldability. In origami design problems, the goal is to design an object that can be folded out of paper given a specific target configuration. In origami foldability problems, the goal is to fold something using creases of an initial configuration. Results in origami design problems have been more accessible than in origami foldability problems.

History

See also: History of origami

In 1893, Indian civil servant T. Sundara Rao published Geometric Exercises in Paper Folding which used paper folding to demonstrate proofs of geometrical constructions. This work was inspired by the use of origami in the kindergarten system. Rao demonstrated an approximate trisection of angles and implied construction of a cube root was impossible.

In 1922, Harry Houdini published "Houdini's Paper Magic," which described origami techniques that drew informally from mathematical approaches that were later formalized.

The Beloch fold

In 1936 Margharita P. Beloch showed that use of the 'Beloch fold', later used in the sixth of the Huzita–Hatori axioms, allowed the general cubic equation to be solved using origami.

In 1949, R C Yeates' book "Geometric Methods" described three allowed constructions corresponding to the first, second, and fifth of the Huzita–Hatori axioms.

The Yoshizawa–Randlett system of instruction by diagram was introduced in 1961.

Crease pattern for a Miura fold. The parallelograms of this example have 84° and 96° angles.

In 1980 was reported a construction which enabled an angle to be trisected. Trisections are impossible under Euclidean rules.

Also in 1980, Kōryō Miura and Masamori Sakamaki demonstrated a novel map-folding technique whereby the folds are made in a prescribed parallelogram pattern, which allows the map to be expandable without any right-angle folds in the conventional manner. Their pattern allows the fold lines to be interdependent, and hence the map can be unpacked in one motion by pulling on its opposite ends, and likewise folded by pushing the two ends together. No unduly complicated series of movements are required, and folded Miura-ori can be packed into a very compact shape. In 1985 Miura reported a method of packaging and deployment of large membranes in outer space, and as early as 2012 this technique had been applied to solar panels on spacecraft.

A diagram showing the first and last step of how origami can double the cube

In 1986, Messer reported a construction by which one could double the cube, which is impossible with Euclidean constructions.

The first complete statement of the seven axioms of origami by French folder and mathematician Jacques Justin was written in 1986, but were overlooked until the first six were rediscovered by Humiaki Huzita in 1989. The first International Meeting of Origami Science and Technology (now known as the International Conference on Origami in Science, Math, and Education) was held in 1989 in Ferrara, Italy. At this meeting, a construction was given by Scimemi for the regular heptagon.

Around 1990, Robert J. Lang and others first attempted to write computer code that would solve origami problems.

Mountain-valley counting

In 1996, Marshall Bern and Barry Hayes showed to be an NP-complete problem the assignation of a crease pattern of mountain and valley folds in order to produce a flat origami structure starting from a flat sheet of paper.

In 1999, a theorem due to Haga provided constructions used to divide the side of a square into rational fractions.

In late 2001 and early 2002, Britney Gallivan proved the minimum length of paper necessary to fold it in half a certain number of times and folded a 4,000-foot-long (1,200 m) piece of toilet paper twelve times.

In 2002, belcastro and Hull brought to the theoretical origami the language of affine transformations, with an extension from ${\displaystyle R}$² to ${\displaystyle R}$³ in only the case of single-vertex construction.

In 2002, Alperin solved Alhazen's problem of spherical optics. In the same paper, Alperin showed a construction for a regular heptagon. In 2004, was proven algorithmically the fold pattern for a regular heptagon. Bisections and trisections were used by Alperin in 2005 for the same construction.

In 2003, Jeremy Gibbons, a researcher from the University of Oxford, described a style of functional programming in terms of origami. He coined this paradigm as "origami programming." He characterizes fold and unfolds as natural patterns of computation over recursive datatypes that can be framed in the context of origami.

In 2005, principles and concepts from mathematical and computational origami were applied to solve Countdown, a game popularized in British television in which competitors used a list of source numbers to build an arithmetic expression as close to the target number as possible.

In 2009, Alperin and Lang extended the theoretical origami to rational equations of arbitrary degree, with the concept of manifold creases. This work was a formal extension of Lang's unpublished 2004 demonstration of angle quintisection.

Pure origami

Flat folding

Two-colorability

 

Angles around a vertex

The construction of origami models is sometimes shown as crease patterns. The major question about such crease patterns is whether a given crease pattern can be folded to a flat model, and if so, how to fold them; this is an NP-complete problem. Related problems when the creases are orthogonal are called map folding problems. There are three mathematical rules for producing flat-foldable origami crease patterns:

1. Maekawa's theorem: at any vertex the number of valley and mountain folds always differ by two.

   It follows from this that every vertex has an even number of creases, and therefore also the regions between the creases can be colored with two colors.

2. Kawasaki's theorem or Kawasaki-Justin theorem: at any vertex, the sum of all the odd angles adds up to 180 degrees, as do the even.
3. A sheet can never penetrate a fold.

Paper exhibits zero Gaussian curvature at all points on its surface, and only folds naturally along lines of zero curvature. Curved surfaces that can't be flattened can be produced using a non-folded crease in the paper, as is easily done with wet paper or a fingernail.

Assigning a crease pattern mountain and valley folds in order to produce a flat model has been proven by Marshall Bern and Barry Hayes to be NP-complete. Further references and technical results are discussed in Part II of Geometric Folding Algorithms.

Huzita–Justin axioms

Main article: Huzita–Hatori axioms

Some classical construction problems of geometry — namely trisecting an arbitrary angle or doubling the cube — are proven to be unsolvable using compass and straightedge, but can be solved using only a few paper folds. Paper fold strips can be constructed to solve equations up to degree 4. The Huzita–Justin axioms or Huzita–Hatori axioms are an important contribution to this field of study. These describe what can be constructed using a sequence of creases with at most two point or line alignments at once. Complete methods for solving all equations up to degree 4 by applying methods satisfying these axioms are discussed in detail in Geometric Origami.

Constructions

As a result of origami study through the application of geometric principles, methods such as Haga's theorem have allowed paperfolders to accurately fold the side of a square into thirds, fifths, sevenths, and ninths. Other theorems and methods have allowed paperfolders to get other shapes from a square, such as equilateral triangles, pentagons, hexagons, and special rectangles such as the golden rectangle and the silver rectangle. Methods for folding most regular polygons up to and including the regular 19-gon have been developed. A regular n-gon can be constructed by paper folding if and only if n is a product of distinct Pierpont primes, powers of two, and powers of three.

Haga's theorems

BQ is always rational if AP is.

The side of a square can be divided at an arbitrary rational fraction in a variety of ways. Haga's theorems say that a particular set of constructions can be used for such divisions. Surprisingly few folds are necessary to generate large odd fractions. For instance 1⁄5 can be generated with three folds; first halve a side, then use Haga's theorem twice to produce first 2⁄3 and then 1⁄5.

