Cahart, Richard and Cenian, Adam, Implication of Proven Limits on Scientific Knowledge

8/3/2019 Cahart, Richard and Cenian, Adam, Implication of Proven Limits on Scientific Knowledge

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PL ISSN 0459-6854

B U L L E T I N

DE LA SOCIETE DES SCIENCES ET DES LETTRES DE LODZ

2009 Vol. LIX

Recherches sur les deformations Vol. LVIII

pp. 718

Richard A. Carhart and Adam Cenian

IMPLICATION OF PROVEN LIMITS ON SCIENTIFIC

KNOWLEDGE: GODELS PROOF, QUANTUM UNCERTAINTY,

CHAOS THEORY AND SPECIFIED COMPLEXITY

OF INFORMATION THEORY

Summary

Each step of progress in science and technology has encouraged people to believe andto proclaim that we can use it to achieve full knowledge and control over the world. Someprominent modern scientists (like Dawkins) even claim that scientific knowledge is the onlyvalid knowledge of reality humans can achieve. However, four discoveries of modern sci-ence: Gdels incompleteness theorems, quantum uncertainty, chaos theory, and, tentatively,complex specified information theory show us specific ways in which our ability to knowand control nature is limited in principle, not only in practice. These limitations on humanscientific knowledge are explored in this paper, and a possible, more encompassing worldview than mere ontological naturalism is suggested.

1. Introduction

For centuries the human race has wanted to achieve full knowledge and control of

the world. Each step of progress in science and technology has encouraged people to

believe this can be done. The great success of science and technology has led modern

people to believe that we can understand and control any part of nature and human

life that we choose to.

One should really admire the new achievements of microelectronics or medical

science. Fig. 1 present a microchip in the mouth of an ant, showing the fascinating

ability of miniaturization of electronic devices. This example is only a beginning, as

many applications of nanotechnology are already in advanced development.

Laser technologies applied in medical sciences enable not only precise readjust-ment of our lenses (see Fig. 2a), but also precise treatment of cancer cells or laser

bio-stimulation of skin healing (see Fig. 2b.)


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8 R. A. Carhart and A. Cenian

Fig. 1: New electronic chip technology enables fascinating density of electronic elements onsurface (after Gitt [1]).

(a) (b)

Fig. 2: Laser applications in medical science: (a) apparatus for vision correction (Lasik

technology); (b) effect of laser bio-stimulation of skin healing (after Fiedor et al. [2]).

Each time a new field of science is opened, we are encouraged to expect that all

human problems related to this field will be solved. For example, molecular biologists

are telling us that they will be able to cure all chronic diseases by modifying the sick

persons DNA. Many want to produce human embryos in order to harvest embryonic

stem cells and grow replacement organs. They predict that we can enjoy extremely

long life spans in this way.

What are the real prospects for complete knowledge and mastery of the world

based on the laws of science? Does what we know of science and mathematics point

in the direction of complete knowledge and control?

A second related claim by many scientists today is that only scientific knowledgeis real, rational, and objective. They say that all other knowledge, such as the ex-

istence of a Creator of the world, is purely an opinion and is completely personal.


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Implication of proven limits on scientific knowledge 9

For example, Peter Atkins says, There is no reason to suppose that science cannot

deal with every aspect of existence [3]. In particular, many say that it is all right

to speak of God or religion as long as people dont claim that God has any objective

existence, or that religious belief constitutes actual knowledge of reality. Only science

deals with the lawful world of real events that can be observed and measured.

This view automatically rules out the idea that the universe was created for a

purpose or was designed. It denies the objective existence of a Being that created

the universe and could act in the material world as well as beyond it. It also implies

there is no way to have a real experience of a personal God who actually exists, or

any revelation of valid knowledge about God or the intended pattern and purpose

of life.

The Judeo-Christian Bible claims to be a self-revelation of the Creators char-

acter, purposes, and plan for human life. This is a truth claim. It is either true or

false, not just a matter of private opinion, no matter how difficult it is to decide the

question. The Bible contains teaching that many believe illuminates aspects of the

origin and nature of the real physical world. One such very important teaching is

that the natural world is rationally intelligible to humans.

