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Philosophical problem
In philosophy of mind, the hard problem of consciousness (or simply the hard problem) is to explain how and why organisms have qualia, phenomenal consciousness
Hard_problem_of_consciousness
2015 play by Tom Stoppard
The Hard Problem is a play by Tom Stoppard, first produced in 2015. The title refers to the hard problem of consciousness, which Stoppard defines as having
The_Hard_Problem
Topics referred to by the same term
Hard problem may refer to: The Hard Problem, a 2015 play by Tom Stoppard Hard problems, in computational complexity theory Hard problem of consciousness
Hard_problem
Complexity class
computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time
NP-hardness
Irish actor
Stoppard's The Hard Problem, which ran until 17 May 2015 and also had a worldwide broadcast via NT Live, on 16 April 2015. Both plays were directed by the then
Damien_Molony
Unsolved problem in computer science
Unsolved problem in computer science If the solution to a problem can be checked in polynomial time, must the problem be solvable in polynomial time? More
P_versus_NP_problem
View that mind is a ubiquitous feature of reality
in the mid-20th century associated with the rise of logical positivism. Recent interest in the hard problem of consciousness and developments in the fields
Panpsychism
points on dream consciousness as explained in his works. The “Hard problem” is defined as the difficulty in specifying how subjective awareness could arise
Dream_consciousness
Ability to make choices voluntarily
It has been noted that the laws of physics have yet to resolve the hard problem of consciousness: "Solving the hard problem of consciousness involves
Free_will
Theory within consciousness research
so-called "hard problem". Rather than try to start from physical principles and arrive at consciousness, IIT "starts with consciousness" (accepts the existence
Integrated_information_theory
Thought experiment in philosophy
against forms of physicalism and in defense of the hard problem of consciousness, which is the problem of accounting in physical terms for subjective
Philosophical_zombie
Conscious event, perception or practical knowledge
experience is involved in the mind–body problem and the hard problem of consciousness, both of which try to explain the relation between matter and
Experience
American actor (born 1978)
vivid Iranian voice". The Guardian. Retrieved March 24, 2019. Staff (November 4, 2019). "L.A. Theatre Works Records The Hard Problem By Tom Stoppard At UCLA"
Eddie_Cahill
Australian philosopher and cognitive scientist (born 1966)
Sciences. Chalmers is best known for formulating the hard problem of consciousness, and for popularizing the philosophical zombie thought experiment. Chalmers
David_Chalmers
Branch of philosophy
issues are addressed, such as the hard problem of consciousness and the nature of particular mental states. Aspects of the mind that are studied include
Philosophy_of_mind
NP-hard problem in combinatorial optimization
cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial
Travelling_salesman_problem
Optimization problem in computer science
problems is central to the construction of secure lattice-based cryptosystems: lattice problems are an example of NP-hard problems which have been shown
Lattice_problem
The Philosophical Quarterly. 32 (127): 127–136. doi:10.2307/2960077. JSTOR 2960077. Block, Ned (2002). "The Harder Problem of Consciousness". The Journal
List of philosophical problems
List_of_philosophical_problems
English actress
Lear at The Royal National Theatre. In 2015, Vinall took centre stage again at National Theatre Live in Tom Stoppard's play The Hard Problem as Hilary
Olivia_Vinall
Totality of psychological phenomena
mind–body problem by arguing that it is based on an artificial dichotomy not present in the phenomenological description of experience. The hard problem of consciousness
Mind
Ascribing an impossible property to a thing
Professor of Philosophy at the City University of New York, argues that the "hard problem of consciousness", as expressed by David Chalmers and others, rests
Category_mistake
American cognitive psychologist and popular science author
scientific explanation. Hoffman proposes a solution to the hard problem of consciousness by adopting the converse view that consciousness causes brain activity
