# We Know So Little About So Much

I find it very interesting that even with the exponential growth in knowledge that we have witnessed from ancient times through the industrial age to the digital age, there still remains so much that is simply unknown to us. I have no doubt that the human spirit will in time conquer each and every question that it poses to itself. The following is a list of unsolved problems in various fields of scientific and philosophical inquiry. Aside from the solutions being interesting in themselves and offering the opportunity of contributing to our collective history, some of these problems even offer monetary incentives for proven solutions. So go ahead and tackle one!

We know very little, and yet it is astonishing that we know so much, and still more astonishing that so little knowledge can give us so much power.

– Bertrand Russell

## Unsolved Problems in Artificial Intelligence

In the field of artificial intelligence, the most difficult problems are informally known as AI-complete or AI-hard, implying that the difficulty of these computational problems is equivalent to that of solving the central artificial intelligence problem—making computers as intelligent as people, or strong AI.[1] To call a problem AI-complete reflects an attitude that it would not be solved by a simple specific algorithm.

AI-complete problems are hypothesised to include computer vision, natural language understanding, and dealing with unexpected circumstances while solving any real world problem.[2]

Currently, AI-complete problems cannot be solved with modern computer technology alone, but would also require human computation. This property can be useful, for instance to test for the presence of humans as with CAPTCHAs, and for computer security to circumvent brute-force attacks.[3][4]

### History

The term was coined by Fanya Montalvo by analogy with NP-complete and NP-hard in complexity theory, which formally describes the most famous class of difficult problems.[5] Early uses of the term are in Erik Mueller’s 1987 Ph.D. dissertation[6] and in Eric Raymond‘s 1991 Jargon File.[7]

### AI-complete problems

AI-complete problems are hypothesised to include:

### Machine translation

Main article: Machine translation

To translate accurately, a machine must be able to understand the text. It must be able to follow the author’s argument, so it must have some ability to reason. It must have extensive world knowledge so that it knows what is being discussed — it must at least be familiar with all the same commonsense facts that the average human translator knows. Some of this knowledge is in the form of facts that can be explicitly represented, but some knowledge is unconscious and closely tied to the human body: for example, the machine may need to understand how an ocean makes one feel to accurately translate a specific metaphor in the text. It must also model the authors’ goals, intentions, and emotional states to accurately reproduce them in a new language. In short, the machine is required to have wide variety of human intellectual skills, including reason, commonsense knowledge and the intuitions that underlie motion and manipulation, perception, and social intelligence.Machine translation, therefore, is believed to be AI-complete: it may require strong AI to be done as well as humans can do it.

### Software brittleness

Main article: Software brittleness

Current AI systems can solve very simple restricted versions of AI-complete problems, but never in their full generality. When AI researchers attempt to “scale up” their systems to handle more complicated, real world situations, the programs tend to become excessively brittle without commonsense knowledge or a rudimentary understanding of the situation: they fail as unexpected circumstances outside of its original problem context begin to appear. When human beings are dealing with new situations in the world, they are helped immensely by the fact that they know what to expect: they know what all things around them are, why they are there, what they are likely to do and so on. They can recognize unusual situations and adjust accordingly. A machine without strong AI has no other skills to fall back on.[8]

### Formalization

Computational complexity theory deals with the relative computational difficulty of computable functions. By definition it does not cover problems whose solution is unknown or has not been characterised formally. Since many AI problems have no formalisation yet, conventional complexity theory does not allow the definition of AI-completeness.

To address this problem, a complexity theory for AI has been proposed.[9] It is based on a model of computation that splits the computational burden between a computer and a human: one part is solved by computer and the other part solved by human. This is formalised by a human-assisted Turing machine. The formalisation defines algorithm complexity, problem complexity and reducibility which in turn allows equivalence classes to be defined.

The complexity of executing an algorithm with a human-assisted Turing machine is given by a pair $\langle\Phi_{H},\Phi_{M}\rangle$, where the first element represents the complexity of the human’s part and the second element is the complexity of the machine’s part.

### Results

The complexity of solving the following problems with a human-assisted Turing machine is:[9]

• Optical character recognition for printed text: $\langle O(1), poly(n) \rangle$
• Turing test:
• for an $n$-sentence conversation where the oracle remembers the conversation history (persistent oracle): $\langle O(n), O(n) \rangle$
• for an $n$-sentence conversation where the conversation history must be retransmitted: $\langle O(n), O(n^2) \rangle$
• for an $n$-sentence conversation where the conversation history must be retransmitted and the person takes linear time to read the query: $\langle O(n^2), O(n^2) \rangle$
• ESP game: $\langle O(n), O(n) \rangle$
• Image labelling (based on the Arthur–Merlin protocol): $\langle O(n), O(n) \rangle$
• Image classification: human only: $\langle O(n), O(n) \rangle$, and with less reliance on the human: $\langle O(\log n), O(n \log n) \rangle$.