The accompanying diagram shows Haga's first theorem:

${\displaystyle BQ={\frac {2AP}{1+AP}}.}$

The function changing the length AP to QC is self inverse. Let x be AP then a number of other lengths are also rational functions of x. For example:

Haga's first theorem

AP	BQ	QC	AR	PQ
${\displaystyle x}$	${\displaystyle {\frac {2x}{1+x}}}$	${\displaystyle {\frac {1-x}{1+x}}}$	${\displaystyle {\frac {1-x^{2}}{2}}}$	${\displaystyle {\frac {1+x^{2}}{1+x}}}$
1⁄2	2⁄3	1⁄3	3⁄8	5⁄6
1⁄3	1⁄2	1⁄2	4⁄9	5⁄6
2⁄3	4⁄5	1⁄5	5⁄18	13⁄15
1⁄5	1⁄3	2⁄3	12⁄25	13⁄15

A generalization of Haga's theorems

Haga's theorems are generalized as follows:

${\displaystyle {\frac {BQ}{CQ}}={\frac {2AP}{BP}}.}$

Therefore, BQ:CQ=k:1 implies AP:BP=k:2 for a positive real number k.

Doubling the cube

Doubling the cube: PB/PA = cube root of 2

The classical problem of doubling the cube can be solved using origami. This construction is due to Peter Messer: A square of paper is first creased into three equal strips as shown in the diagram. Then the bottom edge is positioned so the corner point P is on the top edge and the crease mark on the edge meets the other crease mark Q. The length PB will then be the cube root of 2 times the length of AP.

The edge with the crease mark is considered a marked straightedge, something which is not allowed in compass and straightedge constructions. Using a marked straightedge in this way is called a neusis construction in geometry.

Trisecting an angle

Trisecting the angle CAB

Angle trisection is another of the classical problems that cannot be solved using a compass and unmarked ruler but can be solved using origami. This construction, which was reported in 1980, is due to Hisashi Abe. The angle CAB is trisected by making folds PP' and QQ' parallel to the base with QQ' halfway in between. Then point P is folded over to lie on line AC and at the same time point A is made to lie on line QQ' at A'. The angle A'AB is one third of the original angle CAB. This is because PAQ, A'AQ and A'AR are three congruent triangles. Aligning the two points on the two lines is another neusis construction as in the solution to doubling the cube.

Related problems

The problem of rigid origami, treating the folds as hinges joining two flat, rigid surfaces, such as sheet metal, has great practical importance. For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites.

The napkin folding problem is the problem of whether a square or rectangle of paper can be folded so the perimeter of the flat figure is greater than that of the original square.

The placement of a point on a curved fold in the pattern may require the solution of elliptic integrals. Curved origami allows the paper to form developable surfaces that are not flat. Wet-folding origami is a technique evolved by Yoshizawa that allows curved folds to create an even greater range of shapes of higher order complexity.

The maximum number of times an incompressible material can be folded has been derived. With each fold a certain amount of paper is lost to potential folding. The loss function for folding paper in half in a single direction was given to be ${\displaystyle L={\tfrac {\pi t}{6}}(2^{n}+4)(2^{n}-1)}$, where L is the minimum length of the paper (or other material), t is the material's thickness, and n is the number of folds possible. The distances L and t must be expressed in the same units, such as inches. This result was derived by Britney Gallivan, a high schooler from California, in December 2001. In January 2002, she folded a 4,000-foot-long (1,200 m) piece of toilet paper twelve times in the same direction, debunking a long-standing myth that paper cannot be folded in half more than eight times.

The fold-and-cut problem asks what shapes can be obtained by folding a piece of paper flat, and making a single straight complete cut. The solution, known as the fold-and-cut theorem, states that any shape with straight sides can be obtained.

A practical problem is how to fold a map so that it may be manipulated with minimal effort or movements. The Miura fold is a solution to the problem, and several others have been proposed.

Computational Origami

Computational origami is a branch of computer science that is concerned with studying algorithms for solving paper-folding problems. In the early 1990s, origamists participated in a series of origami contests called the Bug Wars in which artists attempted to out-compete their peers by adding complexity to their origami bugs. Most competitors in the contest belonged to the Origami Detectives, a group of acclaimed Japanese artists. Robert Lang, a research-scientist from Stanford University and the California Institute of Technology, also participated in the contest. The contest helped initialize a collective interest in developing universal models and tools to aid in origami design and foldability.

Research

Paper-folding problems are classified as either origami design or origami foldability problems. There are predominantly three current categories of computational origami research: universality results, efficient decision algorithms, and computational intractability results. A universality result defines the bounds of possibility given a particular model of folding. For example, a large enough piece of paper can be folded into any tree-shaped origami base, polygonal silhouette, and polyhedral surface. When universality results are not attainable, efficient decision algorithms can be used to test whether an object is foldable in polynomial time. Certain paper-folding problems do not have efficient algorithms. Computational intractability results show that there are no such polynomial-time algorithms that currently exist to solve certain folding problems. For example, it is NP-hard to evaluate whether a given crease pattern folds into any flat origami.

In 2017, Erik Demaine of the Massachusetts Institute of Technology and Tomohiro Tachi of the University of Tokyo published a new universal algorithm that generates practical paper-folding patterns to produce any 3-D structure. The new algorithm built upon work that they presented in their paper in 1999 that first introduced a universal algorithm for folding origami shapes that guarantees a minimum number of seams. The algorithm will be included in Origamizer, a free software for generating origami crease patterns that was first released by Tachi in 2008.

Software & Tools

There are several software design tools that are used for origami design. Users specify the desired shape or functionality and the software tool constructs the fold pattern and/or 2D or 3D model of the result. Researchers at the Massachusetts Institute of Technology, Georgia Tech, University of California Irvine, University of Tsukuba, and University of Tokyo have developed and posted publicly available tools in computational origami. TreeMaker, ReferenceFinder, OrigamiDraw, and Origamizer are among the tools that have been used in origami design.

There are other software solutions associated with building computational origami models using non-paper materials such as Cadnano in DNA origami.

Applications

Computational origami has contributed to applications in robotics, biotechnology & medicine, industrial design. Applications for origami have also been developed in the study of programming languages and programming paradigms, particular in the setting of functional programming.

Robert Lang participated in a project with researchers at EASi Engineering in Germany to develop automotive airbag folding designs. In the mid-2000s, Lang worked with researchers at the Lawrence Livermore National Laboratory to develop a solution for the James Webb Space Telescope, particularly its large mirrors, to fit into a rocket using principles and algorithms from computational origami.