2. The foundation of science; belief in the rational intelligibility

of nature

Noble Laureate Prof. Eugene Wigner has argued at length that we have no right

to expect nature to be rationally intelligible and understandable in terms of human

logic and mathematics [4]. Without assurance of rational intelligibility, science itself

has no basis to claim validity. If all things arise out of an automatic, purposeless

machine of nature that simply exists, then how can we trust the results that the

human organism obtains in experimental observations, logic, and mathematics?

Dr. John Lennox, among others, has clearly explained in more detail the irra-

tionality of the purely naturalistic view, its self-contradiction, and how it underminesthe legitimacy of science itself [5].

Pure Naturalism gives no real explanation for the rational intelligibility of the

natural world, but as we shall discuss below, the Bible does give a clear, simple,

logical explanation of this miracle that Wigner writes about so eloquently.

3. Proven limits on scientific knowledge

Our first important question is, Within science, how sure or certain is the body

of knowledge and what are its proven limits, if any? Science has proven that it

cannot produce a complete and accurate prediction of all real physical events in

three specific firmly established mathematical and physical theorems or principles,and probably a fourth limiting theorem that is being developed. Fig. 3 illustrates this

schematically. The first three are Godels Theorems, quantum uncertainty, and the


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time development of deterministic macroscopic chaotic systems. It is likely that a

fourth area, the origin of complex specified information in living systems, will yield

new principles involving an extended form of information theory. We will discuss

each of these four limits in more detail.

3.1. Loss of logical completeness: Godels theorems (1931)Logic and mathematics are the basis for all scientific work, the base upon which

the scientific enterprise rests, along with our ability to observe nature directly and

measure many aspects of it. Difficulty in logic and mathematics, therefore, causes

direct difficulty in the certainty of scientific knowledge. Everybody thought that

with the standard axioms of established mathematical systems there would be a

proof that any meaningful theorem you could formulate can be proven either true

or false.

Euclid dreamed about a formula-

Fig. 3: Limits to scientific knowledge.

tion of mathematical (geometrical)

statements that would produce one

complete set of all true assertions, avirtual heaven for mathematicians.

At the end of the 19th Century, David

Hilbert entered into a bitter dispute

on the limits of scientific knowledge

with a German physician and phys-

iologist Emil du Bois-Reymond. The

latter was the main proponent of the

famous Latin maxim ignoramus et ig-

norabimus: we do not know and will

not know.

On 8 September 1930 Hilbert proudly opposed Bois-Reymonds view in a cele-

brated address to the Society of German Scientists and Physicians, in Knigsberg:We must not believe those, who today, with philosophical bearing and deliberative

tone, prophesy the fall of culture and accept the ignorabimus. For us there is no

ignorabimus, and in my opinion, none whatever in natural science. In opposition

to the foolish ignorabimus our slogan shall be: We must know we will know!

Unfortunately for Hilbert, another mathematician, Kurt Godel, finally resolved the

ignorabimus problem in a way which destroyed mathematical heaven.

Godels two incompleteness theorems established that within any system as com-

plicated as ordinary arithmetic, theorems may be stated that cannot be proven

either true or false. Therefore, we are in the uncomfortable position that the basic

mathematics and logic underlying all science is incomplete.

The significance of Godels incompleteness theorems for empirical science wasnot immediately evident. But authors like Stanley Jaki and Stephen Hawking have

publicly written that our hopes for a theory of everything are shaken by them.


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Hawking says, Maybe it is not possible to formulate the theory of the universe

in a finite number of statements. This is very reminiscent of Godels theorem [6].

Jaki says that it is not maybe, but that it is transparently true that a theory of

everything with a finite number of laws is not possible [7]. The theorems imply that

every formulation of physics, no matter how advanced or complex, will be incomplete.

It is impossible to have an ultimate theory containing a finite number of principles of

which it can be said with certainty that this theory is final. Though incomplete in

the sense proven by Gdel, logic and mathematics have shown themselves to be quite

powerful as the basis of science, and we expect to continue to rely on them. However,

our confidence in the perfection of the underlying mathematics has been shaken. We

should be more humble in our attitude toward describing the world.

3.2. Loss of microscopic determinism: the quantum uncertainty principle

In quantum mechanics we must adopt a formulation that sets limits on simultaneous

knowledge of important complementary variables in physical systems, such as the

position and velocity of any particle. Thus, motion becomes essentially statistical on

the microscopic level and not deterministic.

