Gödel, Escher, Bach: An Eternal Golden Braid (64 page)

Systems which are made up of "reliable" subsystems only-that is, subsystems whose behavior can be reliably predicted from chunked descriptions-play inestimably important roles in our daily lives, because they are pillars of stability. We can rely on walls not to fall down, on sidewalks to go where they went yesterday, on the sun to shine, on clocks to tell the time correctly, and so on.

Chunked models of such systems are virtually entirely deterministic. Of course, the other kind of system which plays a very large role in our lives is a system that has variable behavior which depends on some internal microscopic parameters-often a very large number of them, moreover-which we cannot directly observe.

Our chunked model of such a system is necessarily in terms of the "space" of operation, and involves probabilistic estimates of landing in different regions of that space.

A container of gas, which, as I already pointed out, is a reliable system Because of many canceling effects, obeys precise, deterministic laws of physics.

Such laws are chunked laws, in that they deal with the gas as a whole, nd ignore its constituents. Furthermore, the microscopic and macroscopic descriptions of a gas use entirely different terms. The former requires the pacification of the position and velocity of every single component molecule; the latter requires only the specification of three new quantities: temperature, pressure, and volume, the first two of which do not even have microscopic counterparts. The simple mathematical relationship which elates these three parameters- pV = cT, where c is a constant-is a law which depends on, yet is independent of, the lower-level phenomena. Less paradoxically, this law can be derived from the laws governing the molecular level; in that sense it depends on the lower level. On the other hand, it is law which allows you to ignore the lower level completely, if you wish: in hat sense it is independent of the lower level.

It is important to realize that the high-level law cannot be stated in the vocabulary of the low-level description. "Pressure" and "temperature" are new terms which experience with the low level alone cannot convey. We humans perceive temperature and pressure directly; that is how we are guilt, so that it is not amazing that we should have found this law. But creatures which knew gases only as theoretical mathematical constructs would have to have an ability to synthesize new concepts, if they were to discover this law.

Epiphenomena

In drawing this Chapter to a close, I would like to relate a story about a complex system. I was talking one day with two systems programmers for he computer I was using. They mentioned that the operating system seemed to be able to handle up to about thirty-five users with great comfort, but at about thirty-five users or so, the response time all of a sudden hot up, getting so slow that you might as well log off and go home and wait until later. Jokingly I said, "Well, that's simple to fix just find the place in he operating system where the number `35' is stored, and change it to 60'!" Everyone laughed. The point is, of course, that there is no such place. where, then, does the critical number-35 users-come from? The answer is:
It is a visible consequence of the overall system organization
-an

"
epiphenometon
,,.

Similarly, you might ask about a sprinter, "Where is thè9.3' stored, hat makes him be able to run 100 yards in 9.3 seconds?" Obviously, it is not stored anywhere. His time is a result of how he is built, what his reaction time is, a million factors all interacting when he runs. The time is quite 'reproducible, but it is not stored in his body anywhere. It is spread around among all the cells of his body and only manifests itself in the act of the print itself.

Epiphenomena abound. In the game of "Go", there is the feature that “two eyes live”. It is not built into the rules, but it is a consequence of the rules. In the human brain, there is gullibility. How gullible are you? Is your gullibility located in some "gullibility center" in your brain? Could a neurosurgeon reach in and perform some delicate operation to lower your gullibility, otherwise leaving you alone? If you believe this, you are pretty gullible, and should perhaps consider such an operation.

Mind
vs
. Brain

In coming Chapters, where we discuss the brain, we shall examine whether the brain's top level-the mind-can be understood without understanding the lower levels on which it both depends and does not depend. Are there laws of thinking which are "sealed off" from the lower laws that govern the microscopic activity in the cells of the brain? Can mind be "skimmed" off of brain and transplanted into other systems? Or is it impossible to unravel thinking processes into neat and modular subsystems? Is the brain more like an atom, a renormalized electron, a nucleus, a neutron, or a quark? Is consciousness an epiphenomenon? To understand the mind, must one go all the way down to the level of nerve cells?

English French German Suite

By Lewis Carroll .. .

... et Frank L. Warrin .. . ..

. and Robert Scott

'Twas brillig, and the slithy toves

Did gyre and gimble in the wabe:

All mimsy were the borogoves,

And the mome raths outgrabe.

I1 brilgue: les toves lubricilleux

Se gyrent en vrillant dans le guave.

Enmimes sont les gougebosqueux

Et le momerade horsgrave.

Es brillig war. Die schlichten Toven

Wirrten and wimmelten in Waben;

Und aller-mumsige Burggoven

Die mohmen Rath' ausgraben.

"Beware the Jabberwock, my son!

The jaws that bite, the claws that catch!

Beware the Jubjub bird, and shun

The frumious Bandersnatch!"

((Garde-toi du Jaseroque, mon fits!

La gueule qui mord; la griffe qui prend!

Garde-toi de I'oiseau Jube, evite

Le frumieux Band-a-prend!))

))Bewahre doch vor Jammerwoch!

Die Zahne knirschen, Krallen kratzen!

Bewahr' vor Jubjub-Vogel, vor

Frumiosen Banderschnatzchen!)),

He took his vorpal sword in hand:

Long time the manxome foe he sought

So rested he by the Tumtum tree,

And stood awhile in thought.

Son glaive vorpal en main, it va

T-a la recherche du fauve manscant;

Puis arrive a I'arbre Te-te,

l y reste, reflechissant

Er griff sein vorpals Schwertchen zu,

Er suchte lang das manchsam' Ding;

Dann, stehend unterm Tumtum Baum,

Er an-zu-denken-fing.