Donald_D._Hoffman
American actor
of the Class. Hall began her professional acting career in the theater in 2016, when she played the role of Cathy Krohl in The Hard Problem at the Studio
Katie_Beth_Hall
Open question in philosophy of how abstract minds interact with physical bodies
The mind–body problem is a philosophical problem concerning the relationship between thought and consciousness in the human mind and body. It addresses
Mind–body_problem
Model of consciousness
conscious: the hard problem of consciousness. However, the abstract of Avshalom Elitzur's 1997 paper summarized that while GWT "does not address the 'hard problems
Global_workspace_theory
2021 book by Anil Seth
Seth's position on the hard problem of consciousness to fall in the middle between the two positions of either finding the hard problem to be meaningful
Being You: A New Science of Consciousness
Being_You:_A_New_Science_of_Consciousness
Awareness of internal and external existence
he calls this the hard problem of consciousness. Some philosophers believe that Block's two types of consciousness are not the end of the story. William
Consciousness
Thought experiment on artificial intelligence
consciousness is at the root of the matter" of the Chinese room. Colin McGinn argues that the Chinese room provides evidence that the hard problem of consciousness
Chinese_room
Problem of communication when asking for help
The XY problem is a communication problem encountered in help desk, technical support, software engineering, or customer service situations where the
XY_problem
Mathematical problem in operations research
optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible
Cutting_stock_problem
Hypothetical process of digitally emulating a brain
described by Alexey Turchin. The main philosophical problem faced by mind uploading is the hard problem of consciousness: the difficulty of explaining how
Mind_uploading
Hypothetical internal cognitive symbol that represents external reality
about the nature of phenomenal character, as well as offer a potential solution to the hard problem of consciousness. The successful reduction of the phenomenal
Mental_representation
British actor (born 1953)
London, and in 2015 in the world premiere production of Stoppard's The Hard Problem. Jonathan Coy at IMDb The Unseen Hook at the Internet Movie Database
Jonathan_Coy
NP-complete problem in computer science
that solve the problem in many instances, either optimally or approximately. For this reason, it has been called "the easiest hard problem". There is
Partition_problem
Hypothesis in computational complexity theory
like the planted clique conjecture. However, for cryptographic applications, knowing that a problem has some hard instance (the problem is hard in the worst-case)
Computational hardness assumption
Computational_hardness_assumption
American actor
played the role of Spike in Tom Stoppard's The Hard Problem at the Lincoln Center. In November 2020, O'Shea was cast in a recurring role on the third season
Christopher_O'Shea
Class of metaphysical theories in the philosophy of mind
within the philosophy of mind, specifically the mind–body problem and the hard problem of consciousness. The mind–body problem is the problem of explaining
Neutral_monism
Ability to readily identify logical or mathematical truth
(PDF) from the original on 2019-10-21. Retrieved October 21, 2019. Aas, Benjamin (2011). "Body-Gödel-Mind: The unsolvability of the hard problem of consciousness"
Logical_intuition
NP-hard problem in combinatorial optimization
The ring star problem (RSP) is a NP-hard problem in combinatorial optimization. In a complete weighted mixed graph, the ring star problem aims to find
Ring_star_problem
American sci-fi television series
Problem is an American science fiction television series created by David Benioff, D. B. Weiss, and Alexander Woo. It is the third adaptation of the Chinese
3_Body_Problem_(TV_series)
Research into the problem of consciousness
Neurophenomenology refers to a scientific research program aimed at addressing the hard problem of consciousness in a pragmatic way. It combines neuroscience with
Neurophenomenology
American writer
A Brief Guide to the Fundamental Mystery of the Mind. Key subjects of Conscious include free will, panpsychism and the hard problem of consciousness.