In 2014, researchers at the Massachusetts Institute of Technology, Harvard University, and the Wyss Institute for Biologically Inspired Engineering published a method for building self-folding machines and credited advances in computational origami for the project's success. Their origami-inspired robot was reported to fold itself in 4 minutes and walk away without human intervention, which demonstrated the potential for autonomous self-controlled assembly in robotics.

Other applications include DNA origami and RNA origami, folding of manufacturing instruments, and surgery by tiny origami robots.

Applications of computational origami have been featured by various production companies and commercials. Lang famously worked with Toyota Avalon to feature an animated origami sequence, Mitsubishi Endeavor to create a world entirely out of origami figures, and McDonald's to form numerous origami figures from cheeseburger wrappers.

Kamikaze

From Wikipedia, the free encyclopedia

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

USS Bunker Hill, an aircraft carrier, was hit by two kamikazes on 11 May 1945, resulting in 389 personnel dead or missing and 264 wounded.

 

Kiyoshi Ogawa (left), 22, and Seizō Yasunori, 21, the pilots who flew their aircraft into Bunker Hill

Kamikaze (神風, pronounced [kamiꜜkaze]; "divine wind" or "spirit wind"), officially Shinpū Tokubetsu Kōgekitai (神風特別攻撃隊, "Divine Wind Special Attack Unit"), were a part of the Japanese Special Attack Units of military aviators who flew suicide attacks for the Empire of Japan against Allied naval vessels in the closing stages of the Pacific campaign of World War II, intending to destroy warships more effectively than with conventional air attacks. About 3,800 kamikaze pilots died during the war, and more than 7,000 naval personnel were killed by kamikaze attacks.

Kamikaze aircraft were essentially pilot-guided explosive missiles, purpose-built or converted from conventional aircraft. Pilots would attempt to crash their aircraft into enemy ships in what was called a "body attack" (tai-atari) in aircraft loaded with bombs, torpedoes or other explosives. About 19% of kamikaze attacks were successful. The Japanese considered the goal of damaging or sinking large numbers of Allied ships to be a just reason for suicide attacks; kamikaze was more accurate than conventional attacks and often caused more damage. Some kamikazes were still able to hit their targets even after their aircraft had been crippled.

The attacks began in October 1944, at a time when the war was looking increasingly bleak for the Japanese. They had lost several important battles, many of their best pilots had been killed, their aircraft were becoming outdated, and they had lost command of the air. Japan was losing pilots faster than it could train their replacements, and the nation's industrial capacity was diminishing relative to that of the Allies. These factors, along with Japan's unwillingness to surrender, led to the use of kamikaze tactics as Allied forces advanced towards the Japanese home islands.

The tradition of death instead of defeat, capture, and shame was deeply entrenched in Japanese military culture; one of the primary values in the samurai life and the Bushido code was loyalty and honor until death. In addition to kamikazes, the Japanese military also used or made plans for non-aerial Japanese Special Attack Units, including those involving Kairyu (submarines), Kaiten human torpedoes, Shinyo speedboats and Fukuryu divers.

Definition and origin

Main article: Kamikaze (typhoon)

Further information: Battle of Bun'ei and Battle of Kōan

See also: Mongol invasions of Japan

 

The Mongol fleet destroyed in a typhoon, by Kikuchi Yōsai, 1847

The Japanese word kamikaze is usually translated as "divine wind" (kami is the word for "god", "spirit", or "divinity", and kaze for "wind"). The word originated from Makurakotoba of waka poetry modifying "Ise" and has been used since August 1281 to refer to the major typhoons that dispersed Mongol-Koryo fleets who invaded Japan under Kublai Khan in 1274.

A Japanese monoplane that made a record-breaking flight from Tokyo to London in 1937 for the Asahi newspaper group was named Kamikaze. She was a prototype for the Mitsubishi Ki-15 ("Babs").

In Japanese, the formal term used for units carrying out suicide attacks during 1944–1945 is tokubetsu kōgekitai (特別攻撃隊), which literally means "special attack unit". This is usually abbreviated to tokkōtai (特攻隊). More specifically, air suicide attack units from the Imperial Japanese Navy were officially called shinpū tokubetsu kōgeki tai (神風特別攻撃隊, "divine wind special attack units"). Shinpū is the on-reading (on'yomi or Chinese-derived pronunciation) of the same characters as the kun-reading (kun'yomi or Japanese pronunciation) kamikaze in Japanese. During World War II, the pronunciation kamikaze was used only informally in the Japanese press in relation to suicide attacks, but after the war, this usage gained acceptance worldwide and was re-imported into Japan. As a result, the special attack units are sometimes known in Japan as kamikaze tokubetsu kōgeki tai.

History

Background

Lt. Yoshinori Yamaguchi's Yokosuka D4Y3 (Type 33 Suisei) "Judy" in a suicide dive against USS Essex on 25 November 1944. The attack left 15 killed and 44 wounded. The dive brakes are extended and the non-self-sealing port wing tank trails fuel vapor and/or smoke.

Before the formation of kamikaze units, pilots had made deliberate crashes as a last resort when their aircraft had suffered severe damage and they did not want to risk being captured or wanted to do as much damage to the enemy as possible, since they were crashing anyway. Such situations occurred in both the Axis and Allied air forces. Axell and Kase see these suicides as "individual, impromptu decisions by men who were mentally prepared to die".

One example of this may have occurred on 7 December 1941 during the attack on Pearl Harbor. First Lieutenant Fusata Iida's aircraft had taken a hit and had started leaking fuel when he apparently used it to make a suicide attack on Naval Air Station Kaneohe. Before taking off, he had told his men that if his aircraft were to become badly damaged he would crash it into a "worthy enemy target". Another possible example occurred at the Battle of Midway when a damaged American bomber flew at the Akagi's bridge but missed. But in most cases, little evidence exists that such hits represented more than accidental collisions of the kind that sometimes happen in intense sea or air battles.

The carrier battles in 1942, particularly Midway, inflicted irreparable damage on the Imperial Japanese Navy Air Service (IJNAS), such that they could no longer put together a large number of fleet carriers with well-trained aircrews. Japanese planners had assumed a quick war and lacked comprehensive programs to replace the losses of ships, pilots, and sailors; and Midway; the Solomon Islands campaign (1942–1945) and the New Guinea campaign (1942–1945), notably the Battles of Eastern Solomons (August 1942); and Santa Cruz (October 1942), decimated the IJNAS veteran aircrews, and replacing their combat experience proved impossible.

