The Entropy FunctionThis function is relevant to Paul Samuelson because information theory grew out of statistical mechanics, which was Samuelson's favorite tool.
This chart says that a coin with equiprobability of heads or tails will deliver the most information over a large number of coin flips. If the coin always turns up tails, there is no information gained by coin flipping. Nor is any information gains when heads always turns up.
Leading us to Huffman coding. The idea with Huffman coding is to spend the most bits on the least probable events. Common events are coded with the least amount of bits. Hence, the communications channel devotes the proper amount of bandwidth to the according to event probability. Thus bandwidth is allocated such that symbols arrive with equiprobability and one gets maximum entropy as in the equiprobable coin toss.
The equation above is of the form P(X)log(P(x)). which I take to be the amount of work required to get maximum information entropy. The Huffman coder actually resembles a distribution network and the number of decisions on the network should correspond to a NlogN format. Operation counts and the maximum entropy function should be related.
What does this have to do with the economy? The economy is a noisy channel which must allocate inventory investment to goods whose domain is the relative constraint of the good, and whose range is the inventory space allocated for the good. The allocation of symbols, in the economy, is what I call setting the lot size; the bits are the stages of production. The result is inventories can arrive with the same variance regardless of the constraint, the inventory channels are maximum entropy.
When referring to the Shannon coding theorem, remember my a priori is that the noise level is a constant, biologically driven. Well, let me just write out the equation in a form we need.
2**(C/B) = 1 + snr
SNR, signal to noise ratio is fixed. B: the bandwidth of the channel, or in our case, the bandwidth of the industrial production equipment. C: channel capacity is the transaction rate at each level, in our case. For now lets treat it as the scalar transaction rate at the retail level. The Hidden Hand tries to adjust C such that 1+snr is met, making the human happy. We adjust C, the number symbols, or sales, mainly by changing lot sizes, or in the channel case, reallocating bits so they are used to minimize transaction for restrained resources.
I have to be careful that the concepts of deflates and inflated states get understood by me with respect to bit assignment in a Huffman encoder. Also I introduce the second constraint in the system, the cost of providing additional NlogN chunks of labor. And, still, my thinking on the asymmetry problem, muddled. More later.
Consider the supply chain for consumer electronics with inventories growing at all levels from producer to consumer. This is productivity increasing faster than demand, excess profits are plowed into specialization and the industry inflates, increasing the stages of production but offering more specialized offerings to the consumer. The consumer is happier with the lower volume but greater specialization. The system has matched the consumer snr levels. Increasing the number of bits increases the precision of the product.
Changing B in the production system is a longer term process, involving a supply chain adjustments in lot sizes and technology to the industrial machines.
The key to understanding the deflation/inflation tipping points is to understand the nature of the delta NlogN in transaction rates across the jump.
Where is this leading? First, I probably got signs wrong,. I usually do. Second, the B and C become matrices, and the channel equation above, the left side becomes a matrix power series. The Eigenfuntions on the right will be snr * 2**i, i finite and small. The power series gives the vector of inventory variances and the solution will actually be the lot size, in units of snr. An example might be taking a consumer survey to discover the smallest noticable consumption of water, and then computing the lot sizes, which yield the inventory capacity in a N stage, smooth earth water distribution system.
This chart says that a coin with equiprobability of heads or tails will deliver the most information over a large number of coin flips. If the coin always turns up tails, there is no information gained by coin flipping. Nor is any information gains when heads always turns up.
Leading us to Huffman coding. The idea with Huffman coding is to spend the most bits on the least probable events. Common events are coded with the least amount of bits. Hence, the communications channel devotes the proper amount of bandwidth to the according to event probability. Thus bandwidth is allocated such that symbols arrive with equiprobability and one gets maximum entropy as in the equiprobable coin toss.
The equation above is of the form P(X)log(P(x)). which I take to be the amount of work required to get maximum information entropy. The Huffman coder actually resembles a distribution network and the number of decisions on the network should correspond to a NlogN format. Operation counts and the maximum entropy function should be related.
What does this have to do with the economy? The economy is a noisy channel which must allocate inventory investment to goods whose domain is the relative constraint of the good, and whose range is the inventory space allocated for the good. The allocation of symbols, in the economy, is what I call setting the lot size; the bits are the stages of production. The result is inventories can arrive with the same variance regardless of the constraint, the inventory channels are maximum entropy.
When referring to the Shannon coding theorem, remember my a priori is that the noise level is a constant, biologically driven. Well, let me just write out the equation in a form we need.
2**(C/B) = 1 + snr
SNR, signal to noise ratio is fixed. B: the bandwidth of the channel, or in our case, the bandwidth of the industrial production equipment. C: channel capacity is the transaction rate at each level, in our case. For now lets treat it as the scalar transaction rate at the retail level. The Hidden Hand tries to adjust C such that 1+snr is met, making the human happy. We adjust C, the number symbols, or sales, mainly by changing lot sizes, or in the channel case, reallocating bits so they are used to minimize transaction for restrained resources.
I have to be careful that the concepts of deflates and inflated states get understood by me with respect to bit assignment in a Huffman encoder. Also I introduce the second constraint in the system, the cost of providing additional NlogN chunks of labor. And, still, my thinking on the asymmetry problem, muddled. More later.
Consider the supply chain for consumer electronics with inventories growing at all levels from producer to consumer. This is productivity increasing faster than demand, excess profits are plowed into specialization and the industry inflates, increasing the stages of production but offering more specialized offerings to the consumer. The consumer is happier with the lower volume but greater specialization. The system has matched the consumer snr levels. Increasing the number of bits increases the precision of the product.
Changing B in the production system is a longer term process, involving a supply chain adjustments in lot sizes and technology to the industrial machines.
The key to understanding the deflation/inflation tipping points is to understand the nature of the delta NlogN in transaction rates across the jump.
Where is this leading? First, I probably got signs wrong,. I usually do. Second, the B and C become matrices, and the channel equation above, the left side becomes a matrix power series. The Eigenfuntions on the right will be snr * 2**i, i finite and small. The power series gives the vector of inventory variances and the solution will actually be the lot size, in units of snr. An example might be taking a consumer survey to discover the smallest noticable consumption of water, and then computing the lot sizes, which yield the inventory capacity in a N stage, smooth earth water distribution system.
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