Law of excluded middle

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Law_of_excluded_middle

In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true. It is one of the three laws of thought, along with the law of noncontradiction and the law of identity; however, no system of logic is built on just these laws, and none of these laws provides inference rules, such as modus ponens or De Morgan's laws. The law is also known as the law/principle of the excluded third, in Latin principium tertii exclusi. Another Latin designation for this law is tertium non datur or "no third [possibility] is given". In classical logic, the law is a tautology.

In contemporary logic the principle is distinguished from the semantical principle of bivalence, which states that every proposition is either true or false. The principle of bivalence always implies the law of excluded middle, while the converse is not always true. A commonly cited counterexample uses statements unprovable now, but provable in the future to show that the law of excluded middle may apply when the principle of bivalence fails.

History

Aristotle

The earliest known formulation is in Aristotle's discussion of the principle of non-contradiction, first proposed in On Interpretation, where he says that of two contradictory propositions (i.e. where one proposition is the negation of the other) one must be true, and the other false. He also states it as a principle in the Metaphysics book 4, saying that it is necessary in every case to affirm or deny, and that it is impossible that there should be anything between the two parts of a contradiction.

Aristotle wrote that ambiguity can arise from the use of ambiguous names, but cannot exist in the facts themselves:

It is impossible, then, that "being a man" should mean precisely "not being a man", if "man" not only signifies something about one subject but also has one significance. … And it will not be possible to be and not to be the same thing, except in virtue of an ambiguity, just as if one whom we call "man", and others were to call "not-man"; but the point in question is not this, whether the same thing can at the same time be and not be a man in name, but whether it can be in fact. (Metaphysics 4.4, W. D. Ross (trans.), GBWW 8, 525–526).

Aristotle's assertion that "it will not be possible to be and not to be the same thing" would be written in propositional logic as ~(P ∧ ~P). In modern so called classical logic, this statement is equivalent to the law of excluded middle (P ∨ ~P), through distribution of the negation in Aristotle's assertion. The former claims that no statement is both true and false, while the latter requires that any statement is either true or false. (Refer to the List of logic symbols for the meaning of symbols used in this article).

But Aristotle also writes, "since it is impossible that contradictories should be at the same time true of the same thing, obviously contraries also cannot belong at the same time to the same thing" (Book IV, CH 6, p. 531). He then proposes that "there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate" (Book IV, CH 7, p. 531). In the context of Aristotle's traditional logic, this is a remarkably precise statement of the law of excluded middle, P ∨ ~P.

Yet in On Interpretation Aristotle seems to deny the law of excluded middle in the case of future contingents, in his discussion on the sea battle.

Leibniz

Its usual form, "Every judgment is either true or false" [footnote 9] …"(from Kolmogorov in van Heijenoort, p. 421) footnote 9: "This is Leibniz's very simple formulation (see Nouveaux Essais, IV,2)" (ibid p 421)

Bertrand Russell and Principia Mathematica

The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as:

${\displaystyle \mathbf{\ast }\mathbf{2}\cdot \mathbf{11}.⊢.p\vee \sim p}$.^[8]

So just what is "truth" and "falsehood"? At the opening PM quickly announces some definitions:

Truth-values. The "truth-value" of a proposition is truth if it is true and falsehood if it is false* [*This phrase is due to Frege] … the truth-value of "p ∨ q" is truth if the truth-value of either p or q is truth, and is falsehood otherwise … that of "~ p" is the opposite of that of p …" (pp. 7–8)

This is not much help. But later, in a much deeper discussion ("Definition and systematic ambiguity of Truth and Falsehood" Chapter II part III, p. 41 ff), PM defines truth and falsehood in terms of a relationship between the "a" and the "b" and the "percipient". For example "This 'a' is 'b'" (e.g. "This 'object a' is 'red'") really means "'object a' is a sense-datum" and "'red' is a sense-datum", and they "stand in relation" to one another and in relation to "I". Thus what we really mean is: "I perceive that 'This object a is red'" and this is an undeniable-by-3rd-party "truth".

PM further defines a distinction between a "sense-datum" and a "sensation":

That is, when we judge (say) "this is red", what occurs is a relation of three terms, the mind, and "this", and "red". On the other hand, when we perceive "the redness of this", there is a relation of two terms, namely the mind and the complex object "the redness of this" (pp. 43–44).

Russell reiterated his distinction between "sense-datum" and "sensation" in his book The Problems of Philosophy (1912), published at the same time as PM (1910–1913):

Let us give the name of "sense-data" to the things that are immediately known in sensation: such things as colours, sounds, smells, hardnesses, roughnesses, and so on. We shall give the name "sensation" to the experience of being immediately aware of these things … The colour itself is a sense-datum, not a sensation. (p. 12)

Russell further described his reasoning behind his definitions of "truth" and "falsehood" in the same book (Chapter XII, Truth and Falsehood).

Consequences of the law of excluded middle in Principia Mathematica

From the law of excluded middle, formula ✸2.1 in Principia Mathematica, Whitehead and Russell derive some of the most powerful tools in the logician's argumentation toolkit. (In Principia Mathematica, formulas and propositions are identified by a leading asterisk and two numbers, such as "✸2.1".)

✸2.1 ~p ∨ p "This is the Law of excluded middle" (PM, p. 101).

The proof of ✸2.1 is roughly as follows: "primitive idea" 1.08 defines p → q = ~p ∨ q. Substituting p for q in this rule yields p → p = ~p ∨ p. Since p → p is true (this is Theorem 2.08, which is proved separately), then ~p ∨ p must be true.

✸2.11 p ∨ ~p (Permutation of the assertions is allowed by axiom 1.4)
✸2.12 p → ~(~p) (Principle of double negation, part 1: if "this rose is red" is true then it's not true that "'this rose is not-red' is true".)
✸2.13 p ∨ ~{~(~p)} (Lemma together with 2.12 used to derive 2.14)
✸2.14 ~(~p) → p (Principle of double negation, part 2)
✸2.15 (~p → q) → (~q → p) (One of the four "Principles of transposition". Similar to 1.03, 1.16 and 1.17. A very long demonstration was required here.)
✸2.16 (p → q) → (~q → ~p) (If it's true that "If this rose is red then this pig flies" then it's true that "If this pig doesn't fly then this rose isn't red.")
✸2.17 ( ~p → ~q ) → (q → p) (Another of the "Principles of transposition".)
✸2.18 (~p → p) → p (Called "The complement of reductio ad absurdum. It states that a proposition which follows from the hypothesis of its own falsehood is true" (PM, pp. 103–104).)

