First, some announcements. Tao Yucheng invites the winners of the poetry contest he hosted earlier this year to contact him at taoyucheng921129@proton.me. He’ll send out the prize money this month. He also announces that no one person won the Honorable Mention (there was a tie among multiple pieces) so he will automatically enter those pieces in the next competition, which will be at a yet-to-be-determined date this summer.

Also, contributor Mykyta Ryzhykh has a new book out, Tombboy, from Lost Telegram Press.

“In his book, as in books of poems written in poetic forms and free verse, language moves through a pattern, and the basic organizing unit is the line. In tombboy, the line may be a syllable, a sign, an image, or even a dot… Readers may rightfully assume that many, even all the poems in tombboy are anti-war poems… yet it would be inaccurate to infer these concrete poems are doctrinaire, or purely political. Nor are they autobiographical. But they are personal, intuitive, original, and memorable, each with something to show…”
– Peter Mladinic, author of House Sitting, Knives on the Table and many other books

“tombboy is filled with an experimental spirit, combining fearless phrasing with satirical madness. The result is a fascinating examination of the human condition… it seems there are no limits to his masterful creativity. Each page of this book will grab your attention. tombboy deserves a prominent spot on your bookshelf.”
– Roberta Beach Jacobson, editor of Five Fleas Itchy Poetry and smols poetry journal

Tombboy is available here.

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Welcome to Synchronized Chaos’ mid-April issue: A Chorus at the Threshold. This issue presents a chorus of voices singing, speaking, sometimes whispering, at different types of thresholds. People of different ages and backgrounds come together in this issue, each sharing thoughts, observations, and feelings at points of shifting and transformation.

Some of these thresholds are deeply interior. Adalat Gafarov Izzet oglu’s poetry is contemplative and reverent, with a focus on spirituality and the search for meaning. John Culp speaks to self-discovery, love, and finding one’s own rhythm in life. Duane Vorhees’ poetry forms a cohesive meditation on struggle, distance, and the human effort to bridge impossible gaps—whether spiritual, emotional, or existential. Mesfakus Salahin’s piece highlights self-exploration in times of solitude, as Maja Milojkovic laments the increasing unwanted loneliness caused by the setup of much of modern life. Mahbub Alam probes the highs and lows and capacities of human nature, highlighting the need for empathy and compassion. Prasanna Kumar Dalai’s poetry is romantic and melancholic, expressing deep emotions and longing. Poet and physician Anwer Ghani suggests that despite our attempts to conceal our emotions, they can still be sensed and felt.

J.J. Campbell’s writing touches on his inner shadows: feelings of isolation, the desire for a simple, authentic life, and the pain of his loneliness and inner demons. Ana May likewise writes from the doorway between suffering and transformation, insisting that pain must be faced if it is ever to yield meaning. Fhen M.’s eerie poem recollects the legend of G. Bragolin’s Crying Boy painting surviving house fires, meditating on trauma and memory. Thi Lan Anh Tran depicts the complex, multilayered social and psychological effects of both romantic love and war. Amina Kasim Muhammad’s poem illuminates how people rebuild after the loss of a loved one, growing around rather than overcoming grief. In David Sapp’s vignettes and Eva Lianou Petropoulou’s scenes of personal and public tragedy, ordinary life itself becomes a threshold where loss is transfigured through memory and grief into reverence.

Other voices gather at the threshold between childhood and adulthood. Yeon Myeong-ji and Hamdamova Dilzodaxon Halimjon qizi craft scenes of family love, care, and loss. Their work, and Jacques Fleury’s return to his father and their childhood treehouse, all stand in that tender doorway between then and now. Sarvinoz Bakhtiyorova depicts the impact of remembering one’s past and how that can shape one’s identity. Here, affection survives distance and the past remains startlingly alive.

Nature, too, shifts throughout this issue, with pieces about seasons and the liminal spaces between dreams and reality. In Stephen Jarrell Williams’s idyllic vision, the act of learning to fly becomes an awakening into another mode of being. Elaine Murray’s visionary reflections on natural landscapes, Charos Ismoilova’s gratitude for the sunrise, Ananya Guha’s pensive thoughts on seasonal time, Graciela Noemi Villaverde’s vision of a world where humans protect and care for the natural world, Joseph Ogbonna’s song to a nightingale, and Brian Barbeito’s dream journey scenes of birds, constellations, and moonlight all invite us to the threshold between the visible and the unseen. Sayani Mukherjee’s luminous piece on the sacred mystery of existence completes this movement, reminding us that existence itself is a continual process of change.