Model 52c Zeros ready to take part in a kamikaze attack (early 1945)

During 1943–1944, U.S. forces steadily advanced toward Japan. Newer U.S.-made aircraft, especially the Grumman F6F Hellcat and Vought F4U Corsair, outclassed and soon outnumbered Japan's fighters. Tropical diseases, as well as shortages of spare parts and fuel, made operations more and more difficult for the IJNAS. By the Battle of the Philippine Sea (June 1944), the Japanese had to make do with obsolete aircraft and inexperienced aviators in the fight against better-trained and more experienced US Navy airmen who flew radar-directed combat air patrols. The Japanese lost over 400 carrier-based aircraft and pilots in the Battle of the Philippine Sea, effectively putting an end to their carriers' potency. Allied aviators called the action the "Great Marianas Turkey Shoot".

On 19 June 1944, aircraft from the carrier Chiyoda approached a US task group. According to some accounts, two made suicide attacks, one of which hit USS Indiana.

The important Japanese base of Saipan fell to the Allied forces on 15 July 1944. Its capture provided adequate forward bases that enabled U.S. air forces using the Boeing B-29 Superfortress to strike at the Japanese home islands. After the fall of Saipan, the Japanese High Command predicted that the Allies would try to capture the Philippines, strategically important to Tokyo because of the islands' location between the oilfields of Southeast Asia and Japan.

Beginnings

A kamikaze aircraft explodes after crashing into Essex's flight deck amidships 25 November 1944.

Captain Motoharu Okamura, in charge of the Tateyama Base in Tokyo, as well as the 341st Air Group Home, was, according to some sources, the first officer to officially propose kamikaze attack tactics. With his superiors, he arranged the first investigations into the plausibility and mechanisms of intentional suicide attacks on 15 June 1944.

In August 1944, it was announced by the Domei news agency that a flight instructor named Takeo Tagata was training pilots in Taiwan for suicide missions.

One source claims that the first kamikaze mission occurred on 13 September 1944. A group of pilots from the army's 31st Fighter Squadron on Negros Island decided to launch a suicide attack the following morning. First Lieutenant Takeshi Kosai and a sergeant were selected. Two 100 kg (220 lb) bombs were attached to two fighters, and the pilots took off before dawn, planning to crash into carriers. They never returned, but there is no record of a Kamikaze hitting an Allied ship that day.

According to some sources, on 14 October 1944, USS Reno was hit by a deliberately crashed Japanese aircraft.

Rear Admiral Masafumi Arima

Rear Admiral Masafumi Arima, the commander of the 26th Air Flotilla (part of the 11th Air Fleet), is sometimes credited with inventing the kamikaze tactic. Arima personally led an attack by a Mitsubishi G4M "Betty" twin engined bomber against a large Essex-class aircraft carrier, USS Franklin, near Leyte Gulf, on or about 15 October 1944. Arima was killed and part of an aircraft hit Franklin. The Japanese high command and propagandists seized on Arima's example. He was promoted posthumously to Vice Admiral and was given official credit for making the first kamikaze attack. It is not clear that this was a planned suicide attack, and official Japanese accounts of Arima's attack bore little resemblance to the actual events.

On 17 October 1944, Allied forces assaulted Suluan Island, beginning the Battle of Leyte Gulf. The Imperial Japanese Navy's 1st Air Fleet, based at Manila, was assigned the task of assisting the Japanese ships that would attempt to destroy Allied forces in Leyte Gulf. That unit had only 41 aircraft: 34 Mitsubishi A6M Zero ("Zeke") carrier-based fighters, three Nakajima B6N Tenzan ("Jill") torpedo bombers, one Mitsubishi G4M ("Betty") and two Yokosuka P1Y Ginga ("Frances") land-based bombers, and one additional reconnaissance aircraft. The task facing the Japanese air forces seemed impossible. The 1st Air Fleet commandant, Vice Admiral Takijirō Ōnishi, decided to form a suicide offensive force, the Special Attack Unit. In a meeting on 19 October at Mabalacat Airfield (known to the U.S. military as Clark Air Base) near Manila, Onishi told officers of the 201st Flying Group headquarters: "I don't think there would be any other certain way to carry out the operation [to hold the Philippines] than to put a 250 kg bomb on a Zero and let it crash into a U.S. carrier, in order to disable her for a week."

First unit

26 May 1945. Corporal Yukio Araki, holding a puppy, with four other pilots of the 72nd Shinbu Squadron at Bansei, Kagoshima. Araki died the following day, at the age of 17, in a suicide attack on ships near Okinawa.

Commander Asaichi Tamai asked a group of 23 talented student pilots, all of whom he had trained, to volunteer for the special attack force. All of the pilots raised both of their hands, volunteering to join the operation. Later, Tamai asked Lieutenant Yukio Seki to command the special attack force. Seki is said to have closed his eyes, lowered his head, and thought for ten seconds before saying: "Please do appoint me to the post." Seki became the 24th kamikaze pilot to be chosen. He later said: "Japan's future is bleak if it is forced to kill one of its best pilots" and "I am not going on this mission for the Emperor or for the Empire ... I am going because I was ordered to."

The names of the four subunits within the Kamikaze Special Attack Force were Unit Shikishima, Unit Yamato, Unit Asahi and Unit Yamazakura. These names were taken from a patriotic death poem, Shikishima no Yamato-gokoro wo hito towaba, asahi ni niou yamazakura bana by the Japanese classical scholar, Motoori Norinaga. The poem reads:

If someone asks about the Yamato spirit [Spirit of Old/True Japan] of Shikishima [a poetic name for Japan] – it is the flowers of yamazakura [mountain cherry blossom] that are fragrant in the Asahi [rising sun].

A less literal translation is:

Asked about the soul of Japan,
I would say
That it is
Like wild cherry blossoms
Glowing in the morning sun.

Ōnishi, addressing this unit, told them that their nobility of spirit would keep the homeland from ruin even in defeat.

Leyte Gulf: the first attacks

St Lo attacked by kamikazes, 25 October 1944

 

Starboard horizontal stabilizer from the tail of a "Judy" on the deck of USS Kitkun Bay. The "Judy" made a run on the ship approaching from dead astern; it was met by effective fire and the aircraft passed over the island and exploded. Parts of the aircraft and the pilot were scattered over the flight deck and the forecastle.

Several suicide attacks, carried out during the invasion of Leyte by Japanese pilots from units other than the Special Attack Force, have been described as the first kamikaze attacks. Early on 21 October 1944, a Japanese aircraft deliberately crashed into the foremast of the heavy cruiser HMAS Australia. This aircraft was possibly either an Aichi D3A dive bomber, from an unidentified unit of the Imperial Japanese Navy Air Service, or a Mitsubishi Ki-51 of the 6th Flying Brigade, Imperial Japanese Army Air Force. The attack killed 30 personnel, including the cruiser's captain, Emile Dechaineux, and wounded 64, including the Australian force commander, Commodore John Collins. The Australian official history of the war claimed that this was the first kamikaze attack on an Allied ship. Other sources disagree because it was not a planned attack by a member of the Special Attack Force and was most likely undertaken on the pilot's own initiative.

