Some Problems Can Be Proved Unsolvable

“Here are a couple of difficult mathematical problems for you to work on in your spare time, and one difficult problem from biology:

  1. Find positive integers x,y and z, such that x3+y3=z3.
  2. Draw a 2D map that is impossible to color (such that countries which share a border have different colors) with fewer than 5 colors.
  3. Explain how life could have originated and evolved into what we see today, through entirely unintelligent processes.


You can spend a lot of time trying different solutions to mathematical problem #1. After a while you might begin to wonder if it can be done, but don’t give up, there are always other integers to try. You can also spend a lot of time drawing maps. If one map doesn’t work, don’t give up, there are always others you can try. I once told my 10-year-old son that if he could find such a map, he would be famous. He drew map after map and gave them to his older brother, who always was able to color them using four colors. He finally gave up. More than one mathematician actually thought he had found such a map, but it always proved to be possible to color them with four or fewer colors after all.

A number of theories as to how life could have originated through entirely unintelligent processes have been proposed, but none are convincing, and this problem is generally considered to have not yet been solved. But new theories are constantly being proposed, as it would be unscientific to give up and declare the problem to be unsolvable. Charles Darwin felt he had explained how life and even human intelligence evolved from the first organisms though entirely unintelligent processes. Today his theory is doubted by an increasing number of scientists. Most of these doubters have proposed modifications to his theory or alternative theories of their own, but there are always serious problems with the alternative theories too. However scientists should never give up, even if none of the theories proposed so far are plausible. Who knows what new theories future scientists will come up with, the problem will surely be solved eventually.

Well, mathematicians sometimes do give up, after we have proved a problem to be impossible to solve. How can you prove a problem is impossible to solve, if you can’t try every possible solution? Often you say, assume there is a solution, then using that assumption you prove something that is obviously false, or known to be false. Andrew Wiles proved in 1995 that mathematical problem #1 did not have a solution (he actually proved something more general than this, called “Fermat’s last theorem,” 358 years after this famous theorem was first proposed). And in 1976, Kenneth Appel and Wolfgang Haken ended 124 years of uncertainty by proving that mathematical problem #2 could not be solved (they proved the “four color theorem” ).

The proofs that the above mathematical problems are impossible to solve were quite difficult, but there is a very simple proof that the biological problem #3 posed above is impossible to solve. All one needs to do is realize that if a solution were found, we would have proved something obviously false, that a few (four, apparently) fundamental, unintelligent forces of physics alone could have rearranged the fundamental particles of physics into libraries full of science texts and encyclopedias, computers connected to monitors, keyboards, laser printers and the Internet, cars, trucks, airplanes, nuclear power plants and Apple iPhones.

In other areas of science, when one theory fails, scientists propose new ones, and usually a better one is eventually found which is successful. Thus it is not surprising that those of us who claim that the biological problem posed above is impossible to solve are criticized as not understanding how science works. But anyone who spends much time trying to explain how atoms spontaneously rearranged themselves into the first living things, and how genetic accidents then produced more and more complicated arrangements of atoms, and how eventually something called “intelligence” allowed some of these complicated arrangements of atoms to design cars and computers and Apple iPhones, finally starts to realize, or at least should start to realize, that this problem is different. Just as mathematicians who repeatedly tried and failed to solve problems #1 and #2 eventually turned their attention to proving that these problems were unsolvable, biologists should, after repeated failures on problem #3, begin to suspect that there is some fundamental principle involved here that cannot be overcome simply by working harder and producing better theories.

Although it is hard to find a claim that will be met with harsher criticism from the scientific community, I claim that this principle is in fact the fundamental principle behind the second law of thermodynamics. If the principle which dooms all attempts to solve problem #3 is not one of the human statements of this law, it is at least the fundamental natural principle behind this law, as I argue in my June 2013 BIO-Complexity article “Entropy and Evolution.” But please note that the proof given above that problem #3 is impossible to solve does not really depend on whether or not what has happened on Earth technically violates the second law, it is much simpler than that.