History and heritage form another vital threshold in these pages—the place where inheritance meets the present moment. Dr. Jihane El Feghali’s tribute to Lebanon, radiant with resilience and memory, stands beside Ilya Ganpantsura’s portrait of Pushkin, writing in a nation poised between autocracy and intellectual freedom. Abdulaxilova Sevara’s meditation on Yusuf and Zulayha reveals divine and human love, earthly devotion blended with spiritual transcendence. Eva Lianou Petropoulou shares the tale of miraculous holy fire burning the day before Easter in Jerusalem’s Church of the Holy Sepulchre. Lan Xin acknowledges the shared humanity and commonalities within the heritage of the world’s people, finding harmony within global religious teachings, and Bhagirath Chowdhary echoes that sentiment in his poem. Mohizoda Xurshiq qizi Roziqova discusses Uzbekistan’s legacy of teacher-apprentice training in the trades as Shokhida Nazirova highlights the Uzbek government’s investment in youth education, athletics, and personal development. The works rooted in Uzbek heritage further remind us that culture survives through crossings: hand to hand, teacher to student, voice to voice.

The chorus also rises at the threshold leading to justice.

Sim Wooki confronts racism and colonial power, while Patricia Doyne and Manik Chakraborty write from the brink where historical violence and oppression not only cast a shadow upon the present, but continues to this day. Alan Catlin and Stephen House stand at the moral threshold of witness, asking what it means to remain human before scenes of suffering, ecological damage, and collective harm. These are works that refuse the comfort of distance. They ask us not merely to observe, but to consider the ethics of paying attention.

Elsewhere, the collection turns toward personal thresholds of growth and development. Axmatova Maxliyo Ag’zam qizi discusses challenges in ESL education. Satimboyeva Risolat Ilhomboy qizi compares AI technology to the human brain as Adkham Mukhiddinov outlines how integral calculus can function in economic analysis. Khamidova Shahzoda Kholbozor qizi’s poem extols the promise of Uzbekistan’s next generation as Tursunoy Akramjon qizi Umirzaqova highlights the potential power of computer technology to improve traffic flow and safety. Ibroximova Hayitbon Mirzoxidjon qizi explores another potential role for AI in education, developing individual study plans. Yoqubova Barnoxon Baxtiyorjon qizi suggests ways to harness digital technologies in preschool education. Yunusova Robiyakhon Khayotbek qizi discusses challenges and opportunities for new technologies in the financial services sector. Charos Yusupboyeva outlines the promise of online education for remote areas. Doniyorbek G’ulomjonov and Tillayeva Muslimaxon Yashnarjon qizi examine the evolving role of technology in education, Saitkulova Fotima reflects on how living standards and education have greatly improved over the years in Uzbekistan, Axmatova Maxliyo Ag’zam qizi suggests ways to improve language students’ writing competence, O’rinova Diyora outlines methods for improving language learners’ speech, Kurbonova Mohinur Abdumuxtor qizi discusses challenges in translating idioms between English and Uzbek, while Rakhmonova Gulzoda Sodiq qizi stands at the threshold of a career in medicine, drawn forward by compassion, intellect, and personal resolve.

Jernail S. Anand looks at compassion, care and the consequences of individual actions. Mykyta Ryzhykh highlights the dissonance between our ideals of gentleness and innocence and abusive human behavior that falls short of these ideals. Asalbonu Otamurodova’s reflections on boundaries offer another kind of threshold: the necessary line where care for others must meet care for the self.

Art itself becomes another form of threshold, creating space for various ideas and sensibilities to meet and overlap. Noah Berlatsky considers how even a weathered, broken artwork can convey meaning, how the breakage can become part of the work. Doug Hawley and Bill Tope’s joint short story humorously compares an ordinary couple with historically famous idealized sculptures of people, finding in favor of the average, imperfect, but real, married couple. To’lquinay Ubukulova points out creative people’s current dependence on technology of various sorts. Jerrice J. Baptiste’s poems and paintings of women highlight their individuality, strength of character, and connection to the natural world. Juraeva Aziza Rakhmatovna interviews Croatian writer and poet Ankica Anchia, illuminating her love for her nation and birthplace as creative inspiration.

Ummusalma Nasir Mukhtar celebrates the power of writers to move society forward through their creativity, as Bill Tope explores his personal literary motivations. Ri Hossain analyzes themes in his own poetry, highlighting his combination of materialism and surrealism and how he renders urban realities through free verse. Gionni Valentin’s fragmented thoughts, images, and reflections explore themes of creativity, self-discovery, and the human condition. Kandy Fontaine describes post-Beat poetics, defined by inclusivity, community, focus on embodied and lived experience with living writers, and rejection of hierarchies and trophies. Patrick Sweeney’s tiny poetic fragments touch on art, identity, nature, history, and relationships. Joshua Martin’s poems combine lexical debris, media fragments, bureaucratic residue, and historical ruin, while Mark Young’s fragmented transmissions emerge from different frequencies of reality.

