White Noise Exemplifies the Constrained Disorder Principle-Based Concept of Overcoming Malfunctions

Abstract

The Constrained Disorder Principle (CDP) characterizes systems by their inherent variability, which is regulated within dynamic boundaries to ensure optimal function and adaptability. In biological systems, this variability, or “noise”, is crucial for resilience and flexibility at various scales, ranging from genes and cells to more complex organ systems. Disruption of the boundaries that control this noise—whether through amplification or suppression—can lead to malfunctions and result in pathological conditions. White noise (WN), defined by equal intensity across all audible frequencies, is an exemplary clinical application of the CDP. It has been shown to stabilize disrupted processes and restore functional states by utilizing its stochastic properties within the auditory system. This paper explores WN-based therapies, specifically for the masking, habituation, and alleviation of tinnitus, a subjective perception of sound. It describes the potential to improve WN-based therapies’ effectiveness by applying the CDP and CDP-based second-generation artificial intelligence systems. Understanding the characteristics and limitations of these approaches is essential for their effective implementation across various fields.

1. Introduction

The Constrained Disorder Principle (CDP) defines systems based on their inherent noise, restricted by dynamic boundaries that influence the noise level. This framework allows for improved functionality in response to disturbances. The CDP suggests that noise can address malfunctions in complex systems [1].

White noise (WN) is a random signal that has equal intensity at all frequencies. It is a type of sound characterized by a uniform energy distribution across various frequency bands resulting from combining sounds at different frequencies [2]. WN is a fundamental concept in signal processing and statistical analysis. Due to its unique characteristics and behavior, white noise has various applications across various scientific fields [3].

This paper examines how WN-based therapy exemplifies the application of the CDP in clinical practice and supports the idea that order can emerge from disorder. It highlights the potential of utilizing WN to improve and correct disrupted systems, as well as the possibility of using CDP-based platforms to enhance effectiveness and overcome some of the challenges associated with the clinical use of WN.

1.1. The Constrained Disorder Principle Accounts for All Types of Noise in the Universe

The CDP describes systems according to their inherent noise, limited by dynamic boundaries that affect the noise level. It applies to all systems in the universe, characterizing them by their inherent variability. This variability is regulated by dynamic boundaries that continuously manage it, allowing for optimal adaptations to changes in both internal and external environments [1,4,5,6]. Per the CDP, all biological systems exhibit a certain noise level crucial for proper functioning. This noise affects genes, cellular activities, and entire organs [4,7,8,9,10,11,12,13,14,15,16,17,18,19,20].

According to the CDP, malfunctions in these systems arise from dysfunctions at their boundaries, leading to either excessive or insufficient variability needed for optimal efficiency. This understanding allows for the development of second-generation artificial intelligence (AI) systems capable of regulating the degree of noise in complex systems to address and prevent malfunctions [21].

1.2. White Noise Is a Random Signal with Equal Intensity Across Different Frequencies, Resulting in a Constant Power Spectral Density

White noise effectively demonstrates the CDP in the auditory system as a random signal. WN is a type of sound characterized by a uniform energy distribution across different frequency bands. It consists of all frequencies within the audible spectrum (20 Hz to 20,000 Hz) at equal intensity [22]. The spectral density of WN is flat, meaning its intensity remains constant across the human audible frequency range. Several vital characteristics define white Noise (WN): it has a continuous power spectral density across all frequencies, zero autocorrelation at any non-zero lag, and a flat frequency spectrum [23].

Additionally, it exhibits statistical independence between any two points in time. Its statistical features include a mean value typically zero, a probability distribution often Gaussian, and a constant and finite variance. When all the sounds a person can hear are combined, they create WN. Consequently, WN has unlimited bandwidth and a linear spectrum [24].

WN has several physical manifestations, including acoustic, electronic, and digital forms. Acoustic WN produces a consistent “shhhh” sound with equal energy across all frequency bands. Some tangible and straightforward examples of WN include the sounds of the sea crashing, rainfall, air conditioning units, fans, and static television [25,26]. Electronic WN refers to thermal noise found in resistors and shot noise produced by electronic devices. This noise results from the random movement of electrons. Digital WN consists of computer-generated random sequences, including pseudo-random number generators, commonly used in digital signal processing. WN exists within a spectrum of noise colors [27,28]. For example, Pink noise has decreasing intensity at higher frequencies; brown noise emphasizes lower frequencies, and blue noise shows increasing intensity at higher frequencies [29].