Meanwhile, I don’t spend much time trying to find positive integer solutions to x3+y3=z3, or trying to draw maps that require five colors, and I really don’t feel I need to understand each new theory on the origin or evolution of life that is proposed. You can say this is a very unscientific attitude, and if you want to work on these problems I am certainly not going to try to stop you, but I would rather spend my time on problems that have not yet been proved to be unsolvable.”

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How the Brain Responds to Missing Information

“It sometimes happens that when someone asks a question, the addressee does not give an adequate answer, for instance by leaving out part of the required information. The person who posed the question may wonder why the information was omitted, and engage in extensive processing to find out what the partial answer actually means. The present study looks at the neural correlates of the pragmatic processes invoked by partial answers to questions. Two experiments are presented in which participants read mini-dialogues while their Event-Related brain Potentials (ERPs) are being measured. In both experiments, violating the dependency between questions and answers was found to lead to an increase in the amplitude of the P600 component. We interpret these P600-effects as reflecting the increased effort in creating a coherent representation of what is communicated. This effortful processing might include the computation of what the dialogue participant meant to communicate by withholding information. Our study is one of few investigating language processing in conversation, be it that our participants were ‘eavesdroppers’ instead of real interactants. Our results contribute to the as of yet small range of pragmatic phenomena that modulate the processes underlying the P600 component, and suggest that people immediately attempt to regain cohesion if a question-answer dependency is violated in an ongoing conversation.”



During conversation, speakers and listeners act upon certain basic assumptions which enable them to communicate swiftly, and seemingly effortlessly [1][5]. If, for instance, someone asks a question, both speaker and hearer have knowledge of what would constitute a valid answer. To be more specific, a question can be said to impose constraints and create expectations regarding both the information structure (i.e., specifying what is given and what is new, and thus how the information contained in an utterance should be linked to the existing discourse representation) and the content of the answer. Consider for instance someone inquiring about the activities of two protagonists, ‘John’ and ‘Peter’:

1. What did John and Peter do?

On the level of information structure, this question introduces two entities that make them likelytopics in the answer, where a topic can be loosely described as the entity about which the sentence imparts information [6]. On the content level, in turn, the question requires the answer to impart on the activities of these specific people (‘John’ and ‘Peter’), and not, for instance, about their respective spouses. Answer (2) satisfies both of these constraints.

2. John cleaned the house and Peter fixed the window.

In contrast, by leaving out information about the second protagonist, answer (3) violates expectations regarding both information structure and content. Utterance (3) is thus pragmatically infelicitous as an answer to question (1).

3. John cleaned the house.

If there is no additional information, and the answer consists of only this sentence, the person who posed the question is faced with the task of determining what the speaker meant to communicate by being incomplete. The speaker might, for instance, be taken to convey that Peter did nothing, that what he did was of no importance, or just that Peter is terribly lazy [1],[7]. The computation of such beliefs, and thus of a coherent mental representation of intended meaning, may require extensive pragmatic processing [Regel, Gunter, & Friederici [8] provide a similar argument on the computation of ironic meaning]. How the human language processor deals with this kind of processing is still poorly understood, and neurocognitive investigations of such phenomena are scarce.

This study presents two Event-Related brain Potential (ERP) experiments that examine the neural correlates of the pragmatic processes invoked by partial answers to questions. ERPs provide a means of disentangling different processes involved in online language comprehension, on the basis of the qualitatively different signatures they leave behind. There are many ERP studies on word- and sentence-level processing [Kutas, van Petten, & Kluender[9] provide an overview], but researchers have only recently started to use ERPs to investigate pragmatic processing [8][10][13]. These latter studies provide evidence that pragmatic processes such as the computation of bridging inferences or of ironic meaning modulate the amplitude of the P600 component, a positive deflection of the ERP signal that usually peaks around 600 ms post stimulus onset.

