[4] Mach was born in Chrlice (German: Chirlitz), Moravia, Austrian Empire (now part of Brno in the Czech Republic).

His father Jan Nepomuk Mach, who had graduated from Charles-Ferdinand University in Prague, acted as tutor to the noble Brethon family in Zlín in eastern Moravia.

Some sources give Mach's birthplace as Tuřany (German: Turas, also part of Brno), the site of the Chirlitz registry office.

"[12] In 1898, Mach survived a paralytic stroke, and in 1901, he retired from the University of Vienna and was appointed to the upper chamber of the Austrian Parliament.

On leaving Vienna in 1913, he moved to his son's home in Vaterstetten, near Munich, where he continued writing and corresponding until his death in 1916, one day after his 78th birthday.

[8] Born to a liberal family, Mach lamented that a "very reactionary-clerical" period followed the 1848 revolutions, prompting him to plan to emigrate to America.

[16] Mach was critical of the European powers' colonial conquests, saying that they "will constitute...the most distasteful chapter of history for coming generations".

[17] Most of Mach's initial studies in experimental physics concentrated on the interference, diffraction, polarization and refraction of light in different media under external influences.

Mach and physicist-photographer Peter Salcher presented their paper on this subject[18] in 1887; it correctly describes the sound effects observed during the supersonic motion of a projectile.

[8] From 1895 to 1901, Mach held a newly created chair for "the history and philosophy of the inductive sciences" at the University of Vienna.

He originally saw scientific laws as summaries of experimental events, constructed for the purpose of making complex data comprehensible, but later emphasized mathematical functions as a more useful way to describe sensory appearances.

When the human mind, with its limited powers, attempts to mirror in itself the rich life of the world, of which it itself is only a small part, and which it can never hope to exhaust, it has every reason for proceeding economically.

[20] In 1908, Lenin wrote a philosophical work, Materialism and Empirio-criticism,[21] in which he criticized Machism and the views of "Russian Machists".

If the "sensible content" of our sensations is not the external world then nothing exists save this naked I engaged in empty "philosophical" acrobatics.Empirio-criticism is the term for the rigorously positivist and radically empiricist philosophy established by the German philosopher Richard Avenarius and further developed by Mach, Joseph Petzoldt, and others, that claims that all we can know is our sensations and that knowledge should be confined to pure experience.

"[c] Friedrich Hayek wrote that, when he attended the University of Vienna from 1918 to 1921, "as far as philosophical discussion went it essentially revolved around Mach's ideas".

[30] In 1873, independently of each other,[31] Mach and the physiologist and physician Josef Breuer discovered how the sense of balance (i.e., the perception of the head's imbalance) functions, tracing its management by information the brain receives from the movement of a fluid in the semicircular canals of the inner ear.

The effect exaggerates the contrast between edges of the slightly differing shades of gray as soon as they make contact, by triggering edge-detection in the human visual system.