The sinking of the ocean tug USS Sonoma on 24 October is listed in some sources as the first ship lost to a kamikaze strike, but the attack occurred before the first mission of the Special Attack Force (on 25 October) and the aircraft used, a Mitsubishi G4M, was not flown by the original four Special Attack Squadrons.

On 25 October 1944, during the Battle of Leyte Gulf, the Kamikaze Special Attack Force carried out its first mission. Five A6M Zeros, led by Lieutenant Seki, were escorted to the target by leading Japanese ace Hiroyoshi Nishizawa where they attacked several escort carriers. One Zero attempted to hit the bridge of USS Kitkun Bay but instead exploded on the port catwalk and cartwheeled into the sea. Two others dived at USS Fanshaw Bay but were destroyed by anti-aircraft fire. The last two ran at USS White Plains. One, under heavy fire and trailing smoke, aborted the attempt on White Plains and instead banked toward USS St. Lo, diving into the flight deck, where its bomb caused fires that resulted in the bomb magazine exploding, sinking the carrier.

By 26 October day's end, 55 kamikazes from the Special Attack Force had also damaged three large escort carriers: USS Sangamon, Santee, and Suwannee (which had taken a kamikaze strike forward of its aft elevator the day before); and three smaller escorts: USS White Plains, Kalinin Bay, and Kitkun Bay. In total, seven carriers were hit, as well as 40 other ships (five sunk, 23 heavily damaged and 12 moderately damaged).

Main wave of attacks

USS Columbia is attacked by a Mitsubishi Ki-51 kamikaze off Lingayen Gulf, 6 January 1945

 

The kamikaze hits Columbia at 17:29. The aircraft and its bomb penetrated two decks before exploding, killing 13 and wounding 44.

Early successes – such as the sinking of USS St. Lo – were followed by an immediate expansion of the program, and over the next few months over 2,000 aircraft made such attacks.

When Japan began to suffer intense strategic bombing by Boeing B-29 Superfortresses, the Japanese military attempted to use suicide attacks against this threat. During the northern hemisphere winter of 1944–45, the IJAAF formed the 47th Air Regiment, also known as the Shinten Special Unit (Shinten Seiku Tai) at Narimasu Airfield, Nerima, Tokyo, to defend the Tokyo Metropolitan Area. The unit was equipped with Nakajima Ki-44 Shoki ("Tojo") fighters, whose pilots were instructed to collide with United States Army Air Forces (USAAF) B-29s approaching Japan. Targeting the aircraft proved to be much less successful and practical than attacks against warships, as the bombers made for much faster, more manoeuvrable and smaller targets. The B-29 also had formidable defensive weaponry, so suicide attacks against B-29s demanded considerable piloting skill to be successful, which worked against the very purpose of using expendable pilots. Even encouraging capable pilots to bail out before impact was ineffective because vital personnel were often lost when they mistimed their exits and were killed as a result.

On 11 March, the U.S. carrier USS Randolph was hit and moderately damaged at Ulithi Atoll, in the Caroline Islands, by a kamikaze that had flown almost 4,000 km (2,500 mi) from Japan, in a mission called Operation Tan No. 2. On 20 March, the submarine USS Devilfish survived a hit from an aircraft just off Japan.

Purpose-built kamikazes, opposed to converted fighters and dive-bombers, were also being constructed. Ensign Mitsuo Ohta had suggested that piloted glider bombs, carried within range of targets by a mother aircraft, should be developed. The First Naval Air Technical Bureau (Kugisho) in Yokosuka refined Ohta's idea. Yokosuka MXY-7 Ohka rocket-powered aircraft, launched from bombers, were first deployed in kamikaze attacks from March 1945. U.S. personnel gave them the derisive nickname "Baka Bombs" (baka is Japanese for "idiot" or "stupid"). The Nakajima Ki-115 Tsurugi was a simple, easily built propeller aircraft with a wooden airframe that used engines from existing stocks. Its non-retractable landing gear was jettisoned shortly after takeoff for a suicide mission, recovered and reused. Obsolete aircraft such as Yokosuka K5Y biplane trainers were also converted to kamikazes. During 1945, the Japanese military began stockpiling Tsurugi, Yokosuka MXY-7 Ohka, other aircraft and suicide boats for use against Allied forces expected to invade Japan. The invasion never happened, and few were ever used.

Allied defensive tactics

An A6M Zero (A6M2 Model 21) towards the end of its run at the escort carrier USS White Plains on 25 October 1944. The aircraft exploded in mid-air moments after the picture was taken, scattering debris across the deck.

In early 1945, U.S. Navy aviator Commander John Thach, already famous for developing effective aerial tactics against the Japanese such as the Thach Weave, developed a defensive strategy against kamikazes called the "big blue blanket" to establish Allied air supremacy well away from the carrier force. This recommended combat air patrols (CAP) that were larger and operated further from the carriers than before, a line of picket destroyers and destroyer escorts at least 80 km (50 mi) from the main body of the fleet to provide earlier radar interception and improved coordination between fighter direction officers on carriers. This plan also called for around-the-clock fighter patrols over Allied fleets. A final element included intensive fighter sweeps over Japanese airfields, and bombing Japanese runways, using delayed-action bombs making repairs more difficult.

Late in 1944, the British Pacific Fleet (BPF) used the high-altitude performance of its Supermarine Seafires (the naval version of the Spitfire) on combat air patrol duties. Seafires were involved in countering the kamikaze attacks during the Iwo Jima landings and beyond. The Seafires' best day was 15 August 1945, shooting down eight attacking aircraft with a single loss.

An A6M5 "Zero" diving towards American ships in the Philippines in early 1945

Allied pilots were more experienced, better trained and in command of superior aircraft, making the poorly trained kamikaze pilots easy targets. The U.S. Fast Carrier Task Force alone could bring over 1,000 fighter aircraft into play. Allied pilots became adept at destroying enemy aircraft before they struck ships.

Allied gunners had begun to develop techniques to negate kamikaze attacks. Light rapid-fire anti-aircraft weapons such as the 20 mm Oerlikon autocannons were still useful though the 40 mm Bofors was preferred, and though their high rate of fire and quick training remained advantageous, they lacked the punch to take down a kamikaze bearing down on the ship they defended. It was found that heavy anti-aircraft guns such as the 5"/38 caliber gun (127 mm) were the most effective as they had sufficient firepower to destroy aircraft at a safe range from the ship, which was preferable since even a heavily damaged kamikaze could reach its target. The speedy Ohkas presented a very difficult problem for anti-aircraft fire, since their velocity made fire control extremely difficult. By 1945, large numbers of anti-aircraft shells with radiofrequency proximity fuzes, on average seven times more effective than regular shells, became available, and the U.S. Navy recommended their use against kamikaze attacks.

