Interesting quotes by Feynman, da Vinci and Davies

[nightflyer]

I have some quotes from various books I have read recently, that I would love to hear your thoughts on:

Richard Feynman:

"All these [chemical] rules were ultimately explained in principle by quantum mechanics, so that theoretical chemistry is in fact physics. On the other hand, it must be emphasized that this explanation is in principle. We have already discussed the difference between knowing the rules of the game of chess, and being able to play."

Is the difficulty of not being able to play the game of chemistry, one that is related to lack of computational power? In other words, will we become better at playing the game as computational power continues to grow exponentially each year? Or is the difficulty a principal one, related to the clash between the quantum world and the classical world, requiring completely new theories to fill in the gap?

Leonardo da Vinci:

"No human investigation can be called real science if it can not be demonstrated mathematically."

Do you sympathize with this statement? Would da Vinci say that biology is not a science, because we can not describe it mathematically? Do you believe all processes in the world, no matter how complex, must ultimately be possible to formulate by some mathematical formula, as da Vinci seems to suggest?

Paul Davies:

"Eddington's implicit boast of being the only person other than Einstein able to understand the general theory of relativity did not mean, I believe, that he and Einstein alone could visualize the revolutionary new concepts such as curved spacetime. But he may well have been among the first physicists to appreciate that in this subject true understanding comes only by relinquishing the need to visualize."

Is this true for modern physics such as relativity theory and quantum mechanics? Do you have to give up the need to visualize, because we do not have any everyday experience of the concepts that are dealt with? If so, how can one gain true understanding of these theories? Or should one simply give up such an ambition, much like Davies seems to be suggesting? To quote Feynman once again, "If you think you understand quantum mechanics, you don't understand quantum mechanics." If you agree with Davies and Feynman, do you find the lack of understanding in modern physics frustrating, or do you think it makes the field even more exciting?

 

[Crosson]

1) Based on current methods, and the ultimate physical limitations on computing (a subject expounded by R.P. Feynman) , we will never complete the program of reducing on chemistry knowledge to physics. Quantum Computing in the far future perhaps, but not machines based on the Von Neumann architecture (in fact, a quantum computer could potentially do native simulations of chemistry).

2) Not every mathematical demonstration is a formula, so it is not the lack of formulae in fundamental biology that make the subject non-mathematical (and hence non-scientific). As Rutherford said "all science is either physics or stamp collecting", and so the sense in which Leonardo's quote is meant is that Biology is essentially a well-organized list of observations.

Its just an issue of how abstract we want an explanation to be; Biology always explains one observation in terms of another. There are no "rules" from which one cannot generate all of biology, unless we count physics, but that gets stuck at chemistry.

In my opinion the most promising direction for making Biology a true science is outlined by Stephen Wolfram in his massive work A New Kind of Science. His vision is ambitious, and just like Francis Bacon elevating the power of reason before the time of Newton, these remain only promises for now.

3) One non-visual way to understand quantum mechanics is as a theory about knowledge. The wavefunction is like an oracle, containing information about our physical system, and we can ask it various questions, receiving answers phrased in terms of probability.

Heisenburg knew that we could not visualize (his) quantum mechanics, but he made the mistake of assuming that humans can not visualize the microworld.

This cannot be the case because all visualizations are generated by our brains, from the void, according to sensory information. From this point of view, visualizations are not correct or incorrect, because they can be anything whatsoever (arbitrarily generated by our brains).

 

[Cleve]

All these [chemical] rules were ultimately explained in principle by quantum mechanics, so that theoretical chemistry is in fact physics. ;

If chemicals can be explanied with quantum mechanics, math, then chemical processes, like radiation, which given "time" breaks down, or a chemical reaction in the body needs "x" amount of a chemical to make cells react. "Time" is part of Davies and Einstein’s theories.

So Feyman gave us the math, Einstein gave us the time, so Da Vinci could see it. Chemistry and Biology can be seen reacting and figured by mathematical equations.

I hope I did not take you in a circle without an end.

 

[nightflyer]

Crosson:

1. Could you please elaborate on why current methods of computing will ultimately fail to reduce chemistry to physics? Is this something that is possible to explain to a layman like me, who only knows about the very fundamental aspects of quantum mechanics?

2. Would you care to outline what you find promising about Wolfram's book, and how it is related to making biology a true science? By the way, would you say that chemistry is a true science?


Cleve:

Could you please elaborate on your statement that "Chemistry and Biology can be seen reacting and figured by mathematical equations"?

 

[Crosson]

1) Suppose that you wanted to simulate the solar system on a computers. Here is the most natural thing to do:

Step 1: Based on the positions of all the planets, calculate the forces they are exerting on each other.

Step 2: Move the planets according to the forces calculated in step 1, but only for a very short time (0.01 seconds, for example) because then we should go back to step 1 and recalculate the forces (because the positions have changed so have the forces.

The process I have described above is called "numerical solution of differential equations", and its success depends only on the accuracy and speed of our computers.

An example of reducing Chemistry to Physics might be to calculate the energy released in a particular reaction (Chemist do this using empirical guesswork and ad hoc equations). It maybe that the reaction involves 100s of particles, but that wouldn't stop a good physicist from being able to write down the differential equation that describes the situation.

Lets look at the numerical solution process in detail. The event takes ~.01 seconds, and so to get good accuracy let's say we use a time step of [tex]10^{-12}[/tex] seconds. But each calculation involves unavoidable machine error of [tex]10^{-16}[/tex], and with a hundred particles this leads to an error of [tex]10^{-14}[/tex] per time step, so the final result has an unacceptable error approximately ~0.01.

The bottom line comes down to time/space limitations. As the number of particles and the complexity of the simulation goes up, the amount of computer memory and time to calculate goes up exponentially. Exponential scaling is unacceptable in computer science, because soon you find that a supercomputer the size of the earth, or the universe, is too small for what you want to do.

The solution to doing chemistry with physics will come from many angles:

1) Physicists using symmetry to simplify the differential equations that come from the quantum situation.

2) Computer scientist writing better algorithms for solving differential equations in general.

3) Computer Engineers making machines get "smarter", not "bigger" (because big is never big enough).

As for chemistry being a science: Science, like any English word, does not have a meaning that is static over time. Chemists cling very dearly to their idea of "science", and would be insulted if I said they were not scientist. As a physicist, I am (silently) insulted to be called a scientist, and this is because chemist/biologist/psychologists have stolen the meaning of science to refer to what they do, not to what we do in physics. I don't care who gets what label, but if it were up to me I would say physics is a category, and science is a category containing chemistry.

I will post later about Wolfram's book, but also check out the website:

www.wolframscience.com

 

[nightflyer]

Crosson:

Thanks for a great post! Now I understand why computer simulations of the workings of drugs are so expensive and time demanding; drugs taken orally will affect the whole organism which is one giant system, and immensely complex to make calculations on following your logic.

I guess one additional alternative (which I think you mentioned in your previous post) is to build quantum computers. Do you have any idea about how far off into the future they are?