Most of these theorems—in particular ✸2.1, ✸2.11, and ✸2.14—are rejected by intuitionism. These tools are recast into another form that Kolmogorov cites as "Hilbert's four axioms of implication" and "Hilbert's two axioms of negation" (Kolmogorov in van Heijenoort, p. 335).

Propositions ✸2.12 and ✸2.14, "double negation": The intuitionist writings of L. E. J. Brouwer refer to what he calls "the principle of the reciprocity of the multiple species, that is, the principle that for every system the correctness of a property follows from the impossibility of the impossibility of this property" (Brouwer, ibid, p. 335).

This principle is commonly called "the principle of double negation" (PM, pp. 101–102). From the law of excluded middle (✸2.1 and ✸2.11), PM derives principle ✸2.12 immediately. We substitute ~p for p in 2.11 to yield ~p ∨ ~(~p), and by the definition of implication (i.e. 1.01 p → q = ~p ∨ q) then ~p ∨ ~(~p)= p → ~(~p). QED (The derivation of 2.14 is a bit more involved.)

Reichenbach

It is correct, at least for bivalent logic—i.e. it can be seen with a Karnaugh map—that this law removes "the middle" of the inclusive-or used in his law (3). And this is the point of Reichenbach's demonstration that some believe the exclusive-or should take the place of the inclusive-or.

About this issue (in admittedly very technical terms) Reichenbach observes:

The tertium non datur

29. (x)[f(x) ∨ ~f(x)]

is not exhaustive in its major terms and is therefore an inflated formula. This fact may perhaps explain why some people consider it unreasonable to write (29) with the inclusive-'or', and want to have it written with the sign of the exclusive-'or'

30. (x)[f(x) ⊕ ~f(x)], where the symbol "⊕" signifies exclusive-or

in which form it would be fully exhaustive and therefore nomological in the narrower sense. (Reichenbach, p. 376)

In line (30) the "(x)" means "for all" or "for every", a form used by Russell and Reichenbach; today the symbolism is usually ${\displaystyle \mathrm{\forall }}$ x. Thus an example of the expression would look like this:

• (pig): (Flies(pig) ⊕ ~Flies(pig))
• (For all instances of "pig" seen and unseen): ("Pig does fly" or "Pig does not fly" but not both simultaneously)

Formalists versus Intuitionists

From the late 1800s through the 1930s, a bitter, persistent debate raged between Hilbert and his followers versus Hermann Weyl and L. E. J. Brouwer. Brouwer's philosophy, called intuitionism, started in earnest with Leopold Kronecker in the late 1800s.

Hilbert intensely disliked Kronecker's ideas:

Kronecker insisted that there could be no existence without construction. For him, as for Paul Gordan [another elderly mathematician], Hilbert's proof of the finiteness of the basis of the invariant system was simply not mathematics. Hilbert, on the other hand, throughout his life was to insist that if one can prove that the attributes assigned to a concept will never lead to a contradiction, the mathematical existence of the concept is thereby established (Reid p. 34)

It was his [Kronecker's] contention that nothing could be said to have mathematical existence unless it could actually be constructed with a finite number of positive integers (Reid p. 26)

The debate had a profound effect on Hilbert. Reid indicates that Hilbert's second problem (one of Hilbert's problems from the Second International Conference in Paris in 1900) evolved from this debate (italics in the original):

In his second problem, [Hilbert] had asked for a mathematical proof of the consistency of the axioms of the arithmetic of real numbers.

To show the significance of this problem, he added the following observation:

"If contradictory attributes be assigned to a concept, I say that mathematically the concept does not exist" (Reid p. 71)

Thus, Hilbert was saying: "If p and ~p are both shown to be true, then p does not exist", and was thereby invoking the law of excluded middle cast into the form of the law of contradiction.

And finally constructivists … restricted mathematics to the study of concrete operations on finite or potentially (but not actually) infinite structures; completed infinite totalities … were rejected, as were indirect proof based on the Law of Excluded Middle. Most radical among the constructivists were the intuitionists, led by the erstwhile topologist L. E. J. Brouwer (Dawson p. 49)

The rancorous debate continued through the early 1900s into the 1920s; in 1927 Brouwer complained about "polemicizing against it [intuitionism] in sneering tones" (Brouwer in van Heijenoort, p. 492). But the debate was fertile: it resulted in Principia Mathematica (1910–1913), and that work gave a precise definition to the law of excluded middle, and all this provided an intellectual setting and the tools necessary for the mathematicians of the early 20th century:

Out of the rancor, and spawned in part by it, there arose several important logical developments; Zermelo's axiomatization of set theory (1908a), that was followed two years later by the first volume of Principia Mathematica, in which Russell and Whitehead showed how, via the theory of types: much of arithmetic could be developed by logicist means (Dawson p. 49)

Brouwer reduced the debate to the use of proofs designed from "negative" or "non-existence" versus "constructive" proof:

According to Brouwer, a statement that an object exists having a given property means that, and is only proved, when a method is known which in principle at least will enable such an object to be found or constructed …

Hilbert naturally disagreed.

"pure existence proofs have been the most important landmarks in the historical development of our science," he maintained. (Reid p. 155)

Brouwer refused to accept the logical principle of the excluded middle, His argument was the following:

"Suppose that A is the statement "There exists a member of the set S having the property P." If the set is finite, it is possible—in principle—to examine each member of S and determine whether there is a member of S with the property P or that every member of S lacks the property P." For finite sets, therefore, Brouwer accepted the principle of the excluded middle as valid. He refused to accept it for infinite sets because if the set S is infinite, we cannot—even in principle—examine each member of the set. If, during the course of our examination, we find a member of the set with the property P, the first alternative is substantiated; but if we never find such a member, the second alternative is still not substantiated.

Since mathematical theorems are often proved by establishing that the negation would involve us in a contradiction, this third possibility which Brouwer suggested would throw into question many of the mathematical statements currently accepted.

"Taking the Principle of the Excluded Middle from the mathematician," Hilbert said, "is the same as … prohibiting the boxer the use of his fists."

"The possible loss did not seem to bother Weyl … Brouwer's program was the coming thing, he insisted to his friends in Zürich." (Reid, p. 149)

In his lecture in 1941 at Yale and the subsequent paper, Gödel proposed a solution: "that the negation of a universal proposition was to be understood as asserting the existence … of a counterexample" (Dawson, p. 157)

Gödel's approach to the law of excluded middle was to assert that objections against "the use of 'impredicative definitions'" had "carried more weight" than "the law of excluded middle and related theorems of the propositional calculus" (Dawson p. 156). He proposed his "system Σ … and he concluded by mentioning several applications of his interpretation. Among them were a proof of the consistency with intuitionistic logic of the principle ~ (∀A: (A ∨ ~A)) (despite the inconsistency of the assumption ∃ A: ~ (A ∨ ~A))" (Dawson, p. 157)

The debate seemed to weaken: mathematicians, logicians and engineers continue to use the law of excluded middle (and double negation) in their daily work.