Final phase

USS Louisville is struck by a Mitsubishi Ki-51 kamikaze at the Battle of Lingayen Gulf, 6 January 1945.

 

USS Missouri shortly before being hit by a Mitsubishi A6M Zero (visible top left), 11 April 1945

The peak period of kamikaze attack frequency came during April–June 1945 at the Battle of Okinawa. On 6 April 1945, waves of aircraft made hundreds of attacks in Operation Kikusui ("floating chrysanthemums"). At Okinawa, kamikaze attacks focused at first on Allied destroyers on picket duty, and then on the carriers in the middle of the fleet. Suicide attacks by aircraft or boats at Okinawa sank or put out of action at least 30 U.S. warships and at least three U.S. merchant ships, along with some from other Allied forces. The attacks expended 1,465 aircraft. Many warships of all classes were damaged, some severely, but no aircraft carriers, battleships or cruisers were sunk by kamikaze at Okinawa. Most of the ships lost were destroyers or smaller vessels, especially those on picket duty. The destroyer USS Laffey earned the nickname "The Ship That Would Not Die" after surviving six kamikaze attacks and four bomb hits during this battle.

U.S. carriers, with their wooden flight decks, appeared to suffer more damage from kamikaze hits than the armoured-decked carriers from the British Pacific Fleet. U.S. carriers also suffered considerably heavier casualties from kamikaze strikes; for instance, 389 men were killed in one attack on USS Bunker Hill, greater than the combined number of fatalities suffered on all six Royal Navy armoured carriers from all forms of attack during the entire war. Bunker Hill and Franklin were both hit (in Franklin's case, although by a dive bomber and not a kamikaze) while conducting operations with fully fueled and armed aircraft spotted on deck for takeoff, an extremely vulnerable state for any carrier. Eight kamikaze hits on five British carriers resulted in only 20 deaths while a combined total of 15 bomb hits, most of 500 kg (1,100 lb) weight or greater, and one torpedo hit on four carriers caused 193 fatal casualties earlier in the war – striking proof of the protective value of the armoured flight deck.

Aircraft carrier HMS Formidable after being struck by a kamikaze off the Sakishima Islands. The kamikaze made a dent 3 metres (9.8 ft) long and 0.6 metres (2 ft 0 in) wide and deep in the armored flight deck. Eight crew members were killed, forty-seven were wounded, and 11 aircraft were destroyed.

 

Kamikaze damage to the destroyer USS Newcomb following action off Okinawa, Newcomb was damaged beyond economical repair and scrapped after the war.

The resilience of well-armoured vessels was shown on 4 May, just after 11:30, when there was a wave of suicide attacks against the British Pacific Fleet. One Japanese aircraft made a steep dive from "a great height" at the carrier HMS Formidable and was engaged by anti-aircraft guns. Although the kamikaze was hit by gunfire, it managed to drop a bomb that detonated on the flight deck, making a crater 3 m (9.8 ft) long, 0.6 m (2 ft) wide and 0.6 m (2 ft) deep. A long steel splinter speared down through the hangar deck and the main boiler room (where it ruptured a steam line) before coming to rest in a fuel tank near the aircraft park, where it started a major fire. Eight personnel were killed and 47 were wounded. One Corsair and 10 Grumman Avengers were destroyed. The fires were gradually brought under control, and the crater in the deck was repaired with concrete and steel plate. By 17:00, Corsairs were able to land. On 9 May, Formidable was again damaged by a kamikaze, as were the carrier HMS Victorious and the battleship HMS Howe. The British were able to clear the flight deck and resume flight operations in just hours, while their American counterparts took a few days or even months, as observed by a U.S. Navy liaison officer on HMS Indefatigable who commented: "When a kamikaze hits a U.S. carrier it means six months of repair at Pearl Harbor. When a kamikaze hits a Limey carrier it's just a case of 'Sweepers, man your brooms'."occasionally used in planned kamikaze attacks. For example, Mitsubishi Ki-67 Hiryū ("Peggy") medium bombers, based on Formosa, undertook kamikaze attacks on Allied forces off Okinawa, while a pair of Kawasaki Ki-45 Toryu ("Nick") heavy fighters caused enough damage for the destroyer USS Dickerson to be scuttled. The last ship in the war to be sunk, the Fletcher-class destroyer USS Callaghan, was sunk by an obsolete wood and fabric Yokosuka K5Y kamikaze biplane while on the radar picket line off Okinawa.

Vice Admiral Matome Ugaki, the commander of the IJN 5th Air Fleet based in Kyushu, participated in one of the final kamikaze attacks on American ships on 15 August 1945, hours after Japan's announced surrender.

At the time of the surrender, the Japanese had more than 9,000 aircraft in the home islands available for Kamikaze attack, and more than 5,000 had already been specially fitted for suicide attack to resist the planned American invasion.

Effects

Ugaki, shortly before taking off in a Yokosuka D4Y3 to participate in one of the final kamikaze strikes, 15 August 1945

As the end of the war approached, the Allies did not suffer more serious significant losses, despite having far more ships and facing a greater intensity of kamikaze attacks. Although causing some of the heaviest casualties on U.S. carriers in 1945 (particularly as Bunker Hill was unlucky to get hit with fueled and armed aircraft on deck), the IJN had sacrificed 2,525 kamikaze pilots and the IJAAF 1,387 – without successfully sinking any fleet carriers, cruisers, nor battleships. This was far more than the IJN had lost in 1942 when it sank or crippled three U.S. fleet carriers (albeit without inflicting significant casualties). In 1942, when U.S. Navy vessels were scarce, the temporary absence of key warships from the combat zone would tie up operational initiatives. By 1945, however, the U.S. Navy was large enough that damaged ships could be detached back home for repair without significantly hampering the fleet's operational capability. The only U.S. surface losses were escort carriers, destroyers and smaller ships, all of which lacked the armor protection and/or capability to sustain heavy damage. Overall, the kamikazes were unable to turn the tide of the war and stop the Allied invasion.

In the immediate aftermath of kamikaze strikes, British fleet carriers with their armoured flight decks recovered more quickly compared to their US counterparts. Post-war analysis showed that some British carriers such as HMS Formidable suffered structural damage that led to them being scrapped, as being beyond economic repair. Britain's post-war economic situation played a role in the decision to not repair damaged carriers, while even seriously damaged American carriers such as USS Bunker Hill were repaired, although they were then mothballed or sold off as surplus after World War II without re-entering service.

A crewman in an AA gun aboard the battleship New Jersey watches a kamikaze aircraft dive at Intrepid 25 November 1944. Over 75 men were killed or missing and 100 wounded.

