On the one hand, you hope he’s got a good copy of the original cast recording of “Man of La Mancha,” with the late Richard Kiley singing the importance of dreaming the impossible dream. On the other hand, you hope it’s not an impossible situation at all.

**Mathematics Professor Lorenzo Sadun declared his candidacy for the Texas State Board of Education seat representing District 10. **He’ll be running against incumbent Cynthia Dunbar in a district that has a history of electing people with little or no education background and a commitment to scorched Earth conservative policies — if Dunbar chooses to run again. Dunbar has not announced her intentions.

Sadun is professor of mathematics at the University of Texas, in Austin.

In the 2006 election, there was no Democratic nominee. Dunbar ran against a Libertarian and won approximately 70 percent of the vote. The 2010 primary election is scheduled for March, and Sadun declared last week that he will seek the Democratic nomination.

The Place 10 seat-holder may become very influential. With the board almost evenly split, a negative or positive vote can greatly affect educational policy and standards.

If Sadun is elected, he will be the only scientist on the board.He said that even though he may encounter opposition from members of the board, he will find a common ground with his colleagues and will pursue agreement without sacrificing the quality of education for Texas students.“Despite my taking a fairly hard line, I am a conciliator,” Sadun said. “I have not met a person who knew so much I couldn’t teach them something, and I’ve never met someone who knew so little that they couldn’t teach me something.”

District 10 includes 14 counties surrounding Travis County to the east of the county, and the northern part of Travis County. Travis, home to the Texas state capital Austin and one of Texas’s five supercounties, was split in education board districts to limit the influence of its highly-educated, more liberal voter population.

Burnt Orange Report wrote that Dunbar will face opposition if she chooses to run again.

- Dr. Rebecca Osborne, a teacher in the Roundrock ISD, has also announced her intention to run for the District 10 seat, as a Republican.
- Austin education activist Julie Cowan will run for the Republican nomination
- Judy Jennings will run for the Democratic nomination. She is Director of Assessment at Resources for Learning.
- Democratic Party activist Susan Shelton will also seek the Democratic nomination.

Events in District 10 offer a sign of hope that the era ended when apathy from candidates and voters allowe anti-public education forces to dominate the Texas State Board of Education. And if Sadun were to win, it would be the first time a working scientist was elected to SBOE.

Who knows? Sadun could succeed — but if he wins a seat on the SBOE, it’s not likely he’d sing that other song Richard Kiley made famous, “Stranger in Paradise.” He’s no stranger to quality education, and SBOE isn’t paradise.

DB: I hope the mathematician gets elected. For the sake of science!

Me too.

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I admit defeat and am glad I didn’t place a bet on the outcome.

Regardless our discussion, I hope the mathematician gets elected. For the sake of science!

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Here’s another perspective:

http://www.stolaf.edu/people/steen/Papers/integrating.html

Integrating School Science and Mathematics: Fad or Folly?

Lynn Arthur Steen, St. Olaf College

“These differences are essential to proper understanding of a fundamental difference between mathematics and science:

Science seeks to understand nature.

Mathematics reveals order and pattern.

The subject of science is nature; the subject of mathematics is pattern. Each can contribute to the other, but they are fundamentally different enterprises. “

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DB: How did he come to discovery? By observing relationships of shapes.

Again, not relevant. What anyone’s inspiration is has nothing to do with how their ideas are validated.

Let me again point out that by “observation” I am including measurement. In science, ideas are tested against the real world. From my earlier post “By establishing suitable postulates it is always possible to make a system of mathematics, just as Euclid did, but we cannot make a mathematics of the world, because sooner or later we have to find out whether the axioms are valid for the objects of nature.”

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DB: Now you give me an example of a mathematical theorem still used that has been proven wrong by observation.

I would say we still have no idea what the other is talking about.

It is impossible for me to give such an example because math results cannot be disproven by observation. My whole point that math results are proved by recourse to assumptions, not observations.

To prove Pythagoras’ theorem, you do not measure anything. From wikipedia “Euclidean geometry … consists of assuming a small set of intuitively appealing axioms, and then proving many other propositions (theorems) from those axioms.” It is an entirely self-contained field.

The Pythagorean theorem is true in Euclidean geometry, but not in other types in which his 5th axiom is changed. From exampleproblems.com:

The Pythagorean theorem in non-Euclidean geometry

The Pythagorean theorem is derived from the axioms of Euclidean geometry, and in fact, the Euclidean form of the Pythagorean theorem given above does not hold in non-Euclidean geometry. For example, in spherical geometry, all three sides of the right triangle bounding an octant of the unit sphere have length equal to π / 2; this violates the Euclidean Pythagorean theorem because (\pi/2)^2+(\pi/2)^2\neq (\pi/2)^2.

This means that in non-Euclidean geometry, the Pythagorean theorem must necessarily take a different form from the Euclidean theorem. There are two cases to consider — spherical geometry and hyperbolic plane geometry; in each case, as in the Euclidean case, the result follows from the appropriate law of cosines:

* For any right triangle on a sphere of radius R, the Pythagorean theorem takes the form

\cos \left(\frac{c}{R}\right)=\cos \left(\frac{a}{R}\right)\,\cos \left(\frac{b}{R}\right).