Brouwer, Fitz, & Hoeks [14] have recently argued, on the basis of a thorough review of the ERP literature, that the P600 component is best defined as a family of late positivities that reflect the processing involved in the word-by-word construction, reorganization, or updating of a mental representation of what is being communicated (MRC)–see also [15][16]. Different varieties of the P600-effect (in terms of electrophysiological properties like onset, amplitude, duration, and scalp distribution) are assumed to reflect different sub-processes of MRC construction. These sub-processes may include, among other things, the accommodation of new discourse referents, the establishment of relations between entities, thematic role assignment and revision, and for instance, the resolution of conflicts between different information sources (e.g., with respect to world knowledge). For instance, in the computation of bridging inferences, as in a sentence pair like “We went for a picnic. The beer was warm” [17], some of the sub-processes involved will concern the accommodation of the new discourse referent “The beer”. The computation of ironic meaning, on the other hand, may involve more sub-processes aimed at overcoming the conflict between the unfolding discourse and the ‘literal meaning’ of the ironic utterance—cf. “These artists are gifted!” in the context of a bad musical performance, see [8].

The present study investigates whether the processes invoked by partial answers to questions also produce an increase in P600 amplitude, which would provide strong support for the MRC hypothesis discussed above (i.e., P600 amplitude reflects ease of ‘making sense’).


Experiment 1

In the first experiment, participants read short question-answer pairs that appeared word-by-word in the middle of a computer screen, and were occasionally asked to answer a comprehension question (see Procedure section below). During reading, brain activity of the participants was monitored through ERP recording. The question-answer pairs differed in the pragmatic felicity of the answer given the preceding question. We used two types of questions: ‘neutral’ questions like (4), which do not impose any strong constraints on the information structure of the answer, and questions such as (5) that require the answer to contain two topics in a so-called ‘contrastive topic’ information structure—cf. [18]. For the answers we used Dutch sentences containing NP-coordinations with a one-topic information structure, based on materials taken from [19]. In these sentences, the NP following the coordinator is temporarily ambiguous between being the subject of a new clause, or the object of the present clause. In Dutch and also in other languages, the object reading is preferred [20]. If such a one-topic answer follows a contrastive-topic question, as in (5), this constitutes a pragmatic violation: The question requires the answer to impart on the activities of two topics (“the mayor” and “the alderman”); in the answer these entities are mentioned, but only one of them (“the mayor”) turns out to be a topic.

It is important to note that in Dutch (unlike in English), the presence of the adverb at the end of the sentence unambiguously indicates that the ambiguous NP (“the alderman”) cannot be a topic, and that the sentence only has one topic. Thus at the adverb, the reader is confronted with a clear pragmatic violation. It should be noted, however, that whereas in the experiment there is no sentence following the partial answer, the missing information could in principle be given in a next sentence (e.g., question: “What did the mayor and the alderman do?”—answer: “The mayor praised the councilor and the alderman exuberantly. The alderman therefore thanked the mayor”). It would be interesting for a future experiment to manipulate the presence or absence of such an additional sentence.

4. Neutral

Q: Wat gebeurde er?

‘What happened?’

A: De burgemeester prees het raadslid en de wethouder uitbundig.

‘The mayor praised the councilor and the alderman exuberantly.’

5. Violation

Q: Wat deden de burgemeester en de wethouder?

‘What did the mayor and the alderman do?’

A: De burgemeester prees het raadslid en de wethouder uitbundig.

‘The mayor praised the councilor and the alderman exuberantly.’

Data analysis.

Participants were reading attentively, answering on average 85% (SD = 5.6) of the 35 content questions correctly. ERP waveforms were time-locked to the presentation of the critical adverb (“exuberantly”), see Figure 1.


Figure 1. ERP waveforms for the two conditions in Experiment 1:

Neutral (black line) and Violation (red line); topographic maps represent Violation minus Neutral; there is an extended pre-stimulus time-window in which the onset of the coordinator (CRD), determiner (DET), and noun (N) is indicated by arrows.