### References

1. Jump up^ Shapiro, Stuart C. (1992). Artificial Intelligence In Stuart C. Shapiro (Ed.), Encyclopedia of Artificial Intelligence (Second Edition, pp. 54–57). New York: John Wiley. (Section 4 is on “AI-Complete Tasks”.)
2. Jump up^ Roman V. Yampolskiy. Turing Test as a Defining Feature of AI-Completeness . In Artificial Intelligence, Evolutionary Computation and Metaheuristics (AIECM) –In the footsteps of Alan Turing. Xin-She Yang (Ed.). pp. 3-17. (Chapter 1). Springer, London. 2013. http://cecs.louisville.edu/ry/TuringTestasaDefiningFeature04270003.pdf
3. Jump up^ Luis von Ahn, Manuel Blum, Nicholas Hopper, and John Langford. CAPTCHA: Using Hard AI Problems for Security. In Proceedings of Eurocrypt, Vol. 2656 (2003), pp. 294-311.
4. Jump up^ Bergmair, Richard (January 7, 2006). “Natural Language Steganography and an “AI-complete” Security Primitive”. CiteSeerX: 10.1.1.105.129. (unpublished?)
5. Jump up^ Mallery, John C. (1988), “Thinking About Foreign Policy: Finding an Appropriate Role for Artificially Intelligent Computers”, The 1988 Annual Meeting of the International Studies Association., St. Louis, MO.
6. Jump up^ Mueller, Erik T. (1987, March). Daydreaming and Computation (Technical Report CSD-870017) Ph.D. dissertation, University of California, Los Angeles. (“Daydreaming is but one more AI-complete problem: if we could solve any one artificial intelligence problem, we could solve all the others”, p. 302)
7. Jump up^ Raymond, Eric S. (1991, March 22). Jargon File Version 2.8.1 (Definition of “AI-complete” first added to jargon file.)
8. Jump up^ Lenat, Douglas; Guha, R. V. (1989), Building Large Knowledge-Based Systems, Addison-Wesley, pp. 1–5
9. Dafna Shahaf and Eyal Amir (2007) Towards a theory of AI completeness. Commonsense 2007, 8th International Symposium on Logical Formalizations of Commonsense Reasoning.

## Unsolved Problems in Biology

 Adaptation At present there is no theoretical model for how adaptation occurs that is close to being complete. Mathematical models of evolution (e.g. within population genetics) describe how the process of natural selection influences the frequency of already-existing gene variants based on their relative fitnesses. Only a small amount of theory treats the problem of modelling the generation of new variants through mutation, in terms of either the fitnesses or phenotypic forms they confer. Alkaloids The function of these substances in living organisms which produce them is not known[1] Arthropod head problem A long-standing zoological dispute concerning the segmental composition of the heads of the various arthropod groups, and how they are evolutionarily related to each other. Basking shark Only the right ovary in this fish appears to function, the reason is unknown. Biological aging There are a number of hypotheses why senescence occurs including those that it is programmed by gene expression changes and that it is the accumulative damage of biological processes. Blue Whale There is not much data on the sexuality of the biggest animal ever.[2] Botany/Plants What is the exact evolutionary history of flowers and their blossoms? Butterfly migration How do the descendants of Monarch butterfly all over Canada and the US eventually, after migrating for several generations, manage to return to a few relatively small overwintering spots? Cambrian explosion What is the cause of the apparent rapid diversification of multicellular animal life around the beginning of the Cambrian, resulting in the emergence of almost all modern animal phyla? Consciousness What is the brain basis of subjective experience, cognition, wakefulness, alertness, arousal, and attention? Is there a “hard problem of consciousness“? If so, how is it solved? What, if any, is the function of consciousness?[3][4] Evolution of sex What selective advantages drove the development of sexual reproduction, and how did it develop?[5] Extraterrestrial life Might life which does not originate from planet Earth also have developed on other planets? Might this life be intelligent? Gall wasp It is largely unknown how these insects induce gall formation in plants; chemical, mechanical, and viral triggers have been discussed. Glycogen body The function of this structure is not known. Golgi apparatus In cell theory, what is the exact transport mechanism by which proteins travel through the Golgi apparatus? Hammerhead shark The reason for their distinctive and unusual head structure is not known. Homing (biology) A satisfactory explanation for the neurobiological mechanisms that allow Homing, has yet to be found. Korarchaeota Their metabolic processes are so far unclear. Latitudinal diversity gradient Why does biodiversity increase when going from the poles towards the equator? Loricifera There are at least 100 species of this phylum that are yet to be described, but none of them is known to be present in the fossil record. Origin of life Exactly how and when did life on Earth originate? Which, if any, of the many hypotheses is correct? Paradox of the plankton The high diversity of phytoplankton seems to violate the competitive exclusion principle.