The exact number of ships sunk is a matter of debate. According to a wartime Japanese propaganda announcement, the missions sank 81 ships and damaged 195, and according to a Japanese tally, kamikaze attacks accounted for up to 80% of the U.S. losses in the final phase of the war in the Pacific. In a 2004 book, World War II, the historians Willmott, Cross and Messenger stated that more than 70 U.S. vessels were "sunk or damaged beyond repair" by kamikazes.

According to the United States Strategic Bombing Survey, from October 1944 until the end of the war, 2,550 Kamikaze missions were flown with only 475 (or 18.6%) achieving a hit or a damaging near miss. Warships of all types were damaged including 12 aircraft carriers, 15 battleships, and 16 light and escort carriers. However, no ship larger than an escort carrier was sunk. Approximately 45 ships were sunk, the bulk of which were destroyers. To the United States, the losses were of such concern that more than 2,000 B-29 sorties were diverted from attacking Japanese cities and industries to striking Kamikaze air fields in Kyushu.

According to a U.S. Air Force webpage:

Approximately 2,800 Kamikaze attackers sank 34 Navy ships, damaged 368 others, killed 4,900 sailors, and wounded over 4,800. Despite radar detection and cuing, airborne interception, attrition, and massive anti-aircraft barrages, 14 per cent of Kamikazes survived to score a hit on a ship; nearly 8.5 per cent of all ships hit by Kamikazes sank.

Australian journalists Denis and Peggy Warner, in a 1982 book with Japanese naval historian Sadao Seno (The Sacred Warriors: Japan's Suicide Legions), arrived at a total of 57 ships sunk by kamikazes. Bill Gordon, an American Japanologist who specializes in kamikazes, lists in a 2007 article 47 ships known to have been sunk by kamikaze aircraft. Gordon says that the Warners and Seno included ten ships that did not sink. He lists:

• three escort carriers: USS St. Lo, USS Ommaney Bay, and USS Bismarck Sea
• 14 destroyers, including the last ship to be sunk, USS Callaghan (DD-792) on 29 July 1945, off Okinawa
• three high-speed transport ships
• five Landing Ship, Tank
• four Landing Ship Medium
• three Landing Ship Medium (Rocket)
• one auxiliary tanker
• three Victory ships
• three Liberty ships
• two high-speed minesweepers
• one Auk class minesweeper
• one submarine chaser
• two PT boats
• two Landing Craft Support

Recruitment

Japanese Yokosuka MXY-7 Ohka ("cherry blossom"), a specially built rocket-powered kamikaze aircraft used towards the end of the war. The U.S. called them Baka Bombs ("idiot bombs").

It was claimed by the Japanese forces at the time that there were many volunteers for the suicidal forces. Captain Motoharu Okamura commented that "there were so many volunteers for suicide missions that he referred to them as a swarm of bees", explaining: "Bees die after they have stung." Okamura is credited with being the first to propose the kamikaze attacks. He had expressed his desire to lead a volunteer group of suicide attacks some four months before Admiral Takijiro Ohnishi, commander of the Japanese naval air forces in the Philippines, presented the idea to his staff. While Vice-Admiral Shigeru Fukudome, commander of the second air fleet, was inspecting the 341st Air Group, Captain Okamura took the chance to express his ideas on crash-dive tactics:

In our present situation, I firmly believe that the only way to swing the war in our favor is to resort to crash-dive attacks with our aircraft. There is no other way. There will be more than enough volunteers for this chance to save our country, and I would like to command such an operation. Provide me with 300 aircraft and I will turn the tide of war.

When the volunteers arrived for duty in the corps, there were twice as many persons as aircraft available. "After the war, some commanders would express regret for allowing superfluous crews to accompany sorties, sometimes squeezing themselves aboard bombers and fighters so as to encourage the suicide pilots and, it seems, join in the exultation of sinking a large enemy vessel." Many of the kamikaze pilots believed their death would pay the debt they owed and show the love they had for their families, friends and emperor. "So eager were many minimally trained pilots to take part in suicide missions that when their sorties were delayed or aborted, the pilots became deeply despondent. Many of those who were selected for a body crashing mission were described as being extraordinarily blissful immediately before their final sortie."

As time wore on, modern critics questioned the nationalist portrayal of kamikaze pilots as noble soldiers willing to sacrifice their lives for the country. In 2006, Tsuneo Watanabe, editor-in-chief of the Yomiuri Shimbun, criticized Japanese nationalists' glorification of kamikaze attacks:

It's all a lie that they left filled with braveness and joy, crying, "Long live the emperor!" They were sheep at a slaughterhouse. Everybody was looking down and tottering. Some were unable to stand up and were carried and pushed into their aircraft by maintenance soldiers.

Training

When you eliminate all thoughts about life and death, you will be able to totally disregard your earthly life. This will also enable you to concentrate your attention on eradicating the enemy with unwavering determination, meanwhile reinforcing your excellence in flight skills.

— Excerpt from a kamikaze pilots' manual.

Tokkōtai pilot training, as described by Takeo Kasuga, generally "consisted of incredibly strenuous training, coupled with cruel and torturous corporal punishment as a daily routine". The training, in theory, lasted for thirty days, but because of American raids and shortage of fuel it could last up to two months.

Daikichi Irokawa, who trained at Tsuchiura Naval Air Base, recalled that he "was struck on the face so hard and frequently that [his] face was no longer recognizable". He also wrote: "I was hit so hard that I could no longer see and fell on the floor. The minute I got up, I was hit again by a club so that I would confess." This brutal "training" was justified by the idea that it would instil a "soldier's fighting spirit", but daily beatings and corporal punishment eliminated patriotism among many pilots.

We tried to live with 120 per cent intensity, rather than waiting for death. We read and read, trying to understand why we had to die in our early twenties. We felt the clock ticking away towards our death, every sound of the clock shortening our lives.

Irokawa Daikichi, Kamikaze Diaries: Reflections of Japanese Student Soldiers

Pilots were given a manual that detailed how they were supposed to think, prepare and attack. From this manual, pilots were told to "attain a high level of spiritual training", and to "keep [their] health in the very best condition". These instructions, among others, were meant to make pilots mentally ready to die.

The tokkōtai pilot's manual also explained how a pilot may turn back if he could not locate a target, and that a pilot "should not waste [his] life lightly". One pilot, a graduate from Waseda University, who continually came back to base was shot after his ninth return.

The manual was very detailed in how a pilot should attack. A pilot would dive towards his target and "aim for a point between the bridge tower and the smokestacks". Entering a smokestack was also said to be "effective". Pilots were told not to aim at a carrier's bridge tower but instead to target the elevators or the flight deck. For horizontal attacks, the pilot was to "aim at the middle of the vessel, slightly higher than the waterline" or to "aim at the entrance to the aircraft hangar, or the bottom of the stack" if the former was too difficult.