Three time-windows for statistical analysis were chosen a priori: a window in which early effects might be observed (150–350 ms post-onset), a time-window in which possible N400 effects might be observed (350–550 ms post-onset), and a later time-window for a possible P600 (600–900 ms post-onset). For each of those intervals, average ERPs were computed for participant, condition and electrode separately. Prior to averaging, trials with ocular or amplifier-related artifacts were excluded from the analysis. For analysis purposes, three sets of electrodes were created: the three prefrontal electrodes FP1, FZA, and FP2; the two occipital electrodes O1 and O2; and the main set of the 15 remaining electrodes. For each of those sets, Repeated Measures ANOVAs were conducted with Violation (violation vs. neutral), Laterality and Anteriority as within-participant factors. In the prefrontal analysis, Laterality had 3 levels (i.e., left, midline, and right side of the scalp); in the occipital analysis, Laterality had 2 levels (i.e., left and right); for the main analysis, Laterality had 5 levels (far left, left, middle, right, far right), and Anteriority had 3 levels (anterior, central, and posterior). Where appropriate, the Huynh-Feldt correction was applied; corrected p-values will be reported with the original degrees of freedom. Only effects involving the factor Violation will be discussed.

Non-standard baseline. The pre-critical word (the ambiguous NP “the alderman”) in the target sentence is introduced in the context question of the violation condition, but not in the neutral condition. This gives rise to 1) a ‘repetition’ N400-effect, where the N400 in the violation condition is attenuated (as compared to the neutral condition) through word repetition; 2) a P600 effect, due to the fact that in the neutral condition “the alderman” is a new discourse entity, whereas in the violation condition it is already given [10][14][16]. As we wanted to avoid including these effects in our baseline, we chose a baseline on the coordinator “en” (“and”) that precedes the ambiguous NP (i.e., “… and the alderman exuberantly.”). Importantly, the presence of the positivity for the neutral condition may still affect the size of subsequent effects (if we assume that ERP waves are additive), as the violation condition starts out more negative than the neutral condition at some of the electrodes. Hence, our ‘early-baseline’ procedure may overestimate the size of negativities following the target word in the violation condition. Conversely, the fact that the violation condition is more negative to begin with may have decreased the amplitude of subsequent positivities associated with the violation condition. Thus, the early-baseline procedure may underestimate the size of any positivity following the target word in the violation condition.

Early Time Window (150–350 ms post-onset).

In the analysis of the main set of electrodes, there was a marginally significant interaction of Violation×Anteriority (F(2,30) = 3.1; p = .08). Follow-up analyses showed that this trend towards an interaction was most probably caused by a negativity for the violation condition (as compared to the neutral condition) that was largest at the frontal electrodes (violation: 2.1 µV(SE = 0.6); neutral: 4.3 µV (SE = 1.3)), smaller at central sites (violation: 2.7 µV (SE = 0.7); neutral: 3.7 µV (SE = 1.1)) and smallest at posterior electrodes (violation: 1.5 µV (SE = 0.9)); neutral: 1.6 µV (SE = 1.0)). At the prefrontal electrodes there was a marginally significant main effect of condition, again with violation being more negative than neutral (violation: 2.9 µV (SE = 0.7); neutral: 5.3 µV (SE = 1.1); F(1,15) = 3.9; p = .066). No effects were found in the analysis of the occipital electrodes.

N400 Time-Window (350–550 ms post-onset).

We did not find significant effects for the main set or for the prefrontal electrodes (all p-values>.27). At the occipital electrodes there was a marginally significant interaction of Violation×Laterality (F(1,15) = 3.5; p = .08), most probably because the positivity elicited in the violation condition was bigger at the left than at the right of the scalp (Left: violation: −0.28 µV(SE = 0.9); neutral: −1.25 µV (SE = 0.7); Right: violation: −0.65 µV (SE = 0.8); neutral: −0.88 µV (SE = 0.7)).

P600 Time-Window (600–900 ms post-onset).