Intuitionist definitions of the law (principle) of excluded middle

The following highlights the deep mathematical and philosophic problem behind what it means to "know", and also helps elucidate what the "law" implies (i.e. what the law really means). Their difficulties with the law emerge: that they do not want to accept as true implications drawn from that which is unverifiable (untestable, unknowable) or from the impossible or the false. (All quotes are from van Heijenoort, italics added).

Brouwer offers his definition of "principle of excluded middle"; we see here also the issue of "testability":

On the basis of the testability just mentioned, there hold, for properties conceived within a specific finite main system, the "principle of excluded middle", that is, the principle that for every system every property is either correct [richtig] or impossible, and in particular the principle of the reciprocity of the complementary species, that is, the principle that for every system the correctness of a property follows from the impossibility of the impossibility of this property. (335)

Kolmogorov's definition cites Hilbert's two axioms of negation

5. A → (~A → B)
6. (A → B) → { (~A → B) → B}

Hilbert's first axiom of negation, "anything follows from the false", made its appearance only with the rise of symbolic logic, as did the first axiom of implication … while … the axiom under consideration [axiom 5] asserts something about the consequences of something impossible: we have to accept B if the true judgment A is regarded as false …

Hilbert's second axiom of negation expresses the principle of excluded middle. The principle is expressed here in the form in which is it used for derivations: if B follows from A as well as from ~A, then B is true. Its usual form, "every judgment is either true or false" is equivalent to that given above".

From the first interpretation of negation, that is, the interdiction from regarding the judgment as true, it is impossible to obtain the certitude that the principle of excluded middle is true … Brouwer showed that in the case of such transfinite judgments the principle of excluded middle cannot be considered obvious

footnote 9: "This is Leibniz's very simple formulation (see Nouveaux Essais, IV,2). The formulation "A is either B or not-B" has nothing to do with the logic of judgments.

footnote 10: "Symbolically the second form is expressed thus

A ∨ ~A

where ∨ means "or". The equivalence of the two forms is easily proved (p. 421)

Examples

For example, if P is the proposition:

Socrates is mortal.

then the law of excluded middle holds that the logical disjunction:

Either Socrates is mortal, or it is not the case that Socrates is mortal.

is true by virtue of its form alone. That is, the "middle" position, that Socrates is neither mortal nor not-mortal, is excluded by logic, and therefore either the first possibility (Socrates is mortal) or its negation (it is not the case that Socrates is mortal) must be true.

An example of an argument that depends on the law of excluded middle follows. We seek to prove that

there exist two irrational numbers ${\displaystyle a}$ and ${\displaystyle b}$ such that ${\displaystyle a^b}$ is rational.

It is known that ${\displaystyle \sqrt{2}}$ is irrational (see proof). Consider the number

${\displaystyle {\sqrt{2}}^{\sqrt{2}}}$.

Clearly (excluded middle) this number is either rational or irrational. If it is rational, the proof is complete, and

${\displaystyle a=\sqrt{2}}$ and ${\displaystyle b=\sqrt{2}}$.

But if ${\displaystyle {\sqrt{2}}^{\sqrt{2}}}$ is irrational, then let

${\displaystyle a={\sqrt{2}}^{\sqrt{2}}}$ and ${\displaystyle b=\sqrt{2}}$.

Then

${\displaystyle a^b={\left({\sqrt{2}}^{\sqrt{2}}\right)}^{\sqrt{2}}={\sqrt{2}}^{\left(\sqrt{2}\cdot \sqrt{2}\right)}={\sqrt{2}}^2=2}$,

and 2 is certainly rational. This concludes the proof.

In the above argument, the assertion "this number is either rational or irrational" invokes the law of excluded middle. An intuitionist, for example, would not accept this argument without further support for that statement. This might come in the form of a proof that the number in question is in fact irrational (or rational, as the case may be); or a finite algorithm that could determine whether the number is rational.

Non-constructive proofs over the infinite

The above proof is an example of a non-constructive proof disallowed by intuitionists:

The proof is non-constructive because it doesn't give specific numbers ${\displaystyle a}$ and ${\displaystyle b}$ that satisfy the theorem but only two separate possibilities, one of which must work. (Actually ${\displaystyle a={\sqrt{2}}^{\sqrt{2}}}$ is irrational but there is no known easy proof of that fact.) (Davis 2000:220)

(Constructive proofs of the specific example above are not hard to produce; for example ${\displaystyle a=\sqrt{2}}$ and ${\displaystyle b={\log }_{2}9}$ are both easily shown to be irrational, and ${\displaystyle a^b=3}$; a proof allowed by intuitionists).

By non-constructive Davis means that "a proof that there actually are mathematic entities satisfying certain conditions would not have to provide a method to exhibit explicitly the entities in question." (p. 85). Such proofs presume the existence of a totality that is complete, a notion disallowed by intuitionists when extended to the infinite—for them the infinite can never be completed:

In classical mathematics there occur non-constructive or indirect existence proofs, which intuitionists do not accept. For example, to prove there exists an n such that P(n), the classical mathematician may deduce a contradiction from the assumption for all n, not P(n). Under both the classical and the intuitionistic logic, by reductio ad absurdum this gives not for all n, not P(n). The classical logic allows this result to be transformed into there exists an n such that P(n), but not in general the intuitionistic … the classical meaning, that somewhere in the completed infinite totality of the natural numbers there occurs an n such that P(n), is not available to him, since he does not conceive the natural numbers as a completed totality. (Kleene 1952:49–50)

David Hilbert and Luitzen E. J. Brouwer both give examples of the law of excluded middle extended to the infinite. Hilbert's example: "the assertion that either there are only finitely many prime numbers or there are infinitely many" (quoted in Davis 2000:97); and Brouwer's: "Every mathematical species is either finite or infinite." (Brouwer 1923 in van Heijenoort 1967:336). In general, intuitionists allow the use of the law of excluded middle when it is confined to discourse over finite collections (sets), but not when it is used in discourse over infinite sets (e.g. the natural numbers). Thus intuitionists absolutely disallow the blanket assertion: "For all propositions P concerning infinite sets D: P or ~P" (Kleene 1952:48).

Putative counterexamples to the law of excluded middle include the liar paradox or Quine's paradox. Certain resolutions of these paradoxes, particularly Graham Priest's dialetheism as formalised in LP, have the law of excluded middle as a theorem, but resolve out the Liar as both true and false. In this way, the law of excluded middle is true, but because truth itself, and therefore disjunction, is not exclusive, it says next to nothing if one of the disjuncts is paradoxical, or both true and false.

