Hofstadter, Dennett - The Mind's I

Rediscovering the Mind 43ence, beauty, weirdness, and mysticism to “sound right.”However, it is an idea that in many ways opposes an importantthem of this book, which is that nonquantum-mechanicalcomputational models of mind (all that goes along with mind) arepossible in principle. Bur right or wrong – and it is too earlyto say – the ideas that Morowitz presents are worth thinkingabout, for there is a certainly no question that the problem ofthe interaction of subjective and objective viewpoints is aconceptual difficulty at the heart of quantum mechanics. Inparticular, quantum mechanics as it is usually cast accords aprivileged causal status to certain systems known as “observers”without spelling out whether consciousness is a necessaryingredient of observer status). To clarify this point we mustpresent a quick overview of the “measurement problem” in quantummechanics, and we will invoke the metaphor of the “quantum wavefaucet” for that purpose.Imagine a faucet with two knobs – hot and cold – each ofwhich you can twist continuously. Water comes streaming out ofthe faucet, but there is a strange property to this system. Thewater is always totally hot or totally cold – no in-between.These are called the “two temperature eigenstates” of the water.The only way you can tell which eigenstate the water is in is bysticking your hand in and feeling it. Actually, in orthodoxquantum mechanics it is trickier than that. It is the act ofputting your hand under the water that throws the water into oneor the other eigenstate. Up until that very instant, the wateris said to have be in a superposition of states (or moreaccurately, a superposition of eigenstates)Depending on the setting of the knobs, the likely hood ofcold water will vary. Of course, if you turn on only the “H”tap, then you’ll get hot water always, and if you turn on only“C,” then you’ll get cold water for sure. If you open bothvalves, however, you’ll create a superposition of states. Bytrying it over and over again with one setting, you can measurethe probability tat you’ll get cold water with that setting.After that, you can change the setting and try again. There willbe some crossover point where hot and cold are equally likely.It will be like flipping a coin. (This quantum water faucet issadly reminiscent of many a bathroom shower.) Eventually you canbuild up enough data to draw a graph of the probability of coldwater as a function of the knobs’ settings.Quantum phenomena are like this. Physicist can twiddle knobs andput systems into superpositions of states analogous to our hotcoldsuperpositions. As long as no measurement is made of thesystem, the physicists cannot know which eigenstate the system Isin. Indeed it can