Once you get a B.S., you think "you know everything". Once you get an M.S., you realize "you know nothing". Once you get a Ph.D., you realize that "yes, you know nothing, but that is not a problem, because nobody knows anything!"This turned out to be a nice read. The author, Stuart Firestein, has a very interesting background. He was working at a theater, and started a biology undergraduate at 30, and got his PhD at 40.

Here are some tidbits from the book.

**Leibniz. page 38**

The 17th-century German philosopher and mathematician Gottfried Leibniz, one of the inventors of calculus, had a lifelong project to construct a "basic alphabet of human thoughts" that would allow one to take combinations of simple thoughts and form any complex idea, just as a limited number of words can be combined endlessly to form any sentence -- including sentences never before heard or spoken. Thus, with a few primary simple thoughts and the rules of combination one could generate computationally (although in Leibniz's day it would have been mechanically) all the possible human thoughts. It was Leibniz's idea that this procedure would allow one to determine immediately if a thought were true or valuable or interesting in much the same way these judgments can be made about a sentence of an equation -- is it properly formed, does it make sense, is it interesting?

**He was famously quoted as saying that any dispute could be settled by calculating-- "Let us calculate!" he was apparently known to blurt out in the middle of a bar brawl**. It was this obsession that led Leibniz to develop the branch of mathematics known today as combinatorics. This in turn sprang from the original insight that all truths can be deduced from a smaller number of primary or primitive statements, which could be made no simpler, and that mathematical operations (multiplication was the one Leibniz proposed but also prime factorization) could derive all subsequents thoughts. In many ways this was the beginning of modern logic' indeed, some consider his /On the Art of Combinations/ the major step leading from Aristotle to modern logic, although Leibniz himself never made such claims.

**Godel. page 41**

What Godel showed, using a strange new correspondence between mathematics and logic that he invented, was that if a system were the rules of that system. This means that something that could be shown to be true using the system could not in fact be proved to be so. Since proofs are the foundation of mathematics, it is quite curious when obviously true statements cannot be proved.

**Godel. page 42**

Was this the end of the messianic program to establish the primacy of mathematics and of logical thinking? As it turns out, quite the contrary. Godel's small, by comparison, but revolutionary output is so asttonishing because of the technical and philosophical research opportunities it has created. Previously unconsidered ideas about reccursiveness, paradox, algorithms, and even consciousness owe their foundations to Godel's ideas about imcompleteness. What at first seems like a negative --eternal incompleteness-- turns out to be fruitful beyond imagining. Perhaps much of computer science, an area one might think was most dependent on empirical statements of unimpeachable logic, could not have progressed without the seminal ideas of Godel. Indeed, unknowability and incompleteness are the best things that ever happened to science.

**Hilbert. page 48**

In fact, one of the most predictable things about predictions is how often they're wrong. Nonetheless, they are a measure, even if somewhat imprecise, of our ignorance. They are a catalog of what we think the important ignorance is, and perhaps also a judgment of what we think is the most solvable ignorance.

**May ignorance lead your research. page 55**

Ignorance is not just an excuse for poor planning. We must think about how ignorance works, and we have to be explicit about how to make it work to our advantage. While for many experienced scientists this is intuitive, it is not so obvious to the layperson, and it often seems not so apparent to young scientists starting out their career and worrying about grant support and tenure.

**Grants. page 59**

How do scientists ponder these big questions about ignorance? How do they get from these and other interesting and important issues to an actual scientific research program? Well, at the most pedestrian, but nonetheless critical level, there are grant proposals. Every scientist spends a significant percentage of his or her time writing grants. Many complain about this, but I actually think it's a good idea. These documents are, after all, a detailed statement of what the scientist hopes to know, but doesn't, as well as a rudimentary plan for finding it out.

**Models. page 70**

This strategy of using smaller questions to ask larger ones, is, if not particular to science, one of its foundations. In scientific parlance this is called using a "model system". As Marvin Minsky, one of the fathers of artificial intelligence, points out, "In science one can learn the most by studying the least". Think how much more we know about viruses and how they work than about elephants and how they work. The brain, for example, is a very complicated piece of biological machinery. Figuring out how it works is understandably one of humankind's great quests. But, unlike a real machine, a man-made, designed machine, we have no schematic. We have to discover, uncover, the inner workings by dissection-- we have to take it apart. Not just physically but also functionally. That's a tall order since there are some 80 billion nerve cells that make up the human brain, and they make about 100 trillion connections with each other. ... So instead of a human brain, neuroscientists study rat and mouse brains, fly brains because they can do some very fancy genetics on them, or even the nervous system of the nematode worm, which has exactly 302 neurons.

## MAD questions

*1. What do you feel ignorant about in your line of work?*
## 1 comment:

Dear professor, I am following your blog & recommending it to my friends for these great insights. Thank you for sharing information about this interesting book. It's next in my reading list :-)

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