Criticisms

The Catuṣkoṭi (tetralemma) is an ancient alternative to the law of excluded middle, which examines all four possible assignments of truth values to a proposition and its negation. It has been important in Indian logic and Buddhist logic as well as the ancient Greek philosophical school known as Pyrrhonism.

Many modern logic systems replace the law of excluded middle with the concept of negation as failure. Instead of a proposition's being either true or false, a proposition is either true or not able to be proved true. These two dichotomies only differ in logical systems that are not complete. The principle of negation as failure is used as a foundation for autoepistemic logic, and is widely used in logic programming. In these systems, the programmer is free to assert the law of excluded middle as a true fact, but it is not built-in a priori into these systems.

Mathematicians such as L. E. J. Brouwer and Arend Heyting have also contested the usefulness of the law of excluded middle in the context of modern mathematics.

In mathematical logic

In modern mathematical logic, the excluded middle has been argued to result in possible self-contradiction. It is possible in logic to make well-constructed propositions that can be neither true nor false; a common example of this is the "Liar's paradox", the statement "this statement is false", which is argued to itself be neither true nor false. Arthur Prior has argued that the Paradox is not an example of a statement that cannot be true or false. The law of excluded middle still holds here as the negation of this statement "This statement is not false", can be assigned true. In set theory, such a self-referential paradox can be constructed by examining the set "the set of all sets that do not contain themselves". This set is unambiguously defined, but leads to a Russell's paradox: does the set contain, as one of its elements, itself? However, in the modern Zermelo–Fraenkel set theory, this type of contradiction is no longer admitted. Furthermore, paradoxes of self reference can be constructed without even invoking negation at all, as in Curry's paradox.

Analogous laws

Some systems of logic have different but analogous laws. For some finite n-valued logics, there is an analogous law called the law of excluded n+1th. If negation is cyclic and "∨" is a "max operator", then the law can be expressed in the object language by (P ∨ ~P ∨ ~~P ∨ ... ∨ ~...~P), where "~...~" represents n−1 negation signs and "∨ ... ∨" n−1 disjunction signs. It is easy to check that the sentence must receive at least one of the n truth values (and not a value that is not one of the n).

Other systems reject the law entirely.

Law of the weak excluded middle

A particularly well-studied intermediate logic is given by De Morgan logic, which adds the axiom ${\displaystyle \mathrm{\neg }P\vee \mathrm{\neg }\mathrm{\neg }P}$ to intuitionistic logic, which is sometimes called the law of the weak excluded middle.

This is equivalent to a few other statements:

• Satisfying all of De Morgan's laws including ${\displaystyle \mathrm{\neg }(P\wedge Q)\leftrightarrow \mathrm{\neg }P\vee \mathrm{\neg }Q}$
• ${\displaystyle (P\to Q)\vee (\mathrm{\neg }P\to \mathrm{\neg }Q)}$
• ${\displaystyle (P\to (Q\vee \mathrm{\neg }R))\to ((P\to Q)\vee (P\to \mathrm{\neg }R))}$

Asian giant hornet

From Wikipedia, the free encyclopedia

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

 

Asian giant hornet Temporal range: Miocene–present, 15.97–0 Ma PreꞒ Ꞓ O S D C P T J K Pg N
Scientific classification
Kingdom:	Animalia
Phylum:	Arthropoda
Class:	Insecta
Order:	Hymenoptera
Family:	Vespidae
Genus:	Vespa
Species:	V. mandarinia
Binomial name
Vespa mandarinia Smith, 1852
Synonyms
Vespa magnifica Smith, 1852 Vespa japonica Radoszkowski, 1857 Vespa bellona Smith, 1871 Vespa magnifica var. latilineata Cameron, 1903 Vespa mandarina Dalla Torre, 1894 (misspelling) Vespa mandarinia nobilis Sonan, 1929 Vespa magnifica sonani Matsumura, 1930

The Asian giant hornet (Vespa mandarinia), also known as the northern giant hornet, and the Japanese giant hornet, is the world's largest hornet. It is native to temperate and tropical East Asia, South Asia, mainland Southeast Asia, and parts of the Russian Far East. It was also found in the Pacific Northwest of North America in late 2019, with a few more additional sightings in 2020, and nests found in 2021, prompting concern that it could become an invasive species, but in December 2024, the species was announced to have been eradicated completely from the United States.

Asian giant hornets prefer to live in low mountains and forests, while almost completely avoiding plains and high-altitude climates. V. mandarinia creates nests by digging, co-opting pre-existing tunnels dug by rodents, or occupying spaces near rotten pine roots. It feeds primarily on larger insects, colonies of other eusocial insects, tree sap, and honey from honeybee colonies. The hornet has a body length of 45 mm (1+3⁄4 in), a wingspan around 75 mm (3 in), and a stinger 6 mm (1⁄4 in) long, which injects a large amount of potent venom.

Taxonomy and phylogeny

form "magnifica"

V. mandarinia is a species in the genus Vespa, which comprises all true hornets. Along with seven other species, V. mandarinia is a part of the V. tropica species group, defined by the single notch located on the apical margin of the seventh gastral sternum of the male. The most closely related species within the species group is V. soror. The triangular shape of the apical margin of the clypeus of the female is diagnostic, the vertex of both species is enlarged, and the shape of the apex of the aedeagus is distinct and similar.

Division of the genus into subgenera has been attempted in the past, but has been abandoned, due to the anatomical similarity among species and because behavioral similarity is not associated with phylogeny. The species has existed since the Miocene epoch, as indicated by fossils found in the Shanwang Formation.

As of 2012, three subspecies were recognized: V. m. mandarinia, V. m. magnifica, and V. m. nobilis. The former subspecies referred to as V. m. japonica has not been considered valid since 1997. The most recent revision in 2020 eliminated all of the subspecies rankings entirely, with "japonica", "magnifica", and "nobilis" now relegated to informal non-taxonomic names for different color forms.

Common names

Since its discovery in North America, the scientific literature and official government sources refer to this species by its established common name, Asian giant hornet, whilst the mainstream media have taken to using the nickname "murder hornet". In July 2022, the Entomological Society of America stated that they will adopt the common name northern giant hornet for the species to avoid potentially discriminatory language, citing xenophobia and racism related to the COVID-19 pandemic.

