mathematics

Philipp Frank

Philipp Frank is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Philipp Frank rather than just read about it. In short: Philipp Frank (Austrian German: [fraŋk]; March 20, 1884 – July 21, 1966) was an Austrian-American physicist, mathematician and philosopher of the early-to-mid 20th century. He was a logical positivist, and a member of the Vienna Circle.

Key takeaways

Philipp Frank belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Philipp Frank to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Philipp Frank from memory before moving on to harder problems.

Reference excerpt

Philipp Frank (Austrian German: [fraŋk]; March 20, 1884 – July 21, 1966) was an Austrian-American physicist, mathematician and philosopher of the early-to-mid 20th century. He was a logical positivist, and a member of the Vienna Circle. He was influenced by Mach and was one of the Machists criticised by Lenin in Materialism and Empirio-criticism.

Biography Frank studied physics at the University of Vienna and graduated in 1907 with a thesis in theoretical physics under the supervision of Ludwig Boltzmann. He joined the faculty there in 1910. Albert Einstein recommended him as his successor for a professorship at the German Charles-Ferdinand University of Prague, a position which he held from 1912 until 1938. Doctoral students included Reinhold Furth and Peter Bergmann. In 1938, he was invited by Harvard University to America as a visiting lecturer on quantum theory and the philosophy of modern physics. The Germans having invaded Czechoslovakia as he was about to begin his scheduled lecture tour, Frank, a Jew, never returned to his position at Prague and instead became a lecturer on physics and mathematics at Harvard from that year until his retirement in 1954. In 1947, he founded the Institute for the Unity of Science as part of the American Academy of Arts and Sciences (AAAS). This arose after Howard Mumford Jones (then president of the AAAS) had issued a call to overcome the fractionalization of knowledge, which he felt the AAAS well suited to address. The institute held regular meetings attracting a broad range of participants. Quine regarded the organisation as a "Vienna Circle in exile". Politically Frank was a socialist. Astronomer Halton Arp described Frank's "Philosophy of Science" class at Harvard as being his favorite elective. His younger brother Josef Frank was a noted architect and designer.

Frank on Mach's principle In lectures given during World War II at Harvard, Frank attributed to Mach himself the following graphic expression of Mach's principle: "When the subway jerks, it's the fixed stars that throw you down." In commenting on this formulation of the principle, Frank pointed out that Mach chose the subway for his example because it shows that inertial effects are not shielded (by the mass of the earth): The action of distant masses on the subway-rider's mass is direct and instantaneous. It is apparent why Mach's Principle, stated in this fashion, does not fit with Einstein's conception of the retardation of all distant action.

Select publications Das kausalgesetz und seine grenzen (1932), translated to English by Marie Neurath and Robert S. Cohen as The law of causality and its limits (Dordrecht : Kluwer Academic Publishers, 1998) Interpretations and misinterpretations of modern physics (1938) Between physics and philosophy (1941) Relativity and its astronomical implications : the significance of general relativity presented in the language of the layman (1943) Foundations of Physics, University of Chicago Press (1946) Einstein: His Life and Times, A. A. Knopf (1947); 2nd edition, Da Capo Press (2002) Einstein, his life and times (1948) "Einstein's Philosophy of Science," Review of Modern Physics, 21, 349 (1949) Relativity : a richer truth (1950). With foreword by Albert Einstein Modern science and its philosophy (1955) Philosophy of Science, Prentice Hall (1957)

Illustrations

Worked examples

Example 1 — a first encounter with Philipp Frank

Start with the simplest possible case. Write down what Philipp Frank claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Philipp Frank before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Philipp Frank ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Philipp Frank

In research: Philipp Frank appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Philipp Frank in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Philipp Frank is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1884 births, 1966 deaths, Austrian socialists, so understanding it makes those chapters shorter.
In everyday life: Look for Philipp Frank outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Philipp Frank in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Philipp Frank means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Philipp Frank out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Philipp Frank in simple terms?

Why does Philipp Frank matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Philipp Frank?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Philipp Frank.