astronomy

Simon B. Kochen

Simon B. Kochen is a astronomy 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 Simon B. Kochen rather than just read about it. In short: Simon Bernhard Kochen (; born 14 August 1934) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics. Education and career Kochen was born in Antwerp, Belgium, and escaped the Nazis with his family, thanks to a courageous Norwegian ship captain.

Key takeaways

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

Reference excerpt

Simon Bernhard Kochen (; born 14 August 1934) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics.

Education and career Kochen was born in Antwerp, Belgium, and escaped the Nazis with his family, thanks to a courageous Norwegian ship captain. Raised in England, he attended grammar school before moving to Canada. Kochen attended McGill University and obtained his bachelor’s and master’s degrees there. He moved to the US afterwards and received his Ph.D. (Ultrafiltered Products and Arithmetical Extensions) from Princeton University in 1958 under the direction of Alonzo Church. Since 1967 he has been a member of Princeton's Department of Mathematics. He chaired the department from 1989 to 1992 and became the Henry Burchard Fine Professor in mathematics in 1994. During 1966–1967 and 1978–1979, Kochen was at the Institute for Advanced Study. In 1967 he was awarded, together with James Ax, the seventh Frank Nelson Cole Prize in Number Theory for a series of three joint papers on Diophantine problems involving p-adic techniques. Kochen and Ax also co-authored the Ax–Kochen theorem, an application of model theory to algebra. In 1967 Kochen and Ernst Specker proved the Kochen–Specker theorem in quantum mechanics and quantum contextuality. In 2004 Kochen and John Horton Conway proved the free will theorem. The theorem states that if we have a certain amount of free will, then, subject to certain assumptions, so must some elementary particles.

Worked examples

Example 1 — a first encounter with Simon B. Kochen

Start with the simplest possible case. Write down what Simon B. Kochen claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Simon B. Kochen 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 Simon B. Kochen 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 Simon B. Kochen

In research: Simon B. Kochen appears in astronomy 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 Simon B. Kochen 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: Simon B. Kochen is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1934 births, Cornell University faculty, Institute for Advanced Study visiting scholars, so understanding it makes those chapters shorter.
In everyday life: Look for Simon B. Kochen 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 Simon B. Kochen in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Simon B. Kochen 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 Simon B. Kochen out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Simon B. Kochen in simple terms?

Simon Bernhard Kochen (; born 14 August 1934) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics. Education and career Kochen was born in Antwerp, Belgium, and escaped the Nazis with his family, thanks to a courageous Norwegian ship captain.

Why does Simon B. Kochen matter?

Because it connects several astronomy 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 Simon B. Kochen?

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 Simon B. Kochen.