Annaka_Harris
Branch of computational complexity theory
parameters. This allows the classification of NP-hard problems on a finer scale than in the classical setting, where the complexity of a problem is only measured
Parameterized_complexity
2019 book by Philip Goff
Philip Goff. The book presents a defense of the theory of panpsychism as the solution to the hard problem of consciousness. The title of the book refers
Galileo's_Error
on some hard mathematical problem, and it is proved that finding collisions of the hash function is as hard as breaking the underlying problem. This gives
Security of cryptographic hash functions
Security_of_cryptographic_hash_functions
American philosopher
of the hard problem of consciousness, and as one of the main objections materialist theories in the philosophy of mind must address. The idea of the explanatory
Joseph_Levine_(philosopher)
Combinatorial optimization problem
Intuitively, the objective function encourages facilities with high flows between each other to be placed close together. The problem is NP-hard, so there
Quadratic_assignment_problem
Problem in computer science
In computability theory, the halting problem is the decision problem of, given an arbitrary computer program and an input, determining whether said program
Halting_problem
2014 book by Stanislas Dehaene
consciousness but feels that the hard problem remains unresolved. Like Kalat, Hutson finds Dehaene's dismissal of the hard problem unjustified because consciousness
Consciousness_and_the_Brain
Philosophical position on the mind-body problem
position proposing that the hard problem of consciousness cannot be resolved by humans. The unresolvable problem is how to explain the existence of qualia
New_mysterianism
Unsolved problem in computational complexity theory
solution to a GI-hard problem would yield a polynomial-time solution to the graph isomorphism problem (and so all problems in GI). A problem X {\displaystyle
Graph_isomorphism_problem
Observation that perception requires more computation than reasoning
wrote in 1994 that "the main lesson of thirty-five years of AI research is that the hard problems are easy and the easy problems are hard". One possible explanation
Moravec's_paradox
Inherent difficulty of computational problems
particular, the set of problems that are hard for NP is the set of NP-hard problems. If a problem X {\displaystyle X} is in C {\displaystyle C} and hard for C
Computational complexity theory
Computational_complexity_theory
Problem that is difficult or impossible to solve
recognize. It refers to an idea or problem that cannot be fixed, where there is no single solution to the problem; "wicked" does not indicate evil, but
Wicked_problem
Subfield of mathematical optimization
travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously
Combinatorial_optimization
1996 philosophy book by David Chalmers
they claim to have solved the "hard problem of consciousness", when really all they have solved are certain "easy problems of consciousness". Chalmers
The_Conscious_Mind
Problem in combinatorial optimization
The traveling purchaser problem (TPP) is an NP-hard problem studied in operations research and theoretical computer science. Given a list of marketplaces
Traveling_purchaser_problem
Combinatorial optimization problem
problem with a wide range of applications from finance and economics to machine learning. QUBO is an NP hard problem, and for many classical problems
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
Unrelated vertices in graphs
problem of finding such a set is called the maximum independent set problem. It is a strongly NP-hard problem. As such, it is unlikely that there exists
Independent set (graph theory)
Independent_set_(graph_theory)
Inability to describe conscious experiences in solely physical or structural terms
explanation for experience and qualia) is known as "the hard problem". The hardness of the problem is such that mysterians believe it can never be solved
Explanatory_gap
Type of computational problem
{\displaystyle R} . A problem R {\displaystyle R} is FNP-complete if it is FNP-hard and in FNP. The problem FSAT is an FNP-complete problem, and hence by self-reducibility
Function_problem
Hindu monk
conversation on the Hard problem of consciousness. Fortune India mentions Sarvapriyananda as "one of the best known lecturers of the Vedanta in the world today"
Swami_Sarvapriyananda
Decision problem in computer science
SSP is NP-hard. The complexity of the best known algorithms is exponential in the smaller of the two parameters n and L. The problem is NP-hard even when
Subset_sum_problem
Use of tape machine record head as playback head in order to sync with new recording
head. The hard problem was the switching of a track between record and playback mode, as the impedance of record heads is quite different from the impedance
Sel-Sync
Theories proposing consciousness as an electromagnetic phenomenon
