# High-dimensional and one-dimensional value world

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A few days ago I went to Leipzig, Germany, to participate in the ISC Student Cluster Competition . About this game is under limited power (3000W) conditions to optimize performance computing clusters. Each team clusters are provided by sponsors, Tsinghua University team is the wave of corporate sponsorship. It is impossible due to hardware and other schools than we had come from the optimization software, game programs include the LINPACK , the HPCC , HPCG , the Quantum ESPRESSO and Gadget . Tsinghua University team won the final third of the world, it can be considered the best - after all, we did not cluster even GPU, and many team configuration extravagant, like the University of Edinburgh even liquid cooling systems are on.

## "Fastest" supercomputer in the world.

During the ISC meeting, we learned that the China's "Milky Way No. 2" at a speed of LINPACK peak 54902.4 TFlop / S maintains the supercomputer TOP500 list, the global media coverage. However, various media reports, we see the "Milky Way 2" has become "the world's fastest supercomputers," as Forbes reports, which have overlooked an important detail, namely the speed TOP500 ranking based LINPACK of. LINPACK benchmark problem solving is a dense system of linear equations, it is entirely compute-intensive applications, the memory access, parallel communication, disk read and write does not become a bottleneck. Therefore been criticized numerical LINPACK offer is "substantially unable to reach, there are a handful of bored programmers optimize its code, in order to make their machines to get better value." In fact, a measure of computer performance is good or bad, to estimate the sweeping absolutely true system performance also depends on integer computing performance, memory access performance, network traffic and disk read and write performance is calculated only by the floating-point-intensive applications and so on all aspects of performance. Even if it is only in the field of scientific computing, in many applications, not just to solve dense linear equations. Many times it can think LINPACK reference values do not have any sense, because most of the performance bottleneck is simply not scientific computing applications in this way.

Tianhe-2 as a "national security strategic investment", presumably a lot of time in solving the problem is to crack the password. However, a terrible fact is that a large number of cryptographic algorithms, including hash, asymmetric encryption (such as MD5, RSA), are only integer calculations , without any floating point computing operations. It seems the pursuit of high LINPACK value to improve the performance of password cracking, almost futile.

## Relationship between high-dimensional world order

When it comes to CPU performance, a few years ago, everyone to buy computer equipment at the time look at CPU clock speed, the higher the frequency, the better. So Intel in order to meet the market, introduced the Pentium D 3.0GHz or 3.6GHz clock speed of the CPU. Later into the multicore era, we see the number of cores, dual-core is definitely better than a good single-core, quad-core dual-core definitely better than good. CPU performance is good or bad does not know that there are too many parameters, the blind pursuit of high-frequency or the number of cores does not make sense. Not just the CPU, think about when you buy a digital camera to see what? Many people first reaction of course is a pixel ah. Lens anti-pay? Aperture size! Buying a car? Displacement! Buy a house? area!

In fact the truth easy to understand, but people are powerless in it. As there is no knowledge of the average consumer, in the face of this world is really complicated argument is powerless, so he had to choose the parameters a "recognized" as the benchmark.

Root of all this is that vector and vector can not compare the size, only scalar to compare. Only through some transformation vector to scalar functions to compare, such as modulus length, or projected onto a space. Any thing in the world can be used to represent a high-dimensional vector, but in order to obtain the order relation, we usually can map it to a one-dimensional space. In this process, a lot of information is lost. For the same set of vectors with a different function, its ordinal relationship can be completely different.

This is a easy to understand truth, and people can not do anything. Because people naturally tend to use a one-dimensional value to compare all of the same things (or even different types of things), but things are inherently high-dimensional.

## Values from the high-dimensional space is a one-dimensional mapping of

People often talk about values, such as values, not different people together through values of modern society, the people are divided into different groups. Value **is** actually **a high-dimensional space from the one-dimensional mapping,** which is a high-dimensional vector functions. People are faced with complicated things, it is an innate urge to be evaluated and then compared with each other and other things. In this process, the values of different people use different functions, so the result is very different.

