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'-ical' words
Many adjectives end in `-ic' or `-ical'.
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adjectives related to '-ic' nouns
Sometimes an adjective ending in `-ical' is related to a noun ending in `-ic'.

She loved music and played the piano well.

The majority of the finance for musical performances comes from the audiences.

Pareto was a cynic, disillusioned by the society of his day.

...a cynical contempt for truth and decency.

The owner of the hotel is a sports fanatic.

...a fanatical supporter of the government.

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The words in the following two lists are nouns ending in `-ic' which have related adjectives ending in `-ical'.
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These nouns refer to things:
arithmetic, comic, logic, magic, music, tactic
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These nouns refer to people:
comic, critic, cynic, fanatic, mystic, sceptic
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Note that `comic' can refer to a thing (a cartoon magazine) or a person (a comedian).
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`Comic', `fanatic', `magic', and `mystic' can themselves be used as adjectives.
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Many other nouns end in `-ic', for example `fabric', `panic', and `relic', but they do not have related adjectives ending in `-ical'.
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adjectives related to '-ics' nouns
Many nouns end in `-ics'. Sometimes the adjective related to them ends in `-ic' and sometimes it ends in `-ical'.
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The following nouns have related adjectives ending in `-ic':
acoustics, acrobatics, aerobatics, aerobics, aerodynamics, athletics, basics, economics, electronics, genetics, graphics, gymnastics, heroics, histrionics, italics, linguistics, obstetrics, specifics, thermodynamics

...the amazing developments in genetics that have taken place recently.

...the rapid progress being made in the field of genetic research.

...a paper on linguistics and literary criticism.

...students with linguistic ability.

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The following nouns have related adjectives ending in `-ical':
aeronautics, classics, ethics, hysterics, mathematics, physics, statistics, tropics

...the doctor's code of ethics.

...the kinds of ethical and moral problems that will arise.

She was having a fit of hysterics.

It's nothing to get hysterical about, darling.

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Note that `logistics' has two related adjectives: `logistic' and `logistical'.
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'-ic' and '-ical' adjectives
A number of adjectives have forms ending in `-ic' and `-ical', with no great difference in meaning.

There was some scattered ironic applause from the crowd.

He smiled a friendly, slightly ironical smile.

The whole business becomes problematic, tinged with anxiety.

The relationship between private business and government remains unsolved and problematical.

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The following pairs of adjectives have similar meanings:
cyclic - cyclical, egoistic - egoistical, egotistic - egotistical, fanatic - fanatical, geographic - geographical, geometric - geometrical, ironic - ironical, logistic - logistical, mystic - mystical, problematic - problematical, rhythmic - rhythmical, syntactic - syntactical
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Sometimes there is a difference in meaning or use between pairs of adjectives ending in `-ic' and `-ical'. See entries at ↑ classic - classical, ↑ comic - comical, ↑ electric - electrical, ↑ historic - historical, and magic - magical. See also entry at ↑ economics for the difference between `economic' and `economical'.
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other '-ic' adjectives
Some adjectives not mentioned above consist of a noun with `-ic' on the end. The adjective indicates that something is connected with the thing referred to by the noun. For example, if a drink is `alcoholic', it contains alcohol, something that is `magnetic' is like a magnet and causes metal objects to stick to it.

Daniel laughed with idiotic pleasure.

He took a carving knife from a magnetic board on the wall.

I was getting more and more journalistic work.

...distributing photographic products to retailers.

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Sometimes it may not be very clear what noun an `-ic' adjective is related to. For example, `ironic' is related to `irony', not to `iron'; `organic' means `relating to organisms' (living things), not `relating to an organ'; and `manic' means `very energetic or excited', not `relating to a man'.
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Useful english dictionary. 2012.