What binds these many works is not sameness, but shared arrival. Each piece stands at some edge—of understanding, of memory, of identity, of survival—and from that edge it calls out. The result is a true chorus: not a single melody, but many voices meeting in resonance.

Chorus at the Threshold sums up this collection because every page invites crossing. Between sorrow and wonder. Between history and dream. Between the self we have been and the self we are still becoming. Yet, many of these doors remain open, so that the thoughts and impressions in one “room” carry forward along one’s journey or can be remembered.

May you enter these pages with openness, attentiveness, and the quiet recognition that something in you may emerge changed.

Education 

Education means 

Learning about history and geography and culture 

School is a place where you can meet your friends and discover so many things about life 

One day fire fall down 

Crushed to the class

Killing so many children 

Innocence met death

So many souls go to heaven 

We pray everyday 

Children who will never see the colour of the rainbow 

…..

Contact

 I forgot what a kiss is The taste of an afternoon coffee.

So as the waves pulled from the land, I feel like a desert ship.

Contact I forgot what that word means, Shipwreck for months In books I look for a meaning to embrace me, to tell me everything will be fine ..

 To go and leave those roses in my father’s memory, To light a candle to the Virgin Mary.

Contact, To be in your dream hug Let me see your eyes To smell your perfume I’m looking for that word in that old dictionary

BEHIND THE VEIL

I want to tell you

that even your magic veil

cannot hide your secret smile.

And despite its red color,

it cannot hide the radiance

of your glowing cheeks.

I feel your racing heartbeat

and sense your burning longing

behind the veil.

On the shores of your wishes,

I see the smile on my face

that joy left years ago.

Anwer Ghani 

A poet and physician

Iraq

LINKTREE

Ana May 

The real name of the author is Makhmutova Alina Railevna. Russia , the Republic of Tatarstan, Kazan. Writer, Poet, Photographer.

Catch a Cold Souls

Souls are chilled,
in them — the pain of the age:
viruses and wars.

We must know: a cold can be cured —
the prescription is written by writers and poets,
turning the pages
of tender silence,
romantic melancholy,
languid loneliness.
A text is a second pseudonym,
the equivalent of breathing.

Even though pain leaves its traces in the heart:
Don’t run from pain,
live through it.
You are not unbearably stuffy. Breathe.

Admit that today
the pain in your chest,
the one that clenches your heart —
is an important step.
The first medicine —
acceptance,
and then,
breathing again,
though with an amber aftertaste of fear.

The second — living through it,
not silencing it,
but embracing it.
Every wound
will surely heal.
Yes, it will leave scars on the heart, but it will heal.

A writing person is the link
between truth and freedom of speech.
A writer or poet is a bridge
between time and the people.
In the architecture of words lie not only truth and power,
but also healing.
The writer helps not only others,
but also themselves:
You are you,
and this is the beginning
of your healing.

going to the church of the wind
in the tops of the trees


        *


she comes to the window for the red fox at dusk


        *


he told himself not to stare at the newborn violets


        *


in the same photo,
the pacing cheetah and her grandfather's cane 


        *


he gave no reason for wanting to soak his feet in the Lower Vistula


        *


when they tell you to dye your hair
and change the locks


        *


Elvis never borrowed my brother's comb,
but everybody loved the lie


        *


it was Frankie's job to doctor up the coffee
for the grumpy saints


        *


the world going back to ignoring the green forsythia


        *


my destiny is already on its third cup of coffee


        *


"the objective correlative"
must include the worn gray socks of Pete Maravich


        *


throwing a chunk of coal for a touchdown in Jim Thorpe, PA


        *


though he makes room,
the regulars on the city bus would rather stand


        *



Patrick Sweeney is a short form poet and devotee of the public library.

The Application of Integrals and Integral Calculus in Economic Analysis

Adkham Muhiddinov,

1st-year student at 

Karshi State Technical University.

Abstract: This article explores the fundamental role of integral calculus in modern economic theory and practical financial modeling. While differential calculus focuses on marginal changes, integral calculus provides the methodology for aggregating these changes to determine total values, such as total revenue, total cost, and total social welfare. The study delves into the application of definite and indefinite integrals in calculating consumer and producer surpluses, analyzing income inequality through the Lorenz curve and Gini coefficient, and modeling capital accumulation over time. By synthesizing mathematical rigor with economic intuition, this research demonstrates how integration serves as a critical bridge between theoretical microeconomic models and macro-level policy evaluations.