The analysis on the main set of electrodes produced a significant interaction of Violation×nteriority×Laterality (F(8,120) = 2.5; p<.05). Follow-up analyses per level of Laterality suggested that this interaction was due to a specific pattern of results for electrodes situated at the far left (Violation×Anteriority: F(2,30) = 3.3; p = .059), indicating a positivity for the violation condition that was present at T7 (violation: 3.2 µV (SE = 0.8); neutral: 1.6 µV (SE = 0.7); F(1,15) = 4.5; p = .05) and P7 (violation: 1.1 µV (SE = 1.1); neutral: −1.1 µV (SE = 1.0); F(1,15) = 6.0; p<.05), but not at F7 (violation: 1.9 µV (SE = 0.8); neutral: 1.9 µV (SE = 1.3); F<1). At the other levels of Laterality, the violation condition was always more positive than the neutral condition, but none of these differences were significant (e.g., left: violation: 3.5 µV (SE = 0.7); neutral: 1.7 µV (SE = 1.0); middle: violation: 4.2 µV (SE = .7); neutral: 3.1 µV (SE = 1.3); right: violation: 4.3 µV (SE = 0.7); neutral: 2.9 µV (SE = 1.1); far right: violation: 3.1 µV(SE = 0.5); neutral: 1.8 µV (SE = 1.0); all p-values>.10). Analysis of the occipital electrodes showed a significant interaction of Violation×Laterality (F(1,15) = 2.8; p<.01), due to a larger positivity for the violation condition at the left side (O1: violation: 0.9 µV (SE = 1.2); neutral: −0.7 µV (SE = 1.2)) than at the right side (O2: violation: 0.6 µV (SE = 1.1); neutral: 0.3 µV (SE = 1.1)). At prefrontal electrodes, the violation condition (4.6 µV (SE = 0.9)) was numerically more positive than the neutral condition (3.2 µV (SE = 1.3)) but this difference did not reach significance (p>.12).


Leaving a question partially unanswered gave rise to a significant, left-lateralized positive shift (600–900 ms after the onset of the target) which we interpret as a P600. The marginally significant effect at occipital electrodes in the “N400 time-window” suggests that this positivity already started earlier (350–550 ms post-onset), though with a different scalp distribution. These findings are consistent with the MRC hypothesis [14], where difficulties in creating a mental representation of language input are assumed to be reflected in (late) positivities. In addition to these positive effects, we found evidence for an early negativity (150–350 ms post-onset) with a frontal focus.

To start with this early negativity, Lau, Stroud, Plesch, and Phillips [21] reported a very similar finding in sentences containing a word category violation. They interpreted this effect as an Early Left Anterior Negativity or ELAN [22][23]—see [24] for a critical review. ELAN effects are typically observed when the syntactic category of the presented word does not match reader expectation. In the present study, the question in the violation condition sets up the expectation that the two protagonists in the answer act as AGENTS, each involved in a separate event (e.g., an event depicting what “the mayor” did, and another event depicting what “the alderman” did). However, instead of with the expected verb, readers were presented with an adverb. This mismatch in category may have produced the ELAN-effect.

After reading the disambiguating adverb, the reader must deal with the fact that the mental representation of the sentence, based on the assigned information structure and on the assigned thematic roles, is partially incorrect and in need of revision: “the alderman” is (i) not a topic, but should become part of the comment, and (ii) not an AGENT but a PATIENT. However, this ‘local’ revision of the mental representation created thus far will not solve the larger, more ‘global’ problem of the missing information, which may require extensive pragmatic processing. That is, after revising the interpretation to reflect that “the alderman” is a PATIENT and part of a comment, rather than an AGENT and a topic, one is still faced with the problem of what is meant by leaving out information on what “the alderman” did. Hence, to regain a coherent interpretation of the unfolding dialogue, people have to update their mental representation to reflect, for instance, that the speaker has left out the information on purpose, for instance, to communicate that “the alderman” was passive, and did nothing at all.