Fig. 4: Scheme of classical and quantum motion.


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For example, for an electron only the motion of the probability wave (wave func-

tion) describing its state of motion is deterministic in the standard formulation of

quantum mechanics. The difficulty is that although the probability wave moves de-

terministically, its absolute square has the essential meaning of the probability for

where one will measure an electron in that state of motion. The actual measurement

values for position and velocity are statistically random within that probability dis-

tribution.

For example, in classical mechanics people thought of an electron as a small

hard ball (like a billiard ball). By equations of classical mechanics the electron has

a definite path and speed at each moment, and suffered known collisions. But in

quantum mechanics, valid at the atomic level, only the probability wave for the

electrons location has a deterministic motion, as shown in Fig.4.

Therefore, actual events on the microscopic level cannot be predicted determin-

istically, but only statistically. This fact is not a temporary practical limitation, but

an inherent limitation we cannot go beyond. It cuts deeply into human hopes for

predicting and controlling the world completely.

One important example is whether the functioning of the human brain can be

taken as deterministic from a scientific viewpoint. Since thought processes are prob-ably initiated at the molecular level by events subject to quantum uncertainty, we

should not assume that human thought can be described scientifically in a fully

deterministic way.

3.3. Uncertainty predicting the future in macroscopic, deterministic sys-

tems: chaos theory

The statistical effects of the uncertainty principle become immeasurably small as

we go from the microscopic world of atoms and nuclei to the macroscopic world of

meters and kilograms where we live. It has been proven that systems of differential

equations for macroscopic systems will give essentially deterministic predictions.

It would appear that we can recover our hopes for prediction and control in themacroscopic world. However, another type of limitation on scientific prediction has

been proven for the nonlinear systems that creates a kind ofmacroscopic uncertainty

principle!

Systems of ordinary or partial differential equations with nonlinear couplings are

called chaotic systems for certain ranges of initial conditions. Almost all interest-

ing macroscopic systems we want to study obey equations of this type. For chaotic

systems it has been proven that no matter how accurately we know the initial con-

ditions of the system, the difference between the solution and the actual physical

system will grow rapidly over time and become great. We hoped that small uncer-

tainties in initial conditions would lead to solutions that only differed a little over

time from physical reality, as is true for linear systems. This is not the case, and wecannot prevent large differences from occurring over time by knowing the beginning

conditions of a system more accurately. In fact, arbitrarily small differences in ini-


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(a)

(b)

(c)

Fig. 5: Predictions for hurricane Isabel in 2003. (a) Prediction on 13 Sept. 2003, 17:00(5.5 days before landfall). (b) Prediction on 15 Sept. 2003, 11:00 (3 days before landfall).

(c) Prediction on 16 Sept. 2003, 11:00 (2 days before landfall).


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In the entire experience of the human race apart from living systems, no such

specified complex systems, very rich in information, ever arise except as the result of

the design and action of an intelligent source. That source is usually a human being.

There has been no demonstration within molecular biology of how such information

can arise spontaneously within a natural system. Thus, it may be necessary to pos-

tulate action of an intelligence inside [8] or outside of the natural order to explain

the origin of the complex specified information (CSI) in living organisms.

Application of information theory to systems rich in complex specified informa-

tion is still in the descriptive phase of investigation. Proven precise theorems are

not yet available. Still, some concepts are emerging and gaining acceptance among

scientists. Systems contain complex specified information when they can carry out

a complex set of interrelated complicated processes to achieve a recognizable goal.

The more numerous and complex the processes, the higher the complex specified

information (CSI) content of the system. Scientists have not yet been able to define

CSI quantitatively, as they have done for Shannon information.

Shannon information concept could not be applied strightforwardly to the CSI

content in the system. According to his definition, a longer string of binary bits

has larger information content than a shorter one. And if the string contains toomuch noise, the receiver of the string will not be able to obtain the information

content accurately. But, as W. Gitt rightly points out [1], this is not the case when

the information must produce a single specific action or a sequence or network of

interlocking actions. This is the case when the DNA code directs the processes of life.

In the case of the information basis of life, Gitt discusses a hierarchy of information

types, including statistics analogous to Shannons concept, but also including syntax,

semantics, pragmatics and apobetics. The information theory which could apply to

the CSI content of living systems, Gitt says, must include all of these levels. Even

in Shannons theory, you must have two intelligent agents involved: a sender and a

receiver of the information.