And, as in uffish thought he stood,

The Jabberwock, with eyes of flame.

Came whiffling through the tulgey wood,

And burbled as it came!

Pendant qu'il pense, tout uffuse,

Le Jaseroque, a l'oeil flambant,

Vient siblant par le bois tullegeais,

Et burbule en venant.

Als stand er tief in Andacht auf,

Des Jammerwochen's Augen-feuer

Durch turgen Wald mit Wiffek kam

Fin burbelnd Ungeheuer!

One, two! One, two! And through and through

The vorpal blade went snicker-snack!

He left it dead, and with its head

He went galumphing back.

Un deux, un deux, par le milieu,

Le glaive vorpal fait pat-a-pan!

La bete defaite, avec sa tete,

Il rentre gallomphant.

Eins, Zwei! Eins, Zwei! Und durch and durch

Sein vorpals Schwert zerschnifer-schnuck,

Da blieb es todt! Er, Kopf in Hand,

Gelaumfig zog zuriick.

"And hast thou slain the Jabberwock?

Come to my arms, my beamish boy!

0 frabjous day! Callooh! Callay!"

He chortled in his joy.

((As-tu tue le Jaseroque?

Viens a mon coeur, fils rayonnais!

O jour frabbejais! Calleau! Callai!))

Il cortule clans sa joie.

))Und schlugst Du ja den Jammerwoch?

Umarme mich, mein Bohm'sches Kind!

O Freuden-Tag! 0 Halloo-Schlag!((

Er schortelt froh-gesinnt.

'Twas brillig, and the slithy toves

Did gyre and gimble in the wabe:

All mimsy were the borogoves,

And the mome raths outgrabe.

Il brilgue: les toves lubricilleux

Se gyrent en vrillant dans le guave.

Enmimes sont les gougebosqueux

Et le momerade horsgrave.

Es brillig war. Die schlichten Toven

Wirrten and wimmelten in Waben:

Und aller-mumsige Burggoven

Die mohmen Rath' ausgraben.

Can Minds Be Mapped onto Each Other?

Now THAT WE have hypothesized the existence of very high-level active subsystems of the brain (symbols), we may return to the matter of a possible isomorphism, or partial isomorphism, between two brains. Instead of asking about an isomorphism on the neural level (which surely does not exist), or on the macroscopic suborgan level (which surely does exist but does not tell us very much), we ask about the possibility of an isomorphism between brains on the symbol level: a correspondence which not only maps symbols in one brain onto symbols in another brain, but also maps triggering patterns onto triggering patterns. This means that corresponding symbols in the two brains are linked in corresponding ways. This would be a true
functional
isomorphism-the same type of isomorphism as we spoke of when trying to characterize what it is that is invariant about all butterflies,

It is clear from the outset that such an isomorphism does not exist between any pair of human beings. If it did, they would be completely indistinguishable in their thoughts; but in order for that to be true, they would have to have completely indistinguishable memories, which would mean they would have to have led one and the same life. Even identical twins do not approach, in the remotest degree, this ideal.

How about a single individual% When you look back over things which you yourself wrote a few years ago, you think "How awful!" and smile with amusement at the person you once were. What is worse is when you do the same thing with something you wrote or said five minutes ago. When this happens, it shows that you do not fully understand the person you were moments ago. The isomorphism from your brain
now
to your brain
then
is imperfect. What, then, of the isomorphisms to other people, other species ...

The opposite side of the coin is shown by the power of the communication that arises between the unlikeliest partners. Think of the barriers spanned when you read lines of poetry penned in jail by Francois Villon, the French poet of the 1400's. Another human being, in another era, captive in jail, speaking another language ... How can you ever hope to have a sense of the connotations behind the facade of his words, translated into English% Yet a wealth of meaning comes through.

Thus, on the one hand, we can drop all hopes of finding exactly isomorphic software in humans, but on the other, it is clear that some people think more alike than others do. It would seem an obvious conclu

FIGURE 70. A tiny portion of the author's "semantic network".

sion that there is some sort of partial software isomorphism connecting the brains of people wbose style of thinking is similar-in particular, a correspondence of (1) the repertoire of symbols, and (2) the triggering patterns of symbols
Comparing Different Semantic Networks

But what is a
partial
isomorphism? This is a most difficult question to answer. It is made even more difficult by the fact that no one has found an adequate way to represent the network of symbols and their triggering patterns. Sometimes a picture of a small part of such a network of symbols is drawn, where each symbol is represented as a node into which, and out of which, lead some arcs. The lines represent triggering relationships-in some sense. Such figures attempt to capture something of the intuitively sensible notion of "conceptual nearness". However, there are many different kinds of nearness, and different ones are relevant in different contexts. A tiny portion of my own "semantic network" is shown in Figure 70. The problem is that representing a complex interdependency of many symbols cannot be carried out very easily with just a few lines joining vertices.

Another problem with such a diagram is that it is not accurate to think of a symbol as simply "on" or "off". While this is true of neurons, it does not carry upwards, to collections of them. In this respect, symbols are quite a bit more complicated than neurons-as you might expect, since they are made up of many neurons. The messages that are exchanged between symbols are more complex than the mere fact, "I am now activated". That is more like the neuron-level messages. Each symbol can be activated in many different ways, and the type of activation will be influential in determining which other symbols it tries to activate. How these intertwining triggering relationships can be represented in a pictorial manner-indeed, whether they can be at all-is not clear.