In discrete time, WN is a discrete signal made up of samples that create a sequence of serially uncorrelated random variables. Each of these variables has a mean of zero and a finite variance. A single instance of white noise can be regarded as a random shock. Furthermore, a random vector is classified as a WN vector or white random vector if each of its components has a probability distribution with a mean of zero, finite variance, and the components are statistically independent [30,31]. The joint probability distribution of a vector must equal the product of the individual distributions of its components. Sometimes, the samples need to be independent and have identical probability distributions. Independent and identically distributed random variables represent the simplest form of WN. The signal is referred to as additive white Gaussian noise if each sample follows a normal distribution with a mean of zero [32].

The samples of a white noise (WN) signal can be organized sequentially in time or along one or more spatial dimensions. In digital image processing, the pixels of a WN image are arranged in a rectangular grid. These pixels are independent random variables with a uniform probability distribution over a specified interval. Additionally, white noise can be applied to signals distributed over more complex domains, such as a sphere or a torus [33,34]. An infinite-bandwidth white noise signal is purely theoretical. The bandwidth of white noise is constrained by factors such as the noise generation mechanism, the transmission medium, and the limited capabilities of observation [35]. Therefore, signals are WN if they exhibit a flat spectrum across frequencies relevant to the specific context. Even a binary signal that can only take values of 1 or −1 can be considered WN if the sequence is statistically uncorrelated. Additionally, noise with a continuous distribution, like a normal distribution, can also be classified as white noise. The measure of WN is a generalization that applies to random elements in infinite-dimensional spaces, such as random fields [36,37].

To define the concept of WN in the context of continuous-time signals, it is essential to replace the notion of a random vector with that of a continuous-time random signal. A process is WN in the strongest sense if it consists of random variables that are statistically independent of their entire prior history [35,38]. In phylogenetically based statistical methods, WN can signify a lack of phylogenetic patterns in comparative data. In everyday contexts, it sometimes suggests “random conversation without substantial content” [39].

The characteristics of the WN demonstrate the CDP-based concept of “order from disorder” [7,8,9,10].

1.3. Platforms That Use the CDP to Leverage Noise to Correct Malfunctions

The CDP-based second-generation AI system is a platform that utilizes variability to address malfunctions [21]. Introducing variability into the stimulation regimens has been shown to enhance response to vagal stimulation for weight loss [40]. In patients with chronic diseases who experience a complete or partial loss of medication effectiveness, incorporating variability in dosing and timing—within predefined ranges—has effectively overcome this loss of response [1,6,21,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75].

The CDP-based platform functions through three main steps. The first step employs an open-loop system that introduces variability within predefined ranges. The second step utilizes a closed-loop system that personalizes and adjusts this variability to achieve optimal outcomes. Finally, the third step quantifies physiological variability signatures and integrates them into the algorithm, enhancing the system’s overall effectiveness [6,65,76,77].

1.4. Using White Noise to Treat Clinical Conditions

The CDP outlines a framework for using noise to correct system malfunctions [71,73,74]. Using WN to treat the disorder exemplifies the CDP-based concept of using noise. True WN is theoretically impossible to produce because of infinite bandwidth; however, practical implementations are limited by bandwidth [78]. The quality of WN depends on the effectiveness of the algorithm used. WN effectively masks unwanted sounds by adding either a natural or artificial sound to the environment. Research has also examined the changes in Mismatch Negativity (MMN) using WN masking. Notably, the amplitude of MMN is significantly reduced when subjected to contralateral WN masking [79,80]. WN can be generated digitally with a digital signal processor, microprocessor, or microcontroller. This process typically involves feeding a suitable stream of random numbers into a digital-to-analog converter. Different sources of WN are marketed as privacy enhancers, sleep aids, and tinnitus masks. Alternatively, tuning an AM radio to unused frequencies, often called “static”, is a more straightforward way to generate WN. Fans and air conditioners generate WN by producing countless audio frequencies, preventing the human brain from registering surrounding noises unless they are excessively loud [81,82,83].