new physics can resolve the hard problem of consciousness. He argues that quantum theories of consciousness suffer from the same weakness as more conventional
Electromagnetic theories of consciousness
Electromagnetic_theories_of_consciousness
1988 film by John McTiernan
Die Hard is a 1988 American action film directed by John McTiernan and written by Jeb Stuart and Steven E. de Souza, based on the 1979 novel Nothing Lasts
Die_Hard
Type of AI with wide-ranging abilities
unknown to the AGI developers before the test is administered. A problem is informally called "AI-complete" or "AI-hard" if it is believed that AGI would
Artificial general intelligence
Artificial_general_intelligence
Cryptographic primitives that involve lattices
average-case lattice problem, known as short integer solutions (SIS), is at least as hard to solve as a worst-case lattice problem. She then showed a cryptographic
Lattice-based_cryptography
Task of computing complete subgraphs
networks, the clique problem also has many applications in bioinformatics, and computational chemistry. Most versions of the clique problem are hard. The clique
Clique_problem
British psychologist (1934–2004)
solution to the 'hard problem' of how consciousness arises. Gray was opposed to the idea that the brain contains a representation of the external world
Jeffrey_Alan_Gray
Problem in cryptography
that over many groups the DHP is almost as hard as the DLP. There is no proof to date that either the DHP or the DLP is a hard problem, except in generic
Diffie–Hellman_problem
British actor
Rycroft Twelfth Night (2017) as Malvolio at the Royal Exchange, Manchester The Hard Problem (2015) Stephen Ward the Musical (2013–2014) Private Lives (2013)
Anthony_Calf
Malaysian actress and writer
production as artistic director for the National Theatre, Tom Stoppard's The Hard Problem. The play was Stoppard's first for the theatre since 2006 and a special
Vera_Chok
Interdisciplinary scientific study of cognitive processes
for articulating the hard problem of consciousness, and Douglas Hofstadter, famous for writing Gödel, Escher, Bach, which questions the nature of words
Cognitive_science
Subdivision of vertices into disjoint sets
and maximum cut problems. Typically, graph partition problems fall under the category of NP-hard problems. Solutions to these problems are generally derived
Graph_partition
Intelligence of machines
(AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving
Artificial_intelligence
Complexity class
in NP. A problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems are thus, in a sense, the hardest problems in NP. The Cook–Levin
NP-completeness
Open problem on 3x+1 and x/2 functions
for all n > 0? Modifying the condition in this way can make a problem either harder or easier to solve (intuitively, it is harder to justify a positive answer
Collatz_conjecture
Problem of finding the best feasible solution
economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two
Optimization_problem
Process of achieving a goal by overcoming obstacles
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from
Problem_solving
word-representants? Is the line graph of a non-word-representable graph always non-word-representable? Which (hard) problems on graphs can be translated
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
problem. This problem is easier to solve than integer factorization, so the assumption that this problem is hard to solve is stronger than the assumption
Higher_residuosity_problem
Minimum-cost tree with exactly k vertices
for variable k, the k-minimum spanning tree problem has been shown to be NP-hard by a reduction from the Steiner tree problem. The reduction takes as
K-minimum_spanning_tree
Class of algorithms that find approximate solutions to optimization problems
solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation
Approximation_algorithm
Artificial intelligence (AI) program
an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language model (LLM)
AlphaGeometry
Instances of subjective experience
actually exists, the possibility is raised as a refutation of physicalism, and in defense of the hard problem of consciousness (the problem of accounting
Qualia
Branch of philosophy
"Facing up to the hard problem of consciousness." Journal of Consciousness Studies 2, 3, 200–219. Dretske, Fred (1981). Knowledge and the Flow of Information
Philosophy_of_perception
Probability of shared birthdays
theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday. The birthday
Birthday_problem
Node labeling problem in graph theory
} Both the unweighted and weighted versions are special cases of the quadratic bottleneck assignment problem. The bandwidth problem is NP-hard, even for
Graph_bandwidth
Sequence of operations for a task
that is close to the true solution. Such algorithms have practical value for many hard problems. For example, the Knapsack problem, where there is a
Algorithm
2008 science fiction novel by Liu Cixin