By using the Maclaurin series for the cosine function, it can be shown that as the radius R approaches infinity, the spherical form of the Pythagorean theorem approaches the Euclidean form.

* For any triangle in the hyperbolic plane (with Gaussian curvature −1), the Pythagorean theorem takes the form

\cosh c=\cosh a\,\cosh b

where cosh is the hyperbolic cosine. By using the Maclaurin series for this function, it can be shown that as a hyperbolic triangle becomes very small (i.e., as a, b, and c all approach zero), the hyperbolic form of the Pythagorean theorem approaches the Euclidean form.

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Let’s go back to Pythagoras then. How did he come to discovery? By observing relationships of shapes. He didn’t invent the right triangle to explain his math, he invented the math to explain his observation.

Now you give me an example of a mathematical theorem still used that has been proven wrong by observation. I’m not asking for one that hasn’t been yet proved because our powers of observation aren’t that well developed yet.

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I should say something when the other person is explaining it perfectly well?

Or perhaps a certain higgins shouldn’t make silly assumptions.

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DB: My premise is that mathematics is based on — and proven — by observation. Therefore it is a science, albeit one approached from another perspective.

Can you give me an example? [By observation I mean measurement and comparison with the world.]

I gave an earlier example of the Pythagorean example and what I thought were “scientific” and mathematical approaches to the problem. Also the text I scanned in says there is a difference between science and math.

[I see NK has bailed out.]

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My learning (and it’s more than possible it’s insufficient) is that the rules of mathematics were based on observation. Further development of mathematics sought to predict what observation would prove. If observation did not prove what a mathematical theorem predicted, the theorem was… prima facie… false.

j a higginbotham — your premise is that mathematics is not a science because it is not based on observation. My premise is that mathematics is based on — and proven — by observation. Therefore it is a science, albeit one approached from another perspective.

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DB: Is not mathematics proven in observance of nature?

No. Mathematics is proven based on its postulates. Below I have appended the Contents of The Annals of Mathematics, Vol. 169, No. 2, 2009. I looked at the abstracts but not the papers. I see nothing that suggests any of these papers are based on observance of nature. [Am I correct in assuming that you believe observance of nature to be a necessary component of science?]

DB: How else do mathematics make sense?

I don’t understand this question.

DB: If mathematics is separate from nature, surely I could prove that 4+3=8, could I not?

[If English is separate from nature, surely I could prove that “They is …” is proper usage, could I not?]

In math, statements can be proven. In science, statements are not “proved”. See the text I scanned in earlier.

DB: If 4+3 actually did equal 8, all of science would be sorta screwed.

—–

Why? Because there is some inconsistency? What about radiation – does light behave like particles or waves? Isn’t that a similar inconsistency?

http://annals.princeton.edu/annals/2009/169-2/index.xhtml

An embedded genus-one helicoid 347-448

Matthias Weber & David Hoffman & Michael Wolf

Nontangential limits in Pt(µ)-spaces and the index of invariant subgroups 449-490

Alexandru Aleman & Stefan Richter & Carl Sundberg

The geometry of fronts 491-529

Kentaro Saji & Masaaki Umehara & Kotaro Yamada

Curvature of vector bundles associated to holomorphic fibrations 531-560

Bo Berndtsson

The quasi-additivity law in conformal geometry

561-593

Jeremy Kahn & Mikhail Lyubich

Inverse Littlewood–Offord theorems and the condition number of random discrete matrices 595-632

Terence Tao & Van H. Vu

A combinatorial description of knot Floer homology 633-660

Ciprian Manolescu & Peter S. Ozsváth & Sucharit Sarkar

The concept of duality in convex analysis, and the characterization of the Legendre transform 661-674

Shiri Artstein-Avidan & Vitali Milman

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DB: How can science progress beyond mere observance with mathematics?

I’ve already addressed this point. Mathematics is essential to science but it is not science. Paintbrushes are essential to art painting but paintbrushes are not art.

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NK:The point I was making, Higgin, is that the process that science and mathematics engages in is the same process.

No, the point you are *stating* is that they are the same.

I have repeatedly ssaid that my understanding of science requires some recourse to the natural world; you have repeatedly ignored this.

1) Does your definition of “science” require inclusion of any observational data?

2) If so, how does the field of mathematics conform?

Another example for you: The Pythagorean theorem.

Mathematical approach: Prove the equation starting from various accepted statements. Note that none of the hundreds of proofs require any observations of reality.

Scientific approach: Gather things which look like right-angle triangles, measure sides, and check if numbers are close to prediction of equation. [Note: This is not a proof.]

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“4+3=8″ — that’s creationism. –Ed

The amazing thing about mathematics is that it can be used to predict nature. If 4+3 actually did equal 8, all of science would be sorta screwed.

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The point I was making, Higgin, is that the process that science and mathematics engages in is the same process.

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“4+3=8” — that’s creationism.

