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Vernon Butte
Unfortunately, we don't live in a world in which problems are instantly resolved with the snap of our fingers. Knowing how to effectively solve problems is an important professional skill to hone. If you have a problem that needs to be solved, what is the right process to use to ensure you get the most effective solution?
Trial and error problem solving doesn't usually require a whole team of people to solve. To use trial and error problem solving, identify the cause of the problem, and then rapidly test possible solutions to see if anything changes.
Instead of returning the entire quantum state, a quantum computer returns one state as the result of a computation. This unique characteristic is why we write the algorithm in such a way that produces the desired answer with the highest probability. For this reason, problems that require a limited number of values are more applicable.
Imagine you have a large factory and the goal is to maximize output. To do so, each individual process would need to be optimized on its own, as well as compared against the whole. Here the possible configurations of all the processes that need to be considered are exponentially larger than the size of the input data. With a search space exponentially bigger than the input data, optimization problems are feasible for a quantum computer.
Additionally, due to the unique requirements of quantum programming, one of the unexpected benefits of developing quantum algorithms is identifying new methods to solve problems. In many cases, these new methods can be brought back to classical computing, yielding significant improvements. Implementing these new techniques in the cloud is what we refer to as quantum-inspired algorithms.
Because such teams routinely organize themselves, people do not expect to follow others indefinitely. Teams usually disband after the successful conclusion of the mission. In a permanent group, a leader is expected to delegate assignments and design incentives for people to do work they would not otherwise find compelling. But in a team made up of challenge-driven leaders, the key abilities to acquire are identifying cool problems, intriguing and inspiring others who might want to be part of the solution, and collaboratively assessing how the problem might be solved, in light of state-of-the-art technologies and understanding.
Like other challenge-driven leaders, Karp identifies himself more as a problem-solver than as a leader of people. When asked why talented people want to work with him, he credits the intriguing challenge of the work, rather than any charismatic presence or power-endowed position of his own. But he also, significantly, mentions how critical it is to have a clear design process for helping people easily move from idea to product and back to new idea. He has learned to repeat the challenge-driven leadership process in an organizational setting.
When organizing and operating a value-added business, disagreements can arise among committee members or project managers over how to solve problems facing the project or business. Using good communication skills can help the group find solutions. Practice the suggestions below to improve your communication skills during problem solving discussions.
Problem solving is a complex behavior that requires a network of cortical areas for all types of solving strategies and solutions, so solving problems with and without insight likely invokes many shared cognitive processes and neural mechanisms. One critical cognitive process distinguishing insight solutions from noninsight solutions is that solving with insight requires solvers to recognize distant or novel semantic (or associative) relations; hence, insight-specific neural activity should reflect that process. The most likely area to contribute to this component of insight problem solving is the anterior superior temporal gyrus (aSTG) of the RH. Language comprehension studies demonstrate that the RH is particularly important for recognizing distant semantic relations (Chiarello et al. 1990; Beeman 1998), and bilateral aSTG is involved in semantic integration. For example, sentences and complex discourse increase neural activity in aSTG bilaterally (Mazoyer et al. 1993; Stowe et al. 1999), and discourse that places particular demands on recognizing or computing distant semantic relations specifically increases neural activity in RH temporal areas (St. George et al. 1999; Mason and Just 2004), especially aSTG (Meyer et al. 2000; Kircher et al. 2001). If this prediction of RH aSTG involvement is confirmed, it will help constrain neurocognitive theories of insight. Other cortical areas, such as prefrontal cortex and the anterior cingulate (AC) may also be differentially involved in producing insight and noninsight solutions.
We used functional magnetic resonance imaging (FMRI) in Experiment 1 and electroencephalogram (EEG) measurement in Experiment 2 to test the empirically and theoretically derived hypothesis that solving problems with insight requires engagement of (or increased emphasis on) distinct neural mechanisms, particularly in the RH anterior temporal lobe. Event-related experimental designs compared neural activity when people solved verbal problems with insight to neural activity when they solved problems (from the same problem set) without insight.