WN has shown promise in treating various sleep-related conditions [3]. It has been found to improve sleep in environments with high levels of noise, based on both subjective reports and objective measurements from individuals having trouble sleeping due to such disturbances. WN improves sleep–wake cycles and decreases the time it takes to fall asleep. For patients with insomnia, it masks environmental disturbances, creates a consistent sound environment, and helps maintain sleep continuity. WN effectively reduces sleep latency in controlled environments, improves sleep quality metrics, and enhances overall sleep maintenance. WN decreases the difference between background and peak noise levels, raising the arousal threshold to noise [83,84,85]. WN leads to deeper sleep with fewer awakenings during the night. WN in the 50 to 75 dB range has positively affected participants’ sleep and wake cycles. When mixed-frequency WN was added to ambient noise, it significantly reduced sleep-induced arousal and disturbances, as the difference between background noise and peak sounds was considerably minimized [3,86,87]. It aligns with the CDP-based notion of the advantage of adding noise for overcoming challenges [4,5]. WN has also positively impacted sleep patterns in newborns, reducing crying in colicky babies and enhancing the sleep environment in neonatal intensive care units (NICUs). Infants exposed to WN have shown fewer nighttime awakenings and improved sleep quality. Children with autism spectrum disorder (ASD) reported fewer delays in sleep onset and a reduction in night waking after this intervention [88,89,90].

WN is effective in treating conditions such as depression, anxiety, stress, schizophrenia, and dementia, as well as in relieving pain [3,91,92,93]. It can help reduce stress responses and anxiety disorders by lowering cortisol levels and improving focus during anxiety-inducing situations. WN has also been beneficial in nursing homes, where it reduces verbal agitation in patients with dementia. Additionally, it decreased behavioral and psychological symptoms in patients with schizophrenia who also had dementia, and its improved symptoms of depression and anxiety. In elderly patients admitted to the intensive care units, WN contributed to a decreased heart rate, alleviated pain during vaccinations, and supported the development of sucking behaviors in newborns [94,95,96,97].

The impact of WN on cognitive function is mixed, which supports the CDP concept’s requirement for an appropriate range of noise under varying conditions. WN can enhance attention and concentration [98,99,100]. When played at volumes between 60 and 86 dB, white noise helps to reduce environmental distractions and improve attention, learning, and memory. The text enhances performance in tasks that involve sequential short-term memory. WN improves information processing in the nervous system, benefiting cognitive functions such as learning, memory, attention, and concentration. By engaging long-term memory structures like the hippocampus, WN effectively boosts learning capacity, making it easier to acquire new vocabulary [99,101,102,103].

WN can effectively address specific symptoms of attention deficit hyperactivity disorder (ADHD) [104]. Research has demonstrated that WN can enhance reading and writing speed, improve speech recognition, aid in managing behaviors outside of work, increase awareness, support working memory tasks, and sometimes improve task accuracy. For individuals with ADHD, WN can lead to better cognitive functioning by compensating for low basal dopamine levels that often occur due to dopamine transport disorders. However, WN may not have the same positive effects, or could even be counterproductive, for individuals with normal or high levels of attention. Background stimulation from WN enhances cognitive functioning in secondary students with ADHD while potentially decreasing performance among non-ADHD students [105,106,107,108].

WN can enhance work productivity. Implementing systems that mask ambient noise and improve concentration is essential to leverage the benefits of an open office layout while maintaining employee attention and focus [3,103,109]. WN-based systems that reduce distracting background noise are crucial in such environments. By minimizing noise fluctuations and creating a sense of privacy, WN decreases distractions, boosts employee moods, and improves performance, although it may hinder cognitive performance in complex card-sorting tasks. Additionally, WN offers several advantages, including enhanced learning abilities and improved memory retention, by optimizing the study environment. An experiment was conducted with sixty-six healthy participants to explore the benefits of using WN in a learning setting [103,110].