Description

Regardless of sex, the hornet's head is a light shade of orange and its antennae are brown with a yellow-orange base. Its eyes and ocelli are dark brown to black. V. mandarinia is distinguished from other hornets by its pronounced clypeus and large genae. Its orange mandible contains a black tooth that it uses for digging. The thorax is dark brown, with two grey wings varying in span from 35 to 76 mm (1+3⁄8 to 3 in).

Its forelegs are brighter than the mid- and hindlegs. The base of the forelegs is darker than the rest. The abdomen alternates between bands of dark brown or black, and a yellow-orange hue (consistent with its head color). The sixth segment is yellow. Its stinger is typically 6 mm (1⁄4 in) long and delivers a potent venom that in cases of multiple hornets stinging simultaneously, or by rare allergic reaction, can kill a human.

Queens and workers

The queens are considerably larger than workers. Queens can exceed 50 mm (2 in), while workers are between 35 and 40 mm (1+2⁄5 and 1+3⁄5 in). The reproductive anatomy is consistent between the two, but workers do not reproduce.

Drones

Drones (males) are similar to females, and can attain 38 millimetres (1+1⁄2 in) in length, but lack stingers. This is a consistent feature among the Hymenoptera.

Larvae

Larvae spin a silk cocoon when they complete development and are ready to pupate. Larval silk proteins have a wide variety of potential applications due to their wide variety of potential morphologies, including the native fiber form, but also sponge, film, and gel.

Genome

The mitochondrial genome is provided by Chen et al., 2015. This information has also been important to confirm the place of the wider Vespidae family in the Vespoidea superfamily, and confirms that Vespoidea is monophyletic.

Misidentifications

Within two days of the initial 2020 news report on V. mandarinia, insect identification centers in the Eastern United States (where the wasp does not occur) began getting identification requests, and were swamped for the next several months, though not one of the thousands of submitted photos or samples was of V. mandarinia, but were instead primarily wasps such as the European hornet (V. crabro), the eastern cicada killer (Sphecius speciosus), or the southern yellowjacket (Vespula squamosa).

Submissions suspected by laypeople to be V. mandarinia also include other wasps of various sizes, bees, sawflies, horntails, wasp-mimicking flies, beetles, Jerusalem crickets, cicadas, and even a plastic children's toy that was wasp-like in appearance, all of which were routinely estimated to be 130–185% of their actual size.

Reports of this species from other parts of the world appear to be erroneous identifications of other introduced hornet species, such as V. orientalis in several locations around the world, and V. velutina in Europe.

Distribution

Ecological distribution

V. mandarinia is primarily a forest dweller. When it does live in urban landscapes, it is highly associated with green space. It is the most dependent upon green space of the Vespa species (with V. analis the least). Extremely urbanized areas provide a refuge for V. analis, whereas V. mandarinia – its predator – is entirely absent.

Geographic distribution

Asia

The Asian giant hornet can be found in:

• Russia – Primorsky Krai, Khabarovsk Krai (southern part only), and Jewish Autonomous Oblast region
• Korea (where it is called 장수말벌 (Jaŋsumalbôl) "general giant wasp, general hornet")
• Mainland China
• Taiwan (traditional Chinese: 大虎頭蜂; simplified Chinese: 大虎头蜂 (dàhǔtóufēng); lit. 'giant tiger head bee')
• Laos
• Thailand
• Cambodia
• Myanmar
• Vietnam
• Nepal
• India
• Bhutan
• Sri Lanka
• Malaysia
• Japan – It is common in Japan. It prefers rural areas where it can find trees in which to nest, and is known as the ōsuzumebachi (オオスズメバチ(大雀蜂); literally, "giant sparrow bee, giant hornet"). At least as early as 2008, some popular and sensationalist media outlets in Japan also began referring to this wasp as satsujin suzumebachi (殺人スズメバチ; literally, "murderer sparrow hornet").

North America

The first confirmed sightings of the Asian giant hornet in North America were confirmed in 2019 and were mainly concentrated in the Vancouver area, with nests also discovered in neighboring Whatcom County, Washington, in the United States.

• In August 2019, three hornets were found in Nanaimo on Vancouver Island, and a large nest was found and destroyed shortly thereafter.
• At the end of September, a worker was reported in Blaine, Washington.
• Another worker was found in Blaine in October.
• In December 2019, another worker was found in Blaine.
• Two specimens were collected in May 2020, one from Langley, British Columbia, about 13 kilometres (8 miles) north of Blaine, and one from Custer, Washington, 14 km (9 mi) southeast of Blaine.
• One queen sighting in June 2020 was from Bellingham, Washington, 24 km (15 mi) south of Custer.
• An unmated queen was trapped in July 2020, near Birch Bay, Washington, 10 km (6 mi) west of Custer.
• A male hornet was captured in Custer, Washington, in July 2020.
• A hornet of unknown caste was reported in August 2020, in Birch Bay, and another was trapped in the same area the following day.
• Three hornets were seen southeast of Blaine on 21 and 25 September 2020, and three more were found in the same area on 29 and 30 September, prompting officials to report that attempts were underway to pinpoint and destroy a nest believed to be in the area.
• In October 2020, the Washington State Department of Agriculture announced that a nest was found 2.5 metres (8.3 ft) above ground in a cavity of a tree in Blaine, with dozens of hornets entering and leaving. The nest was eradicated the next day, including the immediate discovery and removal of about 100 hornets. At first, the owner of the land required the nest to be returned, and he advertised it for sale. A local beekeeper bought it from him and gave it back to the state entomology team. Further analysis determined that the nest had contained about 500 live specimens, including about 200 queens. Some of these specimens were sent to the Smithsonian Institution to become a part of the NMNH Biorepository permanent cryogenic collection. It was announced that several undiscovered live nests were also believed to exist within Washington State, because the captures of individual hornets in Birch, Blaine, and Custer were all relatively far from the discovered nest. However, officials expressed cautious optimism, adding that eradicating the hornets before they became established in the area might still be possible. A Canadian official said that although individual specimens had been found in Canada and some nests were suspected to exist there, the hornets' presence seemed to be only in areas near the US-Canadian border, while the center of the invasion appeared to be in Washington.
• In November 2020, one individual was found in Abbotsford, BC. As a result the BC government asked Abbotsford beekeepers and residents to report any sightings.
• In November 2020, a queen was found in Aldergrove, BC.
• In August 2021, a nest was discovered in Whatcom County, Washington near Blaine, only 2 miles (3.2 km) from the nest WSDA eradicated in 2020. This nest was destroyed two weeks later on 25 August, before it could produce new queens.
• In September 2021, two more nests were found near Blaine, in the vicinity of the nest found in August, and a "potential sighting" was reported from near Everson, some 25 miles (40 km) east of Blaine.