Figure 2 illustrates the most robust insight effect: as predicted, insight solutions were associated with greater neural activity in the RH aSTG than noninsight solutions. The active area was slightly anterior to primary auditory cortex, posterior to temporal pole, and along the medial aspect of the aSTG, extending down the lateral edge of the descending ramus of the Sylvian fissure to midway through the middle temporal gyrus (MTG). (This site is also close to the superior temporal sulcus, which has been implicated in language). Across all 13 subjects, the peak signal difference at a single voxel within the RH aSTG was 0.25% across the 6-s window, and 0.30% at a single time to repetition (TR), i.e., the time needed to repeat the image of the whole brain. Overall signal in this region was robust, reaching 96.8% of the brainwide average (after removing voxels in other brain areas with signal below a standard criterion). Within the cluster of voxels identified across the group, 12 subjects showed from 0.03% to 0.35% greater signal for insight than for noninsight solutions; one subject showed 0.02% greater signal for the noninsight solutions. It is not likely that RH aSTG is involved only in output or in emotional response following insight solutions, because neural activity in this area also increased when subjects first encountered each problem (Figure 3). Thus, RH aSTG is involved in processing the problem words both initially and at solution. (Of course, event-related FMRI signal occurred in many other cortical regions at problem onset, especially visual cortex). There was no insight effect in response windows immediately preceding or following the defined response window. All indications point to a striking transient event in the RH aSTG near the time when subjects solve problems with insight.
Several other cortical areas showing insight effects that did not meet significance criteria are listed in Table 1 (see also Figure S1). Some of these effects were in frontal cortex, which is notable because various frontal areas have been implicated in problem solving and reasoning. Patients with prefrontal damage have particular difficulty integrating relations in reasoning tasks (Waltz et al. 1999), and when healthy subjects perform the same task, neural activity increases in rostrolateral prefrontal cortext (Christoff et al. 2001). Some problem solving increases activity in dorsolateral prefrontal cortex (Prabhakaran et al. 1997), perhaps because of working memory demands. Solving of poorly structured problems seems particularly impaired following damage to the prefrontal cortex of the RH (Goel and Grafman 2000). Moreover, the inferior frontal gyrus (IFG) is highly active when people engage in directed semantic retrieval (Wagner et al. 2001) or when they select particular semantic concepts over competing ones (Thompson-Schill et al. 1997), e.g., to generate a response (Frith et al. 1991). Usually in these circumstances the IFG activity is stronger in the LH, even when people are reasoning about spatial problems (Goel et al. 1998), but the IFG responds particularly strongly in the RH when subjects select more distant semantic relations because of task demands (Seger et al. 2000) or comprehension goals (Robertson et al. 2000). Because of its putative importance for problem solving, semantic retrieval, and semantic selection, IFG was an a priori region of interest. One question we had hoped to answer was whether the semantic selection of insight solutions would preferentially evoke activity in RH or LH IFG, but the insight effects in both areas were too small (in area and in reliability) to test this question. When a more lenient statistical threshold was adopted, small clusters of signal were observed in both RH and LH IFG (Table 1; Figure S1A). Indeed, within the small region surpassing this weak statistical threshold, signal change in the RH IFG region was moderately strong (peak = 0.21% across the whole window). However, as is often the case, FMRI signal in this region was low (about 72% of the brainwide average) and variability was high, decreasing our confidence in the effect.
There also was an insight effect in small clusters in or near bilateral amygdala or parahippocampal gyrus. Again, regional signal was low (83% of the brainwide average), and the signal difference was small (peak = 0.16%). However, an amygdalar response may be expected, given the emotional sensation of the insight experience (Parsons and Osherson, 2001). Hippocampal or parahippocampal involvement is also plausible, if memory interacts with insight solutions differently from how it interacts with noninsight solutions. For instance, insight problems may encourage distinct memory encoding (Wills et al. 2000) or may require distinct retrieval. Finally, a small cluster in the LH posterior cingulate (PC) also showed an insight effect. There was strong, sustained FMRI signal for both solution types in this region; on the fringe of this responding region, FMRI signal began earlier following insight than noninsight solutions. The lateness of the FMRI signal across LH PC suggests that this effect began later in the response sequence, rather than during solution generation. Finally, as in most FMRI studies, signal was relatively weak in temporal pole and orbitofrontal areas due to magnetic susceptibility artifact, so we cannot rule out undetected effects in those areas.
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