The Three-Body Problem (Chinese: 三体; pinyin: Sān tǐ; lit. 'three body') is a 2008 novel by the Chinese hard science fiction author Liu Cixin. It is the
The Three-Body Problem (novel)
The_Three-Body_Problem_(novel)
Optimizing objective functions that have constrained variables
programming problem. If all the hard constraints are linear and some are inequalities, but the objective function is quadratic, the problem is a quadratic
Constrained_optimization
Study of general and fundamental questions
terms of the functional or causal roles they play. The mind-body problem is closely related to the hard problem of consciousness, which asks how the physical
Philosophy
Cryptography secured against quantum computers
security to a known hard problem would have a provable security reduction of the Merkle tree signature to that known hard problem. The Post-Quantum Cryptography
Post-quantum_cryptography
science, the closest string is an NP-hard computational problem, which tries to find the geometrical center of a set of input strings. To understand the word
Closest_string
Hypothesis that reality could be a computer simulation
system that implements the right computational structures and processes (see Hard problem of consciousness). Variations on the idea have also been featured
Simulation_hypothesis
Term used in animal husbandry
and is prone to obesity and other health problems associated with a too-rich diet. In contrast, a truly hard keeper is almost never fat under any circumstances
Hard_keeper
(or NP-hard) problem is weakly NP-complete (or weakly NP-hard) if there is an algorithm for the problem whose running time is polynomial in the dimension
Weak_NP-completeness
Topics referred to by the same term
A$AP Rocky "Problem", in Hotel Transylvania (film) § Soundtrack, 2012 "Problem", on The Hard Way (Deluxe) (2025) by Cameron Whitcomb "Problem", 2011 single
Problem_(disambiguation)
1982 studio album by the Who
It's Hard is the tenth studio album by the English rock band the Who. Released in September 1982, it was the final Who album to feature bassist John Entwistle
It's_Hard
THE HARD-PROBLEM
THE HARD-PROBLEM
Surname or Lastname
English and German
English and German : nickname for someone with a deformed hand or who had lost one hand, from Middle English hand, Middle High German hant, found in such appellations as Liebhard mit der Hand (Augsburg 1383).Jewish (Ashkenazic) : nickname from German Hand ‘hand’ (see 1).Irish : Anglicized form of Gaelic Ó Flaithimh (see Guthrie), resulting from an erroneous association of the Gaelic name with the Gaelic word lámh ‘hand’. It is used as an English equivalent for several other names of Gaelic origin too, e.g. Claffey, Glavin, and McClave.Dutch : from a variant of hont ‘dog’, ‘hound’, either a derogatory nickname, or a habitational name for someone living at a house distinguished by the sign of a dog.
Surname or Lastname
English, Scottish, and French
English, Scottish, and French : nickname for a brave or
foolhardy man, from Old French, Middle English hardi ‘bold’,
‘courageous’ (of Germanic origin; compare Hard 1).Irish : in addition to being an importation of the English name,
this is also found as an Anglicized form (by partial translation) of
Gaelic Mac Giolla Deacair ‘son of the hard lad’.Scottish : variant spelling of Hardie 2.Bearers of the surname Hardy from Anjou and Normandy, France, are documented
in Quebec City in 1669. The secondary surnames Châtillon,
Boy/Male
Hindu, Indian
Hearts Feelings
Male
German
Short form of German Harman, HARM means "bold/hardy man." In use by the Dutch.
Male
Hindi/Indian
(हरि) Hindi name HARI means "he who takes away." In Hindu mythology, this is a name borne by Vishnu.
Surname or Lastname
English and North German
English and North German : from a personal name or nickname meaning ‘stag’, Middle English hert, Middle Low German hërte, harte.German : variant spelling of Hardt 1 and 2.Jewish (Ashkenazic) : ornamental name or a nickname from German and Yiddish hart ‘hard’.Irish : Anglicized form of Gaelic Ó hAirt ‘descendant of Art’, a byname meaning ‘bear’, ‘hero’. The English name became established in Ireland in the 17th century.French : from an Old French word meaning ‘rope’, hence possibly a metonymic occupational name for a rope maker or a hangman.Dutch : nickname from Middle Dutch hart, hert ‘hard’, ‘strong’, ‘ruthless’, ‘unruly’.This name was brought independently to New England by many bearers from the 17th century onward. Stephen Hart was one of the founders of Hartford, CT, (coming from Cambridge, MA, with Thomas Hooker) in 1635.
Surname or Lastname
English
English : variant of Herd.Respelling of Swedish HÃ¥rd (see Hard 2).
Boy/Male
British, English, German
From the Yard on a Hill; Hard Warrior
Male
Egyptian
, Horus the Executer of Justice.
Male
Japanese
(1-晴, 2-春, 3-陽) Japanese unisex name HARU means 1) "clear up," 2) "spring," or 3) "sun, sunlight." Compare with another form of Haru.