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How can science progress beyond mere observance with mathematics? Surely, you are familiar with Jakob Bernoulli and calculus? Zeno and time?

Is not mathematics proven in observance of nature? How else do mathematics make sense?

If mathematics is separate from nature, surely I could prove that 4+3=8, could I not?

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NK: No, it’s you missing something there, Higgin.

Then perhaps you can explain what I am missing rather than just repeatedly telling me I am wrong and missing the point.

NK: Because the point I was making is a simple point.

Then perhaps you could explain it. I have given you several posts and explanations; your sole response is to tell me how simple it is and how wrong I am.

Perhaps you are using a different definition of science which somehow includes math. Then you could try to explain what meaning you attach to “science”.

You could explain your interpretation of “we cannot make a mathematics of the world, because sooner or later we have to find out whether the axioms are valid for the objects of nature”. To me that excludes math from the realm of science.

PS Have you ever convinced anyone to change their mind by merely repeating “I’m right and you’re wrong”?

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No, it’s you missing something there, Higgin.

When you read what I wrote keep it simple. Because the point I was making is a simple point.

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NK: Two sentences that say exactly the same thing.

What am I missing or what are you missing?

Science is validated against a physical reality.

Mathematics is validated against abstract starting assumptions.

Try this quote for a different perspective:

One may be dissatisfied with the approximate view of nature that physics tries to obtain (the attempt is always to increase the accuracy of the approximation), and may prefer a mathematical definition; but mathematical definitions can never work in the real world. A mathematical definition will be good for mathematics, in which all the logic can be followed out completely, but the physical world is complex, as we have indicated in a number of examples, such as those of the ocean waves and a glass of wine. When we try to isolate pieces of it, to talk about one mass, the wine and the glass, how can we know which is which, when one dissolves in the other? The forces on a single thing already involve approximation, and if we have a system of discourse about the real world, then that system, at least for the present day, must involve approximations of some kind.

This system is quite unlike the case of mathematics, in which everything can be defined, and then we do not know what we are talking about. In fact, the glory of mathematics is that we do not have to say what we are talking about. The glory is that the laws, the arguments, and the logic are independent of what “it” is. If we have any other set of objects that obey the same system of axioms as Euclid’s geometry, then if we make new definitions and follow them out with correct logic, all the consequences will be correct, and it makes no difference what the subject was. In nature, however, when we draw a line or establish a line by using a light beam and a theodolite, as we do in surveying, are we measuring a line in the sense of Euclid? No, we are making an approximation; the cross hair has some width, but a geometrical line has no width, and so, whether Euclidean geometry can be used for surveying or not is a physical question, not a mathematical question. However, from an experimental standpoint, not a mathematical standpoint, we need to know whether the laws of Euclid apply to the kind of geometry that we use in measuring land; so we make a hypothesis that it does, and it works pretty well; but it is not precise, because our surveying lines are not really geometrical lines. Whether or not those lines of Euclid, which are really abstract, apply to the lines of experience is a question for experience; it is not a question that can be answered by sheer reason.

In the same way, we cannot just call F = ma a definition, deduce everything purely mathematically, and make mechanics a mathematical theory, when mechanics is a description of nature. By establishing suitable postulates it is always possible to make a system of mathematics, just as Euclid did, but we cannot make a mathematics of the world, because sooner or later we have to find out whether the axioms are valid for the objects of nature. Thus we immediately get involved with these complicated and “dirty” objects of nature, but with approximations ever increasing in accuracy.

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Higgin writes:

The validity of a scientific argument depends on whether it is consistent with the natural world. The validity of a mathematical argument depends on whether it is consistent with the original postulates.

Two sentences that say exactly the same thing.

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NK: Hell, the language of the nature is math.

DB: Empirical knowledge is limited unless mathematics is used to explain and extend it.

These statements argue that mathematics is essential to most science. [I definitely agree with this position.] However the two replies do not address my basic position, that math is not a science. The validity of a scientific argument depends on whether it is consistent with the natural world. The validity of a mathematical argument depends on whether it is consistent with the original postulates.

I realize that some people disagree with this position, but I am not seeing any arguments against it here.

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Higgin’s, the language of science is math. Hell, the language of the nature is math. There is no excluding math from the, pardon the pun, equation.

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Empirical knowledge is limited unless mathematics is used to explain and extend it.

Empirical science is also useful in extending mathematics, e.g., quantum mechanics and randomness.

Science would likely not have expanded beyond description and categorization without mathematics.

But, if you are defining science as merely description and categorization, then I concede that you are correct in excluding mathematics.

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Not at all. Science is a study of the natural world. Scientific results are based on observations. Mathematics is a system of logic. Mathematical results are based on an arbitrary set of axioms and rules.

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j a higginbotham… you’re just joking around with us, right?

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He is in the College of Natural Sciences at Texas, but I have never considered math to be a science. It is hard to see how he has a chance in a district which would elect Dunbar.

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No fair! The guy’s a ringer! They’re not gonna take lightly to a guy who knows what he’s talking about when it comes to science!

Why, they might even dismiss him altogether by calling him… gulp!…

an expert!LikeLike