Based on these considerations we must imagine action from an intelligent agent

to build a system with a high CSI score. At the very least, these systems are designed

and assembled by even more CSI-rich systems. One widely quoted example of such

specified complexity is the cascade of reactions necessary for human blood to clot.

A second common example of a high degree of specified complexity is the flagellar

motor used for locomotion by E. coli bacteria. The DNA for E. coli contains about

4.000 genes and 4 million base pairs. The number of possible sequences of this length

is 102.400.000. The particular sequences having the amount of CSI needed to code for

even this simple bacterium with its flagellar motor, are extremely improbable. The

DNA must not only code for the proteins needed for the 40 subunits of the motor.

It must also provide the correct assembly sequence, and the switching on and off of

production when the right size subunit has been made.

Amazingly, this information is also written with the highest known informationdensity of 1, 88 1021 bite/cm3 [1].


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Further fascinating examples can be viewed on the internet in an 8-minute an-

imation film commissioned by Harvard University Medical School for its medical

students available at http://multimedia.mcb.harvard.edu/anim innerlife hi.html.

Can you find the bipedal locomotor in the film. If it is designed, the Designer

must have a sense of humor!

These ideas, while clearly empirical and scientific, are as yet only descriptive and

tentative. What is needed to establish these ideas as a firm scientific limit, is to

develop a quantitative measure of complex specified information (CSI), as was done

in information theory for Shannon information of signals. Then, theorems must be

proven to determine what level of CSI can arise from natural processes.

Even Shannon information theory and other theorems related to coding systems

(like the DNA/protein relationship) have yielded tentative information theory limits

on our scientific knowledge of biological systems. One researcher who has produced

a body of respected research [9] on the limitations imposed by theorems on only the

Shannon information in organisms and its transmission with regard to our theories

of the origin of life is Hubert Yockey. Yockey concludes, The segregated, linear and

digital character of the genome has allowed us to apply information theory and other

mathematical theorems about sequences or strings of symbols to make a quantitativerather than an anecdotal and ad hoc discussion of significant problems in molecular

biology. This procedure has led us to avoid a number of illusions common in the liter-

ature. The application of these mathematical procedures will play a role in molecular

biology analogous to that of thermodynamics in chemistry.

A very helpful further discussion of the information issues relating to biological

life based on very recent research results has been assembled by John Lennox in the

book already cited [10]. Although mainly qualitative, his treatment helps define the

quantitative directions biologists either are pursuing or need to consider. It seems

that the scientific community may be so comfortable with Neo-Darwinism that it

has not invested in the scientific development of life-related information theory. This

is a genuine issue of freedom of inquiry in intellectual life, whether in the university

or the academy. This author recommends: give free inquiry a chance!

4. A possible more encompassing world view

Four discoveries of modern science: Godels incompleteness theorems, quantum un-

certainty, chaos theory, and, tentatively, specified complexity of information theory,

show us specific ways in which we cannot achieve complete knowledge and control

of nature. This enforces humility and shows us that science cannot serve as a God

substitute. Science and technology will continue to be very useful, but we will not

be able to use them to understand and control the world completely! We should be

humble, honest, and careful with our science and technology.It is interesting that if we combine scientific results with the possible truth of the

Bibles claim to be an accurate revelation to us from the Creator of the universe,


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we can achieve a firm basis for science and a broader explanatory system. The Bible

makes four relevant statements:

1. There is a supernatural Designer who created and maintains the Universe and

its laws [11].

2. Humans are made in The Creators image so we can understand nature [12].

3. Mathematics and science give us much valuable knowledge and control of na-

ture [13].

4. Our knowledge is imperfect and incomplete, so science cannot enable us to

play God [14].

The first two points guarantee the ultimate validity of the scientific enterprise

against a variety of contemporary attacks (including postmodern one) and assure us

of the rational intelligibility of nature. They explain the origin of the miracle that

Wigner (an atheist) mentions 12 times in his article [4]. They also tell us to whom

we should express the gratitude that Wigner says 4 times we should experience.