Using noise-reducing earplugs alongside rational and emotional treatment enhances the emotional and sleep states of colorectal cancer patients, yielding specific positive effects. This approach could serve as a potential nursing plan for these individuals [111]. Unperceivable electrical noise stimulation has improved postural control by enhancing somatosensory feedback. Pink and white noise signals alter the temporal behavior of the foot center of pressure (CoP) during quiet standing [112]. WN is commonly used in electronic music production, either directly or as an input for filters to generate noise signals. It plays a significant role in audio synthesis, particularly for replicating percussive instruments like cymbals and snare drums, which contain a considerable amount of high-frequency noise. WN also serves as the foundation for some random number generators [113,114].

These examples support the CDP-based concept of using noise within constraints to improve system functionality and overcome disturbances.

1.5. Using White Noise to Treat Tinnitus

Subjective tinnitus, defined as the perception of a sound without an external source, affects approximately 25% of the US population, with about 8% experiencing a chronic and debilitating condition [115,116]. It is associated with a nearly threefold increase in rates of depression and anxiety [117,118]. While factors such as noise exposure, sensorineural hearing loss, traumatic brain injury, concussion, drug exposure, and others are thought to contribute to tinnitus, most cases lack an identifiable cause [119]. Tinnitus arises primarily from the nervous system’s activity rather than mechanical or vibrational activity in the cochlea or external stimuli [120]. For individuals with mild hearing loss or the elderly, WN still affects their hearing. Since individuals with hearing loss often suffer from tinnitus, cognitive dysfunction, and depression, WN may provide a means of therapy for these patients [121,122,123].

Tinnitus is considered a brain disorder initiated by cochlear trauma, followed by neuronal hyperactivity in the cochlear nucleus and higher regions of the central auditory system, including the inferior colliculus, thalamus, and auditory cortex [124]. Neurons in these areas show increased activity in individuals with tinnitus, firing synchronously to compensate for cochlear hair cell damage [124]. There is no standardized treatment for tinnitus. Available options, including hearing aids, sound masking, drug therapies, acupuncture, and neuromodulation, have shown limited effectiveness. Cognitive-behavioral therapy has improved quality of life but does not significantly reduce tinnitus loudness [125,126,127].

Sound masking, employing broadband sound to alleviate tinnitus, was first described in the late 1970s [128]. WN provides sound masking, reduces the perceived intensity of tinnitus, and assists patients in habituating to the sounds associated with tinnitus [129,130]. This approach relieves stress with soothing sounds, diverts attention from tinnitus by increasing background noise, and alleviates the emotional burden of tinnitus [131]. Some individuals even report tinnitus suppression or temporary disappearance following masking therapy. However, evidence supporting its ability to suppress tinnitus remains limited [132,133]. A Cochrane review by Hobson et al. found no significant benefits of sound therapy alone. Still, the authors claimed that the “absence of conclusive evidence should not be interpreted as evidence of ineffectiveness” [132].

Early sound therapy approaches, known as “complete masking”, used devices resembling hearing aids to generate white noise at increased levels that completely obscured the tinnitus. Later, a different approach emerged, using the minimal appreciable level of white noise to promote habituation to the disordered auditory perception [132]. Another technique, “sound enrichment”, adjusts noise generators to produce sound at a level where the tinnitus and external noise blend. This method forms the basis of Tinnitus Retraining Therapy (TRT), which combines sound therapy with behavioral counseling [134]. Clinical trials comparing TRT with complete masking have shown that both methods significantly reduce tinnitus-related distress, with TRT yielding slightly more significant benefits [135,136]. Neuromonics Tinnitus Treatment (NTT) represents another method, combining noise with music to alleviate tinnitus. This six-month intervention requires patients to listen for at least two hours daily. During the initial two months, wideband noise is added to the music to mask tinnitus audibility during the quiet portions of the music. In the subsequent four months, the noise is removed, and patients gradually reduce the music volume to minimize the interaction between tinnitus and the music [137].