## Price and value of goods

As a general measure of value tools, commodity prices has become a widely used scale. Prices of short term response relationship between supply and demand, but essentially reflect the value of a long-term, many. Mathematical representation of the language, the **price is a high-dimensional Functional (Functional),** wherein each dimension of the variable values is an individual function, or is represented by the following code (OCaml):

`(* 價值觀是一個從任意向量到整數的函數*) type value = (anything -> int) (* 價格是一個從多個價值觀函數到一個價值觀函數的函數(泛函) *) val price : (values_of_all : value list) -> value (* 一個簡單實現：價格即爲所有人價值觀的平均值*) let price values_of_all = fun thing -> let sum = List.fold_left ( fun sum value_function -> sum + (value_function thing) ) 0 values_of_all in let number_of_people = (List.length values_of_all) in sum / number_of_people` ) `(* 價值觀是一個從任意向量到整數的函數*) type value = (anything -> int) (* 價格是一個從多個價值觀函數到一個價值觀函數的函數(泛函) *) val price : (values_of_all : value list) -> value (* 一個簡單實現：價格即爲所有人價值觀的平均值*) let price values_of_all = fun thing -> let sum = List.fold_left ( fun sum value_function -> sum + (value_function thing) ) 0 values_of_all in let number_of_people = (List.length values_of_all) in sum / number_of_people` ) -> value `(* 價值觀是一個從任意向量到整數的函數*) type value = (anything -> int) (* 價格是一個從多個價值觀函數到一個價值觀函數的函數(泛函) *) val price : (values_of_all : value list) -> value (* 一個簡單實現：價格即爲所有人價值觀的平均值*) let price values_of_all = fun thing -> let sum = List.fold_left ( fun sum value_function -> sum + (value_function thing) ) 0 values_of_all in let number_of_people = (List.length values_of_all) in sum / number_of_people` value_function thing) `(* 價值觀是一個從任意向量到整數的函數*) type value = (anything -> int) (* 價格是一個從多個價值觀函數到一個價值觀函數的函數(泛函) *) val price : (values_of_all : value list) -> value (* 一個簡單實現：價格即爲所有人價值觀的平均值*) let price values_of_all = fun thing -> let sum = List.fold_left ( fun sum value_function -> sum + (value_function thing) ) 0 values_of_all in let number_of_people = (List.length values_of_all) in sum / number_of_people`

Substitution saying that prices reflect the values of all producers and consumers, although it may vary, but with a tool to unify them up into a single value can be measured as a function of different things. For an individual, the individual commodity prices may deviate from the value of the goods to measure, so there will be the feeling feels cheap or expensive. Whether personal money, personal measure of value will be different, personal assets can be used as a function of the values of other parameters.

The method used to measure the value of the price of seemingly simple and crude, there are many problems, but it also has other ways unparalleled advantages. Its biggest advantage is simplicity, because the human understanding of the complexity of things is very limited. This is also a reason why the planned economy can not be executed, because no one is mapped to all the one-dimensional function, or the function of sampling is too limited, only a small number of reaction will of the rulers.

## Value of diversity

Monism Despite the advantages of relatively easy sort of, but it will lead to the optimization of a single objective. For example, only supercomputers optimized LINPACK performance or some other students in order to meet the college entrance examination to become a machine to do the title, the whole society "to see the money" moral bankruptcy and so on. Although not in itself a problem, but it will lead to potential bias risk assessment. In this regard, a wide range of value propositions have been put forward. Diversification is the value of a one-dimensional scalar value becomes multidimensional vector, it can also be understood as a combination of multiple value function. After the value of diversity, the value itself again become incommensurable, only relatively (or the value of the vector function) in accordance with the dimensions.

In my opinion, the value of diversification does not solve too many problems, but the loss of the order relation, in fact, a self-deceiving way. Value of diversity is equivalent to no value, just a high-dimensional vector mapped to another vector, we lost not only information, but also can not be compared. Value of diversity can be used as further comparison of the value of "intermediate results" facilitate further calculations only, ultimately it comes down to one-dimensional. Measure everything with money one dollar value Although you can not solve many problems, but it is currently capable of human thought and practice in the most effective way. Hopefully there will be a better way to be invented.