A mitochondrial DNA analysis was performed to determine the maternal population(s) ancestral to the British Columbia and Washington introduced populations. The high dissimilarity between these two was similar to the mutual distances between each of the Chinese, Japanese, and Korean native populations suggesting the specimens collected in 2019 were from two different maternal populations, Japanese in BC and South Korean in Washington. This suggests that two separate introductions of the Asian giant hornet occurred in North America within about 80 km (50 mi) of one another within a few months.

In April 2020, authorities in Washington asked members of the public to be alert and report any sightings of these hornets, which are expected to become active in April if they are in the area. If they become established, the hornets "could decimate bee populations in the United States and establish such a deep presence that all hope for eradication could be lost." A "full-scale hunt" for the species by the WSDA was then underway. Two assessment models of their potential to spread from their present location on the US–Canadian border suggested that they could spread northward into coastal British Columbia and Southeast Alaska, and southward as far as southern Oregon. The USDA's Agricultural Research Service is engaged in lure/attractant development and molecular genetics research, both as part of its normal research mission, but also to further the near-term eradication goal in Washington.

In 2020, the United States Congress considered specific legislation to eradicate V. mandarinia including a proposal by the interior secretary, the Fish and Wildlife director, and the other relevant agencies, which has been introduced as an amendment to the appropriations omnibus. British Columbia Agriculture is prepared for a "long fight" lasting years, if necessary. One advantage humans will have is the lack of diversity of such an invasive population – leaving the hornets less prepared for novel environments and challenges.

In June 2021, a dead, desiccated male was found near Marysville, Snohomish County, Washington, and reported to WSDA. Its different, more reddish color form immediately suggested yet another parental population from the Japanese and Korean ones already known. The USDA Animal and Plant Health Inspection Service performed a genetic analysis several days later, and together with WSDA, confirmed it was of a third, unrelated population. The discovery of a male in June is "perplexing" given that the earliest male emergence in 2020 was July, which was already earlier than normal for the home range. This and its desiccated state indicate it did not emerge in 2021 at all, but is instead a dead specimen that had already emerged in a previous year.

The WSDA announced in December 2022 that "no confirmed sightings" of the hornet were reported in the state for that year, and in December 2023 stated no sightings occurred in 2023, and in December of 2024, WSDA declared that the hornets had been eradicated from North America.

Nesting

V. mandarinia nests in low mountain foothills and lowland forests. As a particularly dominant species, no efforts are directed toward conserving V. mandarinia or its habitats, as they are common in areas of low human disturbance. Unlike other species of Vespa, V. mandarinia almost exclusively inhabits subterranean nests – in 1978, that aerial nests were unlikely, as Matsuura and Sakagami reported this to be unknown in Japan in 1973. and aerial nesting is still described as extremely rare in Japan, and yet as of 2021 all nests in the invasive range have been aerial.

In a study of 31 nests, 25 were found around rotten pine roots, and another study found only 9 of 56 nests above ground. Additionally, rodents, snakes, or other burrowing animals previously made some of the tunnels. The depth of these nests was between 6.0 and 60 cm (2 and 24 in). The entrance at the ground surface varies in length from 2.0 to 60 cm (1 to 24 in) either horizontally, inclined, or vertically. The queens that found the nest prefer narrow cavities.

Nests of V. mandarinia typically lack a developed envelope. During the initial stages of development, the envelope is in an inverted-bowl shape. As the nest develops, one to three rough sheets of combs are created. Often, single primordial combs are created simultaneously and then fused into a single comb.

A system of one main pillar and secondary pillars connects the combs. Nests usually have four to seven combs. The top comb is abandoned after summer and left to rot. The largest comb is at the middle to bottom portion of the nest. The largest combs created by V. mandarinia measured 49.5 by 45.5 cm (19+1⁄2 by 18 in) with 1,192 cells (no obstacles, circular) and 61.0 by 48.0 cm (24 by 19 in) (elliptical; wrapped around a root system).

Colony cycle

The nesting cycle of V. mandarinia is fairly consistent with that of other eusocial insects. Six phases occur in each cycle.

Prenesting period

Inseminated and uninseminated queens enter hibernation following a cycle. They first appear in early to mid-April and begin feeding on the sap of Quercus (oak) trees. Although this timing is consistent among hornets, V. mandarinia dominates the order, receiving preference for premium sap sources. Among the V. mandarinia queens is a dominance hierarchy. The top-ranked queen begins feeding, while the other queens form a circle around her. Once the top queen finishes, the second-highest-ranking queen feeds. This process repeats until the last queen feeds at a poor hour.

Solitary, cooperative, and polyethic periods

Inseminated queens start to search for nesting sites in late April. The uninseminated queens do not search for nests, since their ovaries never fully develop. They continue to feed, but then disappear in early July.

An inseminated queen begins to create relatively small cells in which she raises around 40 small workers. Workers do not begin to work outside of the hive until July. Queens participate in activities outside the hive until mid-July, when they stay inside the nest and allow workers to do extranidal activities. Early August marks a fully developed nest, containing three combs holding 500 cells and 100 workers. After mid-September, no more eggs are laid and the focus shifts to caring for larvae. The queens die in late October.

Dissolution and hibernating period

Male

Males and new queens take on their responsibilities in mid-September and mid-October, respectively. During this time, their body color becomes intense and the weights of the queens increase about 20%. Once the males and queens leave the nest, they do not return. In V. mandarinia, males wait outside the nest entrance until the queens emerge, when males intercept them in midair, bring them to the ground, and copulate from 8 to 45 seconds. After this episode, the males return to the entrance for a second chance, while the now-mated queens leave to hibernate. Many queens (up to 65%) attempt to fight off the males and leave unfertilized, at least temporarily. After this episode, prehibernating queens are found in moist, subterranean habitats.

When sexed individuals emerge, workers shift their focus from protein and animal foods to carbohydrates. The last sexed individuals to emerge may die of starvation.

Sting

The stinger of the Asian giant hornet is about 6 mm (1⁄4 in) long. Their stinger injects an especially potent venom that contains mastoparan-M. Mastoparans are found in many bee and wasp venoms. They are cytolytic peptides that can damage tissue by stimulating phospholipase action, in addition to its own phospholipase. Masato Ono, an entomologist at Tamagawa University, described the sensation of being stung as feeling "like a hot nail being driven into my leg". Besides using their stingers to inject venom, Asian giant hornets are apparently able to spray venom into a person's eyes under certain circumstances, with one report in 2020 from Japan of long-term damage, though the exact extent of actual visual impairment still remains unassessed.