Patients often find that they respond better to external sounds that match the frequency of their tinnitus. Since white noise (WN) covers a broad range of frequencies, it can be particularly effective for treating various types of tinnitus because it can effectively mask different sounds at multiple frequencies. Using a tinnitus masker that continuously generates specific sound frequencies—often white noise—may be a successful treatment option for alleviating tinnitus symptoms. The intensity required to mask the tinnitus is typically lower when the masking noise is close to the frequency of the tinnitus itself. Patients with low-frequency tinnitus require higher intensity levels when using high-frequency narrowband noise and white noise, compared to those with high-frequency tinnitus. WN may facilitate the release of cognitive resources and reduce auditory effort under these conditions [132,138,139,140].

Other sound-based treatments, such as modulated sounds (low-rate amplitude tones within the tinnitus pitch range), pink noise (resembling natural sounds), speech noise, and high tones, have been shown to reduce patients’ complaints and even provide temporary tinnitus suppression [140,141,142].

Sound therapy is currently included as an optional treatment for managing tinnitus symptoms in clinical practice guidelines by the American Academy of Otolaryngology-Head and Neck Surgery [133]. These therapies are offered through devices worn in or behind the ear, often combined with hearing aids to enhance the patient’s hearing. They are also accessible via smartphone applications, gaming consoles, headphones, and audio devices [143].

Despite the lack of large randomized controlled trials confirming the efficacy of sound therapy for eliminating or significantly alleviating bothersome tinnitus, the existing literature highlights the rationale and variable success rates of different approaches. While sound therapy is generally considered safe with no reported side effects, it can be costly and requires prolonged use, often involving several hours of daily listening for months. Recent studies suggest that unstructured or random acoustic input can induce maladaptive neuroplastic changes in the central auditory system, even at levels below those considered harmful. Over time, this may undermine its structural and functional integrity, potentially worsening tinnitus [129].

Sensory input plays a crucial role in shaping neuronal organization and the development of sensory maps in the brain. Research has illuminated the mechanisms that regulate the plasticity of the auditory pathway, particularly by examining the effects of altered auditory input during critical developmental periods. During these times, plasticity optimizes neural circuits to better align with the external environment. Furthermore, studies conducted in adulthood indicate that hearing loss is often linked to the emergence of tinnitus [144,145]. The molecular, cellular, and circuit-level mechanisms that regulate neuronal organization and tonotopic map plasticity during both developmental critical periods and adulthood have been described. These mechanisms play a role in modulating disinhibitory networks, as well as in influencing synaptic structure and function, along with the structural barriers to plasticity [146]. The regulation of plasticity also involves neuromodulatory circuits that link plasticity to learning and attention. Both ascending and descending auditory circuits connect the auditory cortex to lower brain structures [147].

1.6. Potential Mechanisms Underlying the Positive Effects of WN

The CDP offers a platform that utilizes variability for the purpose of improvement [6,65,76,77,148]. It suggests bringing the system closer to its normal physiology by introducing noise where necessary. The exact mechanism behind WN’s benefits remains unclear, but they can be attributed to two well-known phenomena: stochastic resonance (SR) and noise masking [3,149,150,151].

Stochastic resonance (SR) is a well-established phenomenon in psychophysics that may explain the positive effects of white noise therapy [152]. Signal recovery (SR) occurs when a signal is too weak to be detected but can be amplified by adding noise. This random noise enhances neural communication through the phenomenon of SR, making the signal easier to detect. In the auditory nerve, many of the nerve fibers have a high spontaneous firing rate in silence, typically reaching up to 100 spikes per second. When there is a very small input of sound energy, the firing rate can increase to 105 spikes per second, indicating that the system is highly sensitive to minor changes. However, the actual signal-to-noise ratio is quite low, meaning that most of the detected signals are actually noise [153,154].

When unpredictable noise, such as WN, increases, it leads to a higher signal transmission and detection level, resulting in a better SNR [150,155]. The SR effect is influenced by both signal level and noise, following an inverted U-shaped curve where performance is highest at moderate noise levels [156,157,158]. Moderate levels of WN can enhance performance by providing enough power to elevate the signal above the detection threshold [150,159,160]. SR has several limitations, including the inverted U-curve dependency on noise levels [159]. This concept aligns with the CDP-based method of using noise to address malfunctions, and the noise needs to be constrained for optimal effects [6].

