In recent decades urban scholarship has witnessed a ‘vertical’ or ‘volumetric’ turn that has advanced understandings of the multi-modal power asymmetries cutting through and organising urban space. Yet, this volumetric scholarship often remains locked into binary critiques – of success/failure, inclusion/exclusion, luxury/abjection, dispossession/accumulation, arborescent/rhizomatic, horizontal/vertical. This special issue tinkers with the limitations of these (unwittingly) binary urban geometries and volumetrologies – material as well as metaphorical ones. By building the etymological opposition of ‘the vertical’ with ‘the radical’ into the title of the volume (via the Latin root radix, meaning ‘root’), we seek to make the radical itself work with geometric and morphological associations. The papers in this special issue proffer diverse ethnographic, geographic and conceptual material for considering and theorising urban verticality in concert with rather than in opposition to its incumbent horizontalisms, diagonals, curls, zigzags and scattered planes. As we completed work on the special issue, the horrors of russia’s full-scale invasion of Ukrainian territory played out before our eyes. Accordingly, we make use of the introduction to reflect upon the insight that the war in Ukraine brings to bear on the intersection between domains of the urban, the vertical and the radical in the fraught, tense, vicious, fragile – but resistant – urban worlds of today. In doing so, we seek not only to render more clearly visible the violent effects of power verticals on lives, worlds and cities, but also to find seeds of hope in emergent, insurgent forms of (vertical as well as horizontal, and neither vertical nor horizontal) resistance.

中文翻译：

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简介：垂直性、激进主义、抵抗

近几十年来，城市学术经历了“垂直”或“体积”转变，加深了对贯穿和组织城市空间的多模式权力不对称的理解。然而，这种体积庞大的学术研究往往仍然局限于二元批评——成功/失败、包容/排斥、奢侈/落魄、剥夺/积累、树状/根状、水平/垂直。本期特刊修补了这些（无意中）二元城市几何学和体积学的局限性——物质的和隐喻的。通过将“垂直”与“部首”的词源对立构建到卷的标题中（通过拉丁语根基数，意思是“根”），我们试图使部首本身与几何和形态学关联发挥作用。本期特刊中的论文提供了多种民族志、地理和概念材料，用于考虑和理论化城市垂直性，使其与现有的水平主义、对角线、卷曲、之字形和分散的平面相一致，而不是相反。当我们完成特刊的工作时，俄罗斯全面入侵乌克兰领土的恐怖就展现在我们眼前。因此，我们利用引言来反思乌克兰战争对城市领域、垂直领域和激进领域之间的交叉点产生的影响，在充满忧虑、紧张、邪恶、脆弱但具有抵抗力的城市世界中今天的。在这样做的过程中，我们不仅寻求更清晰地呈现垂直权力对生活、世界和城市的暴力影响，而且还寻求在新兴的、叛乱形式（垂直的和水平的，既不是垂直的也不是垂直的）中找到希望的种子。水平）阻力。