The third point encourages us to pursue scientific knowledge and its technological

application. The final point agrees with the proven scientific limitations discussedabove, and keeps us from expecting too much from science. It encourages us to find

ultimate meaning in another place.

Our best course may be to integrate knowledge from different valid sources to

achieve a fuller knowledge of the real nature of our actual universe. Scientific knowl-

edge has definite proven limitations, and you cannot find the equations of Einsteins

general theory of relativity in the Bible.

References

[1] W. Gitt, Am Anfang war die Information, Haenssler, Ulm 2002.

[2] P. Fiedor, T. Kecik, et al., Review of laser application in medicine (in polish), Dom

Wydawniczy Ankar, Warszawa 1995.

[3] Natures Imagination: the Frontiers of Scientific Vision, ed. J. Cornwell, Oxford Uni-versity Press, Oxford 1995, p. 125.

[4] E. P. Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sci-ences, Communications On Pure And Applied Mathematics, 13 (1960) 114.

[5] J. C. Lennox, Gods Undertaker: Has Science Buried God? (in english), Lion Hudsonplc, Oxford 2007, p. 3843.

[6] S. Hawking, Godel and the End of Physics,http://www.damtp.cam.ac.uk/strings02/dirac/hawking/

[7] S. Jaki, A Late Awakening to Godel in Physics,http://pirate.shu.edu/ jakistan/JakiGodel.pdf

[8] For an example of inside the natural order, see: F. Crick and L. Orgel, Directed

Panspermia, Icarus 19 (1973) 341 ff.[9] H. P. Yockey, Origin of Life on Earth and Shannons Theory of Communication, Com-

puters and Chemistry 24 (2000) 105123; Information Theory, Evolution and the


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Origin of Life, Information Sciences 141 (2002) 219225; Information Theory, Evo-lution and the Origin of Life, Cambridge University Press, New York 2005, p. 259.

[10] op. cit., p. 117165

[11] For example, Genesis 1:124, John 1:17 (Word in the Greek manuscript is logos,the root of logic), and Colossians 1:1517

[12] For example, Genesis 1:2628

[13] For example, II Chronicles 1:10, II Chronicles 2:13, II Chronicles 9:18, and Proverbs6:68.

[14] For example, Isaiah 55:89.

Faculty of Physics The Szewalski Institute

University of Illinois at Chicago of Fluid-Flow Machinery

3605 Brierhill Drive Polish Academy of Sciences

Island Lake, IL 60042 Gen. Fiszera 14

USA PL-80-231 Gdansk

and Poland

European Scientific Network e-mail: [email protected]

e-mail: [email protected]

Presented by Leszek Wojtczak at the Session of the Mathematical-Physical Com-

mission of the Lodz Society of Sciences and Arts on November 19, 2008

SKUTKI I ZNACZENIE GRANIC WIEDZY NAUKOWEJ

WYNIKAJACYCH Z TWIERDZENIA NIEZUPELNOSCI GODLA,

ZASADY NIEOZNACZONOSCI HEISENBERGA,

DETERMINISTYCZNEGO CHAOSU ORAZ WYSPECYFIKOWANEJ

ZLOZONOSCI W TEORII INFORMACJI

S t r e s z c z e n i e

Staly postep w nauce i technologii zacheca ludzi by wierzyc, a nawet glosic, ze naukaumozliwia pelna wiedze oraz kontrole nad swiatem. Ponadto, pewni prominentni naukowcy jak Dawkins glosza dzis, ze nauka jest jedynym zrodlem sprawdzonej wiedzy jakludzkosc moze zdobyc na temat rzeczywistosci. Jednakze, cztery odkrycia nowoczesnejnauki: twierdzenia niezupelnosci Godla, zasada nieoznaczonosci Heisenberga, chaos deter-ministyczny oraz prawdopodobnie wyspecyfikowana zlozonosc w teorii informacji dowodzaw sposob szczegolowy, gdzie nasza wiedza i mozliwosci kontroli nad natura trafiaja nagranice wynikajace z praw natury, a nie jedynie praktyki. W pracy przedstawiono i pod-dano analizie te ograniczenia ludzkiej wiedzy naukowej oraz zaproponowano swiatopogladduzo szerszy niz naturalizm ontologiczny w czystej formie.

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Cahart, Richard and Cenian, Adam, Implication of Proven Limits on Scientific Knowledge