In the present experiment, it is not possible to separate processes of local revision and global pragmatic processes, although one might be tempted to speculate that the local revision is reflected by the early positivity in the N400 window (the size of this effect was rather small, but possibly underestimated through the early baseline procedure, see Data Analysis section above), and the global, more pragmatic processing by the later positivity. In order to disentangle these processes, we conducted a second experiment, using target sentences which did not contain the ambiguous NP (“the alderman”), thereby eliminating the need for local revision.


From Plos One, the whole article:;jsessionid=9ECB98F0E056D62CC03F6A2DD4FE8307

#brain, #plosone, #research, #science, #science-news

US Military Develops 3D Printed Human-On-A-Chip For Chemical Weapons Research

The testing of medical procedures and medication is important as it determines its effectiveness and helps scientists to learn about their side effects.  But testing on animals is often considered to be morally wrong, and sometimes its illegal.  Testing on humans can be acceptable, though it’s quite hard to find subjects willing to go through various procedures simultaneously.  So what are scientists and researchers to do?  Why, they simply put a human-on-a-chip 🙂

Gone are the days when replicating a human organ was something only found in sci-fi movies or books.  That is now a reality and many labs and research facilities are already making use of human-on-a-chip technology.

Though the name suggests that there is actually human implanted onto a microchip, it is not an actual human, more like a sample of an organ that is able to perform its function in a controlled environment.  Also, the organ is not an actual organ, more like a tissue sample of that organ, or a miniature version of that organ, depending on the lab and what the researchers need.  The samples are obtained via Bioprinting or 3D printing, using live undifferentiated cells or stem cells, to create the tissue which will function just as human organs such as the heart, liver, lungs, and blood vessels do.  The cells are printed on hydrogel-based scaffolds and the cells are connected to each other by  microfluidics, tiny micro channels that functions like blood vessels.

The size of the human-on-a-chip is comparable to a thumb drive, which makes it easier to use in labs, instead of using live people or animals.

The technique will help labs in producing vaccines or medications without having to use real live humans as test subjects.  Though this will be greatly beneficial in the healthcare field, the initiative has more use cases, such as chemical warfare.

Fortunately, the Defense Threat Reduction Agency is not using human-on-a-chip to find out how to kill people with chemical weapons. Rather, it’s funding a five-year research project at the U.S. Army Edgewood Chemical Biological Center (ECBC) that aims to create a platform of in vitro human organ constructs in communication with each other, as well as assess the effectiveness and toxicity of drugs in a way that is relevant to humans’, and their ability to process these drugs.

“Today, the use of stem cells in our research program is moving us toward that goal,” Harry Salem, Ph.D., ECBC’s chief scientist for Life Sciences, said.

“Here at ECBC, the screening models will be used to assess the efficacy and safety of medical mitigation procedures and countermeasures for the soldier and the nation as a whole.”

The US Department of Defense also recently invested $24 million in the new technology.

The Wake Forest Institute for Regenerative Medicine in North Carolina developed the bioprinter and was the first to combine several organs on the same chip, which shows how a human body reacts to chemical toxins or biologic agents.

Biochemical agents can wipe out an entire population in as short as a month, so the interest in technology that could help in defending against these weapons is significant. By using these organoids or human-on-a-chip, scientists can get the most accurate results since they are basically testing on humans.  Unlike with testing on animals, where sometimes they get positive results, when tested on humans the results are different.

3D printers have come a long way from being bulky printers that takes hours or even days to print a small objects. Today, we have 3D desktops printers that can print the same small objects in just a few minutes, as well as far more complex things like an affordable yet highly functional prosthetic limb.

There’s a chance that in the future, humans would no longer need organ donors – spare organs could literally be ‘printed’ in a matter of a few hours.  Though that would mean a way to extend people’s lives, it’s still probably decades away from being a reality, as printing a miniature heart or kidney, the size of a biscuit, already takes 30 minutes.  Printing a full scale organ, with all the complex structures could take days or even weeks.


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