Keywords: Integral Calculus, Marginal Analysis, Consumer Surplus, Lorenz Curve, Capital Accumulation, Economic Dynamics, Gini Coefficient

   Main Analysis

​The evolution of economic science has been inextricably linked to the advancement of mathematical tools. Among these, the development of calculus by Newton and Leibniz provided economists with the language necessary to describe change and equilibrium. While the “Marginal Revolution” of the late 19th century initially prioritized differentiation to understand how individuals make decisions at the margin, it soon became clear that understanding the cumulative effect of these decisions required the inverse operation: integration. In the context of economic theory, if a derivative represents a rate of change—such as marginal cost or marginal utility—then the integral represents the “accumulation” of that rate into a total stock or total value.

​One of the most foundational applications of integration in economics lies in the transition from marginal functions to total functions. In a production environment, firms often operate based on marginal cost (MC), which is the cost of producing one additional unit of a good. However, for budgeting and strategic planning, the total cost (TC) is the variable of interest. Mathematically, the total cost function is the indefinite integral of the marginal cost function. This relationship is expressed as TC(q) = \int MC(q) dq + FC, where FC represents the fixed costs or the constant of integration. This simple mathematical identity allows economists to recover the entire cost structure of a firm simply by observing its behavior at the production margin. Similarly, total revenue and total utility can be reconstructed from their respective marginal counterparts, allowing for a comprehensive view of firm and consumer behavior that would be impossible through simple arithmetic alone.

​Beyond the recovery of total functions, the definite integral serves as the primary tool for measuring economic welfare. In welfare economics, the concept of “surplus” is used to quantify the benefits that consumers and producers derive from market transactions. Consumer Surplus (CS) represents the difference between what consumers are willing to pay for a good and what they actually pay. Since the demand curve reflects the marginal willingness to pay, the area under the demand curve from zero to the equilibrium quantity, minus the total expenditure, gives the consumer surplus. This area is precisely defined by the definite integral of the demand function P(d)(q) minus the price level P_0. Specifically, CS = \int_{0}^{Q_0} [P_d(q) – P_0] dq. This calculation is not merely a geometric exercise; it is the standard method used by antitrust authorities and policy makers to evaluate the impact of mergers, taxes, or subsidies on public well-being. A similar logic applies to Producer Surplus (PS), where the integral of the price minus the supply function measures the benefit to firms.

​As we move from microeconomic agents to macroeconomic structures, integral calculus becomes indispensable for analyzing social equity and income distribution. The most prominent tool in this regard is the Lorenz Curve, which plots the cumulative percentage of total income received against the cumulative percentage of the population. A perfectly equal society would have a Lorenz Curve that is a straight 45-degree diagonal line. In reality, the curve bows downward. The degree of this “bowing” represents the level of inequality in a society. To quantify this, economists use the Gini Coefficient, which is the ratio of the area between the line of perfect equality and the Lorenz Curve to the total area under the line of equality. Calculating this area requires the use of definite integrals. If L(x) represents the Lorenz function, the Gini Coefficient (G) is derived as G = 2 \int_{0}^{1} [x – L(x)] dx. This application of integration allows for a precise, objective comparison of economic health between different nations and historical eras, moving the discussion of inequality from subjective observation to rigorous mathematical analysis.

In the realm of intertemporal economics—the study of how choices are made over time—integration is used to model the accumulation of capital and the valuation of future cash flows. Investment is defined as the rate of change of the capital stock. Therefore, to find the total capital stock at a given time T, one must integrate the net investment function I(t) over the interval [0, T]. This is particularly relevant in the study of economic growth, where the Solow-Swan model and other growth theories rely on differential equations that are solved through integration to predict the long-term steady state of an economy. Furthermore, the concept of “Present Value” (PV) in finance relies on the continuous discounting of future income streams. For a continuous flow of income R(t) discounted at a rate r, the present value is the integral PV = \int_{0}^{T} R(t) e^{-rt} dt. This formula is the bedrock of modern asset pricing, allowing investors to determine the fair value of bonds, stocks, and entire corporations by aggregating future expectations into a single, current figure.

​Furthermore, integral calculus plays a significant role in probability and econometrics, which are essential for empirical economic research. Many economic variables, such as household income or stock market returns, are modeled as continuous random variables. To find the probability that a variable falls within a certain range, or to calculate the expected value (the mean) of an economic indicator, economists integrate the probability density function (PDF). For instance, the expected return on a portfolio is the integral of the possible returns weighted by their likelihood. Without integration, econometrics would be limited to discrete models, which are often insufficient for capturing the fluid and continuous nature of global financial markets.

