Candidates: 32 ... Bh4, 32 ... Rd4

A) 32 ... Bh4 wins R (33. Rg1?? Qxg1+ 34. Kxg1 Rd1+, etc. )

B) 32 ... Rd4 33. Qe5 unclear

I was certain that the bishop should move to D2, then if

33. Rd1 Bxc1
or if

33. Bxd2 Rxd2 with some fending off of a Q attack on the 8th rank, but ultimately mate on g2.

Ugh.

<The Roman Lucretius's scientific poem "On the Nature of Things" (c. 60 BC) has a remarkable description of Brownian motion of dust particles. He uses this as a proof of the existence of atoms:

"Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves [i.e., spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible."

Although the mingling motion of dust particles is caused largely by air currents, the glittering, tumbling motion of small dust particles is, indeed, caused chiefly by true Brownian dynamics.>

In 1827 a biologist Robert Brown was using a new fangled microscope to see pollen floating in water. To his surprise he saw them wiggling around, as if they had tiny legs or something. Ideas were formed about how pollen might literally "grab" the things around it with tiny appendages.

Of course those theories were just hooey. Many years later a fellow named Albert Einstein opined that Mr. Brown was witnessing the light delicate pollen grains being buffeted around by fast-moving water molecules or other atoms. Because the pollen is just as likely to be hit from above as below, or from the left as from the right, they tend to wiggle around randomly. Whether in physics or mathematics, this random wiggling is referred to as Brownian motion (with an "i").

"Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves [i.e., spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible."

Jan Ingenhousz had described the irregular motion of coal dust particles on the surface of alcohol in 1785 — nevertheless the discovery is often credited to the botanist Robert Brown in 1827. Brown was studying pollen grains of the plant Clarkia pulchella suspended in water under a microscope when he observed minute particles, ejected by the pollen grains, executing a jittery motion. By repeating the experiment with particles of inorganic matter he was able to rule out that the motion was life-related, although its origin was yet to be explained.

The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in a paper on the method of least squares published in 1880. This was followed independently by Louis Bachelier in 1900 in his PhD thesis "The theory of speculation", in which he presented a stochastic analysis of the stock and option markets. Albert Einstein (in one of his 1905 papers) and Marian Smoluchowski (1906) brought the solution of the problem to the attention of physicists, and presented it as a way to indirectly confirm the existence of atoms and molecules. Their equations describing Brownian motion were subsequently verified by the experimental work of Jean Baptiste Perrin in 1913.

Reference: Wikipedia

In 1827 the English botanist Robert Brown noticed that pollen grains suspended in water jiggled about under the lens of the microscope, following a zigzag path. Even more remarkable was the fact that pollen grains that had been stored for a century moved in the same way.

In 1889 G.L. Gouy found that the "Brownian" movement was more rapid for smaller particles (we do not notice Brownian movement of cars, bricks, or people). =Although the late has good sized legs (two each) and other animals have four each=. In 1900 F.M. Exner undertook the first quantitative studies, measuring how the motion depended on temperature and particle size.

The first good explanation of Brownian movement was advanced by Desaulx in 1877: "In my way of thinking the phenomenon is a result of thermal molecular motion in the liquid environment (of the particles)." This is indeed the case. A suspended particle is constantly and randomly bombarded from all sides by molecules of the liquid. If the particle is very small, the hits it takes from one side will be stronger than the bumps from other side, causing it to jump. These small random jumps are what make up Brownian motion.

13...ab 14 cb Nxd4?! 15 Qxc7 Nxe2+ Kf1 and black is down lots of material