Purely by coincidence, we visited the National Air and Space Museum on Saturday which happened to be the 45th anniversary of the first Moon landing. There, I again met my old nemesis, Sputnik. It was launched by the former Soviet Union on October 4, 1957. I was two years old. My father used to tell me that I was very concerned that Sputnik "was gonna get me." No, I am not neurotic. I suspect some encouragement by my parents.
Last Thursday, I spent a pleasant morning at the Starbucks at the Hoffman Center talking with Jake, who is one of the regulars. He shared a way to understand the difference between neurosis and psychosis. "A neurotic is someone who believes that two plus two equals four and is deeply troubled by it. A psychotic is someone who believes that two plus two equals five and is quite happy about it."
Two monks were arguing about a flag. One said, "The flag is moving." The other said, "The wind is moving." The sixth patriarch, Zeno, happened to be passing by. He told them, "Not the wind, not the flag; mind is moving."
-- "Gödel, Escher, Bach", Douglas Hofstadter, pg. 30
Is thought material or immaterial? By "material" I mean an observable part of the universe such as matter, energy, space, charge, motion, time, etc... By "immaterial" would be meant something other than these things.
The problem with which we are now concerned is a very old one, since it was brought into philosophy by Plato. Plato's 'theory of ideas' is an attempt to solve this very problem, and in my opinion it is one of the most successful attempts hitherto made. … Thus Plato is led to a supra-sensible world, more real than the common world of sense, the unchangeable world of ideas, which alone gives to the world of sense whatever pale reflection of reality may belong to it. The truly real world, for Plato, is the world of ideas; for whatever we may attempt to say about things in the world of sense, we can only succeed in saying that they participate in such and such ideas, which, therefore, constitute all their character. Hence it is easy to pass on into a mysticism. We may hope, in a mystic illumination, to see the ideas as we see objects of sense; and we may imagine that the ideas exist in heaven. These mystical developments are very natural, but the basis of the theory is in logic, and it is as based in logic that we have to consider it. [It] is neither in space nor in time, neither material nor mental; yet it is something. [Chapter 9]
I claim that Russell and Plato are wrong. Not necessarily that ideas exist independently from the material. They might.1 Rather, I claim that if ideas do exist apart from the physical universe, then we can't prove that this is the case. The following is a bare minimum outline of why.
LogicLogic deals with the combination of separate objects. Consider the case of boolean logic. There are sixteen way to combine apples and oranges, such that two input objects result in one output object. These sixteen possible combinations are enumerated here. The table uses 1's and 0's instead of apples and oranges, but that doesn't matter. It could just as well be bees and bears. For now, the form of the matter doesn't matter. What's important is the outputs associated with the inputs2.
CompositionSuppose, for the sake of argument, that we have 16 devices that combine things according to each of the 16 possible ways to combine two things into one. We can compose a sequence of those devices where the output of one device becomes the input to another device. We first observe that we don't really need 16 different devices. If we can somehow change an "orange" into an "apple" (or 1 into 0, or a bee into a bear) and vice versa, then we only need 8 devices. Half of them are the same as the other half, with the additional step of "flipping" the output. With a bit more work, we can show that two of the sixteen devices when chained can produce the same output as any of the sixteen devices. These two devices, known as "NOT OR" (or NOR) and "NOT AND" (or NAND) are called "universal" logic devices because of this property. So if we have one device, say a NAND gate, we can do all of the operations associated with Boolean logic.3
CalculationNAND devices (henceforth called gates) are a basis for modern computers. The composition of NAND gates can perform addition, subtraction, multiplication, division, and so on. As an example, the previously referenced page concluded by using NAND gates to build a circuit that added binary numbers. This circuit was further simplified here and then here.
MemoryWe further observe that by connecting two NAND gates a certain way that we can implement memory.
ComputationMemory and calculation, all of which are implemented by arrangements of NAND gates, are sufficient to compute anything which can be computed (cf. Turing machines and the Church-Turing thesis).