Female
German
Pet form of German Kätharina, KÄTHE means "pure."
Surname or Lastname
English
English : habitational name from Chard or South Chard in Somerset, recorded in Domesday Book as Cerdren, possibly from Old English ceart ‘rough heathland’ + ærn ‘building’, ‘dwelling’. In some instances the surname may have arisen simply as a topographic name from ceart.French : from the personal name Chard, a short form of Richard;French : habitational name for someone from Chard in the department of Creuse.
Boy/Male
American, Anglo, Arabic, Australian, British, Christian, English, German, Irish, Jamaican, Teutonic
Bard; Surname; Guardian; Watchman
Surname or Lastname
English
English : from the Old English personal name Heard or a Norman cognate Hard(on), also of Germanic origin. This was a byname meaning ‘hardy’, ‘brave’, ‘strong’, but it also seems to have been used as a short form of the various compound names containing this as a first element. Occasionally this may also be a variant of Hardy.English, German, Dutch, and Swedish (Hård) : nickname for a stern or severe man, from Middle English, Middle Low German hard, Middle Dutch hart, hert, Swedish hård ‘hard’, ‘inflexible’. The Swedish name was probably originally a soldier’s name.English : topographic name for someone who lived on a patch of particularly hard ground or one that was difficult to farm. Compare Hardacre.Dutch : occupational name from Middle Dutch harde, herde ‘herder’.
Surname or Lastname
English (chiefly Midlands)
English (chiefly Midlands) : variant spelling of Heard.
Surname or Lastname
English
English : from the possessive case of the personal name Hard, denoting a son or servant of someone called Hard.
Boy/Male
Hindu
Hearts feeling, Main, Meaning
Surname or Lastname
English
English : variant of Heard.
Male
English
Pet name for longer English names containing Hard- or Hart-, HARDY means "brave, hardy, strong."Â
Surname or Lastname
English (chiefly Yorkshire and Northumbria), also Scottish
English (chiefly Yorkshire and Northumbria), also Scottish : variant spelling of Heard.
THE HARD-PROBLEM
THE HARD-PROBLEM
THE HARD-PROBLEM
THE HARD-PROBLEM
THE HARD-PROBLEM
THE HARD-PROBLEM
THE HARD-PROBLEM
a.
Hard-featured; ill-looking; as, Vulcan was hard-favored.
v. t.
To confine (cattle) to the yard; to shut up, or keep, in a yard; as, to yard cows.
superl.
Difficult to please or influence; stern; unyielding; obdurate; unsympathetic; unfeeling; cruel; as, a hard master; a hard heart; hard words; a hard character.
v. t.
To give, pass, or transmit with the hand; as, he handed them the letter.
superl.
Not easily penetrated, cut, or separated into parts; not yielding to pressure; firm; solid; compact; -- applied to material bodies, and opposed to soft; as, hard wood; hard flesh; a hard apple.
superl.
Rough; acid; sour, as liquors; as, hard cider.
adv.
With difficulty; as, the vehicle moves hard.
superl.
Not easy or agreeable to the taste; stiff; rigid; ungraceful; repelling; as, a hard style.
v. t.
To harden; to make hard.
v. t.
To pledge by the hand; to handfast.
n.
The hard wing case of a beetle.
n.
To play on the harp.
superl.
Wanting softness or smoothness of utterance; harsh; as, a hard tone.
superl.
Difficult to bear or endure; not easy to put up with or consent to; hence, severe; rigorous; oppressive; distressing; unjust; grasping; as, a hard lot; hard times; hard fare; a hard winter; hard conditions or terms.
a.
Having hard or strong hands; as, a hard-fisted laborer.
a. Vigorously
contested; as, a hard-fought battle.
a.
Having hard hands, as a manual laborer.
adv.
With tension or strain of the powers; violently; with force; tempestuously; vehemently; vigorously; energetically; as, to press, to blow, to rain hard; hence, rapidly; as, to run hard.
superl.
Difficult, mentally or judicially; not easily apprehended, decided, or resolved; as a hard problem.
superl.
Difficult to accomplish; full of obstacles; laborious; fatiguing; arduous; as, a hard task; a disease hard to cure.