The CDP specifies various noise levels essential for optimal system performance, emphasizing the importance of dynamic noise boundaries to regulate noise levels and ensure effective adaptation to different environments [1,6,21,69,70,71,72]. Similarly, if there is too much WN, it can overpower the signal and hinder attention and performance [159].

It supports the CDP-based concept of a dynamic zone and suggests that an optimal level of variability is necessary for achieving peak performance. According to the CDP, the required degree of variability is influenced by both internal and external disruptions to systems [4,5,161].

SR attempts to clarify the paradox that the brain uses WN to differentiate between targeted stimuli and non-target noise. The central nervous system can distinguish the actual signal—representing the information being conveyed—from noise, which includes undefined neural inputs that can interfere with this signal. By modifying neural synchronization, specific brain regions responsible for certain functions can create transient networks that enhance perception, cognition, or action. Consequently, random noise can improve the detection of weak sensory signals, a phenomenon explained by SR [162,163,164].

WN masking is based on the idea that the brain tends to focus on recognizable patterns, such as speech, while filtering out indistinct sounds, like static noise [3,165,166]. Noise masking involves introducing low-level, random background white noise that corresponds to the frequencies of human speech, making it particularly useful in environments like workplaces. It is crucial to manage the volume and frequency of the added noise effectively. The noise should be loud enough to obscure conversations within a certain distance. Still, if it is too noisy, the brain may find it difficult to ignore, potentially disrupting other cognitive processes. When correctly managed, WN can mask speech without distracting or irritating the listener [79,100].

As outlined in the CDP, the necessity of managing noise levels emphasizes the significance of denoising methods in specific situations [1]. A new lightweight denoising technique for infrared images has been proposed, based on adversarial transfer learning. This method employs a generative adversarial network (GAN) framework and improves the model through a phased transfer learning strategy. It eliminates additive white Gaussian noise from infrared images, demonstrating exceptional denoising performance [167].

1.7. The CDP Addresses Some of the Current Challenges Associated with White Noise

There are several challenges associated with the use of WN. There is significant variability in how individuals respond to it, both within the same person and among different people. The effects of WN on cognitive functions are mixed, and there is a lack of validated treatment regimens. For maximum therapeutic benefit, it is recommended to use WN at a volume of 50–60 decibels—like the level of conversation—throughout the sleep period and at a distance of 1–2 m from the sound source. However, the long-term effects of continuous exposure and the optimal frequency distributions for specific conditions have yet to be defined [104,159,167,168,169].

According to the CDP, smart devices equipped with adaptive noise generation, which personalizes the degree and range of decibels of WN, can lead to better long-term outcomes [148,161,170,171,172,173]. By implementing a CDP-based algorithm that incorporates noise into treatment, adjusting the decibel range and treatment duration within predefined limits may enhance clinical effectiveness and address issues like incomplete response and loss of response seen in some patients [4,5,161].

The CDP-based AI system may regulate the treatment of WN at three levels [21]. The first level is an open-loop system that introduces randomization of the decibel range and treatment length within predefined limits. The second level is a closed-loop system that uses clinical response as an endpoint. It allows for dynamic personalization of decibel variability and treatment duration to achieve the desired outcome. The third level comprises variability markers, such as heart rate variability, neuronal noise, or sleep waves, which are quantified and integrated into treatment regimens. These variability signatures can also be biomarkers for predicting prognosis and selecting the most appropriate treatment plan [1,6,21,69,70,71,72]. The creation of variability-based diagnostic and treatment tools may improve their accuracy [68,72]. Figure 1 summarizes the use of WN based on the CDP concept and its potential applications.

2. Summary

WN has potential applications across multiple disciplines. Its mathematical properties and practical uses indicate its relevance in both theoretical research and practical applications. Understanding its characteristics and limitations is essential for effective implementation in various fields. Many of WN’s functionalities are based on the CDP and using CDP-based algorithms may enhance the effectiveness of this approach in clinical practice. Controlled trials are necessary to assess its effects on patients with tinnitus.