MeaningElectrons flowing through NAND gates don't mean anything. It's just the combination and recombination of high and low voltages. How can it mean anything? Meaning arises out of the way the circuits are wired together. Consider a simple circuit that takes two inputs, A and/or B. If both inputs are A it outputs A, if both inputs are B then it outputs A, and if one input is A and the other is B, it outputs B. By making the arbitrary choice that "A" represents "yes" or "true" or "equal", more complex circuits can be built that determine the equivalence of two things. This is the simplified version of Hofstadter's claim:
When a system of "meaningless" symbols has patterns in it that accurately track, or mirror, various phenomena in the world, then that tracking or mirroring imbues the symbols with some degree of meaning -- indeed, such tracking or mirroring is no less and no more than what meaning is.
-- Gödel, Escher, Bach; pg P-3
Neurons and NAND gatesThe brain is a collection of neurons and axons through which electrons flow. A computer is a collection of NAND gates and wires through which electrons flow. The differences are the number of neurons compared to the number of NAND gates, the number and arrangement of wires, and the underlying substrate. One is based on carbon, the other on silicon. But the substrate doesn't matter.
That neurons and NAND gates are functionally equivalent isn't hard to demonstrate. Neurons can be arranged so that they perform the same logical operation as a NAND gate. A neuron acts by summing weighted inputs, comparing to a threshold, and "firing" if the weighted sum is greater than the threshold. It's a calculation that can be done by a circuit of NAND gates.
Logic, Matter, and WavesIt's possible to create logic gates using particles. See, for example, the Billiard-ball computer, or fluid-based gates where particles (whether billiard balls or streams of water) bounce off each other such that the way they bounce can implement a universal gate.
It's also possible to create logic gates using waves. See, for example, here [PDF] and here [paid access] for gates using acoustics and optics.
I suspect, but need to research further, that waves are the proper way to model logic, since it seems more natural to me that the combination of bees and bears is a subset of wave interference rather than particle deflection.
4 So why are Russell and Plato wrong? It is because it is the logic gates in our brains that recognize logic, i.e. the way physical things combine. Just as a sequence of NAND gates can output "A" if the inputs are both A or both B; a sequence of NAND gates can recognize itself. Change a wire and the ability to recognize the self goes away. That's why dogs don't discuss Plato. Their brains aren't wired for it. Change the wiring in our brains and we wouldn't, either. Hence, while we can separate ideas from matter in our heads, it is only because of a particular arrangement of matter in our heads. There's no way for us to break this "vicious" circle.
Footnotes "In the beginning was the Word..." As a Christian, I take it on faith that the immaterial, transcendent, uncreated God created the physical universe.
 Note that the "laws of logic" follow from the world of oranges and apples, bees and bears, 1s and 0s. Something is either an orange or an apple, a bee or a bear. Thus the "law" of contradiction. An apple is an apple, a zero is a zero. Thus the "law" of identity. Since there are only two things in the system, the law of the excluded middle follows.
 This previous post shows how NAND gates can be composed to calculate all sixteen possible ways to combine two things.
 "Drawing Hands", M. C. Escher
05/17/14 14:30 Filed in: Books
I first read Tower of Glass as a teenager and remembered very little about it. There is a dim recollection of reading it in the car while on a family trip. On a whim I bought an eBook version and had a hard time putting it down.
A message has been received from interstellar space. Simeon Krug, having made a vast fortune by creating and commercializing androids, uses android labor to construct a vast tower in the Canadian tundra -- a tower that will house a tachyon transmitter to send a reply.
The tower is but a framing device -- a re-imagined tower of Babel -- to explore what it means to be human. I now appreciate why it was nominated for both Hugo and Nebula awards.
04/23/14 18:47 Filed in: Life
-- "Bodies", Robbie Williams, "Reality Killed the Video Star"
All we've ever wanted is to look good naked
Hope that someone can take it
God save me rejection from my reflection,
I want perfection.
-- "Wasted on the Way", Crosby, Stills & Nash, "Daylight Again"
And there's so much time to make up everywhere you turn
Time we have wasted on the way
So much water moving underneath the bridge
Let the water come and carry us away.
-- "Running on Empty", Jackson Browne, "Love Is Strange"
Running on, running on empty
Running on, running blind
Running on, running into the sun
But I'm running behind.