### References

1. Jump up^ Aniszewski, p. 142
2. Jump up^ Articleworld.org Blue Whale
3. Jump up^ Sejnowski, Terrence J.; Hemmen, J. L. van (2006). 23 problems in systems neuroscience (PDF). Oxford [Oxfordshire]: Oxford University Press. ISBN 0-19-514822-3.
4. Jump up^ Tononi, G; Koch, C. (2015). “Consciousness: Here, there and everywhere?” (PDF). Philosophical Transactions of the Royal Society London B.
5. Jump up^ Thomas N. Sherratt, David M. Wilkinson. Big questions in ecology and evolution. Oxford University Press US, 2009. ISBN 978-0-19-954861-3

## Unsolved Problems in Chemistry

Unsolved problems in chemistry tend to be questions of the kind “Can we make X chemical compound?”, “Can we analyse it?”, “Can we purify it?” and are commonly solved rather quickly, but may just as well require considerable efforts to be solved. However, there are also some questions with deeper implications. This article tends to deal with the areas that are the center of new scientific research in chemistry. Problems in chemistry are considered unsolved when an expert in the field considers it unsolved or when several experts in the field disagree about a solution to a problem.

### Organic chemistry problems

In addition to these, it is noteworthy that many mechanisms proposed for catalytic processes are poorly understood[which?] and often fail to explain all relevant phenomena.[citation needed]

### Biochemistry problems

• Enzyme kinetics: Why do some enzymes exhibit faster-than-diffusion kinetics?[8]
• Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?[5][9] This has been achieved for several small globular proteins in recent years.[10]
• RNA folding problem: Is it possible to accurately predict the secondary, tertiary and quaternary structure of a polyribonucleic acid sequence based on its sequence and environment?
• What are the chemical origins of life? How did non-living chemical compounds generate self-replicating, complex life forms?
• Protein design: Is it possible to design highly active enzymes de novo for any desired reaction?[11]
• Biosynthesis: Can desired molecules, natural products or otherwise, be produced in high yield through biosynthetic pathway manipulation?[12]

### References

1. The Future of Post-Human Chemistry: A Preface to a New Theory of Substances …, de Peter Baofu, page 285
2. Jump up^ The problem may actually occur at approximately Element 173, given the finite extension of nuclear-charge distribution.[citation needed] See the article on Extension of the periodic table beyond the seventh period, and the article section Relativistic effects of Atomic orbital.
3. Jump up^ Duffie, John A. (August 2006). Solar Engineering of Thermal Processes. Wiley-Interscience. p. 928. ISBN 978-0-471-69867-8.
4. Jump up^ Brabec, Christoph; Vladimir Dyakonov; Jürgen Parisi; Niyazi Serdar Sarıçiftçi (March 2006). Organic Photovoltaics: Concepts and Realization. Springer. p. 300. ISBN 978-3-540-00405-9.
5. “So much more to know”. Science 309 (5731): 78–102. July 2005. doi:10.1126/science.309.5731.78b. PMID 15994524.
6. Jump up^ S. Narayan, J. Muldoon, M.G. Finn, V.V. Fokin, H.C. Kolb, K.B. Sharpless,2005, “On Water: Unique Reactivity of Organic Compounds in Aqueous Suspension,” Angew. Chem. Int. Ed. 21:3157, see [onlinelibrary.wiley.com/doi/10.1002/anie.200462883/full]. accessed 15 December 2015.
7. Jump up^ Fredrik von Kieseritzky, 2013, “What is the true nature of gold-sulfur bonds?”, see [1], accessed 15 December 2014.
8. Jump up^ Hsieh M, Brenowitz M (August 1997). “Comparison of the DNA association kinetics of the Lac repressor tetramer, its dimeric mutant LacIadi, and the native dimeric Gal repressor”. J. Biol. Chem. 272 (35): 22092–6. doi:10.1074/jbc.272.35.22092. PMID 9268351.
9. Jump up^ King, Jonathan (2007). “MIT OpenCourseWare – 7.88J / 5.48J / 7.24J / 10.543J Protein Folding Problem, Fall 2007 Lecture Notes – 1”. MIT OpenCourseWare. RetrievedJune 22, 2013.
10. Jump up^ Dill KA; et al. (June 2008). “The Protein Folding Problem”. Annu Rev Biophys 37: 289–316. doi:10.1146/annurev.biophys.37.092707.153558. PMID 9268351.
11. Jump up^ http://depts.washington.edu/bakerpg/drupal/node/465
12. Jump up^ http://www.nature.com/nature/journal/v488/n7411/full/nature11478.html

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