Saturday, July 04, 2009

Two infinities.

I was talking with my best chum Yoshi Tamori.

Yoshi is a mathematical genius. He likes to talk about iterations and infinities.
One of Yoshi's favorite topics is the Euler–Mascheroni constant. One is filled with a sense of wonder when you ponder its definition.

Both the harmonic series and the natural logarithm of N tends to infinity as N->inifinite. However, the difference between these two infinities is finite, namely

gamma = 0.57721 56649 01532 86060 65120 90082 40243 10421 59335 93992.

The two infinities are "relatives" separated exactly by this finite number.

Myself (left) and Yoshi Tamori at the Hermitage Museum, St. Petersburg, Russia.


Anonymous said...

^_^ I fully support this post...infinite series are amazing!

Utako said...

Another support

You and Mr.Tamori are talking about this topic at the bar "littleneck clam". A middle aged gardener of Shinagawa Ward is there by chance. He strains his ears to catch the conversation at the next table.

"Infinity" he murmurs sipping at ume(plum)liqueur. He recalls his task of pruning.
"Does the branch grow infinitely?" he says to himself. Then he heard the words "finite" and "difference".

"Yeah,I hear you. The growth isn't infinite of course. There are no sky-high trees. But I have to cut the branch every year. If I didn't do so, the growth would stop someday...I mean that the sum of length which I cut never shape into a true tree... I heard a good conversation." he thought.

"Though I understood just three words, hit on an unusual thing." He drew True tree on his own bottle, and left the bar.

masami said...

I got it.