The tokkōtai pilot's manual told pilots to never close their eyes, as this would lower the chances of hitting their targets. In the final moments before the crash, the pilot was to yell "hissatsu" (必殺) at the top of his lungs, which translates to "certain kill" or "sink without fail".

Cultural background

In 1944–45, US military leaders invented the term "State Shinto" as part of the Shinto Directive to differentiate the Japanese state's ideology from traditional Shinto practices. As time went on, Americans claimed, Shinto was used increasingly in the promotion of nationalist sentiment. In 1890, the Imperial Rescript on Education was passed, under which students were required to ritually recite its oath to offer themselves "courageously to the state" as well as protect the Imperial family. The ultimate offering was to give up one's life. It was an honour to die for Japan and the Emperor. Axell and Kase pointed out: "The fact is that innumerable soldiers, sailors and pilots were determined to die, to become eirei, that is 'guardian spirits' of the country. ... Many Japanese felt that to be enshrined at Yasukuni was a special honour because the Emperor visited the shrine to pay homage twice a year. Yasukuni is the only shrine deifying common men which the Emperor would visit to pay his respects." Young Japanese people were indoctrinated from an early age with these ideals.

First recruits for Japanese Kamikaze suicide pilots in 1944

Following the commencement of the kamikaze tactic, newspapers and books ran advertisements, articles and stories regarding the suicide bombers to aid in recruiting and support. In October 1944, the Nippon Times quoted Lieutenant Sekio Nishina: "The spirit of the Special Attack Corps is the great spirit that runs in the blood of every Japanese ... The crashing action which simultaneously kills the enemy and oneself without fail is called the Special Attack ... Every Japanese is capable of becoming a member of the Special Attack Corps." Publishers also played up the idea that the kamikaze were enshrined at Yasukuni and ran exaggerated stories of kamikaze bravery – there were even fairy tales for little children that promoted the kamikaze. A Foreign Office official named Toshikazu Kase said: "It was customary for GHQ [in Tokyo] to make false announcements of victory in utter disregard of facts, and for the elated and complacent public to believe them."

While many stories were falsified, some were true, such as that of Kiyu Ishikawa, who saved a Japanese ship when he crashed his aircraft into a torpedo that an American submarine had launched. The sergeant-major was posthumously promoted to second lieutenant by the emperor and was enshrined at Yasukuni. Stories like these, which showed the kind of praise and honour death produced, encouraged young Japanese to volunteer for the Special Attack Corps and instilled a desire in the youth to die as a kamikaze.

Ceremonies were carried out before kamikaze pilots departed on their final mission. The kamikaze shared ceremonial cups of sake or water known as "mizu no sakazuki". Many kamikaze Army officers took their swords along, while the Navy pilots (as a general rule) did not. The kamikaze, along with all Japanese aviators flying over unfriendly territory, were issued (or purchased, if they were officers) a Nambu pistol with which to end their lives if they risked being captured. Like all Army and Navy servicemen, the kamikaze would wear their senninbari, a "belt of a thousand stitches" given to them by their mothers. They also composed and read a death poem, a tradition stemming from the samurai, who did so before committing seppuku. Pilots carried prayers from their families and were given military decorations. The kamikaze were escorted by other pilots whose function was to protect them en route to their destination and report on the results. Some of these escort pilots, such as Zero pilot Toshimitsu Imaizumi, were later sent out on their own kamikaze missions.

Chiran high school girls wave farewell with cherry blossom branches to departing kamikaze pilot in a Nakajima Ki-43-IIIa Hayabusa.

While it is commonly perceived that volunteers signed up in droves for kamikaze missions, it has also been contended that there was extensive coercion and peer pressure involved in recruiting soldiers for the sacrifice. Their motivations in "volunteering" were complex and not simply about patriotism or bringing honour to their families. Firsthand interviews with surviving kamikaze and escort pilots has revealed that they were motivated by a desire to protect their families from perceived atrocities and possible extinction at the hands of the Allies. They viewed themselves as the last defense.

At least one of these pilots was a conscripted Korean with a Japanese name, adopted under the pre-war Soshi-kaimei ordinance that compelled Koreans to take Japanese personal names. Eleven of the 1,036 IJA kamikaze pilots who died in sorties from Chiran and other Japanese air bases during the Battle of Okinawa were Koreans.

It is said that young pilots on kamikaze missions often flew southwest from Japan over the 922 m (3,025 ft) Mount Kaimon. The mountain is also called "Satsuma Fuji" (meaning a mountain like Mount Fuji but located in the Satsuma Province region). Suicide-mission pilots looked over their shoulders to see the mountain, the southernmost on the Japanese mainland, said farewell to their country and saluted the mountain. Residents on Kikaishima Island, east of Amami Ōshima, say that pilots from suicide-mission units dropped flowers from the air as they departed on their final missions.

Kamikaze pilots who were unable to complete their missions (because of mechanical failure, interception, etc.) were stigmatized in the years following the war. This stigma began to diminish some 50 years after the war as scholars and publishers began to distribute the survivors' stories.

Some Japanese military personnel were critical of the policy. Officers such as Minoru Genda, Tadashi Minobe and Yoshio Shiga, refused to obey the policy. They said that the commander of a kamikaze attack should engage in the task first. Some persons who obeyed the policy, such as Kiyokuma Okajima, Saburo Shindo and Iyozo Fujita, were also critical of the policy. Saburō Sakai said: "We never dared to question orders, to doubt authority, to do anything but immediately carry out all the commands of our superiors. We were automatons who obeyed without thinking." Tetsuzō Iwamoto refused to engage in a kamikaze attack because he thought the task of fighter pilots was to shoot down aircraft.

Film

• Saigo no Tokkōtai (最後の特攻隊, The Last Kamikaze in English), released in 1970, produced by Toei, directed by Junya Sato and starring Kōji Tsuruta, Ken Takakura and Shinichi Chiba
• Toei also produced a biographical film about Takijirō Ōnishi in 1974 called Ā Kessen Kōkūtai (あゝ決戦航空隊, Father of the Kamikaze in English), directed by Kōsaku Yamashita.
• The Cockpit, an anthology of short films containing one about a kamikaze pilot
• Masami Takahashi, Last Kamikaze Testimonials from WWII Suicide Pilots (Watertown, MA: Documentary Educational Resources, 2008)
• Risa Morimoto, Wings of Defeat (Harriman, NY: New Day Films, 2007)
• Ore wa, kimi no tameni koso (2007, For Those We Love in English)
• Assault on the Pacific – Kamikaze (2007), directed by Taku Shinjo (Original title: "俺は、君のためにこそ死ににいく" Ore wa, Kimi no Tame ni Koso Shini ni Iku)
• The Eternal Zero (永遠の0 Eien no Zero) – 2013 film directed by Takashi Yamazaki