The venom contains a neurotoxin called mandaratoxin, a single-chain polypeptide with a molecular weight around 20 kDa. While a single wasp cannot inject a lethal dose, multiple stings can be lethal even to people who are not allergic if the dose is sufficient, and allergy to the venom greatly increases the risk of death. Tests involving mice found that the venom falls short of being the most lethal of all wasp venoms, having an LD₅₀ of 4.0 mg/kg. In comparison, the deadliest wasp venom (at least to laboratory mice) by weight belongs to V. luctuosa at 1.6 mg/kg. The potency of the V. mandarinia sting is due, rather, to the relatively large amount of venom injected.

Immunogenicity

Evidence is insufficient to believe that prophylactic immunotherapy for the venom of other Vespidae will prevent allergic reaction to V. mandarinia venom, because of wide differences in venom chemistry.

Effects on humans

In 1957, van der Vecht was under the impression humans in the native range lived in constant fear of V. mandarinia and Iwata reported in 1976 that research and removal were hampered by its attacks.

Parasites

The strepsipteran Xenos moutoni is a common parasite among Vespa species. In a study of parasites among species of Vespa, 4.3% of V. mandarinia females were parasitized. Males were not stylopized (parasitization by stylopid strepsipterans, such as X. moutoni) at all. The major consequence of being parasitized is the inability to reproduce, and stylopized queens follow the same fate as uninseminated queens. They do not search for an area to create a new colony and feed on sap until early July, when they disappear. In other species of Vespa, males also have a chance of being stylopized. The consequences between the two sexes are similar, as neither sex is able to reproduce.

Communication and perception

V. mandarinia uses both visual and chemical cues as a means of navigating itself and others to the desired location. Scent marking was discussed as a way for hornets to direct other members of the colony to a food source. Even with antennae damage, V. mandarinia was able to navigate itself. It was unable to find its destination only when vision impairment was induced. This implies that while chemical signaling is important, visual cues play an equally important role in guiding individuals. Other behaviors include the formation of a "royal court" consisting of workers that lick and bite the queen, thereby ingesting her pheromones.

These pheromones could directly communicate between the queen and her court or indirectly between her court and other workers due to the ingested pheromones. This is merely speculation, as no direct evidence has been collected to suggest the latter. V. mandarinia communicates acoustically, as well. When larvae are hungry, they scrape their mandibles against the walls of the cell. Furthermore, adult hornets click their mandibles as a warning to other creatures that encroach upon their territories.

Scent marking

V. mandarinia is the only species of social wasp known to apply a scent to direct its colony to a food source. The hornet secretes the chemical from the sixth sternal gland, also known as van der Vecht's gland. This behavior is observed during autumnal raids after the hornets begin hunting in groups instead of individually. The ability to apply scents may have arisen because the Asian giant hornet relies heavily on honey bee colonies as its main food source.

A single hornet is unable to take on an entire colony of honey bees because species such as Apis cerana have a well-organized defense mechanism. The honey bees swarm one wasp and vibrate their thoracic muscles to heat up the hornet and raise carbon dioxide to a lethal level. So, organized attacks are much more effective and easily devastate a colony of tens of thousands of honey bees.

Interspecies dominance

In an experiment observing four different species of Vespa (V. ducalis, V. crabro, V. analis, and V. mandarinia), V. mandarinia was the dominant species. Multiple parameters were set to determine this. The first set parameter observed interaction-mediated departures, which are defined as scenarios wherein one species leaves its position due to the arrival of a more dominant individual. The proportion of interaction-mediated departures was the lowest for V. mandarinia. Another measured parameter was attempted patch entry. Over the observed time, conspecifics (interactions with the same species) resulted in refused entry far more than heterospecifics (interactions with different species).

Lastly, when feeding at sap flows, fights between these hornets, Pseudotorynorrhina japonica, Neope goschkevitschii, and Lethe sicelis were observed, and once more V. mandarinia was the most dominant species. In 57 separate fights, one loss was observed to Neope goschkevitschii, giving V. mandarinia a win rate of 98.3%. Based on interaction-mediated departures, attempted patch entry, and interspecific fights, V. mandarinia is the most dominant Vespa species.

Diet

Feeding on a mantis

The Asian giant hornet is intensely predatory; it hunts medium- to large-sized insects, such as bees, other hornet and wasp species, beetles, hornworms, and mantises. The latter are favored targets in late summer and fall. Large insects such as mantises are key protein sources to feed queen and drone larvae. Workers forage to feed their larvae, and since their prey can include crop pests, the hornets are sometimes regarded as beneficial.

This hornet often attacks colonies of other Vespa species (V. simillima being the usual prey species), Vespula species, and honey bee (such as Apis cerana and A. mellifera) hives to obtain the adults, pupae, and larvae as food for their own larvae. Sometimes, they cannibalize each other's colonies. A single scout, sometimes two or three, cautiously approaches the hive, producing pheromones to lead its nest-mates to the hive. The hornets can devastate a colony of honey bees, especially if it is the introduced western honey bee. A single hornet can kill as many as 40 bees per minute due to its large mandibles, which can quickly strike and decapitate prey.

The honey bees' stings are ineffective because the hornets are five times their size and heavily armored. Only a few hornets (under 50) can exterminate a colony of tens of thousands of bees in a few hours. The hornets can fly up to 100 km (60 mi) in a single day, at speeds up to 40 km/h (25 mph). The smaller Asian hornet similarly preys on honey bees, and has been spreading throughout Europe.

Hornet larvae, but not adults, can digest solid protein. The adult hornets can only drink the juices of their victims, and they chew their prey into a paste to feed to their larvae. The workers dismember the bodies of their prey to return only the most nutrient-rich body parts, such as flight muscles, to the nest. Larvae of predatory social vespids generally, not just Vespa, secrete a clear liquid, sometimes referred to as Vespa amino acid mixture, the exact amino acid composition of which varies considerably from species to species, and which they produce to feed the adults on demand.

Native honey bees

A defensive ball of Japanese honey bees (A. c. japonica) in which two Japanese hornets (V. simillima xanthoptera) are engulfed, incapacitated, heated, and eventually killed. This sort of defense is also used against the Asian giant hornet.

Beekeepers in Japan attempted to introduce western honey bees (Apis mellifera) because of their high productivity. Western honey bees have no innate defense against the hornets, which can rapidly destroy their colonies. Kakugo virus infection, though, may provide an extrinsic defence. Although a handful of Asian giant hornets can easily defeat the uncoordinated defenses of a western honey bee colony, the Japanese honey bee (Apis cerana japonica) has an effective strategy. When a hornet scout locates and approaches a Japanese honey bee hive, she emits specific pheromonal hunting signals. When the Japanese honey bees detect these pheromones, 100 or so gather near the entrance of the nest and set up a trap, keeping the entrance open.