      Conclusion

   In conclusion, the application of integrals in economics represents a sophisticated synthesis of mathematics and social science. By providing the tools to move from the specific to the general—from marginal changes to total accumulations—integration allows economists to model the world with a degree of precision that qualitative analysis cannot match. Whether it is measuring the welfare loss caused by a new tariff, calculating the sustainability of national debt, or assessing the gap between the rich and the poor, integral calculus remains at the heart of the discipline. As economic systems become increasingly complex and data-driven, the reliance on these mathematical foundations will only grow, ensuring that the integral remains a vital instrument for any serious economic practitioner or researcher.

​References

1. 1Chiang, A. C., & Wainwright, K. (2005). Fundamental Methods of Mathematical Economics. McGraw-Hill Education. (A standard text for understanding the transition from calculus to economic models).
2. ​Varian, H. R. (2014). Intermediate Microeconomics: A Modern Approach. W.W. Norton & Company. (Detailed chapters on consumer surplus and market equilibrium).
3. ​Hoy, M., Livernois, J., & McKenna, C. (2011). Mathematics for Economics. MIT Press. (Focuses on the rigorous proof of integral applications).
4. ​Sydsaeter, K., & Hammond, P. (2016). Essential Mathematics for Economic Analysis. Pearson. (Explains the use of integrals in finance and capital growth).
5. ​Piketty, T. (2014). Capital in the Twenty-First Century. Belknap Press. (While primarily historical, it utilizes the concepts of accumulation and distribution analyzed through integral-like logic).
6. ​Barro, R. J., & Sala-i-Martin, X. (2004). Economic Growth. MIT Press. (Advanced use of integrals in modeling global economic dynamics).

Myths are public dreams. Dreams are private myths. 

-Joseph Campbell

Watery Winter Field

there was a man on a boat a while back that looked like a person I used to know long before. and, much later, a woman sitting by a window with her husband in an eatery that looked like my kind and departed aunt. there was another man standing that strongly resembled my high school Latin teacher. This person looked like that person. I remembered that I read somewhere Joseph Campbell said or wrote that over thirty, everyone can kind of reminded you of someone else. Campbell was saying it neutrally. I found it sad for some reason. 

The funny thing to me was that though I look as different than Joseph Campbell as much as anything,- I started to notice that he reminded me of someone. I couldn’t place it at first. Then I realized he looked and spoke like my maternal grandfather. If someone said, ‘These two are brothers,’ there is nobody that would question that. 

I was soon in a field and wore the wrong shoes. Though it was saturated with water in most parts,- I somehow managed not to get too wet. But there was no hawk or anything of much interest. Hmm,- I thought, ~There is simply nothing going on.~ I wished that it was an old summer, or a new one, or any summer, if it had flowers and the warm earth, some verdant scenes, and blue skies. I could even be riding a horse somewhere, and at that place there would be tree branches providing moments of shade, a respite from the sun when it became too bright.

And the branches that cast shadows would be so interesting as they looked like the arms of forest creatures benevolent gesturing, so animated as they were having great conversations about the history of the woodlands whimsical and wild but maybe even,- who is to say?- loquacious talk about the history of the whole world? I thought briefly of a soul that reminded me of the beauty of the moon. The moon does not have cheekbones or beautiful dark eyes, clean long hair that shines, so this makes no sense,- but- the soul’s energetic countenance reminded one of the good senses of the moon. and I thought that in the far past, when I stood on a sand shore by the sea and the dusk dimmed the world, that it was interesting to experience that. 

I remembered a dream but didn’t understand the meaning. Inside the dream a person sat to my left. I knew them a very little bit in the dream. I did not recognize them at all from real life. I guessed something about them correctly. 

‘I am making the guess that you are a Libra.’

‘I am.’

‘Wow. I guessed right.’

‘Yes. How did you know?’

‘I don’t know how I knew. But it’s pretty good because if there are ten signs it would be a ten percent chance at guessing correctly. Since there are twelve signs, the chance of guessing is less than ten percent.’ 

I didn’t dislike Libras. or really like them. I wondered why it couldn’t be a Leo or Aries, or even Virgo. something like that. Libra? Libra didn’t mean much to me. I would have to think about the dream. Something about fairness and balance?-or justice?- I didn’t know. I put my right hand in real life,- while pausing in the watery winter field, on the back of my neck. to help prevent a headache. my neck was cold. I was tired. Looking around whilst I did this, I did see a bird atop a tree. I don’t know what kind of bird it was, but it was looking at me. It remained still. I liked this bird. A loner bird. I looked on. It looked on. then I began my way back home at least having seen something.