This permits the hornet to enter the hive. As the hornet enters, a mob of hundreds of bees surrounds it in a ball, completely covering it and preventing it from reacting effectively. The bees violently vibrate their flight muscles in much the same way as they do to heat the hive in cold conditions. This raises the temperature in the ball to the critical temperature of 46 °C (115 °F).

In addition, the exertions of the honey bees raise the level of carbon dioxide (CO₂) in the ball. The bees can tolerate up to 50 °C (122 °F) even at that concentration of CO₂, but the hornet cannot survive the combination of high temperature and high carbon dioxide level. Some honey bees do die along with the intruder, much as happens when they attack other intruders with their stings, but by killing the hornet scout, they prevent it from summoning reinforcements that would wipe out the entire colony.

Detailed research suggests this account of the behavior of the honey bees and a few species of hornets is incomplete and that the honey bees and the predators are developing strategies to avoid expensive and mutually unprofitable conflict. Instead, when honey bees detect scouting hornets, they transmit an "I see you" signal that commonly warns off the predator. Another defence used by Apis cerana is speeding up dramatically when returning to the colony, to avoid midair attacks.

Diet in North America

Based on an examination of larval waste products, the Washington State Department of Agriculture determined that the prey of V. mandarinia included cluster fly, orange legged drone fly, bristle fly, bronze birch borer beetle, western honey bee, western yellowjacket, German yellowjacket, aerial yellowjacket, bald faced hornet, European paper wasp, golden paper wasp, paddle-tailed darner dragonfly, shadow darner dragonfly, large yellow underwing moth, blinded sphinx moth, and red admiral butterfly (Vanessa atalanta). They had also eaten cow's meat, but the WSDA suggests that this may have been beef from a hamburger.

Predators

The Asian giant hornet has very few natural predators. However, V. mandarinia nests are attacked by conspecific colonies, and crested honey buzzards may prey on this hornet. Besides the honey buzzard and each other, there are also instances of other insects such as mantises killing Asian giant hornets.

Pollination capability

V. mandarinia is not solely carnivorous, but also a pollinator. It is among the diurnal pollinators of the obligate plant parasite Mitrastemon yamamotoi. It is among the most common pollinators of Musella lasiocarpa in the Yunnan Province of China.

Extermination methods

As of 1973, six different methods were used to control hornets in Japan; these methods decrease damage done by V. mandarinia.

Beating

Hornets are crushed with wooden sticks with flat heads. Hornets do not counterattack when they are in the bee-hunting phase or the hive-attack phase ("slaughter"), but they aggressively guard a beehive once they kill the defenders and occupy it. The biggest expenditure in this method is time, as the process is inefficient.

Nest removal

Applying poisons or fires at night is an effective way of exterminating a colony. The most difficult part about this tactic is finding the subterranean nests. The most common method of discovering nests is giving a piece of frog or fish meat attached to a cotton ball to a wasp and following it back to its nest. With V. mandarinia, this is particularly difficult considering its common home flight radius of 1–2 kilometres (0.62–1.24 mi). V. mandarinia travels up to 8 kilometres (5.0 mi) away from the nest.

For the rare nest that is up in a tree, wrapping the tree in plastic and vacuuming the hornets out is used.

Bait traps

Bait traps can be placed in apiaries. The system consists of multiple compartments that direct the hornet into a one-sided hole which is difficult to return through once it is in the cul-de-sac compartment, an area located at the top of the box from which honey bees can escape through a mesh opening, but wasps cannot due to their large size. Baits used to attract the hornets include a diluted millet jelly solution or a crude sugar solution with a mixture of intoxicants, vinegar, or fruit essence.

The WSDA has been using plastic bottle traps, baited with fruit juice and added alcohol. The alcohol is used because it repels bees, but not V. mandarinia, thus reducing the bycatch.

Mass poisoning

Hornets at the apiary are captured and fed a sugar solution or bee that has been poisoned with malathion. The toxin is expected to spread through trophallaxis. This method is good in principle, but has not been tested extensively.

Trapping at hive entrances

The trap is attached to the front of beehives. The effectiveness of the trap is determined by its ability to capture hornets while allowing honey bees to escape easily. The hornet enters the trap and catches a bee. When it tries to fly back through the entrance of the hive, it hits the front of the trap. The hornet flies upwards to escape and enters the capture chamber, where the hornets are left to die. Some hornets find a way to escape the trap through the front, so these traps can be very inefficient.

Protective screens

As explained in the trapping section, if met by resistance, hornets lose the urge to attack and instead retreat. Different measures of resistance include weeds, wire, or fishing nets or limiting the passage size so only honey bees can make it through. Experienced hornets catch on and eventually stay on these traps, awaiting the arrival of bees. The best method of controlling hornets is to combine protective screens with traps.

Glue traps

Some Japanese beekeepers place glue traps, similar to the ones commonly used against mice, atop the bees' artificial nesting box with a disarmed giant hornet stuck to the glue. The struggling hornet attracts more hornets who try to help and then get trapped on the glue sheet.

Human consumption

Hornet larva

In some Japanese mountain villages, the nests are excavated and the larvae are considered a delicacy when fried. In the central Chūbu region, these wasps are sometimes eaten as snacks or an ingredient in drinks. The grubs are often preserved in jars, pan-fried or steamed with rice to make a savory dish called hebo-gohan or hebo-han (へぼ飯). The adults are fried on skewers with the stinger still attached until the body becomes crunchy. Within this region, historically residents would hunt for wasp nests as a social activity, fostering the practice of wasp harvesting as well as establishing it as cultural heritage, celebrated in the Kushihara Hebo Matsuri, a festival celebrating wasp-based cuisine.

Asian giant hornets are also cultivated in Nagaland and Manipur, in eastern India.

Potential economic impact

If V. mandarinia were to settle all suitable habitats in North America, potential control costs in the United States would be over US$113.7 million/year (possibly significantly higher). Washington was the only state with confirmed sightings, and there were no confirmed sightings in Washington after 2021, and is now considered extirpated.

If V. mandarinia were to reach all suitable habitats in North America, bee products would bring in US$11.98 ± 0.64 million less per year, and bee-pollinated crops would produce US$101.8 million less per year. New York, Massachusetts, Pennsylvania, Connecticut, North Carolina, New Jersey, and Virginia would be most severely affected. By region, New England would be worst hit, and to a lesser degree the entire northeast and the entirety of eastern North America. New England would potentially become by far the greatest concentration of V. mandarinia in the world, far surpassing the original introduction site (the Pacific Northwest), and even its home range of East Asia. Alfalfa / other hays, apples, grapes, tobacco, cotton, and blueberries would be the crops most severely affected.